Antiseismic Method of Prestressed Fabricated Building ...

12
Research Article Antiseismic Method of Prestressed Fabricated Building Structure under Intelligent Big Data Zhonghong Li 1 and Yong Huang 2,3,4,5,6 1 School of Architectural Engineering, Chongqing Chemical Industry Vocational College, Chongqing 401228, China 2 College of Chemistry, Xinjiang University, Urumqi 830000, Xinjiang, China 3 e Province and Ministry Jointly Established the State Key Laboratory of “Carbon-based Energy Resource Chemistry and Utilization”, Xinjiang University, Urumqi 830000, Xinjiang, China 4 Xinjiang Communication Construction Co. Ltd (XCCG), Urumqi 830000, Xinjiang, China 5 Transpotation Industry Highway Maintenance Collaborative Innovation Platform under Complicated Conditions of Western China, Urumqi 830000, Xinjiang, China 6 Western Sub-Alliance of Zhongguancun Zhongke Highway Maintenance Technology Innovation Alliance, Urumqi 830000, Xinjiang, China Correspondence should be addressed to Yong Huang; [email protected] Received 27 August 2021; Revised 25 September 2021; Accepted 5 October 2021; Published 8 November 2021 Academic Editor: Sang-Bing Tsai Copyright © 2021 Zhonghong Li and Yong Huang. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Compared with traditional buildings, prefabricated buildings have the advantages of simple construction technology, low construction requirements, and shorter construction time, which can generate more economic benefits for the construction industry. In order to study the seismic capacity of prestressed fabricated building structures under intelligent big data, this article takes fabricated frame structures as the research object and the reinforced walls at the nodes as the starting point to study the damage patterns and energy dissipation capabilities of different seismic waves on the structure. In order to observe the overall seismic performance, the fabricated frame structure was used. e results of the study found that the prestressed fabricated building structure has the best seismic effect when the axial compression is 0.3, and the prestressed degree is below 0.5, which meets the seismic requirements. erefore, the prestressed degree of the prestressed fabricated building structure should be below 0.5. According to statistics on the results of structural residual deformation and steel bar deformation of buildings under different seismic waves, it can be found that the prestressed fabricated building structure has better self-recovery ability and can better respond to earthquakes with different seismic waves. 1. Introduction With the rapid development of the Chinese economy, people’s structural requirements for residential buildings are increasing, and more multistorey residential buildings are available. At present, the main form of high-rise residential buildings in my country is still the cast-in-place concrete frame shear wall structure or pure shear wall structure; this structuralformhascertaindefectsfromitsownpointofview [1]. Affected by the environment or the labor level of on-site workers during the construction process, the quality of the construction cannot be well guaranteed. A large number of formworks are required to pour concrete on site, which increases the amount of materials and increases the cost. High-rise residential buildings in our country should move towards fast construction speed, short cycle, low labor in- tensity, and high degree of industrialization and minimize on-site “wet work,” which is helpful to the development of environmental protection and other aspects. In response to these problems, people have gradually realized that Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 9834770, 12 pages https://doi.org/10.1155/2021/9834770

Transcript of Antiseismic Method of Prestressed Fabricated Building ...

Page 1: Antiseismic Method of Prestressed Fabricated Building ...

Research ArticleAntiseismic Method of Prestressed Fabricated BuildingStructure under Intelligent Big Data

Zhonghong Li1 and Yong Huang 23456

1School of Architectural Engineering Chongqing Chemical Industry Vocational College Chongqing 401228 China2College of Chemistry Xinjiang University Urumqi 830000 Xinjiang China3e Province and Ministry Jointly Established the State Key Laboratory of ldquoCarbon-based EnergyResource Chemistry and Utilizationrdquo Xinjiang University Urumqi 830000 Xinjiang China4Xinjiang Communication Construction Co Ltd (XCCG) Urumqi 830000 Xinjiang China5Transpotation Industry Highway Maintenance Collaborative Innovation Platform under ComplicatedConditions of Western China Urumqi 830000 Xinjiang China6Western Sub-Alliance of Zhongguancun Zhongke Highway Maintenance Technology Innovation Alliance Urumqi 830000Xinjiang China

Correspondence should be addressed to Yong Huang yong_huangseuedumk

Received 27 August 2021 Revised 25 September 2021 Accepted 5 October 2021 Published 8 November 2021

Academic Editor Sang-Bing Tsai

Copyright copy 2021 Zhonghong Li and Yong Huang -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Compared with traditional buildings prefabricated buildings have the advantages of simple construction technology lowconstruction requirements and shorter construction time which can generate more economic benefits for the constructionindustry In order to study the seismic capacity of prestressed fabricated building structures under intelligent big data this articletakes fabricated frame structures as the research object and the reinforced walls at the nodes as the starting point to study thedamage patterns and energy dissipation capabilities of different seismic waves on the structure In order to observe the overallseismic performance the fabricated frame structure was used -e results of the study found that the prestressed fabricatedbuilding structure has the best seismic effect when the axial compression is 03 and the prestressed degree is below 05 whichmeets the seismic requirements -erefore the prestressed degree of the prestressed fabricated building structure should be below05 According to statistics on the results of structural residual deformation and steel bar deformation of buildings under differentseismic waves it can be found that the prestressed fabricated building structure has better self-recovery ability and can betterrespond to earthquakes with different seismic waves

1 Introduction

With the rapid development of the Chinese economypeoplersquos structural requirements for residential buildings areincreasing and more multistorey residential buildings areavailable At present the main form of high-rise residentialbuildings in my country is still the cast-in-place concreteframe shear wall structure or pure shear wall structure thisstructural form has certain defects from its own point of view[1] Affected by the environment or the labor level of on-site

workers during the construction process the quality of theconstruction cannot be well guaranteed A large number offormworks are required to pour concrete on site whichincreases the amount of materials and increases the costHigh-rise residential buildings in our country should movetowards fast construction speed short cycle low labor in-tensity and high degree of industrialization and minimizeon-site ldquowet workrdquo which is helpful to the development ofenvironmental protection and other aspects In response tothese problems people have gradually realized that

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 9834770 12 pageshttpsdoiorg10115520219834770

fabricated concrete structures have more advantages thantraditional cast-in-place concrete structures [2]

-e development of prefabricated buildings has broadmarket prospects and good policy support in my country Atthe same time the fabricated prestressed concrete shear wallsystem is formed by combining the fabricated concretestructure with the shear wall system commonly used inresidential buildings in my country which solves the currentsocial problems such as labor shortage and housingshortage and compared with the cast-in-place reinforcedconcrete shear wall it also has certain advantages in terms ofperformance so it has high research value [3] Howeverthere are also factors limiting the development of pre-fabricated buildings in my country Prefabricated structureshave a form of building -e prefabricated constructionindustry chain needs a complete industrial system to sup-port But the current prefabricated construction system inmy country is not perfect and cannot form large-scaleproduction Transport assembly etc all of this must besolved by us [4]

For prestressed fabricated buildings experts at home andabroad also have a lot of research Erhard believed that theminimum reinforcement of the flexurally strengthenedmasonry should not be less than 005 percent of the effectivemasonry cross section of the building component in whichsteel bars contribute to the load bearing capacity of thesection and the effective masonry cross section is theproduct of the effective width and the building element -eusable height d based on the area of the steel bar should notbe less than 003 of the total cross-sectional area specifyingthe minimum amount of reinforcement to avoid brittlebehavior of the building When the first crack is formed orlimits the cracking element check the elements given in theminimum number of reinforcement for reinforced masonrybeams [5] Gao tested two prefabricated shear walls with ascale of 50 One model is that the partially assembledprestressed concrete shear wall unit uses carbon fiberbundles as prestressed tendons and replaces ordinary con-crete with reinforced fiber concrete At the same time steelplates are installed at the bottom of the wall limbs and steeldiagonal braces are embedded in the prefabricated walls asenergy-consuming elements -e connection structure ofthe simulated cast-in-place assembled shear wall unit canachieve the integrity of the wall and the base which isbasically equivalent to the cast-in-place shear wall but theresidual deformation is large and the damage is serious [6]Gueguen et al conducted an experimental study on theprefabricated hollow wall panel combination -e combi-nation is composed of 2 load-bearing panels at both endsand 4 nonload-bearing panels in the middle -e load-bearing wall panels are connected to the bottom platethrough prestressed compression -e load-bearing wall-board is only placed on the bottom plate by rubber blocksand the rubber blocks form a two-point connection betweeneach wallboard and the sealant is filled-e test results showthat the precast concrete hollow wallboard combination hasbetter lateral resistance [7] Fujie et al conducted an ex-perimental analysis on the seismic performance of the in-line T-shaped and double-leg prestressed shear walls and

compared them with the cast-in-place shear walls -e testresults showed that the precast shear walls are in rigidityyield strength and ultimate strength Compared with thecast-in-place shear wall it is greatly improved and theability to resist cracking and elastic deformation is stronger-e damage of the wall is mainly concentrated at the root ofthe wall and the intersection of the connecting beam and thewall -e whole wall is damaged by bending and shearingBending damage is the main cause energy consumption andductility are poor Because the structure itself has goodelasticity and self-healing it is easier to repair after crackingwhich has good social benefits [8] -ese studies have acertain reference effect for this article but the sample limit ofthe study is severe and it is difficult to reproduce in practice

-is study studies the seismic performance of pre-fabricated building structures and establishes a prefabricatednode model -e establishment of the model needs toconsider the influence of factors such as the selection ofcross sections the characteristics of materials the division ofelements and the nonlinear analysis -e seismic perfor-mance analysis and comparison of the frame structure andthe prefabricated building structure are carried out using thedynamic time history analysis method under the same siteconditions and the same construction conditions to carryout the quasirare earthquake analysis which is the pre-fabricated prestressed building structure in the actualproject -e application provides suggestions

2 Seismic Research Methods of PrestressedFabricated Building Structures

21 Prestressed Fabricated Building Structure -e key to thestudy of prefabricated structures is the study of joint con-nections -e connection technology is mainly divided intotwo types rigid connection and dry connection which is thebasic technology of prefabricated concrete structures [9]Research through related experiments shows thatstrengthening the connection at the node can improve theoverall performance of the structure and the precast con-crete structure can meet the energy consumption perfor-mance requirements

In order to improve the energy consumption andductility of the fabricated shear wall and to reduce thehorizontal shear slip and the degree of joint opening of thefabricated concrete shear wall this study proposed twoconnection methods one is the bottom cast in place -eupper part adopts the prestressed press-joined assembledshear wall the other adopts the continuous steel bar with apartially reduced section to transfer the plastic hinge fromthe splicing joint to the wall as shown in Figure 1 [10 11]

Aiming at the problem of poor energy absorption effi-ciency of constructed concrete shear walls many studieshave introduced energy dispersion elements into fabricatedconcrete shear walls such as liquid damping and abrasiondamping -is approach is solving energy consumptionAlthough the capacity is insufficient it also strengthens theintegrity of the walls and reduces the horizontaldisplacement

2 Mathematical Problems in Engineering

Aiming at the problem of poor energy dissipationperformance of fabricated prestressed concrete shear wallsmany studies have introduced energy dissipation elementsinto fabricated prestressed concrete shear walls such as fluiddamping and friction damping -is approach is solvingenergy consumption Although the capacity is insufficient italso strengthens the integrity of the walls and reduces thehorizontal displacement-is means that ordinary steel rodsare added based on the discounted tendons and the energyabsorption efficiency of the discounted concrete bar isimproved through the performance of ordinary steel rodsPlain steel rods have a certain length in the nonroofedsection -e ordinary steel bars in the bottom layer aremoved to the middle of the wall and the positions of theother layers remain unchanged -e stirrups are alsochanged from circular spiral stirrups to rectangular closedstirrups to increase large concrete core area [12] Relevantstudies have proved (1) -e main mode of horizontal de-formation of hybrid fabricated shear wall is the opening ofthe gap at the joint and the shear wall can basically beregarded as a rigid body around the joint Rotation thedamage degree is obviously lower than that of the cast-in-place shear wall (2) In the unloading stage due to the elasticaction of the prestressed tendons the shear wall is providedwith a vertical restoring force which can reduce the residualdeformation of the component after the earthquake (3) -eyield of local unbonded ordinary steel bars is obviouslylagging behind which also avoids the occurrence of low-cycle fatigue fracture-emixed fabricated shear wall and itsimproved wall are shown in Figure 2

In summary our countryrsquos research on prefabricatedconcrete is mainly focused on several specific structuralforms such as fabricated frame structure fabricated con-crete shear wall structure and prestressed fabricatedstructure [13] -e research on prefabricated concreteshear walls is more about the seismic performance of thejoints whereas the overall seismic research of the structure

is less At present the three connection methods of cor-rugated pipe grout anchor lap connection sleeve groutingconnection and constrained grout anchor lap connectionare the most widely used in prefabricated concrete shearwalls and they have achieved rapid promotion and ap-plication [14]

22 Calculation of Partial Deformation of Building ConcreteWe take a prefabricated slab in the floor as an insulator asshown in Figure 3

According to the beam theory and the force relationshipthe bending angle θc under the action of the in-planebending moment M is obtained as

θc Mb

EcIc

(1)

Among them b is the width of the isolator Ic is thebending moment of inertia in the plane of the isolator andEc is the elastic modulus of the concrete According to thematerial mechanics shear deformation calculation formulaof beam theory the shear deformation Δc of the concretefloor is calculated as

Δc 12Vb

GcAc

(2)

According to the mechanical performance test at floorlevel the axial force of the cross joints is basically a straightline except for the anchored joints at the edge of the slab sothe joints can be described by the flat section hypothesisUnder the action of the in-plane bending moment M thebending angle of the plate seam connector is θj Consideringthe deformation of the connector under the action ofbending moment according to the balance of the axialtension and pressure of the plate joint connector it is ob-tained as follows

PC

PVCpipe

ReducedRebararea

Nonshrinkmortar

(a)

PC

ReducedRebararea

Nonshrinkmortar

(b)

PC

RC

Nonshrinkmortar

(c)

Figure 1 Different base connection methods (a) PC with unbonded partially reduced rebar area (b) PC wall with partially reduced rebararea (c) RC-PC hybrid wall

Mathematical Problems in Engineering 3

Wall root section

Ordinary steelbar

Prestressed steelbar

1 w

1 w

1st floor slab

2st floor slab

3st floor slab

4st floor slab

5st floor slab

6st floor slab

Roof

Ordinary steel bar

Prestressed steel bar

(a)

Wall root section

Stirrup

Prestressedsteel bar

Energyconsuming

steel barOrdinary steel

bar

Vertical section

Prestressed steel bar Anchorage

Horizontal node

wallboard

hardware cloth

Ordinary steelbar

Wrap upGround floor

wallboard

grouting

Energyconsuming

steel bar

Basics

(b)

Figure 2 Hybrid fabricated shear wall and its improvement (a) Hybrid fabricated shear wall system (b) Improved hybrid fabricated shearwall system

Chord connector

Neutral axis

d

b

Seam connector

M M

V

y

V

Figure 3 Building isolation layer

4 Mathematical Problems in Engineering

1113944

n

i1Fiδi( 1113857 0 (3)

Let y be the distance between the section and the wheeland the lower edge of the plate and yi is the distance betweenthe i-th joint node and the lower edge of the plate then

δi

y minus yi

tan θj

1113944

n

i1ki y minus yi( 1113857tan θj1113960 1113961 0

(4)

Available tan θne 0 from

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (5)

According to the balance of bending moment

1113944

n

i1Mi 1113944

n

i1kiδi y minus yi( 11138571113858 1113859 1113944

n

i1ki y minus yi( 1113857

2 tan θj1113960 1113961 M

(6)

It can be considered that θj tan θj therefore

θj M

1113936

n

i 1ki

21113960 1113961

(7)

ki is the axial stiffness of the i-th connector -e flexuralrigidity of the plate seam connector is

Kθj 1113944

n

i1ki y minus yi( 1113857

21113960 1113961 (8)

According to the axial mechanical balance relationshipat the plate seam

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (9)

-is can be transformed into

y 1113944n

i1ki minus d 1113944

n

i1

i minus 1m minus 1

ki1113874 1113875 0 (10)

-erefore the position of the neutral axis is

y d 1113936

ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

(11)

-erefore

Kθj 1113944

n

i1ki

d 1113936ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

minusi minus 1n minus 1

d1113890 11138911113896

2

(12)

-erefore the equivalent beam is under the action ofuniformly distributed load q and the boundary condition issimply supported the bending deformation is

χ1 q

24EIl3x minus 2lx

3+ x

41113872 1113873 (13)

-e new fully prefabricated building is assembled frommultiple prefabricated slabs and its continuity is not asgood as cast-in-situ flooring so it cannot be considered ahomogeneous body for calculating rigidity within theaircraft We use the equivalent beam model to calculatethe midspan deflection and its deformation includesshear deformation and bending deformation Howeverstudies have shown that the deformation under horizontalload is dominated by shear deformation so the midspandeflection deformation can be regarded as the displace-ment caused by equivalent shear deformation and the in-plane stiffness of the floor is the equivalent shear stiffness[15 16]

23eoretical AnalysisModel of Building Seismic ResistanceCompared with cast-in-place slabs prestressed fabricatedbuilding structures havemuch greater in-plane deformationand the building cannot be simply regarded as infinite in-plane rigidity -erefore a multistory structure composed ofprestressed fabricated building structures is constructedWhen there is horizontal free vibration or forced vibrationunder the action of a horizontal earthquake each floor of themultistory structure undergoes translational vibration andoverall rotation at the same time producing horizontaldeformation so that the lateral displacement value of eachvertical member is not the same [17] -erefore it is nolonger possible to use the ldquoseries mass point systemrdquo modelin the seismic code for structural seismic analysis Insteadeach vertical member should be connected by each layer ofsemirigid floor to form a space structure After discretiza-tion a ldquostringrdquo is formed [18]

For the analysis of the spatial structure of the pre-fabricated structure this chapter will adopt the modeanalysis method based on the response spectrum theory thatis it will use the free vibration equation of the multiparticlesystem to solve the physical vibration period and the modeof operation of the structure and then using the theory ofdecomposition and response spectrum acquires the hori-zontal seismic action of the structure [19] Comparing thefree vibration equation of the ldquoseries-parallel multiparticlesystemrdquo with the free vibration equation of the ldquoseries-parallel multiparticle systemrdquo it has the followingcharacteristics

(1) If the vertical bar where the mass point of the two-way shear bar is located it represents a frame thatdoes not consider the vertical deformation of the barthe horizontal bar represents the assembled rein-forced concrete floor that is regarded as an equiv-alent shear beam that is where the mass point isboth the vertical rod and the horizontal rod are shearrods [20] -en the restoring force received by themass point is only affected by the side shift of onemass point up and down and left and right except forits own side shift -e side shifts of other mass pointshave no effect on it as shown in Figure 4(a)

Mathematical Problems in Engineering 5

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 2: Antiseismic Method of Prestressed Fabricated Building ...

fabricated concrete structures have more advantages thantraditional cast-in-place concrete structures [2]

-e development of prefabricated buildings has broadmarket prospects and good policy support in my country Atthe same time the fabricated prestressed concrete shear wallsystem is formed by combining the fabricated concretestructure with the shear wall system commonly used inresidential buildings in my country which solves the currentsocial problems such as labor shortage and housingshortage and compared with the cast-in-place reinforcedconcrete shear wall it also has certain advantages in terms ofperformance so it has high research value [3] Howeverthere are also factors limiting the development of pre-fabricated buildings in my country Prefabricated structureshave a form of building -e prefabricated constructionindustry chain needs a complete industrial system to sup-port But the current prefabricated construction system inmy country is not perfect and cannot form large-scaleproduction Transport assembly etc all of this must besolved by us [4]

For prestressed fabricated buildings experts at home andabroad also have a lot of research Erhard believed that theminimum reinforcement of the flexurally strengthenedmasonry should not be less than 005 percent of the effectivemasonry cross section of the building component in whichsteel bars contribute to the load bearing capacity of thesection and the effective masonry cross section is theproduct of the effective width and the building element -eusable height d based on the area of the steel bar should notbe less than 003 of the total cross-sectional area specifyingthe minimum amount of reinforcement to avoid brittlebehavior of the building When the first crack is formed orlimits the cracking element check the elements given in theminimum number of reinforcement for reinforced masonrybeams [5] Gao tested two prefabricated shear walls with ascale of 50 One model is that the partially assembledprestressed concrete shear wall unit uses carbon fiberbundles as prestressed tendons and replaces ordinary con-crete with reinforced fiber concrete At the same time steelplates are installed at the bottom of the wall limbs and steeldiagonal braces are embedded in the prefabricated walls asenergy-consuming elements -e connection structure ofthe simulated cast-in-place assembled shear wall unit canachieve the integrity of the wall and the base which isbasically equivalent to the cast-in-place shear wall but theresidual deformation is large and the damage is serious [6]Gueguen et al conducted an experimental study on theprefabricated hollow wall panel combination -e combi-nation is composed of 2 load-bearing panels at both endsand 4 nonload-bearing panels in the middle -e load-bearing wall panels are connected to the bottom platethrough prestressed compression -e load-bearing wall-board is only placed on the bottom plate by rubber blocksand the rubber blocks form a two-point connection betweeneach wallboard and the sealant is filled-e test results showthat the precast concrete hollow wallboard combination hasbetter lateral resistance [7] Fujie et al conducted an ex-perimental analysis on the seismic performance of the in-line T-shaped and double-leg prestressed shear walls and

compared them with the cast-in-place shear walls -e testresults showed that the precast shear walls are in rigidityyield strength and ultimate strength Compared with thecast-in-place shear wall it is greatly improved and theability to resist cracking and elastic deformation is stronger-e damage of the wall is mainly concentrated at the root ofthe wall and the intersection of the connecting beam and thewall -e whole wall is damaged by bending and shearingBending damage is the main cause energy consumption andductility are poor Because the structure itself has goodelasticity and self-healing it is easier to repair after crackingwhich has good social benefits [8] -ese studies have acertain reference effect for this article but the sample limit ofthe study is severe and it is difficult to reproduce in practice

-is study studies the seismic performance of pre-fabricated building structures and establishes a prefabricatednode model -e establishment of the model needs toconsider the influence of factors such as the selection ofcross sections the characteristics of materials the division ofelements and the nonlinear analysis -e seismic perfor-mance analysis and comparison of the frame structure andthe prefabricated building structure are carried out using thedynamic time history analysis method under the same siteconditions and the same construction conditions to carryout the quasirare earthquake analysis which is the pre-fabricated prestressed building structure in the actualproject -e application provides suggestions

2 Seismic Research Methods of PrestressedFabricated Building Structures

21 Prestressed Fabricated Building Structure -e key to thestudy of prefabricated structures is the study of joint con-nections -e connection technology is mainly divided intotwo types rigid connection and dry connection which is thebasic technology of prefabricated concrete structures [9]Research through related experiments shows thatstrengthening the connection at the node can improve theoverall performance of the structure and the precast con-crete structure can meet the energy consumption perfor-mance requirements

In order to improve the energy consumption andductility of the fabricated shear wall and to reduce thehorizontal shear slip and the degree of joint opening of thefabricated concrete shear wall this study proposed twoconnection methods one is the bottom cast in place -eupper part adopts the prestressed press-joined assembledshear wall the other adopts the continuous steel bar with apartially reduced section to transfer the plastic hinge fromthe splicing joint to the wall as shown in Figure 1 [10 11]

Aiming at the problem of poor energy absorption effi-ciency of constructed concrete shear walls many studieshave introduced energy dispersion elements into fabricatedconcrete shear walls such as liquid damping and abrasiondamping -is approach is solving energy consumptionAlthough the capacity is insufficient it also strengthens theintegrity of the walls and reduces the horizontaldisplacement

2 Mathematical Problems in Engineering

Aiming at the problem of poor energy dissipationperformance of fabricated prestressed concrete shear wallsmany studies have introduced energy dissipation elementsinto fabricated prestressed concrete shear walls such as fluiddamping and friction damping -is approach is solvingenergy consumption Although the capacity is insufficient italso strengthens the integrity of the walls and reduces thehorizontal displacement-is means that ordinary steel rodsare added based on the discounted tendons and the energyabsorption efficiency of the discounted concrete bar isimproved through the performance of ordinary steel rodsPlain steel rods have a certain length in the nonroofedsection -e ordinary steel bars in the bottom layer aremoved to the middle of the wall and the positions of theother layers remain unchanged -e stirrups are alsochanged from circular spiral stirrups to rectangular closedstirrups to increase large concrete core area [12] Relevantstudies have proved (1) -e main mode of horizontal de-formation of hybrid fabricated shear wall is the opening ofthe gap at the joint and the shear wall can basically beregarded as a rigid body around the joint Rotation thedamage degree is obviously lower than that of the cast-in-place shear wall (2) In the unloading stage due to the elasticaction of the prestressed tendons the shear wall is providedwith a vertical restoring force which can reduce the residualdeformation of the component after the earthquake (3) -eyield of local unbonded ordinary steel bars is obviouslylagging behind which also avoids the occurrence of low-cycle fatigue fracture-emixed fabricated shear wall and itsimproved wall are shown in Figure 2

In summary our countryrsquos research on prefabricatedconcrete is mainly focused on several specific structuralforms such as fabricated frame structure fabricated con-crete shear wall structure and prestressed fabricatedstructure [13] -e research on prefabricated concreteshear walls is more about the seismic performance of thejoints whereas the overall seismic research of the structure

is less At present the three connection methods of cor-rugated pipe grout anchor lap connection sleeve groutingconnection and constrained grout anchor lap connectionare the most widely used in prefabricated concrete shearwalls and they have achieved rapid promotion and ap-plication [14]

22 Calculation of Partial Deformation of Building ConcreteWe take a prefabricated slab in the floor as an insulator asshown in Figure 3

According to the beam theory and the force relationshipthe bending angle θc under the action of the in-planebending moment M is obtained as

θc Mb

EcIc

(1)

Among them b is the width of the isolator Ic is thebending moment of inertia in the plane of the isolator andEc is the elastic modulus of the concrete According to thematerial mechanics shear deformation calculation formulaof beam theory the shear deformation Δc of the concretefloor is calculated as

Δc 12Vb

GcAc

(2)

According to the mechanical performance test at floorlevel the axial force of the cross joints is basically a straightline except for the anchored joints at the edge of the slab sothe joints can be described by the flat section hypothesisUnder the action of the in-plane bending moment M thebending angle of the plate seam connector is θj Consideringthe deformation of the connector under the action ofbending moment according to the balance of the axialtension and pressure of the plate joint connector it is ob-tained as follows

PC

PVCpipe

ReducedRebararea

Nonshrinkmortar

(a)

PC

ReducedRebararea

Nonshrinkmortar

(b)

PC

RC

Nonshrinkmortar

(c)

Figure 1 Different base connection methods (a) PC with unbonded partially reduced rebar area (b) PC wall with partially reduced rebararea (c) RC-PC hybrid wall

Mathematical Problems in Engineering 3

Wall root section

Ordinary steelbar

Prestressed steelbar

1 w

1 w

1st floor slab

2st floor slab

3st floor slab

4st floor slab

5st floor slab

6st floor slab

Roof

Ordinary steel bar

Prestressed steel bar

(a)

Wall root section

Stirrup

Prestressedsteel bar

Energyconsuming

steel barOrdinary steel

bar

Vertical section

Prestressed steel bar Anchorage

Horizontal node

wallboard

hardware cloth

Ordinary steelbar

Wrap upGround floor

wallboard

grouting

Energyconsuming

steel bar

Basics

(b)

Figure 2 Hybrid fabricated shear wall and its improvement (a) Hybrid fabricated shear wall system (b) Improved hybrid fabricated shearwall system

Chord connector

Neutral axis

d

b

Seam connector

M M

V

y

V

Figure 3 Building isolation layer

4 Mathematical Problems in Engineering

1113944

n

i1Fiδi( 1113857 0 (3)

Let y be the distance between the section and the wheeland the lower edge of the plate and yi is the distance betweenthe i-th joint node and the lower edge of the plate then

δi

y minus yi

tan θj

1113944

n

i1ki y minus yi( 1113857tan θj1113960 1113961 0

(4)

Available tan θne 0 from

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (5)

According to the balance of bending moment

1113944

n

i1Mi 1113944

n

i1kiδi y minus yi( 11138571113858 1113859 1113944

n

i1ki y minus yi( 1113857

2 tan θj1113960 1113961 M

(6)

It can be considered that θj tan θj therefore

θj M

1113936

n

i 1ki

21113960 1113961

(7)

ki is the axial stiffness of the i-th connector -e flexuralrigidity of the plate seam connector is

Kθj 1113944

n

i1ki y minus yi( 1113857

21113960 1113961 (8)

According to the axial mechanical balance relationshipat the plate seam

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (9)

-is can be transformed into

y 1113944n

i1ki minus d 1113944

n

i1

i minus 1m minus 1

ki1113874 1113875 0 (10)

-erefore the position of the neutral axis is

y d 1113936

ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

(11)

-erefore

Kθj 1113944

n

i1ki

d 1113936ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

minusi minus 1n minus 1

d1113890 11138911113896

2

(12)

-erefore the equivalent beam is under the action ofuniformly distributed load q and the boundary condition issimply supported the bending deformation is

χ1 q

24EIl3x minus 2lx

3+ x

41113872 1113873 (13)

-e new fully prefabricated building is assembled frommultiple prefabricated slabs and its continuity is not asgood as cast-in-situ flooring so it cannot be considered ahomogeneous body for calculating rigidity within theaircraft We use the equivalent beam model to calculatethe midspan deflection and its deformation includesshear deformation and bending deformation Howeverstudies have shown that the deformation under horizontalload is dominated by shear deformation so the midspandeflection deformation can be regarded as the displace-ment caused by equivalent shear deformation and the in-plane stiffness of the floor is the equivalent shear stiffness[15 16]

23eoretical AnalysisModel of Building Seismic ResistanceCompared with cast-in-place slabs prestressed fabricatedbuilding structures havemuch greater in-plane deformationand the building cannot be simply regarded as infinite in-plane rigidity -erefore a multistory structure composed ofprestressed fabricated building structures is constructedWhen there is horizontal free vibration or forced vibrationunder the action of a horizontal earthquake each floor of themultistory structure undergoes translational vibration andoverall rotation at the same time producing horizontaldeformation so that the lateral displacement value of eachvertical member is not the same [17] -erefore it is nolonger possible to use the ldquoseries mass point systemrdquo modelin the seismic code for structural seismic analysis Insteadeach vertical member should be connected by each layer ofsemirigid floor to form a space structure After discretiza-tion a ldquostringrdquo is formed [18]

For the analysis of the spatial structure of the pre-fabricated structure this chapter will adopt the modeanalysis method based on the response spectrum theory thatis it will use the free vibration equation of the multiparticlesystem to solve the physical vibration period and the modeof operation of the structure and then using the theory ofdecomposition and response spectrum acquires the hori-zontal seismic action of the structure [19] Comparing thefree vibration equation of the ldquoseries-parallel multiparticlesystemrdquo with the free vibration equation of the ldquoseries-parallel multiparticle systemrdquo it has the followingcharacteristics

(1) If the vertical bar where the mass point of the two-way shear bar is located it represents a frame thatdoes not consider the vertical deformation of the barthe horizontal bar represents the assembled rein-forced concrete floor that is regarded as an equiv-alent shear beam that is where the mass point isboth the vertical rod and the horizontal rod are shearrods [20] -en the restoring force received by themass point is only affected by the side shift of onemass point up and down and left and right except forits own side shift -e side shifts of other mass pointshave no effect on it as shown in Figure 4(a)

Mathematical Problems in Engineering 5

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 3: Antiseismic Method of Prestressed Fabricated Building ...

Aiming at the problem of poor energy dissipationperformance of fabricated prestressed concrete shear wallsmany studies have introduced energy dissipation elementsinto fabricated prestressed concrete shear walls such as fluiddamping and friction damping -is approach is solvingenergy consumption Although the capacity is insufficient italso strengthens the integrity of the walls and reduces thehorizontal displacement-is means that ordinary steel rodsare added based on the discounted tendons and the energyabsorption efficiency of the discounted concrete bar isimproved through the performance of ordinary steel rodsPlain steel rods have a certain length in the nonroofedsection -e ordinary steel bars in the bottom layer aremoved to the middle of the wall and the positions of theother layers remain unchanged -e stirrups are alsochanged from circular spiral stirrups to rectangular closedstirrups to increase large concrete core area [12] Relevantstudies have proved (1) -e main mode of horizontal de-formation of hybrid fabricated shear wall is the opening ofthe gap at the joint and the shear wall can basically beregarded as a rigid body around the joint Rotation thedamage degree is obviously lower than that of the cast-in-place shear wall (2) In the unloading stage due to the elasticaction of the prestressed tendons the shear wall is providedwith a vertical restoring force which can reduce the residualdeformation of the component after the earthquake (3) -eyield of local unbonded ordinary steel bars is obviouslylagging behind which also avoids the occurrence of low-cycle fatigue fracture-emixed fabricated shear wall and itsimproved wall are shown in Figure 2

In summary our countryrsquos research on prefabricatedconcrete is mainly focused on several specific structuralforms such as fabricated frame structure fabricated con-crete shear wall structure and prestressed fabricatedstructure [13] -e research on prefabricated concreteshear walls is more about the seismic performance of thejoints whereas the overall seismic research of the structure

is less At present the three connection methods of cor-rugated pipe grout anchor lap connection sleeve groutingconnection and constrained grout anchor lap connectionare the most widely used in prefabricated concrete shearwalls and they have achieved rapid promotion and ap-plication [14]

22 Calculation of Partial Deformation of Building ConcreteWe take a prefabricated slab in the floor as an insulator asshown in Figure 3

According to the beam theory and the force relationshipthe bending angle θc under the action of the in-planebending moment M is obtained as

θc Mb

EcIc

(1)

Among them b is the width of the isolator Ic is thebending moment of inertia in the plane of the isolator andEc is the elastic modulus of the concrete According to thematerial mechanics shear deformation calculation formulaof beam theory the shear deformation Δc of the concretefloor is calculated as

Δc 12Vb

GcAc

(2)

According to the mechanical performance test at floorlevel the axial force of the cross joints is basically a straightline except for the anchored joints at the edge of the slab sothe joints can be described by the flat section hypothesisUnder the action of the in-plane bending moment M thebending angle of the plate seam connector is θj Consideringthe deformation of the connector under the action ofbending moment according to the balance of the axialtension and pressure of the plate joint connector it is ob-tained as follows

PC

PVCpipe

ReducedRebararea

Nonshrinkmortar

(a)

PC

ReducedRebararea

Nonshrinkmortar

(b)

PC

RC

Nonshrinkmortar

(c)

Figure 1 Different base connection methods (a) PC with unbonded partially reduced rebar area (b) PC wall with partially reduced rebararea (c) RC-PC hybrid wall

Mathematical Problems in Engineering 3

Wall root section

Ordinary steelbar

Prestressed steelbar

1 w

1 w

1st floor slab

2st floor slab

3st floor slab

4st floor slab

5st floor slab

6st floor slab

Roof

Ordinary steel bar

Prestressed steel bar

(a)

Wall root section

Stirrup

Prestressedsteel bar

Energyconsuming

steel barOrdinary steel

bar

Vertical section

Prestressed steel bar Anchorage

Horizontal node

wallboard

hardware cloth

Ordinary steelbar

Wrap upGround floor

wallboard

grouting

Energyconsuming

steel bar

Basics

(b)

Figure 2 Hybrid fabricated shear wall and its improvement (a) Hybrid fabricated shear wall system (b) Improved hybrid fabricated shearwall system

Chord connector

Neutral axis

d

b

Seam connector

M M

V

y

V

Figure 3 Building isolation layer

4 Mathematical Problems in Engineering

1113944

n

i1Fiδi( 1113857 0 (3)

Let y be the distance between the section and the wheeland the lower edge of the plate and yi is the distance betweenthe i-th joint node and the lower edge of the plate then

δi

y minus yi

tan θj

1113944

n

i1ki y minus yi( 1113857tan θj1113960 1113961 0

(4)

Available tan θne 0 from

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (5)

According to the balance of bending moment

1113944

n

i1Mi 1113944

n

i1kiδi y minus yi( 11138571113858 1113859 1113944

n

i1ki y minus yi( 1113857

2 tan θj1113960 1113961 M

(6)

It can be considered that θj tan θj therefore

θj M

1113936

n

i 1ki

21113960 1113961

(7)

ki is the axial stiffness of the i-th connector -e flexuralrigidity of the plate seam connector is

Kθj 1113944

n

i1ki y minus yi( 1113857

21113960 1113961 (8)

According to the axial mechanical balance relationshipat the plate seam

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (9)

-is can be transformed into

y 1113944n

i1ki minus d 1113944

n

i1

i minus 1m minus 1

ki1113874 1113875 0 (10)

-erefore the position of the neutral axis is

y d 1113936

ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

(11)

-erefore

Kθj 1113944

n

i1ki

d 1113936ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

minusi minus 1n minus 1

d1113890 11138911113896

2

(12)

-erefore the equivalent beam is under the action ofuniformly distributed load q and the boundary condition issimply supported the bending deformation is

χ1 q

24EIl3x minus 2lx

3+ x

41113872 1113873 (13)

-e new fully prefabricated building is assembled frommultiple prefabricated slabs and its continuity is not asgood as cast-in-situ flooring so it cannot be considered ahomogeneous body for calculating rigidity within theaircraft We use the equivalent beam model to calculatethe midspan deflection and its deformation includesshear deformation and bending deformation Howeverstudies have shown that the deformation under horizontalload is dominated by shear deformation so the midspandeflection deformation can be regarded as the displace-ment caused by equivalent shear deformation and the in-plane stiffness of the floor is the equivalent shear stiffness[15 16]

23eoretical AnalysisModel of Building Seismic ResistanceCompared with cast-in-place slabs prestressed fabricatedbuilding structures havemuch greater in-plane deformationand the building cannot be simply regarded as infinite in-plane rigidity -erefore a multistory structure composed ofprestressed fabricated building structures is constructedWhen there is horizontal free vibration or forced vibrationunder the action of a horizontal earthquake each floor of themultistory structure undergoes translational vibration andoverall rotation at the same time producing horizontaldeformation so that the lateral displacement value of eachvertical member is not the same [17] -erefore it is nolonger possible to use the ldquoseries mass point systemrdquo modelin the seismic code for structural seismic analysis Insteadeach vertical member should be connected by each layer ofsemirigid floor to form a space structure After discretiza-tion a ldquostringrdquo is formed [18]

For the analysis of the spatial structure of the pre-fabricated structure this chapter will adopt the modeanalysis method based on the response spectrum theory thatis it will use the free vibration equation of the multiparticlesystem to solve the physical vibration period and the modeof operation of the structure and then using the theory ofdecomposition and response spectrum acquires the hori-zontal seismic action of the structure [19] Comparing thefree vibration equation of the ldquoseries-parallel multiparticlesystemrdquo with the free vibration equation of the ldquoseries-parallel multiparticle systemrdquo it has the followingcharacteristics

(1) If the vertical bar where the mass point of the two-way shear bar is located it represents a frame thatdoes not consider the vertical deformation of the barthe horizontal bar represents the assembled rein-forced concrete floor that is regarded as an equiv-alent shear beam that is where the mass point isboth the vertical rod and the horizontal rod are shearrods [20] -en the restoring force received by themass point is only affected by the side shift of onemass point up and down and left and right except forits own side shift -e side shifts of other mass pointshave no effect on it as shown in Figure 4(a)

Mathematical Problems in Engineering 5

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 4: Antiseismic Method of Prestressed Fabricated Building ...

Wall root section

Ordinary steelbar

Prestressed steelbar

1 w

1 w

1st floor slab

2st floor slab

3st floor slab

4st floor slab

5st floor slab

6st floor slab

Roof

Ordinary steel bar

Prestressed steel bar

(a)

Wall root section

Stirrup

Prestressedsteel bar

Energyconsuming

steel barOrdinary steel

bar

Vertical section

Prestressed steel bar Anchorage

Horizontal node

wallboard

hardware cloth

Ordinary steelbar

Wrap upGround floor

wallboard

grouting

Energyconsuming

steel bar

Basics

(b)

Figure 2 Hybrid fabricated shear wall and its improvement (a) Hybrid fabricated shear wall system (b) Improved hybrid fabricated shearwall system

Chord connector

Neutral axis

d

b

Seam connector

M M

V

y

V

Figure 3 Building isolation layer

4 Mathematical Problems in Engineering

1113944

n

i1Fiδi( 1113857 0 (3)

Let y be the distance between the section and the wheeland the lower edge of the plate and yi is the distance betweenthe i-th joint node and the lower edge of the plate then

δi

y minus yi

tan θj

1113944

n

i1ki y minus yi( 1113857tan θj1113960 1113961 0

(4)

Available tan θne 0 from

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (5)

According to the balance of bending moment

1113944

n

i1Mi 1113944

n

i1kiδi y minus yi( 11138571113858 1113859 1113944

n

i1ki y minus yi( 1113857

2 tan θj1113960 1113961 M

(6)

It can be considered that θj tan θj therefore

θj M

1113936

n

i 1ki

21113960 1113961

(7)

ki is the axial stiffness of the i-th connector -e flexuralrigidity of the plate seam connector is

Kθj 1113944

n

i1ki y minus yi( 1113857

21113960 1113961 (8)

According to the axial mechanical balance relationshipat the plate seam

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (9)

-is can be transformed into

y 1113944n

i1ki minus d 1113944

n

i1

i minus 1m minus 1

ki1113874 1113875 0 (10)

-erefore the position of the neutral axis is

y d 1113936

ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

(11)

-erefore

Kθj 1113944

n

i1ki

d 1113936ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

minusi minus 1n minus 1

d1113890 11138911113896

2

(12)

-erefore the equivalent beam is under the action ofuniformly distributed load q and the boundary condition issimply supported the bending deformation is

χ1 q

24EIl3x minus 2lx

3+ x

41113872 1113873 (13)

-e new fully prefabricated building is assembled frommultiple prefabricated slabs and its continuity is not asgood as cast-in-situ flooring so it cannot be considered ahomogeneous body for calculating rigidity within theaircraft We use the equivalent beam model to calculatethe midspan deflection and its deformation includesshear deformation and bending deformation Howeverstudies have shown that the deformation under horizontalload is dominated by shear deformation so the midspandeflection deformation can be regarded as the displace-ment caused by equivalent shear deformation and the in-plane stiffness of the floor is the equivalent shear stiffness[15 16]

23eoretical AnalysisModel of Building Seismic ResistanceCompared with cast-in-place slabs prestressed fabricatedbuilding structures havemuch greater in-plane deformationand the building cannot be simply regarded as infinite in-plane rigidity -erefore a multistory structure composed ofprestressed fabricated building structures is constructedWhen there is horizontal free vibration or forced vibrationunder the action of a horizontal earthquake each floor of themultistory structure undergoes translational vibration andoverall rotation at the same time producing horizontaldeformation so that the lateral displacement value of eachvertical member is not the same [17] -erefore it is nolonger possible to use the ldquoseries mass point systemrdquo modelin the seismic code for structural seismic analysis Insteadeach vertical member should be connected by each layer ofsemirigid floor to form a space structure After discretiza-tion a ldquostringrdquo is formed [18]

For the analysis of the spatial structure of the pre-fabricated structure this chapter will adopt the modeanalysis method based on the response spectrum theory thatis it will use the free vibration equation of the multiparticlesystem to solve the physical vibration period and the modeof operation of the structure and then using the theory ofdecomposition and response spectrum acquires the hori-zontal seismic action of the structure [19] Comparing thefree vibration equation of the ldquoseries-parallel multiparticlesystemrdquo with the free vibration equation of the ldquoseries-parallel multiparticle systemrdquo it has the followingcharacteristics

(1) If the vertical bar where the mass point of the two-way shear bar is located it represents a frame thatdoes not consider the vertical deformation of the barthe horizontal bar represents the assembled rein-forced concrete floor that is regarded as an equiv-alent shear beam that is where the mass point isboth the vertical rod and the horizontal rod are shearrods [20] -en the restoring force received by themass point is only affected by the side shift of onemass point up and down and left and right except forits own side shift -e side shifts of other mass pointshave no effect on it as shown in Figure 4(a)

Mathematical Problems in Engineering 5

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 5: Antiseismic Method of Prestressed Fabricated Building ...

1113944

n

i1Fiδi( 1113857 0 (3)

Let y be the distance between the section and the wheeland the lower edge of the plate and yi is the distance betweenthe i-th joint node and the lower edge of the plate then

δi

y minus yi

tan θj

1113944

n

i1ki y minus yi( 1113857tan θj1113960 1113961 0

(4)

Available tan θne 0 from

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (5)

According to the balance of bending moment

1113944

n

i1Mi 1113944

n

i1kiδi y minus yi( 11138571113858 1113859 1113944

n

i1ki y minus yi( 1113857

2 tan θj1113960 1113961 M

(6)

It can be considered that θj tan θj therefore

θj M

1113936

n

i 1ki

21113960 1113961

(7)

ki is the axial stiffness of the i-th connector -e flexuralrigidity of the plate seam connector is

Kθj 1113944

n

i1ki y minus yi( 1113857

21113960 1113961 (8)

According to the axial mechanical balance relationshipat the plate seam

1113944

n

i1ki y minus yi( 11138571113858 1113859 0 (9)

-is can be transformed into

y 1113944n

i1ki minus d 1113944

n

i1

i minus 1m minus 1

ki1113874 1113875 0 (10)

-erefore the position of the neutral axis is

y d 1113936

ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

(11)

-erefore

Kθj 1113944

n

i1ki

d 1113936ni1 i minus 1n minus 1ki( 1113857

1113936ni1 ki

minusi minus 1n minus 1

d1113890 11138911113896

2

(12)

-erefore the equivalent beam is under the action ofuniformly distributed load q and the boundary condition issimply supported the bending deformation is

χ1 q

24EIl3x minus 2lx

3+ x

41113872 1113873 (13)

-e new fully prefabricated building is assembled frommultiple prefabricated slabs and its continuity is not asgood as cast-in-situ flooring so it cannot be considered ahomogeneous body for calculating rigidity within theaircraft We use the equivalent beam model to calculatethe midspan deflection and its deformation includesshear deformation and bending deformation Howeverstudies have shown that the deformation under horizontalload is dominated by shear deformation so the midspandeflection deformation can be regarded as the displace-ment caused by equivalent shear deformation and the in-plane stiffness of the floor is the equivalent shear stiffness[15 16]

23eoretical AnalysisModel of Building Seismic ResistanceCompared with cast-in-place slabs prestressed fabricatedbuilding structures havemuch greater in-plane deformationand the building cannot be simply regarded as infinite in-plane rigidity -erefore a multistory structure composed ofprestressed fabricated building structures is constructedWhen there is horizontal free vibration or forced vibrationunder the action of a horizontal earthquake each floor of themultistory structure undergoes translational vibration andoverall rotation at the same time producing horizontaldeformation so that the lateral displacement value of eachvertical member is not the same [17] -erefore it is nolonger possible to use the ldquoseries mass point systemrdquo modelin the seismic code for structural seismic analysis Insteadeach vertical member should be connected by each layer ofsemirigid floor to form a space structure After discretiza-tion a ldquostringrdquo is formed [18]

For the analysis of the spatial structure of the pre-fabricated structure this chapter will adopt the modeanalysis method based on the response spectrum theory thatis it will use the free vibration equation of the multiparticlesystem to solve the physical vibration period and the modeof operation of the structure and then using the theory ofdecomposition and response spectrum acquires the hori-zontal seismic action of the structure [19] Comparing thefree vibration equation of the ldquoseries-parallel multiparticlesystemrdquo with the free vibration equation of the ldquoseries-parallel multiparticle systemrdquo it has the followingcharacteristics

(1) If the vertical bar where the mass point of the two-way shear bar is located it represents a frame thatdoes not consider the vertical deformation of the barthe horizontal bar represents the assembled rein-forced concrete floor that is regarded as an equiv-alent shear beam that is where the mass point isboth the vertical rod and the horizontal rod are shearrods [20] -en the restoring force received by themass point is only affected by the side shift of onemass point up and down and left and right except forits own side shift -e side shifts of other mass pointshave no effect on it as shown in Figure 4(a)

Mathematical Problems in Engineering 5

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 6: Antiseismic Method of Prestressed Fabricated Building ...

(2) One-way bending shear bar If the vertical bar wherethe mass point is located it represents the seismicwall belonging to the bending shear type memberand the horizontal bar still represents the pre-fabricated reinforced concrete floor [21] -en therestoring force of this mass point is affected by theside shift of other mass points the horizontal di-rection is still one mass point on the left and rightand the vertical direction expands to all the masspoints of the vertical rod as shown in Figure 4(b)

(3) Two-way bending shear bars if the vertical bar andhorizontal bar where the mass point is locatedrepresent the seismic wall and the cast-in-placereinforced concrete floor respectively they are allbending shear-type members [22]-en the range ofthe side shift of other particles affected by the re-storing force of a certain mass point will be furtherexpanded to all mass points where the mass point sitson the vertical rod and the horizontal rod as shownin Figure 4(c)

-e current analysis methods for concrete structures aremainly elastic analysis However for the increasinglycomplex concrete structures this method appears to beinadequate -erefore the nonlinear analysis method hasdeveloped rapidly -is method can more fully simulate thebehavior of concrete structures under seismic action and hasa great effect on the behavior of specific structures underseismic action For the research and analysis of the seismicperformance of traditional concrete structures there aremainly two types rod model and story model [23 24]

-e floor model balances the entire structure into acantilever beam and each floor is equivalent to a concen-trated mass point and the stiffness is reflected by the steelbars between the mass points-e advantage of this model isthat due to the low degree of freedom of the layer model andthe low amount of calculation it can quickly obtain dis-placement and layer shear but because the layer model hasbeen greatly simplified it can only bear the overall seismicstructure Response results cannot reach the results of each

component -e calculation results of internal strength anddeformation are rough

We use low-cycle cyclic load to simulate the model thatis use a specific load test or deformation test to load thesample repeatedly at low cycles to make the sample from theelastic stage to fracture In the cyclic loading process thecumulative damage of the components will inevitably lead toa gradual decrease in structural rigidity weakening of energyconsumption capacity and a degradation phenomenon [25]-erefore this decomposition effect of the structure must beconsidered when creating a restoring force model -e re-storing force model is a practical mathematical model ob-tained by appropriately subtracting and simplifying therelationship between restoring force and deformation ob-tained from a large number of experiments It is a concretemanifestation of the seismic performance of structuralmembers in the analysis of structural elastoplastic seismicresponse At present most of the proposed recovery strengthmodels mainly focus on the hysteresis performance underrepeated loads However for concrete shaft members due tothe large difference in hysteresis between the compressiondirection and the tension direction the strength model mustbe specially studied [26]

3 Seismic Test of Prestressed FabricatedBuilding Structure

31 Model Parameters To verify the effectiveness of theprefabricated structure analysis this chapter simulates thecast shear wall test and compares the SAP2000 simulationresults with the experimental results -e specific compo-nent parameters are as follows Shear wall concrete thedesign is C35 concrete After testing the actual compressivestrength of C35 concrete is 412MPa and the thickness ofthe concrete protective layer is 25mm-e longitudinal steelbars of the edge members adopt HRB400 hot-rolled steelbars with a diameter of 16mm Other vertical distributionsteel bars adopt HRB400-grade hot-rolled steel bars with adiameter of 10mm -e horizontal distribution steel barsadopt HRB400-grade hot-rolled steel bars with a diameter of

(a) (b) (c)

Figure 4 Characteristics of restoring force of series-parallel mass point system (a) Two-way shear bar (b) One-way bending shear bar (c)Two-way bending shear bar

6 Mathematical Problems in Engineering

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 7: Antiseismic Method of Prestressed Fabricated Building ...

10mm -e stirrups are made of HRB400 hot-rolled steelbars with a diameter of 8mm HRB335 grade hot-rolled steelbars -e structural reinforcement diagram is shown inFigure 5 -e building wall table is shown in Table 1

32 Prestressed Reinforcement and NonprestressedReinforcement To achieve a good prestress effect the pre-operated tendons must have high strength to ensure hightension is created in the preoperated tendons thus im-proving the crack resistance of the preoperated concretemembers -e prestressed steel used for prestressed concretecomponents mainly includes steel yarn prestressed steelwire and prestressed spiral steel wire -e nonprestressedreinforcement must be HRB400 and HRB335 steel In thisstudy 1860 prestressed steel strands are used to simulateprestressed bars with a diameter of 152mm and an area of139mm2 -e nonprestressed bars are HRB400-grade bars

33 Types of Prestress Loss -e factors that cause the loss ofprestress mainly include the following aspects the shrinkageand creep of concrete cause the prestress loss of the pre-stressed tendons in the tension zone and the compressionzone the prestress loss caused by the friction between theprestressed tendons and the tunnel wall during heating andcuring the prestress loss caused by the temperature dif-ference between the tensioned prestressed tendons and theequipment that bears the tension and the prestress losscaused by the linear prestressed tendons due to the defor-mation of the anchor and the shrinkage of the prestressedtendons Due to the discrete nature of the prestress loss theloss value of the prestress in the actual project may be higherthan the loss value calculated according to the specification-erefore if the loss value calculated by the calculation is lessthan the following value the following value should beselected

34 Statistics When designing the prestressed tendons ofthe in-line prestressed shear wall refer to the general cal-culation method for the prestressed design of the prestressedconcrete shear wall and adopt the value of the effectiveprestress of the concrete on the wall section to be greaterthan or equal to the standard value of the concrete tensilestrength -e calculation principle is designed and calcu-lated In the actual project in order to consider the con-venience of construction the prestressed tendons arearranged in a concentrated manner with bonded prestressedtendons that is the calculated prestressed steel strands arearranged in a bundle

4 Seismic Experimental Analysis of PrestressedFabricated Building Structure

41 Influence of Axial Compression Ratio on EarthquakeResistance -is part studies the effect of axial compressionratio on the seismic performance of prestressed concreteshear walls By comparing the nonprestressed and pre-stressed shear walls with different axial compression ratios

the most suitable axial compression ratio for prestressing isstudied In this part the axial compression ratio of the in-line shear wall is controlled at 01 02 03 04 05 and 06respectively and horizontal load is applied by the method ofdisplacement-controlled loading -e prestress is applied bythe cooling method and the analysis statistics of the next-shaped shear wall with different axial compression ratioswithout prestress and applied prestress are shown in Table 2

According to the calculation results in Table 2 when theaxial compression ratio of the in-line shear wall is 0106 thebearing capacity of the in-line shear wall is increased by75 127 and 153 respectively and the prestressing isincreased by 35 When the axial compression ratio is 03the prestressed bearing capacity increases the most With theincrease of the axial compression ratio the peak loadgradually increases We have also made statistics on theductility coefficient of the bearing capacity of the structureunder different axial compression ratios as shown inFigure 6

It is found that the application of gears improves thestiffness and productivity of the wall and reduces theplasticity -e increase of loading capacity and stiffness ismore important in low axial compression ratios so thecompression ratio of the axle shaft should not be too high-e axial compression ratio is between 01 and 03 and theductility reduction is relatively small When the axialcompression ratio is 03 the ductility coefficient is 43 whichmeets the seismic requirements -erefore it is recom-mended that the prestressed axial compression ratio shouldnot exceed 03

Figure 7 shows the wall stress cloud when the steel bar ofthe prestressed concrete wall under 03 yields

42 Influence of Prestressing Tendon Distribution on theSeismic Performance of Walls Based on the analysis andsummary of the axial compression of the in-line shear wallthis section studies the influence of the prestressed tendonarrangement on the seismic performance of the in-line shearwall and the axial compression ratio is determined to be 03Under the same other conditions change the way of pre-stressed tendons -e prestressed tendons are divided intothree ways concentrated on the edge members concen-trated on the middle wall and evenly distributed on theentire wall in order to better reflect the influence of thearrangement of different prestressed tendons on the seismicperformance of the shear wall -e prestressed tendons aresimulated by the distributed arrangement of bonded pre-stressed tendons As shown in Figures 8 and 9 the pre-stressed tendons are concentratedly arranged in the middlewall and uniformly arranged Schematic diagram of stiff-eners scattered throughout the wall Table 3 shows thestatistical results of building analysis of different prestressedtendons

From the diagram it can be seen that when the tendonprotrusions are concentrated at the ends their capacity andstiffness are greatest followed by evenly spaced across thewall and finally concentrated in the middle wall and theconvex tendons are placed at the edge -e time delay of the

Mathematical Problems in Engineering 7

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 8: Antiseismic Method of Prestressed Fabricated Building ...

1

2 2

12300

650

3400

250

1700

250

240

650

700

1-1

Loading beam Horizontal steelbar

Stirrup

Longitudinalreinforcement

125 180 125 190 207 207 180 125 180 125

134

Horizontal steel bar Stirrup

2-2

Figure 5 Structural reinforcement diagram

Table 1 Reinforcement diagram of building structure

Name Wall thickness (mm) Length (mm) Horizontal distribution rib Vertically distributed ribsQ1 200 750 8200 8200

Table 2 Statistical results

Axial pressure ratio Construct Yield displacement Limit displacement Yield load Peak load Ductility coefficient

01 No prestressed 301 177 258 560 58Prestress 313 153 316 602 48

02 No prestressed 265 168 342 659 47Prestress 321 148 380 744 45

03 No prestressed 301 126 427 756 44Prestress 335 135 488 857 42

04 No prestressed 302 125 537 835 42Prestress 384 119 536 874 32

05 No prestressed 205 102 609 920 33Prestress 401 121 567 937 27

06 No prestressed 304 98 637 959 32Prestress 409 106 599 968 26

8 Mathematical Problems in Engineering

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 9: Antiseismic Method of Prestressed Fabricated Building ...

component is the worst but the ductility coefficient is notvery different from the other two arrangements -e duc-tility coefficient is 42 whichmeets the seismic requirements

We make statistics on the results of structural residualdeformation and steel bar deformation of buildings underdifferent seismic waves as shown in Tables 4 and 5

It can be seen from the table that under the action ofTafts wave the entire vibration process of the first floor of theprestressed fabricated building structure is relatively strongso the residual deformation is relatively insignificant Whenthe vibration process becomes stable the displacement curveof the bottom layer is generally concentrated at about 0

0

5

10

15

20

01 02 03 04 05 06 07

Incr

ease

()

Axial pressure

Increase

65

13

154

25 26 321

2

25

3

35

4

45

5

01 02 03 04 05 06 07

Exye

mso

pm fa

ctor

Axial pressure

Extension factor

4745

41

333

26

Figure 6 Different shaft compression parameters

200

150

100

50

00

-50

-100

-150

-200

-250

-300

-350

-400

-450

Figure 7 03 axial compression ratio steel bar yield wall stress diagram

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

1700

134

125 180 125 180 207 207 180 125 180 125

Figure 8 Prestressed tendons are arranged in the middle wall

Mathematical Problems in Engineering 9

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 10: Antiseismic Method of Prestressed Fabricated Building ...

which shows the excellent self-recovery ability of the pre-stressed assembly frame -is is because under the action ofseismic excitation the prestress inside the main beam canforcibly restore the larger deformed beam to its originalposition It can be concluded that the seismic performance ofthe prestressed fabricated frame is higher than that of thetraditional cast-in-place frame structure in dealing with theresidual deformation of the structure

On the whole the residual strain value of the steel bar ofthe fabricated frame structure is much smaller than theresidual strain value of the cast-in-place structure Aftercomparative analysis the prestressed fabricated buildingstructure has better self-healing deformation ability Whenthe seismic grade is level 2 for in-line and T-shaped shearwalls prestress is applied to increase the bearing capacityand rigidity of the shear wall but reduce its ductility As theprestress degree increases the rigidity and bearing capacityof the in-line shear wall gradually slow down and theductility becomes worse and worse When the prestressdegree is from 03 to 05 the extent of ductility declinegradually slows down When the strength is 05 the ductilitycoefficient is 346 which meets the seismic requirements As

the prestress degree increases the stiffness and bearingcapacity of the T-shaped shear wall gradually slow downand the ductility becomes worse and worse When theprestress degree is from 03 to 06 the ductility declinesslowly and so the prestress degree When it is 06 theductility coefficient is 604 which meets the seismic re-quirements Considering the influence of the prestress de-gree on the bearing capacity stiffness and ductility of theshear wall it is recommended that the prestress degree of thefabricated prestressed reinforced concrete shear wall shouldnot exceed 05

5 Conclusion

Combining a real and regular roof wall structure this studymainly studies the effect of different axial compression ra-tios different preview methods and different preseismicdegrees on the seismic performance of prefabricatedbuilding structures -is study designed different parame-ters different working condition combinations established alarge number of comparative models for finite elementcalculation and analysis and put forward suggestions for the

134

1700

Longitudinal ribsHorizontal steel

barPrestressed steel

strand Stirrup

125 180 125 180 207 207 180 125 180 125

Figure 9 Prestressed tendons are concentrated on the entire wall

Table 3 Statistical results of building analysis with different prestressed tendons

Method of prestressed tendons Yield displacement(mm)

Limit displacement(mm)

Yield load(kN)

Peak load(kN)

Ductilityratio

Focus on edge components 326 134 489 878 42Distribute the walls evenly 307 142 427 809 45Centrally arrange the middle part of thewall 262 132 421 776 48

Table 4 Residual deformation under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 3 14 09 04Tafts seismic wave 2 0 0 04Artificial seismic wave 2 0 0 0

Table 5 Residual deformation of reinforcement under seismic wave

Residual deformation Cast in place (mm) Assembly 16mm (mm) Assembly 18mm (mm) Assembly 20mm (mm)El Centro seismic wave 7 054 037 03Tafts seismic wave 79 04 024 01Artificial seismic wave 11 15 13 12

10 Mathematical Problems in Engineering

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 11: Antiseismic Method of Prestressed Fabricated Building ...

application of prestressed fabricated building structures inactual projects Research should be done on the axialcompression ratio different prestressed tendon arrangementmethods and the influence of prestress under differentseismic fortification intensity and seismic grade on theseismic performance of shear walls and find out the ap-propriate axial compression ratio and prestressed tendonlayout that can be prestressed -e reinforcement method isused to achieve the appropriate prestress level but becausethe content of the analysis is not very comprehensive onlymonotonically increasing horizontal force loading is per-formed and reciprocating loading simulation is not per-formed -erefore the hysteresis curve cannot be obtainedand the energy consumption structure and performancecannot be analyzed In addition it is necessary to comparethe seismic analysis of the overall structure with and withoutprestressing so as to have a clearer understanding of theseismic performance of the structure

Data Availability

No data were used to support this study

Conflicts of Interest

-e authors have no potential conflicts of interest in thisstudy

Acknowledgments

-is work was supported by the Scientific Research YouthProject of Chongqing Education Commission (Contract noKJQN202004502) Natural Science Foundation of XinjiangUygur Autonomous Region (General Project 2021D01A68)Sino-Ukrainian Science and Technology Exchange Project(CU03-32) Hebei Provincial Department of TransportationScience and Technology Project (TH-201918) and XinjiangProvincial Department of Science and Technology Project(2018E02075)

References

[1] L Luo G Q Shen G Xu and Y Liu ldquoStakeholder-associatedsupply chain risks and their interactions in a prefabricatedbuilding project in Hong Kongrdquo Journal of Management inEngineering vol 35 no 2 pp 94ndash107 2019

[2] K M A El-Abidi G Ofori S A S Zakaria and A R A AzizldquoUsing prefabricated building to address housing needs inLibya a study based on local expert perspectivesrdquo ArabianJournal for Science and Engineering vol 44 no 10pp 8289ndash8304 2019

[3] J G B Wesz C T Formoso and P Tzortzopoulos ldquoPlanningand controlling design in engineered-to-order prefabricatedbuilding systemsrdquo Engineering Construction and Architec-tural Management vol 25 no 2 pp 134ndash152 2018

[4] G Tumminia F Guarino S Longo M Ferraro M Celluraand V Antonucci ldquoLife cycle energy performances and en-vironmental impacts of a prefabricated building modulerdquoRenewable and Sustainable Energy Reviews vol 92 no SEPpp 272ndash283 2018

[5] G Erhard ldquoMinimum reinforcement of beam-type reinforcedmasonry constructionsndashproposals for future regulationsrdquoDasMauerwerk vol 23 no 4 pp 209ndash226 2019

[6] H Gao ldquoCrustal seismic structure beneath the source area ofthe Columbia River flood basalt bifurcation of the Mohodriven by lithosphere delaminationrdquo Geophysical ResearchLetters vol 42 no 22 pp 9764ndash9771 2016

[7] P Gueguen P Johnson and P Roux ldquoNonlinear dynamicsinduced in a structure by seismic and environmental loadingrdquoJournal of the Acoustical Society of America vol 140 no 1pp 582ndash590 2016

[8] G Fujie S Kodaira T Sato and T Takahashi ldquoAlong-trenchvariations in the seismic structure of the incoming Pacificplate at the outer rise of the northern Japan Trenchrdquo Geo-physical Research Letters vol 43 no 2 pp 228ndash232 2016

[9] X Chen and C Liu ldquoComplex seismic focus structure andearthquake-triggered landslide distributionanalysis of the2014 ludian M_w61 earthquake in Yunnanrdquo Acta GeologicaSinica vol 2 no v91 pp 365-366 2017

[10] K Wan S Xia J Cao J Sun and H Xu ldquoDeep seismicstructure of the northeastern South China Sea origin of ahigh-velocity layer in the lower crustrdquo Journal of GeophysicalResearch Solid Earth vol 122 no 4 pp 2831ndash2858 2017

[11] M S Ekka V Ghangas P Roy and O P Mishra ldquoCoda waveseismic structure beneath the Indian Ocean region and itsimplications to seismotectonics and structural heterogeneityrdquoJournal of Asian Earth Sciences vol 188 no Feb pp 1ndash292020

[12] V M Solovrsquoev V S Seleznev A S Salrsquonikov et al ldquoDeepseismic structure of the boundary zone between the Eurasianand Okhotsk plates in eastern Russia (along the 3DV deepseismic sounding profile)rdquo Russian Geology amp Geophysicsvol 57 no 11 pp 1613ndash1625 2016

[13] H Zhu Y Tian D Zhao H Li and C Liu ldquoSeismic structureof the Changbai intraplate volcano from joint inversion ofambient noise and receiver functionsrdquo Acta Geologica Sinica-English Edition vol 93 no S1 p 262 2019

[14] A Ohira S Kodaira G Fujie et al ldquoSeismic structure of theoceanic crust around petit-spot volcanoes in the outer-riseregion of the Japan trenchrdquo Geophysical Research Lettersvol 45 no 20 pp 123ndash129 2018

[15] Y Xu X Li and S Wang ldquoSeismic structure beneath theTengchong volcanic area (southwest China) from receiverfunction analysisrdquo Journal of Volcanology and GeothermalResearch vol 357 no may15 pp 339ndash348 2018

[16] C Jiang B Schmandt K M Ward F-C Lin andL L Worthington ldquoUpper mantle seismic structure of Alaskafrom Rayleigh and S wave tomographyrdquo Geophysical ResearchLetters vol 45 no 19 pp 350ndash359 2018

[17] T Ohtaki S Tanaka S Kaneshima et al ldquoSeismic velocitystructure of the upper inner core in the north polar regionrdquoPhysics of the Earth and Planetary Interiors vol 311 no 1pp 106636ndash106639 2020

[18] S Vijayaraghavan and M Saimurugan ldquoSeismic analysisbased structure integrity assessment of steam generator in fastbreeder reactorrdquo Materials Today Proceedings vol 22 no 4pp 3152ndash3161 2020

[19] G Hou M Li S Hai et al ldquoInnovative seismic resistantstructure of shield building with base isolation and tuned-mass-damping for AP1000 nuclear power plantsrdquo EngineeringComputations vol 36 no 4 pp 1238ndash1257 2019

[20] A Hedayat andM J Alborzi ldquo-e seismic analysis of the corestructure in a pool-type material test reactor using 3-D finite

Mathematical Problems in Engineering 11

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering

Page 12: Antiseismic Method of Prestressed Fabricated Building ...

difference methodrdquo Progress in Nuclear Energy vol 106no jul pp 162ndash180 2018

[21] Y Zhou and Y Chi ldquoSeismic noise attenuation using animproved variational mode decomposition methodrdquo Journalof Seismic Exploration vol 29 no 1 pp 29ndash47 2020

[22] A Shito S Matsumoto H Shimizu et al ldquoSeismic velocitystructure in the source region of the 2016 Kumamotoearthquake sequence Japanrdquo Geophysical Research Lettersvol 44 no 15 pp 7766ndash7772 2017

[23] S-K Tan W Guo B Zhou and S Han ldquoRandom seismicresponse analysis of jacket structure with Timoshenkorsquos beamtheoryrdquo Ships and Offshore Structures vol 11 no 34pp 438ndash444 2016

[24] E Mistakidis and D Pantousa ldquoFire-after-earthquake resis-tance of steel structures using rotational capacity limitsrdquoEarthquake and Structures An International Journal ofEarthquake Engineering amp Earthquake Effects On Structuresvol 10 no 4 pp 867ndash891 2016

[25] C Yong J Hu and F Peng ldquoSeismological challenges inearthquake hazard reductions reflections on the 2008Wenchuan earthquakerdquo Science Bulletin vol 63 no 17pp 1159ndash1166 2018

[26] B B Gupta P Chaudhary and S Gupta ldquoDesigning a XSSdefensive framework for web servers deployed in the existingsmart city infrastructurerdquo Journal of Organizational and EndUser Computing vol 32 no 4 pp 85ndash111 2020

12 Mathematical Problems in Engineering