Nonlinear time history analysis of a super-tall building...

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. (2011)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/tal.717

Nonlinear time history analysis of a super-tall building withsetbacks in elevation

Xilin Lu, Ningfen Su*,† and Ying Zhou

State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, China

SUMMARY

Standing 260m above the ground, the super-tall building employs steel reinforced concrete frame andreinforced concrete core wall system strengthened by a belt truss story to resist lateral and vertical loads. Ithas two setbacks in elevation. One is structurally designed by direct termination of vertical members, andthe other is realized by inclining columns. Because of these characteristics, the building is classified as anirregular and complex structure. To investigate the seismic behavior of the structure under rare earthquakeaction, a refined finite element model was developed by using ABAQUS (Dassault Systèmes Simulia Corp.,Providence, RI, USA). Nonlinear time history analyses were conducted using explicit integration method.The results show that the structural system has sufficient seismic capacity and ductility to resist rareearthquake. The plastic deformation capacity of this building can meet the requirement of Chinese code,and seismic performance objective of no collapse under rare earthquake can be reached. However,deformations were found concentrated in members within and adjacent to setback stories, at the bottomstrengthening portion of core walls and its upper story where lateral stiffness suddenly changed. It wassuggested that transfer stories should be placed above or below these stories to improve the concentration ofstrain and deformation. Copyright # 2011 John Wiley & Sons, Ltd.

Received 7 January 2011; Revised 22 April 2011; Accepted 21 June 2011

KEY WORDS: steel reinforced concrete frame; core wall; super-tall building; setback; nonlinear time history analysis

1. INTRODUCTION

In order to make the design unique and add beauty to cities, many new buildings adopt novelarchitectural styles, such as the wheel-shaped Icon Hotel in Dubai (Berahman, 2010) and the ChinaPavilion for Expo 2010 Shanghai (Yang et al., 2010). However, irregularity and complexity ofstructures are inevitable for these special buildings. This requires structural engineers to thoroughlyunderstand how these structures behave, especially in future earthquakes.Among these irregularities, setback might be the most historic one, which was used by ancient

builders to increase the height of masonry structures through distributing gravity loads produced bythe building material such as clay, stone or brick. The most graphic example of a setback technique isthe step pyramids of Mesopotamia and Ancient Egypt. Nowadays, driven by the limited urban land,modern buildings grow taller and taller. To get access to fresh air, skyline views and recreational usessuch as hanging garden and outdoor swimming pool, setback is frequently adopted.However, setback usually means discontinuity and termination of partial bending resistance

members, which will lead to inappropriate load transfer and sudden change of lateral stiffness. Thenonuniform vertical mass distribution caused by setback may have a significant influence on theresponse to seismic loading. For asymmetric setback structure, torsion effect might be remarkable.

*Correspondence to: Ningfen Su, B306, Civil Engineering Building, College of Civil Engineering, Tongji University,1239 Siping Road, Shanghai 200092, China.†E-mail: [email protected]

Copyright # 2011 John Wiley & Sons, Ltd.

X. LU, N. SU AND Y. ZHOU

Consequently, the setback level may become a weak point and vulnerable when attacked byearthquakes.Many researchers investigated the response of setback structures. To name a few, Humar and

Wright (1977) studied the seismic response of steel frames with setbacks by using one ground motion.The most notable observations in their study were altered displacements and high ductility demands inthe vicinity of the irregularities. Aranda (1984) made a comparison of ductility demands betweensetback and regular structures. He observed higher ductility demands for setback structures than for theregular ones and found this increase to bemore pronounced in the portion above the setback. Khoury et al.(2005) considered four nine-story asymmetric setback perimeter frame structures that differed from eachother in the location of the setback along the height. Nonlinear dynamic analyseswere performed, and a 3Dstructural model was used under bidirectional ground motions. Results showed that higher vibrationmodes have significant influence, particularly the torsional ones. Seismic codes make specifications ondesign of such vertical irregular structures as well. Nevertheless, setback structures have never been freefrom earthquake damages. Figure 1 shows unrecoverable damage that occurred in a building with setbackin 27 February 2010 offshoreMaule, Chile, earthquake (Lew et al., 2010). It is indicated that, in spite of thestudies above, further study on the structure with setbacks is still needed.One way to investigate the seismic behavior of an irregular building is shaking table model test,

which is thought to be one of the most effective ways to study complex buildings (Lu et al., 2007).However, when time and cost are considered, an alternative way is to perform nonlinear analysis usingfinite element method to get insights about the performance of complex buildings. Yahyai et al. (2009)used finite element model analysis to study the nonlinear seismic response of Milad Tower. Epackachiet al. (2010) conducted a seismic evaluation of a 56-story residential reinforced concrete buildingbased on nonlinear dynamic time history analysis of finite element model. Krawinkler (2006) believesthat earthquake engineering is relying more and more on nonlinear analysis as a tool for evaluatingstructural performance and nonlinear analysis will be a good trend.

Figure 1. Setback damage in Chile earthquake (Lew et al., 2010).

Copyright # 2011 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. (2011)DOI: 10.1002/tal

NONLINEAR TIME HISTORY ANALYSIS OF A SUPER-TALL BUILDING

In this paper, a super-tall building with setbacks in elevation is introduced. Considering that a code-exceeding design is employed, detailed investigation is necessary and essential to verify the feasibilityof preliminary design and guarantee its safety and also to provide guidance and advice to engineers forsimilar projects concerned. Three main parts are included. First, a refined finite element analysismodel of this building is developed by using ABAQUS and its user material subroutine program.Then, nonlinear dynamic time history analysis under rare earthquake action is conducted to thiscomplex building via explicit integration numerical solution method. Finally, the nonlinear dynamicresponses including roof acceleration and displacement, interstory drift and damage of main lateralforce-resisting members are presented and discussed. Moreover, practical suggestions are proposed onthe basis of analysis results.

2. DESCRIPTION OF THE STRUCTURE

2.1. Basic information

The target building is a multifunctional building located in Shanghai, China, which has 58 storiesabove the ground including a 24-story hotel part, a 23-story office part and a four-story basementunderneath. It has a total architectural height of 260m, and the structural height is 244.8m. Dimensionof the typical plan is 59.52m by 59.52m at the bottom, 52.02m by 53.52m in the middle and 28.02mby 53.52m at the top. Figures 2 and 3 show the typical plan layouts and south elevation, respectively.

X

Y

(a) The1st to the 13th floor (b) The14th to the 20th floor

(c) The 21st to the 31st floor (d) The 32nd to the 58th floor

Figure 2. Typical plan layouts of each part.


Figure 3. South elevation.


2.2. Lateral force-resisting system

The structure employs the steel reinforced concrete (SRC) frame and the reinforced concrete (RC)core wall system to resist lateral and vertical loads. The cross-sectional dimensions of the core wallsand of main the SRC columns and the reinforcement ratios are listed in Tables 1 and 2, respectively.Owing to the weak connection between the frame and the core wall in the upper hotel part, a belt trussis arranged in the 46th floor to serve as a strengthened story (Figure 4).

Table 1. Cross-sectional dimensions of main lateral force-resisting elements.

Members Story Elevation (m)

Dimensions (mm)

Flange wall Web wall

Wall 1–5 0–26.7 1000/1200 400/6006–21 26.7–94.9 800/1000 400/600

21+1–31 94.9–141.9 600/800 400/60031+–58 141.9–244.8 600 400

Column 1–5 0–26.7 2200�2200; 2000�2000;6–13 26.7–60.3 2200�2200; 2000�2000; 1850�185014–20 60.3–90.7 2000�2000; 1800�1800; 1850�185021–31 90.7–141.9 1600�1600; 1350�135031+–58 141.9–244.8 1000�1500; 1200�1200

1Story 21+ is a mezzanine between the 21st and 22nd story.


Table 2. Reinforcement ratio of main lateral force-resisting elements.

Members Story

Reinforcement ratio (%)

Horizontal Vertical

Confining boundary elements

Horizontal Vertical

Wall 1–6 0.3 0.5 1.8 2.57–28 0.3 0.5 1.8 2.029–36 0.3 0.5 1.8 2.537–58 0.3 0.5 1.8 2.0

Column 1–29 1.230–58 1.5

Figure 4. Belt truss in the 46th story.


2.3. Setbacks

With the alteration of plan arrangement, two setbacks are formed in elevation in the 20th and 31ststory, respectively (Figure 5). The former is realized by inclining two sets of columns (see thefollowing section), whereas the core wall remains unchanged. The latter is structurally designed bydirect termination of bending resistance members and 50% reduction of floor size, leaving a largesetback in the core wall in the 31st story (Figure 6). The height of the tower structure above thissetback level is 101.9m, which is about 41.7% of the overall structural height. To guarantee that theload from the upper structure transfers smoothly to the lower story, diagonal bracings (Figure 7) areadded between the SRC frame and the core wall in the story right below this setback, and the thicknessof slab in this story is increased. Newly added columns of the tower structure above the setback arerooted to the base structure below the setback level by extending them two stories down (Figure 7).In addition, the plan of core wall cuts off a corner from the 13th story and forms a relatively small

setback (Figure 6). A column is used instead.

2.4. Inclined columns

The two sets of inclined columns (Figure 8a) tilt respectively from the 16th floor to the 20th floor(Figure 8b) and from the 20th floor to the 21st mezzanine floor (Figure 8c). The angles of the inclinedcolumns to the vertical direction are 11.5� and 13.2�, respectively. Beams connected to these columnsare strengthened by using SRC beams.

2.5. Items beyond code limitation

According to the Chinese Code for Seismic Design of Building (CCSDB, GB 50011-2001) (Ministryof Construction of the People's Republic of China, 2001) and Technical Specification for ConcreteStructures of Tall Building (TSCSTB, JGJ3-2002) (Ministry of Construction of the People's Republicof China, 2002), the height of this building exceeds the specified maximum height of 190m for SRC


Figure 5. Setbacks in elevation.


frame and RC core wall system. Besides, the setback dimension in the 31st story is beyond theelevation layout requirement of TSCSTB (Figure 9a). Therefore, this building is classified as a verticalirregular one, and elasto-plastic time history analysis is required to investigate its seismic behaviorunder rare earthquake (2–3% probability of exceedance in 50years) action.

3. FINITE ELEMENT MODEL

ABAQUS (version 6.9-1) was used to build finite element model and conduct nonlinear dynamic timehistory analysis.

3.1. Element type selection

All members of the SRC frame including embedded boundary members in walls were modeled usinga first-order 3D Timoshenko beam element (B31), in which the transverse shear deformation wasallowed. The beam section was divided into an array of fibers or section points, at which beamelement's response were calculated and outputted. For space beam element with rectangular profile, 25section points were considered by default in ABAQUS.The linear, reduced-integration, quadrilateral shell element (S4R) was used to model shear wall and

slab, in which in-plane bending and shear and out-of-plane bending can be simulated simultaneously.Numerical integration was performed at a number of section points through the shell thickness tocalculate the stresses and strains independently at each section point. By default, ABAQUS uses fivesection points through the thickness of a homogeneous shell, which is sufficient for most nonlineardesign problems. Considering the complexity of the structure and the importance of this study, ninewere used herein.


Figure 6. Setbacks in core wall.

Figure 7. Diagonal bracing.


The simulation of reinforcements can be achieved by two methods. One is to model eachreinforcement bar separately. In this way, reinforcement should be embedded into concrete elementsor through node coupling to make them work together with concrete. The other is to treat the rebarlayer as a smeared layer with a constant thickness equal to the area of each reinforcing bar divided bythe reinforcing bar spacing, which is preferred for defining reinforcement in wall or slab. Here, the


(a) (b) (c)

Figure 8. Inclined columns.

Figure 9. Requirement for elevation layout in Chinese code.


former one was used to model reinforcement in beams and columns, steel in columns and boundarymembers in core wall, and the latter one was used to model reinforcement in wall and slab.The coupling beams, which usually damage first, are of great importance in dissipating energy

inputted by earthquake and thus influence the ductility and seismic performance of the core wall. Inorder to observe the development of damage in detail, S4R was used again to model the couplingbeam.Along the longitudinal direction of beams and columns and the two directions of wall, members

were divided into several elements to improve accuracy. The length of beam element and shellelement should be less than 2.5m. As far as running time is concerned, element should be better longerthan 1m. Finally, the nonlinear analysis model (Figure 10) is comprised of 88297 elements and 158747 nodes in all.

3.2. Material constitutive models

The isotropic bilinear kinematics hardening model was used for reinforcement and steel, in whichBauschinger effect was considered. During the cyclic loading, no degradation was developed. Theratio of ultimate strength to the yield strength was 1.2 for reinforcement bar and 1.3 for steel. Theultimate plastic strain corresponding to the ultimate stress was considered as 0.025. Check Table 3 fordetails.Properties of concrete used in this building are listed in Table 4.The damaged plasticity model was used to simulate the behavior of concrete in the core wall, which

used concepts of isotropic damaged elasticity in combination with isotropic tensile and compressiveplasticity to represent the inelastic behavior of concrete (ABAQUS, 2009). The model made use of the


Table 3. Properties of the steel.

Steel grade Yield stress (MPa)Ultimate stress (MPa)Ultimate plastic strainModulus of elasticity (MPa)

HRB335 335 402 0.025 2.06E+5HRB400 400 480 0.025 2.06E+5Q345(t>35–50) 295 384 0.025 2.06E+5Q345(t>16–35) 328 426 0.025 2.06E+5

Figure 10. Nonlinear analysis model.

Table 4. Properties of the concrete.

Concrete grade

Design values of concrete strength (MPa)

Poisson ratio

Modulus ofelasticity(MPa)Compressive Tensile

C35 (beam/slab) 16.7 1.57 0.2 3.15E+4C60 (wall/column) 27.5 2.04 0.2 3.60E+4


yield function of Lubliner et al. (1989), with the modifications proposed by Lee and Fenves (1998) toaccount for the different evolution of strength under tension and compression. It assumednonassociated potential plastic flow. The flow potential used for this model was the Drucker–Prager


Figure 11. Response of concrete to uniaxial loading in tension (a) and compression (b).


hyperbolic function. The response of concrete to uniaxial loading in tension and compression areshown in Figure 11, where dc and dt are the compressive and tensile damage variable respectively andused to characterize the degradation of the elastic stiffness. The damage variables can take values fromzero, representing the undamaged material, to one, which represents total loss of strength. Figure 12shows the mechanical response of concrete under cyclic loading (tension–compression–tension),where wc and wt are the compressive and tensile stiffness recovery factor respectively to control therecovery of compressive and tensile stiffness upon load reversal.Since there was no proper concrete material model available for B31 element in current ABAQUS

edition, a user material subroutine was written and incorporated into ABAQUS via VUMAT subroutine.This usermaterial uses the uniaxial concrete constitutivemodel proposed byMander et al. (1988a, 1988b),

Figure 12. Uniaxial load cycle (tension–compression–tension) assuming wc=1 and wt=0.



which takes into account the influence of various types of confinement by defining an effective lateralconfining stress.

4. NONLINEAR TIME HISTORY ANALYSIS

4.1. Input ground motions

It is specified in TSCSTB that no less than two strong earthquake records and a syntheticaccelerogram should be selected for elasto-plastic time history analysis. The duration should be noshorter than 12s. Soil condition should be taken into account. According to the CCSDB, the site soil inShanghai is categorized as type IV, which is defined as soil whose soft layer thickness is more than 80m, and average velocity of shear wave in the soil layer is not more than 140m/s. In consideration ofthe factors mentioned above, two strong earthquake records (Table 5) and Shanghai syntheticaccelerogram SHW1 were selected. SHW1 is specified for the particular soil conditions of Shanghaiand can be found in the Shanghai Code of Seismic Design of Buildings (SCSDB, DGJ08-9-2003)(Shanghai Government Construction and Management Commission, 2003). Figures 13–15 show timehistories (normalized to 1g) and spectrum accelerations of selected accelerograms when damping ratiois 0.05. Figure 16 shows the displacement response spectrum of each accelerogram given a 5%damping ratio.The seismic protection intensity of Shanghai is 7, and the corresponding design basic

acceleration of ground motion is 0.1g, which means 10% probability of exceedance in 50years.Since seismic behavior under rare earthquake action was investigated mainly in this paper, thepeak ground acceleration (PGA) of selected earthquake accelerograms were scaled to 0.2g, whichwas specified in SCSDB to characterize the seismic risk of 2% probability of exceedance in 50years in the seismic protection zone of 7. During the analysis, the two strong earthquake recordswere inputted in two principal directions simultaneously (the N–S record is inputted in the Xdirection) with the PGA ratio of 1:0.85, whereas the synthetic accelerogram was inputted in onedirection.

4.2. Damping ratio

As specified by TSCSTB, a damping ratio of 0.04 for SRC frame–RC core wall structural system wasadopted.

4.3. Numerical solver of the nonlinear equations of motion

The direct-integration dynamic procedure provided in ABAQUS/Standard uses the implicitHilber–Hughes–Taylor operator for integration of the equations of motion, whereas ABAQUS/Explicit uses the central-difference operator. In an implicit dynamic analysis, the integrationoperator matrix must be inverted, and a set of nonlinear equilibrium equations must be solved ateach time increment. In an explicit dynamic analysis, displacements and velocities are calculatedin terms of quantities that are known at the beginning of an increment; therefore, the global mass

Table 5. Characteristics of selected records.

Earthquake Station MagnitudeEpicentral distance

(km)PGA(g)

El Centro N–S Imperial Valley18/5/1940

117 El Centro Array #9 7.1 12.99 0.349El CentroE–W 0.215Pasadena N–S Kern County

21/7/195280053 Pasadena—CIT

Athenaeum7.36 125.81 0.053

Pasadena E–W 0.045

PGA, peak ground acceleration.


-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45 50 55

Time(s)

Acc

eler

atio

n(g)

(a)

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45 50 55

Time(s)

Acc

eler

atio

n(g)

(b)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6

Spec

trum

Acc

eler

atio

n(g) Target Spectrum

El Centro N-SEl Centro E-W

(c)Period(s)

Figure 13. El Centro accelerogram: (a) time history of acceleration in N–S direction; (b) time historyof acceleration in E–W direction; (c) spectrum acceleration.


and stiffness matrices need not be formed and inverted, which means that each increment isrelatively inexpensive compared with the increments in an implicit integration scheme. Theanalysis cost rises only linearly with problem size for explicit integration, whereas the cost ofsolving the nonlinear equations associated with implicit integration rises more rapidly thanlinearly with problem size. Therefore, explicit analysis method is attractive for very largeproblems (ABAQUS, 2009). Here, explicit method was selected.

5. ANALYTICAL RESULTS

Prior to the nonlinear dynamic time history analysis, stress generated by static load such as gravity andservice load has already acted on the structure, which serves as the initial state of nonlinear dynamicanalysis. So, a static analysis was performed before time history analysis to obtain the initial stressstate in structure members. According to the static analysis results, the structure totally weights 2764660kN.A modal analysis was conducted to get the natural vibration characteristics of the structure.Material nonlinearity and geometric nonlinearity were considered in the time history analysis. Main

results are summarized and discussed in the following sections.


-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45

Time(s)

Acc

eler

atio

n(g)

(a)

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45Time(s)

Acc

eler

atio

n(g)

(b)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6

Period(s)

Spec

trum

Acc

eler

atio

n(g) Target Spectrum

Pasadena N-SPasadena E-W

(c)

Figure 14. Pasadena accelerogram: (a) time history of acceleration in N–S direction; (b) time historyof acceleration in E–W direction; (c) spectrum acceleration.


5.1. Natural vibration characteristics

The results of modal analysis are listed in Table 6. Figure 17 shows the first three mode shapes.

5.2. Base shear and moment

Results of maximum base shear and moment when subjected to different ground motions are listed inTable 7. It is clear that a difference exists between structural responses to the three inputs, in whichresponses under SHW1 are significantly greater than that of the other two. This is true not only for themaximum base shear and moment but also for roof displacement and interstory drift results, whichwill be discussed in the following sections. Acceleration and displacement response spectrum mayexplain this to some extent. From Figures 13–16, we can see that the response spectrum of SHW1 isthe one that matches the target spectrum most in the period range interested, whereas that of El Centroin two directions and Pasadena in E–W direction are smaller than the target spectrum. The responsespectrum of Pasadena in N–S direction exhibits a peak at about 1.6s larger than that of SHW1 butturns smaller after 3s.According to the CCSDB, design seismic action is determined by using seismic coefficient, which

is derived from acceleration response spectrum. For a long-period structure, lower spectrum value isusually obtained and consequently leading to lower design seismic action. In order to guarantee thesafety of designed buildings, seismic shear factor is introduced. It is defined as the ratio of horizontal


-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40Time(s)

Acc

eler

atio

n(g)

(a)

(b)

Figure 15. SHW1 accelerogram: (a) time history of acceleration; (b) spectrum acceleration.

Figure 16. Displacement response spectrum of each accelerogram.


seismic shear force to the representative value of gravity load of the structure and is used to preventthe design seismic action from becoming too small. Usually, there is a minimum value for seismiccoefficient in seismic design code. As far as seismic protection intensity 7 is concerned, the factor


Table 6. Natural vibration frequencies.

No. Frequency (cycle/time) Period (s) Mode shape

1 0.227 4.405 Translation in X2 0.251 3.984 Translation in Y3 0.328 3.049 Torsion4 0.552 1.812 Translation in X5 0.680 1.471 Translation in Y6 0.742 1.348 Torsion

(a) (b) (c)

Figure 17. First three mode shapes: (a) the first mode (translation in X); (b) the second mode(translation in Y); (c) the third mode (torsion).

Table 7. Results of maximum base shear and moment.

Input ground motions El Centro Pasadena SHW1

Principal direction X Y X Y X YMaximum base moment (108Nm) 3.848 6.694 4.743 4.045 9.914 12.780Maximum base shear (105kN) 2.089 2.662 2.526 2.043 3.343 3.489Seismic shear factor at ground floor 7.56% 9.63% 9.14% 7.39% 12.09% 12.62%


should be no less than 0.016 for structures with obvious torsion effect or fundamental period of lessthan 3.5s and 0.012 for structures with fundamental period greater than 5.0s. The seismic shear factorsat ground floor of this building satisfy the requirement of 1.84% interpolated to its period of 4.4s.

5.3. Roof acceleration

Figure 18 shows the time history of roof acceleration response when SHW1 was inputted. Table 8 liststhe maximum responses of roof acceleration when different ground motions were inputted. Theacceleration amplification coefficient is the ratio of maximum roof acceleration response to theinputted maximum ground acceleration. The results show that the whipping-lash effect is not verysignificant for this building.


-0.5

-0.25

0

0.25

0.5

0 6 12 18 24 30 36Time (s)

Acc

eler

atio

n (g

)

-0.5

-0.25

0

0.25

0.5

0 6 12 18 24 30 36Time (s)

Acc

eler

atio

n (g

)

(a) (b)

Figure 18. Roof acceleration response when SHW1 is inputted: (a) in X direction; (b) in Y direction.

Table 8. Results of roof acceleration responses.


Principal direction X Y X Y X YMaximum roof acceleration response (g) 0.420 0.355 0.554 0.311 0.424 0.444Inputted maximum ground acceleration (g) 0.200 0.200 0.200 0.200 0.200 0.200Acceleration amplification coefficient 2.10 1.78 2.77 1.56 2.12 2.22


5.4. Roof displacement

Figure 19 shows the roof displacement response history of the structure. The maximum roofdisplacement response, generated by SHW1, is 1.643m in the X direction and 1.576m in the Ydirection, respectively. The ratio of maximum roof displacement response to the height of the wholestructure is 1/149 and 1/155 in the X and Y directions. To gain a better understanding of the nonlineardynamic behavior, an elastic time history analysis was conducted, in which SHW1 was inputted withthe same PGA as elasto-plastic analysis. The two results of roof displacement response are comparedin Figure 20. It is shown that the elastic and elasto-plastic analysis results are nearly the same in thefirst 2s, during which the structure remains elastic. From 2–7s, there developed little differencebetween the two results, which indicates that damages have been generated in the structural members.After 7s, the two curves were separated, obvious damages were observed and the structure stiffnessbegan to degrade. The vibration frequency decreased, time corresponding to the peak value of elasto-plastic roof displacement response lagged behind to that of the elastic response and elasto-plasticdisplacement response decreased quickly after reaching the maximum.

5.5. Interstory drift

Results of interstory drift are shown in Figure 21. Sudden changes exist in the 20th and 31st setbackstory and the 46th belt truss story. The reason for these sudden changes may be attributed to thedecrease or increase of lateral stiffness in these stories. The belt truss improved the integrity of lateralforce-resisting system. Therefore, the lateral stiffness was greater than that of the adjacent stories. Themaximum interstory drift resulted and the corresponding stories are listed in Table 9. The maximum

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 4 8 12 16 20 24 28 32 36

Time(s)

Roo

f di

spla

cem

ent i

n X

dire

ctio

n(m

)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 4 8 12 16 20 24 28 32 36

Time(s)

Roo

f di

spla

cem

ent i

n Y

dire

ctio

n(m

)

(a) (b)

Figure 19. Elasto-plastic response of roof displacement: (a) in X direction; (b) in Y direction.


0

5

10

15

20

25

30

35

40

45

50

55

60

0 0.002 0.004 0.006 0.008 0.01 0.012

Inter-storey drift

Stor

ey

SHW1

El Centro

Pasadena

1/1000

5

10

15

20

25

30

35

40

45

50

55

60

0 0.002 0.004 0.006 0.008 0.01 0.012

Inter-storey drift

Stor

ey

SHW1

El Centro

Pasadena

1/100

(a) (b)

Figure 21. Interstory drift: (a) in X direction; (b) in Y direction.

Table 9. Maximum interstory drift results.


Principal directions X Y X Y X YMaximum interstory drift 1/313 1/210 1/145 1/392 1/103 1/130Story where maximum value developed F47 F31+1 F47 F42 F34 F211Story 31+ is a mezzanine between the 31st and 32nd story.

-2-1.5

-1-0.5

00.5

11.5

2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Time(s)

Roo

f di

spla

cem

ent i

n X

dire

ctio

n(m

)

-2-1.5

-1-0.5

00.5

11.5

2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Time(s)

Roo

f di

spla

cem

ent i

n Y

dire

ctio

n(m

)

(a) (b)

Figure 20. Comparison of elasto-plastic and elastic responses of roof displacement under SHW1 withthe same peak value: (a) in X direction; (b) in Y direction.


interstory drift when subjected to rare earthquake can meet the requirement of TSCSTB of no greaterthan 1/100 for frame–core wall structure.

5.6. Damage results of core wall

Considering the structural response when SHW1 was inputted is more significant than that of the othertwo; responses generated by SHW1 were taken for example to illustrate in detail the damagedevelopment in the core wall in the course of ground vibration.



When ground motion was inputted along the X direction, the structure was elastic in the first 2s.From 4s on, plastic deformation began to occur in the coupling beams of stories adjacent to the 13thfloor where a setback exists in the core wall and a slight damage develops in the wall of these stories.When time came to 6.5s, mild damage came out in the walls above the bottom strengthening portion(specified by CCSDB, is a height range or several stories at the bottom of walls for wall structure; forthis building, it ranges from the first to the fifth story) of the core wall, and the coupling beams alongthe X direction began to yield. During this period, damages in other places extended quickly. At 7.5s,the walls of bottom strengthening portion were damaged, and the compressive damage variableexceeded 0.3, which means that the elastic modulus of concrete was reduced by 30%. Then, damagedeveloped in walls in the X direction adjacent to the 31st setback story and spread quickly soonafterwards. After 10s, the damages accumulated, and the compressive damage variable of couplingbeams and walls in and adjacent to the bottom strengthening portion reached 0.9. Figure 22 presentsthe compressive damage variable in different times.When ground motion was inputted along the Y direction, the structure remained elastic in the first 2s.

From 2–4s, coupling beams in and adjacent to the 13th setback story yielded first, and plasticdeformation began to develop. From 4–6s, slight damages occurred in the walls of the 12th to 14th story.From 6.5s on, walls in bottom strengthening portion began to develop mild damage. Until 9s, allcoupling beams under the 31st story yielded, and plastic deformation spread to the lateral wallsconnected to the coupling beam. From 10s on, coupling beams in the Y direction above the 31st setbackstory yielded one after another also. In the end, the compressive damage variable of the coupling beamsand walls in and adjacent to the bottom strengthening portion reached 0.9. Figure 23 shows thecompressive damage variable in different times.In conclusion, damages focus on the coupling beams and walls in and adjacent to the bottom

strengthening portion and walls in stories adjacent to setbacks. Since coupling beams serve as the firstseismic defense line, they should yield and dissipate seismic energy prior to the other structuralmembers when attacked by earthquake. At the bottom strengthening portion of the core wall, arelatively great number of steel-reinforced confining boundary members are configured according toCCSDB, compared with the neighboring sixth story. On the other hand, the thickness of peripheralwalls changes in the sixth story. Therefore, considerable stress concentrates in the sixth to the seventhstory, which in turn develops great plastic deformation in these places and extends to the story aboveand below. It is suggested that a transfer story should be placed above the bottom strengtheningportion of the core wall to keep the gradual alteration of lateral stiffness and consequently decrease thestress concentration effect. Besides, damage concentrates in stories adjacent to setbacks where lateral

Figure 22. Compressive damage development in core wall at 4s, 7.5s and 36s when SHW1 isinputted in X direction.


Figure 23. Compressive damage development in core wall at 4s, 9s and 36s when SHW1 is inputtedin Y direction.


stiffness changes too. Measures should be taken to improve the seismic performance of setbackstories.As specified in CCSDB, the strengthening portion at the bottom and its adjacent upper one story

shall be erected with confining boundary elements for wall structures, whereas ordinary boundaryelements shall be erected at the other portion of the wall. Usually, the former is larger in size andhigher in strength than the latter. In this building, confining boundary elements were located in the firstsix stories. For the steel of boundary members in the core wall, plastic strain occurred in the 13th storyfirst, and then, the steel in the sixth floor yielded too. Eventually, the plastic strain concentrated in thefew members of the 13th and sixth story whereas the rest remained elastic. Figure 24 shows the plasticstrain developed in the steel of boundary members.

5.7. Responses of frame

Inclined columns, members in the belt truss and diagonal braces in the 31st and 56th story behavedelastically in the course of vibration. No obvious damage was observed in the peripheral framestructure. The maximum stress occurred in the 31st setback story in shaped steel in columns(Figure 25). Concrete in the two ends of a few beams yielded, and the whole SRC frame has sufficientearthquake-resisting capacity left.

6. CONCLUSIONS AND SUGGESTIONS

In this paper, seismic behavior under rare earthquake of a super-tall building with setbacks in elevationwas studied through nonlinear dynamic time history analysis. On the basis of the analytical results, thefollowing conclusions can be drawn:

• When subjected to rare earthquake action, the target building develops damage mainly in the corewall, whereas a majority of the members in the peripheral frame remain elastic. The plasticdeformation capacity of this complex building can meet the requirement of CCSDB (GB 50011-2001), and the seismic protection objective of no collapse under rare earthquake can be reached.

• For the SRC frame–RC core wall structural system, the RC core wall serves as the first seismicdefense line and the main lateral force-resisting member and shows considerable seismic capacity


(a) (b)

Figure 25. Stress in steel of columns when SHW1 is inputted: (a) in X direction; (b) in Y direction.

(a) (b)

Figure 24. Plastic strain in steel of boundary members when SHW1 is inputted: (a) in X direction;(b) in Y direction.


and ductility when subjected to rare earthquake action. Coupling beams could yield and dissipateseismic energy prior to the core wall, which realizes a favorable energy dissipation mechanism.

• For a structure with setbacks, sudden change of lateral stiffness caused by the termination orreduction of vertical members at setback level has a great effect on the structural seismic behavior.Damages concentrate in members within and adjacent to the setback story. Therefore, a transferstory is suggested to be placed above or below the setback. More specifically, the seismic details of



members in the several stories above and below the setback should be increased. For asymmetricsetback structures, since responses of peripheral columns in the setback story are likely to increasedramatically due to the torsion effect of structure, details of seismic design of peripheral columnsshould be improved.

• As specified in CCSDB (GB 50011-2001), the strengthening portion at bottom and its adjacentupper one story shall be configured with confining boundary elements for wall structures, whereasordinary boundary elements shall be configured at the other portion of the wall. In this study, stressconcentration is observed at the interface story where confining boundary elements change toordinary boundary elements. It is suggested that boundary elements should be reduced graduallystory by story.

ACKNOWLEDGEMENTS

The authors are grateful for the partial financial support from Kwang-Hua Fund for College of CivilEngineering, Tongji University, National Natural Science Foundation of China (grant no. 90815029,51078274 and 51021140006) and the Beijing Science & Technology Program (grant no.D09050600370000). The authors wish also to thank Doctor Hu Qi who provided the user materialsubroutine program and structural engineer Jinsheng Zeng of China Architectural Design & ResearchGroup who provided great help in using the ABAQUS.

REFERENCES

ABAQUS. 2009. ABAQUS Theory Manual and User' Manual, version 6.9. Dassault Systèmes Simulia Corp.: Providence,RI, USA.

Aranda GR. 1984. Ductility demands for R/C frames irregular in elevation. Proceedings of the 8th world conference onEarthquake Engineering, San Francisco, USA 4: 559–566.

Berahman F. 2010. Performance-based seismic evaluation of the Icon Hotel in Dubai United Arab Emirates. The StructuralDesign of Tall and Special Buildings. Published online: 7 Dec 2010. DOI: 10.1002/tal.688

Epackachi S, Mirghaderi R, Esmaili O et al. 2010. Seismic evaluation of a 56-story residential reinforced concrete high-risebuilding based on nonlinear dynamic time history analysis. The Structural Design of Tall and Special Buildings. Publishedonline: 8 Mar 2010. DOI: 10.1002/tal.586

Humar JL, Wright EW. 1977. Earthquake response of steel-framed multistory buildings with set-backs. Earthquake Engineeringand Structural Dynamics 5(1): 15–39.

Khoury W, Rutenberg A, Levy R. 2005. On the seismic response of asymmetric setback perimeter-frame structures.Proceedings of the 4th European workshop on the seismic behavior of irregular and complex structures, Thessaloniki,August 2005.

Krawinkler H. 2006. Importance of good nonlinear analysis. The Structural Design of Tall and Special Buildings 15: 515–531.DOI: 10.1002/tal.379

Lee J, Fenves GL. 1998. Plastic-damage model for cyclic loading of concrete structure. Journal of Engineering MechanicsASCE 124: 892–900

Lew M, Naeim F, Carpenter LD, Youssef NF et al. 2010. The significance of the 27 February 2010 offshore Maule, Chileearthquake. The Structural Design of Tall and Special Buildings 19: 826–837. DOI: 10.1002/tal.668

Lu XL, Zhou Y, Lu WS. 2007. Shaking table model test and numerical analysis of a complex high-rise building. The StructuralDesign of Tall and Special Buildings 16: 131–164. DOI: 10.1002/tal.302

Lubliner J, Oliver J, Oller S, Oñate E. 1989. A plastic-damage model for concrete. International Journal of Solids andStructures 25(3): 299–326.

Mander JB, Priestly MJN, Park R. 1988a. Theoretical stress-strain model for confined concrete. Journal of StructuralEngineering ASCE 114: 1804–1826.

Mander JB, Priestly MJN, Park R. 1988b. Observed stress-strain behavior of confined concrete. Journal of StructuralEngineering ASCE 114: 1827–1849.

Ministry of Construction of the People's Republic of China. 2001. Code for Seismic Design of Buildings (GB 50011-2001).China Architecture and Building Press: Beijing, China.

Ministry of Construction of the People's Republic of China. 2002. Technical Specification for Concrete Structures of TallBuilding (JGJ 3-2002). China Architecture and Building Press: Beijing, China (in Chinese).

Shanghai Government Construction and Management Commission. 2003. Code for Seismic Design of Buildings (DGJ 08-9-2003).Shanghai Standardization Office: Shanghai, China (in Chinese).

Yahyai M, Rezayibana B, Daryan AS. 2009. Nonlinear seismic response of Milad Tower using finite element model. TheStructural Design of Tall and Special Buildings 18: 877–890. DOI: 10.1002/tal.468

Yang JH, Chen Y, Jiang HJ, Lu XL. 2010. Shaking table tests on China pavilion for Expo 2010 Shanghai China. The StructuralDesign of Tall and Special Buildings. Published online: 11 Mar 2010. DOI: 10.1002/tal.591



AUTHORS’ BIOGRAPHIES

XILIN LU born in 1955, received his doctoral degree from Tongji University in 1984, and nowworking as a professor at State Key Laboratory of Disaster Reduction in Civil Engineering, TongjiUniversity, Shanghai, China. His research focuses on seismic performance of tall and specialbuildings, performance-based seismic design method, nonlinear analysis of reinforced concretestructure, retrofitting design of building structures. He has authored 10 books in the field of seismicdesign theory and application and published over 280 journal papers, in which over 140 were cited bySCI or EI.

NINGFEN SU born in 1981, is pursuing her doctoral degree in Tongji University.

YING ZHOU born in 1978, is working as an associate professor at State Key Laboratory of DisasterReduction in Civil Engineering, Tongji University, Shanghai, China. She received her doctoral degreefrom Tongji University in 2005 and worked as a visiting scholar at University of California atBerkeley, USA from January 2010 to January 2011. Her research interests lie in seismic performanceof tall and special buildings, structural passive control of buildings, earthquake resilient buildingdesign, and structural dynamic testing technology.


Nonlinear time history analysis of a super-tall building...

Documents

Transcript of Nonlinear time history analysis of a super-tall building...