CASE STUDY OF A 40-STOREY BUCKLING … · CASE STUDY OF A 40-STOREY BUCKLING-RESTRAINED BRACED...

CASE STUDY OF A 40-STOREY BUCKLING-RESTRAINED BRACED FRAME BUILDING LOCATED IN LOS ANGELES

ANINDYA DUTTA* AND RONALD O. HAMBURGERSimpson Gumpertz & Heger, San Francisco, California, USA

SUMMARY

Simpson Gumpertz & Heger has prepared two prototypical designs for a 40-storey buckling-restrained braced steel-framed offi ce building located at a generic site in Los Angeles, CA. One of these designs conforms in all respects, except height limits with the design criteria contained in the 2007 California Building Code and ASCE 7.05 Standard for Minimum Design Loads for Buildings and Other Structures. The second design has been con-ducted using a performance-based approach generally based on the criteria contained in guidelines published by the Los Angeles Tall Buildings Council. The performance-based design incorporates fewer bays of bracing and lighter members than the code-based design, but is intended to provide performance at least equivalent to that anticipated for code-designed buildings. The purpose of this work was to permit study of the performance capa-bility of buildings designed to alternative criteria. This work was performed in support and under funding provided by the Pacifi c Earthquake Engineering Research Center’s Tall Buildings Initiative. Copyright © 2009 John Wiley & Sons, Ltd.

1. OBJECTIVE AND SCOPE OF WORK

Simpson Gumpertz & Heger, Inc. developed two alternative designs of a 40-storey steel building on behalf of the Pacifi c Earthquake Engineering Research Center (PEER) under its Tall Buildings Initia-tive (TBI). The objective of the TBI is to develop recommended performance-based design criteria for tall buildings as an alternative to the criteria contained in present building codes and standards. These alternative performance-based criteria are intended to provide performance that is at least equivalent to that intended for buildings designed in conformance with the code. The buildings pre-sented in this paper, together with designs using other structural systems developed by other designers, will be used by PEER to assess the cost and performance capability of buildings designed using alternative design approaches and criteria. This information will guide the development of the PEER recommendations.

We developed the designs to a schematic level. We sized the gravity load system, including fl oors, systems and columns considering blanket superimposed and live loads, but neglecting miscellaneous openings, cladding supports and similar information that typically becomes available later in the design process. Seismic analysis, including linear response spectrum analysis for the code-based design and nonlinear response history analysis for the performance-based design, was performed, and members of the seismic force-resisting system were proportioned as required to meet the respective criteria. We designed the foundations to a suffi cient level to determine mat thickness, but did not determine rein-forcing. Detailing of the structure was not performed.

Copyright © 2009 John Wiley & Sons, Ltd.

* Correspondence to: Anindya Dutta, Simpson Gumpertz & Herger, The Landmark at One Market, Suite 600, San Francisco, CA94105. E-mail: [email protected]

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 19, 77–93 (2010)Published online 30 October 2009 in Wiley Interscience (www.interscience.wiley.com). DOI: 10.1002/tal.543

78 A. DUTTA AND R. O. HAMBURGER

Copyright © 2009 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 19, 77–93 (2010) DOI: 10.1002/tal

In parallel with our work, two other fi rms performed similar designs of buildings using reinforced concrete structural systems. All buildings were assumed to be located on the same generic site in downtown Los Angeles. PEER provided site criteria for us in our design including site class, permis-sible bearing pressures, spectral response ordinates and ground motion acceleration histories.

Our scope of work included the following:

(1) Meet with representatives of PEER and other design consultants engaged in the TBI project to develop the general criteria for the designs.

(2) Develop a design, to a schematic level, for an essentially code-conforming steel-framed building.

(3) Develop a design, to a schematic level, for a performance-based steel-framed building, of similar height and footprint, using the procedures contained in design recommendations prepared by the Los Angeles Tall Buildings Council.

(4) Prepare schematic-level drawings documenting the design.

2. BUILDING DESCRIPTION

Both designs have typical above-grade fl oors comprised of 6 ¼ in. lightweight concrete fi ll on metal deck supported by composite steel framing with a foot print of 170 by 107 ft. Both designs have four basement levels with a foot print of 227 by 220 ft. Both structures have lateral force-resisting systems comprised of buckling-restrained braced frames without backup moment frames.

The site class was assumed as class C. Spectral response ordinates were: Ss = 2·15 and S1 = 0·72. For the performance-based design, we used a suite of seven acceleration histories provided by PEER.

3. CODE-BASED DESIGN

3.1 Purpose

This section provides a brief overview of the code-based design. As discussed earlier, we used the 2007 California Building Code to perform this design.

3.2 Design description

This design was conducted in conformance with all the prescriptive provisions of the 2007 California Building Code and its referenced standards, except for the limitation on the building height. The California Building Code requires that buildings in excess of 160 ft and located on the site selected for this building incorporate a special moment-resisting frame capable of resisting at least 25% of the specifi ed design seismic forces. This design did not incorporate such a frame. Figure 1 shows building plan views at various levels, and salient features of this design are described further below.

3.3 Gravity analysis and design

We designed the building’s vertical load-resisting system using gravity loads that include a combina-tion of structure self-weight and additional superimposed loads. The design criteria document provided to us by PEER specifi ed the superimposed loads at various fl oors shown in Table 1. We combined the element self-weights with the superimposed loading from this table, and performed a gravity-load design using the RAM Structural System software, version 12.1.

ARCHETYPICAL DESIGNS FOR A 40-STOREY BRB 79


Figure 1. Plan view of the building at various fl oors



3.4 Lateral analysis

Following design of the vertical load-carrying elements, we performed a lateral analysis of the build-ing. We considered both wind and seismic forces, and designed each element for the most severe requirements. A brief description of the wind and seismic design is given below.

3.4.1 Wind analysisWe used ASCE 7-05, method 2 to calculate the wind pressures. Table 2 lists the various parameters used. We considered the four cases depicted in fi gures 6–9 of ASCE 7-05. Each of these cases includes the direct wind force in one of four orthogonal directions either alone or in combination with storey torsional moment caused by the eccentric application of this load. We calculated the gust effect factor (Gf) following section 6.5.8.2 of ASCE 7-05 for fl exible or dynamically sensitive structures with 1% assumed damping.

We calculated wind base shears of 1436 and 2629 kip, respectively, along the two orthogonal directions.

3.4.2 Seismic analysisWe used linear response spectrum analysis to calculate seismic forces and displacements. Per ASCE 7-05, Cl 12.9.4, we scaled the forces to 85% of the base shear obtained from the equivalent lateral force procedure of Cl 12.8. Table 3 lists the various parameters that we used for the seismic design.

Table 1. Gravity loading criteria

Description/Location Superimposed dead Live load Reducability

Roof 28 psf 25 psf YesMechanical, electrical at roof Total of 100 kip – –Residential including balconies 28 psf 40 psf YesCorridors, lobbies and stairs 28 psf 100 psf NoRetail 110 psf 100 psf NoParking garage, ramp 3 psf 40 psf1 YesConstruction loading 3 psf 30 psf NoCladding 15 psf – –

PEER document showed 50 psf. SGH considered 40 psf in keeping with ASCE 7-05.

Table 2. Wind design criteria

Parameter Value

Basic wind speed, 3 s gust (V) 85 mphBasic wind speed, 3 s gust (V), for serviceability wind demands based on a 10-year mean

recurrence interval67 mph

Exposure BOccupancy category IIImportance factor (Iw) 1·0Topographic factor (Kzt) 1·0Exposure classifi cation EnclosedInternal pressure coeffi cient (GCpi) ±0·18Mean roof height (h) 544 ft, 6 in.Wind base shear along two orthogonal directions 1436 and 2629 kip



We performed the lateral analysis using ETABS, version 9.5.0. We used the 5% damped, accel-eration response spectrum shown in Figure 2. We included 120 modes to obtain participation of at least 90% of the structure’s mass. We scaled the results of the response spectrum analysis such that the base shear immediately above the ground fl oor matched 85% of the static base shear from the equivalent static force analysis. Note that for levels below the ground fl oor, the mass of the perimeter walls is automatically calculated by the program.

The 2007 California Building Code requires calculation of the redundancy factor (ρ) for seismic design. In accordance with ASCE 7-05 section 12.3.4.2, buildings qualify for a value of ρ = 1 provided that the removal of an individual brace or connection will not result in more than a 33% reduction in storey strength, nor will the resulting system have an extreme torsional irregularity. Extreme torsional irregularity is defi ned to exist when the maximum storey drift computed including accidental torsion, at one end of the structure transverse to an axis, is more than 1·4 times the average storey drifts at the two ends of the structure.

Table 3. Seismic design parameters

Parameter Value

Building latitude/longitude Undefi nedOccupancy category IIImportance factor (Ie) 1·0Spectral response coeffi cients SDS = 1·145; SD1 = 0·52Seismic design category DLateral system Buckling-restrained braced frames, non-moment-resisting

beam column connectionsResponse modifi cation factor (R) 7Defl ection amplifi cation factor (Cd) 5·5System overstrength factor (Ω0) 2·0Building period (T) using Cl. 12.8.2 3·16 sSeismic response coeffi cient Cs (Eq. 12.8-1) 0·051 W (governed by Cs-min from equation 12.8-5)Scaled spectral base shear 3504 kip (85% of static base shear)Analysis procedure Modal response spectral analysis

Actual period from dynamic model: TY = 5·05 s; TX = 3·62 s.

0

0.4

0.8

1.2

1.6

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Sp

ectr

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ccel

erat

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, Sa

(g)

Period (sec)

Figure 2. Response spectrum for code analysis



In order to calculate the redundancy factor for seismic forces acting in the north–south direction, we removed a brace from line 2 along the full height of the building. The code would actually permit this to be done one storey at a time; however, recognizing that we were being conservative, we removed the brace from all stories simultaneously, to reduce analysis effort. We then subjected the building to the static lateral forces along with the 5% accidental torsion. We term these forces as EQYPL (with the accidental eccentricity towards the positive right) and EQYMN (with the accidental eccentricity towards the negative left). Since the building has at least six bays of braced frame in each principal direction, loss of a brace or connection will never reduce the capacity by 33%. We found that for the north–south direction, the largest ratio of maximum storey drift over the average drift over the height of the building was 1·39 at storey 13. Since this is less than 1·4, we concluded that the redundancy factor in the north–south direction is 1. Figure 3(a) shows the elevation at line 2 after the removal of the brace.

We performed a similar analysis in the X (east–west direction). In this analysis, we removed a single brace from line D and subjected the building to static forces EQXPL (with the accidental eccentricity towards the positive top) and EQXMN (with the accidental eccentricity towards the negative bottom). Figure 3(b) shows the elevation of the frame along line D with the brace removed. We then calculated the ratio of maximum to average drifts, and obtained ratios ranging from 1·468 to 1·408 from the roof to storey 36. However, section 12.3.4.2 stipulates that this ratio should strictly be studied for a fl oor resisting more than 33% of the base shear which is numerically equal to 1156 kip. This only happens below storey 35. In addition, as noted previously, our simultaneous removal of a brace at all levels is conservative. Since the ratio of maximum to average drift is only marginally greater than 1·4 at two stories with a maximum value of 1·408 at storey 34 (D/C of 1·008). We declared that this design met the requirements of ASCE 7-05 for a redundancy coeffi cient, ρ = 1.

3.5 Lateral force-resisting member design

3.5.1 Buckling-restrained brace (BRB) designWe designed the BRBs for the worst of the wind and seismic loads. In almost all cases, seismic loads governed the design. Brace capacity in tension and compression was taken as φAsFy, with φ = 0·9 and Fy = 38 ksi.

3.5.2 Braced frame column designAISC’s Seismic Provisions for Structural Steel Buildings (ANSI/AISC 341-05) require columns in buckling-restrained braced frames to be checked for:

(1) Axial load and moment interaction for code level forces(2) Axial load only corresponding to the sum of the vertical component of the strength of all BRBs

that frame into the column along with tributary gravity loading

We checked the columns for both of the above criteria, and found that the latter generally produced larger D/C ratios. Since the current confi guration uses columns that form part of lateral framing in two orthogonal directions, we used the 100%–30% combination to calculate the maximum compres-sion from the braces. We established the maximum compression forces from the brace as RyωβAsFy, where Ry = 1·1, ω = 1·25 and β = 1·1.

We used built-up square box columns infi lled with high strength ( f ′c = 10 ksi) concrete to resist the large compression force demands. The plate thicknesses of the box columns ranged from 1·5 in. at upper stories to 3 in. at lower ones. The plan dimension of the box columns ranged from 18 to 57 in. We calculated the strength, axial area and stiffness of infi ll columns using the provisions of chapter I



(a) (b)

Figure 3. Elevation of frame along lines 2 and D following removal of a brace. (a) Line 2 and (b) line D

(‘Design of Composite Members’) of the 13th edition LRFD Steel Code (ANSI/AISC 360-05). We included this enhancement of axial area and stiffness over the bare steel section properties in the ETABS analysis model as well. We did this by defi ning a steel box section in ETABS and then using the property modifi er to account for the infi ll concrete.



3.5.3 Braced-frame beam designWe designed the braced-frame beams for the horizontal component of the brace compression along with the unbalanced upward component of the BRB given by RyωAsFy(β-1)sinα, where α is the brace angle. Since BRBs are always stronger in compression than in tension, this moment is opposite in direction to the gravity moment.

3.5.4 Storey drifts for code designWe calculated inter-storey drifts using response spectrum analysis. ASCE 7-05 stipulates the use of a response spectrum that is reduced by the response reduction factor R. It also states that the drifts obtained from this reduced spectral analysis be amplifi ed by Cd to yield design storey drifts. Table 4 shows the design inter-storey drifts (amplifi ed by Cd) obtained at various levels both for the X and Y directions. As can be seen, the maximum storey drifts are less than the permissible value of 0·02 at all levels.

4. PERFORMANCE-BASED DESIGN

We based the seismic design for this alternate on the seismic design criteria (dated 29 April 2008) published by the Los Angeles Tall Buildings Structural Design Council (LATBSDC 2008). Since this design was not required to meet all of the prescriptive criteria contained in the building code, we were able to reduce the size and number of bays of the buckling-restrained frames. Specifi cally, along lines 2 and 7, we omitted two bays of bracing below level 10. Table 5 lists the performance objectives we followed for this design.

Table 4. Storey drifts for code design

Storey Y drifts X drifts Storey Y drifts X drifts

40 0·013 0·005 18 0·011 0·00639 0·014 0·006 17 0·011 0·00638 0·014 0·006 16 0·010 0·00637 0·014 0·006 15 0·010 0·00636 0·014 0·006 14 0·010 0·00535 0·014 0·006 13 0·009 0·00534 0·014 0·006 12 0·008 0·00533 0·014 0·006 11 0·007 0·00532 0·014 0·006 10 0·004 0·00431 0·014 0·006 9 0·004 0·00430 0·014 0·006 8 0·004 0·00429 0·014 0·006 7 0·004 0·00428 0·014 0·006 6 0·004 0·00427 0·013 0·006 5 0·004 0·00426 0·013 0·006 4 0·003 0·00425 0·013 0·006 3 0·003 0·00424 0·013 0·006 2 0·003 0·00323 0·012 0·006 1 0·002 0·00222 0·012 0·00621 0·012 0·00620 0·012 0·00619 0·011 0·006



4.1 Service level earthquake evaluation

We used response spectrum analysis for this evaluation. We used the response spectrum shown in Figure 4, which was provided by PEER. The damping level was set at 2·5%. We neglected accidental torsion. Inter-storey drifts obtained for the service level earthquake are shown in Table 6. As can be seen, the drifts are less than 0·5% at all levels. We also evaluated the building for the same wind forces that we used for the code-based design described in the previous section. We found that wind always governed the required brace strength as compared with service level earthquake demands.

4.2 Maximum considered earthquake evaluation

As required by the LATBSDC document, we performed a nonlinear response history analysis of the building for maximum considered earthquake shaking as defi ned by the building code. We used seven pairs of acceleration histories provided to us by PEER for this purpose. We used CSI Perform, version 4.0.1 with a constant modal damping level of 2·5% and 0·1% Rayleigh damping. We explicitly mod-elled nonlinearities in the BRBs. We modelled columns and beams as elastic elements, and later verifi ed that demands on these elements remained within their elastic capacities. Details of the element modelling are discussed below.

4.2.1 Modelling of BRBsWe modelled the BRBs using the perform BRB inelastic element in series with an elastic spring that models the end attachment of the braces. The BRB backbone curves were modelled as shown in

Table 5. Seismic performance objectives

Level of earthquake Earthquake performance objectives

Frequent/Service: 25-year return period, 2·5% damping

Serviceability: Essentially elastic performance with minor yielding of brbf-s. Drift limited to 0·5%

Maximum considered earthquake (MCE): As defi ned by ASCE 7-05, section 21.2, 2·5% damping

Collapse prevention: Extensive structural damage, repairs are required and may not be economically feasible. Drift limited to 3%

0

0.1

0.2

0.3

0.4

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Sp

ectr

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ccel

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, Sa

(g)

Period (sec)

Figure 4. Response spectrum for serviceability analysis



Table 6. Storey drifts for service level earthquake

Storey Y drifts X drifts Storey Y drifts X drifts

40 0·0031 0·0014 18 0·002 0·001739 0·0032 0·0015 17 0·002 0·001738 0·0033 0·0016 16 0·0019 0·001737 0·0033 0·0017 15 0·0019 0·001636 0·0034 0·0017 14 0·0018 0·001635 0·0033 0·0018 13 0·0018 0·001634 0·0033 0·0018 12 0·0017 0·001633 0·0033 0·0018 11 0·0017 0·001632 0·0032 0·0018 10 0·0016 0·001731 0·0031 0·0018 9 0·0016 0·001730 0·0031 0·0018 8 0·0016 0·001729 0·0029 0·0018 7 0·0015 0·001728 0·0028 0·0018 6 0·0015 0·001727 0·0027 0·0018 5 0·0015 0·001726 0·0026 0·0018 4 0·0014 0·001725 0·0026 0·0018 3 0·0014 0·001624 0·0025 0·0018 2 0·0012 0·001423 0·0024 0·0018 1 0·0008 0·00122 0·0023 0·001821 0·0022 0·001720 0·0021 0·001719 0·0021 0·0017

Figure 5 with Ry = 1·1, ω = 1·25 and β = 1·1. Figure 6 shows a screen shot of the Perform input form for the BRB defi nition. Note that the initial stiffness (K0) of the BRB is based on AsE/L with L equal to 70% of the actual centre-to-centre length of the brace. The remaining 30% of the length is modelled as an essentially rigid element.

4.2.2 Modelling of the columns and beamsWe modelled the columns using the non prismatic steel sections in Perform. The moment of inertia input in the form was adjusted to account for the additional stiffening due to the presence of the infi ll concrete. The axial load and moment strength for the various columns were defi ned in Perform using

RyFyAs

ωRyFyAs

Δy 10Δy 20Δy

Ko

1.25%Ko

Δy10Δy20Δy

RyFyAs

βωRyFyAs

Tension

Compression

Figure 5. Presumed backbone curve for buckling-restrained braces



RyFyAs

70% Actual

1.25% Ko

Figure 6. BRBF property defi nition in Perform

Figure 7. Column strength defi nition in Perform



the same process as for the elastic analysis. We assumed nominal strengths for the columns without any strength reduction or φ factors. Figure 7 shows the column axial load a representative fl exural strength defi nition form in Perform.

The compound column element associated with the geometric location of the column utilizes the cross-sectional information and assembles the column element as an elastic element. We have ensured that the column element always stays elastic during the analysis by monitoring the axial fl exure inter-action ratios so that they are always less than 1.

Beams are modelled in an identical fashion as the columns, except that standard W sections are used. Similar to the columns, the beams are also modelled as elastic elements.

4.2.3 Modelling of the diaphragms at upper, ground and basement levelsWe modelled rigid diaphragms at all elevated fl oors. However, we modelled diaphragms at the ground and all basement fl oors with elastic shell elements using 30% of the gross cross-section properties. We considered an effective thickness comprising the total thickness of the topping plus half the rib thickness. Thus, the ground fl oor was modelled as 10·5-in. thick slab as it represents a 9-in. topping and 1·5-in. half rib height. We followed the same approach for the basement slabs except that the modulus of elasticity also included the λ modifi er corresponding to lightweight concrete.

-5

0

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40

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Sto

ry

Peak Interstory Drift (%)

Peak Interstory Drift in Y Direction

Average Denali Ps Landers Yermo LP Gilroy LP Saratoga Nridge Sylmar CS Nridge Sylmar Hosp Parachute

δy

Figure 8. Peak inter-storey drifts in the Y direction



4.2.4 Modelling of perimeter wallsWe modelled the perimeter shear walls as elastic wall elements with cracked stiffness equalling 50% of the gross stiffness. The elastic shear modulus was considered to be 40% of the gross elastic (Young’s) modulus per ASCE 41, supplement 1.

4.2.5 Selected results from nonlinear analysis4.2.5.1 Storey driftsFigures 8 and 9 present the storey drift profi led obtained from the analyses. Figure 8 shows the drift in the Y direction and Figure 9 the X direction. The maximum drift in the Y direction is around 1·97%, while the maximum in the X direction is at 2·25%. As can be observed from the fi gures, the drifts are less than the permissible value of 3% in both directions, and the mean peak drifts are generally on the order of 1·25% or less.

4.2.5.2 Column axial fl exure interaction ratioSince the beam columns were modelled as elastic elements, we monitored the interaction ratios closely and ensured that they remain less than unity signifying elastic behaviour. We found that the maximum mean interaction ratio was 0·63. The absolute maximum from the seven analyses is 0·83, justifying our assumption regarding the elastic behaviour of the columns.

-5

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30

35

40

0.00 0.50 1.00 1.50 2.00 2.50

Sto

ry

Peak Interstory Drift (%)

Peak Interstory Drift in X Direction


δx

Figure 9. Peak inter-storey drifts in the X direction



Line 2 Line 3 Line 4 Line D

Figure 10. BRBF core strain DCRs along lines 2, 3, 4 and D



-5

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0 2500 5000 7500 10000 12500

Sto

ry

Accumulated Peak Story Shear (kips)

Accumulated Peak Story Shear in Steel Superstructure in Y Direction


Vy

Figure 11. Accumulated peak storey shear in steel superstructure in Y direction

4.2.5.3 BRB core strainWe also monitored strain in the BRB cores, and ensured that the mean strain is less than of 0·013 (10εy) obtained from the test results conducted at the University of Utah by Romero and Reavely. Figure 10 shows the BRB core strain for lines 2, 3, 4 and D, respectively. The results are presented as D/C ratio with the capacity being 0·013. The ratios are all less than unity, and most are substantially less than unity, implying acceptable performance. DCRs indicated in yellow in the fi gure indicate values in excess of 75% of the 0·013 strain limit.

4.2.6 Storey shearsWe also monitored storey shears over the building height. Figures 11 and 12 plot the storey shears in the Y direction and X direction, respectively. The effect of the stiff ground fl oor diaphragms is easily observable from the plots. We have proportioned the ground fl oor slab and the collectors so that it is capable of transferring this large reaction.

5. SUMMARY AND CONCLUSIONS

Simpson Gumpertz & Heger performed two alternative designs of a 40-storey building located at a hypothetical site in Los Angeles. Both buildings utilize buckling-retrained braced frames as the lateral



-5

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0 2000 4000 6000 8000 10000

Sto

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Accumulated Peak Story Shear (kips)

Accumulated Peak Story Shear in Steel Superstructure in X Direction


Vx

Figure 12. Accumulated peak storey shear in steel superstructure in X direction

system. The fi rst design strictly follows the provisions of the 2007 California Building Code except that it exceeds code limitations on the height for structures not having backup special moment frames. The columns and beams are designed using the relevant requirements of AISC 341.05 seismic provisions.

The second design uses the concepts of performance-based engineering and is based on the LATBSDC. A nonlinear time history analysis is performed on this design using maximum credible earthquake input to ensure a safe design.

Generally, the second design produced fewer bays of bracing, smaller sizes of the BRBs and columns. The main savings, however, is likely to be from the design of the foundation. The code design requires that the foundation be designed for the accumulated vertical component of the brace forces over the height of the building. This essentially implies exclusively fi rst-mode behaviour which does not occur in tall buildings. Using the actual demands from the time history analysis, we obtained forces that are smaller and hence more manageable than the code-required forces.

REFERENCES

(American Institute of Steel Construction). ANSI/AISC 341-05, 2005 Seismic Provisions for Structural Steel Buildings. AISC: American Institute of Steel Construction, Chicago, IL.



ANSI/AISC 360-05, 2005, Specifi cation for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL.

ASCE 2005. Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Reston, VA.

LATBSDC (Los Angeles Tall Buildings Structural Design Council). 2008. An Alternative Procedure for Seismic Analysis and Design of Tall Buildings Located in the Los Angeles Region. LATBSDC: Los Angeles, CA.

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