Lu11c-ev

8/13/2019 Lu11c-ev

1/22

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 260 m 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 classied as anirregular and complex structure. To investigate the seismic behavior of the structure under rare earthquakeaction, a renednite element model was developed by using ABAQUS (Dassault Systmes Simulia Corp.,

Providence, RI, USA). Nonlinear time history analyses were conducted using explicit integration method.The results show that the structural system has sufcient 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 novel

architectural styles, such as the wheel-shaped Icon Hotel in Dubai (Berahman, 2010) and the China

Pavilion for Expo 2010 Shanghai (Yang et al., 2010). However, irregularity and complexity of

structures are inevitable for these special buildings. This requires structural engineers to thoroughly

understand 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 by

the building material such as clay, stone or brick. The most graphic example of a setback technique is

the 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 uses

such 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. The

nonuniform vertical mass distribution caused by setback may have a signicant inuence on the

response 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]

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

Copyright# 2011 John Wiley & Sons, Ltd.

8/13/2019 Lu11c-ev

2/22

Consequently, the setback level may become a weak point and vulnerable when attacked by

earthquakes.

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 in

the vicinity of the irregularities. Aranda (1984) made a comparison of ductility demands between

setback and regular structures. He observed higher ductility demands for setback structures than for theregular ones and found this increase to be more pronounced in the portion above the setback. Khoury etal.

(2005) considered four nine-story asymmetric setback perimeter frame structures that differed from each

other in the location of the setback along the height. Nonlinear dynamic analyseswere performed, anda 3D

structural model was used under bidirectional ground motions. Results showed that higher vibration

modes have signicant inuence, particularly the torsional ones. Seismic codes make specications on

design of such vertical irregular structures as well. Nevertheless, setback structures have never been free

from earthquake damages. Figure 1 shows unrecoverable damage that occurred in a building with setback

in 27 February 2010 offshore Maule, Chile, earthquake (Lew etal., 2010). It is indicated that,in spite of the

studies 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 using

nite element method to get insights about the performance of complex buildings. Yahyai et al. (2009)

used nite element model analysis to study the nonlinear seismic response of Milad Tower. Epackachi

et al. (2010) conducted a seismic evaluation of a 56-story residential reinforced concrete building

based on nonlinear dynamic time history analysis ofnite element model. Krawinkler (2006) believes

that earthquake engineering is relying more and more on nonlinear analysis as a tool for evaluating

structural performance and nonlinear analysis will be a good trend.

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

X. LU, N. SU AND Y. ZHOU

Copyright# 2011 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. (2011)

DOI: 10.1002/tal

8/13/2019 Lu11c-ev

3/22

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 feasibility

of preliminary design and guarantee its safety and also to provide guidance and advice to engineers for

similar projects concerned. Three main parts are included. First, a rened nite element analysis

model 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 this

complex building via explicit integration numerical solution method. Finally, the nonlinear dynamicresponses including roof acceleration and displacement, interstory drift and damage of main lateral

force-resisting members are presented and discussed. Moreover, practical suggestions are proposed on

the 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 stories

above the ground including a 24-story hotel part, a 23-story ofce part and a four-story basement

underneath. It has a total architectural height of 260m, and the structural height is 244.8 m. Dimension

of 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 20thfloor

(c) The 21st to the 31stfloor (d)The 32ndto the 58thfloor

Figure 2. Typical plan layouts of each part.

NONLINEAR TIME HISTORY ANALYSIS OF A SUPER-TALL BUILDING


DOI: 10.1002/tal

8/13/2019 Lu11c-ev

4/22

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 walls

and 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 truss

is arranged in the 46th oor to serve as a strengthened story (Figure 4).

Figure 3. South elevation.

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

Members Story Elevation (m)

Dimensions (mm)

Flange wall Web wall

Wall 15 026.7 1000/1200 400/600621 26.794.9 800/1000 400/600

21+131 94.9141.9 600/800 400/600

31+58 141.9244.8 600 400Column 15 026.7 22002200; 20002000;

613 26.760.3 22002200; 20002000; 185018501420 60.390.7 20002000; 18001800; 185018502131 90.7141.9 16001600; 13501350

31+58 141.9244.8 10001500; 12001200

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



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

5/22

2.3. Setbacks

With the alteration of plan arrangement, two setbacks are formed in elevation in the 20th and 31st

story, 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 by

direct termination of bending resistance members and 50% reduction of oor size, leaving a large

setback in the core wall in the 31st story (Figure 6). The height of the tower structure above this

setback level is 101.9m, which is about 41.7% of the overall structural height. To guarantee that the

load from the upper structure transfers smoothly to the lower story, diagonal bracings (Figure 7) are

added between the SRC frame and the core wall in the story right below this setback, and the thickness

of slab in this story is increased. Newly added columns of the tower structure above the setback are

rooted 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 oor to the 20th oor(Figure 8b) and from the 20th oor to the 21st mezzanine oor (Figure 8c). The angles of the inclined

columns to the vertical direction are 11.5 and 13.2, respectively. Beams connected to these columns

are 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) (Ministry

of Construction of the People's Republic of China, 2001) and Technical Specication for Concrete

Structures of Tall Building (TSCSTB, JGJ3-2002) (Ministry of Construction of the People's Republic

of China, 2002), the height of this building exceeds the specied maximum height of 190m for SRC

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

Members Story

Reinforcement ratio (%)

Horizontal Vertical

Confining boundary elements

Horizontal Vertical

Wall 16 0.3 0.5 1.8 2.5728 0.3 0.5 1.8 2.0

2936 0.3 0.5 1.8 2.53758 0.3 0.5 1.8 2.0

Column 129 1.23058 1.5

Figure 4. Belt truss in the 46th story.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

6/22

frame and RC core wall system. Besides, the setback dimension in the 31st story is beyond the

elevation layout requirement of TSCSTB (Figure 9a). Therefore, this building is classied as a vertical

irregular one, and elasto-plastic time history analysis is required to investigate its seismic behavior

under rare earthquake (23% probability of exceedance in 50years) action.

3. FINITE ELEMENT MODEL

ABAQUS (version 6.9-1) was used to build nite element model and conduct nonlinear dynamic time

history analysis.

3.1. Element type selection

All members of the SRC frame including embedded boundary members in walls were modeled using

a

rst-order 3D Timoshenko beam element (B31), in which the transverse shear deformation wasallowed. The beam section was divided into an array of bers or section points, at which beam

element's response were calculated and outputted. For space beam element with rectangular prole, 25

section 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 to

calculate the stresses and strains independently at each section point. By default, ABAQUS uses ve

section points through the thickness of a homogeneous shell, which is sufcient for most nonlinear

design problems. Considering the complexity of the structure and the importance of this study, nine

were used herein.

Figure 5. Setbacks in elevation.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

7/22

The simulation of reinforcements can be achieved by two methods. One is to model each

reinforcement bar separately. In this way, reinforcement should be embedded into concrete elements

or through node coupling to make them work together with concrete. The other is to treat the rebar

layer as a smeared layer with a constant thickness equal to the area of each reinforcing bar divided by

the reinforcing bar spacing, which is preferred for dening reinforcement in wall or slab. Here, the

Figure 6. Setbacks in core wall.

Figure 7. Diagonal bracing.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

8/22

former one was used to model reinforcement in beams and columns, steel in columns and boundary

members in core wall, and the latter one was used to model reinforcement in wall and slab.

The coupling beams, which usually damage rst, are of great importance in dissipating energy

inputted by earthquake and thus inuence the ductility and seismic performance of the core wall. In

order to observe the development of damage in detail, S4R was used again to model the coupling

beam.

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 shell

element should be less than 2.5m. As far as running time is concerned, element should be better longer

than 1m. Finally, the nonlinear analysis model (Figure 10) is comprised of 88297 elements and 158

747 nodes in all.

3.2. Material constitutive models

The isotropic bilinear kinematics hardening model was used for reinforcement and steel, in which

Bauschinger effect was considered. During the cyclic loading, no degradation was developed. The

ratio of ultimate strength to the yield strength was 1.2 for reinforcement bar and 1.3 for steel. The

ultimate plastic strain corresponding to the ultimate stress was considered as 0.025. Check Table 3 for

details.

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 compressive

plasticity to represent the inelastic behavior of concrete (ABAQUS, 2009). The model made use of the

(a) (b) (c)

Figure 8. Inclined columns.

Figure 9. Requirement for elevation layout in Chinese code.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

9/22

yield function of Lublineret al. (1989), with the modications proposed by Lee and Fenves (1998) to

account for the different evolution of strength under tension and compression. It assumed

nonassociated potential plastic ow. The ow potential used for this model was the DruckerPrager

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>3550) 295 384 0.025 2.06E+5Q345(t>1635) 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



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

10/22

hyperbolic function. The response of concrete to uniaxial loading in tension and compression are

shown in Figure 11, wheredcand dtare the compressive and tensile damage variable respectively and

used 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 12

shows the mechanical response of concrete under cyclic loading (tensioncompressiontension),

where wc and wtare the compressive and tensile stiffness recovery factor respectively to control the

recovery 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 user material uses the uniaxial concrete constitutive model proposed by Manderetal. (1988a, 1988b),

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

Figure 12. Uniaxial load cycle (tensioncompressiontension) assuming wc=1 and wt=0.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

11/22

which takes into account the inuence of various types of connement by dening an effective lateral

conning stress.

4. NONLINEAR TIME HISTORY ANALYSIS

4.1. Input ground motions

It is specied in TSCSTB that no less than two strong earthquake records and a synthetic

accelerogram should be selected for elasto-plastic time history analysis. The duration should be no

shorter than 12s. Soil condition should be taken into account. According to the CCSDB, the site soil in

Shanghai is categorized as type IV, which is dened as soil whose soft layer thickness is more than 80

m, and average velocity of shear wave in the soil layer is not more than 140m/s. In consideration of

the factors mentioned above, two strong earthquake records (Table 5) and Shanghai synthetic

accelerogram SHW1 were selected. SHW1 is specied for the particular soil conditions of Shanghai

and can be found in the Shanghai Code of Seismic Design of Buildings (SCSDB, DGJ08-9-2003)

(Shanghai Government Construction and Management Commission, 2003). Figures 1315 show time

histories (normalized to 1g) and spectrum accelerations of selected accelerograms when damping ratio

is 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 basicacceleration of ground motion is 0.1 g, which means 10% probability of exceedance in 50years.

Since seismic behavior under rare earthquake action was investigated mainly in this paper, the

peak ground acceleration (PGA) of selected earthquake accelerograms were scaled to 0.2g, which

was specied in SCSDB to characterize the seismic risk of 2% probability of exceedance in 50

years in the seismic protection zone of 7. During the analysis, the two strong earthquake records

were inputted in two principal directions simultaneously (the NS record is inputted in the X

direction) with the PGA ratio of 1:0.85, whereas the synthetic accelerogram was inputted in one

direction.

4.2. Damping ratio

As specied by TSCSTB, a damping ratio of 0.04 for SRC frameRC core wall structural system was

adopted.

4.3. Numerical solver of the nonlinear equations of motion

The direct-integration dynamic procedure provided in ABAQUS/Standard uses the implicit

HilberHughesTaylor operator for integration of the equations of motion, whereas ABAQUS/

Explicit uses the central-difference operator. In an implicit dynamic analysis, the integration

operator matrix must be inverted, and a set of nonlinear equilibrium equations must be solved at

each time increment. In an explicit dynamic analysis, displacements and velocities are calculated

in 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 NS Imperial Valley18/5/1940

117 El Centro Array #9 7.1 12.99 0.349El CentroEW 0.215Pasadena NS Kern County

21/7/195280053 PasadenaCIT

Athenaeum7.36 125.81 0.053

Pasadena EW 0.045

PGA, peak ground acceleration.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

12/22

and stiffness matrices need not be formed and inverted, which means that each increment is

relatively inexpensive compared with the increments in an implicit integration scheme. The

analysis cost rises only linearly with problem size for explicit integration, whereas the cost of

solving the nonlinear equations associated with implicit integration rises more rapidly than

linearly with problem size. Therefore, explicit analysis method is attractive for very large

problems (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 and

service load has already acted on the structure, which serves as the initial state of nonlinear dynamic

analysis. So, a static analysis was performed before time history analysis to obtain the initial stress

state in structure members. According to the static analysis results, the structure totally weights 2764

660kN.

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 50 55

Time(s)

Acceleration(g)

(a)

-1

-0.5

0

0.5

1

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

Time(s)

Acceleration(g)

(b)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6SpectrumA

cceleration(g)

Target SpectrumEl Centro N-S

El Centro E-W

(c)

Period(s)

Figure 13. El Centro accelerogram: (a) time history of acceleration in NS direction; (b) time historyof acceleration in EW direction; (c) spectrum acceleration.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

13/22

5.1. Natural vibration characteristics

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

5.2. Base shear and moment

Results of maximum base shear and moment when subjected to different ground motions are listed in

Table 7. It is clear that a difference exists between structural responses to the three inputs, in which

responses under SHW1 are signicantly greater than that of the other two. This is true not only for the

maximum 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 may

explain this to some extent. From Figures 1316, we can see that the response spectrum of SHW1 is

the one that matches the target spectrum most in the period range interested, whereas that of El Centro

in two directions and Pasadena in EW direction are smaller than the target spectrum. The response

spectrum of Pasadena in NS direction exhibits a peak at about 1.6s larger than that of SHW1 but

turns smaller after 3s.

According to the CCSDB, design seismic action is determined by using seismic coefcient, which

is derived from acceleration response spectrum. For a long-period structure, lower spectrum value is

usually obtained and consequently leading to lower design seismic action. In order to guarantee the

safety of designed buildings, seismic shear factor is introduced. It is dened as the ratio of horizontal

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45

Time(s)

Acceleration(g)

(a)

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40 45

Time(s)

Acceleration(g)

(b)

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6

Period(s)

SpectrumA

cceleration(g)

Target SpectrumPasadena N-SPasadena E-W

(c)

Figure 14. Pasadena accelerogram: (a) time history of acceleration in NS direction; (b) time history

of acceleration in EW direction; (c) spectrum acceleration.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

14/22

seismic shear force to the representative value of gravity load of the structure and is used to prevent

the design seismic action from becoming too small. Usually, there is a minimum value for seismic

coefcient in seismic design code. As far as seismic protection intensity 7 is concerned, the factor

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40

Time(s)

Acceleration(g)

(a)

(b)

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

Figure 16. Displacement response spectrum of each accelerogram.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

15/22

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 factors

at ground oor 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 lists

the maximum responses of roof acceleration when different ground motions were inputted. The

acceleration amplication coefcient is the ratio of maximum roof acceleration response to the

inputted maximum ground acceleration. The results show that the whipping-lash effect is not very

signicant for this building.

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 Torsion

4 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 rst 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 Y Maximum base moment (10

8Nm) 3.848 6.694 4.743 4.045 9.914 12.780

Maximum base shear (105

kN) 2.089 2.662 2.526 2.043 3.343 3.489Seismic shear factor at ground oor 7.56% 9.63% 9.14% 7.39% 12.09% 12.62%



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

16/22

5.4. Roof displacement

Figure 19 shows the roof displacement response history of the structure. The maximum roof

displacement response, generated by SHW1, is 1.643m in the X direction and 1.576m in the Y

direction, respectively. The ratio of maximum roof displacement response to the height of the whole

structure is 1/149 and 1/155 in the Xand Ydirections. To gain a better understanding of the nonlinear

dynamic behavior, an elastic time history analysis was conducted, in which SHW1 was inputted with

the same PGA as elasto-plastic analysis. The two results of roof displacement response are compared

in Figure 20. It is shown that the elastic and elasto-plastic analysis results are nearly the same in the

rst 2 s, during which the structure remains elastic. From 27s, there developed little difference

between 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 stiffness

began 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-plastic

displacement 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 setback

story and the 46th belt truss story. The reason for these sudden changes may be attributed to the

decrease or increase of lateral stiffness in these stories. The belt truss improved the integrity of lateral

force-resisting system. Therefore, the lateral stiffness was greater than that of the adjacent stories. The

maximum interstory drift resulted and the corresponding stories are listed in Table 9. The maximum

-0.5

-0.25

0

0.25

0.5

0 6 12 18 24 30 36

Time (s)

Acceleration(g)

-0.5

-0.25

0

0.25

0.5

0 6 12 18 24 30 36

Time (s)

Acceleration(g)

(a) (b)

Figure 18. Roof acceleration response when SHW1 is inputted: (a) in Xdirection; (b) in Ydirection.

Table 8. Results of roof acceleration responses.


Principal direction X Y X Y X Y Maximum 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 amplication coefcient 2.10 1.78 2.77 1.56 2.12 2.22

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 4 8 12 16 20 24 28 32 36

Time(s)RoofdisplacementinX

direction(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)RoofdisplacementinY

direction(m)

(a) (b)

Figure 19. Elasto-plastic response of roof displacement: (a) in Xdirection; (b) in Ydirection.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

17/22

interstory drift when subjected to rare earthquake can meet the requirement of TSCSTB of no greater

than 1/100 for framecore wall structure.

5.6. Damage results of core wall

Considering the structural response when SHW1 was inputted is more signicant than that of the other

two; responses generated by SHW1 were taken for example to illustrate in detail the damage

development in the core wall in the course of ground vibration.

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

Storey

SHW1

El Centro

Pasadena

1/100

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

Storey

SHW1

El Centro

Pasadena

1/100

(a) (b)

Figure 21. Interstory drift: (a) in Xdirection; (b) in Ydirection.

Table 9. Maximum interstory drift results.


Principal directions X Y X Y X Y Maximum interstory drift 1/313 1/210 1/145 1/392 1/103 1/130Story where maximum value developed F47 F31+

1F47 F42 F34 F21

1

Story 31+ is a mezzanine between the 31st and 32nd story.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 1012141618202224262830323436

Time(s)

RoofdisplacementinX

direction(m)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 1012141618202224262830323436

Time(s)

RoofdisplacementinY

direction(m)

(a) (b)

Figure 20. Comparison of elasto-plastic and elastic responses of roof displacement under SHW1 with

the same peak value: (a) in Xdirection; (b) in Ydirection.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

18/22

When ground motion was inputted along the Xdirection, the structure was elastic in the rst 2s.

From 4s on, plastic deformation began to occur in the coupling beams of stories adjacent to the 13th

oor 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

(specied by CCSDB, is a height range or several stories at the bottom of walls for wall structure; for

this building, it ranges from the rst to the fth story) of the core wall, and the coupling beams along

theXdirection 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 variable

exceeded 0.3, which means that the elastic modulus of concrete was reduced by 30%. Then, damage

developed in walls in the X direction adjacent to the 31st setback story and spread quickly soon

afterwards. After 10s, the damages accumulated, and the compressive damage variable of coupling

beams and walls in and adjacent to the bottom strengthening portion reached 0.9. Figure 22 presents

the compressive damage variable in different times.

When ground motion was inputted along the Ydirection, the structure remained elastic in the rst 2s.

From 24s, coupling beams in and adjacent to the 13th setback story yielded rst, and plastic

deformation began to develop. From 46s, 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, all

coupling beams under the 31st story yielded, and plastic deformation spread to the lateral walls

connected to the coupling beam. From 10s on, coupling beams in theYdirection above the 31st setback

story yielded one after another also. In the end, the compressive damage variable of the coupling beams

and walls in and adjacent to the bottom strengthening portion reached 0.9. Figure 23 shows the

compressive 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 rst

seismic defense line, they should yield and dissipate seismic energy prior to the other structural

members when attacked by earthquake. At the bottom strengthening portion of the core wall, a

relatively great number of steel-reinforced conning boundary members are congured according to

CCSDB, compared with the neighboring sixth story. On the other hand, the thickness of peripheral

walls changes in the sixth story. Therefore, considerable stress concentrates in the sixth to the seventh

story, which in turn develops great plastic deformation in these places and extends to the story above

and below. It is suggested that a transfer story should be placed above the bottom strengthening

portion 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 is

inputted in Xdirection.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

19/22

stiffness changes too. Measures should be taken to improve the seismic performance of setback

stories.

As specied in CCSDB, the strengthening portion at the bottom and its adjacent upper one story

shall be erected with conning boundary elements for wall structures, whereas ordinary boundary

elements shall be erected at the other portion of the wall. Usually, the former is larger in size and

higher in strength than the latter. In this building, conning boundary elements were located in the rst

six stories. For the steel of boundary members in the core wall, plastic strain occurred in the 13th story

rst, and then, the steel in the sixth oor yielded too. Eventually, the plastic strain concentrated in the

few 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 behaved

elastically in the course of vibration. No obvious damage was observed in the peripheral frame

structure. 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 sufcient

earthquake-resisting capacity left.

6. CONCLUSIONS AND SUGGESTIONS

In this paper, seismic behavior under rare earthquake of a super-tall building with setbacks in elevation

was studied through nonlinear dynamic time history analysis. On the basis of the analytical results, the

following conclusions can be drawn:

When subjected to rare earthquake action, the target building develops damage mainly in the core

wall, whereas a majority of the members in the peripheral frame remain elastic. The plastic

deformation 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 frameRC core wall structural system, the RC core wall serves as the rst seismic

defense line and the main lateral force-resisting member and shows considerable seismic capacity

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

in Ydirection.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

20/22

and ductility when subjected to rare earthquake action. Coupling beams could yield and dissipate

seismic 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 or

reduction 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 transfer

story is suggested to be placed above or below the setback. More specically, the seismic details of

(a) (b)

Figure 25. Stress in steel of columns when SHW1 is inputted: (a) in Xdirection; (b) in Ydirection.

(a) (b)

Figure 24. Plastic strain in steel of boundary members when SHW1 is inputted: (a) in Xdirection;

(b) in Ydirection.



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

21/22

members in the several stories above and below the setback should be increased. For asymmetric

setback structures, since responses of peripheral columns in the setback story are likely to increase

dramatically due to the torsion effect of structure, details of seismic design of peripheral columns

should be improved.

As specied in CCSDB (GB 50011-2001), the strengthening portion at bottom and its adjacent

upper one story shall be congured with conning boundary elements for wall structures, whereas

ordinary boundary elements shall be congured at the other portion of the wall. In this study, stressconcentration is observed at the interface story where conning boundary elements change to

ordinary boundary elements. It is suggested that boundary elements should be reduced gradually

story by story.

ACKNOWLEDGEMENTS

The authors are grateful for the partial nancial support from Kwang-Hua Fund for College of Civil

Engineering, 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 material

subroutine program and structural engineer Jinsheng Zeng of China Architectural Design & Research

Group who provided great help in using the ABAQUS.

REFERENCES

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

RI, USA.

Aranda GR. 1984. Ductility demands for R/C frames irregular in elevation. Proceedings of the 8th world conference on

Earthquake Engineering, San Francisco, USA 4: 559566.

Berahman F. 2010. Performance-based seismic evaluation of the Icon Hotel in Dubai United Arab Emirates. The Structural

Design 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-rise

building based on nonlinear dynamic time history analysis.The Structural Design of Tall and Special Buildings . Published

online: 8 Mar 2010. DOI: 10.1002/tal.586

Humar JL, Wright EW. 1977. Earthquake response of steel-framed multistory buildings with set-backs.Earthquake Engineering

and Structural Dynamics 5(1): 1539.

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: 515531.

DOI: 10.1002/tal.379

Lee J, Fenves GL. 1998. Plastic-damage model for cyclic loading of concrete structure. Journal of Engineering Mechanics

ASCE 124: 892900

Lew M, Naeim F, Carpenter LD, Youssef NF et al. 2010. The signicance of the 27 February 2010 offshore Maule, Chile

earthquake. The Structural Design of Tall and Special Buildings 19: 826837. 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 Structural

Design of Tall and Special Buildings 16: 131164. DOI: 10.1002/tal.302

Lubliner J, Oliver J, Oller S, Oate E. 1989. A plastic-damage model for concrete. International Journal of Solids and

Structures 25(3): 299326.

Mander JB, Priestly MJN, Park R. 1988a. Theoretical stress-strain model for conned concrete. Journal of Structural

Engineering ASCE 114

: 18041826.Mander JB, Priestly MJN, Park R. 1988b. Observed stress-strain behavior of conned concrete. Journal of Structural

Engineering ASCE 114: 18271849.

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 Specication for Concrete Structures of Tall

Building (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 Ofce: Shanghai, China (in Chinese).

Yahyai M, Rezayibana B, Daryan AS. 2009. Nonlinear seismic response of Milad Tower using nite element model. The

Structural Design of Tall and Special Buildings 18: 877890. 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 Structural

Design of Tall and Special Buildings. Published online: 11 Mar 2010. DOI: 10.1002/tal.591



DOI: 10.1002/tal

8/13/2019 Lu11c-ev

22/22

AUTHORS BIOGRAPHIES

XILIN LU born in 1955, received his doctoral degree from Tongji University in 1984, and now

working as a professor at State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji

University, Shanghai, China. His research focuses on seismic performance of tall and special

buildings, performance-based seismic design method, nonlinear analysis of reinforced concrete

structure, retrotting design of building structures. He has authored 10 books in the eld of seismic

design theory and application and published over 280 journal papers, in which over 140 were cited by

SCI 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 Disaster

Reduction in Civil Engineering, Tongji University, Shanghai, China. She received her doctoral degree

from Tongji University in 2005 and worked as a visiting scholar at University of California at

Berkeley, USA from January 2010 to January 2011. Her research interests lie in seismic performance

of tall and special buildings, structural passive control of buildings, earthquake resilient building

design, and structural dynamic testing technology.


Date post:	04-Jun-2018
Category:	Documents
Upload:	eko-budi-wicaksono
View:	216 times
Download:	0 times

Lu11c-ev

Documents