The Structural Performance of Monolithic Intersecting Walls in a Tall Reinforced Concrete Building

THE STRUCTURAL PERFORMANCE OF MONOLITHIC INTERSECTING WALLS IN A TALL REINFORCED

CONCRETE BUILDING

H. MOGHADDAM* AND M. SAMADIDepartment of Civil Engineering, Sharif University of Technology, Tehran, Iran

SUMMARY

Results of the seismic performance assessment of a new structural system that has been used in a 54-story rein-forced concrete building are presented. The structure, which is still under construction, and has a ‘Y-shape’ form, utilizes a special structural system that does not include any beams or columns. Instead, walls and slabs are used for carrying both gravitational and lateral loads. The general distinctions of the system are discussed. The struc-tural effi ciency of the system is compared with other conventional systems in some existing tall buildings. The seismic responses and dynamic behavior of the structure that were achieved by conducting various analyses are presented. The effects of analysis method, as well as some other parameters such as modeling assumptions and bidirectional earthquake excitation on the linear responses, are studied. The infl uence of the number of modes and design spectrum on the spectral analysis results is discussed. Using dynamic analysis, the real heightwise distribution of lateral loads occurring during an earthquake is presented. Copyright © 2007 John Wiley & Sons, Ltd.

1. INTRODUCTION

The lateral loads from wind or earthquake dominate the structural design of tall buildings (Smith and Coul, 1991). The designated structural system must provide stiffness, strength and stability for the tall building. Several structural systems have been presented and utilized in tall buildings, which can be divided to moment frames, braced frames, wall-frames, tubes, core-tubes, bundled tubes, braced tubes, core-outriggers, etc. The main difference between these systems, i.e. their various lateral load-resisting behavior, has been studied by (Smith and Coul, 1991). The effi ciency of these conventional systems is very different. It can easily be verifi ed that for a building with a given area, if its height increases with a defi nite ratio, in order to keep the lateral drift ratio unchanged the required structural weight should be increased with the second order of the height increment ratio, while its total volume is increased with the fi rst order of that ratio. This is also observable in nature, where animals’ skeletons become markedly heavier when their body volume increases. For example, while the weight of the bones of the mouse is just 8% of its body weight, this ratio exceeds 18% for the human (Schueller, 1995).

Many tall buildings have been constructed in high-seismicity regions throughout the world that accommodate large numbers of people. Owing to the signifi cant issue of the seismic stability of high-rise structures, several investigations have been conducted in the fi eld of seismic assessment

Copyright © 2007 John Wiley & Sons, Ltd.

* Correspondence to: H Moghaddam, Department of Civil Engineering, Sharif University of Technology, PO Box 11365-9313, Tehran, Iran. E-mail: [email protected]

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 17, 1–23 (2008)Published online 19 November 2007 in Wiley Interscience (www.interscience.wiley.com). DOI: 10.1002/tal.268

2 H. MOGHADDAM AND M. SAMADI

Copyright © 2007 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 17, 1–23 (2008) DOI: 10.1002/tal

of existing tall buildings. Miranda studied the seismic responses of an instrumented 32-story reinforced concrete building and compared the results with the measured responses of the building to the Loma Prieta earthquake (Miranda et al., 1991). Ventura and Ding studied the seismic behavior of a 52-story steel-frame building using both linear and nonlinear dynamic analysis as well as push-over analysis (Ventura and Ding, 2000).

Providing stability of tall buildings against lateral loads is much more complex than in ordinary structures and choosing an appropriate structural system for enhancing structural performance is important. Consequently, the development of innovative structural forms and systems in tall buildings has been considered as a signifi cant research topic. However, once a new structural system is utilized in a tall building, new investigations are necessary to study its structural behavior, especially under seismic loadings.

This paper presents parts of the results of a study on the seismic evaluation of a 54-story RC build-ing currently under construction that demonstrates the structural and dynamic behavior and perfor-mance of its inventive structural system, i.e., different from the above-mentioned categories. A performance-based strategy was selected for the purpose of evaluating the building. This paper focuses on the following results that mostly implicate the performance of the structural system. The distinctive structural characteristics of its ‘three-wing’ form are discussed. Results of several analyses that were conducted on two distinct fi nite element models of the building are presented. Artifi cial accelerograms compatible with the site response spectrum were generated and used in the dynamic time history analysis of the structure. Owing to long time and large amount of memory required for the analysis of such a large structure, sensitivity analysis was conducted to ascertain the effect of various param-eters on the response values. In this respect the effect of the number of combined modes on the spectral analysis results, the P-∆ effect, bidirectional excitation and modeling assumptions are evalu-ated. The real heightwise lateral force distribution in this structural system is presented and a formula is proposed for the purpose of calculating these loads. Some other results such as nonlinear analysis results, seismic damage evaluation using various damage indices, the acceptability of building perfor-mance during earthquakes of three hazard levels, and the applicability and reliability of some newly proposed nonlinear analysis methods can be found in Moghaddam and Samadi (2003).

2. DESCRIPTION OF THE STRUCTURAL SYSTEM

The studied structure, named ‘Tehran Tower’, is a 54-story reinforced concrete residential building which is still under construction. The height of the building is 164·3 m from the top of the base slab and it will be the largest and tallest building in a high-seismicity area. The structure consists of three basement levels, ground fl oor, mezzanine and 49 stories above them. It includes three intersecting wings with an angle of 120°. The length and width of each wing is 50 m and 21 m, respectively, and they have an area of 912 m2 (Figure 1).

The key benefi t of this structural form when compared to other conventional structural systems for tall buildings is the least distance between the internal building zones to the exterior windows in this tower (which does not exceed 10 m), i.e., a criterion for brightness of the spaces. There is a setback at the ground fl oor level where the area of the building decreases from 3952 m2 in the basements to 2737 m2 in the upper fl oors (Figure 2). Wings A and B in Figure 2 are identical (both structurally and architecturally) whereas wing C is slightly different. Each wing consists of a main longitudinal wall and several transverse walls, called secondary hereafter. The spacing between the secondary walls varies from 3·5 m to 8 m. Up to fi ve different thicknesses have been designated for the primary walls in each story. For example, at the ground fl oor, primary walls have three different thicknesses 195, 155 and 115 cm, in a descending order from center to wing tip (as shown in Figure 2). These values of wall thicknesses are reduced every fi ve stories, such that at the top fi ve levels all of the

STRUCTURAL PERFORMANCE OF MONOLITHIC INTERSECTING WALLS 3


Figure 1. Overview of Tehran Tower

(B) Plan of building in the upper floors including primary and secondary walls

(A) Plan of building in the basement floors including primary and secondary walls

Z

Xwing B

wing C

wing A

70 70 70 70

(C) The primary wall of wing-A at the 54th story

195 155 115

(D) The primary wall of wing-A at the ground floor

Figure 2. Plan of the structure



above-mentioned thicknesses are reduced to a single value of 70 cm (Figure 2). The thickness of the secondary walls generally lies in the range 25–50 cm.

Both main and secondary walls are reinforced in three orthogonal directions. Three to fi ve layers of reinforcement meshes are used in the main walls, and two to three layers in the secondary walls, respectively. These meshes are connected to each other using some bars normal to the plane of wall (link bars), to prevent buckling of the reinforcement meshes, confi ne core concrete, and resist against shear. In both primary and secondary walls, the vertical reinforcement ratio does not exceed 0·5% due to simultaneously having large gravity and lateral loads, as well as large sections. The horizontal reinforcement ratio in primary and secondary walls are 1% and 0·5%, respectively.

The structure is sustained by a three-wing shape mat foundation with a depth of 3 m (Figure 3). The height of all stories is 3 m except in the basement fl oors.

3. GENERAL ASPECTS OF STRUCTURAL BEHAVIOR

The following primary characteristics may be recounted for this structural system.

3.1 Characteristics of ‘three-wing’ structural form

Supposing a three-wing section as depicted in Figure 4, it can easily be verifi ed that the moment of inertia of such a section is independent of its rotation angle (q) and for all q values in Figure 4 is equal to

Figure 3. Structure mat foundation layout

x

Z

θ

z

X

Figure 4. Idealized ‘three-wing’ form of the structure



I I trX Z= = 3 2 (1)

because we have

Ix tr tr= ( ) + +( ) + +( ){ } =3 2 2 2 33 120 240 2cos cos cosθ θ θ (2)

where t and r are the thickness and length of each wing, respectively. However, attention should be paid to the fact that while the moment of inertia about any arbitrary axis is the same, the section modulus in bending about the X-axis takes a maximum value for q = 90° and a minimum value for q = 0°. Therefore, q = 0° results in maximum normal stress from bending which is the critical direction of the section for bending assessment.

Also, as shown in the following equations, shear effects are most critical at q = 0°, where

τ = ( ) = ( ) ( ){ } =QV It tr t r V V A2 2 32 2 (3)

and in the case of q = 90° we have

τ = ( ) = ( ) ( ){ } =QV It tr t r V V A2 2 32 30 2 0 866cos . (4)

3.2 Aspect ratio

The lateral behavior of a tall building is similar to a cantilever beam, where the height of the building is its length and the overall plan dimensions represent the width and depth of its section. Therefore, as the plan dimension increases, the lateral strength, stiffness, and overturning resistance of the build-ing increase more markedly. Also a decrease in the structure height leads to reduction of the lateral defl ection of this assumptive beam. Thus the advantages of this structural system are its short height as well as its large plan width. While the usual story height of tall structures is not less than 4 m because of the required height of girders and also the occupied space for horizontal transmission of facilities (Table 1), this system makes it feasible to reduce the story height to 3 m.

Table 1. The effi ciencies of various structural systems

Building name Construction Stories Height/width

Steel weight per unit area (psf) Height (m) Structural system

Chase Tower 1963 60 7·3 55·2 248 Braced rigid frameEmpire State 1931 102 9·3 42·2 381 Braced rigid frameWorld Trade

Center1972 110 6·9 37 415 Framed tube

Sears Tower 1974 109 6·4 33 443 Bundled tubeUS Steel

Building1971 64 6·3 30 256 Shear walls +

outriggersJohn Hancock

Center1968 100 7·9 29·7 344 Trussed tube

Alcoa Building

1969 26 4 26 96 Latticed tube

Boston Co. 1970 41 4·1 21 152 K braced tubeIDS Center 1971 57 6·1 17·9 235 K braced tube + belt

trussTehran Tower 2005 54 2·2 18·4 164 Monolithic

intersecting walls



In other words, considering that the height of the building is 164 m and the diameter of its periph-eral circle is 100 m reveals that the aspect ratio of the building is almost equal to 1·64, and as classi-fi ed by Nateghi (2000), the structure may be regarded as a medium-height structure and more stable than a slender tall building.

3.3 Structural role of secondary walls

The secondary walls support slabs and transfer their gravitational load to the foundation. They also increase shear and fl exural story strength against lateral loads. In addition, they act as stiffeners for the main walls, enhancing their out-of-plane stiffness. This reduces the local vibrations of each wing and also prevents buckling of the main walls under vertical and lateral loads. The secondary walls also play an important role in increasing the torsional moment of inertia of the structure.

3.4 Seismic performance of reinforced concrete walls

Unlike conventional frame structures, in this building there are just reinforced concrete walls and slabs that participate in load carrying. The use of walls instead of columns is benefi cial because, after incur-ring damage in a severe earthquake, columns may lose their capacity for bearing vertical loads, leading to local or global collapse of the structure, while a reinforced concrete wall can maintain its bearing capacity even after experiencing a large amount of cracking and crushing in a strong earthquake (FEMA 306, 1999). In addition, as opposed to walls, the seismic capacity of columns is very sensitive to design and construction quality such as the details of transverse reinforcements and joints.

3.5 Structural role of basement fl oors

As described previously, greater thicknesses have been considered for walls and slabs in basements as compared with upper fl oors; additionally these fl oors are larger than the upper ones. Hence they act as a stiffener for the mat foundation, reducing its thickness (similar to the stiffeners in the connec-tion of a column to a base plate). Consequently, the foundation behaves like a box rather than a mat system, and this in turn increases the overall stiffness and stability of the foundation.

3.6 Economic considerations

The effi ciencies of various systems are widely different. The effi ciency of the structural system may be quantifi ed in terms of the required structural material, for example the structural steel weight used per unit area of the building, to provide adequate stiffness, strength and stability. Table 1 presents the results of an exploration on some famous tall buildings and their specifi cations are compared with the corresponding values for the studied structure. It is observed that the type of structural system plays the most important role in economic cost reduction. Table 1 also shows that the structural system used in the Tehran Tower is very economical from the viewpoint of the structural steel used.

4. MODELLING THE STRUCTURE

The conventional fi nite element method has been successfully used in various types of analyses of large structures. The use of advanced elements can help engineers to design complex structures, such as tall towers, at lower cost and with lower weight. Many researchers and design engineers have proposed exact and approximate solutions for dynamic analysis of large building structures. However,



in cases of high-rise structures with a lot of structural elements, computer time and memory can be large (Khaloo et al., 2001).

A detailed three-dimensional fi nite element model of the structure was developed by using the ANSYS program. In this 3D model (called ML3d hereafter) that was developed by improving a recently built model, all walls, slabs and foundations were modeled using the SHELL63 element of ANSYS (SAS, 1995). SHELL63 is a four-node element with six DOFs at each node and can consider both membranous and fl exural actions. All structural details, consisting of thicknesses, openings, loads and elastic foundation stiffness (for the foundation elements), were included in this model, and there-fore a total number of 35 types of element characteristics (real constants) were defi ned for the shell elements. Lintels were modeled using the BEAM189 element and there were seven section types in total for these elements in the whole model. This model contained 22 687 SHELL63 elements, 2558 BEAM189 elements, and 130 686 DOFs (Samadi, 2003).

Seismic risk analysis was conducted for different risk levels (Samadi, 2003) and the results are summarized in Table 2. Also response spectra for these levels are depicted in Figure 5 and have been compared with both new and old versions of the Iranian seismic code, 2800 Standard (1999).

Table 2. Description of seismic risk of triple hazard levels

Hazard levelRisk analysis

methodExceedance probability/earthquake magnitude

PGA

Horizontal Vertical

DBE (design basis earthquake) Probabilistic 37% (once in 50 years) 0·32 g 0·23 gMPE (max. probable earthquake) Probabilistic 10% (once in 500 years) 0·49 g 0·36 gMCE (max. considered earthquake) Deterministic MS = 7·1 on a fault with a

distance of 7 km to site0·58 g 0·47 g

Figure 5. Comparison of site design spectra for the three hazard levels with that of 2800 Seismic Code



Several artifi cial accelerograms were generated to be compatible with these spectra by employing the SIMQKE program. Figure 6 shows the generated accelerogram that is compatible with the spec-trum of the MCE level. Only 9 s of generated records was applied because of the large structural model, which requires a large amount of memory and time for conducting time history analysis.

For this structure, owing to having non-orthogonal lateral force-resisting systems, in accordance with FEMA 356 (2000) and commentary to SEAOC Vision 2000 (1995), responses to excitation in any of X or Z directions (Figure 2) were combined with 30% of responses to the orthogonal direction excitation.

As pointed out earlier, the X direction in Figure 2 is the most critical excitation direction for assess-ing both shear and fl exural actions. In order to obtain the effect of this code requirement on response values, four loading cases were taken into account in all analyses, i.e., Ex, Ez, Ex + 0·3Ez, Ez + 0·3Ex, referred to as Ex, Ez, Exz, Ezx hereafter.

5. MODAL ANALYSIS

Results of modal analysis showed that the fi rst mode of the structure is torsional with a period of 3·8 s (Figure 7). The second and the third modes are two symmetric fl exural modes in Z and X directions with a period of 1·5 s, respectively (fi gure 8). This reconfi rms the symmetry of the building. The fourth mode is the second torsional mode. The fi fth and sixth modes are second symmetric fl exural modes in Z and X directions, respectively, and the seventh mode associates with the vertical vibration of the structure.

The fi rst six modes of vibration can be observed in Figure 9. The deformed shape of the structure in the fi rst and the second fl exural modes are clarifi ed in the charts of Figure 10. The fi rst fl exural mode, i.e., the second natural mode, is obviously a combination of fl exural behavior in the down stories and shear behavior in a few of the top stories.

Although the fi rst mode is torsional, due to the symmetry of the structure there is no torsional loading associated with seismic excitation. As shown in Figure 11, the earthquake-induced torques about the center of rigidity of the structure eliminate each other and the resultant torque is zero:

T F d F d F d= ( ) + ( ) − ( ) =2 2 0 (5)

In addition, both recorded and analytical seismic responses of similar structures (a Y-shaped tall building with a dominant torsional natural mode of vibration but without any eccentricity) showed that there is almost no torsional response under earthquake excitation (Miranda et al., 1991). Moreover,

-6

- 4

-2

0

2

4

6

0

1 2 3 4 5 6 7 8 9 10

time (sec)

a

ccel

erat

ion

(m/s

²)

Figure 6. Time history of MCE artifi cial record



Figure 7. First natural vibration mode (top view)

Figure 8. Second natural vibration mode (top view)



1

MN

MX

X

Y

Z

1

MN

MX

X

Y

Z

1

MN

MX

X

Y

Z

1

MN

MX

X

Y

Z

1

MN

MX

X

Y

Z

1

MN

MX

X

Y

Z

T1 (The 1st mode) Z1 (The 2nd mode) X1 (The 3rd mode)

T2 (The 4th mode) Z2 (The 5th mode) X2 (The 6th mode)

0

10

20

30

40

50

60

-1.20 -0.80 -0.40 0.00 0.40 0.80 1.20

relative lateral displacement

stor

y

the 2 nd mode

the 5 th mode

Flexural behavior

Shearbehavior

Figure 9. First six modes of the structure

Figure 10. Displacement vector of centerline nodes in the fi rst and the second fl exural modes



the structure poses a considerable torsional resistance coming from the secondary walls. Consequently, the effects of torsion (and accidental eccentricity) were neglected in the analyses.

6. STATIC FORCE-BASED ANALYSIS

The conventional static analysis suggested by the seismic codes was used for estimating the structural response. The Iranian seismic code, 2800 Standard (1999) coeffi cients were used, presenting a base shear coeffi cient C = 0·096. For evaluating the infl uence of the P-∆ effect, the analysis was conducted with and without P-∆ effect and the results were compared. The results are summarized in Table 3. The lateral displacement is shown in Figure 12. It should be noted that that the ductility-based reduc-tion factor R has been accounted for in these analyses.

The results indicate that the P-∆ effect results in increases of the base shear and tip displace-ment by 0·6% and 1·5%, respectively. This is much less than the 10% value that was suggested by Goel (Sivakumaan and Balendra, 1987). However, these values of increment may be amplifi ed when nonlinearities and interaction with soft soil, if signifi cant, are be taken into account.

d/2

d/4

F

FF

Figure 11. Symmetry about any arbitrary axis inhibits the occurrence of torsional excitations

0

10

20

30

40

50

60

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

lateral displacement (m)

Sto

rey

Figure 12. Lateral displacement of center nodes under equivalent static analysis



7. SPECTRAL ANALYSIS

The modal analysis results were used as the basis for spectral analysis. Four spectra were used for this analysis, including DBE, MPE and MCE spectra and the code design spectrum. Since modal analysis indicated that the mass participation in modes 15–25 is negligible, the maximum structural responses in the fi rst 15 modes are combined using the CQC method (Wilson et al., 1981).

Figure 13 shows the displacement of the centerline of the building under the four foregoing spectra in four different loading cases (Ex to Ezx) in ascending order. It can be seen that the structural responses in two perpendicular directions (Ex, Ez) are approximately identical. This is a result of the symmetry of structure that was pointed out previously. Maximum displacement occurs at the tip of the wings at the roof level, and is equal to 39·1, 30·0, 46·9 and 56·3 cm under 2800, DBE, MPE and MCE spectra in Exz loading, respectively. In addition, it can be concluded from Figure 13 that bidirectional seismic loading can increase the lateral displacement of the building up to 4·6%. The increases in maximum strain and base shear due to bidirectional loading are 8·5% and 5%, respectively.

The story shear diagrams under these four spectra in the most critical loading case (Exz) are shown in Figure 14. The fi gure indicates that a maximum base shear of 2258 MN occurs under the spectrum of the MCE hazard level.

Several formulations have been presented by the codes for distributing base shear in the height of structures for traditional static seismic analysis (Uniform Building Code, 1997; NEHRP85,

0

10

20

30

40

50

60

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Lateral displacement

stor

ey

dbl x

dbl z

2800 x

2800z

dblx+.3z

dbl z+.3x

2800x+.3z

2800z+.3x

mpl x

mpl z

mpl x+.3z

mpl z+.3x

mcl x

mcl z

mcl x+.3z

mcl z+.3x

Figure 13. Maximum displacements of centerline nodes obtained from spectral analysis

Table 3. Summary of the equivalent static analysis results

Equivalent static Maximum response values

Loading case Compressive strain Tensile strain Displacement (m)

Exz 0·00083 0·00047 0·170Exz including P-∆ 0·00084 0·00048 0·172



1985). In this study the real heightwise distribution of the lateral forces in the building under earthquake was determined from the story shears. The computed lateral forces from spectral analysis on the structure versus height are shown in Figure 15. A statistical regression was conducted to fi t a formulation to these data and the following second-order polynomial equation was obtained:

0

10

20

30

40

50

60

0.0E+ 0 5.0E+4 1.0E+5 1.5E+5 2.0E+5 2.5E+5

lateral force (ton)

stor

y

DBL from model

2800 code from model

MPL from model

MCL from model

Figure 14. Story shear forces obtained from spectral analysis

0

10

20

30

40

50

60

-2.0E+3 4.0E+3 1.0E+4 1.6E+4 2.2E+4lateral force (ton)

stor

y

DBL

2800MPL MCL

Figure15. Heightwise distribution of lateral forces from spectral analysis and the proposed regression formula



F h h Vi i i= − + −( )0 9573 6 250 9 62. .e e (6)

where Fi is the lateral force of the ith story except for the roof, hi is the height of the ith story from the seismic base level in meters and V is the base shear in tons.

The coeffi cient of determination of this formula is 0·9988 and reveals that the estimated values closely correspond to the actual data (Figure 15). The computed values from Equation (7) are also drawn in this fi gure for comparison with the actual values. It should also be clarifi ed that the sudden increase in lateral force at the roof level is mostly because of the greater existing mass in that story.

As has been generally accepted, increasing the number of structure natural modes in analysis enhances the accuracy of the results. Conversely, it also increases analysis time. Therefore there is always a question of how many modes should be considered in a spectral analysis. In this research, spectral analyses of the structure for Ex and Ez loading cases were repeated for two different situations to measure the effect of the number of modes. First, all 15 fi rst modes were taken into account, and the analysis was then repeated considering only the fi rst three modes. It should be noted that these three modes are the fi rst torsional, and Z and X fl exural modes, respectively. As depicted in Figure16, in the corresponding earthquakes of all hazard levels, considering only the fi rst three modes would overesti-mate the displacement response of the building up to 14% as compared with 15-mode analysis. Figure16 compares the results of spectral analysis for the Ex loading case for these dual conditions. It is note-worthy that the CQC method has been used as the modal combination rule, while by using the SRSS method the estimated responses always increase by increasing the number of combined modes.

8. TIME HISTORY ANALYSIS

Consider a damped vibration of a structure as follows:

MU CU KU F�� + + = (7)

0

10

20

30

40

50

60

0.00 0.10 0.20 0.30 0.40 0.50 0.60displacement (m)

stor

y

Figure 16. Effect of number of modes on displacement response



where C is the damping matrix. Generally there is no need to express the damping of a typically viscously damped MDOF system by means of the damping matrix because it is represented more conveniently in terms of the modal damping ratios zn. According to the improved Rayleigh method for the formation of a damping matrix, damping is assumed to be proportional to a combination of the mass and stiffness matrices, as given by the following equation:

C a M a K= +0 1 (8)

in which the proportionality constants a0 and a1 can be evaluated by the solution of a pair of simulta-neous equations if the damping ratios zm and zn associated with two specifi c frequencies (modes) wm and wn are known (Clough and Penzin, 1993). By assuming 5% of critical damping as the damping ratio of the second and fi fth modes this pair of equations is:

ξω

ω

ξω

ω

22

0 1 22

55

0 1 52

1

2

1

2

= +( )

= +( )

a a

a a

(9)

The proportionality constants a0 and a1 that were obtained from the above equations were fed into the program for dynamic time history analysis.

As described earlier, artifi cial ground motions consistent with the site-specifi c spectra of three hazard levels were generated. Since the Exz loading case is the most critical situation in all time history analyses, accelerograms scaled to 1 and 0·3 were simultaneously applied to the structure in X and Z directions, respectively. Figure 17 shows the displacement of center points of the roof and 27th fl oor (located on the intersection of the three wings) during 9 s of excitation by MCE-compatible ground motion. It is seen that the maximum displacement of the roof center in the MCE representative arti-fi cial earthquake is 50 cm, occurring at t = 8·18 s. Additionally, there is negligible phase difference in the response of the roof and 27th fl oor, indicating that the building vibrates predominantly in its fi rst natural mode of vibration.

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0 1 2 3 4 5 6 7 8 9 10

time (sec)

disp

lace

men

t (m

)

roof

27th floor

Figure 17. Time history of displacement response at roof and 27th fl oor to MCE accelerogram



In Figure 18 the acceleration response time history of the above-mentioned node is depicted for the roof and 27th fl oor, showing a maximum acceleration of 17 m/s² at the roof story at time 6·54 s of this earthquake. Figure 19 shows the strain contour at the peak deformed shape of the building under the MCE earthquake at 8·18 s of the MCE record. In this fi gure just the walls have been shown, to be more comprehensive.

At this peak response the lateral deformation shape of the structure may be more clearly studied by drawing the lateral displacement of the nodes located on the centerline versus height. This is shown in Figure 20, where the lateral deformation of the centerline has been depicted for peak responses of the structure in the time history analyses under the generated records compatible with the three hazard levels.

The time history of the structure base shear and base moment when excited by the ground motion of the MCE level is shown in Figure 21. It can be seen that the maximum base shear that is developed in an earthquake with a magnitude of 7·1 on the Richter scale at the Tehran northern fault (MCE) is 1400 MN assuming a linear elastic behavior for the structure. This value of the base shear is equiva-lent to 46% of the structure weight and occurs after 7·34 s from the beginning of the motion. In Table 4 the summary of maximum results of various time history analysis under the triple hazard levels in the Exz case, including base shear, displacement and acceleration is presented.

A comparison of the calculated responses from the spectral and time history analyses reveals that the responses obtained from the dynamic time history analysis are always greater than those obtained from the spectral analysis. However, the differences between the responses to the associated earthquake excitation of the three hazard levels are not identical but are generally less than 10%. Additionally the time history of the structural responses to the recorded motion of a real earthquake, i.e., Tabas 1976, was obtained and compared to the triple foregoing responses (Moghaddam and Samadi, 2003).

Structural responses to the El Centro 1940 earthquake were also computed. In order to evaluate the torsional response of the structure to this earthquake excitation, several response quantities at the center of the roof level were compared to those measured at the tip of wing C. In Figure 22 the displacement responses of these points are compared. As can be observed, there is negligible difference between the responses measured at the center and wing tip, implying a very small torsional response. Addition-ally, the acceleration responses of the above-mentioned nodes are shown in Figure 22 in both time

-20

-15

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

time (sec)

acce

lera

tion

(m/s

²)

roof

27th floor

Figure 18. Time history of acceleration response at roof and 27th fl oor to MCE accelerogram



0

10

20

30

40

50

60

0.0 0.1 0.2 0.3 0.4 0.5 0.6

displacement (m)

stor

y

DBLMPLMCL

Figure 19. Peak strain contour in walls under the MCE record

Figure 20. Lateral displacement of centerline at the peak response to the MCE record



-3.0E+06

-2.0E+06

-1.0E+06

0.0E+00

1.0E+06

2.0E+06

3.0E+06

4.0E+06

0 1 2 3 4 5 6 7 8 9 10

time (sec)

base

mom

ent (

t.m)

-2.0E+05

-1.5E+05

-1.0E+05

-5.0E+04

0.0E+00

5.0E+04

1.0E+05

1.5E+05

0 1 2 3 4 5 6 7 8 9 10

time (sec)

base

she

ar (

ton)

Figure 21. Time history of base actions under MCE accelerogram (top) base shear, (bottom) base moment

Table 4. Summary of maximum structure responses from THA

HL

Base shear (MN)

Base moment (MN m)

Displacement (m)

Acceleration (m/s²)

Compressive strain Tensile strain

DBE 803 19 100 0·342 10·1 0·0019 0·00080MPE 1210 27 400 0·514 14·9 0·0025 0·00141MCE 1396 30 000 0·592 16·9 0·0029 0·00166

and frequency domains. These response measurements can also represent similar deductions. The Fourier amplitude spectrum shows that major amplifi cations in the responses take place at the natural frequencies of the structure. The Fourier amplitude spectrum also shows that while responses of the center and wing tip that relate to the lower frequencies are very close together, some divergence is observed with the responses at higher frequencies. It may be concluded that the torsional response



1

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-.8

-.4

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.4

.8

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1.6

2

2.4

(x10**-1)

VALU

01

23

45

67

89

1011

1213

TIME

centerwing-c

(a)

(b)

(c)

0

200

400

600

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0 0.5 1 1.5 2 2.5 3 3.5 4

frequency (HZ)

Fou

rier

ampl

itude

(cm

/s)

center

wing C

the first translational mode

the second translational mode

-15

-10

-5

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210186420

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roof

acc

eler

atio

n (m

/s²)

center

wing C

Figure 22. Comparison of the roof responses to El Centro 1940 earthquake at center and wing tip: (a) displacement; (b) acceleration; (c) Fourier amplitude of acceleration



mostly occurs at the higher-frequency responses. However, this may not be of so much importance for this structure because this range of frequencies is far from the major natural frequencies of the structure that have greater amplitudes.

9. THE ALTERNATIVE SIMPLE MODEL

Parallel to the foregoing ML3D model, all linear analyses were performed on a simple model (here-after called MLB). It consists of 54 beam and 54 mass elements. The structural characteristics of various stories including area and moment of inertia of the set of primary and secondary walls were calculated and assigned to the corresponding beam elements (Table 5).

Regarding the fact that almost half of the story weight was placed in the walls, the distributed mass capability of the ANSYS beam element was applied (SAS, 1995). This simple model, which takes a very short time to be analyzed, was used in order to estimate the effect of modeling assumptions on the accuracy of the results. In Figure 23 the time history of the roof displacement response that has

Table 5. Section properties of the beam model

Stories Ix (m4) Iz (m4) A (m2)

Basement levels 270 295 280 461 713 GF–9 158 093 152 818 403 10–14 148 592 143 913 377 15–19 140 240 136 525 346 20–24 138 371 134 616 335 25–29 130 624 128 140 318 30–34 124 438 122 838 303 35–39 123 205 121 554 296 40–44 120 048 118 217 285 45–49 116 914 114 858 274

-0.60

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-0.20

0.00

0.20

0.40

0.60

0 1 2 3 4 5 6 7 8 9 10

time (sec)

roof

dis

plac

emen

t (m

)

beam3D

Figure 23. Comparison of roof displacement obtained from linear models ML3D and MLB subjected



been obtained from the linear models (ML3D, MLB) when infl uenced by the record of MCE are drawn together. As can be seen, the maximum roof displacements obtained from these models are approxi-mately the same but some phase and amplitude differences over the response time between the results of the two models are observed.

In Figure 24 the lateral displacement vectors of the structure from the two models have been com-pared. It is clear that although the maximum lateral displacements of the structure (which occurs at the roof) in both of these models and under all records of each of the triple hazard levels are approx-imately very close together, there is an apparent difference between the estimated displacements for other stories; i.e., the beam model anticipates a predominant fl exural mode of lateral deformation for the structure, while in the 3D detailed model the displacement shape of the building converts from fl exural to shear at the upper fl oors.

This difference is mainly a result of shear deformations and has been known to be a con-sequence of the shear lag phenomenon. From these results it may be concluded that simple theories of solid mechanics such as the Saint-Venan principle, which assumes that plane sections of a bent beam remain plane, may result in excessive errors in predicting the lateral behavior of a tall building.

10. CONCLUSION

This paper reports the results of a study on the structural characteristics (including the seismic response) of a new structural system in a tall building. Some general conclusions can be drawn. With

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4 0.5 0.6

lateral displacement (m)

stor

y DBL MLB

MPL MLB

MCL MLB

MCL ML3D

MPL ML3D

DBL ML3D

Figure 24. A comparison of displacement responses obtained from linear models ML3D and MLB



respect to the economic considerations, the use of this system reduces the structural steel required when compared to other conventional structural systems in tall buildings, while it increases the volume of the concrete consumed. Regarding the overall structural characteristics, this system makes it fea-sible to reduce the story height and increase the plan width, which fi nally enhances the stiffness, strength and stability. The moment of inertia of the structure about any arbitrary axis is constant. Some specifi c conclusions follow:

(1) The drift ratio of the building in the most considered earthquake does not exceed 0·4%, implicat-ing the great stiffness of the structural system used.

(2) Bidirectional application of earthquake excitation increases the displacement response by 4·6% relative to the monodirectional excitation.

(3) Results indicate that the P-∆ effect increases the base shear and tip displacement of this system by just 0·6% and 1·5%, respectively.

(4) Modal analysis reveals that the fi rst natural vibration mode of this system is torsional.(5) Combining only the fi rst three vibration modes in spectral analysis leads to a 14% overestimation

of the displacement responses relative to the case when all effective modes are taken into account.

(6) The responses obtained from the dynamic time history analysis are always greater than those obtained from spectral analysis. The difference does not usually exceed 10%.

(7) Although the maximum lateral displacement responses occurring at the roof level for the two linear models (MLB and ML3D) are very close, there are apparent differences between the esti-mated displacement responses at other levels.

(8) The simple theories of solids mechanics may result in excessive errors in predicting the lateral behavior of a tall building.

REFERENCES

Clough RW, Penzin J. 1993. Dynamics of Structures. McGraw-Hill: New York.FEMA 306. 1999. Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings. Federal Emergency

Management Agency: Washington, DC.FEMA 356. 2000. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency

Management Agency: Washington, DC.Iranian Seismic Code, 2800 Standard. 1999. Center of Building and Housing Research: Tehran.Khaloo AR, Asadpour N, Horr AM. 2001. Full dynamic analysis of Tehran telecommunication tower. Structural

Design of Tall Buildings 10: 263–281.Miranda E, Anderson JS et al. 1991. Evaluation of the seismic performance of a 30 story reinforced concrete

building. EERC91/16. University of California, Berkeley, CA.Moghaddam H, Samadi M. 2003. Performance based seismic evaluation of an existing 54 story RC

building utilizing an innovative structural system. In 9th National Conference on Civil Engineering (in Farsi).

Nateghi F. 2000. Behavior and Design of Tall Buildings. IIEES: Tehran (in Farsi).Samadi M. 2003. Seismic evaluation of an existing 54 story RC building. MS thesis, Sharif University of technol-

ogy, Iran (in Farsi).SAS. 1995. Ansys General Purpose Finite Element Program, Revision 5.7. Swanson Analysis Systems: Houston,

TX.Schueller W. 1995. The Design of Building Structures. Prentice-Hall: Englewood Cliffs, NJ.SEAOC vision 2000. 1995. Performance-Based Seismic Engineering of Buildings. Vols I and II: Conceptual

Framework. Structural Engineering Association of California: Sacramento, CA.Sivakumaran KS, Balendra T. 1987. Seismic response of multi-story buildings including foundation interaction

and P-∆ effects. Engineering Structures 9: 277–284.



Smith S, Coul A. 1991. Tall Building Structures, Analysis and Design. Wiley: New York.Uniform Building Code. 1997. International Conference of Building Offi cials.Ventura CE, Ding Y. 2000. Linear and nonlinear seismic response of a 52 story steel frame building. Structural

Design of Tall Buildings 9(1): 25–45.Wilson EL, Der Kiureghian A, Bayo EP. 1981. A replacement for the SRSS method seismic analysis. Earthquake

Engineering and Structural Dynamics 9: 187–194.

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