Steel Frame Shear Wall System

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DRIFT DESIGN OF STEEL-FRAME SHEAR-WALL SYSTEMS

FOR TALL BUILDINGS

HYO SEON PARK1*, KAPPYO HONG1 AND JI HYUN SEO2

1Department of Architectural Engineering, Yonsei University, Shinchon-dong, Seoul 120-749, Korea

2Daewoo Institute of Construction Technology, Songjuk-dong, Suwon 440-210, Korea

SUMMARY

Drift design methods based on resizing algorithms are presented to control lateral displacements of steel-frameshear-wall systems for tall buildings. Three algorithms for resizing of structural members of the steel-frame shear-wall systems are derived by formulating the drift design process into an optimization problem that minimizeslateral displacement of the system without changing the weight of a structure. During the drift design process,cost-effective displacement participation factors obtained by the energy method are used to determine the amount

of material to be modified instead of calculating sensitivity coefficients. The overall structural design model withthe drift design method for the steel-frame shear-wall systems is proposed and applied to the structural design ofthree examples. As demonstrated in the examples, the lateral displacement and interstorey drift of a frame shear-wall system can be effectively designed by the drift design method without the time-consuming trial-and-errorprocess. Copyright 2002 John Wiley & Sons, Ltd.

1. INTRODUCTION

The structural design of tall buildings under lateral forces is usually governed by stiffness criteria

rather than strength criteria. Especially for the final stage of the structural design process of tall

buildings, criteria for the lateral displacement at the top of a building and interstorey drifts become of

primary concern. To avoid an excessive drift that causes damage both to structural elements and to

nonstructural elements, the calculated drift at the final stage of design must be checked not to exceed

specified limits for the drift. Those requirements for the drift directly affect the design of the lateral

resisting system of tall buildings. Therefore, the efficiency of the lateral load resisting system or the

amount of material required for a tall building heavily depends on drift design.

However, structural optimization algorithms based on sensitivity coefficients in drift design of high-

rise buildings are far from representing practical applications because of computational requirements

(Park and Adeli, 1997; Rao, 1996). In recent years, various drift design methods have been developed for

sizing members of lateral load resisting systems in tall buildings to satisfy stiffness criteria. In resizing

techniques using energy methods presented by Baker (1990), Charney (1991), and Wada (1991), the

active members, which have a relatively high influence on the magnitude of the target displacement to be

controlled, are selected and the cross-sectional properties of the active members are modified. Chan and

Grierson (1993) have presented an efficient resizing technique for the least-weight design of tall slender

lateral load resisting steel frameworks subjected to multiple interstorey drift constraints. Chan, Grierson

and Sherbourne (1995) described the automatic resizing technique for drift design of tall steel buildings.

THE STRUCTURAL DESIGN OF TALL BUILDINGSStruct. Design Tall Build. 11, 3549 (2002)Published online in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/tal.187

Copyright 2002 John Wiley & Sons, Ltd. Received January 2001

Accepted March 2001

* Correspondence to: Hyo Seon Park, Department of Architectural Engineering, Yonsei University, 134 Shinchon-dong,Seodaemun-ku, Seoul 120-749, Korea. E-mail: [email protected]


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Park and Park (1997) presented the drift control tool for high-rise buildings subjected to lateral forces

based on the unit load method. Resizing algorithms based on displacement participation factors for drift

design of tall steel buildings have been formulated into optimization problems with two different design

variables, such as cross-sectional area and moment of inertia, by Park and Ahn (1998).

The stiffness-based resizing techniques mentioned above are shown to be efficient for the drift

design of multistorey steel buildings where building drift rather than member strength is thecontrolling factor. Thus, time-consuming and labour-intensive trial-and-error processes related to drift

design of tall buildings can be avoided by the resizing techniques. However, all of these resizing

techniques work only for steel frames or steel-braced frames since steel columns, beams and bracing

elements are allowed in optimum material distribution for drift design.

The frame shear-wall system is one of the most popular lateral load resisting systems for tall

buildings. The lateral resistance of the frame-wall system is provided by the interaction between the

two structural systems that enhances the lateral stiffness of the combined system. Many examples of

tall buildings can be found with steel moment frames attached to shear walls around elevators, stairs

and utility shafts. However, no practical algorithm for drift design of the frame shear-wall system for

tall buildings has been reported.

In this paper, three resizing algorithms for drift design of frame shear-wall systems for tall buildings

are presented and examined. The resizing algorithms are formulated into optimization problems basedon displacement participation factors from the unit load method instead of computationally intensive

sensitivity coefficients. Based on the comparison of three alternative algorithms using a verifying

example, an effective structural design model combined with the drift design method is proposed. Two

practical building framework examples such as a 20-storey frame shear-wall system and a 60-storey

frame shear-wall system with outrigger trusses are used to illustrate the effectiveness and practicality

of the proposed drift design model.

2. FORMULATION OF RESIZING ALGORITHMS

In a drift design of tall buildings based on resizing techniques, active members are selected and the

cross-sectional properties of the members are modified for effective control. In this paper, active

members are identified by the member displacement participation factors defined by each memberscontribution to the displacement. From the unit load method, the displacement of a structure can be

found by summing member displacement participation factors for all members in a structure:

mk1

k mk1

l0

NLk NUk

EAkdx

l0

VLk VUk

GAkdx

l0

MLk MUk

EIkdx

& '1

where and kare the displacement to be controlled and the member displacement participation factorof the kth member, respectively. Nk, Vk and Mkare the stress resultants in the kth member arising from

the actual load or the unit load. The stress resultants arising from the actual load and the unit load are

identified by the superscripts L and U, respectively. Eand G are the modulus of elasticity and the shear

modulus of elasticity, respectively. Ak and Ik are the cross-sectional area and moment of inertia of thekth member, respectively. Thus, the displacement of a frame shear-wall framework considered in this

research is be found by summing displacement participation factors for member in both steel-frame

and reinforced-concrete wall:

mk1

k msi1

i mcj1

j 2

36 H. S. PARK ET AL.

Copyright 2002 John Wiley & Sons, Ltd. Struct. Design Tall Build. 11, 3549 (2002)


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where i and j are displacement participation factors for the ith steel member and the jth reinforcedconcrete wall member, respectively; ms and mc represent the number of steel members and the number

of reinforced concrete members in a frame-wall system. In this paper, the amount of material to be

modified for drift design is determined by three resizing algorithms, labeled algorithms I, II and III,

respectively.

2.1. Algorithm I

With the assumption that the displacement participation factor of each member is inversely

proportional to the change of weight of the member, the optimization problem for algorithm I can be

given in the following form:

minimize msi1

ii

mcj1

jj

3

subject to

msi1

iWi 1

n

mcj1

jWj msi1

Wi 1

n

mcj1

Wj 4

where bi and bj are the modification factors applied to the ith steel member and the jth reinforced

concrete wall member, respectively; Wi and Wj are the weight of the ith steel member and the jth

reinforced concrete wall member, respectively; n is the ratio of the modulus of elasticity of steel to the

modulus of elasticity of concrete. In this form of optimization problem, the displacement of frame

shear wall system is minimized without changing the weight of a structure. The constrained

optimization problem in Equations (3) and (4) can be transformed into an unconstrained optimizationproblem by introducing the Lagrange multiplier:

minimize t msi1

ii

mcj1

jj

msi1

iWi Wi 1

n

mcj1

jWj Wj 4 5

5

where t and are the transformed objective function and the Lagrange multiplier, respectively.Taking derivatives of the transformed objective function with respect to bi, bj and , we find

@t

@i

i

2i Wi; i 1;. . .

; ms 6

@t@j

j2j

nWj; j 1; . . . mc 7

@t@

msi1

iWi Wi 1

n

mcj1

jWj Wj 8

STEEL-FRAME SHEAR-WALL SYSTEMS 37



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The modification factors can be found by setting Equations (6)(8) equal to zero:

i i

Wi

1=21

1=2; i 1; . . . ; ms 9

j njWj

1=2 1

1=2

; j 1; . . . ; mc 10

where

1

1=2

msi1

Wi 1

n

mcj1

Wj

2 3 msi1

iWi1=2

1

n

mcj1

njWj1=2

4 5111

According to equations (9) and (10), the displacement to be controlled will be minimized without

changing the total weight of the structure.

2.2. Algorithm II

In a steel-frame shear-wall system, the majority of lateral loads are carried by the shear walls in the

lower portion of the building and mostly by frame action in the top portion. In other words, changes in

thickness of shear walls in the lower and upper portion of a building depending on the displacement

participation factors from algorithm I can be quite substantial. Then, the substantial changes in

thickness of shear-wall members can cause a problem in physical limitation on fabrication. Therefore,

it is desirable to introduce upper and lower bounds on changes in thickness of shear-wall members as

side constraints. For production of an acceptable design, the fabrication constraints in terms of the

modification factors bj are given by

L j U; j 1; . . . ; mc 12

where bL and bU are, respectively, the lower and upper limits on the value of modification factors for

reinforced concrete wall elements.

In the formulation of the optimization problem for algorithm II, the side constraints in Equation (12)

are added to the objective and constraint functions stated in Equations (3) and (4).

2.3. Algorithm III

The drift design based on resizing algorithms is usually accomplished by carrying out a preliminary

strength design, followed by optimum distribution of cross-sectional properties of members based on

displacement participation factors. Also, the topologies or widths of shear walls are typically invariant

during the structural design process, especially at the final stage of the structural design process. Since

a change in the stiffness of a shear wall may produce an unacceptable design, only the cross-sectional

properties of steel members are considered in the distribution of material for minimization of the

displacement without changing the dimensions of shear walls in algorithm III. Note that the weight of

a shear wall is distributed by modifying the thickness of a shear wall in algorithms I and II. The




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optimization problem considered in algorithm III can be cast in the following form:

minimize msi1

ii

mcj1

j 13

subject to

msi1

iWi 1

n

mcj1

Wj msi1

Wi 1

n

mcj1

Wj 14

By transforming the constrained optimization problem into an unconstrained optimization problem

and setting the derivatives of the transformed objective function the modification factors for steel

members are given by

i i

Wi

1=2 msi1

Wi

2 3 msi1

iWi1=2

4 5115

According to Equation (15), the displacement to be controlled will be minimized without changing the

total weight of the structure.

Figure 1. The 30-storey frame shear-wall system




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3. COMPARISON OF ALGORITHMS

A 30-storey 5-bay planar frame shear-wall system is designed to compare the practical applicability

and efficiency of the proposed resizing algorithms I, II and III. The structure has 240 steel members

and 30 reinforced-concrete shear-wall members (Figure 1). All beams and columns for the frame are

rigidly connected, while the interior beams are simply connected to shear walls. Lateral loads due to

wind are computed according to the Standard Design Loads for Buildings (AIK, 2000). Lateral forces

are determined by assuming a basic wind speed of 30 m s1, exposure B and an importance factor of 1.The modulus of elasticity and the yield stress of steel are Es = 2058 GPa and Fy = 2352 MPa,respectively. The modulus of elasticity and the compressive strength of concrete are Ec = 206 GPa andFc' = 235 MPa, respectively. The commonly used design specification, allowable stress design (ASD),is used for preliminary structural member design before applying the algorithms. Column, beam and

wall sizes are shown in Table 1.

From the static analysis using the preliminary design, a lateral displacement of 057 m at the top ofthe structure, equal to 048% of the height of the structure, is estimated by the unit load method inEquation (2). Displacement participation components from columns, beams and shear walls are shown

in Figure 2. From the figure it is clear that the material of column members should be redistributed to

the beam and wall members since the magnitudes of the displacement participation factors of the

columns are much less than those of the beams and walls.

To minimize the lateral displacement of the system, the amount of material to be modified is

determined by the three algorithms presented in this paper. In algorithm II, the lower and upper limits

on the values of modification factors for wall elements are set to 0 5 and 15, respectively. Memberdisplacement participation factors after the modifications based on the three algorithms are shown in

Figure 2. Modified lateral displacements at the top of the structure based on algorithms I, II and III are

032 cm, 034 cm and 041 cm, respectively. There is little difference between the results of algorithmsI and II. However, modified dimensions of the shear wall at the top and bottom levels based on

algorithm I are 3 cm and 133 cm, respectively.

Since the fabrication constraints on dimensions of shear wall are not considered in algorithm I, the

substantial changes in thickness of shear-wall members produced an unacceptable design with sudden

changes in stiffness of walls. In algorithm III, unlike algorithms I and II, it does not account for the

redistribution of weight of walls. Therefore, the modified displacement at the top of the structure based

on algorithm III is much larger than those from algorithms I and II. Also, a careful look at the

distribution of the final dimensions of the members based on algorithm III indicates that a majority of

the column and beam members are found to be overstressed. Therefore, additional material required to

satisfy member strength requirements in algorithm III is relatively larger than those required in

algorithms I and II. Weights of columns, beams, walls and the structure before and after applying

algorithms are shown in Figure 3.

It is evident from this comparison that algorithms I and III are not effective for drift design of tall

Table 1. Preliminary strength member design for the 30-storey example (see Figure 1)

Floors Columns Beams Wall thickness (cm)

2530 H-350 350 12 19 H-496 199 9 14 201924 H-400 400 21 21 H-600 200 11 17 30

1318 H-498 432 45 70 H-600 200 11 17 40712 H-550 550 50 50 H-500 200 10 16 5016 H-700 700 70 70 H-346 174 6 9 60




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buildings. It can be concluded that algorithm II may be used for drift design of a frame shear-wall

system.

4. APPLICATION TO HIGH-RISE BUILDINGS

The drift design method with algorithm II selected on the basis of preceding comparisons is applied to

the optimal drift design of two frame shear-wall systems. The overall structural design model

combined with the drift design method is given in Figure 4. In the structural design model, the

commonly used design specifications allowable stress design is used for preliminary structural

member design before applying the algorithm. Two practical building framework examples such as a

20-storey frame shear-wall system and a 60-storey frame shear-wall system with outrigger trusses are

used to illustrate the effectiveness and practicality of the proposed drift design model.

Lateral loads due to wind are computed according to the Standard Design Loads for Buildings (AIK,2000). For both examples, lateral forces are determined by assuming a basic wind speed of 30 m s1,

exposure B and an importance factor of 1. As usual in the structural design of tall buildings, the drift at

the top of a building is limited to 02% of the height of the structure.

Figure 2. Displacement components for the 30-storey frame shear-wall system illustrated in Figure 1

Figure 3. Weight of components for the 30-storey frame shear-wall system illustrated in Figure 1




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4.1. The 20-storey frame shear wall system

This example is a 20-storey 5-bay frame shear-wall system (Figure 5). The structure has 160 steel

members and 20 reinforced-concrete shear-wall members. The target displacement considered in this

example is the drift at the top of the structure. The dimensions of walls and structural steel shapes

determined from preliminary strength design are shown in Table 2. The modulus of elasticity and yield

stress of steel are Es = 2058 GPa and Fy = 2352 MPa, respectively. The modulus of elasticity andcompressive strength of concrete are Ec = 206 GPa and Fc' = 235 MPa, respectively.

From the static analysis using the preliminary design, a lateral displacement of 2129 cm equal to027% of the height of the structure is estimated by the unit load method in Equation (2); finite elementanalysis gives a displacement of 2100 cm. Displacement participation components from columns,beams and walls are shown in Figure 6. From the figure it is clear that the material of columns should

be redistributed to beam and wall members. Based on the algorithm, a lateral displacement of

1796 cm equal to 022% of the height of the structure is estimated. The lateral displacement of thestructure is reduced by 1565% without changing the weight of the structure.

Figure 4. Structural design model for frame shear-wall systems




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For this example, additional material is required to satisfy drift requirement since the estimated drift

of 1796 cm exceeds the drift limit of 1600 cm equal to 02% of the height of the structure. Afteroverall drift and member strength control processes based on the drift design model, the weight of the

modified structure is increased by 86%. A lateral displacement of 1581 cm equal to 02% of theheight of the structure is estimated. Finite element analysis with the modified cross-sectional

properties gives a displacement of 1456 cm. The error in the displacement from the exact analysis andthe drift design model for this example is found to be 7 9%. The distributions of lateral displacement

through the height of the structure before and after applying the drift design model are shown in Figure7.

In addition to the displacement limit as a serviceability requirement, interstorey drift, defined as the

displacement of one storey level relative to the level above or below, must not exceed a certain limit.

From the static analysis with the preliminary design, the maximum interstorey drift of 142 cm equal to036% of the height of a typical storey is found at the 16th storey level. Based on the drift designmodel, a maximum interstorey drift of 101 cm equal to 025% of the height of a typical story is foundat the 16th storey level. The maximum interstorey drift is reduced by 2887%. The distributions ofinterstorey drift through the height of the structure before and after applying the drift design model are

shown in Figure 8.

Figure 5. The 20-storey frame shear-wall system

Table 2. Preliminary strength member design for the 20-storey example (see Figure 5)

Floors Columns Beams Wall thickness (cm)

1620 H-250 250 14 4 H-400 200 8 13 201115 H-300 300 15 15 H-400 200 8 13 30

610 H-350 350 12 19 H-400 200 8 13 4015 H-400 400 15 15 H-400 200 8 13 50




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4.2. A 60-storey frame shear wall system with outriggers

This example is a 60-storey hybrid structure with reinforced concrete walls, steel frames and outrigger

trusses at the 39th floor (Figures 9 and 10). The example, with a height of 1965 m, has three differentstorey heights, of 32, 45, and 42 m for the typical, technical and the lower two floors, respectively.With the base dimension of 426 m, the structure has a slenderness ratio of 461 in both the xand the ydirections. The outrigger trusses are cantilevered from the wall and hinged to the perimeter columns.

To avoid any gravity moments in the columns, the floor beams are simply connected to the columns.

The modulus of elasticity and yield stress of steel are Es = 2058 GPa and Fy = 3234 MPa,respectively. The modulus of elasticity and compressive strength of concrete are Fc = 235 GPa and

Figure 6. Displacement components for the 20-storey frame shear-wall system illustrated in Figure 5

Figure 7. Distributions of lateral displacement for the 20-storey frame shear-wall system illustrated in Figure 5




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Figure 8. Distributions of interstorey drift for the 20-storey frame shear-wall system illustrated in Figure 5

Figure 9. Typical floor plan for a 60-storey frame shear-wall system with outriggers; dimensions are in millimetres




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Fc' = 392 MPa, respectively. The example structure is primarily designed to be used for offices andhousing.

From the static analysis using the preliminary design, a lateral displacement of 3407 cm equal to017% of the height of the structure is estimated by the unit load method in Equation (2); finite elementanalysis gives a displacement of 3431 cm. Displacement participation components from columns,beams, braces and walls are shown in Figure 11. Based on the algorithm, a lateral displacement of

2223 cm equal to 011% of the height of the structure is estimated. The lateral displacement of thestructure is reduced by 3475% without changing the weight of the structure.

For this example, no additional material is required to satisfy drift requirement since the estimated

drift of 2223 cm does not exceed the drift limit of 40 0 cm equal to 02% of the height of the structure.After the overall member strength control process based on the drift design model, the weight of the

modified structure is increased by 003%. Based on the drift design model, a lateral displacement of2059 cm is estimated. Finite element analysis with the modified cross-sectional properties gives adisplacement of 2115 cm. The error in the displacement from the exact analysis and the drift designmodel for this example is found to be 265%. The distributions of lateral displacement through theheight of the structure before and after applying the drift design model are shown in Figure 12.

From the static analysis with the preliminary design, the maximum interstorey drift of 074 cm equalto 023% of the height of a typical story is found at the 20th storey level. Based on the drift designmodel, a maximum interstorey drift of 049 cm equal to 015% of the height of a typical story is found

Figure 10. Section of the 60-storey frame shear-wall system with outriggers illustrated in Figure 9, dimensions arein millimetres




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at the 25th storey level. The maximum interstorey drift is reduced by 3378%. The distributions ofinterstorey drift through the height of the structure before and after applying the drift design model are

shown in Figure 13.

5. CONCLUSIONS

Three resizing algorithms based on displacement participation factors for the drift design of tall

buildings has been proposed and evaluated. The algorithms were derived by formulating the drift

design process into an optimization problem. During the drift design process, the active members were

Figure 11. Displacement components for the 60-storey frame shear-wall system with outriggers illustrated inFigures 9 and 10

Figure 12. Distributions of lateral displacement for the 60-storey frame shear-wall system with outriggersillustrated in Figures 9 and 10




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identified by computing the displacement participation factors from the unit load method instead of

calculating computationally intensive sensitivity coefficients.

An efficient design model based on the resizing algorithm selected on the basis of the comparisons

has been presented and applied to the drift design of three steel-frame shear-wall systems for high-rise

buildings. As demonstrated in distributions of the displacements through the height of example

structures, the drift and interstorey drift of frame shear-wall systems for high-rise buildings can be

effectively designed by the drift design model without expensive computational cost. For the 60-storey

hybrid structure with reinforced concrete walls, steel frames and outrigger trusses, the drift of

3407 cm at the top of the structure and the maximum interstorey drift of 074 cm are reduced to2115 cm and 049 cm, respectively.

ACKNOWLEDGEMENT

This material is based on work sponsored by Ministry of Construction and Transportation of Korea

under grant R&D97-0002, which is gratefully acknowledged.

REFERENCES

AIK. 2000. Standard Design Loads for Buildings, Architectural Institute of Korea, Seoul, Korea.

Baker WF. 1990. Sizing techniques for lateral systems in multi-story steel buildings. Proceedings of 4th WorldCongress on Tall Building: 2000 and Beyond, Council on Tall Buildings and Urban Habitat (CTBUH), HongKong.

Chan CM, Grierson DE. 1993. An efficient resizing technique for the design of tall buildings subject to multipledrift constraints. The Structural Design of Tall Buildings, 2(1): 1732.

Chan CM, Grierson DE, Sherbourne AN. 1995. Automatic optimal design of tall steel building frameworks.Journal of Structural Engineering, ASCE, 121(5): 838847.

Charney FA. 1991. The use of displacement participation factors in the optimization of drift controlled buildings.

Figure 13. Distributions of interstorey drift for the 60-storey frame shear-wall system with outriggers illustrated inFigures 9 and 10




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Proceedings of 2nd Conference on Tall Buildings in Seismic Regions, 55th Regional Conference , Los Angeles,CA.

Park HS, Adeli H. 1997. Data parallel neural dynamics model for integrated design of large steel structures.Journal of Structural Engineering, ASCE, 123(7): 880888.

Park HS, Ahn SA. 1998. Resizing methods for drift control of tall steel structures. 5th Pacific Structural SteelConference, Techno-Press: Seoul, Korea.

Park HS, Park CL. 1997. Drift control of high-rise buildings with unit load method. The Structural Design of TallBuildings, 6(3): 2335.

Rao SS. 1996. Engineering OptimizationTheory and Practice. John Wiley, New York.Wada A. 1991. Drift control method for structural design of tall buildings. Proceedings of 2nd Conference on Tall

Buildings in Seismic Regions, 55th Regional Conference, Los Angeles, CA.



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