Keywords: optimal design, tall buildings, lateral load resistant system, lateral drift control, lateral-stiffness influence matrix, sensitivity analysis, resizing technique.

The control of lateral drifts such as top lateral drift and interstory drift is an important problem not only for the serviceability but also for the safety in the design of tall buildings. Many design software now provide design features to satisfy member strength requirements according to design codes. However, very little work has been done to consider the more difficult and dominating problem of satisfying lateral drift (stiffness) criteria for tall building.

So far, the general optimal design approaches[1,2,3] of tall building subject to lateral drifts usually consider all degrees of freedom of overall structure, and resize each member under the least-weight design. But, as such structures generally consist of thousands of members, it is very difficult and complicated to resize members so that the lateral drift constraints are satisfied. So, some structural engineers often perform the control of lateral drifts by a trial and error approach based on their experience and repetitious analysis.

Therefore, this study presents the effective optimal resizing technique for tall building subject to lateral drift constraints by considering the characteristics of lateral load resistant system and the rigid diaphragm effect of slab according to each story level of tall building structure.

To this end, it can be assumed that lateral load resistant system such as bracing or shear wall resists mainly lateral loads, and overall stiffness matrix of structure can be reduced to the condensed lateral stiffness matrix by substructuring[4,5] and static condensation technique[6] to have only three degrees of freedom per each floor based on the rigid diaphragm effect of slab.

We can introduced the effective sensitivity analysis algorithm for the condenced matrix with design variable (e.g. lateral stiffness coefficient) and consider the minimization of Lagrangian function which is composed of weight function and drift constraints. Then, we can obtain the optimal required stiffness of each story through the computer process, which also gives the optimal required weight and enables us to resize members of each story.

Several practical examples of tall buildings with bracing or shear wall are presented to illustrate the features of the design method. Wind loads are considered as equivalent static loads applied horizontally on the structure according to the provisions of most current building codes. Top lateral drift and interstory drift are given as drift constraints. While there are no generally established drift criteria for tall building design, the allowable value for overall building drift or interstory drift is usually specified as some ratio of the building or story height (e.g. 1/200 1/600). In conclusion, this study provides an effective means to find the optimal lateral stiffness and weight for each story of a tall building to satisfy lateral drift constraints. Moreover, this enables structural engineers to evaluate easily the overall behavior of tall building structure with lateral load resistant systems and gives the flexibility in resizing members based on the control of the required stiffness of each story.

1

Grierson, D.E., Chan, C.M., "An optimality criteria design method for tall steel buildings", Advances in Engieering Software 16, 119-125, 1993. doi:10.1016/0965-9978(93)90057-Z

2

Karihaloo, B.L., Kanagasundaram, S., "Optimal structures under strength and stiffness constraints", Computer and Structure, 28, 641-661 doi:10.1016/0045-7949(88)90009-0

3

Velivasakis, E., DeScenza, R., "Design optimisation of lateral load resisting frameworks", Proc. 8-th ASCE Conf. On Electric Computation, 130-143

4

Maison, B.F., and Neuss, C.F., "Super-ETABS an enhanced version of the ETABS Program", U.C.Berkely CA, 1985

5

Wilson, E.L., J.P.Holling and H.H.Dovey, "Three dimensional analysis of building systems", 1995

6

Bathe, K.J., "Finite element procedures in engineering analysis", Englewood Cliffs, NJ: Prentice-Hall, 1982

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