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Currently, seismic design provisions of most building codes are based on strength or force (base shear) considerations. These building codes are generally regarding the seismic effects as equivalent static forces with a height wise distribution which is consistent with the first vibration mode shape. However, the design basis is being shifted from strength to deformation in modern performance-based design codes. This paper presents a practical method for optimization of steel moment resisting frames (SMRF), based on the concept of uniform deformation theory. This theory is based on this concept that the structural weight of a lateral load resisting system with uniformly distributed ductility demand-to-capacity ratio (or any other damage index) will be minimal compared to the weight of an ordinary designed system in which deformation is not distributed uniformly and just some of structural elements have reached their ultimate states. The state of uniform deformation can be achieved by gradually shifting inefficient material from strong parts of the structure to the weak areas. In the first part of this paper, the uniform deformation theory is implemented on 3, 5 and 10 story moment resisting frames subjected to 12 earthquake records representing the design spectrum of ASCE/SEI 7-10. This includes design of an initial structure according to conventional elastic design procedures, followed by an iterative assessment process using nonlinear dynamic analyses till the state of uniform deformation is achieved. Results show that the application of uniform deformation theory leads to a structure with a rather uniform inter-story drift distribution. Subsequently, the optimum strength-distribution patterns corresponding to these excitations are determined, and compared to four other loading patterns. Since the optimized frames have uniform distribution of deformation, they undergo less damage in comparison with code-based designed structures. Also, as the shear strength of each story is in proportion to the weight of that story, the optimized structures have minimum structural weight. For further investigation, the 10 story SMRF is redesigned using four existing load patterns and subjected to 12 earthquake excitations. Then a comparison is made between maximum beam rotations of each model and those belonging to the optimized one which revealed that the optimized SMRF behaves generally better than those designed by other loading patterns. Also, it is found that for none of the conventionally designed SMRFs, beam rotation demand is distributed uniformly. In other words, for all of the considered load patterns the maximum rotation of the beams in some stories exceeds the rotation associated with the performance level. Finally, assuming that the probability distribution of maximum rotations under different excitations follows a lognormal distribution, the probability of exceeding the allowable rotation associated with the LS performance level is calculated for different load patterns and compared to each other. Based on this comparison, the efficiency of each loading pattern is evaluated and the best one is determined. Application of optimization method presented in this paper avoids the concentration of deformation and damage in just one story and makes each story deformation and damage uniform over the height of the structure.

Keywords: performance-based design, Structural optimization, Uniform Deformation Theory, Seismic Loading Pattern, nonlinear dynamic analysis

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