Keywords: static procedures, setback buildings, nonlinear dynamic procedure, drift, machine learning, polynomial regression, root mean square error.

The exact evaluation of seismic demands during earthquakes is one of the most important concerns in civil engineering. There are two different methods for this issue, a nonlinear static procedure (NSP) and a nonlinear dynamic procedure (NDP). In this regard the NSP method is more common because of its simplicity and speed. NSP is deficient in structures where the response is significantly affected by higher modes such as tall or irregular buildings. Buildings with eccentric setbacks are a class of structures with both irregularities in plan and elevation. In this study a number of three-dimensional buildings with eccentric setbacks in one and two directions are considered. These models are subjected to nine ordinary earthquake ground motions. All these nine storey buildings are comprised special steel moment frames. Different shapes of eccentric setback are created in order to consider a wide range of rational cases. The accuracy of the NSP is estimated in comparison with a rigorous NDP. It is observed that in the majority of structures conventional NSPs estimate the target displacement with good accuracy but in the structures where the load does not match the displaced shape the proposed methods from FEMA440 [1] underestimate the target displacement. By modification of the relationship between spectral acceleration and base shear, the displacements in upper storeys can be calculated very well albeit with overestimation [2]. But the seismic demands in lower storeys are calculated with underestimation. Obviously, it is because of the pattern of lateral load which conforms to the modal distribution. In order to investigate the effect of the lateral load pattern, the invariant load pattern is also used. It is observed that although the results in lower storeys are improved, drift of upper storeys in all buildings is underestimated. Underestimation is more when setbacks are created in two bays or in two directions.

This underestimation is an inherent weak point of NSP. So it is interesting to use a method that can predict the error of NSP without using NDP. In this regard a reliable method, based on artificial intelligence is proposed. The method is defined as a regression machine learning procedure [3] for predicting the error in the storey drift which is the difference between the NSP and the NDP. The input vector describes the main periods and irregularities in the structure [2,4]. The learning process is executed for three special cases and the root mean square error (RMSE) is used for controlling the accuracy of the method. The results show that machine learning tools are able to find an appropriate model for the present problem. It is also recommended that the data set is enlarged or that the number of input variables is increased to obtain a more accurate learning model.

1

Federal Emergency Management Agency (FEMA), "Improvement of nonlinear static seismic analysis procedures", Report FEMA440, Washington (DC), 2005.

2

A. Emadi, H. Shakib, A. Aghakouchak, "Seismic Evaluation of steel Setback Buildings", 2010. (submitted)

3

E. Alpaydin, "Introduction to machine learning", MIT press, London, 2004.

4

F.M. Mazzolani, V. Piluso, "Theory and design of seismic resistant steel frames", FN & SPON, an Imprint of Chapman & Hall, 1996.

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