Keywords: non-linear, structural optimization, semi-rigid connection, collapse load, genetic algorithm.

Tall steel frames are commonly used as structural systems in modern buildings due to their flexibility of adaptation to complicated architectural requirements. The availability of advanced analysis techniques and modern optimum structural design methods made it possible to achieve the maximum possible reduction in the cost of structure by accounting for the cost of semi-rigid connections in addition to the member costs in the frame while observing the design code limitations. Structural steel members are slender in nature. Under the gravity loads, the lateral displacement of the frame makes it necessary to consider P-delta effects, which yields to use second-order analysis. Furthermore, inspite of the fact that the beam-to-column connections are idealized as pin or rigid in the modeling of the frame while in reality they are semi-rigid. This fact further contributes to the necessity of second order analysis so that stability consideration of the frame can be studied, when a frame becomes unstable under a system of forces it often assumes a configuration, which deviates noticeably from its unreformed configuration.

The present study comes in two phases. In the first phase a genetic algorithm based optimum design method is developed for unbraced non-linear steel frames with semi- rigid beam-to-column connections. Lateral displacements in such frames are much larger than those for rigid frames due to joint flexibility, which necessitate including the geometric non-linearity in the analysis and design. During the optimum design cycles, each connection between beams and columns is designed according to its selected type. Bolt size and other geometrical parameters are determined. These are then used in the standardization functions of the Frye-Morris polynomials, which are adopted to model the semi-rigid connections. The second phase of the study is the computation of collapse load of the optimum steel frames carrying out second order plastic hinge analysis described in [1].

In this study, collapse load of optimally designed unbraced steel frames with flexible connections is investigated. For this purpose, first multistorey steel frames with a typical semi-rigid connection such as top and seat angle with double web cleat are optimally designed by using genetic algorithm based optimum design method. This method accounts for the serviceability and strength constraint as specified in BS 5950 (1990). It uses nonlinear imperical model to include the moment-rotation relation of beam-to-column connections. Furthermore, it also takes into account P-delta effects in the analysis of unbraced frame. Later collapse loads of optimal steel frames are calculated using direct incremental-load technique for both with semi-rigid connections and with rigid connections. The entire load-deformation curve is traced and compared for both frames.

Two examples have been considered in this study to supply an ample view of how the two nonlinearity, the connection flexibility and frame geometric non-linearity, effect the optimum design of unbraced steel frames and their load carrying capacity.

It is noticed from the design examples that when the effect of connection flexibility and geometric nonlinearly are accounted for in optimum design of unbraced steel frame higher load carrying capacity was obtained. This fact works as an alert to the structural designer of steel structures, endorsing the essentiality of inclusion of the above two nonlinearly effects in their design, in order to achieve a much better design.

It has been shown that the flexibly connected frames are heavier than that of rigidly connected ones when effect is accounted for in the analysis of such frames.

As a result, the member costs of unbraced semi-rigid frames exceed that of rigid frame. But the simplicity of the semi-rigid connection details could yield a reduction in the overall cost of the frame.

Further research developments will be devoted to upgrading the program to include the combined cost of members and connections of frames.

1

Chen, T-Y, and Chen, C-J., "Improvement of Simple Genetic Algorithm in Structural Design", Int. Journal for Num. Methods in Engineering, Vol. 40, 1323-1334, 1997. doi:10.1002/(SICI)1097-0207(19970415)40:7<1323::AID-NME117>3.0.CO;2-T

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