Keywords: optimum design, sway frame structures, semi-rigid connections, non-linear analysis, Eurocode 3.

This paper presents a numerical method, based on mathematical programming techniques, for the optimum design of elastic planar steel frames. The design algorithm provides the optimum section for each member of the structure and the optimum stiffness with respect to rotation of the semi-rigid connections between members. In the analysis, second order effects are taken into account for the presence of large axial loads (the P- effect) and for the presence of large displacements (the P- effect) and in addition, for the non-linear behaviour of the semi-rigid connections between the columns and beams. Designing a structure permits us to demonstrate the viability of the method, as well as the influence of the models of structural behaviour considered on the results obtained.

Traditional design methods for structures use two models to describe pinned and fully rigid connections. These approaches have the advantage of simplifying both the analysis and the design; however, they do not reflect the real behaviour of certain structures. The semi-rigid connections, accounting for the behaviour of real connections, transmit part of the bending moments and present a rotation capacity which contributes to the displacements of the whole structure. The increase in lateral sways due to the presence of non-linear semi-rigid connections suggests a need to consider nonlinearities geometrically at the same time, since their effects can be linked.

Extensive work has been carried out to define connection behaviour. Several models have been proposed to define this. The simplest are linear models, the most complex are exponential and power models. The design codes ASCI-LRFD, BS 5950 and Eurocode 3 allow semi-rigid connections to be considered in the analysis but they do not include specific guidelines for their design. In recent years, research work has been done to solve the design problem of steel structures with semi-rigid connections [1,2,3,4,5,6,7]. The procedures of Xu-Grierson [1] and Simões [3] take into consideration the combined cost of members and connections with design variables related to connection stiffnesses. However, a linear behaviour is considered for semi-rigid connections. The procedures of Xu [5], Kameshki and Saka [6] and Hayalioglu and Degertekin [7] produce optimum designs that take into account non-linear semi-rigid connections. Different types of connections are considered with a polynomial Frye-Morris model which generates realistic designs. Nevertheless, the behaviour of the connections is not taken into consideration as a design variable, therefore these methods cannot produce global optimum designs.

The applying of the minimum cost design method to the proposed example shows that the Eurocode 3 procedure that takes into consideration second-order effects with both linear analysis and factored horizontal loads (L), is a little conservative for multi-storey frames with load and stiffness affinity over all storeys. The differences observed between the L and GNL (non-linear analysis with high axial loads and large displacements) designs, in terms of the cost and weight of elements are small. Furthermore, the example shows that the non-linear semi-rigid connection undergoes an important stiffness reduction upon loading, causing, as a consequence, an increase in beam deflections, an important redistribution of internal member forces but, mainly, an increase in lateral sway displacements (the P- effect). Therefore, high optimum values for the initial rotational stiffness of semi-rigid connections in CGNL (non-linear analysis with high axial loads, large displacements and non-linear semi-rigid connections) design and small weight differences between L, GNL and CGNL designs are encountered. This situation produces more expensive CGNL designs than L and GNL ones. These results suggest simultaneously considering both non-linear semi-rigid connections and geometric nonlinearities in the analysis, since their effects are linked.

1

L. Xu, D.E. Grierson, "Computer-Automated Design of Semirigid Steel Frameworks", J. Struct. Eng., ASCE, 119(6), 1740-1760, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:6(1740)

2

T.H. Almusallam, "Effect of Connection Flexibility on the Optimum Design of Steel Frames", in "Developments in Computational Techniques for Civil Engineering", B.H.V. Topping (editor), Civil-Comp Press, Edinburgh, UK, 129-135, 1995. doi:10.4203/ccp.32.6.3

3

L.M.C. Simões, "Optimization of Frames with Semi-Rigid Connections", Comp. & Struc., 60(4), 531-539, 1996. doi:10.1016/0045-7949(95)00427-0

4

B.S. Dhillon, J.W. O'Malley, "Interactive Design of Semi-rigid Steel Frames". J. Struct. Eng., ASCE, 125(5), 556-564, 1999. doi:10.1061/(ASCE)0733-9445(1999)125:5(556)

5

L. Xu, "Design Optimization of Semi-Rigid Steel Frames", in "Practical Analysis for Semi-Rigid Frame Design", W.F. Chen (editor), World Scientific, Singapore, 206-260, 2000.

6

E.S. Kameshki, M.P. Saka, "Genetic Algorithm Based Optimum Design of Nonlinear Planar Steel Frames with Various Semi-Rigid Connections", J. Constr. Steel Res., 59, 109-134, 2003. doi:10.1016/S0143-974X(02)00021-4

7

M.S. Hayalioglu, S.O. Degertekin, "Minimum Cost Design of Steel Frames with Semi-Rigid Connections and Column Bases via Genetic Optimization", Comp. & Struc., 83, 1849-1863, 2005. doi:10.1016/j.compstruc.2005.02.009

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