Finite element stability analysis of thin-walled steel structures

Recent applications in the use of light gauge steel members have been concerned with developing large scale systems built entirely from cold-formed steel members. An explicit analysis of such structures is complicated by the different phenomena that the structure may be prone to during loading. In particular, elastic buckling phenomena is an important consideration in the design of such structures since the load at which buckling occurs often provides a close upper bound to the carrying capacity of the structure. The first part of this two-part thesis (Part I, Chaptersl-8) has been devoted to general methods of analysis of the torsional-flexural buckling of thin-walled structures. A review of previous investigations and the available methods of solution is presented. A general finite element formulation of the torsional-flexural buckling of thin-walled structures has been derived. The resulting elastic geometric matrix can be used to analyse structures with monosymmetrical members. It also includes the effect of sectorial-monosymmetry for cross-sections without any axis of symmetry. A general transformation matrix has been developed to allow for the application of the finite element method to the three-dimensional elastic stability analysis of space and portal frames. The validity and accuracy of the new finite element formulation have been checked by analysing a number of different elastic lateral buckling problems for which exact or highly accurate solutions by other techniques are available. An experimental program was carried out on simply supported cold-formed steel z-beams. The first part of this program was undertaken to check the validity of the finite element calculations of the bimoments caused by nonuniform torsion. The second part was devoted to elastic lateral buckling of z-beams under combined bending and torsion. The second part of this thesis (Part II, Chapter 9) deals with the analysis of hipped roof structures with corrugated steel roof sheeting. A simple theoretical model has been suggested. The model has been used to perform an elastic linear analysis of the behaviour of two types of the hipped roof structures. The theoretical results are compared with previous experimental results for these two structures.

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