Investigating the influence of the axial forces on the plastic analysis of two dimensional frames

Two dimensional frames, having members which are made of ideally elastic and perfectly plastic material, are subjected to incrementally increasing loads so that plastic hinges are assumed to form at member ends and as a result of this a collapse mechanism is developed. Each plastic hinge is accompanied by an additional rotational freedom of the frame. For this reason a frame model is used, where after each plastic hinge formation the dimension of the stiffness matrix is increased by one and sequential elastic analyses are carried out between the two consecutive plastic hinges, in order to perform the elastic-plastic analysis. The last plastic hinge formed in the frame, that makes the stiffness matrix singular, causes the structural collapse so that the collapse load is calculated. The contribution of the bending moment and the axial force are assumed to be important in the formation of the plastic hinges whereas the contribution of the shearing force is assumed to be negligible. The bending moment and the axial force that act at the section, where a plastic hinge is formed, give a point on the assumed plastic flow surface such that this point either plastically flows on this surface according to the normality rule, or, it elastically unloads and moves towards inside the design domain. As the load multiplier increases the plastic rotation angle moduli at plastic hinges also increase. Instead of increasing, if it is decreasing, then, this indicates the elastic unloading of the plastic hinge. By using the developed computer programme it is possible to analyse the two dimensional frames according to different plastic flow rules. In addition to this, the plastic hinge locations are also determined accurately on the members which carry uniformly distributed loads. Fifteen two dimensional sample frames, which are taken from various references, are analysed by the developed computer programme and the collapse load factors are calculated, which are also found to be very close to the load factors given in the references. However, in future research, in order to improve the accuracy of the calculated frame behaviour, it is recommended that the elastic-plastic analysis of the frames should be performed as nonlinear analysis.