Effect of partial plasticity on collapse load of rigid jointed prames

In recent years, due to rapid developments in computers, complicatedengineering problems can be easily and quickly solved. In structuralengineering, the stiffness method has become very powerful in the analysisof structures by the computer. Many computer programs have been writtento solve structures by elastic, elastic-plastic or plastic analysis. Oneof these programs was written by LAU in November 1980, based on thestiffness method, which follows the procedure described by ALLEN & BULSON(reference 4.).The program by LAU is able to solve structures by elastic, elastic-plastic or plastic analysis - it ignores the effect of partial plasticitywithin the members and assumes the moment-curvature relationship is linearup to the formation of plastic hinges. The exact moment-curvaturerelationship is linear up to the yield moment, and then it becomes non-linear, due to partial plasticity effects, up to plastic hinge formation.It has been thought that the effect of partial plasticity at the ends ofthe member reduces its stiffness and then increases the forces andmoments produced by the applied load.at a smaller load factor.This leads to structure collapseIn the project reported ~n this thesis, a computer program has beendeveloped from LAU’s program to take account of the effect of partialplasticity in the member. A new theory has been derived (see Chapter 1),based on the COLUMN ANALOGY HETHOD to incorporate the effect of part i a lplasticity. The new program calculates exactly the collapse load factorand load factors at which hinges form, because it has the ability tochange the load factor increment as required.It should be pointed out now that the effect of partial plasticityhas been taken into account in the plastic analysis, and not in the elastic-plastic analysis. And it is hoped that the next step is a development ofthe program to take into account the effect of partial plasticity in theelastic-plastic analysis.