Secant stiffnesses for ultimate analysis of strain hardening indeterminate RC structures

This paper presents the iterative use of secant EI distributions in stiffness analysis to determine ultimate load factors for statically indeterminate concrete structures which strain harden at critical sections. The computational procedure is novel in that it directly seeks the failure state without considering pre-ultimate behaviour, and also in that it permits clear insight into the important effect of the EI distribution on moments at failure. The procedure iterates until the output moments–in addition to satisfying capacity–give an EI distribution which returns those very moments on input to the stiffness analysis with the same loads. A flowchart for iterating to these conditions is given, with illustrative examples. Then, removal of higher-order terms from nonlinear EI distributions is shown algebraically and by stiffness analysis to compromise neither predictive accuracy nor analysis speed in specific cases. Further algebraic analysis of an encastered span with two section stiffnesses shows that, for elastic (e.g. over-reinforced) failure, a unique coincidence exists between the moment diagram and the EI distribution when turning values of moment occur for any given ratio of the two section stiffnesses. It is concluded that EI distributions are key to assessing failure states of RC structures.