Time Analysis of Partially Prestressed Beam Subjected to Changing Loads

An analytical procedure is presented for the time‐dependent analysis of a partially prestressed concrete cross section subjected to an increasing load history, The load history is such that cracking of the cross section occurs under a moment increment that is applied after a period of sustained bending. The age‐adjusted effective modulus method is used to include the time‐dependent effects of creep and shrinkage in the concrete both before and after cracking. The analysis is divided into several stages and attention is focussed on the solution of the nonlinear problem created by cracking at some time after first loading. Solution of the nonlinear equations to find the depth of cracking on the cross section and the stresses and strains in both the concrete and the steel is achieved using an iterative Newton‐Raphson procedure. The effect of cracking on the stress and strain distributions determined prior to cracking are examined and the inherent difficulties associated with the ageing of concrete are treated in a mathematically tractable solution procedure. Numerical results are included to demonstrate the effectiveness of the proposed method.