Analytical solutions for composite beams with slip, shear-lag and time-dependent effects

Abstract

In this paper, a new solution method is proposed to solve the one-dimensional analytical model of composite beams which is able to simulate the effects of interface slippage, and shear-lag and time-dependent effects. This method involves a solution of space and time variables. To enhance the accuracy of the solution, a space-exact analytical solution rather than the widely used space-approximate numerical solutions is adopted in the model. Furthermore, a step-by-step method which excels the method with single-step algebraic equations is used for the prediction of the time variables. A recursion method is then developed to solve the governing differential equation systems at each time step. The effectiveness and accuracy of the proposed method are validated by using the available test results of instantaneous and long-term tests on composite beams. The validated solution method is applied to time-dependent solutions, including vertical deflection, interface slippage, warping displacement due to shear, and stresses. The results show that concrete shrinkage and creep effects have a significant influence on the structural response of the beams. The characteristics of the shear-lag effects of concrete slabs are closely related to the placement of the prestressing wires. Finally, the solutions of the model that uses a general step-by-step method and that which uses single-step algebraic equations are compared. It is found that the latter can well predict the time-dependent behaviors of composite beams, except for the warping displacement due to shear of the simply supported beam.