Spatial Grid Model with Diagonal Beam Elements Based on the Optimization of Spatial Mechanical Behaviors

A novel spatial grid model with diagonal beam elements is proposed to analyze the spatial mechanical behaviors of concrete box-section girders at the elastic linear state. The establishment of the model is based on an optimization problem: the objective functions are the absolute relative differences between the deformations from the proposed model and the actual plate under three basic types of loads including in-plane axial compression, in-plane shear, and out-of-plane bending; the variable parameters of the functions are the properties of vertical and horizontal beam and diagonal beam elements in the proposed model; the objective for the optimization is to minimize the objective functions. By solving the optimization problem, the spatial grid model with diagonal beam elements based on the optimization of spatial mechanical behaviors is established. The validity of the proposed model is illustrated with a cantilever beam under a concentrated load and a simply supported box-section girder with uniform loads as case examples. The results show that the spatial grid model with diagonal beam elements is not limited by the plane section hypothesis and is capable of accurately predicting the bending stiffness and in-plane shear stiffness. The results also reveal that the proposed model can yield deformation results consistent with the solution based on the mechanics of materials considering shear deformations and with the results from solid element models.