Exact closed-form equations for internal forces functions of bridge-type structures

Influence lines and internal forces functions are vital tools for designing and monitoring engineering structures. This research explored a static method to derive exact closed-form equations for internal forces functions of bridge-type structures, continuous beams, and bridge frames, considering the bending flexibility. For this aim, first, we achieved member-end moment functions by applying the moment-rotation relationships in conjunction with the rotation propagation method. Then, substituting these functions into the static equilibrium equations provided the desired functions in terms of both the unit load and intended cross-section positions all over the structure, subjected to concentrated loads. Finally, the authors solved three illustrative examples to clarify the dominance of their suggested method for constructing both influence line and internal forces diagrams of statically indeterminate structures.