A Practical Method to Determine Influence Surfaces using Commercial Software

Structures are subject to dead load and live load; the latter refers to loads which would act on various possible locations. As such, it is very often necessary for practicing structural engineers to determine how stresses vary due to live loads acting on different locations of the structure. For simple structures and simple loadings, engineers could assign live loads to locations that would generate the most critical stresses at the corresponding design locations, based on experience or simple design charts or tables. For complicated structures, however, the determination of such critical stresses are not obvious, and it would be necessary for engineers to look at the influence lines and/or influence surfaces at the design locations. Such influence lines/surfaces could be obtained automatically only for some simple structures using commercial software. For more complicated ones, engineers need to generate a lot of computing results and post-process the computing results using tools like Excel. In this paper, a simple yet practical and direct method is presented for the generation of influence surfaces or influence lines for linear elastic structures using commercial software. The principle behind is based on the classical reciprocal theorem and the method does not require any additional coding or post-processing of results using data processing tools like Excel. To determine the influence surfaces, one only needs to discretize the structure into a fine finite element mesh using any commercial software. The stiffness matrix of a typical element is then determined using the software. The “stiffness terms” that correspond to the interested stress component are then treated as generalized loads and applied directly to the finite element mesh. The contour of the corresponding displacement component, which could easily generated by most commercial software, can be shown to be identical (except the unit) to the influence surface of the interested stress component. A number of linear elastic structures like frames, box-girder bridges, pipes and plates, plane stress shear wall problems and three-dimensional elastic problem will be demonstrated.