Indirect Müller-Breslau Principle for Construction of Influence Lines and Application to Structural Health Monitoring Algorithm

Construction of influence line is an important issue for the analysis of structures subjected to live and moving loads. Müller-Breslau Principle is one of the most effective methods used for construction of influence lines. It relies on the elastic curve of a structure due to unit displacement imposed on the ‘released’ form of the structure obtained by releasing the degree-of-freedom corresponding to the desired internal force. For large frame structures, the use of general finite element codes is essential for constructing the influence lines. The analysis of the released version of the structure due to an imposed unit displacement however, cannot be implemented conveniently in the commercially available finite element software packages. This paper presents an indirect method proposed to overcome this difficulty. In this approach, the released structure is analyzed by a unit moment or force couple instead of unit relative displacement. The resulting influence line coefficients are then multiplied by a scalar which happens to be the inverse of relative displacement obtained from the analysis due to a unit moment or force couple. The proposed methodology has the potential to be used for structural health monitoring purposes. By constructing the influence line coefficients for bending moments due to moving unit relative rotation across the structural system and storing the bending moment values in a database for all potential plastic moment locations, the bending moment distribution of the structure can be made readily available for the health monitoring algorithm at any time. A numerical example is provided illustrating the application of the proposed methodology.