Slop-Moment Matrix Method and General Deflection Equation

Abstract

In this paper, Slop-Moment matrix method and general deflection equation will be presented, Slop-Moment matrix method is a method for structural analysis by which the support moments can be found for structural elements (1-d) like beams, one-way slabs, bridge girder,…etc. it enables the engineers to conduct structural analysis with very wide options, There are no limitations on number of spans, number and type of loads, end support conditions, section property or material and even it handles the support settlement for any support, these matrices are derived based on the boundary conditions for the supports mainly the continuity for interior supports, the main advantage of this method is the size of solving matrix is small and fixed which depends on number of spans only besides of number and type of loadings, giving new smart techniques in programming and hand calculation.
General deflection equation is derived to give the structural engineers the simplest and exact tool for deflection calculation, where the deflection can be calculated at any point in any span with knowing the moment values only.