The $\varvec{nsm(x)}$ Diagrams

Abstract

The structures in this book are composed of beams and bars (and cables). These are long and relatively slender line elements which have a longitudinal axis passing through the centers of area of the cross-sections. The coordinate along the axis is x. On both sides of virtual sections perpendicular to the axis we find equal and opposite internal forces: normal forces n acting along the axis, shear forces s perpendicular to the axis (along the faces of the section), and equal and opposite couples, the bending moments m. Calculating these internal forces throughout the structure is the main purpose of structural analysis. This chapter shows how to compute and present the internal forces along any line element if the external (applied) forces are all known. The internal forces are functions of x, leading to the normal force distribution n(x), the shear force distribution s(x) and the bending moment distribution m(x) or diagrams, also called nsm(x) or n(x) for short. These distributions are drawn along the elements in a traditional manner, and we will show how to compute and draw these distributions or diagrams.