Zero Force Members

Truss members can have zero internal forces depending on how the loads are applied on the truss. Therefore, identifying these zero force members and eliminating them can simplify truss analysis. There are three main cases where zero force members exist. Case 1: Pin-Pin When members are attached to pin supports AND no applied force is […]

Static Determinacy

When all the forces in a structure can be determined directly from equilibrium equations, the structure is considered statically determinate. In contrast, when all the forces in a structure cannot be determined directly from equilibrium equations, the structure is considered statically indeterminate. In the latter case, there are more unknown forces than available equilibrium equations, and […]

Mohr’s Circle

Intro and Derivation Mohr’s circle is a geometric representation of plane (2D) stress transformation and allows us to quickly visualize how the normal (σ) and shear (τ) stress components change as their plane changes orientation. German civil engineer Otto Mohr developed this method from the good ol’ stress transformation equations. Recall:If we remove θ by squaring both […]

Axial, Shear & Moment Diagrams

Axial, shear, and bending moment diagrams (AFD, SFD, and BMD) show the internal forces and moments along a structural member. They help determine the material, size, and type of a member given a set of loads it can support without structural failure. Keeping a consistent sign convention is extremely important! We are going to define the positive […]

Stress & Strain

Definitions Stress is defined as force per unit cross-sectional area. Some common measurements of stress include Pa (pascal) and psi (pounds per square inch). There are two types of stress: normal and shear. Normal stress includes tensile and compressive stress, because they act normal, or perpendicular, to the stress area. Tensile stress tends to stretch or lengthen the material, […]