Internal Forces

Internal forces of a member can be determined by creating an imaginary cut in a member, and then solving for the internal shear force, normal force, and bending moment (which, after the cut, become "external" forces that can be solved for). To determine how the internal shear force and bending moment change throughout the member, shear force and bending moment diagrams are created. Shear force diagrams provide a graphical representation of the internal shear force within a member, and bending moment diagrams provide a graphical representation of the internal bending moment within a member.

Sign Conventions

General Procedure

Creating a shear force and bending moment diagram allows us to create a graphical representation of \( V \) and \( M \) as a function of the position along the beam, \( x \). Therefore when creating internal loading diagrams we are trying to write equations for \( V(x) \) and \( M(x) \).

General Rules

1. When there is an external concentrated force or moment, there will be a "jump" in the shear force or bending moment diagram
2. w(x)

Shear Force Diagram

Bending Moment Diagram