Internal Forces at a Section

• If a body is in equilibrium, every part of it is also in equilibrium.

• Internal Forces: Taking a free body diagram of a portion of a body in equilibrium shows that there must be internal forces that hold the body together.

• Force balance at a cut: The internal forces acting on one portion of a body at a section where a free body has been cut, are equal and opposite to the internal forces acting on the portion of the body on the opposite side of the cut.

• Internal forces depend on load distribution: The internal forces depend not only on how much load is on a structure, but also on how it is distributed (e.g. standing on a table produced double the bending moment of lying down on the table).

• Types of internal force: There are three basic types of internal forces in linear members in two dimensions:
  • Axial Force: An internal force parallel to the axis of the member.
  • Shear: An internal force perpendicular to the axis of the member.
  • Moment: (aka Bending Moment). A moment about an axis perpendicular to the member axis.

• Note: in three dimensions, there is a fourth type of internal force: torsion, a moment about an axis parallel to the member axis.

Graphing Internal Forces

• Internal forces vary at different points: In designing structures, it is useful to understand how internal forces vary along the length of a structural element.

• Shear and moment diagrams: Graphs of the shear and moment are particularly useful for beams, and are called shear diagrams and moment diagrams.

• Sign conventions for internal force diagrams: Internal force diagrams used sign conventions based on the nature of the deformation that the internal force causes: e.g. tension positive and compression negative, or bending in upward curvature positive and bending in downward curvature negative.