In previous discussion on pure bending of beams the transverse shear forces
and corresponding shear stresses were absent. That absence simplified the
flexure problem as the applied loads (i.e., bending moments) only produced
flexural normal stresses.
In this chapter our focus is on a more general loading condition - one that
involves both bending moment and transverse shear force. The existence of the
latter indicates that we no longer have pure bending problem.
Recall from mechanics of materials that in beam bending transverse shear forces
and bending moments are related to each other. This relationship was displayed
in drawing the shear and moment diagrams for various beams and loading
We first are going to revisit the problems that we encountered in mechanics of
materials course. In order to do that we must recall problem restrictions
and the method of analysis that was used in the solution of those problems.
- Shear stress at every point in the beam must be less than the
elastic limit of the material in shear.
- Normal stress at every point in the beam must be less than the
elastic limit of the material in tension and
- Beam's cross section must contain at least one axis of symmetry.
- The applied transverse (or lateral) force(s) at every point on the beam
must pass through the elastic axis of the beam. Recall that elastic axis is
a line connecting cross-sectional shear centers of the beam. Since shear center
always falls on the cross-sectional axis of symmetry, to assure the previous
statement is satisfied, at every point the transverse force is applied
along the cross-sectional axis of symmetry.
- The length of the beam must be much longer than its cross sectional dimensions.
- The beam's cross section must be uniform along its length.
To Section III.2
To Index Page of
Transverse Shear Loading of Open Sections