Stresses in Beams
In a separate article entitled “Structural Analysis of a Beam” there was a brief discussion of stresses and their function in structural analysis.  In this article there will be a more in dept discussion of normal, bending, and shear stress.

Normal Stress
A normal stress is a stress that occurs when a member is loaded by an axial force.  The value of the normal force for any prismatic section is simply the force divided by the cross sectional area.

Normal Stress

A normal stress will occur when a member is placed in tension or compression.  Examples of members experiencing pure normal forces would include columns, collar ties, etc.

Bending Stress

Beam Design

When a member is being loaded similar to that in figure one bending stress (or flexure stress) will result.  Bending stress is a more specific type of normal stress.  When a beam experiences load like that shown in figure one the top fibers of the beam undergo a normal compressive stress.  The stress at the horizontal plane of the neutral is zero.  The bottom fibers of the beam undergo a normal tensile stress.  It can be concluded therefore that the value of the bending stress will vary linearly with distance from the neutral axis.

Bending Stress

Calculating the maximum bending stress is crucial for determining the adequacy of beams, rafters, joists, etc.

Shear Stress
Normal stress is a result of load applied perpendicular to a member.  Shear stress however results when a load is applied parallel to an area.  Looking again at figure one, it can be seen that both bending and shear stresses will develop.  Like in bending stress, shear stress will vary across the cross sectional area.

Shear Stress

Calculating the maximum shear stress is also crucial for determining the adequacy of beams, rafters, joists, etc.

Final Considerations
When doing any kind of beam design using structural design software will greatly ease the entire process of calculating stresses.  There are several different engineering design software packages available for beams, columns, or foundation design.  StruCalc, Enercalc, Risa, and BeamChek will all take in to account normal and shear stresses when doing any kind of beam design.

Josh Parker, E.I.T.
Cascade Design Group

December 4, 2007

Normal Stress, Bending Stress, & Shear Stress