Last Updated on September 12, 2026 by Maged kamel
Review of Shear Stresses for Steel Beams.
The following slide shows the topics we will discuss in this post.
Introduction to Shear for beams and proof that both vertical and horizontal Shear stresses are equal.
If we take two sections of a Beam apart by a distance at elevation y, two compression forces will result from the moment difference between M and M + dM.
The stress, calculated from the known formula f = M*y/I, will be multiplied by dA, resulting in two compressive forces. These forces are not equal because the Moment difference equals dM. To balance the forces, a horizontal Shear force develops.
As the sum of Fx =0, the Shear force is developed to create a balance; this force value equals Shear stress*area = τ*dx*b = σ’*dA- σ*dA, but (σ’-σ)*dA (dM)*y/Ix, then τ*dx*t=dM*y/I.
How do we derive the Expression for Shear stress?
After integration, we get the stress Expression τ = dM_y dA/(dx t) = VQ/(I t), where V is the Shear force.
Q is the first Moment of the Area at the point of interest, I is the Moment of Inertia for the section, and finally,t is the breadth of the section. Please refer to the following slide image for more details.
Horizontal Shear stress for beams.
For the balance of a Beam element, the horizontal Shear stress should be accompanied by vertical Shear stress, as shown in the next slide.
It is proven that τh = τv, where τv is the vertical Shear stress and τh is the horizontal Shear stress, by multiplying by Area and taking a Moment at the edge.
You can view or download the PDF containing the data for this post from the following link.
This is a link to the next post, ‘A Solved Problem for Shear Stress. The next post will include a solved problem on estimating stress for different shapes.
For more detailed information on Shear in bending, please read the link: Shear in Bending. This links to Boston University’s Mechanical Engineering.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 14th ed. Section 8.3.1 Shear Behavior.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 15th ed. Section 8.3.1 Shear Behavior.
Here is the link to Chapter 8, “Bending Members.” A Beginner’s Guide to the Steel Construction Manual, 16th ed. Section 8.3.1 Shear Behavior.