Transverse shear formula

The transverse shear stress can be calculated as follows:

• V is the shear force applied (units: N or kN)
• I is the moment of inertia of the cross-section (units: m⁴ or mm⁴)
• t is the thickness of the cross-section where you are calculating your shear stress (units: m or mm)
• Q = Aȳ, we’ll explain more below
• Sign: +ve or –ve doesn’t really matter at this point; more on this in stress transformation.

Q = Aȳ

Here is how Q = Aȳ is calculated:

• Q considers the area above the point where you’re calculating your shear stress. It’s the product of A and ȳ.
• A is the area of the region above your point of interest.
• ȳ is the centroid of the area above your point of interest, with respect to the neutral-axis.
• Units: m² (area) × m (ȳ centroid) = m³ or mm³ for Q
• The calculation of Q is the same for either the top half or bottom half of the cross-section, and there’s no –ve Q even when you consider the bottom half.

Shear stress distribution

• At the top and bottom of the cross-section, Q = 0 and therefore τ = 0.
• At the neutral axis, Q is maximum and therefore τ is max.
• Between the neutral-axis and the top/bottom edges, τ varies parabolically.

Let’s look at an example now.