» Shear Stress
Transverse shear forces present during non-pure bending results in a SHEAR STRESS across a beam's cross-section:

t(y1) = V A* y* I t = V Q I t = q t

• Shear stress is zero at the top and bottom surfaces;
• y₁ = y-value of cut (where we are finding the stress);
• V = shear force at the cross-section;
• A^* = area on the opposite side of the "cut" from the neutral axis (area above y₁);
• y^* = distance from neutral axis to the centroid of A^*, NOT the distance to the "cut";
• I = moment of inertia of the entire cross-section;
• t = width of the "cut";
• Q is the first moment of area of A^* with respect to the neutral axis;
• q is the shear flow.

» Special Beams
While the shear stress distribution in channel beams, I-beams, and other thin-walled beams are more complex than rectangular beams, the method for determining the shear stress is the same. For instance to determine the shear in the flange of the channel beam below, a vertical cut may be taken at d-d' as in Figure (b), below. Cuts should always be taken perpendicular to the member. Here t = t flange and A* = A*d. Then:

td = V Ad* y* I tflange

The shear stress distribution is shown in Figure (c). Note that the shear stress at the cross-section in this flange acts horizontally (t_xz) while in the web the shear stress acts vertically (t_xy). Their respective complementary shear stresses (t_zx and t_yx) act out in the x-direction (out of the y-z plane).