Shear Stress Calculator

Shear stress (tau) is the internal stress resulting from forces acting parallel to a cross-section, tending to cause one layer of material to slide over another. Transverse shear stress from a shear force V: tau = VQ / (Ib), where V is the shear force, Q is the first moment of area, I is the moment of inertia, and b is the section width at the point of interest. Torsional shear stress from torque T: tau = Tc / J, where c is the outer radius and J is the polar moment of inertia.

The maximum transverse shear stress in a rectangular beam occurs at the neutral axis: tau_max = (3/2) x V/A, where V is the shear force and A is the cross-sectional area. For a solid circular cross-section, tau_max = (4/3) x V/A. For wide-flange steel I-beams, the web carries most of the shear force; the approximation tau_web = V / (d x tw) is commonly used, where d is the depth and tw is the web thickness.

Torsional shear stress results from a twisting moment (torque) applied about the longitudinal axis of a member. For a solid circular shaft: tau = T x c / J = 16T / (pi x d^3), where T is the torque, c is the outer radius, J = pi x d^4 / 32 is the polar moment of inertia, and d is the diameter. For a hollow shaft: J = pi x (do^4 - di^4) / 32.

The AISC ASD allowable shear stress for structural steel is Fv = 0.40 x Fy. For A36 steel (Fy = 36 ksi): Fv = 14.4 ksi. The simplified check for I-beams is: V / (d x tw) less than or equal to 0.40 x Fy. Shear rarely governs design of typical beams; it becomes critical for short, heavily loaded beams and web openings.

Bending (flexural) stress is normal stress that acts perpendicular to the cross-section, caused by a bending moment. It is maximum at the extreme fibers and zero at the neutral axis. Shear stress acts parallel to the cross-section, caused by the shear force. It is maximum at the neutral axis for rectangular sections and zero at the extreme fibers. Both must be checked in structural beam design.