Maximum Shear Stress in a Rectangular Beam
Maximum Shear Stress in a Rectangular Beam
Transverse shear peaks at the neutral axis, not the edges. For short, heavily loaded beams this can govern over bending.
For a rectangle the maximum shear stress is τ = 1.5·V/A. where V is the shear force and A the cross-section area.
Inputs
V := 80 kN=80000 N
A := 45000 mm^2=0.04 m^2
The parabolic shear distribution peaks 50% above the average V/A.
tau := 1.5·V/A=2.67 MPa
Results
The peak shear stress must stay below the allowable shear. Shear governs in deep, short-span or heavily-loaded beams where bending stress is modest.
Assumptions & limitations
- Solid rectangular section.
- Elastic shear distribution (parabolic).
- Shear and bending checked independently.