Bending & Shear Stress in Beams

Worked: a timber header

A 4 in × 12 in rectangular timber (actual dimensions) carries M = 12 ft-kips and V = 4 kips. I = 4 × 12³/12 = 576 in⁴ and c = 6 in. Convert the moment: 12 ft-kips = 144 in-kips. σ = 144 × 6/576 = 1.50 ksi, the same as M/S = 144/96.

τ_max = 1.5 × 4/48 = 0.125 ksi = 125 psi, at mid-depth where the bending stress is zero.