Analyse the state of stress:

For the cross-section shown in above figure, let us take b = 100 mm, d = 300 mm and M = 9 × 10⁷ N mm and Q = 18 × 10⁴ N and analyse the state of stress at a layer 50 mm below the top layer.

Solution

Using Eqs. (i) and (iii)

σ_x  =     - 9×12 ×10⁷ ×y/100 × 300²

As extreme layers are at 150 mm from neutral axis,

y = 150 - 50 = 100 mm

∴          σ_x  =     - 9×12 ×10⁷ × 100/100 × 300³ = -40N/mm²

τxy = 1.5 × 18 × 10⁴/100×300 (1-4×100²/300²) =5 N/mm²

Hence,

i.e.

σ₂ = -40.616 N/mm²

σ₁ = +0.616 N/mm²

τ_max = 20.616 N/mm²