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 × 10^{7} N mm and Q = 18 × 10^{4} 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 ×10^{7} ×y/100 × 300^{2}
As extreme layers are at 150 mm from neutral axis,
y = 150 - 50 = 100 mm
∴ σ_{x} = - 9×12 ×10^{7} × 100/100 × 300^{3} = -40N/mm^{2}
τxy = 1.5 × 18 × 10^{4}/100×300 (1-4×100^{2}/300^{2}) =5 N/mm^{2}
Hence,
i.e.
σ_{2} = -40.616 N/mm^{2}
σ_{1} = +0.616 N/mm^{2}
τ_{max} = 20.616 N/mm^{2}