Rectangular Cross-section:

The indirect method utilized for elliptical cross-section and equilateral cross-section is not valid for rectangular cross-section. Special methods (Boresi & Chong) are needed to obtain the torsion solution for rectangular cross-section. Some of the results are summarised here.

The maximum shear stress, τ_m, and the angle of the twist, θ, per unit length are given by

τ_m = T/ k₁ (2b) (2h)²

θ=  T / k₂ G (2b) (2h)³

The maximum shear stress occurs at the centre of the long side s,

Figure: Rectangle

Values of the parameters k₁ and k₂ are tabulated for several values of the ratio b/ h.

The factor k₂ G (2b) (2h)³  = G J(torsional rigidity)

∴ J = k₂ (2b) (2h)³

τ_m may be expressed in terms of θ.

τ_m  = 2G θ h k₃

where,     k₃ =      k₂ / k₁                         

  Table: K₁ and K₂ for Rectangular Section