Shear From Torsion [top]

When a torque (moment) is applied about the longitudinal axis of a member, the member twists. This twisting action induces on any cross-section perpendicular to the axis. Unlike direct shear (caused by transverse forces), torsional shear varies across the section and is a primary design consideration for drive shafts, axles, screws, and structural beams.

τ=TrJtau equals the fraction with numerator cap T r and denominator cap J end-fraction is the applied torque, is the radial distance from the center, and is the polar moment of inertia. shear from torsion

Shear stress from torsion arises due to the following reasons: When a torque (moment) is applied about the

[ J = \frac{\pi (0.05)^4}{32} = 6.136 \times 10^{-7} \text{ m}^4 ] [ \tau_{max} = \frac{T R}{J} = \frac{1200 \times 0.025}{6.136 \times 10^{-7}} = 48.9 \text{ MPa} ] [ \phi = \frac{T L}{G J} \quad (\text{for } L=1\text{m}) = \frac{1200 \times 1.0}{80\times10^9 \times 6.136\times10^{-7}} = 0.0244 \text{ rad} = 1.40^\circ ] τ=TrJtau equals the fraction with numerator cap T

Plane sections warp (do not remain plane). Maximum shear stress occurs at the middle of the longer side: [ \tau_{max} = \frac{T}{c_1 a b^2} ] where ( a \ge b ) (longer side ( a ), shorter side ( b )), and ( c_1 ) is a factor (≈ 0.208 for ( a/b \to \infty )).