General solution of the torsion equation

Abstract

The general torsion equation is given by

$$ \varphi^{\prime\prime\prime} - k^{ 2} .\varphi^{\prime} = {{ - T_{X} } \mathord{\left/ {\vphantom {{ - T_{X} } {C_{ 1} }}} \right. \kern-\nulldelimiterspace} {C_{ 1} }} $$

(6.1)

where T _X  = external torque; C = torsional rigidity; C ₁ = warping rigidity $k = \sqrt {{C \mathord{\left/ {\vphantom {C {C_{1} }}} \right. \kern-\nulldelimiterspace} {C_{1} }}}.$