Gj

Fig. 11.33 Distribution of St. Venant and torsion-bending torques along the length of the open section beam shown in Fig. 11.30.

Fig. 11.37 Distribution of axial constraint shear flows, giving

Tr Jo

Hence for a given value of s, (Jq lA^tâs), qT is proportional to Tr (see Fig. 11.33).

Fig. 11.37 Distribution of axial constraint shear flows, giving

Tr Jo

Hence for a given value of s, (Jq lA^tâs), qT is proportional to Tr (see Fig. 11.33).

11.5.1 Distributed torque loading

We now consider the more general case of a beam carrying a distributed torque loading. In Fig. 11.38 an element of a beam is subjected to a distributed torque of intensity Tj(z), i.e. a torque per unit length. At the section z the torque comprises the St. Venant torque Tj plus the torque due to axial constraint Tv. At the section z + 6z the torque increases to T + ST(= Tj + 6Tj + Tr + 6Tr) so that for equilibrium of the beam element

Tj + 6Tj + Tr + 6Tr + Ti{z)6z - Tj - Tr = 0 —Tj(z)6z = 6Tj + 6Tr = ST

Hence dT dz dT dz

0 0

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