The cylindrical bar ABCD shown in Fig. P.3.25 is supported symmetrically at B and C by supports that prevent rotation of the bar about its longitudinal axis. The bar carries a uniformly distributed torque of 2 N m/mm together with concentrated torques of 400 N m at each end. Draw the torsion

Question

The cylindrical bar ABCD shown in Fig. P.3.25 is supported symmetrically at B and C by supports that prevent rotation of the bar about its longitudinal axis. The bar carries a uniformly distributed torque of 2 N m/mm together with concentrated torques of 400 N m at each end. Draw the torsion diagram for the bar and determine the maximum value of torque.

Accepted Answer

From symmetry the support reactions are equal and are each 2400 Nm. Then, referring to Fig. S.3.25(a) the torque at any section a distance x from D is given by

[latex]T_{ DC }=400+2 x \quad(T ext { is in Nm when } x ext { is in } mm )[/latex]

Therefore, when [latex] x=0, T_{ DC }=400 Nm ext { and when } x=0.5 m , T_{ DC }=1400 Nm [/latex].
In CB the torque is given by

[latex]T_{ CB }=400+2 x-2400=2 x-2000[/latex]

and when [latex] x=0.5 m , T_{ CB }=-1000 Nm . ext { Note that } T_{ CB }=0 ext { when } x=1.0 m [/latex]. The remaining distribution follows from antisymmetry and is shown in Fig. S.3.25(b). The maximum value of torque is 1400 Nm and occurs at C and B.

Question 3.25: The cylindrical bar ABCD shown in Fig. P.3.25 is supported s...

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