(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A shaft fixed on both ends is shown below. It is made of a steel tube, which is bonded to a brass core. A torque [tex] T_D[/tex] is applied at location shown. The tube is fixed at both ends.

[PLAIN]http://img202.imageshack.us/img202/2940/problem2eb.jpg [Broken]

Show that the fraction of the torque, [tex] T_D [/tex], resisted by the steel at C labeled as [tex] T_c[/tex] is given by the following expression: [tex] T_c = T_D \left[\frac{G_s J_s}{G_b J_b + G_s J_s}\right]\left[\frac{L_{ad}}{L}\right] [/tex]

2. Relevant equations

[tex] \phi = \frac{TL}{JG} [/tex]

3. The attempt at a solution

So I am thinking I should start with a free body diagram. The shaft is fixed which makes me think that the angle of twist will be zero allowing me to use this equation to solve for torques. If I am not mistaken the torque as C will be [tex] T_D [/tex] in the opposite direction.

At point C I have [tex] \frac{T_c L}{G_sJ_s}= \frac{T_dL_{ad}}{G_bJ_b} + \frac{T_d L_{ad}}{G_sJ_s} [/tex]

Obviously this isn't correct; it seems like they may have simply combined the modulus of rigidiy and polar moments for the part of the shaft AD. Any input, am I on the correct track? Or did I possibly miss something about combining these components when a shaft is bonded to a core of different material?

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# Homework Help: Mechanics of Materials: Torsion

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