A solid circular bar ABCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques To, as shown in the figure. The torques are applied at points B and C, each of which is located at distance m from one end of the bar. (The distance m may vary from zero to L/2.) To To Tp m (a) For what distance m will the angle of twist at points B and C be a maximum? (b) What is the corresponding angle of twist max? [Hint: Use the equations below to obtain the reactive torques. Assume that the shear modulus of elasticity is denoted G, and the polar moment of inertia is denoted Ip.] ToLB TOLA TA = 201B ; TB = L

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Planar Stresses