Review 1 Fall 08 1.Asolid circular bar is fixed against rotation at the ends and loaded by a distributed torque t(x) that varies linearly in intensity from zero at end Ato toat end B(see figure). Assume that the bar has shear modulus Gand diameter d. Find: (a)The reaction torques at two supports. (b)The vale and position of maximum shear stress. (c)The value and position of maximum angle of twist. Solution: FBD EQM LtTTTCAo210+==∑(1) internal torque LxtTxTTAAB2)(:02o−==∑Load/displacement relations ()6121)(2o02o0LtLTGIdxLxtTIGIGdxxTAPLAPLPABAB−=⎟⎟⎠⎞⎜⎜⎝⎛−==∫∫φA B toL t(x)TATCtoTAA TAB (x)xtox/L
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