A solid circular shaft of length L = 0.5 m is made of a material with shear modu

Question

A solid circular shaft of length L = 0.5 m is made of a material with shear modulus G = 80 GPa, and carries a torque T = 100 N.m (see figure P7.1). if the allowable maximum shear stress for the torque is tau_a = 70 MPa, determine a suitable radius a for the shaft. What is the corresponding angle of twist? A circular bellow shaft of length L = 0.5 m is expected to carry a torque T = 100 N.m (see Figure P7, 2) If its angle of twist should be limited to 0.02 rad and its maximum shear stress should be limited to tau_a =50 MPa. select a suitable inner radius, and an .niter radius a_2 for the shaft. A shaft ABC of length 21. and circular cross section is fixed to a wall .it end A From A to B. the shaft is solid, with cross-sectional radius 2_a From B to C the shaft is hollow, with inter­nal radius a and outer radius 2_a (see Figure P7.3 G is the shear modulus of the shall material tau_r is the yield shear stress of the shaft material Suppose that a torque is applied at the free end C Determine the location at which the yielding will begin what is the maximum shear stress in the other segment of the shall when yielding is about to begin in one segment? Determine the maximum torque that may be applied at C before the shaft starts to yield. When the yielding is about to begin, what Is the angle of twist of the shaft (at C with respect to A)? a uniform circular shaft with end torques. A uniform circular bellow shaft with end torques.

Explanation / Answer

7.1 )

max shear stress = G * a/ l

=> a =max stress * l /G = 4 * 10-4 m

angle of twist = l * stress /( G * r ) = 1.09 rad

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