A steel shaft BCD (G=80 GPa) of total length 3 m is encased for 1/3 of its length by a bronze sleeve ABC (G=41 GPa) that is securely bonded to the steel. The diameter of the steel is 60 mm while the outer diameter of the bronze is 80 mm. a. What is the maximum allowable torque in gear A if the allowable shear stresses in the steel and bronze are limited to 110 MPa and 70 MPa, respectively; and the angle of twist between A and D is limited to 9o? b. What power is supplied by the motor that corresponds to the computed torque at A if shaft EF rotates at 200 rpm? The diameter of gear E is 60 mm while gear D has a diameter of 100 mm.

A metal shaft ABCD with variable cross-section is subjected to three external torques (T₁=28 kip- in, T2=8 kip-in, and T3=10 kip-in) as shown in the figure below. Each torque is acting at the locations marked with circular points along the shaft. Note that a 16-inch long segment of the shaft at the free end (right) has a 1-inch diameter bore. The dimensions (lengths and diameters) of the shaft are given in the figure. Assume deformation is linear elastic and take G=12×106 psi. D [3" 16"- X C T₁ 2" -32"- T₂ 1" diam. bore B -16"- A T3 the bar has a uniform diameter d along its full length, but external torques remain the same and are applied at the same locations. If the failure shear stress for the material is equal to Tfail = 10 ksi, and the factor of safety is equal to 2, determine the required (uniform) diameter d for the bar. Assume that the bar is solid for its entire length.

Problem 3

A steel core is bonded firmly to the copper tube (shell) to form the shaft shown. The length of the shaft is 450 mm and the end A is fixed to the wall. Take the shear modulus of steel and copper as 76 GPa and 38 GPa, respectively. The diameter of the core is 60 mm and the outer diameter of the shaft is 100 mm. Determine the maximum external torque (Tmax) so that the absolute maximum shear stress for any point H on the surface of the copper shell does not exceed 50 MPa. 450 mm A 100 mm 60 mm В Tmax =? kN · m

Please help with the stress, mohir circle, etc. Thank you