Final answer:
The question is an engineering problem related to calculating the required diameter of a shaft to avoid exceeding a given allowable shear stress. The calculation uses torsion formulas and considerations from mechanics of materials.
Step-by-step explanation:
The question pertains to the determination of the required diameter of a solid shaft that can withstand certain torsional loadings without exceeding the allowable shear stress of a material. The subject of this question is therefore Engineering, specifically related to mechanics of materials and structural analysis. To solve this problem, one would apply the torsion formula, which relates the shear stress in a shaft to the applied torque and the dimensions of the shaft. This formula is represented by τ = Tc/J, where τ is the shear stress, T is the torque, c is the radius of the shaft, and J is the polar moment of inertia. Given that the allowable shear stress is specified, this formula can be rearranged to solve for the required diameter d of the shaft. A step-by-step approach would include calculating the total torque applied to the shaft, determining the polar moment of inertia for a solid circular shaft (which is J = (π/32)d^4), and then solving for d, ensuring that the calculated shear stress does not surpass the allowable limit.