Final answer:
The required diameter of pins at A and B subjected to double shear can be calculated using the shear stress formula τ = F / (2A), and solving for diameter with the equation d = sqrt((4F) / (πτ allow)), considering the allowable shear stress is 100 MPa.
Step-by-step explanation:
To determine the required diameter of the pins at A and B subjected to double shear, we start with the notion that shear stress τ is given by the force F divided by the area A of the pin in shear. Since the allowable shear stress for the material is τ allow = 100 MPa, and both pins experience double shear, the area subject to shear is doubled, effectively halving the shear stress per area. The formula for shear stress in double shear is τ = F / (2A), where A is the cross-sectional area of the pin.
Given the force F experienced by the pins, the required diameter d can be found using the area for a circle (A = πd²/4) in the shear stress equation. Rearranging the formula to solve for the diameter yields d = sqrt((4F) / (πτ allow)).
Without the specific values for the forces on pins A and B, we cannot calculate the exact diameters. However, once the forces are known, this equation can be used to find the minimum diameters needed to ensure that the shear stress does not exceed the allowable limit, keeping the structure safe and intact.