Difficulty: Easy
Correct Answer: π/2 * d^2 * τ
Explanation:
Introduction / Context:
Riveted joints can experience single or double shear depending on the connection geometry. Determining the shear capacity per pitch length is a standard step in joint design to ensure safety against rivet shearing.
Given Data / Assumptions:
Concept / Approach:
Shear capacity is shear stress times resisting area on all active shear planes. For a circular rivet shank, area per plane is A = π/4 * d^2. With two planes in double shear, the total resisting area is 2A. Multiply by τ to obtain the force to cause shearing.
Step-by-Step Solution:
Verification / Alternative check:
Compare to single shear: P_single = τ * (π/4 * d^2). Doubling the number of planes doubles the capacity, yielding P_double = 2 * P_single, which is the same expression obtained above.
Why Other Options Are Wrong:
Common Pitfalls:
Using rivet nominal diameter instead of finished hole diameter where applicable; confusing single vs. double shear; mixing allowable stresses (shear vs. tensile or bearing).
Final Answer:
π/2 * d^2 * τ
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