Shear of a rivet in double shear per pitch length: If the permissible shear stress is τ and the rivet shank diameter is d, what is the pull required to shear the rivet in double shear per pitch length?

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:

• Rivet diameter = d, allowable shear stress = τ.
• Double shear condition (two shear planes).
• Static loading and uniform shear distribution across the rivet cross-section.

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:

• Expressions with σt relate to tension, not shear.
• π/4 * d^2 * τ is for single shear only.
• π * d^2 * τ overestimates by a factor of 2.

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