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?

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:

  • 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:

Area per shear plane: A = π/4 * d^2.Double shear ⇒ total resisting area = 2 * A = 2 * (π/4 * d^2) = π/2 * d^2.Required pull to reach shear limit: P = τ * (π/2 * d^2) = π/2 * d^2 * τ.


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

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