Riveted joints – shear strength of the rivets in the connection If N rivets each of shank diameter d are used and the permissible shear stress is τ_allow, what is the shear strength of the joint against shearing of rivets?

Introduction / Context:
In riveted (or bolted) joints, one of the basic capacity checks is shear of the fastener shanks. Knowing the correct expression for total shear resistance helps size the number and diameter of rivets safely.

Given Data / Assumptions:

• N rivets share the load equally in shear (idealization).
• Each rivet has shank diameter d and circular cross-section.
• Allowable (permissible) shear stress is τ_allow (single shear).

Concept / Approach:
Shear strength equals allowable shear stress multiplied by resisting area. For a circular shank, resisting area is (π/4) * d^2. With N identical rivets, the total shear strength is N times the single-rivet shear strength.

Step-by-Step Solution:

Verification / Alternative check:
If the joint places a rivet in double shear, multiply the single-rivet capacity by 2. The formula structure remains the same; only the effective area factor changes.

Why Other Options Are Wrong:
Expressions using d * t or (p ± d) * t belong to plate bearing/tearing checks, not rivet shear. The (π/8) * d expression has wrong dimensions.

Common Pitfalls:
Forgetting to use net (threaded) area for bolts in place of shank area; ignoring double-shear conditions; mixing up plate tearing with rivet shear.

Final Answer:
V_shear = N * (π/4) * d^2 * τ_allow