Rivets under combined shear and tension – interaction requirement When rivets are subjected to simultaneous shear and an externally applied tensile force, how should they be proportioned for safe design?

Introduction / Context:
Fasteners such as rivets (or bolts) can experience both shear and tension. A combined-stress interaction check prevents overstress when both actions act together.

Given Data / Assumptions:

• Rivet experiences shear stress τ and tensile stress σ simultaneously.
• τ_allow and σ_allow are the permissible shear and tensile stresses respectively.
• We adopt a common elliptical interaction for working-stress design.

Concept / Approach:
In combined loading, neither the shear nor the tension may independently be at the allowable value. An interaction formula limits the combined effect. A common working-stress interaction is elliptical: (τ/τ_allow)^2 + (σ/σ_allow)^2 ≤ 1.

Step-by-Step Solution:

Verification / Alternative check:
Some practices permit linear interaction (τ/τ_allow + σ/σ_allow ≤ 1) as a conservative simplification. The elliptical form better reflects combined-stress capacity.

Why Other Options Are Wrong:
Options that treat σ or τ in isolation ignore the interaction. The simple product criterion has no basis in standard design. The linear sum may be conservative but is not the most representative choice when an elliptical rule is specified.

Common Pitfalls:
Forgetting to include prying action; using gross instead of net areas; omitting preload effects for high-strength friction-grip bolts (if used).

Final Answer:
(τ/τ_allow)^2 + (σ/σ_allow)^2 ≤ 1