Riveted joints – Crushing (bearing) resistance per pitch length\n\nFor a single rivet in a lap or butt joint, the pull required to crush the rivet per pitch length is given by which expression? (Use d = rivet diameter, t = plate thickness, σc = allowable crushing/bearing stress)

Introduction / Context:
Designing riveted joints requires checking multiple failure modes per pitch: tearing of plate, shearing of rivet, and crushing (bearing) of material. The crushing check uses the projected bearing area and the allowable bearing stress.

Given Data / Assumptions:

• Single rivet considered per pitch length.
• d = rivet diameter; t = plate thickness.
• σc = allowable bearing (crushing) stress of the weaker bearing pair (plate or rivet).

Concept / Approach:
The bearing resistance equals allowable bearing stress multiplied by the projected contact area between rivet and plate. For a round rivet bearing on plate thickness t, projected area = d * t. Thus the force to cause bearing failure is d * t * σc.

Step-by-Step Solution:
Projected bearing area A_b = contact width d * thickness t.Allowable bearing stress = σc.Crushing (bearing) resistance per rivet = A_b * σc = d * t * σc.Compare with other modes to size the joint based on the least capacity.

Verification / Alternative check:
Dimension check: N = (m) * (m) * (N/m^2) → N, consistent with force. Common textbooks derive the same expression for bearing strength.

Why Other Options Are Wrong:
(a) uses pitch p and tensile stress σt, which relates to plate tearing not bearing. (c) and (d) use circular area (π/4 * d^2) relevant to shearing or tensile area, not bearing. (e) introduces an extra p, not part of bearing area.

Common Pitfalls:
Confusing bearing strength with rivet shear or plate tearing; using net-section area instead of projected contact area.

Final Answer:
d * t * σc