Design of riveted joints – Tearing of plate across a pitch length\nWhat is the pull required to tear off the plate per pitch length?\n(Use: p = pitch of rivets, t = plate thickness, σt, τ, σc = permissible tensile, shear, and crushing stresses respectively.)

Introduction / Context:
In riveted joint design, the plate between successive holes can fail in tension. For safe design, we compare the tensile tearing strength of the net section with alternative modes such as rivet shear and bearing (crushing). This question asks for the standard expression of the tensile (tearing) resistance of the plate across one pitch length.

Given Data / Assumptions:

• p = pitch of rivets (centre-to-centre distance along load direction).
• t = plate thickness.
• d = diameter of rivet hole (net width reduction equals d).
• σt, τ, σc are permissible stresses in tension, shear, and crushing respectively.
• Single line of holes considered for tearing across one pitch.

Concept / Approach:
The tearing plane passes through the net cross-section of the plate between the two adjacent holes. The effective (net) width resisting tension equals (p − d). The tearing strength is tensile stress times net area.

Step-by-Step Solution:
Net width resisting tension = (p − d).Net area resisting tension = (p − d) * t.Tearing (tensile) resistance of plate = (p − d) * t * σt.

Verification / Alternative check:
Design checks compare three capacities per pitch: tearing of plate = (p − d) * t * σt; shearing of rivets (single or double shear) = number_of_shear_planes * (π d^2 / 4) * τ; bearing (crushing) = d * t * σc. The smallest governs design and also sets the efficiency.

Why Other Options Are Wrong:
(p − 2d) * t * σc uses bearing stress and incorrect net width; (p − d) * t * τ uses shear stress on a plate tension mode; (2p − d) * t * σt is not a recognized pitch-based expression; p * t * σt ignores the hole completely.

Common Pitfalls:
Using rivet nominal diameter instead of hole diameter for net width; confusing pitch with margin; mixing up stress symbols (σt vs τ vs σc).

Final Answer:
(p - d) * t * σt