Efficiency of a diamond-riveted joint For a plate of width b joined by diamond riveting with rivet-hole diameter d, the (simplified) efficiency based on the net-width criterion across the weakest critical section is:
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A(b - d) / b
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B(b - 2 d) / b
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C(b - 3 d) / b
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D(b - 4 d) / b
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E1 - (π d^2) / (4 b^2)
Answer
Correct Answer: (b - d) / b
Explanation
Introduction / Context:Joint efficiency compares the strength of a riveted (or bolted) joint to that of the unperforated plate. For diamond riveting (a staggered, centrally concentrated pattern), the weakest net section often passes through a single rivet hole on the line of the plate center.
Given Data / Assumptions:
- Plate width b; rivet-hole diameter d (finished hole).
- Critical section governed by net area across the least net width (simplified classical approach).
- Shear/tear or bearing checks are assumed non-governing for this idealized question.
Concept / Approach:Efficiency η (by net-width) = (net tensile strength) / (gross tensile strength) = (b - total hole deduction across the weakest section) / b. In single-line diamond patterns, the weakest section typically cuts only one hole on the central line, so deduction = d.
Step-by-Step Solution:
Identify weakest section through the central single hole.Compute net width = b - d.Efficiency η = (b - d) / b.Verification / Alternative check:For multiple-hole sections (e.g., chain riveting), deductions increase and efficiency reduces accordingly; diamond staggering aims to maximize net width and thus efficiency.
Why Other Options Are Wrong:
- (b - 2d)/b, (b - 3d)/b, (b - 4d)/b correspond to sections cutting more than one hole, not the critical diamond section here.
- 1 - (π d^2) / (4 b^2) is unrelated to net-width criterion (area ratio of a circle to a square band) and not the standard expression.
Common Pitfalls:Using pitch/edge distance rules to adjust the deduction; this simplified question isolates the net-width effect only.
Final Answer:(b - d) / b