In a bracket, if load p acts at an eccentricity e producing moment in the plane of the group of bolts, the stress induced in a bolt at distance r from the centroid of the group due to moment alone is
- Ap e r / Σr
- Bp e r / Σr²Correct
- Cp e / Σr
- DNone of the above
Solution
Concept
Bolt force due to torsion
Formula
F = p e r / Σr²
Step-by-step solution
1. Moment M = p e is resisted by bolt forces proportional to distance: F = k r. 2. Σ(F r) = k Σr² = p e ⇒ F = p e r / Σr².
Explanation
The bolt farthest from the centroid carries the largest force.
Why the other options are wrong
Σr in the denominator ignores the moment arm.
Shortcut
F = M r / Σr².
Common mistake
Using Σr.
Correct answer: B) p e r / Σr²