In case of staggered or zigzag riveting in the design of tension members of steel structures, the net cross-sectional area along the chains of rivets is:
- Aincreased by an amount equal to (s²t) / (8g)
- Bincreased by an amount equal to (s²t) / (4g)Correct
- Cdecreased by an amount equal to (s²t) / (4g)
- Ddecreased by an amount equal to (s²t) / (8g)
Solution
Concept
In a zigzag chain of holes, each inclined (diagonal) gauge line adds s²t/(4g) to the net area.
Formula
An = (b - n·d + Σ s2/(4g))·t
Step-by-step solution
1. Find the gross area along the chosen chain: b × t. 2. Subtract the hole areas: n × d × t. 3. For each diagonal (staggered) line in the chain, add s2 t/(4g). 4. So the net area is increased by s2 t/(4g) for each diagonal line.
Explanation
In staggered riveting the failure path is zigzag, so its length is greater than a straight path. To allow for this, s²t/(4g) is added for each inclined line in the chain (Cochrane's rule). So the net area is increased, not decreased.
Why the other options are wrong
A: The denominator is 4g, not 8g. C and D: For a stagger, the area is increased, not decreased.
Shortcut
Stagger adds area: + s²/(4g) per diagonal line.
Common mistake
Subtracting the stagger term, or using 8g instead of 4g.
Correct answer: B) increased by an amount equal to (s²t) / (4g)