A tension member is made up of a single angle 200 mm × 150 mm × 15 mm with a gross area of 30 cm². Two rows of 18 mm diameter bolts (take hole diameter = 20 mm) are used (as shown in figure (a) and (b)). What is the net area?
- A2460 mm²
- B2500 mm²
- C2400 mm²Correct
- D2560 mm²
Solution
Concept
Net area = gross area minus area of holes on the critical section. For staggered bolts, add p2 t/(4g) for each inclined path.
Formula
An = Ag − n × dh × t + Σ p2 t/(4g)
Step-by-step solution
1. Ag = 30 cm² = 3000 mm², t = 15 mm, dh = 20 mm. 2. Assume the two holes lie in the same cross section (chain bolting). 3. Deduction = 2 × 20 × 15 = 600 mm² 4. An = 3000 − 600 = 2400 mm²
Explanation
With two rows of bolts in line, two holes are cut from one section. Each hole removes dh × t = 20 × 15 = 300 mm². So the net area is 3000 − 600 = 2400 mm².
Why the other options are wrong
A (2460), B (2500) and D (2560) are possible only if the bolts are staggered, which adds the p2 t/(4g) term. The pitch and gauge values are needed for this and they are not given in the text.
Shortcut
Chain bolts: An = Ag − (number of holes × dh × t)
Common mistake
Using the bolt diameter (18 mm) instead of the hole diameter (20 mm), or deducting only one hole.
Correct answer: C) 2400 mm²
