Calculate the net area of the tension member consists a drilled hole of diameter 22 mm to place a M20 bolt. Take thickness of the tension member as 10 mm and gross area 1000 mm².
- A680 mm²
- B780 mm²Correct
- C1000 mm²
- D550 mm²
Solution
Concept
Net area = gross area minus the area removed by the bolt holes (hole diameter × thickness).
Formula
An = Ag - n × dh × t
Step-by-step solution
1. Gross area Ag = 1000 mm². 2. Hole diameter dh = 22 mm, thickness t = 10 mm, number of holes n = 1. 3. Area of hole = 22 × 10 = 220 mm². 4. An = 1000 - 220 = 780 mm².
Explanation
A bolt hole removes material from the member, so less area is left to carry tension. Subtract the hole area (hole diameter × thickness) from the gross area. Net area = 1000 - 220 = 780 mm².
Why the other options are wrong
A: 680 mm² removes too much area (about 32 mm × 10). C: 1000 mm² is the gross area; the hole is not subtracted. D: 550 mm² does not match any correct calculation.
Shortcut
Subtract hole dia × thickness: 1000 - 22×10 = 780.
Common mistake
Using the bolt diameter (20 mm) instead of the hole diameter (22 mm), which gives 800 mm².
Correct answer: B) 780 mm²