Question

What is the net sectional area of a steel plate 40 cm wide and 10 mm thick with one bolt, if the diameter of the bolt hole is 18 mm?
Options:

• A. \( 38.2 \, \text{cm}^2 \)
• B. \( 24.8 \, \text{cm}^2 \)
• C. \( 57.8 \, \text{cm}^2 \)
• D. \( 46.5 \, \text{cm}^2 \)

Hint:

When calculating the net area of a steel plate with bolt holes, always check if the problem specifies the hole diameter or if you need to add clearance (e.g., 2 mm for bolts as per IS 800:2007). Convert units consistently to match the options.

Answer 1

The Correct Option is A

Step 1: Calculate the gross sectional area.
Convert width to mm: \( 40 \, \text{cm} = 400 \, \text{mm} \). Thickness is 10 mm. Gross area: \[ \text{Gross area} = 400 \, \text{mm} \times 10 \, \text{mm} = 4000 \, \text{mm}^2. \]
Step 2: Calculate the area of the bolt hole.
The diameter of the bolt hole is 18 mm. Area removed by the hole: \[ \text{Area of hole} = 18 \, \text{mm} \times 10 \, \text{mm} = 180 \, \text{mm}^2. \]
Step 3: Calculate the net sectional area.
\[ \text{Net area} = 4000 \, \text{mm}^2 - 180 \, \text{mm}^2 = 3820 \, \text{mm}^2. \] Convert to cm\(^2\): \( 3820 \, \text{mm}^2 = 38.2 \, \text{cm}^2 \).
Step 4: Compare with the options.
The net area of 38.2 cm\(^2\) matches option (1), confirming the solution.