Question

A steel plate is 400 mm wide and 10 mm thick. A rivet of nominal diameter 20 mm is driven. The net sectional area of the plate is:

• A. $3800 \text{ mm}^2$
• B. $3780 \text{ mm}^2$
• C. $3785 \text{ mm}^2$
• D. $4215 \text{ mm}^2$

Hint:

The distinction between nominal diameter and gross/hole diameter is crucial in steel design. Always add 1.5 mm for rivets up to 25 mm diameter.

Answer 1

The Correct Option is C

Concept: The net sectional area ($A_{net}$) of a plate is the gross area minus the area of the rivet holes. For a rivet, the hole diameter ($d_h$) is larger than the nominal diameter ($d$).

Step 1: Determine the gross diameter of the rivet hole.
According to standard codes (IS 800):
• If $d \leq 25 \text{ mm}$, $d_h = d + 1.5 \text{ mm}$
• If $d > 25 \text{ mm}$, $d_h = d + 2.0 \text{ mm}$ Given nominal diameter $d = 20 \text{ mm}$: \[ d_h = 20 + 1.5 = 21.5 \text{ mm} \]

Step 2: Calculate the net sectional area.
The formula is: \[ A_{net} = (b - n \cdot d_h) \times t \] Where:
• $b = 400 \text{ mm}$ (width)
• $n = 1$ (assuming one rivet in the section)
• $d_h = 21.5 \text{ mm}$
• $t = 10 \text{ mm}$ (thickness) \[ A_{net} = (400 - 21.5) \times 10 = 378.5 \times 10 = 3785 \text{ mm}^2 \]