Question

A beam of triangular cross-section is subjected to a shear force of 50kN. The base width of the section is 250 mm and the height is 200 mm. The beam is placed with its base horizontal. The shear stress at the neutral axis will be nearly-

• A. 1.2 N/mm\(^2\)
• B. 3.2 N/mm\(^2\)
• C. 3.7 N/mm\(^2\)
• D. 2.4 N/mm\(^2\)

Hint:

To calculate shear stress, divide the shear force by the cross-sectional are(A)

Answer 1

The Correct Option is B

Step 1: Understanding Shear Stress Calculation.
The formula for shear stress (\(\tau\)) at the neutral axis in a beam is given by: \[ \tau = \frac{F}{A} \] Where: - \(F\) = Shear force = 50 kN = 50,000 N - \(A\) = Area of cross-section The triangular cross-section area \(A\) is: \[ A = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 250 \, \text{mm} \times 200 \, \text{mm} = 25,000 \, \text{mm}^2 \] Converting area to m\(^2\), we get: \[ A = 25,000 \, \text{mm}^2 = 25 \times 10^{-3} \, \text{m}^2 \]
Step 2: Calculating Shear Stress.
Now, we calculate the shear stress: \[ \tau = \frac{50,000 \, \text{N}}{25 \times 10^{-3} \, \text{m}^2} = 3.2 \, \text{N/mm}^2 \]
Step 3: Conclusion.
Therefore, the shear stress at the neutral axis is 3.2 N/mm\(^2\), making option (2) the correct answer.

Final Answer: \[ \boxed{3.2 \, \text{N/mm}^2} \]