Question

A beam of a triangular cross-section is subjected to a shear force of 50 kN. 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 a neutral axis will be nearly

1. 2.2 N/mm²
2. 2.7 N/mm²
3. 3.2 N/mm²
4. 3.7 N/mm²

Answer 1

Correct Answer - Option 2 : 2.7 N/mm²

Concept:

Table showing relations between τ_max, τ_N.A and τ_avg

Sr no.	Section	τmax­/τavg	τN.A­/τavg
1.	Rectangular/square	3/2	3/2
2.	Circular	4/3	4/3
3.	Triangle	3/2	4/3
4.	Diamond	9/8	1

 

Calculations:

V = 50 KN

b = 250 mm

h = 200 mm

For triangular cross-setion.

\(\therefore \;{{\rm{\tau }}_{N.A}} = \frac{4}{3}{{\rm{\tau }}_{avg}} = \frac{4}{3}\left( {\frac{V}{{\frac{{b \times h}}{2}}}} \right) = \frac{4}{3} \times \left( {\frac{{50}}{{\frac{{250 \times 200}}{2}}}} \right) = 2.67\; \approx 2.7N/m{m^2}\)