Question

Consider two RCC beams, Pand Q, each of width 400 mm and effective depth 750 mm, made with concrete having a ${\tau }_{cmax}=2.0$ MPa. For the reinforcement provided and the grade of concrete used, it may be assumed that ${\tau }_c=0.75$ MPa. If the design shear for the beams P and Q is 400 kN and 750 kN, respectively, which of the following statements is true considering the provisions of IS 456-2000?

• A. Shear reinforcement should be designed for 175 kN for beam P and the section for beam Q should be revised.
• B. Nominal shear reinforcement is required for beam P and the shear reinforcement should be designed for 120 kN for beam Q.
• C. Shear reinforcement should be designed for 175 kN for beam P and the section for beam Q should be designed for 525 kN for beam Q.
• D. The sections for both beams, P and Q, need to be revised.

Answer 1

The correct option is A Shear reinforcement should be designed for 175 kN for beam P and the section for beam Q should be revised.

Beam P:

$V_u=400kN$

${\tau }_v=\frac{V_u}{bd}=\frac{400\times {10}^3}{400\times 750}$

$=1.33N/m{m}^2<{\tau }_{cmax}=2.0N/m{m}^2$

$\Rightarrow V_{us}=(1.33-0.75)\times 400\times 750=175kN$

Beam Q:

$V_u=750kN$

${\tau }_v=\frac{750\times {10}^3}{400\times 750}$

$=2.5N/m{m}^2>{\tau }_{cmax}=2.0N/m{m}^2$

Not safe, hence section for beam Q should be revised.