Question

Consider two RCC beams, P and Q each having the section 400 mm x 750 mm (effective depth, d = 750 mm) made with concrete having a ${\tau }_{cmax}=2.1N/m{m}^2$. For the reinforcement provided and the grade of concrete used, it may be assumed that the ${\tau }_c=0.75N/m{m}^2$. The design shear in beam P is 400 kN and in beam Q is 750 kN. Considering the provisions of IS : 456-2000, which of the following statements is true?

• 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 designing for 120 kN for beam Q.
• C. Shear reinforcement should be designed for 175 kN for beam P and the shear reinforcement 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
A =400 mm x 700 mm
${\tau }_{cmax}=2.1N/m{m}^2$
${\tau }_c=0.75N/m{m}^2$
Design shear force,
V = 400 kN
Nominal shear stress

${\tau }_v=\frac{V}{A}=\frac{400\times 100}{400\times 750}=\frac{4}{3}$

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

Beam Q
A = 400 mm x 750 mm
${\tau }_{cmax}=2.1N/m{m}^2$
${\tau }_c=0.75N/m{m}^2$
V = 750 kN

${\tau }_v=\frac{V}{A}=\frac{750\times 1000}{400\times 750}$

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

$But{\tau }_v>{\tau }_c$

So section should be revised.
$\therefore$ Shear reinforcement should be provided for shear force

$({\tau }_v-{\tau }_c)A$

$=(\frac{4}{3}-0.75)\times 400\times 750$

= $175000N$ = 175 kN