Question

A reinforced concrete beam, size 250 mm wide and 400 mm deep overall is simply supported over a span of 3m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 20 mm diameter placed at an effective cover of 40 mm on bottom face and provided with nominal shear reinforcement. The characteristic compressive strength and the bending tensile strength of the concrete are $30N/m{m}^2$ and $2.4N/m{m}^2$ respectively. The value of load P (in kN) when the first flexural crack will develop in the beam is [Ignoring the presence of tension reinforcement]

• A. 6.6
• B. 11.6
• C. 16
• D. 28

Answer 1

The correct option is C 16

Bending tensile strength, ${\sigma }_{bt}=2.4N/m{m}^2$
Charactenstic compressive strength,
$f_{ck}=30N/m{m}^2$
$\therefore$ Maximum compressive stress in concrete,
${\sigma }_{cbc}=0.45f_{ck}=0.45\times 30=13.5N/m{m}^2$

Section modulus,
$Z=\frac{b{D}^2}{6}=\frac{250\times (400{)}^2}{6}$
$=6.67\times {10}^{6}m{m}^3$
$\therefore$ Maximum moment that can be carried before development of tension,
$M_{max}=Z{\sigma }_{bt}=6.67\times {10}^6\times 2.4=16.008kN.m$
$M_{max}=\frac{PL}{3}$
$\Rightarrow \frac{P\times 3}{3}=16.008$
$\Rightarrow P=16.008kN\simeq 16kN$