Question

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitudes placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm on bottom face and nominal shear reinforcement. The characteristic compressive strength and the bending tensile strength of the concrete are 20.0 N/mm${}^2$ and 2.2 N/mm${}^2$ respectively.

Ignoring the presence of tensioned reinforcement, the value of load P in kN, when the first flexure crack will develop in the beam is

• A. 4.5
• B. 5.0
• C. 6.6
• D. 7.5

Answer 1

The correct option is C 6.6


bending moment diagram
Maximum value of bending moment,
M = 1000 P
From flexural formula,
Tensile stress at the bottom,

${\sigma }_t=\frac{My}{I}$

Bending tensile strength of concrete

$=\frac{My}{I}$

= 2.2

$=\frac{1000P.\left(300/2\right)}{\frac{200\times {300}^3}{12}}$

$\Rightarrow P=6600$

P = 6.6 kN