Question 12.7: A reinforced concrete beam having an effective depth of 600 ...
A reinforced concrete beam having an effective depth of 600 mm and a breadth of 250 mm is subjected to a bending moment of 350 kN m. If the 28-day cube strength of the concrete is 30 N/mm² and the yield stress in tension of steel is 400 N/mm², determine the required area of reinforcement.
First it is necessary to check whether or not the applied moment exceeds the ultimate moment of resistance provided by the concrete. Hence, using Eq. (12.23)
M_u = 0.15σ_{cu}b(d_1)^2 (12.23)
M_u = 0.15 × 30 × 250 × 600^2 × 10^{−6} = 405 \ kN \ m
Since this is greater than the applied moment, the beam section does not require compression reinforcement.
We now assume the stress distribution shown in Fig. 12.12 in which the neutral axis of the section is at a depth n below the upper surface of the section. Thus, taking moments about the tensile reinforcement we have
350 × 10^6 = 0.4 × 30 × 250 \ n \left(600 – \frac{n}{2} \right)
from which
n = 243.3 mm
The lever arm is therefore equal to 600 − 243.3/2 = 478.4 mm. Now taking moments about the centroid of the concrete we have
0.87 × 400 × A_s × 478.4 = 350 × 10^6
which gives
A_s = 2102.3 \ mm^2
