Question 12.P.6: A reinforced concrete T-beam is required to carry a uniforml...
A reinforced concrete T-beam is required to carry a uniformly distributed load of 42 kN/m on a simply supported span of 6 m. The slab is 125 mm thick, the rib is 250 mm wide and the effective depth to the tensile reinforcement is 550 mm. The working stresses are 8.5 N/ mm² in the concrete and 140 N/mm² in the steel; the modular ratio is 15. Making a reasonable assumption as to the position of the neutral axis find the area of steel reinforcement required and the breadth of the compression flange.
Assume that the neutral axis is at the base of the flange. The maximum bending moment is
M=\frac{42 \times 6^{2}}{8}=189 \mathrm{\ kN} \mathrm{\ m}
Then, taking moments about the resultant compressive force in the concrete flange
140 A_{\mathrm{s}}\left(550-\frac{125}{3}\right)=189 \times 10^{6}
i.e.
A_{s} = 2655.7 mm²
The tensile force in the steel is equal to the compressive force in the concrete, i.e.
140 A_{\mathrm{s}}=\left(\frac{8.5}{2}\right) b \times 125
which gives
b = 699.9 mm
The required width of the flange is therefore 700 mm.