A singly reinforced beam has breadth b, effective depth d, depth of neutral axis n and critical neutral axis n1. If fc and ft are permissible compressive and tensile stresses, the moment to resistance of the beam, is A. $${\text{bn}}\frac{{{{\text{f}}_{\text{c}}}}}{2}\left( {{\text{d}} – \frac{{\text{n}}}{3}} \right)$$ B. $${\text{At}}{{\text{f}}_{\text{t}}}\left( {{\text{d}} – \frac{{\text{n}}}{3}} \right)$$ C. $$\frac{1}{2}{{\text{n}}_1}\left( {1 – \frac{{{{\text{n}}_1}}}{3}} \right){\text{cb}}{{\text{d}}^2}$$ D. All the above

The correct answer is D. All the above.

The moment to resistance of a singly reinforced beam is given by the following equation:

$$M_r = \frac{1}{2}b d f_c \left(d – \frac{n}{3}\right) + A_t f_t \left(d – \frac{n}{3}\right)$$

where:

• $b$ is the breadth of the beam
• $d$ is the effective depth of the beam
• $f_c$ is the permissible compressive stress
• $f_t$ is the permissible tensile stress
• $A_t$ is the area of tension reinforcement
• $n$ is the depth of the neutral axis

The first term in the equation, $\frac{1}{2}b d f_c \left(d – \frac{n}{3}\right)$, represents the contribution of the concrete to the moment to resistance. The second term, $A_t f_t \left(d – \frac{n}{3}\right)$, represents the contribution of the tension reinforcement to the moment to resistance.

The depth of the neutral axis is a function of the beam’s geometry and the material properties of the concrete and steel. The critical neutral axis is the depth of the neutral axis at which the beam will fail in tension.

The moment to resistance of a singly reinforced beam is the maximum moment that the beam can resist without failing.