The correct answer is $\boxed{\text{C}}$.
The strength of a reinforced concrete column is given by the following equation:
$$\sigma_c = \frac{N}{A}$$
where:
- $\sigma_c$ is the compressive stress in the concrete
- $N$ is the axial load on the column
- $A$ is the cross-sectional area of the column
The modular ratio, $m$, is a dimensionless quantity that is defined as the ratio of the elastic modulus of steel to the elastic modulus of concrete. The maximum stress in the concrete, $\sigma_c$, is given by the following equation:
$$\sigma_c = \frac{f_c’}{m}$$
where:
- $f_c’$ is the compressive strength of the concrete
The area of concrete, $A_c$, is given by the following equation:
$$A_c = \pi r^2$$
where:
- $r$ is the radius of the column
The area of longitudinal steel, $A_s$, is given by the following equation:
$$A_s = bh$$
where:
- $b$ is the width of the column
- $h$ is the height of the column
Substituting these equations into the equation for the strength of the column, we get the following equation:
$$\sigma_c = \frac{N}{A} = \frac{f_c’}{m} \pi r^2 + \frac{f_y’}{m} bh$$
where:
- $f_y’$ is the yield strength of the steel
Therefore, the strength of the column is given by the following equation:
$$\sigma_c = \sigma_c\left[ A + \left( m – 1 \right) A_s \right]$$
where:
- $\sigma_c$ is the maximum stress in the concrete
- $A$ is the cross-sectional area of the column
- $A_s$ is the area of longitudinal steel
- $m$ is the modular ratio