Reinforced Concrete Bending Capacity
The **Beam Load Capacity** in bending is quantified by its **Design Moment Capacity ($\phi M_n$)**. This value must always be greater than the maximum factored bending moment ($M_u$) caused by external loads. This check is fundamental to flexural design in reinforced concrete.
Whitney Stress Block & Formulas
The calculation uses the equivalent rectangular stress block (Whitney Stress Block), which simplifies the parabolic stress distribution in the compressed concrete for easier analysis.
1. Depth of Stress Block ($\mathbf{a}$)
The depth $a$ is found by enforcing force equilibrium ($C=T$, where $C$ is concrete compression and $T$ is steel tension).
$$\mathbf{a = \frac{A_s f_y}{0.85 f'_c b}}$$
2. Nominal Moment Capacity ($\mathbf{M_n}$)
The moment is calculated by multiplying the tension force ($T = A_s f_y$) by the internal lever arm ($d - a/2$).
$$\mathbf{M_n = A_s f_y \left(d - \frac{a}{2}\right)}$$
3. Design Capacity ($\mathbf{\phi M_n}$)
The nominal capacity is reduced by a strength reduction factor $\phi$ (typically $0.90$ for tension-controlled beams) to account for construction variability and non-ideal conditions.
Warning on Section Type:
This simplified calculator assumes the section is **tension-controlled** (steel yields before concrete crushes), which is the desirable and required condition for ductility. If the section is over-reinforced, the $\phi$ factor must be reduced, or the design must be revised.