With usual notations the depth of the neutral axis of a balanced section, is given by A. $$\frac{{{\text{mc}}}}{{\text{t}}} = \frac{{{\text{d}} – {\text{n}}}}{{\text{n}}}$$ B. $$\frac{{\text{t}}}{{{\text{mc}}}} = \frac{{\text{n}}}{{{\text{d}} – {\text{n}}}}$$ C. $$\frac{{\text{t}}}{{{\text{mc}}}} = \frac{{{\text{d}} + {\text{n}}}}{{\text{n}}}$$ D. $$\frac{{{\text{mc}}}}{{\text{t}}} = \frac{{\text{n}}}{{{\text{d}} – {\text{n}}}}$$

The correct answer is: $\frac{{{\text{mc}}}}{{\text{t}}} = \frac{{{\text{d}} – {\text{n}}}}{{\text{n}}}$

The neutral axis is an imaginary line in a beam where the strain is zero. The depth of the neutral axis is the distance from the top or bottom of the beam to the neutral axis.

The formula for the depth of the neutral axis of a balanced section is:

$$\frac{{{\text{mc}}}}{{\text{t}}} = \frac{{{\text{d}} – {\text{n}}}}{{\text{n}}}$$

where:

• $m$ is the bending moment
• $c$ is the distance from the neutral axis to the extreme fiber in tension
• $t$ is the thickness of the beam
• $d$ is the depth of the beam
• $n$ is the modulus of elasticity

The modulus of elasticity is a measure of how much a material stretches or deforms under stress. The higher the modulus of elasticity, the less the material will deform.

The depth of the neutral axis is important because it determines the maximum stress in the beam. The maximum stress occurs at the extreme fibers, which are the fibers farthest from the neutral axis. The stress in the beam is proportional to the distance from the neutral axis. Therefore, the fibers farthest from the neutral axis will experience the greatest stress.

The depth of the neutral axis also affects the deflection of the beam. The deflection of the beam is the amount that the beam bends under load. The deflection of the beam is proportional to the square of the distance from the neutral axis. Therefore, the fibers farthest from the neutral axis will experience the greatest deflection.