Neutral Axis and Bending Stress Calculations

- When a beam bends, its
**top is in compression**and its**bottom is in tension.**- This is why non-reinforced concrete beams fail on the underside - concrete is weak in tension.

- The
**neutral axis**is the approximate**centre of the beam's cross section.**- The
**further the distance**from this axis, the**stronger**a beam is in**BENDING**.

- The
- Maximum bending stress can be calculated by:

\begin{align} \frac{M}{I_{xx}} = \frac{E}{r} = \frac{\sigma_b}{y} \end{align}

or

(2)\begin{align} \sigma_b = \frac{My}{I_{xx}} \end{align}

Where:

- M is the Bending Moment at the section (Nm)
- $I_{xx}$ is the second moment of area ($m^4$)
- E is Young's Modulus of the material (Pa)
- r is the radius of curvature (m)
- $\sigma_b$ is the Bending stress at the section (Pa)
- y is the distance from neutral axis to edge (m)

**HINTS**

- The
**Maximum Bending Stress**is determined with the same formulas, by replace $\sigma_b$ with $\sigma_{max}$. - $\sigma_{max}$ is determined by the
**Bending Moment Diagram.**- The maximum moment
**on the BM diagram**is considered the maximum bending stress.

- The maximum moment

page revision: 2, last edited: 05 Jul 2011 08:32