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.
• Maximum bending stress can be calculated by:
(1)
\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.
page revision: 2, last edited: 05 Jul 2011 08:32