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# Moments of Inertia

Worked examples involving Bending Stess and Moments of Inertia. View other versions (4)

## Overview

Bending moment refers to the algebraic sum of all moments located between a cross section and one end of a structural member; a bending moment that bends the beam convex downward is positive, and one that bends it convex upward is negative.

The General Equation for bending is used throughout. The proof of this is to be found in "Engineering/Materials/Bending Stress". For convenience the equation is written here and is as follows: Where
• is the Bending Moment
• is the Moment of Inertia of the section
• is Young's Modulus
• is the Radius of curvature
• is the stress at a distance from the Neutral Axis

It is obviously important to use the same units throughout!

Example:
[imperial]
##### Example - Example 1
Problem
The beam of a symmetrical section is simply supported over a span of 30 ft.

If the maximum permissible stress is 5 tons/sq.in., what concentrated load can be carried at a distance of 10 ft from one support?
Workings