# Structures Simplified

## Bending Strength of the Laterally Supported Beam

July 30, 2020 Posted by Parishith Jayan

Laterally Supported Beam – In general, a beam that does not move nor rotate laterally is termed as “Laterally Supported Beams”. This lateral restraint can be possibly obtained by several means. Few of them are,

·         Compression flange of the element embedded inside the slab
·         Compression flange connected to the slab by means of shear connector
·         Lateral braces provided in the beam

Determining the bending strength of the laterally supported beam is quite straight forward, before moving into it, let's get ourselves clear about the failure modes for the laterally supported beams, from which we can understand which factor governs the bending strength of the beam.

A typical laterally supported beam could fail by anyone of the following failure modes:

·         Shear failure of the section

·         Flexural failure of the section (bending failure)

·         Web crippling/web buckling (local failures)

·         Deflection

Of the above-mentioned failure modes, Flexural failure of the section is a bending failure, occurs when the applied load produces an internal bending moment, which is pretty much higher than the bending strength or moment capacity of the beam.

If we look into the above statement, there are two important terms,

1.    The internal bending moment generated because of the applied load.

2.    Bending or Moment capacity of the beam.

The first one can be determined by simple mechanics. For example, if we have a laterally supported pinned beam of length L and which supports a uniform load of W kN/m. Then the bending moment produced will be WL*L/8.

Our main interest is the Moment capacity of the section. It depends upon the cross-section of the beam as well as material grade.

In general, the Moment capacity of the section equals the product of Section Modulus and Yield strength of the material.

M = Z * fy * (factor of safety as per the specified code)

Thus, we have our required bending capacity or strength of the section.