Bending of Beam

A beam is a rod of uniform cross section of an elastic materials, whose length is much greater as compared to its thickness and breadth.

The beams are usually set in horizontal position and are designed to support heavy loads. They can support heavy loads such as roofs in buildings and heavy vehicles passing over the bridges.

A beam which is clamped at one end and loaded at the other end is called cantilever.

In order to study the bending of beams the following assumptions are made

(i) The weight of the beam is low.

(ii) The cross section of the beam remains same so that the geometrical moment of inertia of the beam remains same.

(iii) There are no shearing forces.

(iv) The beam has small curvature.

The bending of beam occurs when one end of the beam is fixed and other end is loaded with different weights.

Longitudinal filaments

A beam is regarded as made up of a number of thin layers placed in contact parallel to one another. Further each layer is regarded as a collection of thin layers parallel to the length of the beam. These fibres are called longitudinal filaments.

Neutral surface or neutral filament

Let us consider a section

ABCD

of the bent beam (Fig. 1). The filaments lying on the convex side (upper half) of the beam are extended while on the concave side (lower side) are compressed in length. Some where inside the beam there is a layer of filaments whose length remains the same without any change. It is considered to be neutral. This is known as the neutral surface or neutral filament.

Fig. (1) Bending of beam