Applied Physics I: Chapter 1: Properties of Matter - Elasticity
Bending of Beams and Stress due to Bending
A beam is defined as a rod (or) bar, [Circular or rectangular] of uniform cross‒section whose length is very much greater than its other dimensions, such as breadth and thickness.
BENDING
OF BEAMS & STRESS DUE TO BENDING
Beam:
A beam is defined as a rod (or) bar, [Circular or rectangular] of uniform cross‒section
whose length is very much greater than its other dimensions, such as breadth
and thickness. It is commonly used in the construction of bridges to support
roofs of the buildings etc. Since the length of the beam is much greater than
its other dimensions the shearing stresses are very small.
Assumptions
While
studying about the bending of beams, the following assumptions has to be made.
1.
The length of the beam should be large compared to other dimensions.
2.
The load (forces) applied should be large compared to the weight of the beam.
3.
The cross‒section of the beam remains constant and hence the geometrical moment
of inertia Ig also remains constant.
4.
The shearing stresses are negligible.
5.
The curvature of the beam is very small.
BENDING OF A BEAM AND
NEUTRAL AXIS
Let
us consider a beam of uniform rectangular cross section Fig.1.5. A beam may be
assumed to consist of a number of parallel longitudinal metallic fibres placed
one over the other and are called as filaments as shown in Fig 1.6.
Let the beam be subjected to deforming forces at its ends as shown in Fig.1.7. Due to the deforming forces the beam bends. We know the beam consists of many filaments. Let us consider a filament AB at the centre of the beam. It is found that the filaments (layers) lying above AB gets elongated, while the filaments (layers) lying below AB gets compressed. Therefore the filament (i.e) layer AB which remains unaltered is taken as the reference axis called as NEUTRAL AXIS and the plane is called as neutral plane. Further, the deformation of any filament can be measured with reference to the neutral axis.
Applied Physics I: Chapter 1: Properties of Matter - Elasticity : Tag: Applied Physics : - Bending of Beams and Stress due to Bending
Applied Physics I: Chapter 1: Properties of Matter - Elasticity
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