Consider how the bending moment distorts a small element of the beam located along the beam's length?
Consider how the bending moment distorts a small element of the beam located along the beam's length?
Given Data:
- The bending moment acting on the beam is
Take an elemental section of infinitesimal length dx.
The section before deformation has a shape as shown in the figure.
When the beam is subjected to the bending moment M it suffers deformation which can be shown as.
For the element shown the neutral plane is the plane which passes through fibre which suffers no deformation when subjected to the bending moment.
For the analysis of distortion consider a fibre AB which is at a distance of y from neutral plane.
Under deformation, the AB changes to A’B’.
The original length of AB was equal to the fibre lying on the neutral axis. Thus, the length of the fibre AB can be determined as,
The deformed length A’B’ can be determined as,
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