Applied Physics I: Chapter 1: Properties of Matter - Elasticity
Non-Uniform Bending-Depression at the mid-point of a beam loaded at the middle
Due to the load (W) applied, at the middle of the beam the reaction W/2 is acted vertically upwards at each knife edges.
NON‒UNIFORM
BENDING‒DEPRESSION AT THE MID‒POINT OF A BEAM LOADED AT THE MIDDLE.
THEORY
Let
us consider a beam of length ‘l’,
(distance between two knife edges) supported on the two knife edges A and B as
shown in Fig 1.13. The load of weight 'W' is suspended at the centre 'C'. It is
found that the beam bends and the maximum displacement is at the point 'D',
Where the load is given.
Due
to the load (W) applied, at the middle of the beam the reaction W/2 is acted
vertically upwards at each knife edges. The bending is called as non‒uniform bending.
The
beam may be considered as two cantilevers, whose free end carries a load W/2
each of length l/2 and fixed at the
point 'D'.
Hence
we can say the elevation of A above D as the depression of D below 'A'. We know
depression of a cantilever y = Wl3 / 3YIg
Therefore
substituting the value of l as l/2 and W as W/2 in the expression for
the depression of a cantilever, (i.e) y
= Wl3 / 3YIg
we
have
Depression
of D below A = y = (W/2)(l/2)3
/ 3YIg
Note:
Angle of inclination of the tangents at the points A and B is
Applied Physics I: Chapter 1: Properties of Matter - Elasticity : Tag: Applied Physics : - Non-Uniform Bending-Depression at the mid-point of a beam loaded at the middle
Applied Physics I: Chapter 1: Properties of Matter - Elasticity
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