Unit 1 Engineering Physics

1.11. UNIFORM BENDING AND NONUNIFORM BENDING

Load

(kg)

Travelling Microscope

Readings

Elevation

for load

M= 0.05 kg

Load increasing(m) Load decreasing(m) Mean (m) (m)

L+ 0.05

L

L+ 0.10

L+ 0.15

L+ 0.20

L+ 0.25

Mean elevation (y) =

Figure 1.31:Uniform bending - Measurement of elevation at the mid point of the beam

callipers, the breadth (b) of the beam is determined. The thickness (d) of the beam is
measured using a screw gauge. Young’s Modulus of the beam is then calculated from the
expression:

Y =

3

2

M gal^2

bd^3 y

Self Learning Activity : Young’s Modulus Uniform Bending

Using the unifrom bending simulator, determine Young’s

moduli of the available materials.

http://vlab.amrita.edu/?sub=1&brch=280&sim=550&

cnt=1

Worked out Example 1.11.1

A rectangular bar 1m long, 2 cm broad, and 0.5 cm thick is supported symmetrically

on its flat face on two knife edges 70 cm apart. When loads of 200 g are hung from

the two ends, the elevation of the centre of the bar is 4.8 mm. Find the Young’s

modulus of the bar [ 6 ].

Solution:

The beam is bent uniformly because it is supported symmetrically and loaded at

its ends. For this beaml=0. 7 m anda= 0.15 m. Using the expression (1.39)we

calculate the Young’s Modulus of the beam.

Y =

3

2

M gal^2

bd^3 y

=

3(0. 2 kg)(9.8m/s^2 )(0.15m)(0.7m)^2

2(2◊ 10 ≠^2 m)(0. 5 ◊ 10 ≠^2 m)^3 (4. 8 ◊ 10 ≠^3 m)

=18.0GPa

1.11.2 Non-uniform Bending: Theory and Experiment

A beam is supported on two knife edges with a load applied midway between the supports,
as shown shown in Figure1.32, is an example of nonuniform bending [ 7 ]. Letlbe the

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