PH8151 Engineering Physics Chapter 1

36 CHAPTER 1. PROPERTIES OF MATTER

Self Learning Activity : Young’s Modulus Uniform Bending

Using the unifrom bending simulator, determine Young’s

moduli of the available materials.

URL: 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 (1.40)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

l

Load

Pin

Figure 1.32: Non-uniform bending - experimental set up

distance between the two knife edges and let a weightW =Mgis suspended at the
midpoint (i.e., at the distancel/ 2 from the knife edges). Then the reaction at each knife
edge isW/ 2 which acts vertically upwards. The part of the beam between the knife edges
is equivalent to a pair of inverted cantilevers, each of lengthl/ 2 with an upward force
W/ 2 at the inverted free end as shown in Figure1.33. The elevation at the loaded end

36