PH8151 Engineering Physics Chapter 1

32 CHAPTER 1. PROPERTIES OF MATTER

l

Load

Pin

Figure 1.26: Cantilever - determination of Young’s Modulus

Load

(kg)

Travelling Microscope

Readings

Depression

for load

M= 0.05 kg

(m)

Load

increasing(m)

Load

decreasing(m)

Mean

(m)

L+ 0.05

L

L+ 0.10

L+ 0.15

L+ 0.20

L+ 0.25

Mean Depression (y) =

Figure 1.27: Measurement of depression at the loaded end of cantilever

Worked out Example 1.10.1

Calculate the Young’s modulus of the fol-

lowing cantilever. The length of the can-

tilever is 1 m which is suspended with a

load of 150 gm at the free end. The de-

pression is found to be 4 cm. The thick-

ness of the beam is 5 mm and breadth of

the beam is 3 cm [ 6 ].

Solution:

For a rectangular cantilever, the Young’s

Modulus is given by Equation (1.35).

Substituting the relevant quantities,

Y=

4 Mgl^3

bd^3 y

=

4(150◊ 10 ≠^3 kg)(9.8m/s^2 )(1m)^3

(3◊ 10 ≠^2 m)(5◊ 10 ≠^3 m)^3 (4◊ 10 ≠^2 m)

=39.2GPa

1.11 Uniform Bending and Nonuniform Bending

It can be shown thatthe rate of change of the bending moment with respect to distance
along the beam axis is equal to the shear force[ 7 ]. Therefore, if the shear force is zero in
a region of the beam, then the bending moment is constant in that same region. Pure
bending or uniform bending refers to flexure of a beam under a constant bending moment,

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