Unit 1 Engineering Physics

1.11. UNIFORM BENDING AND NONUNIFORM BENDING

lengthlbetween knife edges and suspend a loadLfrom the middle of the beam. A pin
is fixed vertically at the midpoint of the beam. Focus a travelling microscope to the tip
of the pin such that the horizontal cross-wire coincides with the image of pin-tip. Note
down the reading on the vertical scale of the microscope. Increase the load by adding 50
g. Lower the microscope such that the horizontal cross-wire now coincides with the new
position of pin tip image and note down the reading from vertical scale. This is repeated
by increasing the load in steps of 50 g tillL+250 gm and also for decreasing loads. The
readings are tabulated as shown (Figure1.34) and mean depression (y) for M= 0.05 kg
is calculated. Using a vernier calipers, the breadth (b) of the beam is determined. The

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 1.34: Non-Uniform bending - Measurement of depression at the mid point of the
beam

thickness (d) of the beam is measured using a screw gauge. Young’s Modulus of the beam
is then calculated from the expression:

Y=

Mgl^3

4 bd^3 y

Self Learning Activity : Young’s Modulus Non-uniform Bending

Using the non-unifrom bending simulator, determine Young’s

moduli of the available materials.

http://vlab.amrita.edu/?sub=1&brch=280&sim=1509&

cnt=1

Worked out Example 1.11.2

A 1 m bar with square cross-section of side 5 mm is supported horizontally at its

ends and is loaded with 100 g mass at the middle. The mid point is depressed by

1.96 mm due to the load. Calculate the Young’s Modulus of the material of the load.

Solution:

Since the beam is supported at its ends and loaded at the middle, its bending is

nonuniform. Length between supports (l) = 1 m. Square cross-section of side 5 mm

impliesb=d=0. 005 m. Depression at the mid point (y) = 1.96◊ 10 ≠^3 m. Mass

PH8151 37 LICET