PH8151 Engineering Physics Chapter 1

1.11. UNIFORM BENDING AND NONUNIFORM BENDING

Substituting for ( 1 /R)from(1.38) in equation (1.37), we arrive at:

Wa=YIg

3

8 y

l^2

4

Rearranging,

Y =

Wl^2 a

8 Igy

(1.39)

If the beam is of rectangular cross-section, then

Ig=

bd^3

12

(1.40)

wherebis the breath anddis the depth (or thickness) of the beam. If the load is due
the a suspended object of massM, the corresponding weight isW=Mg, wheregis the
acceleration due to gravity. Then the expression (1.39) can be written as:

Y =

3

2

M gal^2

bd^3 y

(1.41)

Experimental Procedure

Support the given beam symmetrically on two knife edges with lengthlbetween knife
edges and suspend two equal loadsLat equal distancesafrom the knife edges as shown
in Figure1.28. A pin is fixed vertically at the mid point 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

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

the load on both sides by adding 50 g each. Raise 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 loads on both sides in steps of 50 g
tillL+250 g and also for decreasing loads. The readings are tabulated as shown (Figure
1.31)and mean elevation (y) for M = 0.05 kg is calculated. Using a vernier 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

PH8151 35 LICET