Experiment 6 MOS LAB

AIM:
To determine the young’s modulus of elasticity of
1. Mild steel
2. Brass
3. Aluminium
By beam deflection method

APPARATUS
 Beam deflection apparatus
 Dial gauge arrangements
 Screw gauge
 Weights
 Hangers

THEORY
 Bending may be accompanied by direct stress,
transverse shear or torsional shear, however for
convenience; bending stresses may be considered
separately .
 In order to separate the stresses it is assumed that the
loads are applied in the following manner:
loads act in a plane of symmetry, no twisting occurs,
deflections are parallel to the plane of the loads, and
no longitudinal forces are induced by the loads or by
the supports

ELEMENTS OF A BENT BEAM : the fibres form concentric arcs, the top fibres are
compressed and bottom fibres are elongated

 “Deflection” of a beam is the displacement of a point
on the neutral surface of a beam from its original
position under the action of applied loads . Before the
proportional limit of the material, the deflection, Δ,
can be calculated using the moment of inertia,
modulus of elasticity along with other section
properties that will depend on the given situation
imposed on the beam. The position of the load, the
type of load applied on the beam, and the length of
beam are examples of section properties that depend
on the situation.

The Euler-Bernoulli equation for the bending of
slender ,isotropic ,homogenous beams of constant
cross-section under an applied transverse load q(x) is
EId^4w(x)/dx^4 = q(x)
where E is the Young’s modulus, I is the area moment
of inertia and w(x) is the deflection of the neutral axis
of the beam

Deflection is a measure of overall stiffness of a given beam
and can be seen to be a function of the stiffness of the
material and proportions of the piece . Deflection
measurements give the engineer a way to calculate the
modulus of elasticity for a material in flexure. The stiffness
of a given material is calculated using the following
equation:
Stiffness = Wa (3L ^2-4a^2)/24EI
where:
 P = load, (N)
 Δ = deflection, (mm)
 Stiffness (N/m)

FAILURE:
A beam may fail in any of the following ways:
A beam may fail by yielding of extreme fibbers, in long
span beams compression fivers act like those of a
column and fail by buckling, in webbed members
excessive shear stress may occur and stress
concentrations may build up in parts of beam adjacent
to bearing blocks

SCOPE AND APPLICATION:
The scope and applicability of the bending tests are defined
as:
a. Used as a direct means of evaluation behaviour under
bending loads, particularly for determining limits of
structural stability of beams of various shapes and sizes.
b. Made to determine strength and stiffness in bending.
c. Occasionally made to get stress distribution in a flexural
member.
d. May be used to determine resilience and toughness of
materials in bending.
e. Uses simple and inexpensive apparatus.
f. Used as control test for brittle materials and not suitable
for determining ultimate strength of ductile materials.

PROCEDURE
1) Draw the sketch of the apparatus and the loading
arrangement
2) Measure the breadth and depth of the beam at a few
locations and obtain the average breadth and depth
3) Measure the span of the beam and mark the loading
points on the beam
4) Set the dial gauge at the span and note the initial reading
5) Put 1/4kgf loads at the loading points and observe the
deflection the dial gauge
6) Repeat the experiment with ½ kgf, ¾ kgf and 1 kgf loads
for mild steel , brass and aluminium beams
7) 7. Plot a graph between W and stiffness and calculate the
value of E from the graph

OBERVATION
TO FIND THE CROSS SECTIONAL DIMENSION
Material Width of beam ‘b’ Depth of beam ‘d’ Moment of inertia
I =bd^3/12
A B C Mean A B C Mean
Mild steel 1 1 1 1 1 1 1 1 0.083
Brass 0.99 0.98 1 0.99 1 1 1 1 0.0825
Aluminium 0.96 0.95 0.98 0.96 0.95 0.94 0.95 0.94 0.0664

DETERMINATION OF E FOR MILD STEEL
Sl. No Material Load
distance
from
support ‘a’
Load ‘w’
kgf
Measured
deflection
‘mm’
E
N/mm^2
Mean E
1 MILD
STEEL
30 ¼ 0.3 165.29 1551.03
2 30 ½ 0.7 771.38
3 30 ¾ 1.12 1851.32
4 30 1 1.55 3416.13

0.25
0.5
0.75
1
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Loadin(kg)
Deflection in (mm)
Load vs Deflection Graph for Mild Steel

DETERMNATION OF E FOR BRASS
distance
from
support ’a’
Load ‘w’
kgf
Measured
deflection
‘mm’
E
N/mm^2
<E
1 BRASS 31 1/4 0.83 464.320 3675.42
2 31 ½ 1.70 1902.05
3 31 ¾ 2.63 4413.87
4 31 1 3.54 7921.47

0.25
0.5
0.75
1
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3 3.5 4
Loadin(kg)
Deflection in (mm)
Load vs Deflection Graph for BRASS

DETERMINATION OF E FOR ALUMINIUM
distance
from
support ’a’
Load ‘w’ kgf Measured
deflection
‘mm’
E
N/mm
Mean E
1 ALUMINIUM 31 ¼ 1.4 630.35 4962.91
2 31 ¼ 3.79 3412.92
3 31 ¾ 4.25 5740.73
4 31 1 5.59 10067.66

0.25
0.5
0.75
1
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6
Loadin(kg)
Deflection in (mm )
Load vs Deflection Graph for ALUMINIUM

PRECAUTIONS
1) Handle the dial gauge with great care and take the
readings very carefully.
2) See that the loading is done exactly at the points
chosen previously
3) The dial gauge should be kept exactly at the mid
span

Experiment 6 MOS LAB

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