Experimental Analysis for Determining Stiffness and Moment of Inertia

Experimental Analysis
Contents
Experiment 1...............................................................................................................................................2
Aim..........................................................................................................................................................3
Formula...................................................................................................................................................3
Procedure................................................................................................................................................3
Observations:..........................................................................................................................................4
Graph.......................................................................................................................................................5
Tabulation................................................................................................................................................5
Graph.......................................................................................................................................................7
Tabulation................................................................................................................................................7
Graph.......................................................................................................................................................8
Result.......................................................................................................................................................9
Experiment2..............................................................................................................................................10
ABSTRACT..............................................................................................................................................10
Aim........................................................................................................................................................11
Procedure..............................................................................................................................................11
Tabulation:............................................................................................................................................11
Graph.....................................................................................................................................................12
Calculation.............................................................................................................................................12
Result.....................................................................................................................................................14
Reference..................................................................................................................................................15

Experiment 1
ABSTRACT
When a spring, a beam or a shaft is subjected to external forces due to their elastic nature they
liberate a vibratory motion. The aim behind this experimentation is to study the transverse
vibration of a simply supported beam when subjected to a load acting at the centre of the beam.
The experimental setup comprises of supports were the beam is to be fixed with the help of
trunnion bearings. The beam is fixed in the slots with the help of the trunnion bearings and
tightened. Loads are applied centrally on the beam. Due to Application of load the beam begins
to deflect. The deflection is measured with the help of a dial indicator. The main objective of the
experiment is to determine the stiffness of different materials under subjected load.Stiffness is an
important property for many applications of materials. The stiffness of a material depends on the
properties of the material and the amount of load applied on the material. By definition, stiffness
is defined as the ratio between load and deflection. (Bahaloo, H., et.al, 2016)

Aim
The aim of this experiment is to determine the stiffness of different materials when subjected to a
definite load.
Formula
Stiffness k = W/δ
Deflection δ= W l3
48 EI
Moment of inertiaI = b d3
12
Procedure
A beam of dimensions 9.5 mm × 3 mm is employed for the determination of stiffness. The beam
employed is made of aluminium. It is fixed to the supports with the help of trunnion bearings and
tightened. On application of load, the beam starts to deflection. The load applied is in terms of
100g and the deflection is calculated. The deflection is measured using the dial indicator. The
values are tabulated and the stiffness of the material is calculated. Similarly, beams of different
materials are employed mainly mild steel and brass and their respective stiffness is calculated. A
graph is plotted between load and deflection for all the three materials and the values are
tabulated (Gutowski, P. and Leus, M., 2015).

Observations:
Beam modulus
Load
applied(Grams)
Weight in
Newton(W)
N
Deflection in
millimeters
Deflectionδ
(m) 48 δI
L3
0 0 0 0 0
100 1 0.60 6.0x10-4 1.32x10-11
200 2 1.20 12.0x10-4 2.64x10-11
300 3 1.71 17.1x10-4 3.76x10-11
400 4 2.30 23.0x10-4 5.10x10-11
500 5 2.80 28.0x10-4 6.16x10-11
Material: Aluminum
Beam size : I =2.14x10-11 m4
Stiffness k = W/δ
δ1=0
δ2= W l3
48 EI = 1(1)3/48(69x109)
δ2=3.0193 ×10−9m