This document summarizes an experiment using strain gauges to measure the deflection of a cantilever beam under different applied masses. Strain gauges measure the voltage change when force is applied. The experiment found that the beam deflected more and the voltage increased more with heavier masses. However, the voltage readings were not perfectly linear with increasing mass. The spring constant of the beam, calculated from the force and deflection, was found to differ by 22.2% between the 100g and 500g masses.

1. Strain Gauge -
Investigation and Use
26th March 2013
by ZHOU Tianxun (Leo)
Li Shuhan
Liu Jihui
Azat

2. Introduction
In this lab session, strain gauges are used in the static response of a
cantilever beam when a force is applied to its free end. Strain gauge
is an engineering tool. It is used for measuring force by voltage
change.
Cantilever
Masses
added
(g)
Initial
Beam
(cm)
Final
Beam
(cm)
Beam
Deflection
(cm)
Voltage
Reading
(v)
Change
in
Voltage
(v)
0 8.7 8.7 0.0 -0.05 0.00
100 8.7 8.9 0.20 0.412 0.462
500 8.7 9.5 0.80 2.428 2.478
Hence, the voltage is -0.05 when 0g weight was used.
change in voltage for 100g weight= 0.462 V
beam deflection for 100g weight= 0.20 cm
change in voltage for 500g weight= 2.478 V
beam deflection for 500g weight= 0.80 cm
Linearity
The Voltage of 100g;0.412+0.05=0.462 V

3. The Voltage of 500g:2.428+0.05=2.478 V
5 * (0.462 V)= 2.31 V which is not same as (2.478 V)
So the voltage reading for 100 g by 5 is not as same as the reading
for 500 g.
Spring constants
According to F=kx
(F is the force applied on the beam (N)
k is spring constant of the beam (Nm^-1)
x is the deflection of the beam (m))
For 100g mass
k=F/x=(100 x 10^-3 x 9.81)/(0.2 x 10^-2)
=490.5(Nm^-1)
For 500g mass
k=F/x=(500 x 10^-3 x 9.81)/(0.8 x 10^-2)
=613.125(Nm^-1)
%difference =(613.125 - 490.5)/((490.5+613.125)/2) x 100
=22.2%
Measurement of