EATS 2470
Introduction to Continuum Mechanics
Instructor: Peter Taylor; TA Shama Sharma
Lab #3: Beam Bending: March 8 and 15, 2011 14:30-17:30 @ PSE 133
Purpose: The aim of this lab is to determine Young’s modulus for steel and aluminum bars by
measuring the amount of deflection beams of known cross section undergo under a specified
load, and to plot the comparisons between theoretical and observed values of displacement at
positions along the beam.
Case 1: Beam is supported at both ends and single load at the centre
1. First find the length (l) of the beam using metre scale. Then
2. Measure width (w) and thickness (h) of the beams using Vernier Callipers.
3. Find moment of Inertia of the beam cross section using Formula
4. Complete the observations for Case1 using two masses for each beam.
Material
Mass
(kg)
Steel
I=
Deflection
at position
x1 (mm)
Deflection
at position
x2 (mm)
Deflection
at position
x3 (mm)
Deflection
at position
x4 (mm)
Young
Modulus for
position x0
0 kg
(m4)
Aluminum
I =
Deflection
at centre,
x0 (mm)
0 kg
(m4)
5. Use your observations for maximun deflection(y) at the centre to find Young’s modulus (E)
for both of the beams using the formula, ymax = Wl3/(48EI)
6. The formula for calculating the amount of deflection between load and support points at
various locations other than the centre is given by y = Wx(3l2-4x2)/(48EI)
7. For one value of W, use your calculated value of E (which is Young’s Modulus) to find
expected value of deflection at particular positions using the following table
Material
Mass(gm)
Expected
value of
Deflection at
position x1
Expected
value of
Deflection at
position x2
Expected
value of
Deflection at
position x3
Expected
value of
Deflection at
position x4
Steel
Aluminum
8. Use plotting software to generate a plot between the variation amount of deflection(y) at
different positions from the load(x) and compare it with the observed values from the experiment
and the expected values from the calculations.
Case 2: Beam is supported at one end and load is applied at the other.
Formula is
Repeat the procedure as in case 1 and fill your observations in the following table
Material
Mass
(kg)
Steel
Deflection
at position
x1 (mm)
Deflection
at position
x2 (mm)
0 kg
I = (m4)
Aluminum 0 kg
I = (m4)
Compare the values of E from both cases..
Deflection
at position
x3 (mm)
Deflection
at end
x4 (mm)
Young
Modulus for
position x4