Modulus of Elasticity Experiment

Introduction:

The purpose of this experiment is to measure the Modulus of Elasticity (Young's Modulus) of an aluminum beam by loading the beam in cantilever bending. The modulus of elasticity, a fundamental constant for linear elastic materials, is an index of the stiffness of the material.

For many common structural materials, including aluminum alloys and steels, strain is an essentially linear function of the stress over the range of stresses normally encountered by load-carrying members.

Figure 1. Stress-strain diagram

Figure (1) represents a typical stress-strain diagram for a metal under uniaxial stress (tension, compression, or bending). By definition, the slope of the linear portion of the diagram is the modulus of elasticity. Therefore,

E = Modulus of Elasticity = DS / De

Where,

E = Modulus of elasticity, psi (N/m2)

S = Stress, psi (N/m2)

e =Strain, in/in (m/m)

 

Equipment and Supplies:

Flexor, cantilever flexure frame

High strength aluminum alloy beam, 1/8 x 1x12-1/2 in (3x25x320 mm)

Micro-measurements temperature -compensated strain gages

1011 Portable Strain Indicator or equivalent

Strain gage Application Kit, containing gage bonding supplies, hook-up wire, etc.

Laboratory weights for loading cantilever beam

Micrometer

Accurate drafting or machinist's scale

 

Procedure:

In this experiment, the flexural stress-strain diagram for an aluminum alloy will be obtained by loading a beam in cantilever bending as shown in Figure(2).

Figure 2. Flexor

With the dimensions of the beam known, the stress as a function of the applied load can be calculated quite accurately from the flexure formula:

 

where,

M = bending moment at gage centerline, in-lbs (N-m)

c = thickness of the beam, in (m)

I = moment of inertia of beam cross -section, in4 (m4)

P = load, lb (N)

L = effective beam length, in (m)

b = beam width, in (m)

t = beam thickness, in (m)

 

The surface strian at the section of interest will be measured by a strain gage bonded at that point. The load will be applied in increments, and the corresponding strains will be recorded. The stresses calculated from the equation above and the strains measured by the strain indicator will be plotted to produce a stress-strain diagram from which the modulus of elasticity can be determined.

Figure 3. Elastic portion of the stress-strain diagram for 6061-T6 Aluminum test specimen.

 

Acquisition of Data:

Back the calibrated loading screw out of the way, and insert the beam into the Flexor, with the gaged end in the clamp, and with the gage on the top surface. Center the free end of the beam between the sides of the Flexor and firmly clamp the beam in place with the knurled clamping screw.

Connect the lead wires from the strain gage to the binding posts on the Flexor as shown in the wiring diagram. Then connect the appropriate gage leads from the Flexor cable to the S-, P+, and D2 binding posts of the 1011 Strain Indicator. See Figure (4) and (5).

Figure 4. Flexor wiring diagram

 

Figure 5. Wiring diagram for the connection of flexor cable to the strain indicator

 

Measure the distance from the centerline of the strain gage grid to the point of load application at the free end of the beam. Measure the width (b) and thickness (t) of the beam.

 

Analysis and Presentation of Data:

For each load increment calculate the beam stress from the equation using the exact loads. Record the load, stress and strain at each load level in the table provided below. Construct the stress-strain diagram on a spread sheet.

Step

Load (lb)

Strain (m e )

Stress (psi)

0

 

 

 

1

 

 

 

2

 

 

 

3

 

 

 

4

 

 

 

5

 

 

 

6

 

 

 

7

 

 

 

8

 

 

 

9

 

 

 

10

 

 

 

 

Report:

Prepare a report describing in your own words the purpose of the experiment, the equipment and setup used, and the procedure followed. Explain the procedure followed for the calibration of load screw. State the results obtained, and include the table of experimental data and the graph of stress versus strain. Discuss the probable sources of error in the experiment, and calculate the percent error.

 

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Last Update: March 14, 2000

By: Serdar Z. Elgun