ENGN 2217 Lab 1

Introduction This lab involves the use a flexure frame and a strain indicator to measure the strain across gauges

on three different aluminium samples. These strain gauges measure the change in resistance across

a point on the sample as it is deformed and the indicator converts this into a strain value. Additional

details and background theory can be found in the E101 handout available on Wattle. In all three

experiments, the samples will be deflected and strain changes measured in order to observe the

strain behaviour of deformed elastic materials.

Equipment Aluminium samples

3 Aluminium samples are provided with strain gauges attached, and wires to be plugged into the

flexure frame. Wiring diagrams can be found in the following sections.

Flexure frame

The black frame provided is used to cantilever each of the three samples. The micrometer fixed to

the end of the frame allows for precise measurement of the deflection (in mm) of each sample. A

collection of wires run from the frame to be plugged into the strain indicator, thus connecting the

sample to the indicator via the frame. Wiring diagrams can be found in the following sections.

Strain indicator

The P-3500 Portable Strain Indicator can run on batteries or AC power via a transformer. Wires from

the flexure frame can be connected to one of four channels to allow changes in strain on the strain

gauges to be read.

Balancing the strain indicator: Strain readings are RELATIVE. The only significant data the indicator

can provide is difference in strain between two gauges, or difference in strain on a gauge between

two states of deflection. As such, the indicator must be balanced (zeroed) before your sample is

strained. To do this, press BAL twice, then RECORD to save the setting.

Setting the correct Gauge Factor: Strain gauges on your samples may have different gauge factors,

and these need to be set on the strain indicator. Press GF/SCALING and adjust the gauge factor to

match your sample. Ensure you are adjusting the gauge factor of the appropriate channel.

Lastly, remember that the strain indicator reports in microstrain () so values must be multiplied

by 10-6

E101: Determination of Young’s Modulus In this experiment, Young’s modulus of your sample will be calculated by measuring the strain at a

given deflection, and using the deflection to calculate the applied force. The force can be used to

find the stress experienced at the gauge, so that the stress can be found for a given strain. You must

plot a stress/strain curve and calculate its gradient, i.e. Young’s modulus, for this material.

Equipment Set-up

The wiring diagram for this experiment is provided in Figure 1, below. Note that the dummy required

in all experiments is D120. When fixing the first sample (3 wires attached) into the flexure frame,

ensure that it is flush against the back wall of the frame, and that it is resting properly in the plastic

housing that holds it in place. Make sure the micrometer is not touching the sample when you

tighten the housing as you could damage both the sample and the micrometer.

Figure 1: Wiring diagram for E101

Sample measurement

Figure 2: Sample lengths required in E101

Before or after this experiment, you will need to take several measurements of your sample in order

to determine the stress induced at the strain gauge. Figure 2 shows the lengths required for stress

calculation – these can be measured with a ruler. The breadth and height of the sample are also

required, as shown in Figure 3. For the sake of accuracy, these measurements should be made by

the micrometer or Vernier callipers provided

Figure 3: Cross section of the aluminium sample

Procedure

Gradually deflect the sample in increments of 50, recording the deflection at each increment up to

450. Then gradually relax the sample, again recording the deflection at 50 increments. If the

values differ significantly on the way back to =0, double check your measurements. Also, remember

to measure the deflection at 0, as this will not read 0mm on your micrometer. Thus, the 0

deflection will need to be subtracted from all others to determine the actual deflection.

Strain

() (increasing) (mm)

(decreasing) (mm)

Average Force (calculated) Stress (calculated)

0

50

100

150

200

250

300

350

400

450

Using the measured sample dimensions and the deflections obtained, force can be calculated using

the following equation:

Where P is the force to be calculated. Assume E = 70GPa. The moment of inertia, I, for a rectangular

cross section is given by the equation:

By sectioning at the strain gauge, the internal moment, M, at the gauge can be found from equations

of equilibrium. The resulting stress at the sample’s surface (i.e.) the gauge location can be calculated

using:

Where y is the distance from the neutral axis to the surface (h/2).

Plot the stress-strain data obtained and calculate the resulting modulus of elasticity.

E102 Poisson’s Ratio While E101 allowed you to measure the strain along the length of a sample, E102 involves

calculating the strain in both the longitudinal and lateral directions. By measuring this strain and

applying a correction factor based on the gauges’ transverse sensitivity, Kt (see E102 document for

more details), Poisson’s ratio can be experimentally determined.

Equipment Set-up

Insert the second sample (four wires attached) into the flexure frame and take note of the Kt value

written on the back. The necessary wiring diagram can be found in Figure 4. Sample dimensions are

not required for this lab.

Figure 4: Wiring diagram for E102

Procedure

Wire #3 corresponds to the longitudinal strain gauge, while wire #4 represents the transverse gauge.

With wire #3 attached to P+ on the strain indicator, balance the indicator so that the longitudinal

strain reads as 0. Now swap wire #4 into P+ and record the strain value. Remember that this

number is not indicative of the actual state of strain, because the indicator is only capable of

measuring differences in strain for a particular gauge. Replace wire #3 in P+ and deflect the sample

until the gauge reads 750. Now insert wire #4 into P+ again and record the new lateral strain. The

difference between initial and final strains represents the total strain caused by the deflection. There

is no need to measure the deflection distance.

Longitudinal strain L () Transverse strain T ()

Initial 0

Final 750

Final minus Initial 750

Because the transverse gauge is on the opposite side of the sample to the longitudinal, the negative

of the transverse must be used.

Use this value as ̂ ̂ ⁄ in the correction chart (Figure 5) along with Kt found on the sample. The

correction value can be found of the chart and applied to the lateral strain. Given that Poisson’s ratio

is defined as the lateral over the longitudinal strain, Poisson’s ratio can now be calculated as:

Find literature values of Poisson’s ratio for the materials listed below and comment on the

differences to aluminium.

Figure 5: Transverse sensitivity correction chart

E103 – Principal Strains and Stresses This experiment involves measuring the strain across three different gauges sitting at a single point,

but oriented at different angles. These configurations are known as ‘rosettes’ with the two most

common called the rectangular rosette, with gauges angled separated by 45, and the delta rosette,

where the gauges are each separated by 120. See the E103 document for more details. The

configuration used in this experiment is the rectangular rosette.

From these three measured strains, the first and second principal strains can be calculated

regardless of the angle of the rosette. Because of the nature of the beam’s deflection, the first and

second principal strains will correspond with the longitudinal and transverse strain respectively. You

will first calculate these principal strains using rosette analysis, then calculate the corresponding

principal stresses based on Young’s modulus. You will also calculate the principal stresses using the

measured deflection and the flexure formula as you did in E101. Comparison of these stress values is

the principal aim of E103.

Equipment Set-up

Figure 6 illustrates the wiring diagram for E103. Wire 3 corresponds to gauge 1, wire 4 to gauge 2

and wire 5 to gauge 3.

Figure 6: Wiring diagram for E-103

Sample measurement

Figure 7: Sample lengths required in E103

The same measurements as made in E-101 are required here, so that the stress at the gauge can be

determined and compared to the stress determined via rosette analysis.

Figure 8: Cross section of the aluminium sample

Procedure

Plug gauge 1 (wire 3) into the indicator and balance the strain without deflecting the sample. You

must also measure the deflection on the micrometer at zero deflection so that this value can be

subtracted from the final reading. Swap gauge 2 in and record the strain. Swap in gauge 3 and do the

same. Now replace gauge 1 and deflect the sample until the strain reads 500. Measure gauges 2

and 3 on the deflected sample, as well as the final deflection in mm.

Initial Reading Final Reading

1 0 500 500

2

3

Displacement (mm)

Using the equations below, calculate coefficients A and B, and use them to determine the first and

second principal strains, p and q respectively.

Now calculate Poisson’s ratio for the material using the principal strains:

|

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The corresponding principal stresses can be calculated now, assuming a modulus of 70GPa.

( )

( )

Using the equations from E101, a different calculation for the first principal stress, i.e. the

longitudinal stress L can be calculated. Use this value to determine new values of the longitudinal

and lateral strain and fill the table below.

The angles, p and q are the angles made between gauge 1 and the first and second principal axes.

Calculate them using the equation below.

Deliverables You do not need to hand anything in at the end of the lab. All lab reports will be due after your final

week of labs has been completed. Each module, (101, 102, 103 etc.) should be written up

individually as a very brief report, including an aim (1 sentence), an introduction (no more than a

paragraph), results, discussion and conclusion.

E101: Include your measurements in the results, include your stress-strain plot and your

calculation of Young’s Modulus. Individual calculations of stress aren’t required (let Excel do

the work), just include an example calculation. Also comment on the significance of

assuming a Young’s modulus of 70GPa in this experiment.

E102: Include calculations made to determine v, compare this to a literature value (find one)

and include the completed table of literature values, commenting on any numbers of

interest.

E103: Include calculations of p and q, include the calculations of L using the E-101

equations, making sure to discuss the comparison between the rosette and flexure methods,

and include the calculation of the angles between the principal axes and gauge 1.