Lab report

2101ENG Mechanics of Materials

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EXPERIMENT E1 – STRESS AND STRAIN IN PLASTIC STRAP

AIMS 1. To use a strain gauge to measure the strain produced when a weight is hung

from a plastic strap. 2. To calculate the stress. 3. To calculate Young’s Modulus for this plastic. THEORY

If a wire is stretched, producing a strain,  /  , the resistance of the wire changes. The relative change of resistance, R/R, is related to the strain by: R l

k R l

    where k is the GAUGE factor.

A strain gauge generally consists of a grid of fine wire or foil, firmly embedded in plastic, which is cemented to an object. If this object is subjected to a strain, the strain gauge suffers the same strain. The resistance of the gauge will then change, and if R/R is measured, and k is known, the strain is calculated from:

Strain= 0 1

s

R

k R

 

where Vo = Out-of-balance voltage Vs = Supply voltage = 2.5 V k = Gauge factor = 2.1

Young’s Modulus, E = stress

strain

/

/

F A mg E

A

EA m

g     

   



  





where m is the mass attached to the wire or strap and A is its cross-sectional area. Thus, a graph of mass, m against the strain,   / , will be a straight line of slope, /s EA g .

PROCEDURE 1. The electrical circuit is as shown in the diagram on the next page (refer to Figure

1). 2. Hang the weight carrier on the strap. 3. Measure the dimensions of the strap and calculate the cross-sectional area. 4. Zero the digital voltmeter (be patient and adjust carefully). 5. Add a weight to the end of the strap. 6. Record the voltmeter reading in millivolts. 7. Record your observations as weights are progressively added. 8. Record readings as the weights are removed as well.

9. Graph m against the strain, e and determine the slope of the graph s = m

kg e

 

10. Determine Young’s Modulus for the strap. /E s g A 

Gain V k 4 V

Gain = Gain factor = 100

2101ENG Mechanics of Materials

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Mass Added

m (kg) Out-of-Balance Voltage Vo, mV Strain e

s 

Adding

Removing

0 0 0 0 0.5 1.0 1.5 2.0 2.5

Figure 1: Electrical circuit for strain gauge measurements 11. Determine the stresses ( /F o r c e A r e a  ) acting on the strap RESULTS AND REPORT: 1. Tabulate the calculated and experimental results. Also, report the reasons for any large discrepancies. 2. Explain clearly (with diagrams where appropriate), how the measurements show the (tensile or compressive) strains.

0 Gain V k

4 Ve 

 



2101ENG Mechanics of Materials

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EXPERIMENT E2 – YOUNG’S MODULUS OF A WIRE

AIM To determine the Young’s Modulus of a steel wire. THEORY

Figure 1: Stretching of a wire If we apply a force F to the end of a wire of initial length l and cross-sectional area A, producing a strain,  / , theory predicts that provided the elastic limit is not exceeded: F

E A

 



 where E = Young’s Modulus.

The equation can be rearranged to EA

F 

 



If the Force F is applied by hanging a mass m on the wire, then F = mg

Thus EA

F mg 

  

 , and

EA m

g  

 .This is an equation of the form: y = kx.

We would then expect that if we apply masses, m and measure the extensions produced, and plot m against extension we should obtain a straight line of slope equal to /EA gl . If we measure the slope of the line and know A and  we can then

estimate E. That is,

If slope = EA

g , then E =

slope g

A

 

PROCEDURE 1. The apparatus should be set up as in the diagram below (see Figure 2). Adding

masses to the weight carrier, causes the wire to extend rotating the pulley and pointer. From the pointer rotation the extension of the wire can be determined.

2. Measure the radius of the pulley, r. Measure the length of the pointer from the centre of the pulley, R. Calculate the amplification ratio /R r  . Note from the

geometry: 1D r

D D r R R  

      



3. With just the weight carrier hanging on the wire, centre the pointer. 4. Measure the diameter of the wire, d. Use the micrometer and repeat your

measurements at several places along the wire to obtain an average value.

5. Calculate the cross-sectional area of the wire 2

4

d A 

6. Measure the length of the wire 

2101ENG Mechanics of Materials

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Figure 2: Schematic diagram of wire tension apparatus

7. Add masses to the weight carrier and note the pointer deflection. Repeat as the masses are removed. Record your measurements in the table below.

Mass added m (kg)

Pointer Deflection D(mm)

Extension of Wire, ext

(mm) Adding Removing Average 0 0

0.5 1.0 1.5 2.0 2.5

8. Graph the mass added against the extension produced.

9. Measure the slope of the graph m kg

s ext m

  

10. Determine Young’s Modulus for this steel:

2

g N E s

A m 



11. Determine the stresses at different load condition. 12. Convert E to MPa (Note: for many steels E = 200,000MPa) RESULTS AND REPORT: 1. Tabulate the calculated and experimental results. Also, report the reasons for any large discrepancies. 2. Explain clearly (with diagrams where appropriate), how the measurements show the (tensile or compressive) strains.