Experiment 2 – Stress and Strain in a Plastic Strap PDF

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Experiment 2 – Stress and Strain in a 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 material is stretched, producing a strain, Δl l , the resistance of the material changes. The relative change of resistance, ΔR R , is related to the strain by:

ΔR Δl =k l R 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 ΔR R is measured, and k is known, the strain is calculated from:

Strain =

4V0 1 ΔR = k R Gain kVs

where Vo = Out-of-balance voltage Vs = Supply voltage = 2.5 V k = Gauge factor = 2.1 and Gain = Gain factor =100 Stress can be determined by manual calculation, by measuring the cross sectional area of the material and converting the mass of the weights into a force. Thus, a graph of stress against strain will be a straight line whose slope is equal to the Young’s Modulus of the material being tested.

Stress

Young’s Modulus, E =฀Strain

Procedure: 1. The electrical circuit is as shown in the diagram on the next page (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. Calculate the stress and strain acting on the strap. 10. Graph stress against the strain, and determine the slope of the graph. 11. Determine the Young’s Modulus for the strap (E).

Figure 1: Electrical circuit for strain gauge measurements Table 1: Observations and calculations Out of Balance Voltage, V0 Mass Added (mV) Force (N) (kg) Adding Removing 0.0 0.5 1.0 1.5 2.0

Strain e=

4 ⋅V0 gain ⋅ k ⋅ Vs

Stress (MPa)

Results and Reporting: 1. Tabulate the calculated and experimental results. Also, report the reasons for any large discrepancies. 2. Graph the stress against strain and determine from the graph the Young’s modulus of the material. Present the required graphs (One for mass adding and one for mass removing). Please ensure the formula for the line and the R2 value are presented. 3. Explain clearly (with diagrams where appropriate), how the measurements show the (tensile or compressive) strains. 4. Produce a concise laboratory report. This should include the aims, theory, procedure and results. Clearly present the graphs used to determine the Young’s modulus of the material as well as your determined value for the Young’s modulus. Please investigate what the expected Young’s modulus of the material should be and report on any discrepancies between the observed and expected results. 5. Please note, your laboratory report will be due by 4pm, 1 week after your scheduled lab session...