MAE 244Electrical Resistance Strain GagesLab-2 c.1

Electrical Resistance Strain Gages - Application to Beam Bending

Experimental Procedures and Guidelines

Introduction

General Background:

The electrical-resistance strain gage is the most frequently used device for experimental stress analysis throughout the world. The strain gage can translate small changes in dimension into an equivalent change of electrical resistance, which is subsequently converted into a voltage change by a proper bridge circuit. The resistance strain gages have also found wide application as sensors in transducers designed to measure quantities such as load, torque, pressure and acceleration.

Objectives:

  1. To obtain strain measurements at the surface of a cantilever beam using strain gages.
  1. To determine the Modulus of Elasticity (Young's Modulus) and the Poisson's Ratio of a material used in a cantilever beam, from strain measurements on the surface of the beam.
  1. To validate the measurements from strain gages, by using elementary, linear beam theory to calculate the corresponding values of theoretical strain.
  1. To assess the differences in elastic properties between fibrous composites and metals.

Experimental Setup and Procedures

Equipment

Cantilever beam made of Aluminum alloy (7075-T6)

Cantilever beam made of Graphite/Epoxy composite (AS4/3501-6)

Portable strain indicator

Switch and Balance Units

Weights for Applying Load

Ruler

Experimental Procedures

  1. Hook up the longitudinal and transverse gagesof the aluminum beam to arm 1 of each bridge of the strain indicator via the switching and balancing unit. Follow the instructions on the switching and balancing unit and on the strain indicator. Complete the bridges with an internal dummy resistor by selecting 120 or 350 ohm internal resistors corresponding to the strain gages being used.
  1. Balance each bridge for zero output by adjusting the controls on the switching and balancing unit while watching the strain indicator display to null out the signal.
  1. Record position (deflection) of the beam on the vertical scale.
  1. Load the beam to a maximum of 2 1/2 lbs in 1/2 lb increments. Record the strain and the vertical position of the beam tip at each load increment, as indicated by the strain indicator for each gage.
  1. Repeat steps 1 - 4 for the composite beam.

Material Information

Aluminum Beam:7075-T6

Elastic Modulus:Ex = 10.4 Msi

Poisson's Ratio:xy = 0.3

Composite Beam:AS4/3501-6 Graphite Epoxy

Lay-up geometry:[0/90/0/0/0/0/90/0/0/0/0]s

Apparent Elastic Modulus:Ex = 16.71 Msi

Poisson's Ratio:xy = 0.0925

REPORT GUIDELINES (Discussion items are indicated in italics)

Aluminum Beam

  1. Calculate the theoretical bending stresses in the beam for each load increment and tabulate the results along with the corresponding test data of longitudinal and transverse strain, as measured by the strain indicator.
  1. Using results of part (1), plot theoretical stress versus measured longitudinal strain for each loading increment. Note: All experimental data must be curve fit through linear regression, and the coefficient of determination must be given. See the handout on "Report Writing Guidelines" for additional information on data analysis methods.
  1. Determine the Young's Modulus (Elastic Modulus, E), as the slope of the stress-stain curve and compare (in a table with % difference) with a textbook value for aluminum, by using a table that shows the percentage differences between your results and the reference data. Comment on the accuracy of the measurement.
  1. On a separate graph, plot the measured values of transverse strain against the corresponding values of longitudinal strain, and determine the Poisson's ratio, as the negative of the ratio of transverse strain over the longitudinal strain. Compare to a textbook value. Comment on the accuracy of the measurement.
  1. Use the tip-deflection data measured in the test, and the proper equation given in the notes, to calculate the theoretical strainat the location of the longitudinal strain gage. Tabulate the results and plot theoretical stress versus theoretical strain values on the same graph as in Part (2) above. Comment on the results, e.g. if the strain calculated from the deflection data matches the values measured by the strain gages? Assume that the strain measured with the strain indicator is the baseline for an exact solution.

Composite Beam

  1. Plot the stress vs. strain results for the composite beam. Use simple beam theory to estimate the stress. Also plot transverse strain against longitudinal strain. Compare the approximate (measured) values of the Elastic Modulus, E, and Poisson’s Ratio, , to the expected values given in the reference handouts. Is the linear, elementary beam theory for isotropic materials a good approximation for beams made of composite materials?
  1. Compare the experimental ratios of Elastic Modulus / Beam Weight (E/weight) for the aluminum and composite beams by using a bar chart (beam weights can be found in Fig. 1.3 of the course handouts). The property defined by such a ratio is referred to as the SPECIFIC Stiffness of the material. Comment on the efficiency of the composite beam, in terms of its specific stiffness.
  1. Plot the tip-deflections of the composite and the aluminum beams, multiplied by their corresponding beam weights, against the applied load. Comment on the efficiency of the composite beam, in comparison with the aluminum specimen.

Error Analysis

  1. In your discussion, comment on the ways in which the Wheatstone bridge can be employed to remove undesirable effects of bending or uni-axial deformation from strain measurements. How can the Wheatstone bridge be used for temperature compensation? Draw figures to aid your discussion.

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