Strain Gauges

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T.C.D | Measurement of Strain using Electrical Resistance Strain Gauges | 3B3 - Mechanics of Solids | | Adam McCreevey | 3/15/2013 |

This is a laboratory to learn how to make measurements using a strain gauge by using different configurations, also to determine experimentally the axial and transverse stress at the surface of the beam and compare them to theoretical calculations |

Introduction

If a length of wire is subject to a stress within its elastic limits, the resulting elongation and change of diameter alters the resistance. The resulting principle is used in the resistance strain gauge, which consists of many turns of resistance wire, wound on an insulating former, the strain gauge wire is selected for the
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Δ=-mx22EI+c1x+c2
Now we work out the values for c1 and c2, we do this by looking at the boundary conditions. These are:
1. x=0, Δ=0
2. x=l, Δ=0
Using the first set of conditions we realise that: c2=0 Using the second set of condition we realise that: c1=ml2EI Subbing these into the full equation, we get:
Δ=-mx22EI+mlx2EI
Finally, we want to measure the deflection at a point where it is a maximum. Because this is a symmetrically loaded beam, the point where max deflection occurs is at the centre, where x=l/2. Subbing this into the equation we get:
Δ=-ml28EI+ml24EI

When calculating the experimental axial stress, we used the formula: σaxial=E1-ν2×εax+ν.εtr When calculating εx, εy and τxy using the rosette strain gauges, we use the following set of simultaneous equations: ε1= εxcosα2+εysinα2+τxysinαcosα ε2= εxcosβ2+εysinβ2+τxysinβcosβ ε3= εxcosϕ2+εysinϕ2+τxysinϕcosϕ

Where ε1, ε2 and ε3 are the measurements from the rosette gauges and α, β and ϕ are the angles each strain gauge makes to the axis of the beam.
When analyzing the mohr circle, we used an equation to calculate the centre of the circle, and an equation to calculate the radius of the circle. Here they are: c=εx+εy2 for the centre and : r=(εx+εy)22+τxy22 for the radius of the circle.

Method and Rig

We used a rig which consisted of a beam which is symmetrically and simply supported on each side. The 5 strain gauges were an
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