lab6 - STRAIN GAUGE MEASUREMENT Last updated Dec. 11, 2007,...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
S TRAIN G AUGE M EASUREMENT Last updated Dec. 11, 2007, M. Lucas Purposes of the Experiment 1) To familiarize the student with the theory of operation of bridge circuits and strain gauges. 2) To illustrate an application of strain gauges in measuring the deflection of a cantilever beam in free vibration and under static loading. 3) To use National Instruments Virtual Bench for performing linear regression analysis, for better understanding the principle behind calibration. Theory Stress and Strain For the sake of simplicity, materials are often considered to be rigid engineering analysis. However, in the real world, materials experience deformation when placed under load. The term stress refers to the internal forces (per unit area) developed in a material that is under load. Strain , on the other hand, is a dimensionless measure of the deformation of such a loaded member. Consider, for example, a cylindrical bar that is loaded in simple axial tension: F F L 0 L 0 + Δ L Figure 1: Bar in Axial Tension
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MEEN 260 Laboratory Manual Texas A&M University 2 The stress, σ , and strain, ε , in the cylindrical bar in Figure 1 above are given, respectively, by 0 L L A F Δ = = Where A is the cross-sectional area of the bar and F is the applied force. Although the above formulas for stress and strain provide a good picture of the physical meaning of these quantities, they are only applicable to this special case. In structural members with different geometries and more complex loadings, it is often more difficult to find the stress and strain at various points in the material. In Lab Exercise 2 below, you will need to follow the instructions of your teaching assistant to determine the stress in a cantilever beam . Hooke’s Law From an empirical standpoint, it is very difficult to directly measure the stress in a material. On the other hand, strain can be measured at the surface of a part without intrusion into the material. Strain gauges are used for this purpose as we shall see below. Once strain is measured at a given point, stress at that point can be inferred from the measured strain using Hooke’s Law (given here for the case of uniaxial stress): Where E represents the modulus of elasticity for the material. (Note the similarity of this relationship with the spring, deflection relationship, kx F = . ) Once we know the stress in a structural component we can assess whether the component may fail or not by comparing this quantity with the ultimate or yield strength of the material. These values are usually tabulated in engineering mechanics and design textbooks and handbooks. Measurement of Strain The most common method of measuring strain is with the use of electrical- resistance wire gauges. The principle underlying these gauges is that the electrical resistance in a wire increases as it is stretched. This is due to the fact that in a simple wire, the resistance, R , is determined from E =
Background image of page 2
MEEN 260 Laboratory Manual Texas A&M University 3 A l R ρ = where is the resistivity constant of the material, l is the length of the wire and A is the cross sectional area of the wire. If the wire stretches by an amount
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/26/2010 for the course MEEN 260 taught by Professor Langari during the Fall '08 term at Texas A&M.

Page1 / 8

lab6 - STRAIN GAUGE MEASUREMENT Last updated Dec. 11, 2007,...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online