AOE 3054 Measuring static displacement and deformation in structures

Transcription

1 AOE 3054 Measuring static displacement and deformation in structures Dr. Eric Johnson Preparation for experiments 2 and 5. elevant reading: Lab manual, experiment 2. Notes on Maxwell s eciprocal Theorem (on website)

2 Why Test Structures? 1. It is For military airplanes: Naval Air Systems Command (NAVAI) of the U.S. Navy or Aeronautical Systems Division (ASD) of the U. S. Air Force. For commercial transports: Federal Aviation Administration (FAA), U. S. Department of Transportation. Federal Aviation egulations (FA), Part 25, Airworthiness Standards: Transport Category Airplanes, spells out the design and test requirements that must be met before a type certificate is issued. Airworthiness is defined as that quality by which an aircraft makes its contribution to the safety of flight. 2. To

3 ange Of Specimens In An Aircraft Structural Test Program

4 Displacement Measurements

5 Displacement Measurements Moving contact on a slide-wire converts linear displacement or angular displacement into an electrical signal. (Holman, p.157) Magnetic core moves freely inside three coils. An alternating voltage is impressed on the primary coil and the output voltage of the device as measured by two secondary coils is determined by the magnetic coupling between the core and secondary coils, which in turn depends on the position of the core. (Holman, p. 158) Holman J P, 1989, Experimental Methods for Engineers, 5th Edition, McGraw Hill, New York.

6 Measurement of Deformation or Strain 1. Strains are defined in terms of derivatives of displacements. Many displacement measurements at various locations may be required to get estimates of derivatives (e.g., by finite difference ratios). Frequently in-plane displacements are very small and difficult to measure. Thus, differentiating measured displacements may not be practical. Caveat: Sophisticated optical techniques, like Moiré interferometry, can give whole-field displacement maps from which strains can be computed. 2.

7 Principle of Electrical Strain Gage 1. Lord Kelvin (1856) established by experiment that 2.

8 Change of Wire esistance Due To Strain The differential of = ρl / A is Divide this equation by to get The area change for a circular cross section is related to the change in diameter by da = ½πD(dD), and the diameter change is due to the Poisson effect dd = (-νε)d, where ν is Poisson s ratio. Hence, the change in area per unit area is Note that the axial normal strain ε is defined as

9 Change of Wire esistance Due To Strain (concluded) Finally we get that the change in resistance divided by the resistance is related to the axial strain and change of resistivity by Gage factor F is defined by and so, The

10 Configuration of Metal Foil Strain Gages (Micro-Measurements)

11 The Wheatstone Bridge as a Direct eadout Device The output voltage e 0 is determined by bridge resistances So e 0 =0 when (called the bridge balance equation )

12 The Wheatstone Bridge as a Direct eadout Device (concluded) Now consider a change in resistance for each resistor ) )( ( ) )( ( ) )( ( E e e = + After some algebra ) ( ) ( O E e = Neglect the quadratic terms and higher powers in since they are small for 5% strain or less. We get the unbalanced bridge equation

13 Quarter Bridge Circuit One Active Strain Gage

14 Quarter Bridge Circuit Two Lead Balance equation: Wire Arrangement Effective gage factor: The increase in resistance caused by the lead wires in strain gage leg of the bridge results in a decrease in voltage at the S- junction. The gage factor from manufacturer is F = ( G / G )/ε. The percentage change due to lead wire resistance, or gage factor desensitization, is F F' 100 = F G L + 1 L2 100 = 1.77% + + L1 L2 for G =120Ω, and 20ft of AWG#30 lead wire.

15 Quarter Bridge Circuit Three Lead Balance equation: Wire Arrangement Effective gage factor: The S- junction shifted electrically to the strain gage tab. The initial imbalance and effective gage factor are reduced. The gage factor desensitization is F F' 100 = F G L = 0.9% + L1 for G =120Ω, and 20ft of AWG#30 lead wire.

16 Effect of Temperature on Measured Strain Thermal Output Once an installed strain gage is connected to a strain indicator and the instrument balanced, a subsequent change in temperature of the gage. N.B.; There is no thermal output strain at a fixed temperature if 1. 2.

17 Causes Of Thermal Output From An Installed Strain Gage When Temperature Changes Thermal output caused by temperature change is potentially the most serious error source in the practice of static strain measurement with strain gages Methods to compensate for thermal output

18 Compensating Strain Gage Method

19 Self-Temperature-Compensated (S-T-C) Strain Gages An installed S-T-C gage minimizes the thermal output strain over a wide temperature range if it is bonded to the intended substrate; i.e., there is little thermal mismatch.

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