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Experimental Stress Analysis
Strain Gauges
MEC 445
Mechanical Engineering
Amrita Vishwavidyapeetham
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Electrical Resistance Strain Gauges
The principle of electrical resistance strain gauge is that theelectrical resistance of a conductor changes proportionally to anystrain applied to it.
Lord Kelvin in 1856 first reported on the relationship between
strain and resistance of wire conductors.
During 1930s Simmons at California Institute of Tech and Rugeat MIT made practical use of it by bonding small diameter wires
to a structure to measure surface strain.
The strain gauges developed by them were known as SR-4Gauges.
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Strain Sensitivity of a Wire
Resistance of a conductor can be written as
Where is the specific resistanceL is the length of the conductor, and A is the cross
sectional area of the conductor
To find out the change in resistance we differentiate the above
If the wire diameter is D, the change in area can be calculated as
.
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Strain Sensitivity of a Wire
From the definition of Poissonsratio we can write
Hence
Strain sensitivity of metallic strain gauges 2
.
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Strain Gauge Construction
SR-4 measured 7000 with
Minimum resistance required from instrumentation point ofview is 100
For a dia of .025mm and R/L =1000 we need 100 mm ofwire.
Even for a reasonably thin wire we need very lengthy wire to
have a base resistance of 100
Scope study is measuring strain at a point. Its not possible tomeasure strain at a point using a long wire.
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Strain Gauge Construction
Gauges are formed by folded grids etched on metal foil.
We are measuring the strain along the gauge length
Strain gauges are available only at certain values
Thin metal foils are very fragile. Proper backing is
necessary.
The backing allows proper alignment and supports the leadwires
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Strain Gauge Construction
Different type of grid patterns are available for differentapplication
Standard resistances available are 120,350
Gauge factor must be measured experimentally
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Gauge Length
The gauge length of a strain gauge is the active or strain sensitive
length of the grid
The gauge measures the axial strain in the direction of the gauge
length.
The end loops and solder tabs are insensitive to strain because of
their relatively large cross-sectional area and low electrical
resistance.
Most common strain gauges have 3 mm gauge length and these
are good enough for a large verity of problems.
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Selection of Gauge Length
Thumb rule in selection of gauge length
Selection of gauge length is very important point in strain
measurement
The gauge length should be no grater than 0.1 times the radius
of a hole, fillet, or notch, or corresponding dimension of any
other stress raiser at which the strain measurement is to be
made.
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Commonly used strain gauge materials
The value of SAdepends upon the degree of cold working
imparted to the conductor during its formation, the impurities in
the alloy, and range of strain over which the measurement of
strain sensitivity is made
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Commonly used strain gauge materials
Most commonly used strain gauge material is an alloy of 55%Copper and 45% Nickel called Constantan/Advance.
SA2.1 for the Advance
SAis linear over a large range of strain ( 0 to 8%).
Constantan has excellent thermal capability
Has high specific resistance ( = 0.49 m)
Easy to develop self compensated strain gauges.(1 /0c)
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Commonly used strain gauge materials
Isoelastic alloy High sensitivity ( SA=3.6) : Advantageous in dynamic applications
where the strain gauge output must be amplified to a considerable
degree before recording.
High fatigue strength : Useful when the gauge is to operate in a
cyclic strain field where the alternative strains exceed 1500
Poor thermal stability : When mounted on steel a 10c wouldproduce a strain of 300 to 400
Useful for dynamic applications where temperature is stable
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Commonly used strain gauge materials
Karma alloy
Fatigue limit is higher than Advance but lower than Isoelastic.
Excellent stability with time: useful for strain measurements over
weeks or months.
Temperature compensation achievable in Karma is better over a widerange of temperature than advance alloy
Useful up to 260 0c in static strain measurements.
Difficult to solder the lead wires to the tabs.
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Commonly used strain gauge materials
Thermally induced apparent strains as a function of temperature
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