Stress & Strain Measurement

Stress & Strain Measurement - ME 3260 Measurement...

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Bi Zhang, UConn 1 ME 3260 Measurement Techniques Stress and Strain Measurements Instructor: Dr. B. Zhang Contents • Hooke’s Law – Relates stress and strain • Principle of strain gages? • Gauge factor (G.F.) • Wheatstone bridge • Strain gage applications • Temperature compensation
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Bi Zhang, UConn 1 Review - Hooke’s Law • Stress ( ) is proportional to strain ( ) = E = E E = elastic modulus (Young’s modulus ) (Pa) Pascal m Newtons Area Force Stress 2 o o o l l l l l length original length in change = Strain Poisson’s Ratio ( ) • For a 3-dimensional solid, the strain in the transverse direction must be considered • Most materials: Poisson’s ratio = 0.25-0.35 transverse strain longitudinal strain  t l Longitudinal Transverse
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Bi Zhang, UConn 1 What Are Strain Gages? • One of several devices that can be used to obtain strains directly. A small device that can be attached directly to the item for which strain data is required. • The device measures strain at the surface of an structural element. • A strain gage is a small wire grid whose electrical resistance changes as it strains . Strain Gauge Made of Cu-Ni or Nichrome alloys
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Bi Zhang, UConn 1 Direction of Sensitivity Foil Grid Single Element Two-Element Rosette Strain Gages Backing Film Solder Tabs (For Leads) Three-Element Rosettes Semiconductor (silicon with impurity Nickle-Plated Copper Ribbons Welded Gold Leads Doped Silicon Crystal (P or N Type) Phenolic Glass Backing Plate Semiconductor (silicon with impurity) • Professor William Thomson (Lord Kelvin) was the first to discover the relationship between electrical Strain Gages to discover the relationship between electrical resistance of wires and induced strains . • Strains imposed by tensile stresses cause an increase in electrical resistance . • Strains imposed by compressive stresses cause a decrease in electrical resistance .
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Bi Zhang, UConn 1 Principle of Strain Gauges A length change of a wire causes a resistance change, which is measured by a strain gauge R L A R = resistance = resistivity (material property) L = length A = cross-sectional area dA A R dL L R d R dR  Change of R with Change of R with L Change of R with A Change of resistance Principle of Strain Gauges dA A R dL L R d R dR Change of R with Change of R with L Change of R with A t strain al Longitudin strain Transverse dR R d dL L (1 2 ) ( Gauge factor) dL L 0 l
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Bi Zhang, UConn 1 Principle of Strain Gauges R L A A l R ln ln ln ln After differentiation A dA l dl d R dR 4 2 D A D A ln 2 4 ln ln Using D dD A dA 2 Where a t D dD 
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This note was uploaded on 02/15/2010 for the course ME 3260 taught by Professor Zhang during the Spring '10 term at UConn.

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Stress & Strain Measurement - ME 3260 Measurement...

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