mae 3113_8 - MAE 3113 3-1 Measurements and Instrumentations...

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School of Mechanical and Aerospace Engineering MAE 3113 3-1 Measurements and Instrumentations Stress and Strain Fall 2006
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School of Mechanical and Aerospace Engineering MAE 3113 3-2 Stress and Strain 1-D Case Positive strain in the axial direction results in negative strain in the lateral or transverse direction. The ratio between the two is known as Poisson’s ratio , and for most materials remains constant over the elastic region. a L strain axial strain lateral ε υ = = _ _
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School of Mechanical and Aerospace Engineering MAE 3113 3-3 Stress and Strain 1-D Case Under no-load conditions the length of the bar is L, the diameter D, and the cross-sectional area A. If a load is applied to the bar, then the axial strain can be found by E A P = ε The simple axial loading is 1 1 2 L L L a - =
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School of Mechanical and Aerospace Engineering MAE 3113 3-4 Stress and Strain 2-D Case Consider stress in the x and y direction applied separately. ε x results in a strain σ x /E and a lateral strain – ε x = - ν σ y /E; a similar effect occurs when σ y is applied. The net strains can therefore: E y x x ν σ σ ε - = E x y y - = Solving for the stresses in the x and y-directions we obtain 2 1 ) ( ν ν ε - + = y x x E 2 1 ) ( - + = x y y E
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School of Mechanical and Aerospace Engineering MAE 3113 3-5 Stress and Strain 2-D Case Example: We are measuring the hoop and longitudinal strains on the outer surface of a thin-walled cylindrical pressure vessel, the sensor indicates that the strains are 425 and 115 μ ε respectively. Determine the hoop and longitudinal stresses assuming that E = 10.3x10 10 and ν = 0.28. Pa x E h l l 7 2 10 61 . 2 1 ) ( = - + = ν ν ε ε σ Pa x E l h h 7 2 10 11 . 5 1 ) ( = - + = Note that the hoop stress is twice as much as the longitudinal stress for the cylindrical pressure vessel. This is why an overcooked hotdog usually cracks along the longitudinal direction first.
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School of Mechanical and Aerospace Engineering MAE 3113 3-6 Strain Gages A simple method of strain measurement is to place some type of grid marking on the surface of the work piece under the ‘zero-load’ condition and then measure the deformation of this grid when the piece is subject to a load. The grid may be scribed on the surface, drawn with a fine ink pen, photo-etched, or simple wire grid.
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School of Mechanical and Aerospace Engineering MAE 3113 3-7 Gage Parameters The installation and operating characteristics of a strain gage are affected by the following parameters: •Self-temperature-compensation number (S-T-C) •Gage Factor Transverse Sensitivity •Fatigue •Backing materials (carrier) •Base grid resistance Gage length
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School of Mechanical and Aerospace Engineering MAE 3113 3-8 Gage Parameters Self-temperature-compensation number Self-temperature-compensated strain gages are designed to produce minimum thermal output (temperature-induced apparent strain) over the temperature range from about -50 deg to +400 deg F (-45 deg to +200 deg C). When
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mae 3113_8 - MAE 3113 3-1 Measurements and Instrumentations...

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