Chapter 11 Notes - Chapter 11 Strain Measurement Material...

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1 Chapter 11 Strain Measurement Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Stress Analysis Stress Analysis is accomplished by measuring deformation of part under load and inferring the existing state of stress from measured deflection. Normal Stress: σ a = F N /A c ; F N =Tension Force, A c =Area, σ a =axial strain Stress Analysis Ratio of change in length of the rod to the original length is axial strain: ε a = δ L/L ; ε a =average strain, δ L=change in length, L=original unloaded length • Lateral strain: ε L = δ d/d Strain is a small quantity, usually reported in units of 10 -6 in/in or 10 -6 m/m.
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2 Hooke’s Law Stress-strain diagrams are very important in understanding the behavior of a material under load. The range of stress over which this linear relationship holds is called the elastic region. The relationship between uniaxial stress and strain for this elastic behavior is expressed as: σ a = E m ε a •E m = modulus of elasticity or Young’s modulus • The relationship is called Hooke’s Law • 30 * 10 6 PSI for steel Hooke’s Law Consider the elongation of the rod shown in Figure 11.1, which occurs as a result of the load F N . As the rod is stretched in the axial direction, the cross-sectional area must decrease, since the total mass (or volume for constant density) must be conserved. Figliola, 2000
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3 Figliola, 2000 Poisson’s Ratio In the elastic range, there is a constant rate of change in the lateral strain as the axial strain increases. The ratio of lateral strain to axial strain is known as Poisson’s ratio: v p = lateral strain axial strain v p = ε L / ε A Poisson’s Ratio Engineering components are seldom subject to one-dimensional axial loading. The relationship between stress and strain must be generalized to a multi- dimensional case. Consider a 2-D geometry subject to tensile loads in both the x and y directions, resulting in normal stresses, σ x and σ y .
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4 Poisson’s Ratio Consider 2 dimensional geometry, subject to tensile loads in both x and y. All stress and strain components lie in the same plan. Since strain is measured on the surface, this gives us information on the stress on the surface. m x p m y y E V E σ σ = ε m y p m x x E V E σ σ = ε 2 1 ) ( p y p x m x v V E + = ε σ 2 1 p x p y m y v V E ε + ε = σ ) ( Resistance Strain Gauges Strain can be measured by methods as simple as observing the change in the distance between two scribe marks on the surface of a load-carrying member, or as advanced as optical holography. Ideal Instrument to Measure
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This note was uploaded on 11/22/2011 for the course ABE 6031 taught by Professor Burks during the Summer '11 term at University of Florida.

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Chapter 11 Notes - Chapter 11 Strain Measurement Material...

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