# 09___Strain - Introduction Although not obvious at first...

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Introduction 1 Although not obvious at first, the measurement of strain in solid objects is common in process control. The reason why it is not obvious is that strain sensors are used as a secondary step in sensors to measure many other process variables, including flow, pressure, weight, and acceleration.

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Introduction 2 There are three most common types of stress-strain relationships: a) Tensile stress – Strain b) Compressive stress – Strain c) Shear stress – Strain
Basic terms Tensile stress - Strain A F = stress tensile 3 In figure, the nature of a tensile force is shown as a force applied to a sample of material so as to elongate or pull apart the sample. In this case, the stress is defined as; where; F = applied force in N A = cross-sectional area of the sample in m 2 The units of stress are N/m 2 in the SI units.

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Basic terms Tensile stress - Strain l l Δ strain tensile = 4 The strain in this case is defined as the fractional change in length of the sample: where; Δ l = change in length (m) l = original length (m) Strain is thus a unitless quantity.
Basic terms Compressional stress - Strain 5 The only differences between compressional and tensile stress are the direction of the applied force and the polarity of the change in length. Thus, in a compressional stress, the force presses in on the sample, as shown in figure. The compressional stress is defined as; A F compressional stress = l l compressional strain =

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Basic terms Shear stress - Strain 6 Figure below shows the nature of the shear stress. In this case, the force is applied tangentially (shear direction), tending to shear off the solid object that separates the force arms. In this case, the stress is again l x shear strain = A F shear stress =
Basic terms Stress – strain curve 7 If a specific sample is exposed to a range of applied stress and the resulting strain is measured, a graph similar to the figure is obtained. This graph shows that the relationship between stress and strain is linear over some range of stress.

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Basic terms Stress – strain curve 8 If the stress is kept within the linear region, the material is essentially elastic in that if the stress is removed, the deformation is also gone. But if the elastic limit is exceeded, permanent deformation results. The material may begin to "neck" at some location and finally break. Within the linear region, a specific type of material will always follow the same curves despite different physical dimensions. Thus, we can say that the linearity and slope are a constant of the type of material only.
Basic terms Stress – strain curve l l A F E / / strain stress = = l x A F M / / strain stress = = 9 In tensile and compressional stress, this constant is called the modulus of elasticity or Young's modulus (N/m 2 ) and given by; In an exactly similar fashion, the shear modulus is defined for shear stress-strain as

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## This note was uploaded on 12/27/2009 for the course MINING ENG MAD 413 taught by Professor Erencanerorhan during the Fall '09 term at Hacettepe Üniversitesi.

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09___Strain - Introduction Although not obvious at first...

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