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2009+8-2StressStrain - Introduction to Solid...

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1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 8 Stress and Strain Chapter 8 Stress and Strain SJTU Introduction to Solid Mechanics -Vm211 STRAIN Today’s Objectives: a) Understand the concept of normal and shear strain, and b) Apply the concept to determine the strains for various types of problems SJTU Introduction to Solid Mechanics -Vm211 Deformation Occurs when a force is applied to a body Can also occur when temperature of a body is changed DEFORMATION SJTU Introduction to Solid Mechanics -Vm211 Deformation Can be highly visible or practically unnoticeable Is not uniform throughout a body s volume, thus change in geometry of any line segment within body may vary along its length DEFORMATION SJTU Introduction to Solid Mechanics -Vm211 To simplify study of deformation Assume lines to be very short and located in neighborhood of a point Take into account the orientation of the line segment at the point DEFORMATION SJTU Introduction to Solid Mechanics -Vm211 Normal strain Defined as the elongation or contraction of a line segment per unit of length Consider line AB in figure below After deformation, Δ s changes to Δ s STRAIN
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2 SJTU Introduction to Solid Mechanics -Vm211 Normal strain If normal strain ε is known, use the equation to obtain approx. final length of a short line segment in direction of n after deformation. Hence, when ε is positive, initial line will elongate, if ε is negative, the line contracts Δ s’ (1 + ε ) Δ s STRAIN SJTU Introduction to Solid Mechanics -Vm211 Normal strain Defining average normal strain using ε avg (epsilon) As Δ s 0, Δ s’ 0 ε avg = Δ s Δ s’ Δ s ε = Δ s Δ s’ Δ s lim B A along n STRAIN SJTU Introduction to Solid Mechanics -Vm211 Units Normal strain is a dimensionless quantity , as it s a ratio of two lengths But common practice to state it in terms of meter/meter (m/m) STRAIN ε = Δ s Δ s’ Δ s lim B A along n SJTU Introduction to Solid Mechanics -Vm211 Units ε is small for most engineering applications, so is normally expressed as micrometers per meter ( μ m/m) where 1 μ m = 10 6 m Also expressed as a percentage Also expressed as a percentage e.g., e.g., 0.001 0.001 m/m
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