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Lect6_strain - STRAIN What is STRAIN Difference between...

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Olek, CE 231,Fall 2004 STRAIN What is STRAIN? Difference between strain and deformation Normal and shear strains defined Strains and volume changes Dilatation Strain transformation equations, sign convention Principal strains Max. in-plane shear strain Mohr’s circle for plane strain
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Olek, CE 231,Fall 2004 Displacement and Deformation Displacement – Movement of a point w.r.t a reference system Can be caused by translation or rotation Deformation - Change in the shape / size of a body related to displacements Deformation is not uniform throughout the body, generally Deformation includes changes in both lengths and angles Curtsey of N. Neithalath
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Olek, CE 231,Fall 2004 Deformation A B C D F G H E A’ B’ C’ D’ F’ G’ H’ E’ L L+ΔL Curtsey of N. Neithalath
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Olek, CE 231,Fall 2004 Strain A quantity used to measure the intensity of deformation (as stress is a measure of the force) A B Δs A’ B’ Δs’ Undeformed body Deformed body Curtsey of N. Neithalath
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Olek, CE 231,Fall 2004 Normal Strain The elongation or contraction of the line segment per unit length (change in length per unit length) Change in length = Δs’- Δs Average normal strain (ε) A B Δs A’ B’ Δs’ ' avg s s s ε ∆ - ∆ = Δs’ ≈(1+ε) Δs Curtsey of N. Neithalath
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Olek, CE 231,Fall 2004 Normal Engineering Strain F F F F L 0 L 0 + Δ L = L 0 0 0 L L L L L = - = ε Average normal strain If the deformation is not uniform, we must define strain at a point
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Olek, CE 231,Fall 2004 Strain is Dimensionless Strain is a dimensionless quantity It is a ratio of two lengths But the common practice is to state the strain in terms of length/length Engineering Strains are usually very small – so it is common practice to express strains as μm / m (called microstrain) 1μm = 10 -6 m Strain can also be expressed as a percent (500 μm/m = 500 x 10 -6 m/m = 500 x 10 -6 /100 = 0.05%) Curtsey of N. Neithalath
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Olek, CE 231,Fall 2004 Shear Strain
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