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Lect6_strain

# 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
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
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
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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