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Lecture23

# Lecture23 - Elastic Modulus = Stress Strain Tensile Stress...

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Elastic Modulus = Stress Strain Young’s Modulus (Y) Resistance to change in length Δ L Tensile Stress Shear Modulus (G) Resistance to shearing Shear Stress Bulk Modulus (B) Resistance to change in volume V Δ V Bulk Stress

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Young Modulus Strain : Measure of the amount of deformation caused by stress Strain = Δ L / L Elastic Modulus ( Y ) = Tensile Stress Tensile Strain Young Modulus (N/m 2 ) Y Δ L / L = F ext / A •The longer - the more it elongates •The ticker - the less it elongates Δ L Tensile Stress F Stress = F ext / A Stress : External force acting on the object per unit area (A)
Shear Modulus Strain : Measure of the amount of deformation caused by stress Strain = Δ x / h Shear Modulus ( S ) = Shear Stress Shear Strain S Δ x / h = F ext / A Stress = F ext / A Stress : Tangential force acting on the object per unit area (area of the face being sheared) Shear Stress Measured in N/ m 2 Δ x = horizontal distance shared face moves h= height of the object

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Bulk Modulus Strain : Measure of the change in volume due to the stress (no change in shape) Strain = Δ V / V Bulk Modulus ( B ) = Volume Stress Volume Strain B Δ V / V = - F / A = - Δ P Stress = F perp / A Stress : Force acting perpendicular on the entire surface of the object 1/B = compressibility Bulk Stress V Δ V F (N/ m 2) An increase in pressure results in a decrease in volume A material with a large bulk modulus is difficult to compress
Elastic limit Elastic Modulus = Stress Strain Maximum stress that can be applied to a material before it becomes permanently deformed Plastic region : Does not go back to its original configuration F = K Δ L Elastic force

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Stronger under compression than under tension Example stress Increase in shear strength Kept in tension until concrete cured Compressive stress on the concrete
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Lecture23 - Elastic Modulus = Stress Strain Tensile Stress...

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