# L5 - =dilatation change in volume • For element subjected...

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Chapter 2 Quick Review: - normal stress/strain due to axial loading - deformation due to axial loading - solving statically indeterminate problems using - compatibility equation - superposition - thermal strain Today: - Poisson’s ratio, multi-dimensional effects due to axial loading, multi-axial loading - Bulk modulus, dilatation - Shear strain, Shear modulus

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Poisson’s Ratio • For a slender bar subjected to axial loading: • Elongation in the x-direction -> contractions in other directions. • If material is isotropic and homogeneous: • Poisson’s ratio is defined as

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Generalized Hooke’s Law • If 1) strain is linearly related to stress 2) deformations are small • Use superposition:
Dilatation: Bulk Modulus • Relative to the unstressed state, the change in volume is

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Unformatted text preview: =dilatation (% change in volume) • For element subjected to uniform hydrostatic pressure, • Subjected to uniform pressure, dilatation must be negative, therefore Shearing Strain • shear strain is quantified in terms of the change in angle between the sides: •Reduction of the angle between two sides ==> + shear stress is the change in angle (radian) • Hooke’s law for shearing stress and strain (small strain): G : modulus of rigidity or shear modulus . E/3 < G < E/2 Shearing Strain cont. Generalized Hooke’s Law Relation Among E , ν , and G • Components of normal and shear strain are related, Axial load results in both normal and shear strain. 2.71 2.77...
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L5 - =dilatation change in volume • For element subjected...

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