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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Multi-axial loading
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Generalized Hooke’s Law • If 1) strain is linearly related to stress 2) deformations are small • Use superposition:
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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) Hookes law for shearing stress and strain (small strain): G : modulus of rigidity or shear modulus . E/3 < G < E/2 Shearing Strain cont. Generalized Hookes Law Relation Among E , , 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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