Advanced Structural Analysis EGF316 Stress and...
Transcript of Advanced Structural Analysis EGF316 Stress and...
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Stress and Strain
The Basics
Advanced Structural Analysis EGF316
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Lecture Content
Fundamentals of Stress and Strain• Stress• Properties of stress• Strain• Properties of strain• Plane stress• Plane strain• Transformation of stresses and strains• Principal planes and principal stresses• Maximum shear stress• Principal strains
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Stress Analysis
• Importance– Load bearing capacity of components– Stress concentration - Critical geometric features– Points of failure
• Techniques– Analytical– Empirical formulae– Experimental– Numerical, typically Finite Element Analysis
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Direct Stress or Cauchy Stress– Stress normal to the material cross-section
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Direct Stress
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Shear Stress– Stress coplanar with the material cross-section
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Generic state of stress
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Local Equilibrium
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Properties of Stress
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Direct Strain
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Shear Strain– Change in the angle
CC’tan(γ) = ------ AC
CC’For small γ, tan(γ) ~= γ = ------ AC
L
A B
DC’C D’
γ γ
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Strain tensor
Infinitesimal strain tensor:
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Plane Stress
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Plane Strain
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Transformation of Stresses
Image source: www.efunda.com
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Transformation of Stresses
For plane stress:
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For each possible stress state, there is one specific orientation of the coordinate axes, such that the shear stresses disappear and the direct stresses adopt maximum and minimum values
Principal Stresses
Principal stresses occur on planes of zero shear stress
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Principal Stresses
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Principal Stresses
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Maximum Shear Stress
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Determine:
(a) The principal planes
(b) The principal stresses
(c) The maximum shear stress and corresponding normal stress
(d) Draw the planes
Example:
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Transformation of Strains
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Principal Strains
• Analogous to principal stresses.• Principal strains occur on planes of zero shear strain and can be shown to be given by: