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1DMcSLecture notes - Chapter 4

# 1DMcSLecture notes - Chapter 4 - MECH401 MechanicalDesign...

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MECH 401  Mechanical Design  Applications Dr. M. K. O’Malley – Master Notes Spring 2007 Dr. D. M. McStravick Rice University

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Design Considerations Stress – Yield Failure or Code Compliance Deflection Strain Stiffness Stability – Important in compressive members Stress and strain relationships can be studied with Mohr’s circle Often the controlling factor for functionality
Deflection  [Everything’s a Spring] When loads are applied, we have deflection Depends on Type of loading Tension Compression Bending Torsion Cross-section of member Comparable to pushing on a spring We can calculate the amount of beam deflection by various methods

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Superposition Determine effects of individual loads separately and add the results [see examples 4-2,3,4] Tables are useful – see A-9 May be applied if Each effect is linearly related to the load that produces it A load does not create a condition that affects the result of another load Deformations resulting from any specific load are not large enough to appreciably alter the geometric relations of the parts of the structural system
Deflection --- Energy Method There are situations where the tables are insufficient We can use energy-methods in these circumstances Define strain energy Define strain energy density** V – volume Put in terms of σ , ε = 1 0 x Fdx U dV dU = μ = = = = = = dV E U dU dV dV dU E E x x x x x x 2 2 2 1 2 1 2 1 σ μ μ σ ε σ μ ε σ

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Example – beam in bending ( 29 dx EI M U dx EI dA y M dAdx EI y M dV EI y M U dA y I = = = = = 2 2 ) ( 2 2 2 2 2 2 2 2 2 2 2 2 2 ) ( 2 2 2 2 2 2 2 2 2 x f EI M dAdx dV dV EI y M U dV E U I My x = = = = = σ σ
Castigliano’s Theorem [He was a Grad Student at the Time!!]

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1DMcSLecture notes - Chapter 4 - MECH401 MechanicalDesign...

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