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zm7notes - Page 1 Statically Indeterminate Structures and...

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Page 1 Statically Indeterminate Structures and Calculation of Deflections Deflection of Trusses Need other two great principles constitutive behavior compatibility Constitutive Behavior for Bars in a Truss Will later show (blocks 2 & 3) that the overall change in length of bar is ( for some range of materials, loads) δ α = + FL AE TL Symbol Meaning Dimensions SI units A = Cross-section area L 2 [ ] m 2 L = Length of bar [ L ] m F = Applied force [ ML/T 2 ] N/ E = Modulus of elasticity [ ML/T 2 .L 2 ] N/M 2 α = Coefficient of thermal expansion L L . θ [ ] M M K T = Temperature difference θ [ ] K Due to a change in temperature Due to force
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Page 2 Check Units δ θ θ = [ ] [ ] + [ ] [ ] = [ ] + [ ] ML T L L ML T L L L L L L OK 2 2 2 2 This is basically the same as F K = δ for zero thermal expansion Set T then FL AE rearranging AE L F = = = 0 δ δ [NOTE: a real spring has added geometry] Compatibility of Displacements
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