Mechanics 1T - 2.001 - MECHANICS AND MATERIALS I Lecture...

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2.001 - MECHANICS AND MATERIALS I Lecture #10 10/16/2006 Prof. Carol Livermore From last time: 1. Equilibrium F BC = P/ cos θ F AB = P tan θ 2. Force deformation relationships (” P = ”) PL tan θ sin θ δ AB = AE δ = AE cos θ 3. Compatibility a. u B x 1
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δ AB = u B 1 x BC B δ 1 = u x sin θ b. u B y δ AB =0 2 δ = u B cos θ 2 x Sum: δ AB δ AB + δ AB = 12 = u B +0= u B = δ AB xx δ δ + δ = = u B sin θ u B cos θ = δ xy PL tan θ sin θ B u = x AE δ u B sin θ u B = x y cos θ cos θ tan θ sin 2 θ u B = y AE cos 2 θ AE cos θ 2
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± ± 2, 3, 4 are statically indeterminate! (more bars than are needed to support the structure) A, E for all bars Forces? Deformations? Displacement of point D? Unconstrained D.O.F 1. u D x 2. u D y Equilibrium F D x =0 P + F DC sin θ F AD sin θ F D y F DC cos θ F AD cos θ F BD Force-Deformation Relationships 3
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F AD = k AD δ AD = AE δ AD L F CD = k δ = AE δ L F BD = k δ = AE δ L cos θ Compatibility D u x δ 1 =0 δ AD = u D sin θ 1 x 4
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δ CD 1 = u D x sin θ u D y Sum: δ BD = u 2 D y δ AD 2 D y = u δ 2 D y = u cos θ cos θ δ AD = u D x D y sin θ + u cos θ δ =0+ u DD y = u y δ = u D x D y sin θ + u cos θ Substitute δ into F AE ( u D x D y cos θ ) sin θ + u F AD = L 5
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±² D y AE F BD = u L cos θ AE ( u D x sin θ + u D y cos
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This note was uploaded on 08/16/2009 for the course ENG C taught by Professor Prof during the Spring '09 term at Ohio University- Athens.

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Mechanics 1T - 2.001 - MECHANICS AND MATERIALS I Lecture...

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