Deflections - Conjugate Beam

Deflections - Conjugate Beam - = Let EI M w-= Conjugate...

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ECIV 320 Structural Analysis I Deflections
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Last Time ASSUMPTION Linear Elastic Material Response A structure subjected to a load will return to its original undeformed position after load is removed Double Integration Method Moment Area Theorems Conjugate Beam OBJECTIVE Calculate Slope and Deflection due to Bending at any point on a Beam METHODS
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Last Time - Double Integration Method Relate Moments to Deflections EI M dx u d = 2 2 ( 29 = = dx x EI x M dx du x ) ( ) ( θ ( 29 ∫ ∫ = 2 ) ( ) ( dx x EI x M x u Integration Constants Use Boundary Conditions to Evaluate Integration Constants
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Conjugate Beam Method Developed by H. Muller Breslau - 1865 Use to find slopes and deflection due to bending of beams Method is based on Principles of Statics Only
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Conjugate Beam w dx dV - = w dx dV dx M d - = = 2 2 Internal Loadings Beam Theory EI M dx d = θ EI M dx d dx u d = = 2 2
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Conjugate Beam - = wdx V [ ] - = dx wdx M Internal Loadings Beam Theory = dx EI M θ dx dx EI M u ∫ ∫
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Unformatted text preview: = Let EI M w-= Conjugate Beam A fictitious beam of the same length as the real beam loaded with the real beams M/EI diagram Real Beam = V Conjugate Beam Real Beam = M Conjugate Beam However. .. Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports Conjugate Beam Supports Shear and Moment at Supports of Conjugate Beam should account for the corresponding slope and deflection of real beam at its supports Examples of Conjugate Beam Supports Examples of Conjugate Beam Supports Examples of Conjugate Beam Supports...
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Deflections - Conjugate Beam - = Let EI M w-= Conjugate...

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