03_SlopeDeflection

03_SlopeDeflection - DISPLACEMENT METHOD OF ANALYSIS SLOPE DEFLECTION EQUATIONS General Case Stiffness Coefficients Stiffness Coefficients

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1 ! General Case ! Stiffness Coefficients ! Stiffness Coefficients Derivation ! Fixed-End Moments ! Pin-Supported End Span ! Typical Problems ! Analysis of Beams ! Analysis of Frames: No Sidesway ! Analysis of Frames: Sidesway DISPLACEMENT METHOD OF ANALYSIS: SLOPE DEFLECTION EQUATIONS

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2 Slope & Deflection Equations settlement = j P i j k w C j M ij M ji w P θ j i ψ i j
3 Degrees of Freedom L θ Α A B M 1 DOF: P Β A B C 2 DOF: Α ,

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4 L A B 1 Stiffness k BA k AA L EI k AA 4 = L EI k BA 2 =
5 L A B 1 k BB k AB L EI k BB 4 = L EI k AB 2 =

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6 Fixed-End Forces Fixed-End Moments: Loads P L/ 2 L/ 2 L w L 8 PL 8 PL 2 P 2 P 12 2 wL 12 2 wL 2 wL 2 wL
7 General Case settlement = j P i j k w C j M ij M ji w P θ j i ψ i j

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8 w P settlement = j (M F ij ) (M F ji ) (M F ij ) Load (M F ji ) Load + M ij M ji θ i j + i j w P M ij M ji settlement = j j i ψ = + j i L EI L EI 2 4 j i L EI L EI 4 2 + = , ) ( ) ( ) 2 ( ) 4 ( Load ij F ij F j i ij M M L EI L EI M + + + = Load ji F ji F j i ji M M L EI L EI M ) ( ) ( ) 4 ( ) 2 ( + + + = L
9 M ji M jk P i j k w C j M ji M jk C j j Equilibrium Equations 0 : 0 = + = Σ + j jk ji j C M M M

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