03_SlopeDeflection

03_SlopeDeflection - DISPLACEMENT METHOD OF ANALYSIS SLOPE...

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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 θ i ψ i j
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3 Degrees of Freedom L θ Α A B M 1 DOF: θ Α P θ Α θ Β A B C 2 DOF: θ Α , θ Β
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4 L A B 1 Stiffness k BA k AA L EI k AA 4 = L EI k BA 2 =
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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
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7 General Case settlement = j P i j k w C j M ij M ji w P θ j θ 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 θ j + i j w P M ij M ji settlement = j θ j θ i ψ = + j i L EI L EI θ θ 2 4 j i L EI L EI θ θ 4 2 + = , ) ( ) ( ) 2 ( ) 4 ( Load ij F ij F j i ij M M L EI L EI M + + + = θ θ Load ji F ji F j i ji M M L EI L EI M ) ( ) ( ) 4 ( ) 2 ( + + + = θ θ L
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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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10 + 1 1 i j M ij M ji θ i θ j L EI k ii 4 = L EI k ji 2 = L EI k ij 2 = L EI k jj 4 = i θ × j θ × Stiffness Coefficients L
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