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BEAM ANALYSIS USING THE STIFFNESS METHOD

BEAM ANALYSIS USING THE STIFFNESS . METHOD . ! Development: The Slope-Deflection Equations ! STIFFNESS Matrix ! General Procedures ! Internal Hinges ! Temperature Effects ! Force & displacement Transformation ! Skew Roller Support 1. Slope Deflection Equations i P j k w Cj settlement = j i P j Mij w Mji i j 2. Degrees of Freedom M.. A B 1 DOF: . L. P.. B 2 DOF: , . A C.. 3. STIFFNESS Definition kAA 1 kBA. A B. L. 4 EI. k AA =. L. 2 EI. k BA =. L. 4. kAB kBB. A 1 B. L. 4 EI. k BB =. L. 2 EI. k AB =. L. 5. Fixed-End Forces Fixed-End Forces: Loads P. PL L/2 L/2 PL. 8 8. L. P P. 2 2. w wL2 wL2. 12 12. L. wL wL. 2 2. 6. General Case j k i P. w Cj settlement = j i P j Mij w Mji i j 7. i P j Mij w Mji i L settlement = j j 4 EI 2 EI 2 EI 4 EI. i + j = M Mji = i + j L L ij L L. j i +. (MFij) (MFji) . settlement = j +.

Stiffness Matrix! General Procedures! Internal Hinges! Temperature Effects! Force & Displacement Transformation! Skew Roller Support BEAM ANALYSIS USING THE STIFFNESS METHOD. 2 Slope ΠDeflection Equations

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