Analysis Lecture 2

Analysis Lecture 2 - CIVL2007 Theory and Design of...

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Unformatted text preview: CIVL2007 Theory and Design of Structures II Analytical Component (9 February 2007) page 28 TOPIC 3: EQUILIBRIUM METHOD SLOPE DEFLECTION METHOD - LECTURE NOTES - General Equilibrium methods are equally applicable to statically determinate and indeterminate structures with both equilibrium and compatibility required to be satisfied. The fundamental equations for the equilibrium method are equations of equilibrium. The compatibility conditions, which include the appropriate displacement boundary conditions, are taken into account as the equations of equilibrium are developed. Solution of the resulting equations yields displacements. The equilibrium method is alternatively known as the Stiffness Method or Displacement Method . The Slope Deflection Method is a classical method of analysis for statically indeterminate beam- and frame-type structures. It is useful for hand solutions to small problems. Larger scale problems can readily be solved via the implementation of commercially available computer programs. Users of such programs must however not treat them as ‘black boxes’ but seek to understand their theoretical basis and ‘check’ the realism of the solution via suitable hand-calculations and engineering judgement. The Slope Deflection Method accounts for flexural deformations but ignores axial and shear deformations. It was first presented by Maney in 1915. The rotational and translational displacements of rigid joints are taken as the primary unknowns. All member end-moments and shears can be expressed in terms of unknown joint displacements. For each unknown joint rotation or translation, there is a corresponding condition of joint- moment or joint-force equilibrium. There are always an equal number of conditions of equilibrium as there are unknown joint displacements. The physical interpretation of the slope deflection method involves the creation of a kinematically determinate primary structure by restraining each structure displacement component (the number of restraints gives the degree of kinematic indeterminacy). For beam- and frame-type structures, CIVL2007 Theory and Design of Structures II Analytical Component (9 February 2007) page 29 since forces are applied between the member ends, individual members are under load in the restrained position. Since the primary structure cannot conform to the expected structural behaviour, the artificially imposed restraints must be relaxed. As this relaxation is allowed to occur, equilibrium must be satisfied for each degree of freedom. The loads applied at the joints as well along the length of the member must be included. CIVL2007 Theory and Design of Structures II Analytical Component (9 February 2007) page 30 Member Force-Deformation Relationships Member force-deformation relationships are needed for the slope deflection method. The degree of kinematic indeterminacy is required in order to describe suitable force-deformation relationships....
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This note was uploaded on 10/24/2009 for the course BENG Civl2007 taught by Professor A.smith during the Spring '09 term at HKU.

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Analysis Lecture 2 - CIVL2007 Theory and Design of...

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