12. KINEMATIC INDETERMINANCY; STIFFNESS METHOD
The chapter explores the stiffness vs flexibility methods in structural analysis, highlighting their distinctions in terms of primary variables and governing relations. It introduces methods for analyzing structures with kinematic relations, emphasizing the development of equations for force-displacement relationships and discussing traditional methodologies like slope deflection and moment distribution. The chapter concludes with practical applications of these methods in solving real-world engineering problems.
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What we have learnt
- The stiffness method focuses on displacements as primary unknowns, while the flexibility method uses forces.
- Static indeterminancy arises when there are more unknowns than equations in a structure.
- Different structural analysis methods include slope deflection, moment distribution, and direct stiffness, each with unique applications.
Key Concepts
- -- Static Indeterminancy
- A condition in structural analysis where the number of unknown reactions exceeds the number of available equilibrium equations.
- -- Kinematic Indeterminancy
- Refers to the number of independent displacements or rotations that can occur in a structure.
- -- Slope Deflection Method
- An analysis technique that results in linear equations involving displacements and internal forces based on beam deflection.
- -- Moment Distribution Method
- An iterative approach used to evaluate displacements and internal moments in continuous beams.
- -- Direct Stiffness Method
- A matrix-based formulation of the stiffness method, facilitating powerful computational structural analysis.
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