Stiffness matrix method of indeterminate Beam3
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This document provides an overview of using finite element analysis to analyze a continuous beam. It lists the steps for the finite element solution of continuous beams, which are: 1) divide the beam into elements, 2) identify degrees of freedom, 3) determine element stiffness matrices, 4) assemble the global stiffness matrix, 5) impose boundary conditions and determine the reduced stiffness matrix, 6) determine the element nodal load vector, 7) determine the equivalent load vector, 8) solve for unknown displacements using equilibrium equations, and 9) determine reactions and moments using equilibrium equations. It also notes that reactions correspond to translations and moments correspond to rotations.
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![FINITE ELEMENT ANALYSIS OF CONTINUOUS BEAM
Steps for the solution of continuous (Indeterminate) beams using
finite element method:
1. Divide the beam into number of elements (Take one member as one
element)
2. Identify total degrees of freedom (Two D.O.F. at each node,
translation and rotation)
3. Determine stiffness matrices of all elements ([K]1, [K]2………)
4. Assemble the global stiffness matrix [K]
5. Impose the boundary conditions and determine reduced stiffness
matrix
6. Determine element nodal load vector [q] (Restrained structure)
7. Determine equivalent load vector [f]
8. Apply equation of equilibrium [K]{Δ}={f} and determine unknown
joint displacements.
9. Apply equation [K]{Δ}+[q] ={f} to determine reactions and
moments](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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- 2. FINITE ELEMENT ANALYSIS OF CONTINUOUS BEAM Steps for the solution of continuous (Indeterminate) beams using finite element method: 1. Divide the beam into number of elements (Take one member as one element) 2. Identify total degrees of freedom (Two D.O.F. at each node, translation and rotation) 3. Determine stiffness matrices of all elements ([K]1, [K]2………) 4. Assemble the global stiffness matrix [K] 5. Impose the boundary conditions and determine reduced stiffness matrix 6. Determine element nodal load vector [q] (Restrained structure) 7. Determine equivalent load vector [f] 8. Apply equation of equilibrium [K]{Δ}={f} and determine unknown joint displacements. 9. Apply equation [K]{Δ}+[q] ={f} to determine reactions and moments
- 3. Note: • Action corresponding t o t r a n s l a t i o n i s reaction. • Action corresponding to rotation is moment.
- 9. THANK YOU