Stiffness matrix method of indeterminate beam-1, finite element method

1. FINITE ELEMENT ANALYSIS
OF CONTINUOUS BEAM
BY-
Ms. JAPE ANUJA S.
ASSISTANT PROFESSOR,
CIVIL ENGINEERING DEPARTMENT,
SRES, SANJIVANI COLLEGE OF ENGINEERING,
KOPARGAON-423603.
MAID ID: anujajape@gmail.com
japeanujacivil@sanjivani.org.in
Example 1: Continuous Beam with One End Fixed And
Other Simple

2. FINITE ELEMENT ANALYSIS OF CONTINUOUS BEAM
• A beam is a structural member which is subjected to bending
deformation.
• Several methods available for the analysis of continuous beam
• Slope deflection method
• Moment distribution method
• Flexibility matrix method
• Stiffness matrix method
• Three moment theorem etc.
• However all these methods have limitations if either geometry,
loading material properties or boundary conditions. Finite element
method can well handle such problems easily.

3. 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

4. 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.

11. THANK YOU