This document summarizes the steps for analyzing a continuous beam using finite element analysis. It begins by dividing the beam into elements, then identifying the degrees of freedom at each node. It explains that the stiffness matrices of each element are determined and assembled into a global stiffness matrix. Boundary conditions are then applied to determine the reduced stiffness matrix. Nodal loads and the equivalent load vector are calculated. Equations of equilibrium are used to solve for unknown displacements, reactions, and moments. Translation results in reactions while rotation results in bending moments.

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 4: Continuous Beam with Guided Support

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.

8. THANK YOU