This document outlines the finite element analysis of continuous beams. It first introduces beams and common analytical methods used for continuous beams, noting limitations. It then describes the finite element method as able to easily handle complex beam geometries, loadings, materials, and boundary conditions. Finally, it lists the 8 steps to solve continuous beams using finite element analysis, including dividing the beam into elements, determining degrees of freedom and stiffness matrices, assembling the global stiffness matrix, applying boundary conditions, determining nodal loads and displacements, and calculating reactions and 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

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
to translation is
reaction.
• Action corresponding
to rotation is moment.

11. THANK YOU