This document discusses using the compatibility method to analyze a continuous beam. The compatibility method involves (1) dividing the continuous beam into separate determinate systems, (2) removing one redundant reaction force, (3) using compatibility equations to calculate the value of the removed reaction force by setting the displacement at a point to zero, and (4) using equilibrium equations to solve for the remaining reaction forces. General expressions for calculating deflections in simple beams due to distributed and end loads are also presented.

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
LET’S SOLVE THE FOLLOWING CONTINUOUS BEAM
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO KNOW THE REACTION FORCE VALUES
We can find them applying the COMPATIBILITY METHOD

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
the COMPATIBILITY METHOD
consists on DIVIDE TO WIN
We REMOVE one of the redundant
reaction forces and transform the
indeterminate system in the addition
of two determinate ones

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
This addition is only true if the value of R
makes the vertical displacement at B ZERO

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
THE COMPATIBILITY EQUATION LET US FIND
THE VALUE OF R, OUR UNKNOWN
General expression
to compute the
deflection in the
middle of the span
of a simple beam
subjected to a
distributed load
General expression
to compute the
deflection in the
middle of the span
of a simple beam
subjected to a end
moment

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
THE COMPATIBILITY EQUATION LET US FIND
THE VALUE OF R, OUR UNKNOWN

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es
ONCE WE KNOW THE VALUE OF THE REACTION FORCE AT B,
APPLYING THE THREE EQUILIBRIUM EQUATIONS, SFx = 0; SFy = 0; SM = 0;
WE CAN FIND THE VALUE OF THE OTHER VERTICAL REACTION FORCES

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
cperez.eps@ceu.es
molina.eps@ceu.es

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
COMPATIBILITY METHOD
CONTINUOUS BEAM
TO THINK ABOUT
How would the value of the reaction forces vary if instead of
IPE270 the beam profile was IPE200?
How would the value of the bending moments vary if instead
of IPE270 the beam profile was IPE200?
How would the value of displacements vary if instead of
IPE270 the beam profile was IPE200?