Analysis of a semi-frame. Slope deflection method

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
cperez.eps@ceu.es
molina.eps@ceu.es
LET’S SOLVE THE FOLLOWING SEMI FRAME
(inclined support + horizontal beam)
EQUILIBRIUM EQUATIONS
ARE NOT ENOUGH TO
ANALYZE THE SYSTEM
AS THE DEGREE OF INDETERMINACY IS HIGH
we consider as unknowns the DEGREES OF FREEDOM
so we apply the SLOPE DEFLECTION METHOD

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
HOW DOES THIS FRAME MOVE?

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE LOADS APPLIED ALONG THE BARS
M=0

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
WE MAKE JOINT B ROTATE AND WE MEASURE THE EFFECT OF THIS ROTATION
M=0

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
WE MAKE JOINT A MOVE AND WE MEASURE THE EFFECT OF THE MOVEMENT
M=0

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
REMEMBER: END MOMENTS DUE TO THE DISPLACEMENT APPEAR ONLY IN
BARS THAT ROTATE AS A CONSEQUENCE OF THE DISPLACEMENT
M=0

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
HOW MANY EQUILIBRIUM EQUATIONS?

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
FIRST EQUATION: S MB = 0
SECOND EQUATION?

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SECOND EQUATION? IT IS INTERESTING FINDING A EQUATION IN WHICH
NO AXIAL FORCES ARE INVOLVED

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SECOND EQUATION? IT IS INTERESTING FINDING A EQUATION IN WHICH
NO AXIAL FORCES ARE INVOLVED
AT O THE AXIAL FORCE ALONG BC AND THE VERTICAL REACTION FORCE AT A INTERSECT
S MO = 0

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
END MOMENTS

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
END MOMENTS AND SHEAR FORCES

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SHEAR FORCE DIAGRAM

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
AXIAL FORCES (ANALYSING JOINT B FIRST
AND WHAT HAPPENS ALONG AB THEN)

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
AXIAL FORCE DIAGRAM

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
BENDING MOMENTS DIAGRAM AND DEFORMED SHAPE

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES