The document discusses the analysis of an inclined support and beam frame using the slope deflection method. It describes applying equilibrium equations to the frame, considering degrees of freedom, and determining end moments, bending moments, and the deformed shape. The effects of loads, joint rotations, and settlements are analyzed using this 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 COMPARE THE BEHAVIOUR OF THESE SEMI-FRAMES
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO ANALYZE THEM
so we will consider as unknowns the DEGREES OF FREEDOM
we will 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
M=0

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

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

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

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

9. 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

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
WHAT HAPPENS IF A 5 cm SETTLEMENT OCCURS AT A?
5 cm

11. 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 + EFFECT OF THE ROTATION
M=0

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE SETTLEMENT
M=0

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

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

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

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

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
DEGREES OF FREEDOM?

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE LOAD + EFFECT OF THE ROTATION

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE JOINT DISPLACEMENTS

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

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

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

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

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

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

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
DEGREES OF FREEDOM?

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE LOAD + EFFECT OF THE ROTATION

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE JOINTS DISPLACEMENTS

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

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

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

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

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

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