STATICALLY INDETERMINATE SYSTEMS. TWO SPAN FRAMES. NON SIDE SWAY FRAMES.

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
TO APPLY THE SLOPE DEFLECTION METHOD WE NEED TO KNOW
THE EFFECT OF LOADS applied along the bars IN THE BAR ENDS
(end moments produced by the loads applied along the bars)
THE EFFECT OF JOINT ROTATIONS IN THE BAR ENDS
(end moments produced by the joints rotations)
THE EFFECT OF JOINT DISPLACEMENTS IN THE BAR ENDS
(end moments produced by the joints displacements)

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
SLOPE DEFLECTION METHOD STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
VERTICAL REACTION FORCES?

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
HORIZONTAL REACTION FORCES?

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
BENDING MOMENT AT D?

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
VERTICAL DISPLACEMENT AT G?

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WHAT HAPPENS IF WE REMOVE THE LOAD 2P?

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
1.- DEGREES OF FREEDOM?

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
ONE DEGREE OF FREEDOM to consider: rotation at D

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
2.- EFFECT OF THE LOAD: only loads applied along the bars

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
5.- HOW MANY EQUILIBRIUM EQUATIONS DO WE NEED?

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
𝑴𝑫 = 𝟎
6.- SOLVE FOR THE UNKOWN ROTATION

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
7.-END MOMENTS

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
9.-SHEAR FORCES

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
9.-AXIAL FORCES

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
10.-DIAGRAMS

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
10.-DIAGRAMS

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
10.-DIAGRAMS

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
11.-DEFORMED SHAPE

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WHAT HAPPENS IF DUE TO A PROBLEM IN THE FOUNDATION A SETTLEMENT OCCURS AT B?
5 cm
settlement

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WHAT’S A FOUNDATION SETLLEMENT?
EFFECTS?

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WHAT’S A FOUNDATION SETLLEMENT?
EFFECTS?

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WE MUST ADD THE EFFECT OF THE DISPLACEMENT

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
NO END MOMENT ZERO

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
ONE END MOMENT ZERO

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
WE MUST ADD THE EFFECT OF THE DISPLACEMENT
DO NOT VARY
DO NOT VARY
WE ADD THE EFFECT OF
THE DISPLACEMENT

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
𝑴𝑫 = 𝟎

29. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

30. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

31. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

32. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

33. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame

34. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
COMPARED BEHAVIOUR
WITHOUT SETTLEMENT WITH SETTLEMENT

35. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports to span frame
COMPARED BEHAVIOUR
WITHOUT SETTLEMENT
WITH SETTLEMENT