The document discusses the slope deflection method for analyzing statically indeterminate beams and frames. It covers determining degrees of freedom, setting up equilibrium equations based on the effects of loads, rotations, and displacements, and solving for member forces and the deformed shape. The method is demonstrated for frames with various boundary conditions, including cantilevers.

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
cperez.eps@ceu.es
molina.eps@ceu.es
VIANA DO CASTELO CULTURAL CENTER. SOUTO DE MOURA. 2013
STATICALLY inDETERMINATE BEAMS AND FRAMES
SLOPE DEFLECTION METHOD

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
1.- DEGREES OF FREEDOM?

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
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)

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
SLOPE DEFLECTION METHOD STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
1.- DEGREES OF FREEDOM?

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
ONE DEGREE OF FREEDOM to consider: rotation at D

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
EFFECT OF THE LOAD + EFFECT OF THE ROTATION

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
HOW MANY EQUILIBRIUM EQUATIONS DO WE NEED?

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
𝑴𝑫 = 𝟎
SOLVE FOR THE UNKOWN ROTATION

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
SHEAR FORCES

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
BENDING MOMENTS AND SHEAR FORCES

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
AXIAL FORCES

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
AXIAL FORCES

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
1.- DEGREES OF FREEDOM?

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
ONE DEGREE OF FREEDOM to consider: rotation at D

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
EFFECT OF THE LOAD + EFFECT OF THE ROTATION

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
HOW MANY EQUILIBRIUM EQUATIONS DO WE NEED?

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
𝑴𝑫 = 𝟎
SOLVE FOR THE UNKOWN ROTATION

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
SHEAR FORCES

29. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
BENDING MOMENTS AND SHEAR FORCES

30. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers

31. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
AXIAL FORCES

32. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE

33. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE

34. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
1.- DEGREES OF FREEDOM?

35. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
TWO DEGREES OF FREEDOM to consider: rotation at I and displacement at u

36. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers

37. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
HOW
MANY
EQUILIBRIUM
EQUATIONS
DO
WE
NEED?

38. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
SOLVE
FOR
THE
UNKOWNS
ROTATION
AND
DISPLACEMENT

39. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS

40. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
END MOMENTS + SHEAR FORCES

41. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
BENDING MOMENTS AND SHEAR FORCES

42. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
AXIAL FORCES

43. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
AXIAL FORCES

44. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Frame with and without cantilevers
DEFORMED SHAPE