ANALYSIS OF STATICALLY INDETERMINATE SYSTEMS. SLOPE DEFLECTION METHOD

1. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
cperez.eps@ceu.es
molina.eps@ceu.es
CASA ENTRE TAPIALES. JESÚS DONAIRE 2017
STATICALLY inDETERMINATE BEAMS AND FRAMES
SLOPE DEFLECTION METHOD

2. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD
CONTINUOUS BEAM
NON-SWAY FRAME

3. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD
CONTINUOUS BEAM
NON-SWAY FRAME

4. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
SLOPE DEFLECTION METHOD versus COMPATIBILITY METHOD
WHAT WOULD YOU DO IF YOU HAD TO SOLVE THIS CONTINUOUS BEAM?

5. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
WHAT DO YOU HAVE TO DO TO APPLY COMPATIBILITY?...
3
COMPATIBILITY
EQUATIONS
3 UNKNOWNS
12 ROTATION
EXPRESSIONS!!!!

6. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
WHEN THE DEGREE OF INDETERMINACY IS HIGH,
THE NUMBER OF DEGREES OF FREEDOM IS LOW
SO IT IS LESS TIRING TO APPLY THE SLOPE DEFLECTION METHOD
INSTEAD OF THE COMPATIBILITY METHOD

7. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
EQUATIONS UNKNOWNS COEFFICIENTS
Compatibility Method
(force method or flexibility
method)
COMPATIBILITY between
movements (rotations or
displacements)
Redundant reaction forces
or Moments or internal
forces or moments
Flexibility coefficients(L/EI)
Slope Deflection Method
(equilibrium method or
displacement method)
EQUILIBRIUM of end
moments or joint forces
MOVEMENTS: rotations or
displacements
Bending stiffness (EI/L)

8. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
EQUATIONS UNKNOWNS COEFFICIENTS
Compatibility Method
(force method or flexibility
method)
COMPATIBILITY between
movements (rotations or
displacements)
Redundant reaction forces
or Moments or internal
forces or moments
Flexibility coefficients(L/EI)
Slope Deflection Method
(equilibrium method or
displacement method)
EQUILIBRIUM of end
moments or joint forces
MOVEMENTS: rotations or
displacements
Bending stiffness (EI/L)

9. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
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)

10. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
LOAD ALONG THE BARS EFFECT

11. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
LOADS EFFECT

12. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
ROTATION EFFECT

13. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
ROTATION EFFECT

14. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
DISPLACEMENT EFFECT

15. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
LET’S SOLVE THIS BEAM APPLYING THE SLOPE DEFLECTION METHOD
THIS METHOD IS ATTRACTIVE IN THIS CASE BECAUSE
THE DEGREE OF INDETERMINACY IS HIGH
THERE IS ONLY ONE DEGREE OF FREEDOM:
the rotation at B

16. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
SLOPE DEFLECTION
METHOD
STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES
FIRST QUESTION: DEGREES OF FREEDOM?
SECOND STEP:
effect of the LOAD?
+
effect of the ROTATION?
+
effect of the DISPLACEMENT?
EQUILIBRIUM EQUATIONS

17. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
DEGREES OF FREEDOM?
or which movements (displacements or rotations) are possible?
NUMBER OF UNKNOWNS?
NUMBER OF EQUILIBRIUM EQUATIONS?

18. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

19. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

20. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
S M = 0
B
EQUILIBRIUM EQUATION

21. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
-41,66 + 18,75 + 8000 gB + 13333,33 gB = 0gB = 1,074 mrad
EQUILIBRIUM EQUATION S M = 0
B

22. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
END MOMENTS
load
rotation
WATCH OUT!
END MOMENTS ARE NOT EQUAL TO BENDING
MOMENTS!

23. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
END MOMENTS

24. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
SHEAR FORCES

25. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

26. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD
CONTINUOUS BEAM
NON-SWAY FRAME

27. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
DEGREES OF FREEDOM?
or which movements (displacements or rotations) are possible?

28. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
EFFECT OF THE LOAD

29. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
LOAD ALONG THE BARS EFFECT

30. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
EFFECT OF THE JOINTS ROTATION

31. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
ROTATION EFFECT

32. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

33. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
END MOMENTS

34. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
END MOMENTS

35. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
HOW TO CALCULATE SHEAR FORCES IN INCLINED BARS?

36. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
HOW TO CALCULATE SHEAR FORCES IN INCLINED BARS?

37. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

38. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

39. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

40. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

41. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

42. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
HOW WOULD THE PROCCESS AND THE RESULTS CHANGE IF THE
SUPPORTS ARE PINNED INSTEAD OF FIXED?

43. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

44. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

45. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

46. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

47. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

48. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

49. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

50. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

51. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTIONSTRUCTURAL ANALYSIS I
2017/2018 CLASS 4

52. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION

53. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
cperez.eps@ceu.es
molina.eps@ceu.es
CASA ENTRE TAPIALES. JESÚS DONAIRE 2017
STATICALLY inDETERMINATE BEAMS AND FRAMES
SLOPE DEFLECTION METHOD

54. STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
SLOPE DEFLECTION
cperez.eps@ceu.es
molina.eps@ceu.es
CASA RUFO. ALBERTO CAMPO BAEZA, 2017
CASA RUFO. ALBERTO CAMPO BAEZA, 1917