STATICALLY INDETERMINATE SYSTEMS. COMPATIBILITY METHOD

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es
STATICALLY inDETERMINATE BEAMS AND FRAMES
COMPATIBILITY METHOD
Bordeaux Law Court, Rogers, Stirk, Habour &Partners 1992-1998

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
PREVIOUSLY IN AE1

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
BEAM 5
BEAM 6
LET’S COMPARE THESE BEAMS BEHAVIOUR
PREVIOUSLY IN AE1

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
BENDING MOMENTS DIAGRAM

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHICH EFFECTS AFFECT THE VERTICAL DISPLACEMENT AT THE END OF THE CANTILEVER?
BEAM 5

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
THE EFFECT OF THE CANTILIVER IMPLIES A ROTATION 0 AT THE FIXED END

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TO CALCULATE THE ROTATION AT B … WHICH EFFECTS DO WE HAVE TO CONSIDER?
BEAM 5

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
THE EFFECT OF THE DISTRIBUTED LOAD PLUS THE EFFECT OF THE END MOMENT

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
THE VERTICAL DISPLACEMENT AT C IS THE ADDITION
OF THE ROTATION AT B EFFECT PLUS THE CANTILEVER LOAD EFFECT

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
BEAM 6
TO CALCULATE THE VERTICAL DISPLACEMENT AT C…
WHICH EFFECTS DO WE HAVE TO CONSIDER?

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TO CALCULATE THE VERTICAL DISPLACEMENT AT C…
WHICH EFFECTS DO WE HAVE TO CONSIDER?
BEAM 6
WE MUST CONSIDER SAME AS BEAM (5)
PLUS THE EFFECT OF THE CABLE ELONGATION

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
BEAM 6

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
BEAM 6
WE WOULD GET SAME RESULT IF WE APPLY UNIT LOAD METHOD
WATCH OUT!!!!!
WE SHOULD CONSIDER
THE BENDING
MOMENTS OF THE
BEAM AND THE AXIAL
FORCE IN THE CABLE!

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
https://kahoot.com/schools-u/

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TEST 2 year 16/17
STATICALLY INDETERMINATE SYSTEM. COMPATIBILITY METHOD
ASSIGNMENT 2 year 17/18
STATICALLY INDETERMINATE SYSTEM. COMPATIBILITY METHOD
STATICALLY INDETERMINATE BEAM
COMPATIBILITY METHOD
ASSIGNMENT 3 year 18/19

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
STATICALLY INDETERMINATE BEAM. COMPATIBILITY METHOD.
WHAT HAPPENS WHEN THE BEAM IS STATICALLY INDETERMINATE?
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO SOLVE IT

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WE CAN CONSIDER THE SYSTEM AS AN ADDITION OF TWO STATICALLY DETERMINATE ONES!
DIVIDE TO WIN!!!!

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WE NEED TO KNOW THE BEAM CROSS SECTION TO CALCULATE THE REACTION FORCES…
IN STATICALLY INDETERMINATE SYSTEMS THE RESULT IS DIFFERENT DEPENDING ON THE
CROSS SECTION DIMENSIONS…

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
DEFLECTION IN THE MIDDLE OF THE SPAN

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
DEFLECTION IN THE MIDDLE OF THE SPAN

29. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
THINK IN AHOTHER WAY TO SOLVE IT! AND OF COURSE GET THE SAME RESULTS….

30. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3c

31. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TEST 2 YEAR 16/17
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?
STATICALLY DETERMINATE
STATICALLY INDETERMINATE

32. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

33. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

34. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

35. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

36. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
EA = 2000 P

37. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

38. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?
STATICALLY DETERMINATE
STATICALLY INDETERMINATE

39. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?

40. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?

41. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

42. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

43. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
NAC, A = - 5 q a x sin α - 2,542 q a x cos α =
-5 q a x 4 / √20 – 2,542 q a x 2 / √20 = -5,609 q a
DO THESE DIAGRAMS MAKE SENSE?

44. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
ANOTHER WAY OF SOLVING THE STATICALLY INDETERMINATE FRAME
BASED ON THE STATICALLY DETERMINATE ONE?

45. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
ANALYZE THE DIFFERENCES
VERTICAL REACTION FORCES?
HORIZONTAL REACTION FORCES?
DISPLACEMENTS?

46. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TODAY’S WORDS
VERTICAL REACTION FORCES?
HORIZONTAL REACTION FORCES?
DISPLACEMENTS?

47. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
DEGREE OF INDETERMINACY?

48. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
I
II

49. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

50. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
II

51. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

52. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

53. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

54. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
WHAT HAPPENS IF THE TRUSS IS STATICALLY INDETERMINATE INTERNALLY?

55. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

56. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

57. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
STRUCTURAL ANALYSIS I
2016/2017 CLASS 3

58. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

59. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
STRUCTURAL ANALYSIS I
2016/2017 CLASS 3

60. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

61. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

62. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
IS IT STATICALLY DETERMINATE?
ASSIGNMENT 2 year 17/18

63. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
TO CALCULATE THE VALUE OF THE CABLE AXIAL FORCE THE THREE
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH
WE NEED AN EXTRA EQUATION (for example a COMPATIBILITY EQUATION)

64. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
𝜕𝐵𝐶,𝑃 + 𝜕𝐵𝐶,𝑁 = Δ 𝐿𝐵𝐶𝑐𝑎𝑏𝑙𝑒

65. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

66. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
𝜕𝐵𝐶,𝑃
𝜕𝐵𝐶,𝑃=
−6𝑃𝑎 𝑥 −6𝑎 +4 𝑥 −3𝑃𝑎 𝑥(−3𝑎)
6𝐸𝐼
x 𝐿𝐴𝑐 = 12 P𝑎2
x 𝐿𝐴𝑐/EI

67. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
𝜕𝐵𝐶,𝑁
𝜕𝐵𝐶,𝑁= 2 x
−6𝑁𝑎 𝑥 6𝑎 +4 𝑥 −3𝑃𝑎 𝑥(3𝑎)
6 𝐸𝐼
x 𝐿𝐴𝑐 = -24 N𝑎2
x 𝐿𝐴𝐵 /EI

68. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
Δ 𝐿𝐵𝐶𝑐𝑎𝑏𝑙𝑒
Δ 𝐿𝐵𝐶𝑐𝑎𝑏𝑙𝑒 =
𝑁 𝑥 𝐿𝐵𝐶
𝐸𝐴

69. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
𝜕𝐵𝐶,𝑃 + 𝜕𝐵𝐶,𝑁 = Δ 𝐿𝐵𝐶𝑐𝑎𝑏𝑙𝑒
12 P𝑎2x 𝐿𝐴𝑐/EI - 24 N𝑎2
x 𝐿𝐴𝐵/EI =
𝑁 𝑥 𝐿𝐵𝐶
𝐸𝐴
N =
12 P𝑎2x 𝐿𝐴𝑐/𝐸𝐼
𝐿𝐵𝐶
𝐸𝐴
+ 24 𝑎2 𝐿𝐴𝐵/𝐸𝐼
IF P = 10 kN a = 1 m EI = 20000 kNm EA = 65971 kN
N = 4,93 kN

70. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

71. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
= 5,76 kN
= 4,23 kN

72. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD

73. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

74. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es
BOURDEAUX HOUSE. OMA 1998
ASSIGNMENT 2 year 18/19

75. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es
ARE THE SYSTEMS STATICALLY DETERMINATE?

76. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es ASSIGNMENT 2 year 20/21

77. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
cperez.eps@ceu.es
molina.eps@ceu.es year 21/22