STATICALLY INDETERMINATE STRUCTURES. COMPATIBILITY METHOD

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
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
19/20 CLASS 3
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

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
STATICALLY INDETERMINATE BEAM. COMPATIBILITY METHOD.
WHAT HAPPENS WHEN THE BEAM IS STATICALLY INDETERMINATE?
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO SOLVE IT

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WE CAN CONSIDER THE SYSTEM AS AN ADDITION OF TWO STATICALLY DETERMINATE ONES!
DIVIDE TO WIN!!!!

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
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…

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
DEFLECTION IN THE MIDDLE OF THE SPAN

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
DEFLECTION IN THE MIDDLE OF THE SPAN

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
THINK IN AHOTHER WAY TO SOLVE IT! AND OF COURSE GET THE SAME RESULTS….

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3c

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
TEST 2 YEAR 16/17
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?
STATICALLY DETERMINATE
STATICALLY INDETERMINATE

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN TRUSS 1 AND TRUSS 2?

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
EA = 2000 P

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?
STATICALLY DETERMINATE
STATICALLY INDETERMINATE

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
WHAT’S THE DIFFERENCE BETWEEN FRAME 1 AND FRAME 2?

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3c
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

29. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
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?

30. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

31. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
ANALYZE THE DIFFERENCES
VERTICAL REACTION FORCES?
HORIZONTAL REACTION FORCES?
DISPLACEMENTS?

32. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

33. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
IS IT STATICALLY DETERMINATE?
ASSIGNMENT 2 year 17/18

34. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
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

35. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
𝜕 𝐵𝐶,𝑃 + 𝜕 𝐵𝐶,𝑁 = Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒

36. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

37. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
𝜕 𝐵𝐶,𝑃
𝜕 𝐵𝐶,𝑃=
−6𝑃𝑎 𝑥 −6𝑎 +4 𝑥 −3𝑃𝑎 𝑥(−3𝑎)
6𝐸𝐼
x 𝐿 𝐴𝑐 = 12 P𝑎2
x 𝐿 𝐴𝑐/EI

38. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
𝜕 𝐵𝐶,𝑁
𝜕 𝐵𝐶,𝑁= 2 x
−6𝑁𝑎 𝑥 6𝑎 +4 𝑥 −3𝑃𝑎 𝑥(3𝑎)
6 𝐸𝐼
x 𝐿 𝐴𝑐 = -24 N𝑎2
x 𝐿 𝐴𝐵 /EI

39. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒 =
𝑁 𝑥 𝐿 𝐵𝐶
𝐸𝐴

40. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
𝜕 𝐵𝐶,𝑃 + 𝜕 𝐵𝐶,𝑁 = Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒
12 P𝑎2x 𝐿 𝐴𝑐/EI - 24 N𝑎2
x 𝐿 𝐴𝐵/EI =
𝑁 𝑥 𝐿 𝐵𝐶
𝐸𝐴
N =
12 P 𝑎2x 𝐿 𝐴𝑐/𝐸𝐼
𝐿 𝐵𝐶
𝐸𝐴
+ 24 𝑎2 𝐿 𝐴𝐵/𝐸𝐼
IF P = 10 kN a = 1 m EI = 20000 kNm EA = 65971 kN
N = 4,93 kN

41. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

42. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
= 5,76 kN= 4,23 kN

43. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3

44. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

45. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
cperez.eps@ceu.es
molina.eps@ceu.es
BOURDEAUX HOUSE. OMA 1998
ASSIGNMENT 2 year 18/19

46. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
cperez.eps@ceu.es
molina.eps@ceu.es
ARE THE SYSTEMS STATICALLY DETERMINATE?

47. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 3
cperez.eps@ceu.es
molina.eps@ceu.es
Bordeaux Law Court, Rogers, Stirk, Habour &Partners 1992-1998
ASSIGNMENT 2 year 19/20