This document contains lecture notes on structural analysis and the compatibility method. It discusses statically indeterminate beams, frames, and trusses, and how the compatibility method is used to solve for unknowns in these systems by using additional equations related to displacements or elongations. Examples shown include calculating reactions in beams, determining axial forces in cables, and analyzing differences between determinate and indeterminate structures.

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
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
COMPATIBILITY METHOD
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
COMPATIBILITY METHOD
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
COMPATIBILITY METHOD

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

7. 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…

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

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

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

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

12. 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

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

14. 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

15. 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….

16. 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

17. 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

18. 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?

19. 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?

20. 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?

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

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

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
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
COMPATIBILITY METHOD
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
COMPATIBILITY METHOD
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
COMPATIBILITY METHOD
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
COMPATIBILITY METHOD

29. 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?

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

31. 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?

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

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

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

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

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

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

39. 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?

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

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
STRUCTURAL ANALYSIS I
2016/2017 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

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

44. 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
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
COMPATIBILITY METHOD

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

47. 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

48. 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

49. 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 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒

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

51. 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 𝐿 𝐴𝑐 = 12 P𝑎2
x 𝐿 𝐴𝑐/EI

52. 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 𝐿 𝐴𝑐 = -24 N𝑎2
x 𝐿 𝐴𝐵 /EI

53. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒 =
𝑁 𝑥 𝐿 𝐵𝐶
𝐸𝐴

54. 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 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

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
= 5,76 kN= 4,23 kN

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

58. 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

59. 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

60. 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?

61. 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