This document contains lecture notes for a Structural Analysis I course focusing on the compatibility method. It discusses statically indeterminate beams and frames, using the compatibility method to solve such systems. Examples include analyzing differences between determinate and indeterminate frames, and applying the compatibility method to solve for forces in an indeterminate truss. The document provides examples from past assignments and exams to demonstrate applying these concepts.

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
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

5. 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

6. 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!!!!

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

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
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…

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

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

16. 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

17. 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….

18. 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

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 FRAME 1 AND FRAME 2?
STATICALLY DETERMINATE
STATICALLY INDETERMINATE

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 FRAME 1 AND FRAME 2?

21. 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?

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
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?

25. 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?

26. 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?

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

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

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

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

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

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

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

34. 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?

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

37. 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

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
STRUCTURAL ANALYSIS I
2016/2017 CLASS 3

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
IS IT STATICALLY DETERMINATE?
ASSIGNMENT 2 year 17/18

43. 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)

44. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
COMPATIBILITY METHOD
https://kahoot.it/challenge/08675034?challenge-
id=363d0596-2099-4c25-bd74-
601ae81a8691_1663830864781

45. 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?

46. 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

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

48. 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

49. 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

50. 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

51. 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

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
= 5,76 kN
= 4,23 kN

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

55. 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

56. 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

57. 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?

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
molina.eps@ceu.es ASSIGNMENT 2 year 20/21

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 year 21/22