Class 3b. Compatibility Method. Trusses statically indeterminate (externally or/and internally)

1. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
Degree in Architecture
Year 3 Term 1
EPS USPCEU

2. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STATICALLY INDETERMINATE STRUCTURES.
COMPATIBILITY METHOD. TRUSSES EXTERNALLY INDETERMINATE.
COMPATIBILITY METHOD. TRUSSES INTERNALLY INDETERMINATE.
ASSIGNMENT 3

3. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

4. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
ARE THESE TRUSSES STATICALLY DETERMINATE?

5. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
DEGREE OF INDETERMINACY?

6. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
I
II

7. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
I

8. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
II

9. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

10. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

11. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
HOW TO CALCULATE THE VERTICAL DISPLACEMENT AT G?
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

12. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
AUXILIARY SYSTEM
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
HOW TO CALCULATE THE VERTICAL DISPLACEMENT AT G?

13. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WHAT HAPPENS IF THE TRUSS IS STATICALLY INDETERMINATE INTERNALLY?

15. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
δ 𝑃 =
−3𝑃 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
+
3𝑃 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
+
−𝑃 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
+
−𝑃 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
AUXILIARY SYSTEM
REAL SYSTEM

16. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
δ 𝑃 =
3𝑃𝑎 2
𝐸𝐴 𝐻𝐸𝐵300
AUXILIARY SYSTEM
REAL SYSTEM

17. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
δ 𝑁 =
2𝑥 −𝑁 2/2 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
+
2𝑥 −𝑁 2/2 𝑥 − 2/2 𝑥 3𝑎
𝐸𝐴 𝐻𝐸𝐵300
+
3𝑥𝑁𝑥1𝑥 3𝑎 2/2
𝐸𝐴 𝐻𝐸𝐵300
AUXILIARY SYSTEM
REAL SYSTEM

18. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
δ 𝑁 =
6 𝑁𝑎+4,5 2 𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
AUXILIARY SYSTEM
REAL SYSTEM

19. δ 𝑁 =
6𝑁𝑎 + 4,5 2𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
δ 𝑃 =
3𝑃𝑎 2
𝐸𝐴 𝐻𝐸𝐵300
ONCE I KNOW THE DISPLACEMENTS IN THE REMOVED BAR DIRECTION…
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b

20. δ 𝑁 =
6𝑁𝑎 + 4,5 2𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
δ 𝑃 =
3𝑃𝑎 2
𝐸𝐴 𝐻𝐸𝐵300
THAT DISPLACEMENT SHOULD EQUAL THE BAR ELONGATION…
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
Δ𝐿 𝐺𝐷 =
−1,5 2 𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
δ 𝑃+ δ 𝑁= Δ𝐿 𝐺𝐷
BE CAREFUL WITH THE SIGN!
ARE G AND D GETTING CLOSER OR FURTHER?

21. 3𝑃𝑎 2
𝐸𝐴 𝐻𝐸𝐵300
+
6𝑁𝑎+4,5 2𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
=
−1,5 2 𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
δ 𝑁 =
6𝑁𝑎 + 4,5 2𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
δ 𝑃 =
3𝑃𝑎 2
𝐸𝐴 𝐻𝐸𝐵300
Δ𝐿 𝐺𝐷 =
−1,5 2 𝑎𝑁
𝐸𝐴 𝐻𝐸𝐵300
WATCH OUT!!! SIGNS ARE VERY IMPORTANT!!! THINK ABOUT THEM

22. 𝑁 = −0,293𝑃
WATCH OUT!!! SIGNS ARE VERY IMPORTANT!!! THINK ABOUT THEM
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
WHAT DOES THIS SIGN MEAN?

23. 𝑁 = −0,293𝑃

24. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

25. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
EXAMPLE 2. TRUSS STATICALLY INDETERMINATE (INTERNALLY)

26. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

27. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

28. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

29. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

30. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

31. STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es