CLASS 4_comptatibility method

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
cperez.eps@ceu.es
molina.eps@ceu.es
BOURDEAUX HOUSE. OMA 1998
STATICALLY inDETERMINATE BEAMS AND FRAMES
COMPATIBILITY METHOD

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
ASSIGNMENT 2 year 17/18
STATICALLY INDETERMINATE SYSTEM. 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
18/19 CLASS 4

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
IS IT STATICALLY DETERMINATE?

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
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

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
𝜕 𝐵𝐶,𝑃 + 𝜕 𝐵𝐶,𝑁 = Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
𝜕 𝐵𝐶,𝑃
𝜕 𝐵𝐶,𝑃=
−6𝑃𝑎 𝑥 −6𝑎 +4 𝑥 −3𝑃𝑎 𝑥(−3𝑎)
6𝐸𝐼
x 𝐿 𝐴𝑐 = 12 P𝑎2
x 𝐿 𝐴𝑐/EI

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
𝜕 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

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒
Δ 𝐿 𝐵𝐶𝑐𝑎𝑏𝑙𝑒 =
𝑁 𝑥 𝐿 𝐵𝐶
𝐸𝐴

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
𝜕 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

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
= 5,76 kN= 4,23 kN

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
cperez.eps@ceu.es
molina.eps@ceu.es
BOURDEAUX HOUSE. OMA 1998
ASSIGNMENT 2 year 18/19

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 4
cperez.eps@ceu.es
molina.eps@ceu.es
ARE THE SYSTEMS STATICALLY DETERMINATE?