3. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PREVIOUSLY ON MATHS 1...
4. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNICULAR POLYGON. SHAPE and FORCES
EXAMPLE 1. POSITION and FORCES MAGNITUDES
EXAMPLE 2. POSITION and FORCES MAGNITUDES
EXAMPLE 3. POSITION and FORCES MAGNITUDES
EXAMPLE 4. POSITION and FORCES MAGNITUDES
EXAMPLE 5. POSITION and FORCES MAGNITUDES
5. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FIRST MINUTE QUESTION
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6. FIRST MINUTE QUESTION
If the horizontal force was 300 kN instead of 500 kN......
The force in the cable AB would be smaller than 539 kN
A
B
C
D The position of joint B will not change
The force in the cable AB would be bigger than 539 kN
The force in the cable AB would be the same 539 kN
7. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Poly Corporation Headquarters. Beijing 2007. SOM
8. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Poly Corporation Headquarters. Beijing 2007. SOM
14. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Quque Goberna
15. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Quque Goberna
16. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
1.- Determine in a geometrical way the coordinates of the intermediate points B, C and D of the funicular polygon
formed by the represented forces. Assume the side joints are A with coordinates [0, 4 m] and E [12 m, 6 m]. Assume
also that the horizontal component of all the forces is 40 kN.
2.- Determine the internal forces in all the cable segments
Seafarers Bridge - Melbourne, Australia
2009 –[Nicholas Grimshaw]
18. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
THERE ARE INFINITEPOSIBLE FORCES DIAGRAMS and FUNICULAR DIAGRAMS. WE NEED SOME REQUIREMENTS
IN THIS EXAMPLE WE HAVE TWO REQUIREMENTS:
- HORIZONTAL FORCE 40 kN
- THE FUNICULAR POLYGON SHOULD START at A AND FINISH at E
19. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
FIRST GUESS: NO MATTER ITS VERTICAL POSITION
20. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
FIRST GUESS: NO MATTER ITS VERTICAL POSITION
21. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
FIRST GUESS: NO MATTER ITS VERTICAL POSITION
22. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
23. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
27. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 40 kN
so the pole is 40 kN away from the vertical forces
SECOND GUESS: THE FUNICULAR POLYGON ENDS at E
28. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Puente de Bacunayagua Cuba - 1959 - [Luis Sáenz Duplace]
1.- Determine in a geometrical way the coordinates of the intermediate points B, C and D of the funicular polygon
formed by the represented forces. Assume that the horizontal component of all the forces is 500 kN.
2.- Determine the internal forces in all the cable segments
29. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 500 kN
30. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 500 kN
so the pole is 500 kN away from the vertical forces
HORIZONTAL FORCE = 500 kN
33. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Pliezhausen footbridge
Reutlingen, Alemania - 2002 - [Holzbau Amann GmbH]
34. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
1.- Determine in a geometrical way the coordinates of the intermediate points B, C, D, E and F of the funicular polygon
formed by the represented forces. Assume that the horizontal component of all the forces is 200 kN. Determine also
the internal forces in all the cable segments for this hypothesis.
2.- How would the funicular polygon vary if the máximum force in the cable segmenst was 250 kN? Draw the funicular
polygonfor thies hypothesis and determine the internal forces in all the cable segments.
35. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
1.- Determine in a geometrical way the coordinates of the intermediate points B, C, D, E and F of the funicular polygon
formed by the represented forces. Assume that the horizontal component of all the forces is 200 kN. Determine also
the internal forces in all the cable segments for this hypothesis.
2.- How would the funicular polygon vary if the máximum force in the cable segmenst was 250 kN? Draw the funicular
polygonfor thies hypothesis and determine the internal forces in all the cable segments.
36. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 200 kN
HORIZONTAL FORCE = 200 kN
so the pole is 200 kN away from the vertical forces
37. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 200 kN
HORIZONTAL FORCE = 200 kN
so the pole is 200 kN away from the vertical forces
FUNICULAR POLYGON
38. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 200 kN
HORIZONTAL FORCE = 200 kN
so the pole is 200 kN away from the vertical forces
FUNICULAR POLYGON
39. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 200 kN
HOW DOES THIS DIAGRAM CHANGES IF THE
MAXIMUM FORCE WAS 250 kN?????
FUNICULAR POLYGON
40. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
HORIZONTAL FORCE = 200 kN
HOW DOES THIS DIAGRAM CHANGES IF THE
MAXIMUM FORCE WAS 250 kN?????
FUNICULAR POLYGON
????
41. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MAXIMUM FORCE = 250 kN
HOW DOES THIS DIAGRAM CHANGES IF THE
MAXIMUM FORCE WAS 250 kN?????
FUNICULAR POLYGON
42. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Today’s words?
43. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
OLYMPIC STADIUM. MUNICH. 1968-1972. FREI OTTO
44. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
OLYMPIC STADIUM. MUNICH. 1968-1972. FREI OTTO