FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTALS OF MATHEMATICS I
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PREVIOUSLY ON MATHS 1...
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MAXWELL-CREMONA
EXAMPLE 15. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD
EXAMPLE 16. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD
Based on the studies of James Clerk Maxwell and Luigi Cremona.
Second part of XIX century
EXAMPLE 17. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FIRST MINUTE QUESTION
Username: First part of your CEU email
For example:
if your email is a.garcia245@uspceu.es
Your username will be a.garcia245
Password: SAME AS USERNAME
FIRST MINUTE QUESTION
Which of these sentences is true?
Bars AJ, JK and it symmetricals should be positive
A
B
C
D All the signs and values are correct
Bar DN and its symmetrical cannot be zero
Bars LM and MN should be equal sign and magnitude
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Borussia Park Stadium - Monchengladbach, Alemania - 2004 - [Planungsgruppe B]
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
EXTERNAL FORCES RECIPROCAL DIAGRAM
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
EXTERNAL FORCES RECIPROCAL DIAGRAM
ZERO BARS?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
EXTERNAL FORCES RECIPROCAL DIAGRAM
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
INTERNAL FORCES RECIPROCAL DIAGRAM
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM= RECIPROCAL DIAGRAM?
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: CNN
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: CNN
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Gaudí Work
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Gaudí Work. Blog Estructurando
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNICULAR POLYGON
The figure formed by a light string hung
between two points from which weights are
suspended at various points.
A force diagram for such a string, in which
the forces (weights and tensions) acting on
points of the string from which weights are
suspended are represented by a series of a
djacent triangles.
McGraw-
Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The Mc
Graw-Hill Companies, Inc.
Source: The Art of Spansh Bridge Designs. Princeton University
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Quque Goberna
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Source: Quque Goberna
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]
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
4 3 2 3
x
4
2
12
6
A
B
C
D
E
10
15
5
y
FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Today’s words?

FM1_geo_1_24_11_7.pptx

  • 1.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY FUNDAMENTALS OF MATHEMATICS I
  • 2.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 3.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY PREVIOUSLY ON MATHS 1...
  • 4.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MAXWELL-CREMONA EXAMPLE 15. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD EXAMPLE 16. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD Based on the studies of James Clerk Maxwell and Luigi Cremona. Second part of XIX century EXAMPLE 17. INTERNAL FORCES IN BARS. MAXWELL-CREMONA METHOD
  • 5.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY FIRST MINUTE QUESTION Username: First part of your CEU email For example: if your email is [email protected] Your username will be a.garcia245 Password: SAME AS USERNAME
  • 6.
    FIRST MINUTE QUESTION Whichof these sentences is true? Bars AJ, JK and it symmetricals should be positive A B C D All the signs and values are correct Bar DN and its symmetrical cannot be zero Bars LM and MN should be equal sign and magnitude
  • 7.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 8.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 9.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 10.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 11.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 12.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Borussia Park Stadium - Monchengladbach, Alemania - 2004 - [Planungsgruppe B]
  • 13.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
  • 14.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM? EXTERNAL FORCES RECIPROCAL DIAGRAM
  • 15.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM? EXTERNAL FORCES RECIPROCAL DIAGRAM ZERO BARS?
  • 16.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM? EXTERNAL FORCES RECIPROCAL DIAGRAM
  • 17.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM? INTERNAL FORCES RECIPROCAL DIAGRAM
  • 18.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
  • 19.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
  • 20.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM? = RECIPROCAL DIAGRAM?
  • 21.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY MODEL OF THE REAL TRUSS = FORM DIAGRAM = GEOMETRY OF THE BARS FORCES DIAGRAM= RECIPROCAL DIAGRAM?
  • 22.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
  • 23.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: CNN
  • 24.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: CNN
  • 25.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: Gaudí Work
  • 26.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: Gaudí Work. Blog Estructurando
  • 27.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY FUNICULAR POLYGON The figure formed by a light string hung between two points from which weights are suspended at various points. A force diagram for such a string, in which the forces (weights and tensions) acting on points of the string from which weights are suspended are represented by a series of a djacent triangles. McGraw- Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The Mc Graw-Hill Companies, Inc. Source: The Art of Spansh Bridge Designs. Princeton University
  • 28.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: Quque Goberna
  • 29.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Source: Quque Goberna
  • 30.
    FUNDAMENTOS MATEMÁTICOS DELA 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]
  • 31.
    FUNDAMENTOS MATEMÁTICOS DELA 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 4 3 2 3 x 4 2 12 6 A B C D E 10 15 5 y
  • 32.
    FUNDAMENTOS MATEMÁTICOS DELA ARQUITECTURA I FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY Today’s words?