STRUCTURAL ANALYSIS MODELS

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Hipódromo de la Zarzuela. Madrid 1931. Archiches y Domínguaz. Eduardo Torroja
STRUCTURAL MODELS

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
2.- STABILITY AND STATICALLY DETERMINACY: REACTION FORCES
1.- STRUCTURAL MODELS:
types of supports and connections
types of loads
bars geometry
5.- ASSIGNMENT 1
3.- INTERNAL FORCES:
AXIAL FORCE
SHEAR FORCE
BENDING MOMENT
TORSION
4.- TEST 0

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL MODELS
WE DO NOTCALCULATE REAL STRUCTURES
BUT MODELS OF THOSE REAL STRUCTURES

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Shigeru Ban. Artek Milan Pavilion 2007
STRUCTURAL MODELS

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
IT IS USELESS TO CALCULATE A MODEL IF IT DOES
NOT BEHAVE AS THE REAL STRUCTURE
STRUCTURAL MODELS

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Norman Foster. Renault Distribution Center 1982
WE MUST BE AWARE OF THE
RELATIONSHIP BETWEEN THE
MODEL AND THE REAL STRUCTURE:
partial model? Ignored effects to
simplify the calculations?...
STRUCTURAL MODELS

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
IT IS VERY IMPORTANT TO UNDERSTAND HOW
THE LOAD “TRAVELS” ALONG THE BUILDING
STRUCTURAL SYSTEM and its effects
EVERY LOAD SHOULD REACH THE GROUND

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
OMA. Shenzhen Stock Exchange 2013
STRUCTURAL MODELS

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
DEPENDING ON THE MOVEMENTS OR ROTATION RESTRICTIONS WE CLASSIFY THE SUPPORTS:
Types of supports and connections
TYPES OF SUPPORTS

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
DEPENDING ON THE MOVEMENTS OR ROTATION RESTRICTIONS WE CLASSIFY THE SUPPORTS:
Types of supports and connections
STRUCTURAL MODELS

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
ROLLER
TYPES OF SUPPORTS

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
PINNED SUPPORT
TYPES OF SUPPORTS

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
FIXED SUPPORT
TYPES OF SUPPORTS

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
DEPENDING ON THE RELATIVE MOVEMENTS OR ROTATION RESTRICTIONS BETWEEN BARS,
WE CLASSIFY THE JOINTS:
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
TYPES OF INTERNAL CONNECTIONS

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
HINGES (PINNED JOINTS)
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
TYPES OF INTERNAL CONNECTIONS

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
RIGID (or FIXED JOINTS)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
TYPES OF INTERNAL CONNECTIONS

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STABILITY AND DETERMINACY
A SYSTEM CAN BE CONSIDERED A STRUCTURE
ONLY IF IT IS IN STABLE EQUILIBRIUM
STABILITY AND DETERMINACY

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

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
1.- STABILITY AND DETERMINACY
nº unknowns
nº equilibrium
equations
<
nº unknowns
nº equilibrium
equations
=
nº unknowns
nº equilibrium
equations
>
Unstable Statically determinate Statically indeterminate
STABILITY AND DETERMINACY

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es STABILITY AND DETERMINACY
STATICALLY
INDETERMINATE
STATICALLY
DETERMINATE
UNSTABLE
STATICALLY
DETERMINATE
UNSTABLE

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
INTERNAL FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
INTERNAL FORCES
ONCE WE KNOW THE EXTERNAL
EQUILIBRIUM (REACTION FORCES)
WE CAN CALCULATE WHAT
HAPPENS “INSIDE” THE BARS OF
THE SYSTEM.
WE CAN CUT THE SYSTEM, ISOLATE
ONE PART OF IT AND APPLY AGAIN
THE EQUILIBRIUM EQUATIONS

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
INTERNAL FORCES
THE FORCE IN THE DIRECTON OF THE BAR DIRECTRIX IS CALLED
AXIAL FORCE

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
INTERNAL FORCES
THE ROPE IS IN TENSION AND WHEN THE CHILDREN PULL
IT GETS…. ¿LONGER OR SHORTER?

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
THE PARTHENON INTERNAL COLUMNS ARE IN COMPRESSION
THEY GET…. ¿LONGER OR SHORTER?

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
BE CAREFUL WITH ELEMENTS UNDER COMPRESSION AND
BUCKLING

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
IS THIS WAY OF BREAKING BREAD EASY? WHY?

27. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
THE EFFECT OF THE SHEAR FORCE IS…

28. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
WHAT HAPPENS WHEN WE APPLY A VERTICAL FORCE IN THE
MIDDLE OF A BEAM?

29. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
HOW COULD YOU REDUCE DE VERTICAL DISPLACEMENT IN THE
MIDDLE OF THE SPAN?

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

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

32. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
WHAT WOULD HAPPEN IF ALL THE PEOPLE DECIDE TO MOVE
TOWARS ONE SIDE OF THE BRIDGE?

33. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
HOW COULD YOU REDUCE THE EFFECT OF TORSION?

34. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es INTERNAL FORCES
FOR WHICH INTERNAL FORCE IS EACH OF THIS PROFILE
EFFECTIVE?

35. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Type of connection?
Which one restrains relative rotation?
Which one restrains relative movement?
TEST 0

36. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Type of connection?
Does any of them allow movement or rotation?
TEST 0

37. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Type of connection?
What happens with the bending moments and the end bar moments?
TEST 0

38. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
San Francisco Suspension Bridge. Built in 1937
TEST 0

39. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
TEST 0

40. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
TEST 0

41. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
CAN YOU TELL THE DIFFERENCE
BETWEEN
A SUSPENSION BRIDGE AND
A CABLE-STAYED BRIDGE?
TEST 0

42. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Puente de Rande cable-stayed Bridge. Vigo 1973
TEST 0

43. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es TEST 0

44. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Vigo cable-stayed Bridge
TEST 0

45. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Chicago John Hancock Tower 1970 TEST 0

46. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Chicago Lake Shore Drive Apartments.
Mies van der Rohe TEST 0

47. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es TEST 0

48. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
John Hancock Center (1970):
Architectural height 1128’ (344 m), 100 stories.
Plan dimensions at the ground floor: 262x164’ (78,6x49,2 m).
Plan dimensions at the top floor: 160x100’ (48x30 m).
Chicago John Hancock Tower 1970
TEST 0

49. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Chicago John Hancock Tower 1970
TEST 0

50. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Miralles-Tagliabue. Santa Caterina Market. Barcelona 1997 / 2005
TEST 0

51. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
REMEMBER
IT IS VERY IMPORTANT TO UNDERSTAND HOW
THE LOAD TRAVELS ALONG THE BUILDING
STRUCTURAL SYSTEM.
EVERY LOAD SHOULD REACH THE GROUND

52. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
Santa Caterina Market (1997/2005):
Central frame span: 42 m.
Roof weight: 92 kp/m2.
7 concrete supports with cross section 90 cm x 90 cm.
2 post tensioned beams with spans of 12-22 m and cantilever from 4-10 m,
cross section beam depth 1,2 m.
Archs of 6 m height.
V shaped beams average 50 m span.
Wooden Arches and Ribs coming from the original market structure in a 50%.
TEST 0

53. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es TEST 0

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

55. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STABILITY AND DETERMINACY?
CAN YOU FIND THE REACTION FORCES?
WHAT’S THE EFFECT OF THE CABLE?
TEST 0

56. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
For the Gerber beam in the figure and the given bending moment diagram, determine:
1. Value of the punctual load P (kN)
2. Value of the distributed load q (kN/m)
3. Sign and value of the vertical reaction at D, Dy (kN)
4. Sign and value of the shear force at A, VA (kN)
TEST 0

57. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
18/19 CLASS 1
cperez.eps@ceu.es
molina.eps@ceu.es
For the Gerber beam in the figure and the given shear force diagram, determine:
1. Value of the distributed load q (kN/m)
2. Value of the length L (m)
3. Sign and value of the bending moment at the middle of CD member, MCD (mkN)
4. Sign and value of the bending moment at B, MB (mkN)
5. Sign and value of the rotation at B, θB (mrad)
6. Equivalent model for the beam ABC (types of supports and external forces).
TEST 0