2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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_year 21/2
7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
cperez.eps@ceu.es
molina.eps@ceu.es
DEPENDING ON THE RELATIVE MOVEMENTS OR ROTATION RESTRICTIONS BETWEEN BARS,
WE CLASSIFY THE JOINTS:
TYPES OF INTERNAL CONNECTIONS
21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
cperez.eps@ceu.es
molina.eps@ceu.es STABILITY AND DETERMINACY
STATICALLY
INDETERMINATE
STATICALLY
DETERMINATE
UNSTABLE
STATICALLY
DETERMINATE
UNSTABLE
23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
cperez.eps@ceu.es
molina.eps@ceu.es
INTERNAL FORCES
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
46. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
DISPLACEMENTS. UNIT LOAD METHOD
REAL SYSTEM
AUXILIARY SYSTEM
EA = 2100000 kN
P* x d real = ∑(N* x ∆Lreal)
1ud x u = 1 x (3 x 4 m x 37,5 / 2100000 )
u = 0,214 mm
TEST 0
55. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
METHOD OF JOINTS
ANALYSING EVERY JOINT EQUILIBRIUM
we get to know every bar internal force
TEST 0
56. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
METHOD OF JOINTS
DOES THESE RESULTS MAKE SENSE?
WHAT WOULD HAPPEN IF THE HORIZONTAL LOAD WAS ZERO?
57. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
ONCE WE KNOW THE VALUE OF THE REACTION FORCES
WE CAN ALSO CALCULATE THE INTERNAL FORCES IN SOMEBARS.
METHOD OF SECTIONS
USEFUL FOR CHECKING
TEST 0
59. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
ONCE WE KNOW THE VALUE OF THE REACTION FORCES
WE CAN ALSO CALCULATE THE INTERNAL FORCES IN SOMEBARS.
METHOD OF SECTIONS
USEFUL FOR CHECKING
TEST 0
78. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
81. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
82. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
85. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
86. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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
93. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STRUCTURAL MODELS
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