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STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
Degree in Architecture
Year 3 Term 1
EPS USPCEU
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
Campo Baeza UFV Sports Center. Madrid 2016
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- STABILITY AND STATICALLY DETERMINACY
1.- STRUCTURAL MODELS:
types of supports and connections
types of loads
bars geometry
3.- STATICALLY DETERMINATE TRUSSES:
definition
external equilibrium (reaction forces)
internal equilibrium (axial forces)
displacements
4.- ASSIGNMENT 1
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1.- STRUCTURAL MODELS
WE DO NOT CALCULATE REAL STRUCTURES
BUT MODELS OF THOSE REAL STRUCTURES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Shigeru Ban. Artek Milan Pavilion 2007
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1.- STRUCTURAL MODELS
IT IS USELESS TO CALCULATE A MODEL IF IT DOES
NOT BEHAVE AS THE REAL STRUCTURE
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
Norman Foster. Renault Distribution Center 1982
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1.- STRUCTURAL MODELS
IT IS VERY IMPORTANT TO UNDERSTAND HOW
THE LOAD TRAVELS ALONG THE BUILDING
STRUCTURAL SYSTEM.
EVERY LOAD SHOULD REACH THE GROUND
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
OMA. Shenzhen Stock Exchange 2013
DEPENDING ON THE MOVEMENTS OR ROTATION RESTRICTIONS WE CLASSIFY THE SUPPORTS:
1.- STRUCTURAL MODELS
a. Types of supports and connections
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
ROLLER
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
PINNED SUPPORT
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
FIXED SUPPORT
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
DEPENDING ON THE RELATIVE MOVEMENTS OR ROTATION RESTRICTIONS BETWEEN BARS,
WE CLASSIFY THE JOINTS:
1.- STRUCTURAL MODELS
a. Types of supports and connections
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
HINGES (PINNED JOINTS)
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
RIGID (or FIXED JOINTS)
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Type of connection?
Which one restrains relative rotation?
Which one restrains relative movement?
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Type of connection?
Does any of them allow movement or rotation?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Type of connection?
What happens with the bending moments and the end bar moments?
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
San Francisco Suspension Bridge
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
CAN YOU TELL THE DIFFERENCE
BETWEEN
A SUSPENSION BRIDGE AND
A CABLE-STAYED BRIDGE?
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Vigo cable-stayed Bridge
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Vigo cable-stayed Bridge
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Chicago John Hancock Tower 1970
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Chicago Lake Shore Drive Apartments.
Mies van der Rohe
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2016/2017 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
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
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Chicago John Hancock Tower 1970
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
Miralles-Tagliabue. Santa Caterina Market. Barcelona 1997 / 2005
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1.- STRUCTURAL MODELS
IT IS VERY IMPORTANT TO UNDERSTAND HOW
THE LOAD TRAVELS ALONG THE BUILDING
STRUCTURAL SYSTEM.
EVERY LOAD SHOULD REACH THE GROUND
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
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%.
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
2.- STABILITY AND DETERMINACY
A SYSTEM CAN BE CONSIDERED A STRUCTURE
ONLY IF IT IS IN STABLE EQUILIBRIUM
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
1.- STABILITY AND DETERMINACY
nº unknowns
nº equilibrium
equations
<
nº unknowns
nº equilibrium
equations
=
nº unknowns
nº equilibrium
equations
>
WATCH OUT! THIS CONDITION IS NOT ENOUGH!!!
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
STABILITY AND DETERMINACY?
CAN YOU FIND THE REACTION FORCES?
WHAT’S THE EFFECT OF THE CABLE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
3.- STATICALLY DETERMINATE TRUSSES:
definition
external equilibrium (reaction forces)
internal equilibrium (axial forces)
displacements (UNIT LOAD METHOD)
The truss in the figure is made up of steel members of 100 cm2 cross-sectional area.
Determine:
1. Sign and value of the AB member axial force, NAB (kN)
2. Sign and value of the BF member axial force, NBF (kN)
3. Sign and value of the horizontal displacement at point D, uD (mm)
4. If the truss height is reduced down to 2 m, determine sign and value of the
horizontal displacement at point D, uD (mm)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
Bridge School at Pinghe (China) designed by Li Xiaodong Atelier in 2009
STRUCTURAL ANALYSIS I
2017/2018 CLASS 1
STRUCTURAL ANALYSIS I
2016/2017 CLASS 1
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1. Is it statically determinate or not? EXTERNALLY // INTERNALLY
2. Reaction forces
3. Axial forces (THINK ABOUT THE ZERO AXIAL FORCE BARS)
4. Displacements
STRUCTURAL ANALYSIS I
2016/2017 CLASS 1
1. Is it statically determinate or not? EXTERNALLY // INTERNALLY
2. Reaction forces
3. Axial forces (THINK ABOUT THE ZERO AXIAL FORCE BARS)
4. Displacements
STRUCTURAL ANALYSIS I
2016/2017 CLASS 1
1. Is it statically determinate or not? EXTERNALLY // INTERNALLY
2. Reaction forces
3. Axial forces (THINK ABOUT THE ZERO AXIAL FORCE BARS)
4. Displacements
STRUCTURAL ANALYSIS I
2016/2017 CLASS 1
STRUCTURAL ANALYSIS I
CLASS 1
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)
STRUCTURAL ANALYSIS I
CLASS 1
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).

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