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F2016abnCables & Arches 1
Lecture 6
Applied Architectural Structures
ARCH 631
six
cables &
arches
lecture
Millennium Bridge in Newcastle, UK
APPLIED ACHITECTURAL STRUCTURES:
STRUCTURAL ANALYSIS AND SYSTEMS
ARCH 631
DR. ANNE NICHOLS
FALL 2016
F2016abnCables & Arches 2
Lecture 6
Applied Architectural Structures
ARCH 631
Cables
• simple
• uses
– suspension bridges
– roof structures
– transmission lines
– guy wires, etc.
• have same tension all along
• can’t stand compression – struts do
http:// nisee.berkeley.edu/godden
F2016abnCables & Arches 3
Lecture 6
Applied Architectural Structures
ARCH 631
Cables
• use high-strength steel
• need
– towers
– anchors
– stiffeners (hangers)
• have spans & sag
• don’t want movement
– dynamic effects of wind
– resonance http:// nisee.berkeley.edu/godden
F2016abnCables & Arches 4
Lecture 6
Applied Architectural Structures
ARCH 631
Cables
F2016abnCables & Arches 5
Lecture 6
Applied Architectural Structures
ARCH 631
Cables
• equilibrium:
– not enough to solve, we have slopes
– X component the same everywhere
A
C
45 kN
4 m
2 m
B 6 m
45 kN
F2016abnCables & Arches 6
Lecture 6
Applied Architectural Structures
ARCH 631
Cable Loads
• straight line
between forces
F2016abnCables & Arches 7
Lecture 6
Applied Architectural Structures
ARCH 631
Cable Loads
• shape directly
related to the
distributed load
F2016abn
• trig:
• parabolic (catenary)
– distributed uniform load
Tx= Tcos
Ty= Tsin
y = 4h(Lx – x2) / L2
𝐿𝑡𝑜𝑡𝑎𝑙 = 𝐿(1 + 3 8 ℎ2𝐿2 − 32
5 ℎ4𝐿4)
Cables & Arches 8
Lecture 6
Applied Architectural Structures
ARCH 631
Cable Loads
hy
x L
F2016abnCables & Arches 9
Lecture 6
Applied Architectural Structures
ARCH 631
Cables & Tension Elements
• typical cross sections
Multi-wire strand
F2016abnCables & Arches 10Lecture 6
Applied Architectural StructuresARCH 631
Cable Structures
• categories
– single drape
– double
• different curvature
• same plane or
different
• cases
– Brooklyn Bridge
– Dulles Terminal
F2016abnCables & Arches 11
Lecture 6
Applied Architectural Structures
ARCH 631
Brooklyn Bridge, Roebling 1883
http:// nisee.berkeley.edu/godden
F2016abnCables & Arches 12
Lecture 6
Applied Architectural Structures
ARCH 631
Brooklyn Bridge, Roebling 1883
F2016abnCables & Arches 13
Lecture 6
Applied Architectural Structures
ARCH 631
Dulles Terminal, Saarinen 1962
F2016abnCables & Arches 14
Lecture 6
Applied Architectural Structures
ARCH 631
Dulles Terminal, Saarinen 1962
F2016abnCables & Arches 15
Lecture 6
Applied Architectural Structures
ARCH 631
Cable-Stayed Structures
• diagonal cables support horizontal
spans
• typically symmetrical
• cases
– Patcenter
– Alamillo
Bridge
F2016abnCables & Arches 16
Lecture 6
Applied Architectural Structures
ARCH 631
Patcenter, Rogers 1986
www.columnbia.edu
F2016abnCables & Arches 17
Lecture 6
Applied Architectural Structures
ARCH 631
Patcenter, Rogers 1986
www.columnbia.edu
F2016abnCables & Arches 18
Lecture 6
Applied Architectural Structures
ARCH 631
Patcenter, Rogers 1986
• dashes – cables pulling
F2016abnCables & Arches 19
Lecture 6
Applied Architectural Structures
ARCH 631
Alamillo Bridge, Calatrava 1992
http://en.structurae.de
F2016abnCables & Arches 20
Lecture 6
Applied Architectural Structures
ARCH 631
Alamillo Bridge, Calatrava 1992
• concrete “mast”
• parallel cable stays
• steel box beam spine in deck
F2016abn
Free Ride Home – Kenneth Snelson
Cables & Arches 21
Lecture 6
Applied Architectural Structures
ARCH 631
Tensegrities
• 3D frame
• discontinuous struts
• continuous cables
F2016abnCables & Arches 22
Lecture 6
Applied Architectural Structures
ARCH 631
Olympic Gymnastics Stadium
• Geiger 1988
www.columnbia.edu
F2016abnCables & Arches 23
Lecture 6
Applied Architectural Structures
ARCH 631
Olympic Gymnastics Stadium
• Geiger 1988
F2016abnCables & Arches 24
Lecture 6
Applied Architectural Structures
ARCH 631
Florida Suncoast Dome, HOK 1989
F2016abnCables & Arches 25
Lecture 6
Applied Architectural Structures
ARCH 631
Florida Suncoast Dome, HOK 1989
F2016abnCables & Arches 26
Lecture 6
Applied Architectural Structures
ARCH 631
Georgia Dome, Stainback 1992
F2016abnCables & Arches 27
Lecture 6
Applied Architectural Structures
ARCH 631
Georgia Dome, Stainback 1992
F2016abnCables & Arches 28
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• curvilinear form
– efficient in compression
– minimal bending stress
F2016abnCables & Arches 29
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• ancient
– stone
– masonry
www.greatbuildings.com
Rainbow Bridge National Monument
Lions Gate
F2016abnCables & Arches 30
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• ancient
– stone
– masonry
Packhorse Bridge, UK
Roman Aquaducts
F2016abnCables & Arches 31
Lecture 6
Applied Architectural Structures
ARCH 631
Arches• terminology
– arch axis
– crown
– rise
– extrados
– intrados
– depth
– spring line
– span
– skewback
– soffit
F2016abnCables & Arches 32
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• behavior
– stabilization
– resist thrust
• materials
– stone
– masonry
– concrete
– laminated wood
– steel
F2016abnCables & Arches 33
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• behavior
– thrust related
to height to width
F2016abnCables & Arches 34
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• common forms
F2016abnCables & Arches 35Lecture 6
Applied Architectural StructuresARCH 631
Arches
• common variations
– two hinged
– three hinged – statically determinate
F2016abnCables & Arches 36
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• requires lateral bracing
– lateral ties
– diagonal ties
http:// nisee.berkeley.edu/godden
F2016abnCables & Arches 37
Lecture 6
Applied Architectural Structures
ARCH 631
Arches
• ... bracing
– lamellas
F2016abnCables & Arches 38
Lecture 6
Applied Architectural Structures
ARCH 631
Vaults
http:// nisee.berkeley.edu/godden
F2016abnCables & Arches 39
Lecture 6
Applied Architectural Structures
ARCH 631
Vaults
• Crypt of the Colonia Güell - Gaudi
F2016abnCables & Arches 40
Lecture 6
Applied Architectural Structures
ARCH 631
Domes
• arch of revolutionary design
• resists
compressive
forces
F2016abnCables & Arches 41
Lecture 6
Applied Architectural Structures
ARCH 631
Domes
• materials & forms
– concrete
– masonry
– steelPantheon
F2016abnCables & Arches 42
Lecture 6
Applied Architectural Structures
ARCH 631
Domes
• materials & forms
– concrete
– masonry
– steel
Union Station Rotunda, Pittsburg
F2016abnCables & Arches 43
Lecture 6
Applied Architectural Structures
ARCH 631
Domes
• stresses and displacements © Harvard GSD
F2016abnCables & Arches 44
Lecture 6
Applied Architectural Structures
ARCH 631
Domes
• Palazzetto dello Sport -Nervi