ACHITECTURAL STRUCTURES: S ANALYSIS AND SYSTEMS ARCH...

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Lecture 6

Applied Architectural Structures

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six

cables &

arches

lecture

Millennium Bridge in Newcastle, UK

APPLIED ACHITECTURAL STRUCTURES:

STRUCTURAL ANALYSIS AND SYSTEMS

ARCH 631

DR. ANNE NICHOLS

FALL 2016

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Lecture 6

Applied Architectural Structures

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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

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Applied Architectural Structures

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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

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Applied Architectural Structures

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Cables

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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

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Applied Architectural Structures

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Cable Loads

• straight line

between forces

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Cable Loads

• shape directly

related to the

distributed load

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• trig:

• parabolic (catenary)

– distributed uniform load

Tx= Tcos

Ty= Tsin

y = 4h(Lx – x2) / L2

𝐿𝑡𝑜𝑡𝑎𝑙 = 𝐿(1 + 3 8 ℎ2𝐿2 − 32

5 ℎ4𝐿4)

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Cable Loads

hy

x L

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Cables & Tension Elements

• typical cross sections

Multi-wire strand

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Applied Architectural StructuresARCH 631

Cable Structures

• categories

– single drape

– double

• different curvature

• same plane or

different

• cases

– Brooklyn Bridge

– Dulles Terminal

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Brooklyn Bridge, Roebling 1883

http:// nisee.berkeley.edu/godden

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Brooklyn Bridge, Roebling 1883

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Dulles Terminal, Saarinen 1962

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Dulles Terminal, Saarinen 1962

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Cable-Stayed Structures

• diagonal cables support horizontal

spans

• typically symmetrical

• cases

– Patcenter

– Alamillo

Bridge

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Patcenter, Rogers 1986

www.columnbia.edu

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Patcenter, Rogers 1986

www.columnbia.edu

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Patcenter, Rogers 1986

• dashes – cables pulling

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Alamillo Bridge, Calatrava 1992

http://en.structurae.de

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Alamillo Bridge, Calatrava 1992

• concrete “mast”

• parallel cable stays

• steel box beam spine in deck

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Free Ride Home – Kenneth Snelson

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Tensegrities

• 3D frame

• discontinuous struts

• continuous cables

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Olympic Gymnastics Stadium

• Geiger 1988

www.columnbia.edu

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Olympic Gymnastics Stadium

• Geiger 1988

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Florida Suncoast Dome, HOK 1989

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Florida Suncoast Dome, HOK 1989

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Georgia Dome, Stainback 1992

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Georgia Dome, Stainback 1992

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Arches

• curvilinear form

– efficient in compression

– minimal bending stress

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Arches

• ancient

– stone

– masonry

www.greatbuildings.com

Rainbow Bridge National Monument

Lions Gate

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Arches

• ancient

– stone

– masonry

Packhorse Bridge, UK

Roman Aquaducts

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Arches• terminology

– arch axis

– crown

– rise

– extrados

– intrados

– depth

– spring line

– span

– skewback

– soffit

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Arches

• behavior

– stabilization

– resist thrust

• materials

– stone

– masonry

– concrete

– laminated wood

– steel

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Arches

• behavior

– thrust related

to height to width

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Arches

• common forms

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Arches

• common variations

– two hinged

– three hinged – statically determinate

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Arches

• requires lateral bracing

– lateral ties

– diagonal ties

http:// nisee.berkeley.edu/godden

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Arches

• ... bracing

– lamellas

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Vaults

http:// nisee.berkeley.edu/godden

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Vaults

• Crypt of the Colonia Güell - Gaudi

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Domes

• arch of revolutionary design

• resists

compressive

forces

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Domes

• materials & forms

– concrete

– masonry

– steelPantheon

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Domes

• materials & forms

– concrete

– masonry

– steel

Union Station Rotunda, Pittsburg

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Domes

• stresses and displacements © Harvard GSD

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Domes

• Palazzetto dello Sport -Nervi