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Basis of Structural Design

Course 5

Structural action:

- Cable structures

- Multi-storey structures

Course notes are available for download athttp://www.ct.upt.ro/users/AurelStratan/

Cable structures

� Cables - good resistance in tension, but no strength in compression

� Tent:

– a cable structure consisting of a waterproofing membrane

supported by ropes or cables and posts

– cables must be maintained in tension by prestressing in order to

avoid large vibrations under wind forces and avoid collapse

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Cables: roof structures

� Cables in a cable-supported roof must be maintained in tension -easily achieved if the roof is saddle-shaped

� Example: hyperbolic paraboloid, with curvatures in opposite senses in directions at right angles

– cables hung in direction BD

– a second set of cables placed over

them, parallel to direction AC and put in

to tension

– cables from the second set press down

on those from the first one, putting them

into tension as well ⇒⇒⇒⇒ fully-tensioned network

Cables: roof structures

� One of the first doubly curved saddle-shaped cable supported roof was the Dorton Arena in Raleigh, North Carolina, built in 1952

� The building has dimensions of 92 m x 97 m

� The roof is suspended between two parabolic arches in reinforced concrete intercrossing each other, and supported by columns

� The cable network consists of 47 prestressed cables with diameter varying from 19 mm to 33 mm

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Suspension bridges

� Suspension bridges: the earliest method of crossing large gaps

� Early bridges realised from a walkway suspended from hanging ropes of vines

� To walk a lighter bridge of this type at a reasonable pace requires a particular gliding step, as the more normal walking step will induce travelling waves that can cause the traveller to pitch (uncomfortably) up and down or side-to-side.

Suspension bridges

� Suspension bridge realised following the simple design of early bridges:

– cables (catenaries)

– light deck

– hangers suspending the deck on catenaries

� Lack of stability in high winds

� Very flexible under concentrated loads, as the form of the cable will adapt to loading form

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Suspension bridges

� Capilano Suspension Bridge, Canada

Suspension bridges

� Improved behaviour under traffic and wind loads: stiffening trusses at the level of the deck, that distributes concentrated loads over greater lengths

� Alternatively: restrain vertical movement of the catenaries by inclined cables attached to the top of the towers or inclined struts below the deck

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Suspension bridges

� The Akashi-Kaikyo Bridge, Japan: 1991 m span

Suspension bridges

� Golden Gate Bridge, California, USA: 1280 m span

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Suspension bridges

� Brooklyn Bridge, USA (the largest from 1883 until 1903): 486 m span

Suspension bridges: famous collapse

� Tacoma Narrows Bridge, USA, collapsed on November 7, 1940 due to wind-induced vibrations. It had been open for traffic for a few months only before collapsing.

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Cable-stayed bridges

� A cable-stayed bridge consists of one or more piers, with cables supporting the bridge deck

� Basic idea: reduce the span of the beam (deck) several times compared to the clear span between the piers

� Steel cable-stayed bridges are regarded as the most economical bridge design for spans ranging between 200 and 400 m

� Shorter spans: truss or box girder bridges

� Larger spans: suspension bridges

Cable-stayed bridges

� Reducing the span of a beam greatly improves the maximum stress and deflection

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Cable-stayed bridges: examples

� Rio-Antirio bridge in Greece. Longest span: 560 m. Total length: 2,880 m.

Cable-stayed bridges: examples

� The Millau Viaduct, France. Longest span: 342 m. Total length: 2,460 m.

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Multi-storey buildings

� Why multi-storey buildings?

– large urban population

– expensive land

� Multi-storey buildings make more efficient use of land: higher the building (more storeys) - larger the ratio of the building floor area to the used land area

� Technological competition (very high buildings)

� Until the end of the 18th century most buildings of several storeys in the Western world were made of:

– continuous walls of brick or stone masonry supporting the roof

– floors from timber beams

� The same structural system used in the Roman city of Herculaneum

Multi-storey buildings: beginnings

� Beginning of the 19th century - forefront of the industrial revolution in England:

– demand for large factory buildings of several storeys and large

clear floor areas

– cast iron available in bulk

– cast iron columns used instead of bearing walls and cast iron

beams instead of timber floor joists

� Elevator invented in USA in 1870, enabling much taller office and apartment buildings to be constructed

� Most multi-storey buildings in USA were still making use of masonry walls instead of columns

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Multi-storey buildings: masonry

� Monadnock building in Chicago

� Built between 1889 and 1891

� 16 storeys, 60 m high

� Tallest masonry building until today

� Walls at the ground floor: almost 1.80 m thick, occupying more than one-fifth of the width of the building

� Wall thickness: rule of thumb - 0.3m3 of exterior walls for each square meter of floor

Multi-storey buildings: skeleton frames

� Home Insurance Building

� Built in 1884 and demolished in 1931

� 10 storeys, 42 m high

� Considered to be the first skyscraper

� Exterior masonry walls

� Cast-iron columns

� Wrought-iron beams

� One of the first to make use of steel skeleton frame instead of masonry walls

⇒⇒⇒⇒ significant reduction of dead weight (1/3 of that of a masonry building)

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Multi-storey buildings: skeleton frames

� Steel skeleton frames

– loads carried by a steel frame composed of columns and beams

rigidly connected between them

– large clear spaces

Traditional load-bearing wall construction

� Outside load-bearing wall support:

– dead weight of the walls

and floors above

– live loads on the floors

– horizontal forces due to

wind pressure

� Columns support gravity loads only

� To avoid tension on the brick walls, the resultant force must lie in the middle third of the

thickness of the wall ⇒⇒⇒⇒very thick walls in the lower storeys

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Load-bearing wall construction

� In modern load-bearing wall construction, lateral forces due to wind are resisted by walls aligned in the direction of the wind

� Such walls are much more effective, because they have a much larger moment resistance

� Transverse walls acts as vertical cantilevers against lateral forces

� In modern construction,load-bearing walls are from reinforcedconcrete

Multi-storey buildings: gravity and lateral loads

� The load-bearing walls must be in the same position in plan to act as a vertical cantilever

� In order to provide clear floor spaces, doors, corridors, lift wells and staircases

� Most buildings realised as a combination of:

– load-bearing walls resisting lateral forces

– frames resisting gravity loads

load-bearing walls

or braced framesload-bearing walls

or braced frames

frames resisting

vertical loads only

frames resisting

vertical loads only

load-bearing walls

for lateral loads

frames resisting

vertical loads only

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Multi-storey buildings: gravity and lateral loads

� Lateral forces on external cladding are transmitted to the bearing walls

– directly, through external cladding

– indirectly, via floors

� Floors must be stiff and strong in their plane in order to allow lateral forces acting on gravity frames to be transmitted to load-bearing walls

� Usually floors are realised from cast in place reinforced concrete to give a monolithic slab over full plan of the building

F F

stiff floor flexible floor

Multi-storey buildings: types of structures

� As the height of the building increases, the more important are wind and earthquake loads in comparison with gravity loading

– In a multi-storey building, acting as a vertical cantilever, bending

stresses at the base increase with the square of its height

– Wind loading increases with the height

– Earthquake loading increases with building weight

� Reinforced concrete structures:

– reinforced concrete frames

– load-bearing walls

� Steel structures:

– moment-resisting frames

– braced frames

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Multi-storey buildings: types of steel structures

� Moment-resisting frames resist lateral loads through flexural strength of members

– clear spaces, but

– large deformations of the structure

– large stresses due to bending

� Braced frames resist lateral loads through direct (axial) stresses in the triangulated system

– obstruction of clear spaces, but

– small deformations (rigid structure)

– smaller stresses due to more efficient

structural behaviour

Multi-storey buildings: braced steel frames

� Concentrically braced frames with diagonal bracing

� Concentrically V-braced frames

� Eccentrically braced frames

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Multi-storey buildings: steel structural systems

Multi-storey buildings: steel structural systems

� Braced frame efficient in reducing lateral deformations at the lower storeys, but becomes inefficient at upper storeys due to overall cantilever-like effect

� Moment-resisting frame: uniform "shear-like" deformations

� Combined moment-resisting frame and braced frame: more rigid overall behaviour due to interaction between the two systems

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Multi-storey buildings: steel structural systems

� Braced frame with central braced span:

– inner columns: large axial stresses due to truss action

– outer columns: small axial stresses

� Outrigger truss: outer columns are "involved" into the truss-like action (axial stresses) through the outrigger truss

Multi-storey buildings: steel structural systems

� Exterior framed tube: closely spaced columns at the exterior of the building, rigidly connected to deep beams

� Acting like a giant rectangular steel hollow section

� Shear-lag effect - non-uniform stresses on web and flanges: middle sections are not very stressed

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Multi-storey buildings: steel structural systems

� Exterior framed tube: World Trade Center, New-York

Multi-storey buildings: steel structural systems

� Exterior framed tube: World Trade Center, New-York

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Multi-storey buildings: steel structural systems

� Exterior framed tube: World Trade Center, New-York

Multi-storey buildings: steel structural systems

� Bundled framed tube: combination of multiple tubes to reduce the shear lag effect

� Sears Tower, Chicago

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Multi-storey buildings: steel structural systems

� Exterior diagonal tube: giant truss-like behaviour

Multi-storey buildings: steel structural systems

� Exterior diagonal tube: John Hancock Center, Chicago