Basis of Structural Design

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1 Basis of Structural Design Course 5 Structural action: - Cable structures - Multi-storey structures Course notes are available for download at 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 1

2 Cables: roof structures Cables in a cable-supported roof must be maintained in tension - easily achieved if the roof is saddleshaped 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 2

3 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 3

4 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 4

5 Suspension bridges The Akashi-Kaikyo Bridge, Japan: 1991 m span Suspension bridges Golden Gate Bridge, California, USA: 1280 m span 5

6 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. 6

7 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 Reducing the span of a beam greatly improves the maximum stress and deflection Cable-stayed bridges 7

8 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. 8

9 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 18 th 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 19 th 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 9

10 Multi-storey buildings: masonry Monadnock building in Chicago Built between 1889 and storeys, 60 m high Tallest masonry building until today Walls at the ground floor: almost 1.80 m thick, occupying more than onefifth of the width of the building Wall thickness: rule of thumb - 0.3m 3 of exterior walls for each square meter of floor Multi-storey buildings: skeleton frames Home Insurance Building Built in 1884 and demolished in 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) 10

11 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 11

12 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 reinforced concrete 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 frames resisting vertical loads only Most buildings realised as a combination of: load-bearing walls resisting lateral forces frames resisting gravity loads load-bearing walls or braced frames load-bearing walls for lateral loads load-bearing walls or braced frames frames resisting vertical loads only frames resisting vertical loads only 12

13 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 13

14 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 14

15 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 15

16 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 - nonuniform stresses on web and flanges: middle sections are not very stressed 16

17 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 17

18 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 18

19 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 19

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