Dina Abdul-Malak Word Count: ~2885 260638963ARCH 241Dec. 11, 2014

Structural analysis of three bridges

Bridges have been, for a long time, an essential part in humans’ life. They exist in many types and serve to connect two pieces of land as well as to allow several types of traffic to exist. Despite their omnipresence, the construction of a bridge takes a lot of time, as its location, its materials, the loads it should bear and the kind of traffic it should hold all affect its structural aspects. In the following structural analysis, three bridges are examined. The first type is a suspension bridge, the Golden Gate Bridge. A suspension bridge is one in which “the weight of the deck is supported by vertical cables suspended from further cables that run between towers and are anchored in abutments at each end1.” The second type is a through arch bridge, the Sydney Harbor Bridge. A through arch bridge is “a bridge made from materials such as steel or reinforced concrete in which the base of an arch structure is below the deck, but the top rises above it, so the deck passes through the arch2”. In other words, the deck does not sit atop the arch, but rather the deck goes through it. The third type is a cantilever bridge, the Firth of Forth Bridge. A cantilever bridge is a bridge “ in which each span is constructed from cantilevers built out sideways from piers3.”

The Golden Gate Bridge

The Golden Gate Bridge is a suspension bridge designed by Joseph Strauss, Irving Morrow and Charles Ellis that connects the San Francisco Bay to the Pacific Ocean; a channel called the Golden Gate strait. The bridge’s construction started in 1933 and was completed in 1937 when it opened to vehicular traffic4. It was considered to be the longest suspension bridge until 1964, with a span of 1 280.2 meters. Its total length is of 2 737.4 meters, its height of 227.4 meters, and its width of 27.4 meters5. Aside from having a vehicular lane, the Golden Gate Bridge includes a pedestrian walkway on the eastern edge and bike paths on either sides of the bridge6. Its location on the foot of the ocean, its renowned orange towers and its large cables make the bridge both a touristic attraction and an important roadway for daily passengers.

The Golden Gate Bridge’s dead load is 31 698 kilograms per linear meter. That includes the weight of the cables, suspender and accessories (9 926 kg/m), the stiffening trusses (4 956 kg/m), the floor system, curbs and railings (5 700 kg/m), the bracing (893 kg/m), the concrete

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paving (9628 kg/m), and the conduits (595 kg/m)7. Any added live load is from the traffic present on the bridge. As for the wind load, the design of the bridge took into account wind pressures of 45 kg/m on the cables and suspended structures, and 74 kg/m on the towers8.

For such a suspension bridge to maintain static equilibrium, the design of the structure is made such that the weight of the bridge deck and moving bodies on the bridge is transferred to the two main suspension cables through the suspender rods which are represented in the figure aside9. In turn, the suspension cable transfers the force to the two towers and the anchor blocks. This leads the main suspension cable to be subject to tension produced by the forces in the suspender rods, and these tension forces on both sides of the main cable pull against each other horizontally all the while pushing down on the tower as well10. The latter, in result, is subject to a compressive force that tends to shorten it and is designed to counteract such a force without crushing or buckling.

All of the horizontal and vertical forces at play in the Golden Gate Bridge must be cancelled out so that the bridge keeps its position and shape. Concerning the horizontal forces, these include the tension forces between the two towers, the tension forces between the anchor blocks and the towers, and the friction forces on the anchor blocks due to the soil and rock11. When the tension forces in the main cable pull on the tower from both sides, they do it horizontally in opposite directions. That way, they cancel some of the total force, whereas the rest of it is transferred down the tower as mentioned earlier. On the edge of the bridge, the tension is directed to the anchor block and to the ground; and it is cancelled by the gravitational force and the frictional force10. Concerning the vertical forces, they include the downward forces exerted on the towers by the cables, the upward force by the towers to resist the compressive forces discussed earlier, the weight of the deck and the traffic, and the tension in the suspender cables7. The weight of the deck and the traffic is directed to the main suspension cables through the suspender rods such that the weight of the deck and the traffic is equal to the tension in suspenders10. Then, for the towers –which are the main support for the bridge- to not bend, they must exert a force upwards to counteract the compressive force resulting from the main cables pushing down on the towers10.

Friction force on anchor.

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Compressive forces Tensile forces The reason behind the Golden Gate Bridge’s strength and durability lies in the use of material when it comes to the three main parts: the two towers, the cables (both the suspension/main and the suspender cables) and the anchor blocks. In fact, for the towers to bear compressive forces, they have to be extremely solid and stable at the base. Thus, the latter for each tower

was made out of concrete9. However, one of them had to be built in the ocean instead of beside the shore, so the base of that tower was put 30 meters below the water surface where they made a huge box from which they pumped the water out to construct a solid concrete base9. The material chosen for the base is essential since the sturdier the base is, the more force it can hold –and the more traffic load it can bear.

As for the cables, they had to be made strong enough to have the deck, which weighs around 150 000 tonnes7, hang safely. This took 90 cm thick cables made up of small steel wires twisted and bundled up over and over, resulting in 130 000 km of wire9. The thicker the cables, the more tension they can bear, the heavier the mass on the deck can be permitted.

Finally, the two anchor blocks at each end are made of reinforced concrete connected to an underlying rock9. Inside the anchorage, the stranded suspension cable is undone and splayed out for a more solid and direct connection with the concrete9. The heavier the anchor block, the more tension it can hold, thus, more weight can be on the deck.

In addition to those, the Golden Gate suspension bridge also has a supporting deck truss beneath the deck that stiffens the latter and limit the roadway’s tendency to sway11.

The Sydney Harbor Bridge

The Sydney Harbor Bridge is one of Australia’s most renowned

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landmarks, whose general designer and chief engineer was Dr. J.J.C Bradfield12. It is a steel through arch bridge above the Sydney Harbour connecting the Sydney central business district and the North Shore13. The Sydney Harbour Bridge has eight road lanes, two rail tracks, one pedestrian way and one cycleway13. Its length is of 1149 meters, its width of 49 meters and it is the world’s largest steel arch bridge with its top at 134 meters above the harbor; it is also nicknamed the “The Coathanger” because of its arch-based appearance14.

The bridge’s construction started in 1924 and it was officially opened in 19329. Since all of the bridge’s plates were riveted, it took six million hand driven rivets and 53 000 tonnes of steel to build the whole structure15. It is a two-hinged arch bridge built with two half arches that are connected with horizontal cross-members. To join the two half arches into one, these two were fastened with wire ropes which, in turn, were fixed in U-shaped tunnels put into the earth 16. After the arch stood completed, these temporary wire rope anchorages were removed whereas creeper cranes moved outward and put down the arch16.

Since it is an arch bridge, the vertical loads on it -which consist of the bridge’s weight as well as that of the bodies passing on it- have the tendency to push against the abutments and flatten the arch17; an abutment being a “substructure at the end of a bridge span whereon the bridge's superstructure rests. [...] it provides vertical and lateral support for the bridge, as well as acts as retaining walls to resist lateral movement of the earthen [ground of the bridge’s lane]18”. In result, as drawn in the figure, vertical (RVA and RVB) and horizontal (RHA and RHB) reaction forces are created at the abutments17.

Furthermore, to allow the arch to move due to changes in temperatures and due to dynamic loads, the Sydney Harbour Bridge has one horizontal, cylindrical forged steel pin as support in the main bearings at each end of the two arches17. The latter are hinges that allow the arch to rotate to adjust for expansion caused by heat or contraction cause by cold, a change in dimension that could go up to 180 millimeters19. These hinges are also to avoid stresses which would have the tendency to damage the bridge12. In fact, these metal hinges of a diameter of 468 mm hold the huge horizontal thrust of 20 000 tonnes coming from the arch21.

One of the nuts holding the arch at its abutments.

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The Sydney Harbour Bridge’s arch is made of 28 stiffening truss panels20 varying from 18 meters each at the centre to 54 meters at the ends, made out of high tensile

steel21. In fact, the truss built in this bridge is a Warren Truss made of angled cross-members that connect the longitudinal members. In result, equilateral

triangle-shaped spaces are formed along the length of the arch that allow no bending or torsional forces on the struts and beams of the arch, only tension and compression such that the live and dead loads –that includes all vertical and horizontal forces at play- are transmitted to the abutments which, in turn, transmit it to the ground17. This type of arch is both light and strong. As for wind resistance, a system of transverse bracing in the plane of the lower chords and another between the upper chords and the end posts were used21.

The bridge’s deck is composed of cross girders suspended from the hangers (that are suspended from the arch), of longitudinal beams between the cross girders and of a steel sheet that holds the deck that’s made of concrete21. All the cross girders are supported by the hangers so that the load on the latter is axial21.

At each end of the arch, there are two 89 meters high concrete pylons19. The latter were not originally part of the design, they were put in because of a public concern as to the bridge’s structural integrity. Thus, they were later added as a frame for the arch’s panels and for visual

One of the nuts holding the arch at its abutments.

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balance19. Although the pylons themselves have no structural purpose, they have abutments at their base that holds the arch’s span in place and resist the loads from the arch20.

The Forth Bridge

The Forth Bridge is a cantilever truss type of bridge that crosses over the Firth of Forth River in Scotland’s east, and it was designed by Sir John Fowler and Sir Benjamin Baker22. Its construction started in 1882 and it was open for traffic in 1890 23. It carries only a railway traffic and has a total length of 2 528.7 meters; its longest span (520 meters) makes it the second longest single cantilever bridge23.

The figure shows that two suspended spans of 105 meters each connect the outer cantilever towers to the central one24. This central section of the Forth Bridge is composed of three piers, out of each two cantilevered arms are constructed. As seen in the figure, two lattice girders of 51 meters each that are carried by masonry piers 40 meters above water level make up the two viaducts connecting the central part of the bridge24. There are six cantilever arms, two out of which are fixed by the two granite abutments at the edge of each viaduct and four are free cantilevers.

The bridge’s structure that receives the live load functions as a truss: some of its members are subject to tension at all times, and some are under compression. In fact, the behavior of the Forth Bridge can be compared to a living model25. The figure shows two man with outstretched arms who are sitting on chairs -they are the main cantilever towers that are anchored by bricks at the sides- and a central span that connects both. Although the Forth Bridge has three cantilever towers not two, the principle is the same: considering the third man is put as a load acting on the central span, the two sitting men’s arms become subject to tension whereas their bodies and the sticks they are holding become subject to compression25.

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Each cantilever tower’s base rests on four separate masonry piers built underneath the river. The cantilevers are composed of two top members that are always in tension and two bottom members that are always in compression26. These members are connected vertically with cross bracing, and the bottom members are also braced together, but horizontally. Each arm of a cantilever is divided into bays because of the cross bracing of the top and bottom members, and each bay is composed of a tension member connecting the bottom to the top layer, and a compression member preventing the buckling of the bottom cantilever member24. All cantilevers are of the same length for the bridge to naturally balance itself under its own weight during its construction24. The piles of bricks in the living model represent the cantilever abutments built out of granite blocks25. They are between the cantilevers at the centre and each of the viaduct that anchor the outer cantilevers in place24.

Steel was relatively a new material in construction at the time the bridge was built, so its behavior was unexpected. However, the material was still used in its most efficient shape under compression –that is, in tubes- which diminishes buckling of surface and stress leading to member failures24. Concerning the tension members, they are all open lattice girders24. The latter are light but strong members that make best use of steel’s characteristics under tension.

The suspended spans between the three cantilever towers behave as trusses which, when subject to loading, have the top member in compression and bottom member in tension. The members’ form is tubular24.

Each of the viaducts leading up to the central cantilever of the Forth Bridge is composed of two lattice truss girders24. A vertical strut is placed at the intersection of the cross bracing and the top member of the truss. It allows the deflection of the top member to be reduced when it is under loading; it also stiffens the viaduct24. In fact, the use of cross bracing prevents buckling. Further, since the material used is steel, to account for expansion due to heat and contraction due to cold weather, expansion joints were added at the viaducts and below the deck at the towers27. This allows movement of the structure caused by weather, traffic and wind speed.

Concerning wind forces, the bridge’s design is made such that at the end of the cantilever arms –where the wind has a dangerous effect- the surface area uncovered is minimum. However,

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where the wind pressure has a less dangerous consequence –that is, directly over the support- the bridge is tall and large24.

The choice of the type of bridge to build is not an easy one, as each location has specific criteria to which the bridge has to respond. Suspension bridges are a great choice for a long distance to span, since it is the only type that can span a distance of 609 meters to 2134 meters 26. They are light but complex to build. Furthermore, suspension bridges are flexible, but are very unstable during strong earthquakes or weather conditions27. Under maximum weight loads, the structure also becomes unstable. The arch bridge, on the other hand, has limited spans (unless it is made out of several arches)26 and can only be built where the ground is very solid and stable since its abutments transfer all horizontal and vertical forces from the deck to the ground28. It is also complex to build since the arches need falsework to join parts of the arch. Cantilever bridges are very rigid because of the depth of the cantilever arms; they can hold heavy railways 29. They are also easy to sustain under thermal expansion and ground movement30. However, they are heavy structures, which is why trusses are used in their construction30.

In conclusion, although bridges are omnipresent everywhere in the world and always seem suitable, their construction resulted from several background studies as to the type of bridge to use; the type of distance to span, the type of traffic that will go over it, as well as the materials and location must be considered.

Not always!

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References* The pictures chosen and represented are taken from the same sources as listed below.

1 "Suspension Bridge." Oxford Dictionary (British & World English). N.p., n.d. Web. 5 Dec. 2014. <http://www.oxforddictionaries.com/definition/english/suspension-bridge>

2 "Through Arch Bridge." Wikipedia. Wikimedia Foundation, 12 Feb. 2014. Web. 5 Dec. 2014. <http://en.wikipedia.org/wiki/through_arch_bridge>

3 "Cantilever Bridge." Oxford Dictionary (British & World English). N.p., n.d. Web. 5 Dec. 2014. <http://www.oxforddictionaries.com/definition/english/cantilever-bridge?q=cantilever+bridge>

4 "Golden Gate Bridge." Wikipedia. Wikimedia Foundation, 12 Nov. 2014. Web. 5 Dec. 2014. <http://en.wikipedia.org/wiki/Golden_Gate_Bridge>

5 "Golden Gate Bridge, San Francisco, California." Maps of the World. N.p., n.d. Web. 22 Nov. 2014. <http://www.mapsofworld.com/san-francisco/attractions/golden-gate-bridge>

6 ”Golden Gate”. Infoplease, n.d. Web. 22 Nov. 2014. <http://www.infoplease.com/spot/goldengate.html>

7 ”Golden Gate Bridge Moveable Median Study.” AECOM. 12 Nov. 2010. Web. 22 Nov. 2014. <http://goldengate.org/board/2013/agendas/documents/BO09.19.13s3b_StructAnalRpt.pdf>

8 "The Golden Gate Bridge." Redshift. N.p., n.d. Web. 22 Nov. 2014. <http://www.redshift.com/~isle/mc/venus.htm>

9 "How Did the Golden Gate Bridge Come to Be an Engineering Classic?" Suspension Bridge. N.p., n.d. Web. 22 Nov. 2014.

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10 Baron Wolman, Horton Tom. Superspan: The Golden Gate Bridge. Review by: David A. Simmons. IA. The Journal of the Society for Industrial Archeology, Vol. 12, No. 1 (1986), p. 74 . N.p. Print. 22 Nov. 2014

11 Lamb, Robert, and Michael Morrissey. “How Bridges Work: The Suspension Bridge.” How Stuff Works, n.d. Web. 22 Nov. 2014. <http://science.howstuffworks.com/engineering/civil/bridge6.htm>

12 "Sydney Harbour Bridge." Structurae. N.p., n.d. Web. 28 Nov. 2014. <http://structurae.net/structures/sydney-harbour-bridge>

13 “Sydney Harbor Bridge." Wikipedia. Wikimedia Foundation, 11 Apr. 2012. Web. 28 Nov. 2014. <http://en.wikipedia.org/wiki/Sydney_Harbour_Bridge>

14 "Sydney Harbour Bridge." Australia. N.p., n.d. Web. 28 Nov. 2014. <http://www.australia.gov.au/about-australia/australian-story/sydney-harbour-bridge>

15 "20 Facts About The Sydney Harbour Bridge." BuzzFeed. N.p., n.d. Web. 28 Nov. 2014. <http://www.buzzfeed.com/bradesposito/facts-about-the-sydney-harbour-bridge>

16 ”The Sydney Harbour Bridge.” Australian Academy of Technological Sciences and Engineering. Australian Science and Technology Heritage Centre. 1988. Web. 28 Nov. 2014. <http://www.austehc.unimelb.edu.au/tia/426.html>

17 "Sydney Harbour Bridge" Bridge Supports. N.p., n.d. Web. 28 Nov. 2014. <http://sydney-harbour-bridge.bos.nsw.edu.au/engineering-studies/bridge-supports.php>

18 “Abutment." Wikipedia. Wikimedia Foundation, 1 Nov. 2013. Web. 28 Nov. 2014. <http://en.wikipedia.org/wiki/Abutment>

19 "Sydney Harbour Bridge." OpenBuildings. N.p., n.d. Web. 28 Nov. 2014. <http://openbuildings.com/buildings/sydney-harbour-bridge-profile-10276?_show_description=1>

20 Engineering: Down Under. Petroski Henry. American Scientist, Vol. 87, No. 2 (March-April 1999), pp. 114-118.

21 "Forth Rail Bridge." Railway Technology. N.p., n.d. Web. 29 Nov. 2014. <http://www.railway-technology.com/projects/forth-rail-bridge-firth-scotland/>

22 “Firth of Forth Bridge." Wikipedia. Wikimedia Foundation, 12 Nov. 2014. Web. 29 Nov. 2014. <http://en.wikipedia.org/wiki/Forth_Bridge>

23 Magee, A.D. “A Critical Analysis of the Forth Bridge.” University of Bath. N.p. 21 April 2007. Web. 29 Nov. 2014. <http://www.bath.ac.uk/ace/uploads/StudentProjects/Bridgeconference2007/conference/mainpage/Magee_Forth_Bridge.pdf>

24 "Firth of Forth Cantile <ver Bridge." PBSLearning Media. N.p., n.d. Web. 29 Nov. 2014. <http://www.pbslearningmedia.org/resource/phy03.sci.phys.mfw.bbcantilever/firth-of-forth-cantilever-bridge/>

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25 "The Forth Rail Bridge." Engineering Timelines. N.p., n.d. Web. 29 Nov. 2014. <http://www.engineering-timelines.com/why/forthRailBridge/forthRailBridge_03.asp>

26 "What about the Weather?" Forth Bridges Forum. N.p., n.d. Web. 29 Dec. 2014. <http://www.forth-bridges.co.uk/forth-road-bridge/features-road.html>

27 "Bridges Type." Design and Technology Online. N.p., n.d. Web. 5 Dec. 2014. <http://www.dtonline.org/vle/mod/lesson/view.php?id=276>

28 "Advantages & Disadvantages of a Suspension Bridge." EHow. Demand Media, 10 Oct. 2009. Web. 5 Dec. 2014. <http://www.ehow.com/facts_5517162_advantages-disadvantages-suspension-bridge.html>

29 "Bridges 2005: Engineering." Minneapolis Riverfront District Engineering. N.p., n.d. Web. 5 Dec. 2014. <http://www.mrdbridges.com/engineering.php>

30 “Cantilever." Brantacan. N.p., n.d. Web. 5 Dec. 2014. <http://www.brantacan.co.uk/cantilever.htm>