Bridge design

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When designing a bridge to traverse an obstacle, several factors need to be considered: safety, strength, traffic, cost, the size and nature of the obstacle, maintenance, and aesthetics.[citation needed][1]

Analysis and engineering

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This highway overpass is being built over Interstate 5 in Burbank, California.

Unlike buildings whose design is led by architects, bridges are usually designed by engineers. This follows from the importance of the engineering requirements; namely spanning the obstacle and having the durability to survive, with minimal maintenance, in an aggressive outdoor environment.[2] Bridges are first analysed; the bending moment and shear force distributions are calculated due to the applied loads. For this, the finite element method is the most popular. The analysis can be one-, two-, or three-dimensional. For the majority of bridges, a two-dimensional plate model (often with stiffening beams) is sufficient or an upstand finite element model.[3] On completion of the analysis, the bridge is designed to resist the applied bending moments and shear forces, section sizes are selected with sufficient capacity to resist the stresses. Many bridges are made of prestressed concrete which has good durability properties, either by pre-tensioning of beams prior to installation or post-tensioning on site.

In most countries, bridges, like other structures, are designed according to Load and Resistance Factor Design (LRFD) principles. In simple terms, this means that the load is factored up by a factor greater than unity, while the resistance or capacity of the structure is factored down, by a factor less than unity. The effect of the factored load (stress, bending moment) should be less than the factored resistance to that effect. Both of these factors allow for uncertainty and are greater when the uncertainty is greater.

Traffic loading

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While the response of a bridge to the applied loading is well understood, the applied traffic loading itself is still the subject of research.[4] This is a statistical problem as loading is highly variable, particularly for road bridges. Load Effects in bridges (stresses, bending moments) are designed for using the principles of Load and Resistance Factor Design. Before factoring to allow for uncertainty, the load effect is generally considered to be the maximum characteristic value in a specified return period. Notably, in Europe, it is the maximum value expected in 1000 years.

Bridge standards generally include a load model, deemed to represent the characteristic maximum load to be expected in the return period. In the past, these load models were agreed by standard drafting committees of experts but today, this situation is changing. It is now possible to measure the components of bridge traffic load, to weigh trucks, using weigh-in-motion (WIM) technologies. With extensive WIM databases, it is possible to calculate the maximum expected load effect in the specified return period. This is an active area of research, addressing issues of opposing direction lanes,[5][6] side-by-side (same direction) lanes,[7][8] traffic growth,[9] permit/non-permit vehicles[10] and long-span bridges (see below). Rather than repeat this complex process every time a bridge is to be designed, standards authorities specify simplified notional load models, notably HL-93,[11][12] intended to give the same load effects as the characteristic maximum values. The Eurocode is an example of a standard for bridge traffic loading that was developed in this way.[13]

On long span bridges

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Traffic on Forth Road Bridge in Scotland prior to its opening to general traffic; traffic has now been moved to the Queensferry Crossing (on left)

Most bridge standards are only applicable for short and medium spans[14] - for example, the Eurocode is only applicable for loaded lengths up to 200 m. Longer spans are dealt with on a case-by-case basis. It is generally accepted that the intensity of load reduces as span increases because the probability of many trucks being closely spaced and extremely heavy reduces as the number of trucks involved increases. It is also generally assumed that short spans are governed by a small number of trucks traveling at high speed, with an allowance for dynamics. Longer spans on the other hand, are governed by congested traffic and no allowance for dynamics is needed.

Calculating the loading due to congested traffic remains a challenge as there is a paucity of data on inter-vehicle gaps, both within-lane and inter-lane, in congested conditions. Weigh-in-Motion (WIM) systems provide data on inter-vehicle gaps but only operate well in free flowing traffic conditions. Some authors have used cameras to measure gaps and vehicle lengths in jammed situations and have inferred weights from lengths using WIM data.[15] Others have used microsimulation to generate typical clusters of vehicles on the bridge.[16][17][18]

Vibration

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Bridges vibrate under load and this contributes, to a greater or lesser extent, to the stresses.[2] Vibration and dynamics are generally more significant for slender structures such as pedestrian bridges and long-span road or rail bridges. One of the most famous examples is the Tacoma Narrows Bridge that collapsed shortly after being constructed due to excessive vibration. More recently, the Millennium Bridge in London vibrated excessively under pedestrian loading and was closed and retrofitted with a system of dampers. For smaller bridges, dynamics is not catastrophic but can contribute an added amplification to the stresses due to static effects. For example, the Eurocode for bridge loading specifies amplifications of between 10% and 70%, depending on the span, the number of traffic lanes and the type of stress (bending moment or shear force).[19]

Vehicle–bridge dynamic interaction

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There have been many studies of the dynamic interaction between vehicles and bridges during vehicle crossing events. Fryba[20] did pioneering work on the interaction of a moving load and an Euler–Bernoulli beam. With increased computing power, vehicle-bridge interaction (VBI) models have become ever more sophisticated.[21][22][23][24] The concern is that one of the many natural frequencies associated with the vehicle will resonate with the bridge's first natural frequency.[25] The vehicle-related frequencies include body bounce and axle hop but there are also pseudo-frequencies associated with the vehicle's speed of crossing[26] and there are many frequencies associated with the surface profile.[4] Given the wide variety of heavy vehicles on road bridges, a statistical approach has been suggested, with VBI analyses carried out for many statically extreme loading events.[27]

Material

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The Iron Bridge in Shropshire, England, completed in 1781, the first cast iron bridge

The materials used to build the structure are also used to categorize bridges. Until the end of the 18th century, bridges were made out of timber, stone and masonry. Modern bridges are currently built in concrete, steel, fiber reinforced polymers (FRP), stainless steel or combinations of those materials. Living bridges have been constructed of live plants such as Ficus elastica tree roots in India[28] and wisteria vines in Japan.[29]

For small footbridges, the cantilevers may be simple beams; however, large cantilever bridges designed to handle road or rail traffic use trusses built from structural steel, or box girders built from prestressed concrete.[30]

Cable-stay bridges typically use cables made of steel cables galvanised with zinc,[citation needed] along with most of the bridge, but some bridges are still made with steel-reinforced concrete.

Arch bridges are sometimes made of stone, brick and other such materials that are strong in compression and somewhat so in shear.

Beam bridges can use pre-stressed concrete, an inexpensive building material, which is then embedded with rebar. The resulting bridge can resist both compression and tension forces.[31]

The triangular pieces of truss bridges are usually manufactured from straight and steel bars, according to the truss bridge designs.[32]

Aesthetics

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The Prins Clausbrug across the Amsterdam–Rhine Canal in Utrecht, Netherlands

Most bridges are utilitarian in appearance, but in some cases, the appearance of the bridge can have great importance.[33]

Bridges are typically more aesthetically pleasing if they are simple in shape, the deck is thinner in proportion to its span, the lines of the structure are continuous, and the shapes of the structural elements reflect the forces acting on them.[34] To create a beautiful image, some bridges are built much taller than necessary. This type, often found in east-Asian style gardens, is called a Moon bridge, evoking a rising full moon. Other garden bridges may cross only a dry bed of stream-washed pebbles, intended only to convey an impression of a stream. Often in palaces, a bridge will be built over an artificial waterway as symbolic of a passage to an important place or state of mind. A set of five bridges cross a sinuous waterway in an important courtyard of the Forbidden City in Beijing, China. The central bridge was reserved exclusively for the use of the Emperor and Empress, with their attendants.

Art Historian Dan Cruickshank writes that bridges are regarded as objects of beauty by many people:[35]

Bridge construction remains... the most absolute expression of the beauty and excitement invoked by man-made constructions.... Bridges that are leaps of faith and imagination.... They are an act of creation that challenge the gods, works that possess the very power of nature itself. They are objects in which beauty is the direct result of functional excellence, conceptual elegance and boldness of design and construction.... A great bridge – one that defies and tames nature — becomes almost in itself a supreme work of nature. Bridges embody the essence of mankind’s structural ingenuity ... with dramatic clarity.... The most thrilling bridges are, in many ways, those not enhanced by superficial or extraneous ornament or cultural references. What moves and impresses is their honest expression of the materials and means of construction — their only ornament is a direct result of the way in which they are built and perform. A great bridge has an emotional impact, it has a sublime quality and a heroic beauty that moves even those who are not accustomed to having their senses inflamed by the visual arts. ... All can see that bridges stand for something most significant, for the indomitable human spirit, the love of daring and of challenge, the power of invention.[35]

References

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Footnotes

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Citations

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  1. ^ Cruickshank 2010, p. 33.
  2. ^ a b O'Brien, Eugene J.; Keogh, Damien L.; O'Connor, Alan J. (6 October 2014). Bridge deck analysis (Second ed.). Boca Raton: CRC Press. ISBN 978-1-4822-2724-6. OCLC 892094185.
  3. ^ O'Brien, E.J; Keogh, D.L (December 1998). "Upstand finite element analysis of slab bridges". Computers & Structures. 69 (6): 671–683. doi:10.1016/S0045-7949(98)00148-5. hdl:10197/4054.
  4. ^ a b OBrien, Eugene J.; Keogh, Damien L.; O'Connor, Alan (2015). Bridge deck analysis. CRC Press. ISBN 978-1-4822-2723-9. OCLC 897489682.
  5. ^ Enright, Bernard; O'Brien, Eugene J. (December 2013). "Monte Carlo simulation of extreme traffic loading on short and medium span bridges". Structure and Infrastructure Engineering. 9 (12): 1267–1282. Bibcode:2013SIEng...9.1267E. doi:10.1080/15732479.2012.688753. hdl:10197/4868. ISSN 1573-2479. S2CID 10042252.
  6. ^ Caprani, Colin C.; OBrien, Eugene J. (March 2010). "The use of predictive likelihood to estimate the distribution of extreme bridge traffic load effect". Structural Safety. 32 (2): 138–144. doi:10.1016/j.strusafe.2009.09.001. hdl:10197/2329. S2CID 44049002.
  7. ^ OBrien, Eugene J.; Enright, Bernard (July 2011). "Modeling same-direction two-lane traffic for bridge loading". Structural Safety. 33 (4–5): 296–304. doi:10.1016/j.strusafe.2011.04.004. hdl:10197/3062. S2CID 53475878.
  8. ^ OBrien, Eugene J.; Leahy, Cathal; Enright, Bernard; Caprani, Colin C. (30 September 2016). "Validation of scenario modelling for bridge loading". The Baltic Journal of Road and Bridge Engineering. 11 (3): 233–241. doi:10.3846/bjrbe.2016.27. hdl:10197/9252. ISSN 1822-427X.
  9. ^ OBrien, E.J.; Bordallo-Ruiz, A.; Enright, B. (September 2014). "Lifetime maximum load effects on short-span bridges subject to growing traffic volumes". Structural Safety. 50: 113–122. doi:10.1016/j.strusafe.2014.05.005. hdl:10197/7069. S2CID 59945573.
  10. ^ Enright, Bernard; OBrien, Eugene J.; Leahy, Cathal (December 2016). "Identifying and modelling permit trucks for bridge loading". Proceedings of the Institution of Civil Engineers - Bridge Engineering. 169 (4): 235–244. doi:10.1680/bren.14.00031. hdl:10197/9246. ISSN 1478-4637.
  11. ^ "HL-93 AASHTO Vehicular Live Loading | Truck | Tandem | Design Lane Load". EngineeringCivil.org. 17 August 2016. Retrieved 15 March 2019.
  12. ^ Leahy, Cathal; OBrien, Eugene J.; Enright, Bernard; Hajializadeh, Donya (October 2015). "Review of HL-93 Bridge Traffic Load Model Using an Extensive WIM Database". Journal of Bridge Engineering. 20 (10) 04014115. doi:10.1061/(ASCE)BE.1943-5592.0000729. hdl:10197/7068. ISSN 1084-0702. S2CID 53503763.
  13. ^ O'Connor, Alan; Jacob, Bernard; O'Brien, Eugène; Prat, Michel (June 2001). "Report of Current Studies Performed on Normal Load Model of EC1: Part 2. Traffic Loads on Bridges". Revue Française de Génie Civil. 5 (4): 411–433. doi:10.1080/12795119.2001.9692315. hdl:10197/4024. ISSN 1279-5119. S2CID 111112374.
  14. ^ A.S, Nowak; M, Lutomirska; F.I, Sheikh Ibrahim (2010). "The development of live load for long span bridges". Bridge Structures. 6 (1, 2): 73–79. doi:10.3233/BRS-2010-006. ISSN 1573-2487.
  15. ^ Micu, Elena Alexandra; Obrien, Eugene John; Malekjafarian, Abdollah; Quilligan, Michael (21 December 2018). "Estimation of Extreme Load Effects on Long-Span Bridges Using Traffic Image Data". The Baltic Journal of Road and Bridge Engineering. 13 (4): 429–446. doi:10.7250/bjrbe.2018-13.427. hdl:10344/7494. ISSN 1822-4288.
  16. ^ OBrien, E. J.; Hayrapetova, A.; Walsh, C. (March 2012). "The use of micro-simulation for congested traffic load modeling of medium- and long-span bridges". Structure and Infrastructure Engineering. 8 (3): 269–276. Bibcode:2012SIEng...8..269O. doi:10.1080/15732471003640477. hdl:10197/3061. ISSN 1573-2479. S2CID 54812838.
  17. ^ Caprani, Colin C.; OBrien, Eugene J.; Lipari, Alessandro (May 2016). "Long-span bridge traffic loading based on multi-lane traffic micro-simulation". Engineering Structures. 115: 207–219. Bibcode:2016EngSt.115..207C. doi:10.1016/j.engstruct.2016.01.045.
  18. ^ OBrien, Eugene J.; Lipari, Alessandro; Caprani, Colin C. (July 2015). "Micro-simulation of single-lane traffic to identify critical loading conditions for long-span bridges". Engineering Structures. 94: 137–148. Bibcode:2015EngSt..94..137O. doi:10.1016/j.engstruct.2015.02.019. hdl:10197/6998. S2CID 56030686.
  19. ^ Dawe, Peter (2003). Research perspectives: traffic loading on highway bridges. London: Thomas Telford. ISBN 0-7277-3241-2. OCLC 53389159.
  20. ^ Fryba, L. (2009). Dynamics of railway bridges. Thomas Telford. ISBN 978-0-7277-3956-8. OCLC 608572498.
  21. ^ Li, Yingyan; OBrien, Eugene; González, Arturo (May 2006). "The development of a dynamic amplification estimator for bridges with good road profiles". Journal of Sound and Vibration. 293 (1–2): 125–137. Bibcode:2006JSV...293..125L. doi:10.1016/j.jsv.2005.09.015. hdl:10197/2529. S2CID 53678242.
  22. ^ Cantero, D.; González, A.; OBrien, E. J. (June 2009). "Maximum dynamic stress on bridges traversed by moving loads". Proceedings of the Institution of Civil Engineers - Bridge Engineering. 162 (2): 75–85. doi:10.1680/bren.2009.162.2.75. hdl:10197/2553. ISSN 1478-4637. S2CID 53057484.
  23. ^ Cantero, D; O'Brien, E J; González, A (June 2010). "Modelling the vehicle in vehicle—infrastructure dynamic interaction studies". Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics. 224 (2): 243–248. doi:10.1243/14644193JMBD228. hdl:10197/2551. ISSN 1464-4193. S2CID 59583241.
  24. ^ González, A.; Cantero, D.; OBrien, E.J. (December 2011). "Dynamic increment for shear force due to heavy vehicles crossing a highway bridge". Computers & Structures. 89 (23–24): 2261–2272. doi:10.1016/j.compstruc.2011.08.009. hdl:10197/3426. S2CID 53367765.
  25. ^ González, Arturo; OBrien, Eugene J.; Cantero, Daniel; Li, Yingyan; Dowling, Jason; Žnidarič, Ales (May 2010). "Critical speed for the dynamics of truck events on bridges with a smooth road surface". Journal of Sound and Vibration. 329 (11): 2127–2146. Bibcode:2010JSV...329.2127G. doi:10.1016/j.jsv.2010.01.002. hdl:10197/2138. S2CID 56078933.
  26. ^ Brady Sean P.; O'Brien Eugene J.; Žnidarič Aleš (1 March 2006). "Effect of Vehicle Velocity on the Dynamic Amplification of a Vehicle Crossing a Simply Supported Bridge". Journal of Bridge Engineering. 11 (2): 241–249. doi:10.1061/(ASCE)1084-0702(2006)11:2(241). hdl:10197/2327. S2CID 53417698.
  27. ^ OBrien, Eugene J.; Cantero, Daniel; Enright, Bernard; González, Arturo (December 2010). "Characteristic Dynamic Increment for extreme traffic loading events on short and medium span highway bridges". Engineering Structures. 32 (12): 3827–3835. Bibcode:2010EngSt..32.3827O. doi:10.1016/j.engstruct.2010.08.018. hdl:10197/4045. S2CID 52250745.
  28. ^ "How are Living Root Bridges Made?". The Living Root Bridge Project. 5 May 2017. Archived from the original on 5 September 2017. Retrieved 8 September 2017.
  29. ^ "The Vine Bridges of Iya Valley". Atlas Obscura. Archived from the original on 8 September 2017. Retrieved 8 September 2017.
  30. ^ "Cantilever". Bridges of Dublin. Archived from the original on 29 October 2014.
  31. ^ "Beam Bridges". Nova Online. PBS. Archived from the original on 6 January 2015.
  32. ^ K, Aggeliki; Stonecypher, Lamar (10 February 2010). "Truss Bridge Designs". Bright Hub Engineering. Archived from the original on 19 February 2015.
  33. ^ Leonhardt, Fritz (1984). Bruc̈ken: Asthetik und Gestaltung [Bridges: aesthetics and design]. Cambridge, MA: MIT Press. ISBN 0-262-12105-0. OCLC 10821288.
  34. ^ "Bridge Aesthetics. Design guideline to improve the appearance of bridges in NSW" (PDF). February 2009. Archived from the original (PDF) on 9 October 2022.
  35. ^ a b Cruickshank 2010, pp. 8–9.

Sources

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Books and journals

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