On Network Arches for Architects and Planners
It is perhaps best to employ two cranes when the unfinished bridge is to be moved to the site. That’s why multiple cranes might be employed.
Uglen can lift the steel skeleton even if the two transverse beams at the end of the lane are cast.
Eide Marine Service`s crane can lift the steel skeleton if the scaffolding and the reinforcements are put in place after the skeleton has been transported.
The numbers under the heading are less reliable than the rest of the numbers in the rest of this thesis, but they illustrate valuable ideas.
Network arches made of concrete on land and then lifted onto the pillars by large floating cranes.
In network arches, pressure is a dominant factor. It is best to take the stress in the lower chord by means of prestressing cables. For long bridges, arches made of concrete can be assembled on land and lifted onto the pillars by means of large floating cranes. There is more on how this can be done in Tveit (2010)
Fig. 39. Every side span is 235 m long (Tveit 2009)
When the arch is round, it will always buckle sideways because the hangers are a stiffer sideways support than the windbracing Thus the arch will always buckle sideways. This simplifies the calculation of the buckling of the arch.
Fig. 40. Prefabricated part of the arch seen from above
Temporary Network Arches between 60 and 105m long. Assembled from parts and components 15 to 20 meters long.
In a conversation in 2009 with Ted Zoli in HNTB in New York, he told the author that the Bailey bridges from the second world war could be used for spans up to 60m. We agreed that network arches could be assembled from standard components, and that they could make up spans that are twice as long.
Fig. 41. Three spans assembled from standard components Fig. 42. Cross section of the arches
Fig. 41 indicates three spans that can be made by employing standard components. Only the length of hangers and nodal points between arch and the ties are different. The arch has a radius of curvature of 67.5 m. Still, an evenly distributed load gives 12% less axial force in the 105 m span. Still, the buckling load is lower in the longest span. The road system influences the length of the standard components.
Fig. 43. Network arch with three and four sets of hangers
Since the temporary lower chord will be light when compared to the traffic loads, it might be best to employ three or four sets of hangers.
Network Arch Railway Bridges
A comparison between network arches and arch bridges with vertical hangers
The diagram in fig. 44 was made by Professor Dr. Frank Schanack in Chile. Network arches make good railway bridges, since they are very stiff, in particular when one considers the amount of steel they require.
Fig. 44. Diagram of steel weights in a railway bridge with two tracks
There is also a need for further investigation into network arches for high speed railways and network arches that suffer multiple hanger failures.
In a German publication on railway bridge (Schlaich et al.) it says:
Fig. 45. Network arches for railway bridges. (Translated to the best of the author’s ability.)
Especially in big spans, the network arch is a very economical alternative compared to arches with vertical hangers. The crossing of hangers leads to extremely slender structures. In spite of the reduced dead load, a well-designed network arch has load carrying capacity and resistance against fatigue like a bridge with vertical hangers.
The network arch has great advantages, because of less deflection and less variation in the end tangent. The network arch has smaller vibrations due to traffic loads. Because of the great stiffness, the network arch can be used for high speed railways.
Where there are vibrations due to traffic loads and vibrations due to wind and rain, the network arch has advantages. This is because the hangers can be tied to each other, where they cross each other. This increases the dampening. [Tveit, P. Introduction to the network arch.]
In spite of its filigree construction, the robustness of a network arch is at least equal to the robustness of an arch with vertical hangers. The breaking of one or more hangers due to collision with traffic is better compensated for in the network arch than in arches with vertical hangers.
It is rare that slender lower chords of network arches come over the top of the rail. This has a favorable simplifying effect on the footpaths and the traffic safety. When the footpath is outside the hangers, one must see to it that there are good openings in the hangers between the footpath and the rails.
In fig. 46 there are a network arch and an arch bridge with vertical hangers.
For loads on half of the spans of bridges, the maximum bending moment in the network arch is only 5% of the corresponding bending moment in the bridge with vertical hangers. For the network arch it is an advantage that the negative bending moment is much smaller than the positive bending moment. In the bridge with vertical hangers, positive and negative bending are equally great.
In fig 45, there is a gradual reduction of the angle between the hangers and the lower chord. See fig 13. We get the biggest reduction in the bending moment when the angle between the lower chord and hangers is 53°. Then the bending moment in the lower chord is only 6% of the bending moment that we had when the hangers were vertical.
There is more about the relaxation of hangers in TNA pp. 67 and 68.
In the USA they seem to have been building many network arches lately.
If a planned bridge turns out to be more costly than expected, they try to find a design much less costly. This has led to the introduction of network arches in two cases that I know about. But there might be more.
The fifth of October this year (2012), the 19th yearly “Bridge design workshop” took place at the Kansas State University in the USA.
Around half the lectures were on network arches.
The author has never experienced anything like it. It fills him with joy on his 82nd birthday, when he stands at the end of his scientific career.
Conclusions after 57 years
A well designed network arch is likely to remain the world’s most slender tied arch bridge.
The slim chords are pleasing to the eye and do not hide the landscape or cityscape behind them.
The slim tie is an advantage when the traffic on the bridge is lifted up to let other traffic pass under it.
Lightness and vertical reactions give savings in the substructure.
If the bridge has 15 m between the planes of the arches, the tie can be a simple concrete slab.
Then the concrete ties should have small edge beams with room for the longitudinal prestressing cables.
If the span of this slab is more than 10 m, transversal prestressing should be considered.
Network arches have very small longitudinal bending moments in the chords.
All members efficiently carry forces that can not be avoided in any simply supported beam.
Tie and hangers give the arch good support and high buckling strength in the plane of the arch.
H-beams with horizontal webs have a favourable distribution of stiffness and give simple details.
Tension is predominant in tie and hangers. All hangers can have nearly the same cross-section.
Network arches are equally well suited for road and rail bridges.
Erection can be done using a temporary lower chord which combined with the structural steel has enough strength and stiffness to carry the casting of the concrete tie.
Other efficient methods of erection are available.
Network arches are not sensitive to uneven settlements in the foundations.
High strength and low weight give the network arch good resistance to earthquakes.
Most concrete parts need more maintenance than a concrete slab with a slight prestress.
Network arches have small surfaces. Thus they need little corrosion protection.
Network arches uses very little steel. High strength steels are well utilised.
If things go well, the network arch can save up to 40 % of the cost and 70 % of the structural steel.
Since network arches need little steel, a high percentage of the cost will be labour.
Since the advantages of the network arch are so great, there is no need to exaggerate.
If the network arch had been a well known type of bridge, it would have been hard to argue convincingly for arch bridges with vertical hangers and many other bridge types.
Conservatism and lack of time are important obstacles to the building of network arches.
List of literature.
Brunn, B. and Schanack, F. (2003) “Calculation of a double track railway network arch bridge applying the European standards“ Graduation thesis at TU-Dresden. August 2003. 320 pages. A revised version of this thesis can be found at http://home.uia.no/pert under the button “Master’s Theses”.
Chan M. and Romanes M. (2008) “New Zealand’s First Network Arch Bridge” Conference paper for the 4th New Zealand Metal Industry Conference, hosted by HERA in October 2008. All conference papers were published ona CD.
Fiedler, E. and Ziemann, J. (1997), “Die Bogenbrücke über die Saale bei Calbe – eine Brücke mit besonderer Bogenform”, (The Arch Bridge over the Saale River at Calbe – a Bridge with an Unusual Arch Shape. In German), Stahlbau, Vol. 66, No. 5, 1997, pp. 263-270, Dokumentation 1997, pp. 329-337, ISBN 3-927535-04-4.
Fisher, John W. Fatigue and Fracture in Steel Bridges. Case Studies, Wiley, New York, 1984.
Herzog, Max. (1975). “Stahlgewichte moderner Eisenbahn- und Straβenbrücken.” (Steel Weights of Modern Rail and Road Bridges.) Der Stahlbau 9/1975. pp. 280-282.
Leonhardt, (1991) “Developing guidelines for aesthetic design.” Bridge aesthetics around the world, M. P. Burke Jr. et al.,eds., Nat. Res. Counsil, Washington, D.C. pp. 32-57.
Nakai, H. et al. (1995) “Proposition of Methods for Checking the Ultimate Strength of Arch Ribs in Steel Nielsen-Lohse Bridges.” Stahlbau 64 (1995) Heft 5, pp.129-137.
Nielsen, O. F. (1929) “Foranderlige Systemer med anvendelse på buer med skraatstillede Hængestenger.” (“Discontinuous systems used on arches with inclined hangers”, in Danish.) 121 pages. Gad Copenhagen. Ph.D. thesis.
Nielsen, O.F. (1932) “Bogenträger mit Schräg gestelten Hängestangen.” (“Arches with inclined hangers,” in German.) Internationale Vereiningung f. Brückenbau und Hochbau. Abhandlungen 1, 1932. pp. 355-363.
Pucher, A. (1977) “Influence Surfaces of Elastic Plates”. Springer-Verlag, Wien. 1977
Räck, M. (2003) “Entwurf einer kombinierten Straßen-Eisenbahn-Netzwerkbogen-brücke“ (Draft of a Network Arch for a Combined Road and Railway Bridge) Graduation thesis at TU-Dresden. August 2003. 237 pages. A revised version of this thesis can be found at http://home.uia.no/pert under the button “Masters Theses”.
Schanack, F. and Brunn, B. (2009) „Analysis of the structural performance of network arch bridges.“ The Indian Concrete Journal. January 2009. pp. 7-13.
Schlaich J., Fackler T., Weißbach M., Schmitt V., Ommert C., Marx S., Krontal L. (2008) “Leitfaden Gestalten von Eisenbahnbrücken” Fischer Druck GMBH, Peine
Selberg, A. (1972) Stålkonstruksjoner 1972. Tapir Trykk. ISBN 8251900050
Steere, P. and Yihui, Wu. (2008). “Design and Construction of the Providence River Bridge” Official Proceedings of the 25th Annual International Bridge Conference, June 2-4, 2008.
Teich, S. and Wendelin, S. (2001) „Vergleichsrechnung einer Netzwerkbogenbrücke unter Einsats des Europäishen Normenkonsepts.“ (In German). Graduation thesis at TU-Dresden. August 2001. 300 pages. A revised version of this thesis can be found at http://home.uia.no/pert under the button “Master’s Theses”.
Tveit, P. (1959) “Bogebruer med skrå krysstilte hengestenger.” (“Arch bridges with inclined intersecting hangers,” in Norwegian.) Ph.D. thesis presented at the Tech. Univ. of Norway. 64 pages, 78 drawings.
Tveit, P. (1964) “Nettverkbogar, ein ny brutype”. (“Network Arches, a New Type of Bridge.) Bygg, Vol. 12, May 1964, pp.105-113.
Tveit, P. (2007) “Visit to the Steinkjer network arch 44 years later”. ARCH’07, 5th International Conference on Arch Bridges. Madeira, 12-14 September 2007. pp. 305-314, © University of Minho. Portugal. ISBN: 978-972-8692-31-5
Tveit, P. (2009a) “Efficient Utilisation of Optimal Network Arches”. Proceedings of the fifth Symposium on Strait Crossings, Trondheim, Norway June 21-24, 2009. ISBN 978-82-92506-69-1 pp. 509-514.
Tveit, P. (2009b) “Genesis and Development of the Network Arch Concept” NSBA World steel Bridge Symposium. San Antonio, Texas. November 17-20, 2009.
Tveit, P. (2009c) “ A Systematic Thesis on Network Arches” . Same home page as above.
Tveit, P. (2009d) “India Needs Network Arches”. Civil Engineering & Construction Review. August 2009. pp. 50-60
Tveit, P. (2009c) “ A Systematic Thesis on Network Arches” . ” In the home page http://home.uia.no/pert under the button Systematic Thesis
Tveit, P. (2010) “Optimal Network Arches For Road and Rail Bridges” Proceedings of the 6th International Conference on Arch Bridges. Fuzhou, Fujian, China. October 11-13, 2010. pp. 271-278. ISBN 978-953-7621-10-0.
Tveit, P. (2011) “Further development of network arches” IABSE-IASS, London Symposium Report. Page 468. ISBN 978-0-7079-7122-3
Yoshikava, O. et al. (1993) “Construction of the Shinamadera Bridge” Stahlbau 63 (1993), Heft 5, pp.125-136.
Wollmann, G. and Zoli, T. (2008) “Bridge Across Ohio River and Blennerhassett Island” Structural Engineering International 1/2008., Number 1, February 2008. pp. 28-30.
Wollmann, G., Zoli, T. and Shook, J. (2005) “Design of Tied Arch Bridge Across Ohio River and Blennerhassett Island” Proceedings, 22nd Annual International Bridge Conference, Pittsburgh, PA, June 13-15.
Wollmann G, et al. (2007) “Construction of Tied Arch Bridge Across Ohio River and Blennerhassett Island” Proceedings, 24th Annual International Bridge Conference, Pitsburgh, Pennsylvania, June 4-6
Zoli, T. and Woodward, R. (2005) “Design of Long Span Bridges for Cable Loss.” IABSE Symposium, Structures and Extreme Events, September 14-17, Lisbon, Portugal.
An extensive list of literature can be found at the end of “The Network Arch”(2011)
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