How to Make a Preliminary Design of a Network Arch for a Road Bridge

How to make a preliminary design of a network arch for a road bridge

This chapter gives simple advice on how to find dimensions for a suggested network arch. Such calculations are meant to serve two purposes. One is to find the dimensions of a network arch that could be used in a computer calculation. The other is to arrive at data for a network arch in order to compare it with other bridge alternatives.

It saves a lot of time doing the preliminary design of a network arch in the following sequence:

1. Decide on span, width of roadway and footpath, and rise of arch.

It is recommended to put the footpath outside the arches. For aesthetic reasons the author favours a rise of 15% of the span. This rise of the arch is assumed in this chapter. A bigger rise gives smaller steel weights. Most Japanese network arch bridges have a rise between 15 and 17 % of the span. Nakai 1995.

1. Make an educated guess about the width of the arch and the distance between the planes of the arches.
2. Calculate the dimensions of the slab between the arches.

The maximum bending in the slab can be found by means of chart 1 in Pucher 1977 or using a similar chart in Bittner 1965. The latter gives slightly smaller dimensions, because it has a more sophisticated approach to the use of the theory of elasticity in cracked concrete slabs. Wide slabs should be prestressed. Deflection of the slab has to be considered. When and if partial prestressing has been generally accepted, it might be used to get a better control of the deflection between the arches.

1. Decide on the shape of the lower chord and calculate the dead load. The steel weight can be taken from fig. 9 on page 8.
2. Find the live load on the bridge in the serviceability limit state.
3. Make a tentative decision on the distance between hangers along the chords. Place the nodes of the hangers in accordance with the advice on page 26. A distance of 3 to 4 metres seems a reasonable choice. The decision depends on the span of the network arch. Smaller spans should have shorter distances between the nodes to reduce bending between the nodes in the arch. The distances between the nodes also depend on the timber available for the temporary lower chord and the deflections that can be tolerated when casting the slab between the transversal beams in the temporary lower chord.
4. Apply the loads to the influence lines for the hangers in the middle of the spans in pages 60, 72 or 80. Your loads are likely to make the hangers in one of these bridges relax. Choose a slope of hangers in the middle of the bridge that will barely make any hanger relax in the serviceability limit state. This is a reasonable guess on the safe side. The slope will have to be adapted to the distance between the nodes.
5. Make a preliminary calculation of the force in the chords in the ultimate limit state. Tveit 66 has formulae for this. It is simpler to use the influence lines on pages 60 or 72. The slope of the hangers will decide which influence lines are preferable. Remember that the ordinates of these influence lines are proportional to the span of the bridge.
6. Choose the cross-section of the arch. If the arch is a Universal Column, it is reasonable to assume that the area of the arch is between 1.8 and 2 times the maximum axial force at the top of the arch divided by the yield stress of the steel. If the arch is a box, this number is likely to lie somewhere near to 1.5.
7. Use the influence lines for hangers on pages 60, 72 or 80 and 81 to find the cross-section of the hangers to be used in the computer calculations. The slope of the hangers will decide which influence lines give the best prediction of the hanger force. Remember that the distance between the nodes and the spans of the bridge both influence the hanger force. Fatigue might have a great influence on the area of the hangers.

Knowledgeable readers will understand that these hints are just a rough guide for the dimensions that should go into the computer, but the author hopes that this advice will be found to be of use. The advice might be revised and improved in new Internet editions of this publication.

94

AcknoWledgements

The author would like to express his heartfelt thanks to everyone that has encouraged and supported his work with network arches over 45 years. The list would fill several pages. Nobody mentioned, nobody forgotten.

In connection with this publication the author would like to give his most sincere thanks to those who arranged to let him lecture on network arches in February and March of this year. Their names are found on the last page of this publication. The author would also like to thank Dr. Chris Grigson and Docent John Conway for help with the English language, and Dr. Bjørn Åkeson of Chalmers University in Gothenburg for many valuable suggestions on an early draft of part of this publication.

The author would also like to thank his wife for her never-ending patience with his work on network arches and for correcting spelling and grammar in early drafts of his publications. Without her help this publication would not have been made.

CONTRIBUTORS to corrections and suggestions to this Internet edition

Professor Dr. Günter Ramberger, TU Wien, Professor Erik Hjorth-Hansen, NTNU Trondheim

Professor Semih S. Tezcan, Bogazici University, Istanbul, Chartered Engineer Øyvind Arntsen,Oslo

Professor Dr. Kolbein Bell, NTNU Trondheim Tekn. Dr. Lennart Fransson, Luleå Technical University

Tekn. Dr Frank Axhag, Swedish Railways, Borlänge, Professor Niels J Gimsimg, NHT, Copenhagen

Professor Dr. Tore H. Søreide, Reinertsen, Trondheim

95

Literature

This list also contains references relevant to network arches not mentioned in this publication.

Andersen, G. (1979) “Brugerveiledning for FEMOPT. Program for optimering af bærende konstruksjoner.” (“Users’ manual for FEMOPT. Program for the optimising of load carrying-structures,” in Danish.) Note no. 7902, Inst. Bldg. Tech. Struct. Engrg., Aalborg Univ. Centre, Aalborg, Denmark.

Bittner. E. (1965) “Platten und Behalter.” Springer-Verlag, Vienna – New York , 1965.

Bretting, A.E. (1936). “Über Bogentrträger mit schräg gestellten Hangestängen.” (“On arches with inclined hangers,” in German.) Internat. Vereiniung für Brückenbau und Hochbau. Zweiter Kongress, Schlussbericht 1936. 514-515.

Cederwall, K. & Fransson, L. (1979) “Förstärkning av ett istäckes bärförmåga med armering.” (Strengthening of Sheets of Ice by Reinforcement.” In Swedish.) Publ. 79:1 från avd før Konstrutionsteknik, Högskolan i Luleå. (Publ 79 from Department of Structural Design, Högskolan i Luleå.)

Eurocode 3: Design of steel structures – Part 2: Steel bridges. ENV 1993-2. CEN, Central Secretariat: rue de Stassart, 36, B-1050 Brussels. Ref. No.ENV 11993-2: 1997E.

Franciosi, V. (1958). “Ponto ad Arco con Implacato Sospenso.” (“Arch bridges with inclined hangers,” in Italian.), Milan, Editore Ulrico Hoepli. 93 pages.

Fries, C. And Hommel, D. (1990) “Great Belt Link – Tender design and contract design for the West Bridge.” Procedings of the 2nd Symposium on Strait Crossings. Trondheim/Norway/10-13 June 1990. Pulished by A:A: Balkema, Rotterdam. P. 305-312. ISBN 90 6191 1184.

Fujiono, T. and Ohsaka, K. (1965) “Stress Analysis of Plane Frame Structure by Digital Computer.” In Japanese. November 1965. Mitsubishi Technical Bulletin MTB 010029. Mutsubishi Heavy Industries, Ltd. Tokyo, Japan. 10 pages.

Gerard, G. (1962) “Introduction to Structural Stability Theory” McGraw-Hill Book Company, Inc. 1962

Guinness Book of World Records (1995). Editor: Peter Matthews, Bantam Books, New York. Page 306.

Gut, H., and Shuwerk, O. (1971) “Die Brücken der SBB im Raume Ziegelbrücke-Weesen.” “The bridges of the SBBin the Ziegelbrûcke-Weesen aerea” Schweizerishe Bauzeitung, 1971, 14, pages 1017-1030.

Herzog, Max. (1975). “Stahlgewichte morderner Eisenbahn- und Strassenbrücken.” (Steel Weights of Modern Rail- and Road-bridges.) Der Stahlbau 9/1975.

Hess, W. L. (1996). “An Alternate Hanger System for Tied Arch Bridges” 13th Annual International Bridge Conference in June 1996 in Pittsburgh, Pennsylvania.

Hiroshi, Y., Satake, M. and Korematsu, M. (1965) “Study on Nielsen System Bridge.” In Japanese. March 1965, Mitsubishi Technical Buletin MTB 010021 Mitsubishi Heavy Industries, Ltd., Tokyo, Japan. 8 pages.

Jay, A. (1998) “Network Arches” In French. Høgskolen i Agder 4890, Grimstad. July 1998.

Kahman R. and Beisel T. (1979) “Eine außergewöhnliche Montagemethode für die Bogenbrücke bei Straubing.” Der Stahlbau 1979. Heft 4. Berlin.

Kikuno, M. (1973) “Ohnura Bay Bridge (Japan).” Acier-Stahl Steel, 41(4) Brussels, Belgium, p.168-171.

Kolm R. (1950) “Bro över Lulefjärden.” (“Bridge over Lulefjärden,” in Swedish.) Svenska Vägföreningens Tidsskrift 1950. No. 7. 7 pages.

96

Krück G. E. (1946) “Eisenbeton-Strassenbrücke über den Mänam Pasak bei Ayuthia, Siam.” (“Concrete road bridge over the Mänam Pasak at Ayutia, Siam,” in German.) Schweizerische Bauzeitung 1946. Vol. 127, pages 139-146, Vol. 128, pages 6-9, 15-19, 27-28.

Kungliga Väg- och vattenbygnadsstyrelsen. (1954) “Bro över Lulefjärden vid Luleå.” (“Bridge over Lulefjärden vid Luleå, in Swedish. ”) 76 pages.

Majid, K.I., Spindel, J. E., Williams, M. S. (1971) “The Design of Inclined Tied Arch Railway Bridges over the M56. Paper 7392, Proceedings of the Institution of Civil Engineers. Vol. 50, Oct. 1971, p. 139-160.

Maier-Leibnitz. (1941) “Grundsätzliches über Modellmessungen der Formänderungen und Spannungen von verankerten Hängebrücken.” (Fundamentals concerning measurements of stresses, strains and deflections on models on anchored suspension bridges.) Die Bautechnik, Heft 46/47, October 1941.

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, p.129-137.

Naruoka, M. (1977) “Nielsen System Bridges in Japan.” Pfluger-Festschrift Hannover, Germany, 1977. 193-202.

Nielsen, O. F. (1930) “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. p.355-363.

Nielsen, O. F. (1936) Same title and periodical as above. Abhandlungen 4, 1936, p.429-438.

Ostenfeld, C. (1976) “Christiani & Nielsen, Jernbetonens danske pionerer” (“Christiani & Nielsen, The Danish Pioneers of Reinforced Concrete,” In Danish.) Polyteknisk Forlag, Lyngby, Denmark.

Pucher , A. (1977) “Einflussfelder elastischer Platten. – Influence Surfaces of Elastic Plates.” Springer-Verlag Wien New York. Fifth revised edition. (Any edition of this book will do.)

Shorning, W. (2000) “Mainbrücke an der NATO-Rampe zwischen den Gemarkungen Sulzbach Und Niedernberg.” Stahlbau 2000, H5. p. 387-390.

Snelling, J. 1980. “Two unusual features of the Merivale Rail Bridge.” Presented at the 11th IABSE Congress, Held in Vienna, Austria, Final Rep., IABSE, ETH-Hönggerberg, CH-8039, Switzerland, p.347-349.

Stein, Peter and Wild, H. (1965). “Das Bogentragwerk der Femarnsundbrücke.” (“The arch of the Fehmarnsound Bridge” In German.). Der Stahlbau, 34(6) Berlin, B.R.D. p.71-186.

Takagi, S. et al. (1970) “Report of Experimental Research on Aki-Ohashi. (Nielsen System Lohse Girder Bridge).” In Japanese. Transactions of JSCE, Vol. 2, Part 1, 1970. p.104-110.

Tveit, P. (1955) Graduation thesis on arch bridges with inclined hangers. Delivered in September 1955. 76 pages.

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, p.105-113.

Tveit, P. (1966) “Design of Network Arches.” Struct. Eng:, 44(7). London, England, p. 247-259.

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Tveit, P. (1972). Discussion to Majid (1971). Proceedings of the Institution of Civil Engineers. Vol.52. August 1972, p.181-184.

Tveit, P. (1973) “Network arch in double track railway bridge.” Presented at Nordic Research. Days for Steel Struct., Held in Oslo, Norway, Pre-print V713. (The publication is much the same as: “Report 7205.” Ren og Anvendt Mekanik, Danmarks Ingeniørakademi, Bygningsafdelingen, Aalborg, Denmark.)

Tveit, P. et al. (1978) “Network arches.” 1st ed., Civil Engrg. Dept., Univ. of Houston, Tex., USA. 93 pages. (Revised edition reprinted at inst. of Bldg. Techn. Struct. Engrg., Aalborg Univ. Centre Aalborg, Denmark, 1980).

Tveit, P. (1980a) “Network arches.” Handout for poster session of IABSE’s 11th Congress, held at Vienna, Publ, by inst. Tech. Struct. Engrg., Aalborg Univ. Centre, Aalborg, Denmark. 45 pages.

Tveit, P. (1980b) “Network Arches.” 11th IABSE Congress, held in Vienna, Austria, Final Report, IABSE, ETH-Hönggerberg, CH-8039, Zürich, Switzerland, p. 817-818.

Tveit, P. (1981) “25 år med nettverkbogar. Resultat og perspektiv.” (“25 years with network arches. Results and perspectiv,” in Norwegian.) Guest lect. at Tech. Univ. of Norway, printed at Inst. of Bldg, Tech. Struct. Engrg., Aalborg Univ. Center, Aalborg, Denmark. 40 pages. IFB/A 8101.

Tveit, P. (1983) “Economic design of network arches.” Rep. No. 8304, Inst. of Bldg. Tech. Strict. Enter., Aalborg Univ. Centre, Aalborg, Denmark, 22 pages. ISSN 0105-7421 Report no, 8304.

Tveit, P. (1984) “Economic design of network arches” Handout for the poster session of IABSE’s 12th congress, Vancouver, September 1984. Published by Inst. Bldg. Tech. Struct. Engrg., Alborg Univ. Centre, Aalborg. 32 pages. ISSN 0105-7321 R8405.

Tveit, P. (1984a) “A network arch with four sets of hangers designed to be cast and erected on ice floating between piers.” Handout for the poster session of IABSE’s 12th Congress, held at Vancouver, Canada. Publ. by Inst. of Bldg. Tech. Struct. Engrg., Alborg Univ. Centre, Aalborg, Denmark. 106 pages.

Tveit, P. (1984b) “Building network arches on reinforced ice between piers.” Final Rep., IABSE’s 12th Congress, held at Vancouver, Canada, publ. by IABSE, ETH-Hönggerberg, CH-8039, Zürich, Switzerland, p.1130.

Tveit, P. (1987) “Considerations for the Design of Network Arches.” Journal of Structural Engineering, Vol. 1113, No.10, October, 1987. ©ASCE, ISSN 0733-9445/87/0010-21897 Paper No. 21892. p.2189-2207.

Tveit, P. (1992) “Network Arches in Perspective” Guest Lecture held at the technical Universities in Prague and Vienna, March 1986. Published by the Agder College of Engineering, Norway. Report 2/92 ISSN 0801-6313, 36 pages.

Tveit, P. (1996) “Wie konstruiert man die schlankste und leichteste Bogenbrücke der Welt - Ein Vortrag Über Netzwerkbögen.” (“How to design the lightest and most slender arch bridge in the World. A lecture on network arches.” In German.) © Høgskolen i Agder, 1995. Publication series no: 2. ISSN: 0806-5942. ISBN: 82-7117-301-4. 24 pages.

Tveit, P. (1999a) Comparison of Steel Weights in Narrow Arch bridges with Medium Spans. A note on the Optimal Design of Network Arches. Published by Agder University College. Publication Series No. 47. 8 pages. Issn: 0806-5942 Isbn: 82-7117-378-2.

Tveit, P. (1999b) Netværksbuer – en interessant brotype. Foredrag i København , Gøteborg og NTNU. March 1999. (Network arches – an interesting type of bridge. Lectures in Copenhagen, Gothenburg and NTNU. March 1999). Published by Agder University College 1999. 30 pages. ISSN: 0806-5942, ISSN: 0806-5942, ISBN: 82-7117-394-4.

Tveit, P. (1999c) Comparison of Steel Weights in Narrow Arch Bridges with Medium Spans. Stahlbau 68 (1999), Heft 9, Berlin, p.753-757

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Tveit, P. (2000) A bridge suitable for India? ICI journal, Indian Concrete Institute. Vol. 1, April – June 2000 no.1, p.7-10.

Tveit, P. (2000) The Network Arch -- A bridge for China. Steel Construction. 2000.4. Vol. 15 No.50 Issn 1007-9963 CN 11-3899/TF------

Union International des Chemins de Fer. (1974) Loading diagram to be taken into consideration for the calculation of rail-carrying structures on lines used buy international services. UIC code – 702V, 2. ed. 1974.

Vejdirektoratet (1974) (Directorate of Highways) Beregnings- og belastningsforskrifter for vejbroer. (Rules for Calculations and Loads for Road Bridges.) May 1974, Copenhagen, Denmark.

Yoshikava, O. et al. (1993) “Construction of the Shinamadera Bridge” Stahlbau 63 (1993), Heft 5, p.125-136.

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Organisers of lectures on network arch bridges

in February and March 2000.

InstitutionPrincipal contact

Delft University of Technology.Dr. ir. A. Romeijn

Universiteit GentProfessor Dr. Ph. Van Bogaert

Bundesanstalt für StraßenwesenDirector und Prof. Dr.-Ing. Fritz Großmann

Brüderstraße 53, Bergisch Gladbach

Technische Universität BraunschweigProf. Dr. Udo Peil, Dr. Thomas Ummenhofer

Dr. Reininghausen

Universität StuttgartProf. Dr.-Ing., Drs. h.c. Jörg Schlaich,

Dr.-ing. Karl-Heinz Reineck

Technische Universität MünchenProf. Dr. -Ing. Gert Albrecht

Ecole Polytechnique Federale de LausanneProf. dr. ing.. Manfred A. Hirt

University of PisaProf. Dr. Francesco Cafarella

Universita Di Roma “La Sapienza”Prof. Dr. Mario Paolo Patrangeli

Bogazici Universitesi, IstanbulProf. Dr. Semih S. Tezcan

University of Architecture Civil Prof. dr. A. D. Tepavitcharov

Engineering & Geodesy, SofiaVice Rector Prof. Dr. Eng. Kostadin Topurov

Budapest University of TechnologyDean Prof. Dr. György Farkas

and EconomicsAssoc. Prof. Dr. Lazlo Dunai

University of Pecs, HungaryProf. Dr. Peter Lenkei

Slovak University of Technology, BratislavaProf. Dr. Ing. Zoltan Agocs

Technischen Universität WienProf. Dr. Günter Ramberger

Technical University of PragueProf. Dr. Jiri Studnicka

Assoc. Professor Dr. Rotter

Technische Universität DresdenProf. Dr.-Ing. habil. Wolfgang Graße

Fachhochschule PotsdamProf. Dr. Andreas Kahlow

Technical University of SzczecinHead of Section, Dr. Wieslav Paczkowski

TU Hamburg-HarburgProf. Dr.-Ing. Günter Valtinat

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Index

Arch
Concrete filled tubes 16,17
Cross-section 6,11,13,25,32,34,63,65,
71,77,94
Aesthetics 5,7,9,18,19,24,26
Bridge at Straubing 13,14
Camber 12,30a
Collapse limit state 22
Concrete
Casting 1,12,16,20,30a,30,40-42,74
Cracks 50
Quality 20
Slab 1,7,8,13,20,24,40,35,94
Strenght 10,32,41
Tie 10
Corrosion protection 24,52
Curvature of arches 5
Bending
Arch 8,22,26
Chords 1,4,5,12,13,14,16,17,26,27
28,30,30a,56,67,68,73
Slab 1,7,13,24,94
Tie 1,7,16,22,24,26,56
Buckling 4,5,8,16,23,26,31,44-49a,89, 91,93
Built in stresses 6,11
Corrosion 10,50
Earthquake 23
Edge beam 7,12,13,24,50,64,74,87
Erection 1,10,12,15,16,17,20,21,24,26,
35,40-43,50-55
On ice 1,30a
Exposed surface
Formwork 35
Hangers 5,35
Adjustment 6,16
Breaking 22,26
Fatigue 23,31,94
Forces 5,6,7,17,26,30,30,32,74,94
Inclination (slope) 1,16,17,19,26,27,30,
68,94
Lack of fit 30,30a
Number 10,26
Optimal arrangement 16,26
Placing of 5,8,26
Relaxation 1,4,5,7,8,16,17,19,
26-30,67,68,74,91
94
Repair and replacing of broken 23,26
Stress relief 23
Tensioning of hangers 6,74
Three or four sets 16,17,30a
Vibration 22,23,24,32 / Loads 9,13,16,24,29,30
Lower Chord 1,10,20,24,50-55
Network arches 3,22
Cost 6,19
Definition 1,5
Deflection 67,73,74,94
Japanese 18,19,24,94
Made of concrete 1,40-43
Maintenance 24
Norwegian 6,7,22,25,27,30,56-58
Preliminary design. 21,94
Railings for 10,25
Slenderness 1,8,9
Vibrations 24
for Vienna 13,14,59-72
Nielsen Bridges 19,23,94
Nodes
Distance between 8,26,30
Placing 5,8,26,94
Pontoons 12,15,20,21,40,41,42,50,
Prestress 1,7,24,31,50,52,94
Prestressing cables (or rods)7,21,24,32,50,
52,55,74
Railway bridges 24,31-39,42
Railings 11,25,54
Ramps 9,24,31
Rise of arch 5,13
Rødby-Puttgarden 40-43
Serviceability limit state 5,30,32,94
Simple details 1,11
Skodje Bridge 21,50-55
Stiffness 1,12,13,25
Steel
Price 10
Strength (quality) 1,5,10,32
Saving 1,8,14,31
Skeleton 1,12,20,50,51
Surface 10,
Weight 1,7,10-14,17,19,23,24,31,32
Three or four parallel arches 1,19,20,30
Temporary lower chord 12,15,16,20,21,24.26,
30,30a,50,52-54,74,94
Trusses 1,4,16,24,27,31,68
Upkeep 7
Ultimate limit state 5,30,74,88,90
Welds 10
Åkvik Sound Bridge 9-12,23,26,73-93

101