20

Bridges D J Lee BScTech, DIC, FEng, FICE,

FIStructE

B Richmond BSc(Eng), PhD, FCGI, FICE Maunsell Group Contents 20.1

Plan of work

20/3

20.2

Economics and choice of structural system

20/3

20.3

Characteristics of bridge structures 20.3.1 Theory of suspension bridges and arch bridges 20.3.2 Bridge girders of open section 20.3.3 More general behaviour of suspension bridges and arches 20.3.4 Single-cell box girder 20.3.5 Boxes with discrete diaphragms 20.3.6 Box beams with continuous diaphragms 20.3.7 Box girders with cantilevers 20.3.8 Multiple web girders of open crosssection 20.3.9 Multiple single-cell box beams 20.3.10 Multicellular bridge decks 20.3.11 Symmetrical loading 20.3.12 Antisymmetrical loading 20.3.13 Design curves

20.4

Stress concentrations 20.4.1 Shear lag due to concentrated loads 20.4.2 Changes in thickness and cut-outs

20/33 20/33 20/33

20/17

20.5

Concrete deck slabs

20/34

20/17 20/21

20.6

Skew and curved bridges 20.6.1 Skew 20.6.2 Curved in plan

20/35 20/35 20/35

20.7

Dynamic response

20/36

20.8

Appendix: Movable bridges

20/38

20.9

Items requiring special consideration

20/38

20/22 20/24 20/25 20/26 20/27 20/27 20/29 20/31 20/31 20/31 20/32

References

20/40

Bibliography

20/41

This page has been reformatted by Knovel to provide easier navigation.

20.1

Plan of work

The design of bridges requires the collection of extensive data and from this the selection of possible options. From such a review the choice is narrowed down to a shortlist of potential bridge designs. A sensible work plan should be devised for the marshalling and deployment of information throughout the project from conception to completion. Such a checklist will vary from project to project but a typical example might be drawn up on the following lines. 1I) Feasibility phase: (a) (b) (c) (d) (e) (f) (g) (h)

data collection; topographical and hydrographical surveys; hydrological information; geological and geotechnical information; site investigation requirements for soil and rock evaluation; Meteorological and aerodynamic data; assembly of basic criteria; likely budget.

(2) Assembly of design criteria'. (a) data and properties on the material to be used including steel, concrete, aluminium, timber, masonry, etc.; (b) foundation considerations; (c) hydraulic considerations, flood, scour; (d) loading and design criteria; (e) clearances height and width (such as for navigation, traffic); (f) criteria for gradients, alignment, etc.; (g) hazards such as impact, accident; (h) proximity to other engineering works, etc.; (i) functional requirements; (j) transportation and traffic planning; (k) highway and/or railway engineering aspects; (I) drainage requirements; (m) provision for services (water, sewage, power, electricity, telephone, gas, communications links, etc.); (n) design life and durability considerations. (3) Design phase: (a) choice of bridge; (b) detailed design of bridge including foundations, substructure and superstructure; (c) production of drawings and documentation, etc.; (d) preparation of quality assurance plan; (e) estimation of cost and programme. (4) Construction phase: (a) (b) (c) (d) (e) (f) (g)

contractual matters; construction methods; budget and financial control; quality control; supervision of construction; commissioning; operating, inspection and maintenance schedules for each part of the work.

(5) Performance phase: (a) (b) (c) (d)

obligations of owner; management of facility; inspection, maintenance and repair; rehabilitation and refurbishment requirements (change of loading, widening, change of use and durability aspects); (e) decommissioning and demolition. Such a project list serves to highlight the various and sometimes conflicting requirements of a bridge project, and those aspects

where the bridge designer should seek the approval of the client throughout all the stages of a project for a truly successful collaboration. This chapter covers the selection and analysis of bridge superstructures and attempts to relate the most frequently used bridging materials - steel and concrete. As extensive treatment as possible is given to box girder analysis, an important aspect of modern bridge construction. Information about individual bridges will be found in the bibliography. Reference to these specific examples will assist an understanding of the historical background and the existing state of the art. A good general review of the structural form of bridges is given by Beckett,' whilst a sensitive aesthetic assessment is provided by Mock.2 Masonry arches and steel trusses have not been dealt with but interesting examples of these types of bridges are contained in the reference list. The principles developed in this chapter for open or closed sections are applicable to trussed structures if suitable modifications are made to allow for shear behaviour of the truss system. Thus, the authors hope that there is adequate information in this chapter to make preliminary assessments for most modern bridge designs by methods which enable the essential natures of structural behaviours to be perceived and which can be developed to detailed analyses without the necessity of revising basic principles.

20.2 Economics and choice of structural system Cost comparisons which would make it possible to arrive at the most economical choice of material, structural form, span, etc. have been sought for many years by bridge engineers, but since the costs of any one bridge depend on the circumstances prevailing at that time, the information is always imprecise. Cost data must be up to date and sufficiently detailed to allow adjustments to be made for changed circumstances. It is the changes in these factors which lead to new methods of construction and new structural systems; a major change of this kind has been that involving box girders, plate girders and trusses. A very early steel box girder bridge, the Britannia Bridge,3 built by Stephenson over the Menai Straits (main spans 14Om, completed in 1850) was very successful and was in regular use for railway trains until it was damaged by fire. Each span was lifted into place in its entirety by hydraulic jacks. The advantages of truss construction were, however, sufficient to convince engineers for the next 100 years that box structures were not economical, though plated structures were used in the form of Ibeams for smaller spans and lighter loads. The steel box girder re-emerged as a structural system for bridges after the Second World War, although short-span multicellular bridges in reinforced concrete had been used for short spans in the 1930s. In 1965 a large proportion of structures other than short spans were built as box structures of one form or another. A greater degree of selectivity then began to emerge and open crosssections, even for substantial spans, were again being used provided no problems of aerodynamic stability arose. The use of plate girders has been further encouraged by the reaction caused by failures of steel box girder bridges but it seems likely that a balanced view of the merits of various forms of construction will prevail. Figure 20.14 shows the possible cross-sections for bridge structures which can include truss systems if the plane of each triangulated panel is represented by either a web or flange member. The significance of box structures in a more general sense now becomes clear. It is the open cross-section that is a particular, although important, form of construction, whereas

orthotropic plates

M Multiple

Q Quadruple T Triple D Double

multiple web (M-1)

multiple box (M-2)

quadruple web (Q-1)

quadruple box (Q-2)

quadruple triple (Q-3)

triple web (T-1)

triple box (T-2)

triple-triple (T-3)

double web (D-1)

double box (D-2)

double triple (D-3)

single web (S-D

single box (S-2)

single triple (S-3)

(M-3) etc

S

Single

single-quadruple (S-4)

multicellular (S-M)

voided slab

Number of webs in each box Figure 20.1 Classification of bridge-deck classifications. (After Lee (1971) The selection of box-beam arrangements in bridge design', Developments in bridge design and construction. (Crosby Lockwood). the box system is perhaps a misleadingly simple description of the general range of structures. The most basic structural dimension for a given span affecting both the least-cost and the least-weight methods of measuring efficiency is the effective lever arm of the structure for resisting bending moments resulting from the vertically acting forces from self-weight and imposed loads and vertical components of the support reactions. In bridges which depend on horizontal reactions from the ground, this distance is the rise of an arch above its foundations, or the dip of a suspension cable between towers. If the supports are at different levels, the dip or rise is measured vertically from the chord joining the supports. The high strength: weight ratio of steel wire and favourable price:strength ratio results in dip:span ratios of 0.1 being suitable for even the longest suspension bridges (Table 20.1). The shallow cable has a higher tension which improves its capacity for carrying uneven loads without large deflection and increases its natural frequency of vibration. The cost of the cable alone is not, however, sufficient to reach conclusions on economics, since the cost of foundations to anchor the cables is substantial and varies with the ground conditions. The lower strength-.weight ratios of steel in compression and concrete combined with the destabilizing effect of the compressive force of the thrust lead to the rise:span ratios being considerably higher on average (Tables 20.3 and 20.4). Good foundations and the requirements of local topography may lead to reduced ratios, and arches - such as at Gladesville,5 which are in flat country and yet have the roadway running above the arch rib - and the requirement for a low rise to minimize the cost of approach embankments. The depth between compression and tension flanges is the lever arm of a simply supported beam structure, such as a truss, plate girder or box girder. If the structure is continuous at both ends, the sum of the depths at the centre span and one of the supports is the lever arm (Tables 20.6 and 20.7).

Table 20.1 The world's leading suspension bridges Main span (m)

Cable sag (m)

Span/ sag

Location

1981

1410

125

11.3

Humber River

1964

1298

117

11.0

Golden Gate 1937 Mackinac Straits 1957 Minami BisanSeto (Road/Rail) u.c. (1988)

1280 1158

145 108

8.8 10.76

New York Harbor San Francisco Michigan

2nd Bosphorus Bosphorus George Washington

1988 1973

1090 1074

93.4

11.5

Ortakoy, Turkey

1932

1067

96

11.1

1013 1006

106 91

9.5 11.0

Hudson River, New York state Lisbon Queensferry

Name oj bridge

Humber Verrazano Narrows

Year

Tagus 1966 Forth 1964 Kita Bisan-Seto (Road/Rail) u.c. (1988)

1100

Inland Sea of Japan

990

Severn 1966 Ohnaruto Tacoma Narrows II 1950

988 876

82

853

87

Lions Gate

846

1938

u.c. = under construction

12.0

9.8

Inland Sea of Japan Beachley, UK Naruto, Japan Puget Sound, Washington Vancouver

Table 20.2 Leading cable-stayed bridges Name

Location

Year

Main span Span length (m) arrangement

Dusseldorf Flehe

Vancouver, Canada 1986 465 u.c. 457 Calcutta, India Sierra Cantabrica, W Spain 440 Iwakurojima (two (u.c. 1987)420 bridges) 404 Loire estuary, Brittany 1974 France 400 Jacksonville, Florida, US Vigo Estuary, Spain 1978 400 1982 372 Mississippi River, Louisiana, US 1979 368 W. Germany

Tjorn

Askerofjord, Sweden

Annacis Hooghly Barrios de Luna Hitsuishijima Saint Nazaire St Johns River Rande Luling

Sunshine Skyway Florida, US Yamatogawa Osaka, Japan Duisberg-Neuenkamp Rhine River, Duisberg-Moers, W. Germany Jindo S. Korea Westgate Yarra River, Melbourne, Australia Guagu, Argentina Brazo Largo

Zarate

Palmas, Argentina

Knie

Brotonne Bratislava

Hamburg, W. Germany Rhine River, Dusseldorf, W. Germany Seine River, Rouen, France Danube River, Czechoslovakia

Material

Function

Planes

Arrangement

Sym Sym

2 2

MF F

St/C St/C

Road

Sym Sym

2 2

F MF

C St

Sym

2

F

St

Road Road and Rail Road

F

C St St

Sym Sym

2 2

F F

Ass

1

1981

366

Sym

2

1987 1970

366 355 350

Sym Sym

I 1 1

H MF

C St St

Road Road Road

1985 1978

345 336

Sym Sym

2 1

F DF

St St/C

Road Road

1977

330

Sym

2

F

St

Road and Rail

1977

330

Sym

2

F

St

Road and Rail Road and Rail

330

C

Part of KojmaSokaido

Road

Multiple side span anchor piers

Road

Replaced steel arch demolished by ship collision

1974

325

Sym

2

MF

St

1969

320

Ass

2

H

St

Road

1977

320

Sym

1

MF

C

Road

1971

316

Ass

1

305 302 300 299 292

Sym Ass Ass Sym Ass

1 2 2 2 1

S side St span, F main span S St F St MF St/C F C MF St

Road Road Road Road Road

Road

Erskine Severins Dnieper Pasco Kennewick Neiwied

Clyde River, Scotland Cologne, W. Germany Kiev, Soviet Union Washington State, US Rhine River, W. Germany

1971 1959 1976 1978

Deggenau

Danube River, W. Germany Mexico Rhine River, Mannheim Nord, W. Germany

1975

290

Ass

1

F

St

Road

1984 1971

288 287

Sym Ass

1 2

MF F

C St

Road Road and tramway

Coatzacoalcos II Kurt Schuhmacher

Special notes

Road Road

H side St/C span, MF main span MF St/C

Posadas-Encarnacion Paraguay, Argentina Kohlbrand

Cables

Connected by long embankment

Multiple side span anchor piers

Two unequal spans, backward leaning tower

Two unequal spans Two unequal spans with longitudinal A frame tower Two unequal spans

Two side span anchor piers

Table 20.2 (cont) Name

Location

Year

Main span Span length (m) arrangement

Cables

Material

Planes

Arrangement

Function

Special notes

Articulated

1971

282

Sym

2

S

C

Road

1965

281

Sym

1

H

St

Road

1967

280

Sym

1

MF

St

Road

u.c. 1975

280 275

Sym Ass

2 1

F

St St

Road

u.c. Ohio River, US Waal River, Holland 1972 Dusseldorf, 1958 W. Germany Dusseldorf, 1976 W. Germany 1967 W. Germany Belgrade, Yugoslavia 1978 1969 Montreal, Canada Tokushima, Japan 1976 1972 Parana River, Corrientes, Argentina 1982 Inverness, Scotland 1962 Lake Maracaibo, Venezuela Beachley, Wales 1966 Malaysia 1980 Zambia 1977 Kobe, Japan

274 267 260

Ass Sym Sym

2 2 2

MF F H

C C St

Road Road Road

258

Ass

1

H

St

255 254 251 250 245

Sym Sym Sym Sym Sym

2 2 1 1 2

H MF F MF F

St St St St C

Road and Multiple side-span streetcar anchor piers Road Railway Road

240 235

Sym Sym

2 2

H S

St C

Road Road

235 225 223 220

Sym Sym

1 2

S H

St C

Road Road

Sym

2

MF

St

Road

New Brunswick, Canada Yodo River, Osaka, Japan Hiroshima Pref., Japan Genoa, Italy

1969

217

1970

216

Sym

1

MF

St

Road

1968

215

Sym

2

F

St

Road

1967

210

Sym

2

S

C

Road

Albert Canal Batman

Godsheide, Belgium Tamar River, Tasmania

1977 1968

210 206

Sym Ass

2 2

MF

St St

Road Road

Arno

Florence, Italy

1977

206

Sym

2

Stromsund Adhamiyah

Sweden Baghdad, Iraq

1955 1984

183 182

Sym Ass

2 1

DF H

St/C St/C

Road Road

New Galecopper

Rhine Canal, 1971 Amsterdam, Holland Rhine River, 1967 W. Germany Simplon Pass, Valais, 1980 Switzerland

180

Sym

1

S

St

Road

175

Ass

1

MF

St

Road

Two unequal spans

174

Sym

2

S

C

Road

Cables enclosed in web extensions. Curved side spans

Wadi-el-Kuf Lever kusen Friedrich-Ebert Dolsan Speyer

East Huntingdon Tiel Theodor Heuss Oberkassel Rees Save Papineau Suchiro Manuel Belgrano

Kessock General Rafael Urdaneta

Wye Penang Crossing Luangwa Rokko Island Double-decked Hawkshaw Toyosato Onomichi Polcevera Creek

Maxau Ganter

Beida, Libya, N. Africa Rhine River, W. Germany Rhine River, Bonn Nord, W. Germany S. Korea Rhine River, W. Germany

S side span, F main span

S side span, F main span S side span, F main span

Road

Road

Two unequal spans

Articulated

Multiple spans. Articulated

Multiple spans. Articulated Two unequal spans. Forward leaning tower Towers lean backwards

Two side-span anchor piers Twin bridges skew spans

Table 20.2 (cont) Name

Location

Year

Main span Span length (m) arrangement Planes

Arrangement

North Elbe

Hamburg, W. Germany Yokohama, Japan Paris, France Linz, Austria Japan Hokkaido, Japan Tokyo, Japan River Usk, Newport, Wales Rio Ebro, Castejon, Spain Danube River, W. Germany Tiber River, Rome, Italy

1962

172

Sym

1

ST

St

1974 1971 1979 1971 1975 1970 1964

165 162 161 160 160 160 152

Ass Sym Ass Sym Sym Sym Sym

2 1 2 1 2 1 2

MF MF S H F H H

St St

MF

C

1

S

C

Daikoku Massena Steyregger Donau Kamatsugawa Ishikara-Kako Arakawa George Street Sancho el Major Metten Magliana

Cables

146 145

Material

St/C

St St St St/C

Function

Special notes

Road

Road Road

Two unequal spans

Road Road Road

1967

145

Ass

2

S

C

Road

Dnieper Maya Ludwigshafen

Kiev, Soviet Union Kobe, Japan W. Germany

1964 1966 1968

144 139 138

Sym Ass Eq

2 1 2

F MF F

C St St

Road

Sitka Harbour Danube Canal Second Main Bridge

Alaska, US Vienna, Austria Frankfurt, W. Germany

1972 1975 1972

137 119 148

Sym Sym Ass

2 2 2

S S H

St/C

Road

C C

Tarano

Alba, Italy

1983

114

Ass

1

S side span, F main span

St

Road

Harm sen Bridge of the Isles

Rotterdam, Holland Montreal, Canada

1968 1967

108 105

Eq

2

S

St/C

Road and rail

St Florent Julicherstrasse

River Loire, France Dusseldorf, W. Germany

1969 1963

104 99

Eq Sym

2 1

F S

St

Road

Road and rail

Curved in plan. Two unequal spans. Backward leaning towers Two unequal spans Four-leg A-frame tower

Articulated main span connects to fin back. Three anchored side spans Two unequal spans. Backward sloping towers

St/C Road

Ass - asymmetric; C - concrete; DF - double fan; Eq - two equal; F - multiple fan; H - harp; MF - modified fan; S - single; St - steel; ST - star; St/C - composite steel and concrete; Sym - symmetric; u.c. - under construction

Table 20.3 The world's leading steel arch bridges Name of bridge

Span (m)

Rise (m)

Rise span

Year

Location

1977

West Virginia, US New York, New York, US Sydney, Australia Portland, Oregon, US Vancouver, Canada Balboa, Panama Trois Rivieres, Canada Lake Orlik, Czechoslovakia Mersey River, England Sabi River, Rhodesia Arizona, US

River Gorge

518

Bayonne

504

81

0.161

1931

Sydney Harbour 503 Fremont* 383

107

0.212

1932 u.c.

Port Mann*

366

Thatcherf Laviolettef

344 335

Zd'akov

330

42.5

0.129

1967

Runcorn-Widnes 330

66.4

0.202

1961

Birchenough

329

65.8

0.200

1935

Glen Canyon LewistonQueenston

313

Hell Gate

298

305

76

0.208

1964 1962 1967

1959 48.4

0.159

RiodasAntas Traneberg

1962 1917

Niagara River, N. America New York, New York, US

Other steel arch bridges of interest Rainbow

289

45.7

0.158

1941

Fehmarnsund*

249

43.6

0.175

1963

Adomi (Volta) Kaiserlei*

245 220

57.4

0.234

1957 1964

Niagara Falls, N. America Fehmarnsund, W. Germany Adomi, Ghana Frankfurt-amMain, W. Germany

Table 20.4 The world's leading concrete arch bridges Span (m)

Rise (m)

Rise span

Year

Location

1980

Adria, Yugoslavia Sydney, Australia Parana River, Brazil-Paraguay Cape Province, South Africa Portugal Angerman River, Sweden Krka River, Yugoslavia Catanzaro, Italy Danube River, Yugoslavia Bregenz, Austria Van Stadens Gorge, S. Africa EsIa River, Spain Cape Province, South Africa

Krk II

390

Gladesville Rio Parana

305 290

Bloukrans

272

Arrabida Sando

270 264

Shibenik

246

Fiumarella Novi Sad

231 211

Linenau Van Stadens

210 200

1967 1971

EsIa Groot River

192 189

1942 1983

40.8 53.0

0.134 0.183

1964 1965 1983

51.9 40.0

0.192 0.151

1963 1943 1967

66.1

0.286

1961 1961

Plougastel (Albert Louppe) 173

28.0 26.2

0.156 0.147

1953 1934

Brazil Stockholm, Sweden

33

0.190

1930

Elorn River, France Yakima, Washington, US Cape Province, South Africa France

Selah Creek

168

1971

Bobbejaans

165

1983

La Roche-Guyonl61 Cowlitz River Bridge 158 CaracasLa Guaira

152

Puddefjord Podolska

145 145

23.0

0.143

1934

Mossyrock, Washington, US 39.0

0.257

1952 1956 1942

Caracas, Venezuela Norway Czechoslovakia

Other concrete arch bridges of interest Revin-Orzy

120

10.0

0.083

Glemstal

114

27.1

0.238

Slangsboda

111

12.0

0.108

1961

Meuse River, France Stuttgart, W. Germany Stockholm, Sweden

u.c. = under construction

u.c. = under construction *Tied arch tCantilever arch

Name of bridge

180 178

Table 20.5 The world's leading truss bridges Name of bridge Quebec Railway Forth Railway Minato Delaware River

Span (m)

Year

549 1918 2 x 5 2 1 1890 510 1974 501

Location Quebec, Canada Queensferry, Scotland Japan Chester, Penn-Bridgeport, New Jersey, US

Greater New Orleans Howrah Transbay

480 1958 457 1943 427 1936

Baton Rouge Tappan Zee Longview

376 1968 369 1955 366 1930

Queensboro I Carquinez Strait

360 1909 2x335

1927

San Francisco, California, US

II Carquinez Strait

2x335 1958

San Francisco, California, US Vancouver, Canada Montreal, Canada Jacksonville, Florida, US

Second Narrows Jacques Cartier Isaiah D. Hart Richmond-San Rafael

335 1960 334 1930 332 1967 2 x 326 1956

Grace Memorial

320 1929

NewburghBeacon Auckland Harbour

305 1963

244 1959

New Orleans, Louisiana, US Calcutta, India San Francisco, California, US Baton Rouge, Louisiana, US Tarrytown, New York, US Columbia River, Washington, US New York, US

San Pablo Bay, California, US Cooper River, South Carolina, US Hudson River, New York, US Auckland, New Zealand

Table 20.6 Some of the world's leading steel girder bridges Name of bridge

Span (m)

Depth (d) at midspan (m)

Depth (d2) at pier (m)

d,+d2 Span

Year

Type

Location

Niteroi Sava I Zoo Sava II Koblenz Foyle San Mateo-Hayward Hochbriicke 'Radar InseK Moselle Milford Haven Fourth Danube Martigues Diisseldorf-Neuss Wiesbaden-Schierstein Europa Koln-Deutz Poplar Street Italia Avonmouth Friarton Gemersheim Speyer Concordia New Temerloh

300 261 259 250 235 234 228 221

7.4 4.6 4.5

12.9 9.8 10.0

0.068 0.055 0.056

1974 1956 1966 1969

4.6 5

9.2 9.5

0.060 0.066

B P B B B B B P

5.9

5.9

0.055

B B B Portal B B P B B B B B B B B B B

Rio de Janeiro, Brazil Belgrade, Yugoslavia Cologne, W. Germany Belgrade, Yugoslavia Rhine River, W. Germany Londonderry, N. Ireland California, US Nord-Ost see Canal, W. Germany Moselle Valley, W. Germany Pembroke Dock, Wales Vienna, Austria France Diisseldorf, W. Germany Rhine River, W. Germany Sill Valley, Austria Rhine River, W. Germany St Louis, Mississippi, US Lao River, Italy Gloucestershire, England Perth, Scotland Rhine River, W. Germany Rhine River, W. Germany Montreal, Canada Temerloh, Malaysia

219 213 210 210 206 205 198 185 183 175 174 174 165 163 160 151

3.3 4.4 7.7

7.8 7.4 7.7

0.054 0.057 0.078

6.2 8.5 2.6 2.7 9.1 3.4 4.9 3.7

7.6 8.5 7.6 7.5 5.4 6.40 4.9 5.9

0.070 0.059 0.059 0.058 0.060 0.060 0.064

1984 1967

1970 1976 1951 1964 1948 1967 1969 1974 1978 1971 1956 1967 1974

Other steel girder bridges of interest Calcasieu River St Alban Amara

137 135 82

2.1 2.8 3.7

7.0 9.3 12.1

0.078 0.062 0.087

1963 1955 1958

P P B

Louisiana, US Basel, Switzerland Tigris River, Iraq

u,c. = under construction Bridge type: B box girder, P plate girder

Table 20.7 Some of the world's leading concrete girder bridges Name of bridge

Span (m)

Depth (d) at midspan (m)

Depth (d 2 ) at pier (m)

d, + d 2 Span

Year

Type

Location

Gateway Hikoshima Urato Three Sisters

260 236 230 229

4.0

14.0

0.069

1986

Brisbane, Australia

4.0

12.5

0.072

1972 u.c.

C C C C

Bendorf Orwell Manazuru Brisbane Water Gardens Point Redheugh

208 190 185 183 183 160

4.4

10.4

0.071

1965

3.1

10.0

Amakusa Nakana Medway Neckarsulm Moscow River Amakusa Kingston Victoria Tocantins Bettingen Don

160 152 151 148 146 143 142 142 140 139

3.0 2.2 4.2

10.0 10.8 7.4

0.086 0.078

2.4

10.0

0.087

u.c.

C C C

c+ss C

3.0

7.0

1963 1968 1957 1966 1970 1970 1961

0.089

1964

c+ss C CG C C

c+ss C C C

Shikoku, Japan Potomac River, Washington, DC, US Bendorf, W. Germany Ipswich, England Japan New South Wales, Australia Brisbane Australia Newcastle upon Tyne, England Japan Rochester, England Neckarsulm, W. Germany Soviet Union Japan Glasgow, Scotland Brisbane, Australia Tocantins River, Brazil Main River, W. Germany Rostow, Soviet Union

Table 20.7 (cont.) Name of bridge

Span (m)

Pine Valley Alno Oland

137 134 130

Depth (d) at midspan (m)

Depth (d2) at pier (m)

d, + d 2 Span

Year

Type

Location

u.c. 1964 1972

CG C C

California, US Alnosund, Sweden Kalmar Sound, Sweden

C C C CG CG C + SS C + SS CG

Rhine River, W. Germany Moselle River, W. Germany Orust, Sweden Eiserfeld, W. Germany Chillon, Switzerland Perth, Australia Singapore Rochefort, France

Other concrete girder bridges of interest Worms Koblenz Notesund Siegtal Chillon Viaduct Narrows Benjamin Sheares Oleron

114 114 110 105 104 97 84 79

2.5 2.7 2.2 5.8 2.2 2.2

6.5 7.2 5.7 5.8 5.6 4.2

0.079 0.087 0.072 0.110 0.072 0.068

2.5

4.5

0.089

1952 1954 1966 1969 1973 1959 1981 1966

u.c. = under construction C - concrete; C + SS - concrete with suspended span; CG - continuous girder

The cable-supported bridge can be seen as either a suspension bridge or a continuous beam with the effective depth at the supports equal to the height of the tower. Figure 20.2 shows the various arrangements of cables that are used, and various finished bridges are shown in Figures 20.3 to 20.9. The choice of span depends on the foundations, depth of water and height of the deck but, in many cases, other requirements - such as navigation clearances - dictate the minimum span. It is usually only shorter spans where, proportionately at any rate, there is considerable variation possible. It has been claimed in the past that at the most economic span of a multispan structure, the cost of foundations equals the cost of the superstructure less the basic deck structure costs. The assumptions necessary for this to be valid are that the cost of superstructure per unit length should increase linearly with span and that that of the substructure should vary inversely with span. The slopes of the respective cost-span curves are then equal and opposite at the point of intersection of the curves provided any constant costs in both foundations and superstructure are first subtracted. If the cost of the superstructure is assumed to increase proportionately to the square root of the span, however, the same approach requires that half the superstructure cost should equal the foundation cost. In modern structures it is difficult to separate the costs of the basic deck system from the total of the multispan structure. The well-known rule - that for maximum economy the total area of the flanges of a beam should equal the area of the web is a more useful guide. Table 20.8 shows that for a given web thickness and a total area of cross-section of 1 .Qt the maximum section modulus is at a depth of 0.75 where the total flange area is one-third the web area, but at a depth of 0.5 where the flange and web areas are equal the section modulus is only 11 % lower. A shallower beam is usually more economical because a simpler web is then possible provided the shear force can be carried. Fabrication, transportation and erection are also less costly. Table 20.9 shows the types of standardized precast concrete beams that are appropriate to various parts of the short-span range. Apart from the cost advantages of standardization and factory production, which may be offset by higher overheads and transport costs, there are the following advantages. (1) Estimates of cost more reliable. (2) Speed of construction. (3) No temporary staging required. (4) Sample beams can be tested to demonstrate level of prestress and ultimate strength.

Figure 20.2 Examples of different cable systems (scale: approximately 1/10000). (a) Fan (Stromsiind); (b) modified fan (Duisberg-Neuenkamp); (c) harp (Theodor Heuss); (d) single cable (Erskine); (e) star (Norderelbe); (f) asymmetric systems (Batman); (g) Bratislava). (Courtesy: Polensky and ZoIIner)

Figure 20.3 Concrete girder bridge, Bettingen, Frankfurt-am-Main

Figure 20.4 Steel girder bridge, Rio-Niteroi, Brazil. (Courtesy: Redpath Dorman Long and the Cleveland Bridge and Engineering Co. Ltd)

Figure 20.5 Concrete cable-stayed bridge, Tempul Aqueduct, Spain. (Courtesy: Torroja Institute, Madrid)

Table 20.8 Depth Af Section modulus Z

0.5 0.25/ 0.167/

0.6 0.2/ 0.180/

0.7 0.15/ 0.187/

0.75 0.125/ 0.1875/

0.8 0.1/ 0.187/

Af = bf x tp (t,tc, tb are small)

Af - bbx tb

Note: Total cross-section throughout = 1.0/

Figure 20.6 Steel trussed cable-stayed bridge. Batman Bridge, Tasmania. (Courtesy: Maunsell and Partners)

Figure 20.7 Concrete-arched bridge, Gladesville, Sydney. (Courtesy: G. Maunsell and Partners)

Figure 20.8 Number suspension bridge. (Courtesy: Freeman Fox and Partners)

Figure 20.9 Annacis cable-stayed bridge, Vancouver. (Courtesy: Buckfand and Taylor Ltd)

In simple right spans, the system chosen, apart from span, depends on construction depth limitations, difficulties of access and, of course, prevailing prices. For example, the top hat beam system6 is suitable for restricted access and small construction depths. The U-beam system7 is suitable for similar conditions but requires an increased depth. At the greater depth it is more economical. An advantage of torsionally stiff structures of this type, particularly when they are designed to be spaced apart in the transverse direction, is that they can readily be fanned out to

support the structures with complex plan forms that are now common. The standard concrete beams are essentially a series of elements that can be placed across the complete span, requiring only simple shuttering to support the transversely spanning top slab. Diaphragm beams at the supports are required and occasionally intermediate diaphragms may be provided. Steel beams can be used as an alternative form of construction in the same span range. Either a series of !-sections or small box girders can be used.

Table 20.9 Precast concrete bridge beams Type of beam

Name of beam

Classification (as Figure 20.1)

Span (m)

I

C&CA !-section beam

M-I

12-36

Inverted T

C&CA inverted T-beam for spans from 7-16 m

Orthotropic slab

7-16 m

Inverted T (M range)

MoT/C & CA prestressed inverted T-beam for spans from 15 to 29m

(a) T-beam M-I (b) Pseudo box S-M

15-29

Box

C & CA box section beam

S-M

12-36

U

U-beam

M-2

15-36

Beam section

Remarks

Section through part of typical deck

Surfacing Structural slab

20 standard sections 01-120) Holes for transverse reinforcement provided at 30-50 mm centres

Transverse diaphragm

Surfacing /n situ concrete

Reinforced concrete topping In situ reinforced concrete infill

(a) T-beam

7 standard sections (Tl-TT)

10 standard sections (Ml-MlO)

(b) Pseudo box

Ini situ concrete Surfacing

Surfacing In situ topping

Permanent soffit shuttering

17 standard sections (Bl-B 17) Transverse prestress used to give optimum load distribution

12 standard sections (Ul-U 12)

Table 20.10 Longitudinal stiffeners for orthotropic decks Type of stiffener

Classification (as Figure 18.1)

Remarks

Flat

M-I, etc.

Torsionally weak. Easily spliced. Poor transverse load distribution. Earliest form.

M-I

Torsionally weak. Easily spliced. Poor transverse load distribution. Bulb flats difficult to obtain. Out of date.

Trapezoidal trough

M-2, etc.

Torsionally stiff. Fabrication difficult through cross-frames. Relatively popular.

V-trough

M-2

Torsionally stiff. Fabrication difficult through cross-frames. Small effective lower flange area. Popular but less efficient than trapezoidal trough

Wineglass

M-2

Torsionally stiff. Very complicated fabrication. Expensive.

(cut from universal beam)

M-I

Easily spliced. Requires large cutout in cross-frame. Torsionally weak. Inefficient.

Bulb

flat

Total tension

L= distance between anchorages Figure 20.10 Suspension-bridge notation Precast or prefabricated elements can be made as transverse rather than longitudinal elements and then joined together on site by prestressing in concrete structures or welding or bolting in steel structures. This approach, sometimes known as segmental construction, was used for the structures of Figure 20.1 l(d), (e), (f), (h), (i), (j) and (k). It was also used for the steel structures of Figure 20.11 (1) and (m). The remaining steel structures shown in Figure 20.11(n) to (r) were constructed by a similar process but with the subdivision taken a stage further. Each transverse slice was built up on the end of the cantilevering structure from several stiffened panels. In situ concrete, reinforced or prestressed, can be used to form complete spans in one operation or else the cantilevering approach can be used. In the latter case, the speed of construction is limited by the time required for the concrete to reach a cube strength adequate for the degree of prestress necessary to support the next section of the cantilever and the erection equipment. Segmental methods of construction8 avoid such delays. In shorter spans, provided that the restrictions on construction depth are not too severe, in situ concrete structures can be built economically using the cross-section of Figure 20.1 l(c). The simple cross-section9 was developed to suit the use of formwork which, after supporting a complete span, could be moved rapidly to the next span. The resulting machine is only economical for multispan structures. The stiffened steel plates (Table 20.10) are used for deck systems of long-span, and movable, bridges in order to reduce the self-weight of the structure.

20.3 Characteristics of bridge structures The following theories have been chosen and developed for their value in demonstrating the principal characteristics of various types of bridge structure. Other methods of calculation, based on finite elements, for example, may be more accurate and more economical in certain circumstances. The theories are, however, linked to the main structural properties of the bridge types considered and are meant to assist the process of synthesis necessary before detailed calculations begin. The concepts described are also useful for idealizing structures when using computer programs and for interpreting and checking the computer output. 20.3.1 Theory of suspension bridges and arch bridges The basic theory of arch and suspension bridges is the same and the equation derived below for suspension bridges is applicable to arches if a change in sign of H and y is made.

20.3.1.1 Suspension bridges with external anchorages The dead load of the cable and stiffening girder is supported by the force per unit length of span produced by the horizontal component of the cable force and the rate of change of slope of the cable: #,y(*) + * = 0

(20.1)

where y, etc. are shown in Figure 20.10. For a parabolic shape of cable corresponding to constant intensity of load across the span /, y"(x) = - 8///2 and: Hg=glW

(20.2)

The cable tension increases under live load p(x) to: H=HK + Hp

(20.3)

The increase in support from the cable is — [Hv" (x) + H^(X)] where v(x) is the vertical deflection of the cable and stiffening girder. The stiffening girder contributes a supporting reaction per unit length of [EIv"(x)]" and adding the cable and stiffening girder contributions and equating them to the intensity of the applied load gives: [EIv"(x)]" - Hv"(x) =p(x) + Hfy"

(20.4)

The term H^y" is added to the live load in order to show that the equation can be represented physically by the substitute structure of Figure 20.12. y" is — 8///2 and therefore represents a force in the opposite direction to the live load. Hp depends on the change in length of the cable and if A&x is the horizontal projection of the change in length of an element ds then for fixed anchorages: JjJdX = O

(20.5)

Integrating along the cable and allowing for a change in temperature of A T gives: fcW*-*Pl^

iMJV^fr-Wfc-O

(20.6)

Approximate values of Lk and L7 are (see Figure 20.13): 2 L^ V°/ 0 ) + -^-+ * (l+8-£ \ /2 + ^tan 2 COS2V1 ~4COS2V2

(20.7) L 1 ^(I + ^ + tan 2 V 0 ) + J j U JL.