J.A.L. Waddell -- Bridge Engineering

List of cross-section diagrams

CHAPTER IV: ALLOY STEELS IN BRIDGEWORK

Fig. 4a. Weights of Double-track, Through, Pin-connected, Petit-truss Spans of Carbon Steel and Nickel Steel 62

Fig. 4b. Weights of Double-track, Through, Pin-connected, Cantilever Bridges of Carbon Steel and Nickel Steel 63

Figs. 4c. and 4d. Comparative Costs of Double-track, Through, Riveted, Pratt-truss Spans of Carbon Steel and Mixed Nickel and Carbon Steels 65

Figs. 4e and 4f. Comparative Costs of Double-track, Through, Pin-connected, Cantilever Bridges of Carbon Steel and Mixed Nickel and Carbon Steels 66

Fig. 4g. Probable Weights of Very-long-span Cantilever Bridges of Carbon Steel and of Nickel Steel 67

Fig. 4h. Poids de Métal par Mètre Courant pour les Ponts Ordinaires à Double Voie 74

Fig. 4i. Poids de Métal par Mètre Courant pour les Ponts Cantilevers à Double Voie 75

Fig. 4j. Prix du Métal en OEuvre par Mètre Courant pour les Ponts Ordinaires à Double Voie 76

Fig. 4k. Prix du Métal en OEuvre par Metre Courant pour les Ponts Cantilevers à Double Voie 77

Fig. 4l. Total Weight of Metal per Lineal Foot of Span for Double-track, Simple-span Bridges of Carbon Steel and Alloy Steels of Different Elastic Limits 78

Fig. 4m. Total Weight of Metal per Lineal Foot of Span for Double-track, Cantilever Bridges of Carbon Steel and Alloy Steels of Different Elastic Limits 80

Fig. 4n. Comparative Costs of Double-track, Simple-span, Railway Bridges of Carbon Steel and Mixed Alloy and Carbon Steels for E = 80,000 lbs 81

Fig. 4o. Comparative Costs of Double-track, Cantilever, Railway Bridges of Carbon Steel and Mixed Alloy and Carbon Steels for E = 80,000 lbs 83

Fig. 4p. Comparative Costs of Double-track, Simple-span, Railway Bridges of Carbon Steel and Mixed Alloy and Carbon Steels, Contrasting Vanadium and Nickel Steels 86

Fig. 4q. Comparative Costs of Double-track, Cantilever, Railway Bridges of Carbon Steel and Mixed Alloy and Carbon Steels, Contrasting Vanadium and Nickel Steels 87

CHAPTER VI: LIVE LOADS

Fig. 6c. Maximum End Shears for Plate-girder Spans of Railway Bridges 104

Fig. 6d. Equivalent Uniform Live Loads for Plate-girder Spans of Railway Bridges 1055

Fig. 6e. Equivalent Uniform Live Loads for Truss Spans of Railway Bridges 106

Fig. 6g. Maximum End Shears for Plate-girder Spans of Electric Railway Bridges 109

Fig. 6h. Equivalent Uniform Live Loads for Plate-girder Spans of Electric Railway Bridges 110

Fig. 6i. Equivalent Uniform Live Loads for Truss Spans with Class 15 Electric Railway Loading 111

Fig. 6j. Equivalent Uniform Live Loads for Truss Spans with Class 20 Electric Railway Loading 112

Fig. 6k. Equivalent Uniform Live Loads for Truss Spans with Class 25 Electric Railway Loading 113

Fig. 6l. Equivalent Uniform Live Loads for Truss Spans with Class 30 Electric Railway Loading 114

Fig. 6m. Equivalent Uniform Live Loads for Truss Spans with Class 35 Electric Railway Loading 115

Fig. 6n. Equivalent Uniform Live Loads for Truss Spans with Class 40 Electric Railway Loading 116

Fig. 6o. Uniformly Distributed Live Loads for Highway Bridges 117

CHAPTER VII: IMPACT LOADS

Fig. 7a. Maximum Impact Percentages by Actual Tests on Plate-girders and Main Members of Truss Spans upon Various Railroads 125

Fig. 7b. Impact Tests and Various Impact Curves 126

Fig. 7c. Coefficients of Impact for Railway Bridges 129

Fig. 7d. Coefficients of Impact for Electric Railway Bridges 130

Fig. 7e. Coefficients of Impact for Highway Bridges 131

CHAPTER VIII: CENTRIFUGAL FORCE AND THE EFFECT OF TRACK CURVATURE

Fig. 8a. Superelevation for Tracks on Curves 135

Fig. 8b. Centrifugal Force for Tracks on Curves 137

CHAPTER IX: WIND LOADS, VIBRATION LOADS, AND TRACTION LOADS

Fig. 9a. Wind Pressures on Inclined Surfaces per Duchemin's Formula 150

Fig. 9b. Wind Loads and Vibration Loads for Railway Bridges 151

Fig. 9c. Areas of Railway Bridges Exposed to Wind 153

Fig. 9d. Wind Loads for Highway and Electric Railway Bridges 154

Fig. 9e. Traction Loads for Railway Bridges 157

CHAPTER X: METHODS OF STRESS COMPUTATION

Fig. 10a. Equivalent Live Loads for Plate-girder Spans for Class 50 167

CHAPTER XVI: DETAILING IN GENERAL

Fig. 16a. Weights of Bar Lacing 287

Fig. 16b. Weights of Angle Lacing 288

Fig. 16c. Diagram for Designing Lacing 289

Fig. 16d. Points of Contraflexure in Braced Columns 294

Fig. 16e. Diagram for Calculating Net Sections of Riveted Tension Members 295

Fig. 16h. Diagram for Designing Timber Beams 303

CHAPTER XXI: PLATE-GIRDER AND ROLLED I-BEAM BRIDGES

Fig. 21a. Total Shears throughout Plate-girder Spans Carrying Uniformly Distributed Live and Dead Loads 413

Fig. 21b. Total Shears throughout Plate-girder Spans without Floor-beams and Stringers Carrying Railway Loading 415

Fig. 21e. Economic Depths of Plate-girders with Riveted End-connections 420

Fig. 21k. Net Areas of Plate-girder Flanges Composed of Two Angles and Cover-plates 429

Fig. 21m. Rivet-pitches in Girder Flanges for Combined Shear and Direct Loads 439

Fig. 21n. Rivet-pitches in Girder Flanges for Combined Shear and Direct Loads 441

Fig. 21s. Diagram for Design of I-Beams for Railway Spans 461

CHAPTER XXII: SIMPLE TRUSS BRIDGES

Fig. 22jjj. Rivet Diagram for 7/8" Rivets 519

Fig. 22kkk. Rivet Diagram for 3/4" Rivets 520

CHAPTER XXV: CANTILEVER BRIDGES

Fig. 25j. Weights of Trusses and Lateral Systems of Cantilever-arms and Anchor-arms in Percentages of Average Truss and Lateral Weight for One Panel of Suspended Span 583

CHAPTER XXVI: ARCH BRIDGES

Fig. 26n. Values of n and r for Arch Ribs 640

CHAPTER XXVIII: MOVABLE BRIDGES IN GENERAL

Fig. 28g. Cost of Power Equipment for Movable Spans 681

CHAPTER XXIX: SWING BRIDGES

Fig. 29a. Reactions for Balanced Loads on Rim-bearing Draw-spans 690

Fig. 29b. Reactions for Centre-bearing Draw-spans 691

CHAPTER XXXVII: REINFORCED-CONCRETE BRIDGES

Fig. 37b. Diagram for the Design of Rectangular Beams 797

Fig. 37c. Diagram for the Design of Slabs and Small Beams 798

Fig. 37e. Diagram for the Design of Double-reinforced Beams in General 802

Fig. 37e'. Special Diagram for the Design of Double-reinforced Beams when fc = 600 and fs = 16,000 803

Fig. 37f. Percentage of Reduction in Concrete and Steel Stresses Due to Compressive Reinforcement 804

Fig. 37h. Diagram for the Design of T-Beams in general 809

Fig. 37h'. Special Diagram for the Design of T-Beams when fc= 600 and fs = 16,000 811

Fig. 37j. Diagram for the Design of Rectangular Beams of Varying Depth 817

Fig. 37k. Diagram for the Design of Columns under Direct Stress Only 819

Fig. 37m. Diagram for the Design of Beams and Columns under Flexure and Direct Stress, with Reinforcement in Tension Face Only 822

Fig. 37o. Diagram for the Design of Beams and Columns under Flexure and Direct, Stress, with Reinforcement in Both Faces—for e/h < 1/4 827

Fig. 37q. Diagram for the Design of Beams and Columns under Flexure and Direct Stress, with Reinforcement in Both Faces—for e/h > 1/7 831

Fig. 37r. Diagram for the Design of Web Reinforcement 835

Fig. 37s. Moments of Inertia of Rectangular Beams 840

Fig. 37t. Moments of Inertia of Columns and Arch Ribs 841

Fig. 37u. Values of k - k3 and 2k - 3k2 + k3 843

Fig. 37v. Moment Coefficients for Continuous Beams 845

Fig. 37x. Diagram for Determining the Distribution of Concentrated Loads over Slabs 853

Fig. 37ee. Values of Live-load Moment Coefficient Cm 870

Fig. 37ff. Position of Point of Contraflexure for Arch Shortening and Temperature Stresses 870

Fig. 37gg. Values of Temperature Stress Coefficient Ct 871

Fig. 37vv. Pressure of Wet Concrete on Forms 948

CHAPTER XLIII: PIERS, PEDESTALS, ABUTMENTS, RETAINING WALLS, AND CULVERTS

Fig. 43c. Earth Pressures for Retaining Walls 1034

CHAPTER XLIX: DETERMINATION OF WATERWAYS

Fig. 49b. Average Run-offs for the United States 1117

CHAPTER LIII: TRUE ECONOMY IN DESIGN

Fig. 53a. Cost of Single-track-railway Embankments 1195

Fig. 53b. Cost of Double-track-railway Embankments 1196

Fig. 58c. Cost of Single-track-railway, Wooden Trestles 1197

Fig. 53d. Cost of Double-track-railway, Wooden Trestles 1198

Fig. 50e. Cost of Plain-concrete Railway-abutments 1199

CHAPTER LV: WEIGHTS OF STEEL SUPERSTRUCTURES

Fig. 55a. Single-track-railway, I-Beam Spans—Total Metal in Span 1220

Fig. 55b. Single-track-railway, Deck, Plate-girder Spans—Total Metal in Span 1221

Fig. 55c. Single-track-railway, Half-through, Plate-girder Spans—Total Metal in Span 1222

Fig. 55d. Single-track-railway, Through, Truss Spans—Metal in Laterals and on Piers 1223

Fig. 55e. Single-track-railway, Through, Riveted, Truss Spans—Metal in Floor System 1224

Fig. 55f. Single-track-railway, Riveted, Pratt-truss Spans—Percentages of Metal in Truss Details 1225

Fig. 55g. Single-track-railway, Through, Riveted, Pratt-truss Spans—Metal in Trusses 1226

Fig. 55h. Single-track-railway, Through, Riveted , Pratt-truss Spans—Total Metal in Span 1227

Fig. 55i. Single-track-railway, Through, Riveted, Petit-truss Spans—Metal in Trusses and Total Metal in Span 1228

Fig. 55j. Single-track-railway, Deck, Riveted, Pratt-truss Spans—Metal in Floor System 1229

Fig. 55k. Single-track-railway, Deck, Riveted, Pratt-truss Spans—Metal in Laterals and on Piers 1230

Fig. 55l. Single-track-railway, Deck, Riveted, Pratt-truss Spans —Metal in Trusses 1231

Fig. 55m. Single-track-railway, Deck, Riveted, Pratt-truss Spans—Total Metal in Span 1232

Fig. 55n. Single-track-railway, Through, Pin-connected, Truss Spans—Metal in Floor System 1233

Fig. 55o. Single-track-railway, Through, Pin-connected, Pratt-truss Spans—Metal in Trusses 1234

Fig. 55p. Single-track-railway, Through, Pin-connected, Pratt-truss Spans—Total Metal in Span 1235

Fig. 55q. Single-track-railway, Through, Pin-connected, Petit-truss Spans—Metal in Trusses and Total Metal in Span 1236

Fig. 55r. Double-track-railway, Half-through, Plate-girder Spans—Total Metal in Span 1237

Fig. 55s. Double-track-railway, Through, Riveted, Pratt-truss Spans—Metal in Floor System 1238

Fig. 55t. Double-track-railway, Through, Riveted, Pratt-truss Spans—Metal in Laterals and on Piers 1239

Fig. 55u. Double-track-railway, Through, Riveted, Pratt-truss Spans—Percentages of Metal in Truss Details 1239

Fig. 55v. Double-track-railway, Through, Riveted, Pratt-truss Spans—Metal in Trusses 1240

Fig. 55w. Double-track-railway, Through, Riveted, Pratt-truss Spans—Total Metal in Span 1241

Fig. 55x. Double-track-railway, Through, Riveted, Petit-truss Spans—Metal in Floor System, Laterals, and on Piers 1242

Fig. 55y. Double-track-railway, Through, Riveted, Petit-truss Spans—Metal in Trusses and Total Metal in Span 1243

Fig. 55z. Double-track-railway, Through, Pin-connected, Pratt-truss Spans—Metal in Floor System, Laterals, and on Piers 1244

Fig. 55aa. Double-track-railway, Through, Pin-connected, Pratt-truss Spans—Metal in Trusses 1245

Fig. 55bb. Double-track-railway, Through, Pin-connected, Pratt-truss Spans—Total Metal in Span 1246

Fig. 55cc. Double-track-railway, Through, Pin-connected, Petit-truss Spans—Metal in Floor System, Laterals, and on Piers 1247

Fig. 55dd. Double-track-railway, Through, Pin-connected, Petit-truss Spans—Metal in Trusses and Total Metal in Span 1248

Fig. 55ee. Metal in Swing Spans in Percentages of Weights of Simple Spans of the same Total Length 1249

Fig. 55ff. Plate-girders with Riveted End-connections—Metal in One Girder 1250

Fig. 55gg. Through, Riveted, Pratt Trusses—Metal in One Truss 1251

Fig. 55hh. Through, Riveted, Petit Trusses—Metal in One Truss 1252

Fig. 55ii. Deck, Riveted, Pratt Trusses—Metal in One Truss 1253

Fig. 55jj. Light, Through, Riveted, Highway Trusses—Metal in One Truss 1254

Fig. 55kk. Through, Pin-connected, Pratt Trusses—Metal in One Truss 1255

Fig. 55ll. Through, Pin-connected, Petit Trusses—Metal in One Truss 1256

Fig. 55mm. Metal on Piers for Truss Spans 1257

Fig. 55nn. Single-track-railway Trestles, Type I—Metal in Girders and Girder Bracing 1258

Fig. 55oo. Single-track-railway Trestles, Type I—Economic Span Lengths 1259

Fig. 55pp. Single-track-railway Trestles, Type I—Metal in Longitudinal and Transverse Bracing of Towers 1260

Fig. 55qq. Single-track-railway Trestles, Type I—Metal in Columns of Towers 1261

Fig. 55rr. Single-track-railway Trestles, Type I—Total Metal in Trestles for Economic Layouts 1262

Fig. 55ss. Single-track-railway Trestles, Type I—Approximate Maximum Loads on Tops of Pedestals 1263

Fig. 55tt. Single-track-railway Trestles, Type II—Metal in Girders and Girder Bracing 1264

Fig. 55uu. Single-track-railway Trestles, Type II—Metal in One Bent 1265

Fig. 55vv. Single-track-railway Trestles, Type II—Metal in One Tower 1266

Fig. 55ww. Single-track-railway Trestles, Type II—Metal in Towers and Bents for Classes 40, 45, and 50 1267

Fig. 55xx. Single-track-railway Trestles, Type II—Metal in Towers and Bents for Classes 55 and 60 1268

Fig. 55yy. Single-track-railway Trestles, Type II—Metal in Towers and Bents for Classes 65 and 70 1269

Fig. 55zz. Single-track-railway Trestles, Type II—Span Lengths and Total Metal in Trestles for Economic Layouts 1270

Fig. 55bbb. Double-track-railway, Cantilever Bridges, Type A—Metal in Floor System, Laterals, and on Piers 1272

Fig. 55ccc. Double-track-railway, Riveted, Cantilever Bridges, Type A—Metal in Trusses and Total Metal in Bridge 1273

Fig. 55ddd. Double-track-railway, Pin-connected, Cantilever Bridges, Type A—Metal in Trusses and Total Metal in Bridge 1275

Fig. 55eee. Double-track-railway, Cantilever Bridges, Type B—Metal in Floor System, Laterals, and on Piers 1277

Fig. 55fff. Double-track-railway, Riveted, Cantilever Bridges, Type B—Metal in Trusses and Total Metal in Bridge 1278

Fig. 55ggg. Double-track-railway, Pin-connected, Cantilever Bridges, Type B—Metal in Trusses and Total Metal in Bridge 1279

Fig. 56hhh. Double-track-railway, Cantilever Bridges, Type C—Metal in Floor System, Laterals, and on Piers 1280

Fig. 55iii. Double-track-railway, Riveted, Cantilever Bridges, Type C—Metal in Trusses and Total Metal in Bridge 1281

Fig. 55jjj. Double-track-railway, Pin-connected, Cantilever Bridges, Type C—Metal in Trusses and Total Metal in Bridge 1282

Fig. 55kkk. Double-track-railway, Cantilever Bridges, Type D—Metal in Floor System, Laterals, and on Piers 1283

Fig. 55lll. Double-track-railway, Riveted, Cantilever Bridges, Type D—Metal in Trusses and Total Metal in Bridge 1284

Fig. 55mmm. Double-track-railway, Pin-connected, Cantilever Bridges, Type D—Metal in Trusses and Total Metal in Bridge 1285

CHAPTER LVI: QUANTITIES FOR PIERS, PEDESTALS, ABUTMENTS, RETAINING WALLS, AND REINFORCED CONCRETE BRIDGES

Fig. 56a. Volumes of Copings and of Shafts of Piers with Vertical Sides 1301

Fig. 56b. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 1/2" to 1'0" 1302

Fig. 56c. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 1/2" to 1'0" 1303

Fig. 56d. Volumes of Strips One Foot Wide in Middle Portion of Round-ended Piers—Batter 1/2" to 1'0" 1304

Fig. 56e. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 3/4" to 1'0" 1305

Fig. 56f. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 3/4" to 1'0" 1306

Fig. 56g. Volumes of Strips One Foot Wide in Middle Portion of Round-ended Piers—Batter 3/4" to 1'0" 1307

Fig. 56h. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 1" to 1'0" 1308

Fig. 56i. Volumes of Truncated Cones Composed of Two Rounded Ends of Piers—Batter 1" to 1'0" 1309

Fig. 56j. Volumes of Strips One Foot Wide in Middle Portions of Round-ended Piers—Batter 1" to 1'0" 1310

Fig. 56k. Volumes of Pedestals 1311

Fig. 56l. Volumes of Pedestals 1312

Fig. 56m. Volumes of Pedestals 1313

Fig. 56o. Volumes of Portions of Wing Abutments above the Base for Single-track-railway Bridges 1315

Fig. 56p. Volumes of Bases of Wing Abutments for Single-track-railway Bridges 1316

Fig. 56q. Volumes of Strips One Foot Wide in Middle Portions of Wing Abutments for Railway Bridges 1317

Fig. 56r. Quantities of Concrete and Metal per Lineal Foot of Reinforced-concrete Retaining Walls 1318

Fig. 56s. Quantities of Concrete per Lineal Foot of Plain Concrete Retaining Walls 1319

Fig. 56t. Reinforced-concrete Bridges, Concrete and Steel in Floor System 1321

Fig. 56u. Reinforced-concrete Bridges, Percentage of Floor System in Slabs 1322

Fig. 56v. Reinforced-concrete Girder Bridges, Concrete and Steel in Main Girders 1223

Fig. 56w. Reinforced-concrete Girder Bridges, Depths of Girders and Footings. 1324

Fig. 56x. Reinforced-concrete Girder Bridges, Concrete in Columns 1326

Fig. 56y. Reinforced-concrete Girder Bridges, Steel in Columns 1327

Fig. 56z. Reinforced-concrete Girder Bridges, Concrete and Steel in Footings 1328

Fig. 56aa. Reinforced-concrete Arch Bridges, Concrete and Steel in Spandrel Girders and Columns 1329

Fig. 56bb. Reinforced-concrete Arch Bridges, Concrete and Steel in Spandrel Walls 1331

Fig. 56cc. Reinforced-concrete Arch Bridges, Concrete and Steel in Arch Ribs 1332

Fig. 56dd. Reinforced-concrete Arch Bridges, Concrete and Steel in Arch Barrels One Foot Wide 1333

Fig. 55ee. Reinforced-concrete Arch Bridges, Approximate Ratios of Volumes of Abutments and Average Piers 1341

Fig. 56ff. Reinforced-concrete Arch Bridges, Exponential Curves for Reduction Equations 1343

CHAPTER LVII: ESTIMATES

Fig. 57a. Cost of Materials in One Cubic Yard of 1:2:4 Concrete 1357

Fig. 57b. Cost of Materials in One Cubic Yard of 1:3:5 Concrete 1358