Civil Engineering Formulas

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Civil Engineering Formulas

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Preface

This handy book presents more than 2000 needed formulas for civil engineers to help them in the design office, in the field, and on a variety of construction jobs, anywhere in the world. These formulas are also useful to design drafters, structural engineers, bridge engineers, foundation builders, field engineers, professional-engineer license examination candidates, concrete specialists, timber-structure builders, and students in a variety of civil engineering pursuits.

The book presents formulas needed in 12 different specialized branches of civil engineering—beams and girders, columns, piles and piling, concrete structures, timber engineering, surveying, soils and earthwork, building structures, bridges, suspension cables, highways and roads, and hydraulics and open-channel flow. Key formulas are presented for each of these topics. Each formula is explained so the engineer, drafter, or designer knows how, where, and when to use the formula in professional work. Formula units are given in both the United States Customary System (USCS) and System International (SI). Hence, the text is usable throughout the world. To assist the civil engineer using this material in worldwide engineering practice, a comprehensive tabulation of conversion factors is presented in Chapter 1. In assembling this collection of formulas, the author was guided by experts who recommended the areas of greatest need for a handy book of practical and applied civil engineering formulas.

Sources for the formulas presented here include the various regulatory and industry groups in the field of civil engineering, authors of recognized books on important topics in the field, drafters, researchers in the field of civil engineering, and a number of design engineers who work daily in the field of civil engineering. These sources are cited in the Acknowledgments.

When using any of the formulas in this book that may come from an industry or regulatory code, the user is cautioned to consult the latest version of the code. Formulas may be changed from one edition of a code to the next. In a work of this magnitude it is difficult to include the latest formulas from the numerous constantly changing codes. Hence, the formulas given here are those current at the time of publication of this book. In a work this large it is possible that errors may occur. Hence, the author will be grateful to any user of the book who detects an error and calls it to the author’s attention. Just write the author in care of the publisher. The error will be corrected in the next printing.

In addition, if a user believes that one or more important formulas have been left out, the author will be happy to consider them for inclusion in the next edition of the book. Again, just write him in care of the publisher.

TOC

Chapter 1.
Conversion Factors for Civil
Engineering Practice 1

Chapter 2. Beam Formulas 15
Continuous Beams / 16
Ultimate Strength of Continuous Beams / 53
Beams of Uniform Strength / 63
Safe Loads for Beams of Various Types / 64
Rolling and Moving Loads / 79
Curved Beams / 82
Elastic Lateral Buckling of Beams / 88
Combined Axial and Bending Loads / 92
Unsymmetrical Bending / 93
Eccentric Loading / 94
Natural Circular Frequencies and Natural Periods
of Vibration of Prismatic Beams / 96

Chapter 3.
Column Formulas 99
General Considerations / 100
Short Columns / 102
Eccentric Loads on Columns / 102
Column Base Plate Design / 111
American Institute of Steel Construction Allowable-Stress
Design Approach / 113
Composite Columns / 115
Elastic Flexural Buckling of Columns / 118
Allowable Design Loads for Aluminum Columns / 121
Ultimate-Strength Design of Concrete Columns / 124

Chapter 4.
Piles and Piling Formulas 131
Allowable Loads on Piles / 132
Laterally Loaded Vertical Piles / 133
Toe Capacity Load / 134
Groups of Piles / 136
Foundation-Stability Analysis / 139
Axial-Load Capacity of Single Piles / 143
Shaft Settlement / 144
Shaft Resistance to Cohesionless Soil / 145

Chapter 5.
Concrete Formulas 147
Reinforced Concrete / 148
Water/Cementitious Materials Ratio / 148
Job Mix Concrete Volume / 149
Modulus of Elasticity of Concrete / 150
Tensile Strength of Concrete / 151
Reinforcing Steel / 151
Continuous Beams and One-Way Slabs / 151
Design Methods for Beams, Columns, and Other Members / 153
Properties in the Hardened State / 167

Chapter 6.
Compression at Angle to Grain / 220
Recommendations of the Forest Products Laboratory / 221
Compression on Oblique Plane / 223
Adjustments Factors for Design Values / 224
Fasteners for Wood / 233
Adjustment of Design Values for Connections with
Fasteners / 236
Roof Slope to Prevent Ponding / 238
Bending and Axial Tension / 239
Bending and Axial Compression / 240

Chapter 7.
Surveying Formulas 243
Units of Measurement / 244
Theory of Errors / 245
Measurement of Distance with Tapes / 247
Vertical Control / 253
Stadia Surveying / 253
Photogrammetry / 255

Chapter 8.
Soil and Earthwork Formulas 257
Physical Properties of Soils / 258
Index Parameters for Soils / 259
Relationship of Weights and Volumes in Soils / 261
Internal Friction and Cohesion / 263
Vertical Pressures in Soils / 264
Lateral Pressures in Soils, Forces on Retaining Walls / 265
Lateral Pressure of Cohesionless Soils / 266
Lateral Pressure of Cohesive Soils / 267
Water Pressure / 268
Lateral Pressure from Surcharge / 268
Stability of Slopes / 269
Bearing Capacity of Soils / 270
Settlement under Foundations / 271
Soil Compaction Tests / 272
Compaction Equipment / 275
Formulas for Earthmoving / 276
Scraper Production / 278
Vibration Control in Blasting / 280

Chapter 9.
Building and Structures Formulas 283
Load-and-Resistance Factor Design for Shear in Buildings / 284
Allowable-Stress Design for Building Columns / 285
Load-and-Resistance Factor Design for Building Columns / 287
Allowable-Stress Design for Building Beams / 287
Load-and-Resistance Factor Design for Building Beams / 290
Allowable-Stress Design for Shear in Buildings / 295
Stresses in Thin Shells / 297
Bearing Plates / 298
Column Base Plates / 300
Bearing on Milled Surfaces / 301
Plate Girders in Buildings / 302
Load Distribution to Bents and Shear Walls / 304
Combined Axial Compression or Tension and Bending / 306
Webs under Concentrated Loads / 308
Design of Stiffeners under Loads / 311
Fasteners for Buildings / 312
Composite Construction / 313
Number of Connectors Required for Building Construction / 316
Ponding Considerations in Buildings / 318

Chapter 10.
Bridge and Suspension-Cable
Formulas 321
Shear Strength Design for Bridges / 322
Allowable-Stress Design for Bridge Columns / 323
Load-and-Resistance Factor Design for Bridge Columns / 324
Allowable-Stress Design for Bridge Beams / 325
Stiffeners on Bridge Girders / 327
Hybrid Bridge Girders / 329
Load-Factor Design for Bridge Beams / 330
Bearing on Milled Surfaces / 332
Bridge Fasteners / 333
Composite Construction in Highway Bridges / 333
Number of Connectors in Bridges / 337
Allowable-Stress Design for Shear in Bridges / 339
Maximum Width/Thickness Ratios for Compression
Elements for Highway Bridges / 341
Suspension Cables / 341
General Relations for Suspension Cables / 345
Cable Systems / 353

Chapter 11.
Highway and Road Formulas 355
Circular Curves / 356
Parabolic Curves / 359
Highway Curves and Driver Safety / 361
Highway Alignments / 362
Structural Numbers for Flexible Pavements / 365
Transition (Spiral) Curves / 370
Designing Highway Culverts / 371
American Iron and Steel Institute (AISI) Design
Procedure / 374

Chapter 12.
Hydraulics and Waterworks
Formulas 381
Capillary Action / 382
Viscosity / 386
Pressure on Submerged Curved Surfaces / 387
Fundamentals of Fluid Flow / 388
Similitude for Physical Models / 392
Fluid Flow in Pipes / 395
Pressure (Head) Changes Caused by Pipe Size Change / 403
Flow through Orifices / 406
Fluid Jets / 409
Orifice Discharge into Diverging Conical Tubes / 410
Water Hammer / 412
Pipe Stresses Perpendicular to the Longitudinal Axis / 412
Temperature Expansion of Pipe / 414
Forces Due to Pipe Bends / 414
Culverts / 417
Open-Channel Flow / 420
Manning’s Equation for Open Channels / 424
Hydraulic Jump / 425
Nonuniform Flow in Open Channels / 429
Weirs / 436
Flow Over Weirs / 438
Prediction of Sediment-Delivery Rate / 440
Evaporation and Transpiration / 442
Method for Determining Runoff for Minor Hydraulic Structures / 443
Computing Rainfall Intensity / 443
Groundwater / 446
Water Flow for Firefighting / 446
Flow from Wells / 447
Economical Sizing of Distribution Piping / 448
Venturi Meter Flow Computation / 448
Hydroelectric Power Generation / 449
Index 451