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### 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