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Engineering Practice 1
Chapter 2. Beam Formulas 11
Continuous Beams / 11
Ultimate Strength of Continuous Beams / 46
Beams of Uniform Strength / 52
Safe Loads for Beams of Various Types / 53
Rolling and Moving Loads / 53
Curved Beams / 65
Elastic Lateral Buckling of Beams / 69
Combined Axial and Bending Loads / 72
Unsymmetrical Bending / 73
Eccentric Loading / 73
Natural Circular Frequencies and Natural Periods of
Vibration of Prismatic Beams / 74
Torsion in Structural Members / 76
Strain Energy in Structural Members / 76
Fixed-End Moments in Beams / 79
Chapter 3. Column Formulas 81
General Considerations / 81
Short Columns / 81
Eccentric Loads on Columns / 83
Columns of Special Materials / 88
Column Base Plate Design / 90
American Institute of Steel Construction
Allowable-Stress Design Approach / 91
Composite Columns / 92
Elastic Flexural Buckling of Columns / 94
Allowable Design Loads for Aluminum Columns / 96
Ultimate Strength Design Concrete Columns / 97
Design of Axially Loaded Steel Columns / 102
vChapter 4. Piles and Piling Formulas 105
Allowable Loads on Piles / 105
Laterally Loaded Vertical Piles / 105
Toe Capacity Load / 107
Groups of Piles / 107
Foundation-Stability Analysis / 109
Axial-Load Capacity of Single Piles / 112
Shaft Settlement / 112
Shaft Resistance in Cohesionless Soils / 113
Chapter 5. Concrete formulas 115
Reinforced Concrete / 115
Water/Cementitious Materials Ratio / 115
Job Mix Concrete Volume / 116
Modulus of Elasticity of Concrete / 116
Tensile Strength of Concrete / 117
Reinforcing Steel / 117
Continuous Beams and One-Way Slabs / 117
Design Methods for Beams,
Columns, and Other Members / 118
Properties in the Hardened State / 127
Tension Development Lengths / 128
Compression Development Lengths / 128
Crack Control of Flexural Members / 128
Required Strength / 129
Deflection Computations and Criteria
for Concrete Beams / 130
Ultimate-Strength Design of Rectangular Beams with
Tension Reinforcement Only / 130
Working-Stress Design of Rectangular Beams with
Tension Reinforcement Only / 133
Ultimate-Strength Design of Rectangular
Beams with Compression Bars / 135
Working-Stress Design of Rectangular
Beams with Compression Bars / 136
Ultimate-Strength Design of I- and T-beams / 138
Working-Stress Design of I- and T-beams / 138
Ultimate-Strength Design for Torsion / 140
Working-Stress Design for Torsion / 141
Flat-Slab Construction / 142
Flat-Plate Construction / 142
Shear in Slabs / 145
Column Moments / 146
Spirals / 147
Braced and Unbraced Frames / 147
Shear Walls / 148
Concrete Gravity Retaining Walls / 150
Cantilever Retaining Walls / 153
Wall Footings / 155
vi CONTENTSChapter 6. Timber Engineering Formulas 157
Grading of Lumber / 157
Size of Lumber / 157
Bearing / 159
Beams / 159
Columns / 160
Combined Bending and Axial Load / 161
Compression at Angle to Grain / 161
Recommendations of the Forest Products Laboratory / 162
Compression on Oblique Plane / 163
Adjustment Factors for Design Values / 164
Fasteners for Wood / 169
Adjustment of Design Values for
Connections with Fasteners / 171
Roof Slope to Prevent Ponding / 172
Bending and Axial Tension / 173
Bending and Axial Compression / 173
Solid Rectangular or Square Columns with Flat Ends / 174
Chapter 7. Surveying Formulas 177
Units of Measurement / 177
Theory of Errors / 178
Measurement of Distance with Tapes / 179
Vertical Control / 182
Stadia Surveying / 183
Photogrammetry / 184
Chapter 8. Soil and Earthwork Formulas 185
Physical Properties of Soils / 185
Index Parameters for Soils / 186
Relationship of Weights and Volumes in Soils / 186
Internal Friction and Cohesion / 188
Vertical Pressures in Soils / 188
Lateral Pressures in Soils,
Forces on Retaining Walls / 189
Lateral Pressure of Cohesionless Soils / 190
Lateral Pressure of Cohesive Soils / 191
Water Pressure / 191
Lateral Pressure from Surcharge / 191
Stability of Slopes / 192
Bearing Capacity of Soils / 192
Settlement under Foundations / 193
Soil Compaction Tests / 193
Compaction Equipment / 195
Formulas for Earthmoving / 196
Scraper Production / 197
Vibration Control in Blasting / 198
CONTENTS viiChapter 9. Building and Structures Formulas 207
Load-and-Resistance Factor Design
for Shear in Buildings / 207
Allowable-Stress Design for Building Columns / 208
Load-and-Resistance Factor Design for Building Columns / 209
Allowable-Stress Design for Building Beams / 209
Load-and-Resistance Factor Design for Building Beams / 211
Allowable-Stress Design for Shear in Buildings / 214
Stresses in Thin Shells / 215
Bearing Plates / 216
Column Base Plates / 217
Bearing on Milled Surfaces / 218
Plate Girders in Buildings / 219
Load Distribution to Bents and Shear Walls / 220
Combined Axial Compression or Tension and Bending / 221
Webs under Concentrated Loads / 222
Design of Stiffeners under Loads / 224
Fasteners in Buildings / 225
Composite Construction / 225
Number of Connectors Required
for Building Construction / 226
Ponding Considerations in Buildings / 228
Lightweight Steel Construction / 228
Choosing the Most Economic Structural Steel / 239
Steel Carbon Content and Weldability / 240
Statically Indeterminate Forces and Moments
in Building Structures / 241
Roof Live Loads / 244
Chapter 10. Bridge and Suspension-Cable Formulas 249
Shear Strength Design for Bridges / 249
Allowable-Stress Design for Bridge Columns / 250
Load-and-Resistance Factor Design for Bridge Columns / 250
Additional Bridge Column Formulas / 251
Allowable-Stress Design for Bridge Beams / 254
Stiffeners on Bridge Girders / 255
Hybrid Bridge Girders / 256
Load-Factor Design for Bridge Beams / 256
Bearing on Milled Surfaces / 258
Bridge Fasteners / 258
Composite Construction in Highway Bridges / 259
Number of Connectors in Bridges / 261
Allowable-Stress Design for Shear in Bridges / 262
Maximum Width/Thickness Ratios for Compression
Elements for Highway Bridges / 263
Suspension Cables / 263
General Relations for Suspension Cables / 267
Cable Systems / 272
Rainwater Accumulation and Drainage on Bridges / 273
viii CONTENTSChapter 11. Highway and Road Formulas 275
Circular Curves / 275
Parabolic Curves / 277
Highway Curves and Driver Safety / 278
Highway Alignments / 279
Structural Numbers for Flexible Pavements / 281
Transition (Spiral) Curves / 284
Designing Highway Culverts / 285
American Iron and Steel Institute (AISI)
Design Procedure / 286
Chapter 12. Hydraulics and Waterworks Formulas 291
Capillary Action / 291
Viscosity / 291
Pressure on Submerged Curved Surfaces / 295
Fundamentals of Fluid Flow / 296
Similitude for Physical Models / 298
Fluid Flow in Pipes / 300
Pressure (Head) Changes Caused by Pipe
Size Change / 306
Flow through Orifices / 308
Fluid Jets / 310
Orifice Discharge into Diverging Conical Tubes / 311
Water Hammer / 312
Pipe Stresses Perpendicular
to the Longitudinal Axis / 312
Temperature Expansion of Pipe / 313
Forces due to Pipe Bends / 313
Culverts / 315
Open-Channel Flow / 318
Manning’s Equation for Open Channels / 320
Hydraulic Jump / 321
Nonuniform Flow in Open Channels / 323
Weirs / 329
Flow over Weirs / 330
Prediction of Sediment-Delivery Rate / 332
Evaporation and Transpiration / 332
Method for Determining Runoff for Minor
Hydraulic Structures / 333
Computing Rainfall Intensity / 333
Groundwater / 334
Water Flow for Fire Fighting / 335
Flow from Wells / 335
Economical Sizing of Distribution Piping / 336
Venturi Meter Flow Computation / 336
Hydroelectric Power Generation / 337
Pumps and Pumping Systems / 338
Hydraulic Turbines / 344
Dams / 348
CONTENTS ixChapter 13. Stormwater, Sewage, Sanitary
Wastewater, and Environmental Protection 361
Determining Storm Water Flow / 361
Flow Velocity in Straight Sewers / 361
Design of a Complete-Mix Activated Sludge Reactor / 364
Design of a Circular Settling Tank / 368
Sizing a Polymer Dilution/Feed System / 369
Design of a Solid-Bowl Centrifuge for Sludge Dewatering / 369
Design of a Trickling Filter Using the NRC Equations / 371
Design of a Rapid-Mix Basin and Flocculation Basin / 373
Design of an Aerobic Digester / 374
Design of a Plastic Media Trickling Filter / 375
Design of an Anaerobic Digestor / 377
Design of a Chlorination System for Wastewater Disinfection / 379
Sanitary Sewer System Design / 380
Design of an Aerated Grit Chamber / 383
Index 385
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