Concrete Pipe Design Manual INDEX OF CONTENTS. FOREWORD... iii. Chapter 1. INTRODUCTION... 1


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1 Concrete Pipe Design Manual INDEX OF CONTENTS FOREWORD iii Chapter 1. INTRODUCTION... 1 Chapter 2. HYDRAULICS OF SEWERS Sanitary Sewers... 3 Determination of Sewer System Type... 3 Determination of Design Flow... 3 Average Flow... 3 Peak Flow... 3 Minimum Flow... 4 Selection of Pipe Size... 4 Manning s Formula... 4 Manning s n Value... 4 Full Flow Graphs... 5 Partially Full Flow Graphs... 5 Determination of Flow Velocity... 5 Minimum Velocity... 5 Maximum Velocity... 5 Storm Sewers... 5 Determination of Sewer System Type... 5 Determination of Design Flow... 5 Runoff Coefficient... 6 Rainfall Intensity... 6 Time of Concentration... 6 Runoff Area... 6 Selection of Pipe Size... 7 Manning s Formula... 7 Manning s n Value... 7 Determination of Flow Velocity... 7 Minimum Velocity... 7 Maximum Velocity... 7 Example Problems Storm Sewer Flow Required Sanitary Sewer Size Storm Sewer Minimum Slope Sanitary Sewer Design Storm Sewer Design Sanitary Sewer Design Chapter 3. HYDRAULICS OF CULVERTS Determination of Design Flow Factors Affecting Culvert Discharge vi
2 Index of Contents vii Inlet Control Outlet Control Critical Depth Selection of Culvert Size Culvert Capacity Chart Procedure Nomograph Procedure Example Problems Culvert Capacity Chart Procedure Nomograph Procedure Culvert Design Culvert Design Chapter 4. LOADS AND SUPPORTING STRENGTHS Installation Types Trench Positive Projecting Embankment Negative Projecting Embankment Jacked or Tunneled Standard Installations Background Introduction Four Installations Load Pressures Selection of Standard Installation Determination of Earth Load Embankment Soil Load Trench Soil Load Negative Projecting Embankment Soil Load Jacked or Tunneled Soil Load Determination of Live Load Highways Airports Rigid Pavement Flexible Pavement Railroads Construction Loads Selection of Bedding Bedding Factors Determination of Bedding Factor Application of Factor of Safety Selection of Pipe Strength Example Problems 41 Trench Installation Positive Projecting Embankment Installation Negative Projecting Embankment Installation... 63
3 viii Concrete Pipe Design Manual 44 Jacked or Tunneled Installation Wide Trench Installation Positive Projecting Embankment Installation Vertical Elliptical Pipe Highway Live Load Aircraft Live Load  Rigid Pavement Aircraft Live Load  Flexible Pavement Railroad Live Load Chapter 5. SUPPLEMENTAL DATA Circular Concrete Pipe Elliptical Concrete Pipe Horizontal Elliptical Pipe Vertical Elliptical Pipe Concrete Arch Pipe Concrete Box Sections Special Sections Precast Concrete Manhole Sections Flat Base Pipe Standard Specifications for Concrete Pipe Pipe Joints Jacking Concrete Pipe Required Characteristics of Concrete Jacking Pipe The Jacking Method Bends and Curves Deflected Straight Pipe Radius Pipe Bends and Special Sections Significance of Cracking TABLES Table 1 Sewage Flows Used For Design Table 2 Sewer Capacity Allowances For Commercial And Industrial Areas Table 3 Full Flow Coefficient Values  Circular Concrete Pipe Table 4 Full Flow Coefficient Values  Elliptical Concrete Pipe Table 5 Full Flow Coefficient Values  Concrete Arch Pipe Table 6 Full Flow Coefficient Values  Precast Concrete Box Sections Table 7 Slopes Required for V = 2 fps at Full and Half Full Flow Table 8 Runoff Coefficients for Various Areas Table 9 Rainfall Intensity Conversion Factors Table 10 Recurrence Interval Factors Table 11 Nationwide FloodFrequency Projects Table 12 Entrance Loss Coefficients Table 13 Transition Widths  12 inch Circular Pipe
4 Index of Contents ix Table 14 Transition Widths  15 inch Circular Pipe Table 15 Transition Widths  18 inch Circular Pipe Table 16 Transition Widths  21 inch Circular Pipe Table 17 Transition Widths  24 inch Circular Pipe Table 18 Transition Widths  27 inch Circular Pipe Table 19 Transition Widths  30 inch Circular Pipe Table 20 Transition Widths  33 inch Circular Pipe Table 21 Transition Widths  36 inch Circular Pipe Table 22 Transition Widths  42 inch Circular Pipe Table 23 Transition Widths  48 inch Circular Pipe Table 24 Transition Widths  54 inch Circular Pipe Table 25 Transition Widths  60 inch Circular Pipe Table 26 Transition Widths  66 inch Circular Pipe Table 27 Transition Widths  72 inch Circular Pipe Table 28 Transition Widths  78 inch Circular Pipe Table 29 Transition Widths  84 inch Circular Pipe Table 30 Transition Widths  90 inch Circular Pipe Table 31 Transition Widths  96 inch Circular Pipe Table 32 Transition Widths inch Circular Pipe Table 33 Transition Widths inch Circular Pipe Table 34 Transition Widths inch Circular Pipe Table 35 Transition Widths inch Circular Pipe Table 36 Transition Widths inch Circular Pipe Table 37 Transition Widths inch Circular Pipe Table 38 Transition Widths inch Circular Pipe Table 39 Transition Widths inch Circular Pipe Table 40 Design Values of Settlement Ratio Table 41 Design Values of Coefficient of Cohesion Table 42 Highway Loads on Circular Pipe Table 43 Highway Loads on Horizontal Elliptical Pipe Table 44 Hghway Loads on Vertical Elliptical Pipe Table 45 Highway Loads on Arch Pipe Table 46 Pressure Coefficients for a Single Load Table 47 Pressure Coefficients for Two Loads Spaced 0.8Rs Apart Table 48 Pressure Coefficients for Two Loads Spaced 1.6Rs Apart Table 49 Pressure Coefficients for Two Loads Spaced 2.4Rs Apart Table 50 Pressure Coefficients for Two Loads Spaced 3.2Rs Apart Table 51 Pressure Coefficients for a Single Load Applied on Subgrade or Flexible Pavement Table 52 Values of Radius of Stiffness Table 53 Aircraft Loads on Circular Pipe Table 54 Aircraft Loads on Horizontal Elliptical Pipe Table 55 Aircraft Loads on Arch Pipe Table 56 Railroad Loads on Circular Pipe Table 57 Railroad Loads on Horizontal Elliptical Pipe
5 x Concrete Pipe Design Manual Table 58 Railroad Loads on Arch Pipe Table 59 Bedding Factors for Vertical Elliptical Pipe Positive Projecting Embankment Installation Table 60 Bedding Factors for Horizonal Elliptical Pipe Positive Projecting Embankment Installation Table 61 Bedding Factors for Arch Pipe Positive Projecting Embankment Installation Table 62 Type I Fill Height Table  1 ft. through 15 ft Table 63 Type I Fill Height Table  16 ft. through 30 ft Table 64 Type I Fill Height Table  31 ft. through 45 ft Table 65 Type I Fill Height Table  46 ft. through 60 ft Table 66 Type 2 Fill Height Table  1 ft. through 15 ft Table 67 Type 2 Fill Height Table  16 ft. through 30 ft Table 68 Type 2 Fill Height Table  31 ft. through 45 ft Table 69 Type 3 Fill Height Table  1 ft. through 18 ft Table 70 Type 3 Fill Height Table  19 ft. through 35 ft Table 71 Type 4 Fill Height Table  1 ft. through 15 ft Table 72 Type 4 Fill Height Table  16 ft. through 23 ft FIGURES Figure 1 Ratio of Extreme Flows to Average Daily Flow Figure 2 Flow for Circular Pipe Flowing Full... n= Figure 3 Flow for Circular Pipe Flowing Full... n= Figure 4 Flow for Circular Pipe Flowing Full... n= Figure 5 Flow for Circular Pipe Flowing Full... n= Figure 6 Flow for Horizontal Elliptical Pipe Flowing Full... n= Figure 7 Flow for Horizontal Elliptical Pipe Flowing Full... n= Figure 8 Flow for Horizontal Elliptical Pipe Flowing Full... n= Figure 9 Flow for Horizontal Elliptical Pipe Flowing Full... n= Figure 10 Flow for Vertical Elliptical Pipe Flowing Full... n= Figure 11 Flow for Vertical Elliptical Pipe Flowing Full... n= Figure 12 Flow for Vertical Elliptical Pipe Flowing Full... n= Figure 13 Flow for Vertical Elliptical Pipe Flowing Full... n= Figure 14 Flow for Arch Pipe Flowing Full... n= Figure 15 Flow for Arch Pipe Flowing Full... n= Figure 16 Flow for Arch Pipe Flowing Full... n= Figure 17 Flow for Arch Pipe Flowing Full... n= Figure 18 Flow for Box Sections Flowing Full... n= Figure 19 Flow for Box Sections Flowing Full... n= Figure 20 Relative Velocity and Flow in Circular Pipe for Any Depth of Flow Figure 21 Relative Velocity and Flow in Horizontal Elliptical Pipe for Any Depth of Flow
6 Index of Contents xi Figure 22 Relative Velocity and Flow in Vertical Elliptical Pipe for Any Depth of Flow Figure 23 Relative Velocity and Flow in Arch Pipe for Any Depth of Flow Figure 24 Relative Velocity and Flow in Precast Concrete Box Sections for Any Depth of Flow Figure 25 2Year, 30 Minute Rainfall Intensity Map Figure 26 IntensityDuration Curve Figure 27 California Chart A for Calculation of Design Discharges Figure 28 Critical Depth Circular Pipe Figure 29 Critical Depth Horizontal Elliptical Pipe Figure 30 Critical Depth Vertical Elliptical Pipe Figure 31 Critical Depth Arch Pipe Figure 32 Critical Depth Precast Concrete Box Sections Figure 33 Headwater Depth for Circular Concrete Pipe Culverts with Inlet Control Figure 34 Headwater Depth for Horizontal Elliptical Concrete Pipe Culverts with Inlet Control Figure 35 Headwater Depth for Vertical Elliptical Concrete Pipe Culverts with Inlet Control Figure 36 Headwater Depth for Arch Concrete Pipe Culverts with Inlet Control Figure 37 Headwater Depth for Concrete Box Culverts with Inlet Control Figure 38 Head for Circular Concrete Culverts Flowing Full Figure 39 Head for Elliptical Concrete Culverts Flowing Full Figure 40 Head for Concrete Arch Culverts Flowing Full Figure 41 Head for Concrete Box Culverts Flowing Full Figure 42 Culvert Capacity 12Inch Diameter Pipe Figure 43 Culvert Capacity 15Inch Diameter Pipe Figure 44 Culvert Capacity 18Inch Diameter Pipe Figure 45 Culvert Capacity 21Inch Diameter Pipe Figure 46 Culvert Capacity 24Inch Diameter Pipe Figure 47 Culvert Capacity 27Inch Diameter Pipe Figure 48 Culvert Capacity 30Inch Diameter Pipe Figure 49 Culvert Capacity 33Inch Diameter Pipe Figure 50 Culvert Capacity 36Inch Diameter Pipe Figure 51 Culvert Capacity 42Inch Diameter Pipe Figure 52 Culvert Capacity 48Inch Diameter Pipe Figure 53 Culvert Capacity 54Inch Diameter Pipe Figure 54 Culvert Capacity 60Inch Diameter Pipe Figure 55 Culvert Capacity 66Inch Diameter Pipe Figure 56 Culvert Capacity 72Inch Diameter Pipe Figure 57 Culvert Capacity 78Inch Diameter Pipe Figure 58 Culvert Capacity 84Inch Diameter Pipe Figure 59 Culvert Capacity 90Inch Diameter Pipe
7 xii Concrete Pipe Design Manual Figure 60 Culvert Capacity 96Inch Diameter Pipe Figure 61 Culvert Capacity 102Inch Diameter Pipe Figure 62 Culvert Capacity 108Inch Diameter Pipe Figure 63 Culvert Capacity 114Inch Diameter Pipe Figure 64 Culvert Capacity 120Inch Diameter Pipe Figure 65 Culvert Capacity 132Inch Diameter Pipe Figure 66 Culvert Capacity 144Inch Diameter Pipe Figure 67 Culvert Capacity 14 x 23Inch Horizontal Ellipitical Equivalent 18Inch Circular Figure 68 Culvert Capacity 19 x 30Inch Horizontal Elliptical Equivalent 24Inch Circular Figure 69 Culvert Capacity 24 x 38Inch Horizontal Elliptical Equivalent 30Inch Circular Figure 70 Culvert Capacity 29 x 45Inch Horizontal Elliptical Equivalent 36Inch Circular Figure71 Culvert Capacity 34 x 54Inch Horizontal Elliptical Equivalent 42Inch Circular Figure 72 Culvert Capacity 38 x 60Inch Horizontal Elliptical Equivalent 48Inch Circular Figure 73 Culvert Capacity 43 x 68Inch Horizontal Elliptical Equivalent 54Inch Circular Figure 74 Culvert Capacity 48 x 76Inch Horizontal Elliptical Equivalent 60Inch Circular Figure 75 Culvert Capacity 53 x 83Inch Horizontal Elliptical Equivalent 66Inch Circular Figure 76 Culvert Capacity 58 x 91Inch Horizontal Elliptical Equivalent 72Inch Circular Figure 77 Culvert Capacity 63 x 98Inch Horizontal Elliptical Equivalent 78Inch Circular Figure 78 Culvert Capacity 68 x 106Inch Horizontal Elliptical Equivalent 84Inch Circular Figure 79 Culvert Capacity 72 x 113 Inch Horizontal Elliptical Equivalent 90Inch Circular Figure 80 Culvert Capacity 77 x 121Inch Horizontal Elliptical Equivalent 96Inch Circular Figure 81 Culvert Capacity 82 x 128Inch Horizontal Elliptical Equivalent 102Inch Circular Figure 82 Culvert Capacity 87 x 136Inch Horizontal Elliptical Equivalent 108Inch Circular Figure 83 Culvert Capacity 92 x 143Inch Horizontal Elliptical Equivalent 114Inch Circular Figure 84 Culvert Capacity 97 x 151 Inch Horizontal Elliptical Equivalent 120Inch Circular Figure 85 Culvert Capacity 106 x 166Inch Horizontal Elliptical Equivalent 132Inch Circular
8 Index of Contents xiii Figure 86 Culvert Capacity 116 x 180Inch Horizontal Elliptical Equivalent 144Inch Circular Figure 87 Culvert Capacity 11 x 18Inch Arch Equivalent 15Inch Circular Figure 88 Culvert Capacity 13 x 22Inch Arch Equivalent 18Inch Circular Figure 89 Culvert Capacity 15 x 26Inch Arch Equivalent 21Inch Circular Figure 90 Culvert Capacity 18 x 28Inch Arch Equivalent 24Inch Circular Figure 91 Culvert Capacity 22 x 36Inch Arch Equivalent 30Inch Circular Figure 92 Culvert Capacity 27 x 44Inch Arch Equivalent 36Inch Circular Figure 93 Culvert Capacity 31 x 51 Inch Arch Equivalent 42Inch Circular Figure 94 Culvert Capacity 36 x 58Inch Arch Equivalent 48Inch Circular Figure 95 Culvert Capacity 40 x 65Inch Arch Equivalent 54Inch Circular Figure 96 Culvert Capacity 45 x 73Inch Arch Equivalent 60Inch Circular Figure 97 Culvert Capacity 54 x 88Inch Arch Equivalent 72Inch Circular Figure 98 Culvert Capacity 62 x 102Inch Arch Equivalent 84Inch Circular Figure 99 Culvert Capacity 72 x 115Inch Arch Equivalent 90Inch Circular Figure 100 Culvert Capacity 77 x 122Inch Arch Equivalent 96Inch Circular Figure 101 Culvert Capacity 87 x 138Inch Arch Equivalent 108Inch Circular Figure 102 Culvert Capacity 97 x 154Inch Arch Equivalent 120Inch Circular Figure 103 Culvert Capacity 106 x 169Inch Arch Equivalent 132Inch Circular Figure 104 Culvert Capacity 3 x 2Foot Box Equivalent 33Inch Circular Figure 105 Culvert Capacity 3 x 3Foot Box Equivalent 39Inch Circular Figure 106 Culvert Capacity 4 x 2Foot Box Equivalent 36Inch Circular Figure 107 Culvert Capacity 4 x 3Foot Box Equivalent 42Inch Circular Figure 108 Culvert Capacity 4 x 4Foot Box Equivalent 54Inch Circular Figure 109 Culvert Capacity 5 x 3Foot Box Equivalent 48Inch Circular Figure 110 Culvert Capacity 5 x 4Foot Box Equivalent 60Inch Circular Figure 111 Culvert Capacity 5 x 5Foot Box Equivalent 66Inch Circular Figure 112 Culvert Capacity 6 x 3Foot Box Equivalent 57Inch Circular
9 xiv Concrete Pipe Design Manual Figure 113 Culvert Capacity 6 x 4Foot Box Equivalent 66Inch Circular Figure 114 Culvert Capacity 6 x 5Foot Box Equivalent 75Inch Circular Figure 115 Culvert Capacity 6 x 6Foot Box Equivalent 81Inch Circular Figure 116 Culvert Capacity 7 x 4Foot Box Equivalent 71Inch Circular Figure 117 Culvert Capacity 7 x 5Foot Box Equivalent 79Inch Circular Figure 118 Culvert Capacity 7 x 6Foot Box Equivalent 87Inch Circular Figure 119 Culvert Capacity 7 x 7Foot Box Equivalent 94Inch Circular Figure 120 Culvert Capacity 8 x 4Foot Box Equivalent 76Inch Circular Figure 121 Culvert Capacity 8 x 5Foot Box Equivalent 85Inch Circular Figure 122 Culvert Capacity 8 x 6Foot Box Equivalent 93Inch Circular Figure 123 Culvert Capacity 8 x 7Foot Box Equivalent 101Inch Circular Figure 124 Culvert Capacity 8 x 8Foot Box Equivalent 108Inch Circular Figure 125 Culvert Capacity 9 x 5Foot Box Equivalent 90Inch Circular Figure 126 Culvert Capacity 9 x 6Foot Box Equivalent 99Inch Circular Figure 127 Culvert Capacity 9 x 7Foot Box Equivalent 107Inch Circular Figure 128 Culvert Capacity 9 x 8Foot Box Equivalent 114Inch Circular Figure 129 Culvert Capacity 9 x 9Foot Box Equivalent 121Inch Circular Figure 130 Culvert Capacity 10 x 5Foot Box Equivalent 94inch Circular Figure 131 Culvert Capacity 10 x 6Foot Box Equivalent 104Inch Circular Figure 132 Culvert Capacity 10 x 7Foot Box Equivalent 112Inch Circular Figure 133 Culvert Capacity 10 x 8Foot Box Equivalent 120Inch Circular Figure 134 Culvert Capacity 10 x 9Foot Box Equivalent 128Inch Circular Figure 135 Culvert Capacity 10 x 10Foot Box Equivalent 135Inch Circular Figure 136 Culvert Capacity 11 x 4Foot Box Equivalent 88Inch Circular Figure 137 Culvert Capacity 11 x 6Foot Box Equivalent 109Inch Circular Figure 138 Culvert Capacity 11 x 8Foot Box Equivalent 126Inch Circular Figure 139 Culvert Capacity 11 x 10Foot Box Equivalent 141Inch Circular Figure 140 Culvert Capacity 11 x 11Foot Box Equivalent 148Inch Circular Figure 141 Culvert Capacity 12 x 4Foot Box Equivalent 92Inch Circular Figure 142 Culvert Capacity 12 x 6Foot Box Equivalent 113Inch Circular Figure 143 Culvert Capacity 12 x 8Foot Box Equivalent 131Inch Circular Figure 144 Culvert Capacity 12 x 10Foot Box Equivalent 147Inch Circular Figure 145 Culvert Capacity 12 x 12Foot Box Equivalent 161Inch Circular Figure 146 Essential Features of Types of Installations Figure 147 Earth Loads on Jacked or Tunneled Installations Sand and Gravel Trench Term Figure 148 Earth Loads on Jacked or Tunneled Installations Sand and Gravel Cohesion Term Figure 149 Earth Loads on Jacked or Tunneled Installations Saturated Top Soil Trench Term Figure 150 Earth Loads on Jacked or Tunneled Installations Saturated Top Soil Cohesion Term Figure 151 Earth Loads on Jacked or Tunneled Installations Ordinary Clay Trench Term
10 Index of Contents xv Figure 152 Figure 153 Figure 154 Figure 155 Figure 156 Figure 157 Figure 158 Figure 159 Figure 160 Figure 161 Figure 162 Figure 163 Figure 164 Figure 165 Figure 166 Figure 167 Figure 168 Figure 169 Figure 170 Figure 171 Figure 172 Figure 173 Earth Loads on Jacked or Tunneled Installations Ordinary Clay Cohesion Term Earth Loads on Jacked or Tunneled Installations Saturated Clay Trench Term Earth Loads on Jacked or Tunneled Installations Saturated Clay Cohesion Term Sand and Gravel (Fill Height = 2 to 10 ft) Sand and Gravel (Fill Height = 10 to 50 ft) Saturated Top Soil (Fill Height = 2 to 10 ft) Saturated Top Soil (Fill Height = 10 to 50) Ordinary Clay (Fill Height = 2 to 10 ft) Ordinary Clay (Fill Height = 10 to 50) Saturated Clay (Fill Height = 2 to 10 ft) Saturated Clay (Fill Height = 10 to 50 ft) Sand and Gravel (Fill Height = 2 to 10 ft) Sand and Gravel (Fill Height = 10 to 50 ft) Saturated Top Soil (Fill Height = 2 to 10 ft) Saturated Top Soil (Fill Height = 10 to 50 ft) Ordinary Clay (Fill Height = 2 to 10 ft) Ordinary Clay (Fill Height = 10 to 50 ft) Saturated Clay (Fill Height = 2 to 10 ft) Saturated Clay (Fill Height = 10 to 50 ft) Trench Backfill Loads on Arch Pipe Sand and Gravel (Fill Height = 2 to 10 ft) Trench Backfill Loads on Arch Pipe Sand and Gravel (Fill Height = 10 to 50 ft) Trench Backfill Loads on Arch Pipe Saturated Top Soil (Fill Height = 2 to 10 ft)
11 xvi Concrete Pipe Design Manual Figure 174 Figure 175 Figure 176 Figure 177 Figure 178 Figure 179 Figure 180 Figure 181 Figure 182 Figure 183 Figure 184 Figure 185 Figure 186 Figure 187 Figure 188 Figure 189 Figure 190 Figure 191 Figure 192 Figure 193 Figure 194 Figure 195 Trench Backfill Loads on Arch Pipe Saturated Top Soil (Fill Height = 10 to 50 ft) Trench Backfill Loads on Arch Pipe Ordinary Clay (Fill Height = 2 to 10 ft) Trench Backfill Loads on Arch Pipe Ordinary Clay (Fill Height = 10 to 50 ft) Trench Backfill Loads on Arch Pipe Saturated Clay (Fill Height = 2 to 10 ft) Trench Backfill Loads on Arch Pipe Saturated Clay (Fill Height = 10 to 50 ft) Embankment Fill Loads on Vertical Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Vertical Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Vertical Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Vertical Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Vertical Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Horizontal Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Horizontal Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Horizontal Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Horizontal Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Horizontal Elliptical Pipe Positive Projecting r sd p = Embankment Fill Loads on Arch Pipe Positive Projecting r sd p = Embankment Fill Loads on Arch Pipe Positive Projecting r sd p = Embankment Fill Loads on Arch Pipe Positive Projecting r sd p = Embankment Fill Loads on Arch Pipe Positive Projecting r sd p = Embankment Fill Loads on Arch Pipe Positive Projecting r sd p = Embankment Fill Loads on Circular Pipe Negative Projecting p = 0.5 r s d = Embankment Fill Loads on Circular Pipe Negative Projecting p = 0.5 r sd =
12 Index of Contents xvii Figure 196 Embankment Fill Loads on Circular Pipe Negative Projecting p = 0.5 r sd = Figure 197 Embankment Fill Loads on Circular Pipe Negative Projecting p = 0.5 r sd = Figure 198 Embankment Fill Loads on Circular Pipe Negative Projecting p = 0.5 r sd = Figure 199 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.0 r sd = Figure 200 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.0 r sd = Figure 201 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.0 r sd = Figure 202 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.0 r sd = Figure 203 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.0 r sd = Figure 204 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.5 r sd = Figure 205 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.5 r sd = Figure 206 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.5 r sd = Figure 207 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.5 r sd = Figure 208 Embankment Fill Loads on Circular Pipe Negative Projecting p = 1.5 r sd = Figure 209 Embankment Fill Loads on Circular Pipe Negative Projecting p = 2.0 r sd = Figure 210 Embankment Fill Loads on Circular Pipe Negative Projecting p = 2.0 r sd = Figure 211 Embankment Fill Loads on Circular Pipe Negative Projecting p = 2.0 r sd = Figure 212 Embankment Fill Loads on Circular Pipe Negative Projecting p = 2.0 r sd = Figure 213 Embankment Fill Loads on Circular Pipe Negative Projecting p = 2.0 r sd = Figure 214 Load Coefficient Diagram for Trench Installations APPENDIX A Table A1 Square Roots of Decimal Number (S 1/2 in Manning s Formula) Table A2 ThreeEighths Powers of Numbers Table A3 TwoThirds Powers of Numbers Table A4 EightThirds Powers of Numbers Table A5 Square Roots and Cube Roots of Numbers
13 xviii Concrete Pipe Design Manual Table A6 Decimal Equivalents of Inches and Feet Table A7 Various Powers of Pipe Diameters Table A8 Areas of Circular Sections (Square Feet) Table A9 Areas of Circular Segments Table A10 Area, Wetted Perimeter and Hydraulic Radius of Partially Filled Circular Pipe Table A11 Headwater Depth for Circular Pipe Culverts with Inlet Control Table A12 Trigonometric Formulas Table A13 Properties of the Circle Table A14 Properties of Geometric Sections Table A15 Properties of Geometric Sections and Structural Shapes Table A16 Four Place Logarithm Tables Table A17 Frequently Used Conversion Factors Table A18 Metric Conversion of Diameter Table A19 Metric Conversion of Wall Thickness APPENDIX B Marston/Spangler Design Procedure Types of Installations Trench Positive Projecting Embankment Negative Projecting Embankment Selection of Bedding Determination of Bedding Factor Application of Factor of Safety Selection of Pipe Strength Example Problems B1 Trench Installation B2 Positive Projecting Embankment Installation B3 Negative Projecting Embankment Installation B4 Wide Trench Installation B5 Positive Projecting Embankment Installation Vertical Elliptical Pipe B6 Highway Live Load APPENDIX B  TABLES AND FIGURES CONDENSED BIBLIOGRAPHY
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