Direct Design Olander vs Heger Margarita Takou Josh

Direct Design Olander vs. Heger Margarita Takou Josh Beakley Pipe School January 6 th, 2017

Outline • Direct Design Method and Steps • Stress Distribution Methods • Olander • Example Low Head Pressure Pipe • Example Gravity Pipe • Heger • Example Low Head Pressure Pipe • Example Gravity Pipe • Comparison Olander vs. Heger • Conclusion 2 Rigid Rugged Resilient

Direct Design Method • Based on: o Pipe Material Properties o Actual in Site Installation Conditions o Total Load Applied on Pipe • Aim to calculate: Forces and Moments applied to the pipe Pipe Requirements to Withstand the Applied Forces 3 Rigid Rugged Resilient

Direct Design Method • Loads applied o Earth Load o Internal Fluid Load o Pipe Weight o Surcharge Load o Live Load • Calculate Forces and Moments applied to the Pipe o Uniform Load System - Paris o Radial Load System - Olander o SIDD Pressure Distribution - Heger 4 Rigid Rugged Resilient Traditional Models Currently Used

Direct Design Method • Uniform Load System - Paris o Rational Approximation o Uniformly distributed vertical and horizontal component of pressure o First proposed by J. M. Paris in the early 1920’s 5 Rigid Rugged Resilient

Direct Design Method • Radial Load System - Olander o Pressure acts normal to the pipe surface o Calculations based on H. C. Olander in 1950 based on trigonometric functions 6 Rigid Rugged Resilient

Moment Coefficient Olander Earth Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 7 Rigid Rugged Resilient

Thrust Coefficient Olander Earth Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 8 Rigid Rugged Resilient

Shear Coefficient Olander Earth Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 9 Rigid Rugged Resilient

Moment Coefficient Olander Dead Load (Self Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 10 Rigid Rugged Resilient

Thrust Coefficient Olander Dead Load (Self Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 11 Rigid Rugged Resilient

Shear Coefficient Olander Dead Load (Self Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 12 Rigid Rugged Resilient

Moment Coefficient Olander Fluid Load (Water Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 13 Rigid Rugged Resilient

Thrust Coefficient Olander Fluid Load (Water Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 14 Rigid Rugged Resilient

Shear Coefficient Olander Fluid Load (Water Weight) Pressure Distribution Angle θ (deg) * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 15 Rigid Rugged Resilient

Direct Design Method • Standard Installation direct design Pressure Distribution o Values obtained from long range research initiated by ACPA in the 1970’s o Referred to as the Heger Pressure Distribution, since he did major work on this research 16 Rigid Rugged Resilient

Heger Pressure Distribution Location Invert Crown Springline 90 o Critical Shear Invert θv=12 o Critical Shear Crown θv=159 o 17 Rigid Rugged Resilient Type 2 Load Type Wp We Wf WL 1 WL 2 Wp We Wf WL 1 Cmi 0. 227 0. 122 0. 111 0. 107 0. 189 0. 079 0. 094 0. 062 0. 08 0. 241 -0. 09 -0. 7 -0. 078 -0. 16 Coefficient Cni 0. 077 0. 169 -0. 437 0. 205 -0. 035 -0. 077 0. 126 -0. 204 0. 171 0. 035 0. 249 0. 5 -0. 068 0. 513 0. 5 0. 177 0. 218 -0. 386 0. 256 -0. 05 0. 185 -0. 181 0. 205 cvi 0. 437 0. 198 0. 193 0. 188 0. 088 0. 136 0. 074 0. 137

Moment coefficient - invert Soil 0. 25 0. 2 0. 15 0. 1 0. 05 0 Type 1 Type 2 Type 3 Type 4 180 120 90 45 Soil Fluid Self 0. 2 0. 175 0. 125 0. 1 0. 075 0. 025 0 0. 25 0. 2 0. 15 0. 1 0. 05 0 Type 1 Type 2 Type 3 Type 4 Self 18 Rigid Rugged Resilient 180 120 90 45 Type 1 Type 2 Type 3 Type 4 Fluid 180 120 90 45

Thrust Coefficient - invert Soil 0. 4 0. 3 0. 2 0. 1 0 Type 1 Type 2 Type 3 Type 4 180 120 90 45 Soil Self 0. 35 0. 3 0. 25 0. 2 0. 15 0. 1 0. 05 0 0. 5 0. 4 0. 3 0. 2 0. 1 0 Type 1 Type 2 Type 3 Type 4 Self 19 Fluid Rigid Rugged Resilient 180 120 90 45 Type 1 Type 2 Type 3 Type 4 Fluid 180 120 90 45

Shear coefficient Heger vs. Olander ASTM C 361 Soil 0. 4 0. 3 0. 2 0. 1 0 Type 1 Type 2 Type 3 Type 4 180 120 90 45 Shear design performed in a section with maximum shear due to all loads Soil Self Fluid 0. 5 0. 4 0. 3 0. 2 0. 1 0 0 Type 1 Type 2 Type 3 Type 4 Self 20 Rigid Rugged Resilient 180 120 90 45 Type 1 Type 2 Type 3 Type 4 Fluid 180 120 90 45

Shear coefficient Heger vs. Olander (AASHTO or ASCE) Soil Shear design performed at the critical section where M/V*d=3 0. 4 0. 3 0. 2 0. 1 0 Type 1 Type 2 Type 3 Type 4 180 120 90 45 Soil Fluid Self 0. 4 0. 5 0. 4 0. 3 0. 2 0. 1 0 0 Type 1 Type 2 Type 3 Type 4 Self 21 Rigid Rugged Resilient 180 120 90 45 Type 1 Type 2 Type 3 Type 4 Fluid 180 120 90 45

Direct Design Method • Performance Modes o Flexure • Produced at locations with tension at the inside (invert and crown) and at the outside of the pipe (springline) • Combined effect of moment and thrust o Concrete Compression • Produced when the compressive strain in the concrete will exceed the maximum compression strain limit o Radial Tension • Developed in the concrete when reinforcement near the inside of the pipe wall is stressed in tension which is produced by the combined effect of moment and shear o Diagonal Tension (Shear) • Maximum shear located: at a section with maximum shear due to all the loads, or at a section with M/V*d=3 - strength reduced by the presence and severity of flexural cracking o Crack Control • An average maximum crack width of 0. 01 inch 22 Rigid Rugged Resilient

Direct Design Method Shear 23 Rigid Rugged Resilient Radial Tension

Gravity Pipe 24 Rigid Rugged Resilient

Example – Gravity Pipe • Pipe Diameter : 84 inch • Wall thickness (B-Wall): 8 inch • Depth: 20 feet • Type 2 Installation • Steel Yielding Stress: fy = 65000 psi • Concrete Compressive Strength: f`c = 5000 psi 25 Rigid Rugged Resilient

Design Steps o Define As based on the tensile yield strength limit o Check Radial Tension o Check Concrete Compression – Maximum Steel Area o Check Crack Control o Check Shear o Modify design if any strength limit is exceeded o If required, design stirrup reinforcement 26 Rigid Rugged Resilient

Heger Pressure Distribution Load cases 27 Moment Coefficient at Invert Thrust Coefficient at Invert Shear Thrust Pipe Weight Cmp = 0. 227 Cnp = 0. 077 cvp = 0. 437 cvnp = 0. 177 Earth Load Cme = 0. 122 Cne = 0. 169 cve = 0. 198 cvne = 0. 218 Fluid Load Cmf = 0. 111 Cnf = -0. 437 cvf = 0. 193 cvnf = -0. 386 Rigid Rugged Resilient Coefficient at 12. 3 o

Example – Gravity Pipe • Applied Loads o Weight of Pipe: 2, 410 lbs/ft o Weight of Water: 2, 400 lbs/ft o Weight of Soil: 28, 200 lbs/ft 28 Rigid Rugged Resilient

Example – Gravity Pipe Service Load Moment and Thrust M = [cmp x Wp + cme x We + cmf x Wf] [(Di + t)/2] N = [cnp x Wp + cne x We + cnf x Wf] Factored Moment and Thrust M u = [cmp x W p x DC + cme x W e x EV x η r + cmf x W f x LW] [(Di + t)/2] N = [cnp x W p + cne x W e + cnf x W f ] 29 Rigid Rugged Resilient

Example – Gravity Pipe Factored Thrust for Checking Tension in Steel Nu = 1. 0 x N Factored Thrust for Checking Compression in Concrete Nuc = [cnp x Wp x DC + cne x We x EV x ηr + cnf x Wf x LW] 30 Rigid Rugged Resilient

Example – Gravity Pipe Factored Shear and Thrust for Shear Check Vu= [cvp x Wp x DC + cve x We x EV x ηr + cvf x Wf x LW] Nuv = [cvnp x Wp + cvne x We + cvnf x Wf ] 31 Rigid Rugged Resilient

Heger – 84” pipe – 20 ft Fill – Gravity Pipe Design Values 32 Ms = 195 kips-in/lin. ft Service Load Moment Ns = 3. 90 kips/lin. ft Service Load Thrust Mu = 250 kips-in/lin. ft Factored Moment Nu = 3. 90 kips/lin. ft Check tension in steel Nuc = 5. 38 kips/lin. ft Check compression in concrete Vu = 9. 04 kips/lin. ft Factored Shear at 12. 3 degrees from invert Nvu = 7. 60 kips/lin. ft Thrust at shear location Rigid Rugged Resilient

Summary Heger Design Values 33 Flexural Steel Area 0. 565 in 2 Max Radial Tension Area 0. 632 in 2 Max Steel Area for Concrete Compression 1. 72 in 2 Crack Control Steel Area 0. 849 in 2 Shear Vu = 9. 08 kip/ft, Vn = 9. 42 kip/ft Index = 9. 08/9. 42 = 0. 96 Required Steel Area 0. 849 in 2 Stirrups? No stirrups Rigid Rugged Resilient Governing

Olander – 84” pipe – 20 ft Fill – Gravity Pipe Olander Pressure Distribution Load cases Moment Coefficient at Invert Thrust Coefficient at Invert Pipe Weight Cmp = 0. 17 Earth Load Fluid Load Bedding factors: 34 Rigid Rugged Resilient Coefficient at max shear Shear Thrust Cnp = 0. 15 cvp = 0. 38 cvnp = 0. 22 Cme = 0. 12 Cne = 0. 33 cve = 0. 28 cvne = 0. 42 Cmf = 0. 12 Cnf = -0. 27 cvf = 0. 26 cvnf = -0. 27 *Pipe weight 450 Max shear location: *Pipe weight 20 o *Earth Load and Fluid Load 900 *Earth Load and Fluid Load 33 o

Olander – 84” pipe – 20 ft Fill – Gravity Pipe Design Values Ms = 188 kips-in/lin. ft Ns = 9. 02 kips/lin. ft Service Load Thrust Mu = 239 kips-in/lin. ft Factored Moment Nu = 9. 02 kips/lin. ft Check tension in steel Nuc = 11. 90 kips/lin. ft Check compression in concrete Vu = 12. 04 kips/lin. ft Shear @ max shear section Nvu = 15. 42 kips/lin. Ft 35 Service Load Moment Rigid Rugged Resilient Thrust @ max shear location

Summary Olander Design Values 36 Flexural Steel Area 0. 484 in 2 Max Radial Tension Area 0. 632 in 2 Max Steel Area for Concrete Compression 1. 65 in 2 Crack Control Steel Area 0. 656 in 2 Shear Vu = 12. 04 kip/ft, Vn = 8. 62 kip/ft Index = 12. 04 / 8. 62 = 1. 39 Required Steel Area 0. 656 in 2 Stirrups? Yes Rigid Rugged Resilient Governing

Olander – 84” pipe – 20 ft Fill – Gravity Pipe Olander Pressure Distribution Load cases Moment Coefficient at Invert Thrust Coefficient at Invert Pipe Weight Cmp = 0. 17 Earth Load Fluid Load Bedding factors: 37 Rigid Rugged Resilient Coefficient at Mnu/Vu*d=3 Shear Thrust Cnp = 0. 15 cvp = 0. 29 cvnp = 0. 17 Cme = 0. 12 Cne = 0. 33 cve = 0. 19 cvne = 0. 42 Cmf = 0. 12 Cnf = -0. 27 cvf = 0. 18 cvnf = -0. 27 *Pipe weight 450 Shear @ section where Mnu/vu*d = 3 *Earth Load and Fluid Load 900 *Pipe weight 11 o *Earth Load and Fluid Load 16 o

Olander – 84” pipe – 20 ft Fill – Gravity Pipe Design Values Ms = 188 kips-in/lin. ft Ns = 9. 02 kips/lin. ft Service Load Thrust Mu = 239 kips-in/lin. ft Factored Moment Nu = 9. 02 kips/lin. ft Nuc = 11. 90 kips/lin. ft Vu = 8. 27 kips/lin. ft Nvu = 15. 26 kips/lin. Ft 38 Service Load Moment Rigid Rugged Resilient Check tension in steel Check compression in concrete Shear @ max shear section Thrust @ max shear location

Summary Olander Design Values 39 Flexural Steel Area 0. 484 in 2 Max Radial Tension Area 0. 632 in 2 Max Steel Area for Concrete Compression 1. 65 in 2 Crack Control Steel Area 0. 656 in 2 Shear Vu = 8. 27 kip/ft, Vn = 8. 62 kip/ft Index = 8. 27 / 8. 62 = 0. 96 Required Steel Area 0. 656 in 2 Stirrups? No Rigid Rugged Resilient Governing

Low-Head Pressure Pipe 40 Rigid Rugged Resilient

Example – Low Head Pressure Pipe • Pipe Diameter : 84 inch • Wall thickness (B-Wall): 8 inch • Depth: 20 feet • Internal Pipe Pressure: 50 ft • Steel Yielding Stress: fy = 65000 psi • Concrete Compressive Strength: f`c = 5000 psi 41 Rigid Rugged Resilient

Example – Low Head Pressure Pipe • Design Cases – ASTM C 361, Section X 2. 4 1. Internal Pressure Only 2. Earth Load, Pipe Weight, and Water Weight 3. External and Internal Loads Acting Together 42 Rigid Rugged Resilient

Olander – 84” pipe – 20 ft Fill – Internal Pressure Design Values Case 3 – External and Internal Load 43 Ms = 193 kips-in/lin. ft Service Load Moment Ns = -2. 1 kips/lin. ft Service Load Thrust Mu = 309 kips-in/lin. ft Factored Moment Nu = -2. 1 kips/lin. ft Check tension in steel Nuc = -7. 87 kips/lin. ft Check compression in concrete Vu = 11. 8 Shear @ section with maximum shear due to all loads Max(Vearth+Vwater+Vdead) Nvu =15. 6 Thrust @ section with maximum shear due to all loads Rigid Rugged Resilient

Summary Olander Design Values Case 3 – External and Internal Load Flexural Steel Area 0. 96 in 2 Max Radial Tension Area 0. 68 in 2 Max Steel Area for Concrete Compression 2. 00 in 2 Crack Control Steel Area 0. 96 in 2 Shear Required Steel Area Stirrups? 44 Rigid Rugged Resilient Governing Vu = 11. 8 kip/ft, Vn = 11. 7 kip/ft Index = 11. 8 / 11. 7 = 1. 01 0. 96 in 2 Yes

Heger – 84” pipe – 20 ft Fill – Internal Pressure Design Values 45 Ms = 195 kips-in/lin. ft Service Load Moment Ns = -7. 04 kips/lin. ft Service Load Thrust Mu = 311 kips-in/lin. ft Factored Moment Nu = -7. 04 kips/lin. ft Check tension in steel Nuc = -13. 1 kips/lin. ft Check compression in concrete Vu = 9. 7 kips/lin. ft Shear at 12. 3 degrees from invert Nvu = 7. 29 kips/lin. ft Thrust @ shear location Rigid Rugged Resilient

Summary Heger Design Values Flexural Steel Area 0. 93 in 2 Max Radial Tension Area 0. 63 in 2 Max Steel Area for Concrete Compression 1. 85 in 2 Crack Control Steel Area 1. 05 in 2 Shear 46 Vu = 9. 7 kip/ft, Vn = 9. 09 kip/ft Index = 9. 7 / 9. 09 = 1. 07 Required Steel Area 1. 05 Stirrups? Yes Rigid Rugged Resilient Governing

Comparison – Gravity Pipe 47 Olander (V @ max) Olander (V @ M/V*d=3) Heger Tensile Steel 0. 547 0. 639 Crack Control 0. 743 0. 963 Shear Index 1. 39 0. 95 0. 96 Stirrups Yes No No Rigid Rugged Resilient

Comparison – Low Head Pressure 48 Rigid Rugged Resilient Olander Heger Tensile Steel 0. 96 0. 93 Crack Control 0. 96 1. 05 Shear Index 1. 02 1. 07 Stirrups Yes

Discussion - Olander • Olander is a historically interesting method • Developed empirically before having finite elements analysis and mechanics • It has been widely used and it is still used for lowhead pressure pipes • Coefficient defined through the perimeter of the pipe 49 Rigid Rugged Resilient

Discussion - Heger • Developed by use of the finite element analysis • Defines coefficient in specific location through the pipe (invert, crown, springline) • Shear defined at the location Mnu/V*d=3 50 Rigid Rugged Resilient

Questions / Comments 51 Rigid Rugged Resilient

• AASHTO 12. 10. 4. 2 • General Section • It is simple (relatively) • It is safe • It is proven 52 Rigid Rugged Resilient Used for anything that is not included in ASTM C 76 • Higher strength pipe • Larger Diameters • Specific loads and load cases • When stirrup reinforcement is required

Direct Design • Reinforcement Proportions • Design more conservative for smaller diameter pipe • Asinvert=Asspringline • Location ASTM C 76 • Size Factor • Wire reinforcement 4” distance ? • Small diameter – from uncracked to first stage cracking to final failure • Larger diameter pipe – from uncracked to first stage cracking to second stage cracking to final failure 53 Rigid Rugged Resilient

Direct Design • Steel Reinforcement Properties • Based on the stress strain curve after the yield there is no plateau • Double Reinforcement • For smaller diameters the second cage may be in tension too because the compressive block is less than 1” in depth 54 Rigid Rugged Resilient

Direct Design – Benefits – Do we have any graph showing these results? ? We have tables • Size Factor: For diameters < 36 inches • Steel Reinforcement Properties: Diameters < 54 inches • Double Reinforcement: Diameters < 60 inches 55 Rigid Rugged Resilient

Direct Design AASHTO – Section 12 • Stress in the reinforcement are not based on the actual stress-strain law • Not accounting for the second layer of reinforcement • No moment redistribution 56 Rigid Rugged Resilient