Direct Design Olander vs. Heger

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

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

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

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

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

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

Olander Earth Pressure Distribution
Moment Coefficient Angle θ (deg) Positive moment when the moment creates compressive stress on the inside face of the pipe, and negative when creates tensile stress on the inside face of the pipe. * Reference: Wayne W. Smith “Stresses in Rigid Pipe”, Technical Publications, ASCE, 1978 Rigid Rugged Resilient

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

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

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

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

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

Heger Pressure Distribution
Type 2 Location Load Type Coefficient Cmi Cni cvi Invert Wp 0.227 0.077 We 0.122 0.169 Wf 0.111 -0.437 WL1 0.107 0.205 WL2 0.189 -0.035 Crown 0.079 -0.077 0.094 0.126 0.062 -0.204 0.08 0.171 0.241 0.035 Springline 90o -0.091 0.249 -0.09 0.5 -0.7 -0.068 -0.078 0.513 -0.16 Critical Shear Invert θv=12o 0.177 0.437 0.218 0.198 -0.386 0.193 0.256 0.188 Critical Shear Crown θv=159o -0.05 0.088 0.185 0.136 -0.181 0.074 0.137 Rigid Rugged Resilient

Moment coefficient - invert
Coefficient at invert Rigid Rugged Resilient

Thrust Coefficient - invert
Coefficient at invert Rigid Rugged Resilient

Shear coefficient Heger vs. Olander ASTM C361
Shear design performed in a section with maximum shear due to all loads ASTM C361 “Standard for Reinforced concrete low-head pressure pipe” – Shear design performed in a section with maximum shear due to all loads Rigid Rugged Resilient

Shear coefficient Heger vs. Olander (AASHTO or ASCE)
Shear design performed at the critical section where M/V*d=3 AASHTO section – the section shall be investigated for shear at a critical section taken where Mnu/Vu*d = 3, where Mnu is a thrust modified moment Rigid Rugged Resilient

Direct Design Method Performance Modes Flexure Concrete Compression
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 Concrete Compression Produced when the compressive strain in the concrete will exceed the maximum compression strain limit 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 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 Crack Control An average maximum crack width of 0.01 inch Rigid Rugged Resilient

Direct Design Method Shear Radial Tension Rigid Rugged Resilient

Gravity Pipe 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 = psi Concrete Compressive Strength: f`c = 5000 psi Rigid Rugged Resilient

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

Moment Coefficient at Invert Thrust Coefficient at Invert
Heger Pressure Distribution Load cases Moment Coefficient at Invert Thrust Coefficient at Invert Coefficient at 12.3o 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 = cvf = 0.193 cvnf = Rigid Rugged Resilient

Example – Gravity Pipe Applied Loads Weight of Pipe: 2,410 lbs/ft
Weight of Water: 2,400 lbs/ft Weight of Soil: 28,200 lbs/ft 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 Mu = [cmp x Wp x DC + cme x We x EV x ηr+ cmf x Wf x LW] [(Di + t)/2] N = [cnp x Wp + cne x We + cnf x Wf] Mean radius 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] 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 ] * Load Factors are omitted since they would give an unconservative result Rigid Rugged Resilient

Heger – 84” pipe – 20 ft Fill – Gravity Pipe
Design Values 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 Governing Design Values Flexural Steel Area 0.565 in2
Max Radial Tension Area 0.632 in2 Max Steel Area for Concrete Compression 1.72 in2 Crack Control Steel Area 0.849 in2 Shear Vu = 9.08 kip/ft, Vn = 9.42 kip/ft Index = 9.08/9.42 = 0.96 Required Steel Area Stirrups? No stirrups Governing Rigid Rugged Resilient

Olander – 84” pipe – 20 ft Fill – Gravity Pipe
Olander Pressure Distribution Load cases Moment Coefficient at Invert Thrust Coefficient at Invert Coefficient at max shear Shear Thrust Pipe Weight Cmp = 0.17 Cnp = 0.15 cvp = 0.38 cvnp = 0.22 Earth Load Cme = 0.12 Cne = 0.33 cve = 0.28 cvne = 0.42 Fluid Load Cmf = 0.12 Cnf = -0.27 cvf = 0.26 cvnf = -0.27 Bedding factors: *Pipe weight Max shear location: *Pipe weight 20o *Earth Load and Fluid Load *Earth Load and Fluid Load 33o Rigid Rugged Resilient

Design Values Ms = 188 kips-in/lin. ft Service Load Moment 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 = kips/lin. ft Check compression in concrete Vu = kips/lin. ft max shear section Nvu = kips/lin. Ft max shear location Rigid Rugged Resilient

Summary Olander Governing Design Values Flexural Steel Area 0.484 in2
Max Radial Tension Area 0.632 in2 Max Steel Area for Concrete Compression 1.65 in2 Crack Control Steel Area 0.656 in2 Shear Vu = kip/ft, Vn = 8.62 kip/ft Index = / 8.62 = 1.39 Required Steel Area Stirrups? Yes Governing Rigid Rugged Resilient

Olander Pressure Distribution Load cases Moment Coefficient at Invert Thrust Coefficient at Invert Coefficient at Mnu/Vu*d=3 Shear Thrust Pipe Weight Cmp = 0.17 Cnp = 0.15 cvp = 0.29 cvnp = 0.17 Earth Load Cme = 0.12 Cne = 0.33 cve = 0.19 cvne = 0.42 Fluid Load Cmf = 0.12 Cnf = -0.27 cvf = 0.18 cvnf = -0.27 Bedding factors: *Pipe weight 450 section where Mnu/vu*d = 3 *Earth Load and Fluid Load 900 *Pipe weight 11o *Earth Load and Fluid Load 16o Rigid Rugged Resilient

Design Values Ms = 188 kips-in/lin. ft Service Load Moment 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 = kips/lin. ft Check compression in concrete Vu = 8.27 kips/lin. ft max shear section Nvu = kips/lin. Ft max shear location Rigid Rugged Resilient

Summary Olander Governing Design Values Flexural Steel Area 0.484 in2
Max Radial Tension Area 0.632 in2 Max Steel Area for Concrete Compression 1.65 in2 Crack Control Steel Area 0.656 in2 Shear Vu = 8.27 kip/ft, Vn = 8.62 kip/ft Index = 8.27 / 8.62 = 0.96 Required Steel Area Stirrups? No Governing Rigid Rugged Resilient

Low-Head Pressure Pipe
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 = psi Concrete Compressive Strength: f`c = 5000 psi Rigid Rugged Resilient

Example – Low Head Pressure Pipe
Design Cases – ASTM C361, Section X2.4 Internal Pressure Only Earth Load, Pipe Weight, and Water Weight External and Internal Loads Acting Together Rigid Rugged Resilient

Olander – 84” pipe – 20 ft Fill – Internal Pressure
Design Values Case 3 – External and Internal Load 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 = kips/lin. ft Check compression in concrete Vu = 11.8 section with maximum shear due to all loads Max(Vearth+Vwater+Vdead) Nvu =15.6 section with maximum shear due to all loads Rigid Rugged Resilient

Design Values Case 3 – External and Internal Load
Summary Olander Design Values Case 3 – External and Internal Load Flexural Steel Area 0.96 in2 Max Radial Tension Area 0.68 in2 Max Steel Area for Concrete Compression 2.00 in2 Crack Control Steel Area Shear Vu = 11.8 kip/ft, Vn = 11.7 kip/ft Index = 11.8 / 11.7 = 1.01 Required Steel Area Stirrups? Yes Governing Rigid Rugged Resilient

Heger – 84” pipe – 20 ft Fill – Internal Pressure
Design Values Ms = 195 kips-in/lin. ft Service Load Moment Ns = kips/lin. ft Service Load Thrust Mu = 311 kips-in/lin. ft Factored Moment Nu = kips/lin. ft Check tension in steel Nuc = kips/lin. ft Check compression in concrete Vu = 9.7 kips/lin. ft Shear at 12.3 degrees from invert Nvu = kips/lin. ft shear location Rigid Rugged Resilient

Summary Heger Design Values Flexural Steel Area 0.93 in2
Max Radial Tension Area 0.63 in2 Max Steel Area for Concrete Compression 1.85 in2 Crack Control Steel Area 1.05 in2 Shear Vu = 9.7 kip/ft, Vn = 9.09 kip/ft Index = 9.7 / 9.09 = 1.07 Required Steel Area 1.05 Stirrups? Yes Governing Rigid Rugged Resilient

Comparison – Gravity Pipe
Olander max) Olander 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 Rigid Rugged Resilient

Comparison – Low Head Pressure
Olander Heger Tensile Steel 0.96 0.93 Crack Control 1.05 Shear Index 1.02 1.07 Stirrups Yes Rigid Rugged Resilient

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 low- head pressure pipes Coefficient defined through the perimeter of the pipe 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 Rigid Rugged Resilient

Questions / Comments Thank you! Rigid Rugged Resilient

Used for anything that is not included in ASTM C76
AASHTO General Section It is simple (relatively) It is safe It is proven Used for anything that is not included in ASTM C76 Higher strength pipe Larger Diameters Specific loads and load cases When stirrup reinforcement is required Simple – Relatively to other design sections. Section 12: one equation for flexure and one for shear. Easy for engineers who do other designs to perform pipe design Safe – same load factors as the rest structures use Proven – it has been used for several years Rigid Rugged Resilient

Direct Design Reinforcement Proportions Size Factor
Design more conservative for smaller diameter pipe Asinvert=Asspringline Location ASTM C76 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 Size Factor: there is no space for crack distribution in smaller diameter pipes due to the limitation of space. There is no area for moment distribution. Non reinforced pipe: after the first crack the pipe will not collapse but a hinge will be created at the crown which will allow for moment redistribution Highest moment at the crown initially – depends on the class of the pipe – the weight is added at the invert – depending on the weight of the pipe Rigid Rugged Resilient

Direct Design Steel Reinforcement Properties Double Reinforcement
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 Rigid Rugged Resilient

Direct Design – Benefits – Do we have any graph showing these results
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 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 Rigid Rugged Resilient

Direct Design Olander vs. Heger

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