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LRFD Design of Precast Concrete Pipe
Josh Beakley – ACPA Director of Technical ServicesSeptember 16th 2010September 16 , 2010
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Design Options12 10 Reinforced Concrete Pipe12.10 Reinforced Concrete Pipe• 12.10.1• “The structural design of the type of
pipes indicated above may proceed p p y pby either of two methods.”
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12 10 Reinforced Concrete Pipe12.10 Reinforced Concrete Pipe• “The direct design method at the g
strength limit state as specified in Article 12.10.4.2 or
• The indirect design method at the service limit state as specified in Article 12.10.4.3”
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Indirect Design MethodIndirect Design Method
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Direct Design per AASHTO Section 12Section 12
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Load FactorsLoad Load Factor
Standard LRFDMinimum MaximumMinimum Maximum
Dead 1.3 0.90 1.25Water 1.3 1.0 1.0E th V ti l 1 3 0 90 1 30Earth – Vertical 1.3 0.90 1.30Earth -Horizontal
1.3 0.90 1.35
Live 1.3 x 1.67 = 2.17 0.0 1.75*
* A multiple presence factor is included in the total load A multiple presence factor is included in the total load
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Per AASHTO LRFD
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Per AASHTO Standard Specifications
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Reason for Differences Between LRFD and Standard SpecificationLRFD and Standard Specification Allowable Fill Heights• Increase in live load concentration 1.15H versus 1.75H distribution
• Increase in impact factor 0.33 to 0 at 8 feet versus 0.30 to 0 at 3
feet• C-wall used in the LRFD tables
versus B-wall in the Standard tables
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LRFD Fill Height Example
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Gi enGiven:• Di = 48 in.i
• t = D/12 + 1.75= 5 75 in5.75 in.
• Do = Di + 2t= 59 5 in= 59.5 in.
• H = 5 ft.120 f• w = 120 pcf
• Type 2 Installation
Soil Load
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AASHTO LRFD 12 10 2 1AASHTO LRFD 12.10.2.1• WE = Fe w Bc HE e c Fe = Soil-structure Interaction Factor w = unit weight of soil (pcf)u t e g t o so (pc ) Bc = outside diameter of pipe (ft) H = height of fill over the pipe (ft)H height of fill over the pipe (ft)
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AASHTO LRFD 12 10 2 1AASHTO LRFD 12.10.2.1• “Standard installations for both
embankments and trenches shall be designed for positive projection, embankment loading conditions where Fe shall be taken as the vertical arching factor VAF specifiedvertical arching factor, VAF, specified in Table 12.10.2.1-3 for each type of standard installation ”standard installation.
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AASHTO LRFD 12.10.2.1
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Embankment InstallationEmbankment Installation
FrictionalSoil Prism
ForcesPrism
N t l G dNatural Ground
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Calculate soil load on the pipe:Calculate soil load on the pipe:
• Prism loadPrism load PL = w[H + (Do(4 –π))/96] Do/12 PL = 3292 lbs/ftPL 3292 lbs/ft
• Vertical Arching Factor Fe = 1 4 Fe = 1.4
• Soil loadW F * PL WE = Fe * PL WE = 4608 lbs/ft
Fluid Load
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AASHTO LRFD 12.10.2.2 – Pipe Fluid WeightFluid Weight• “The unfactored weight of fluid, WF, in g , F,
the pipe shall be considered in design based on a fluid weight of 62.4 lb./ft3, unless otherwise specified.”
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Calculate fluid load in the pipe:U it i ht f t• Unit weight of water γw = 62.4 pcf
• Volume of water V = π[Di/(2*12)] 2 * 1 V = 12.56
• Fluid load WF = γw * V WF = 784.1 lbs/ftF
Live Load
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AASHTO HL-93 Load
• Per Article 3.6.1.2.1, vehicular live ,loading on roadways or bridges shall consist of a combination of the: Design truck or design tandem Design lane load
• Per article 3.6.1.2.2, Design truck = 32 kip axles
• Per article 3.6.1.2.2, Design tandem = 25 kip axleskip axles
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AASHTO LRFD 3.6.1.2.5 – Tire Contact AreaContact Area• “The tire contact area of a wheel
consisting of one or two tires shall be assumed to be a single rectangle, whose width is 20.0 in. and whose length is 10.0 in.”
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27Calculate the Live Load Distribution through Pipe andDistribution through Pipe and Soil
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Critical Live Load ParametersCritical Live Load Parameters
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Live Load SpreadLive Load Spread
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32Live Load Distribution for Select Granular FillFill
• For a vehicle traveling perpendicular:2 05 1 15D H 5 5 2.05 – 1.15Do < H < 5.5
From calculation above P 32 000 lb• P = 32,000 lbs
• Spread a = a + 4 + 1.15H • Spread a = 20/12 + 4 + 1 15(5 0 ft ) = 11 42 ftSpread a = 20/12 + 4 + 1.15(5.0 ft.) = 11.42 ft• Spread b = b + 1.15 H• Spread b = 10/12 + 1.15(5.0 ft.) = 6.58 ft.
Spread wheel load area at outside top of pipe• A = Spread a * Spread b =11.42 ft * 6.58 ft• A = 75.18 ft2
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Pressure at Top of Pipe
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Calculate Average Pressure IntensityIntensity• Impact Factorp IM = [33 (1 - .125(5 ft.)] / 100 = .124
• Average pressure intensity w = [P (1 + IM)] / Aw [P (1 + IM)] / A w = [32,000 lbs( 1+ .124)] / 75.18 ft2
w = 478 4 lbs/ ft2w = 478.4 lbs/ ft
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Live Load Above the PipeLive Load Above the Pipe
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Total Live Load Calculation
• Dimension of area parallel to longitudinal axis of pipe L = Spread a = 11 42 ft L = Spread a = 11.42 ft.
• Lesser of the outside horizontal span, Do, or spread wheel load perpendicular to longitudinal axis of pipeaxis of pipe SL = Do = 4.96 ft.
• Total Live Load WT = wLSL = 478.4 lbs/ft * 11.42 ft. * 4.96 ft. WT = 27,089 lbs.
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Distribution of Live Load Through the Pipest but o o e oad oug t e pe
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Total Live Load per Linear Foot ota e oad pe ea ootCalculation
Eff ti ti l th f i• Effective supporting length of pipe Le = L + 1.75(.75*Ro) Le = 11.42 ft. + 1.75(.75 * 4.96 ft.) =
17.93 ft.
• Total live load in pounds per feet WL = WT / Le = 27089 lbs. / 17.93 ft. WL = 1,511 lbs./ft.
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D-Load Equation
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Extra Safety Factor for Type 1 Installations
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Extra Safety Factor for Type 1 Installations
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E th L d B ddi F tEarth Load Bedding Factor
Interpolate for 48 in pipe BFE = 2.867
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Live Load Bedding Factor
For 48 in pipe @ 5.0 ft of cover BFLL = 2.2
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Calculate the D-load per Equation 12 10 4 3 1 112.10.4.3.1-1
• D0.01 = (12/D)*{[(WE + WF) / BFE] + [WL / 0.01 ( ) { ( E F) FE LBFLL]}
• D0.01 = (12/48)*{[( 4,608 + 784.14) / 2.867] + [1,511 /2.2]}
• D0.01 = 641.9 lbs./ft./ft.
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Per AASHTO LRFD
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Direct Design of Concrete Pipe Using PIPECARPIPECAR
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12.4.2.7 – Yield stress limited to 65 ksi for smooth wire and 70 ksi for deformed welded wire fabric
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5.4.2.1 – concrete strength limited to 10 ksi
5151
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WE= 4608 lbs/ft
Indirect Design Method
WE 4608 lbs/ft
WF = 784.1 lbs/ft
W 1 511 lb /ftwww.concrete-pipe.org
WL = 1,511 lbs./ft.
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48 Inch Class II (1000 lbs/ft/ft) Pipe – C-wall( ) p
Asi = 0.14 SQ. IN./FTAso = 0.08 SQ. IN./FT
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The End
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