appendix d.1 parametric study mathcad calculation...

Appendix D.1

Parametric Study MathCAD Calculation Sheets

MathCAD Example Templates for AASHTO Design Calculations

Table of Contents

Metal Arch AASHTO Design 20.1x9………………………………………………2

Metal Arch AASHTO Design 30.1x18……………………………………………..4

Metal Arch AASHTO Standard Design 20.1x9…………………………………… 6

Metal Arch AASHTO Standard Design 30.1x18………………………………….. 8

Metal Arch AASHTO Proposed Simple Equation 20.1x9………………………… 10

Metal Arch AASHTO Proposed Simple Equation 30.1x18……………………….. 13

Profile Wall 24” – CL85 AASHTO Design……………………………………….. 16

Profile Wall 24” – CL85 AASHTO Standard Design……………………………... 19

Profile Wall 24” – CL85 AASHTO Proposed Simple Equation…………………... 22

RCP AASHTO Design Type 1…………………………………………………….. 25

RCP AASHTO Standard Design Type 1…………………………………………...30

RCP AASHTO Proposed Simple Equation………………………………………... 35

CMP 24” AASHTO Design………………………………………………………...40

CMP 24” AASHTO Standard Design………………………………………………42

CMP 24” AASHTO Proposed Simple Equation…………………………………... 44

CONSULTING ENGINEERS2800 UNIVERSITY AVE SEMINNEAPOLIS, MN 55414

CNAPhone: (612) 379-8805

Fax: (612) 379-8160

CLIENT PROJECT: NCHRP

CALCULATION BY: GL DATE: 9/14/2007

APPROVED BY: CRN DATE: 9/14/2007

OBJECT : Metal Arch - AASHTO LRFD Design_20.1X9

SOURCE: AASHTO LRFD Bridge Design Specifications_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3

Define Variables and Input Design Values

w = unit weight of soil (pcf) w 120

H = Height of fill over pipe (ft.) H 2

S = Span (ft.) S 20.083

R = Rise (ft.) R 9.083

Ru = Upper rise (ft.) Ru 6.5

Rt = Top radius (ft.) Rt 13.083

top = Top angle (deg.) top 80

S/R = Span/ Rise Ratio SR

2.21

LL = total live load applied at surface (lb.) LL 16000

Wt = width of tire (in.) Wt 20

Lt = length of tire parallel to span of culvert (in) Lt 10

LLDF = rate of increase of load spread with increasing depth of fill

LLDF 1.15

whsp 6whsp = wheel spacing (ft.)

LFl 1.75LFl = live load factor

LFd 1.95LFd = dead load factor

SHEET 1 OF 2Page 2 of 46

Total Applied load Values

Soil Unit Weight

We = Crown load (lb/ft) We w H S We 4819.92

Wheel Unit Load (Live Load) (Service load)

Hint = Wheel interaction depth (ft.) Hint

whspWt

12LLDF

Hint 3.77

ALL = Distributed Area (ft2)ALL

Wt

12LLDF H

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H

Lt

12LLDF H H Hintif

ALL 12.43

WLL = live load pressure (lb/ft2) WLLLLALL

H Hintif

2 LLALL

H Hintif WLL 1287.32

Lt.gov = Select controlling load length (ft.) Lt.govLt

12H .82if

Lt

12LLDF H otherwise

Mmpf = Multiple Presence Factor Mmpf 1.2

IM = Dynamic Load Allowance IM1 331 0.125 H

100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25

WL = Service Live Load (lb/ft) WL Mmpf 1 IM( ) WLL min S Lt.gov WL 6038.32

Total Service and Factor Load

Wts = Total Service Load (lb/ft) Wts We WL Wts 10858.2

Wtf LFd We LFl WL Wtf 19965.9Wtf = Total Factor Load (lb/ft)

Factored Thrust ValuesTL

Wtf

2TL = Factored thrust per unit length (lb/ft.) TL 9982.95



CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Metal Arch - AASHTO LRFD Design_30.1X18

SOURCE: AASHTO LRFD Bridge Design Specifications_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




S = Span (ft.) S 30.083

R = Rise (ft.) R 18





1.67





LLDF 1.15






Soil Unit Weight




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H

Lt

12LLDF H H Hintif

ALL 12.43


H Hintif

2 LLALL



12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25






Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Metal Arch - AASHTO Standard Design_20.1X9

SOURCE: AASHTO Standard Bridge Design Specifications_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




S = Span (ft.) S 20.083

R = Rise (ft.) R 9.083





2.21





LLDF 1.75






Soil Unit Weight



Hint = Wheel interaction depth (ft.) Hintwhsp

LLDFHint 3.43

ALL LLDF H( ) LLDF H( ) H Hintif

whsp LLDF H LLDF H( ) H HintifALL = Distributed Area (ft2) ALL 12.25


H Hintif

2 LLALL


I = Impact fraction I 0.3 0 H 1if

0.2 1 H 2if

0.1 2 H 3if

0 H 3if

I 0.2

WL = Service Live Load (lb/ft) WL 1 I( ) WLL min S LLDF H( ) WL 5485.71





Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Metal Arch - AASHTO Standard Design_30.1X18

SOURCE: AASHTO Standard Bridge Design Specifications_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




S = Span (ft.) S 30.083

R = Rise (ft.) R 18





1.67





LLDF 1.75






Soil Unit Weight




LLDFHint 3.43




H Hintif

2 LLALL



0.2 1 H 2if

0.1 2 H 3if

0 H 3if

I 0.2

WL = Service Live Load (lb/ft) WL 1 I( ) WLL min S LLDF H( ) WL 5485.71





Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Metal Arch - Proposed Simplified Design Eqation_20.1X9

SOURCE:_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




S = Span (ft.) S 20.083

R = Rise (ft.) R 9.083





2.21





LLDF 1.15






Soil Unit Weight




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H 0.06 S

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H 0.06S

Lt

12LLDF H H Hintif

ALL 16.2


H Hintif

2 LLALL

H Hintif WLL 987.38


12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25






Factored Thrust Values

TD = Factored thrust per unit length from dead load (lb/ft.) TDLFd We

2TD 4699.42

Fm,arch = Thrust modifier for long-span metal arches Fm.arch0.54 S

Wt

12LLDF H 0.03 S

Fm.arch 2.37

TL = Factored thrust per unit length from live load (lb/ft.) TLLFl WL

2Fm.arch TL 9618.5

TT = Factored thrust per unit length (lb/ft.) TT TD TL TT 14317.921



CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Metal Arch - Proposed Simplified Design Eqation_30.1X18

SOURCE:_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




S = Span (ft.) S 30.083

R = Rise (ft.) R 18





1.67





LLDF 1.15






Soil Unit Weight




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H 0.06 S

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H 0.06S

Lt

12LLDF H H Hintif

ALL 18.08


H Hintif

2 LLALL

H Hintif WLL 884.74


12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25








2TD 7039.42

Fm,arch = Thrust modifier for long-span metal arches Fm.arch0.54 S

Wt

12LLDF H 0.03 S

Fm.arch 3.34


2Fm.arch TL 12114.66




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Profile Wall - AASHTO LRFD Design_cl85

SOURCE: AASHTO LRFD Bridge Design Specifications; ASCE 15-98_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3




Di = inside diameter of pipe (in.) Di 24

h = wall thickness (in.) h 2.16

Do = outside diameter of pipe (in.) Do Di 2 h Do 28.32

Dm = mean diameter of pipe (in.) Dm Di h Dm 26.16

Ap = unit pipe area (in2/in) Ap 0.344





LLDF 1.15






Soil Unit Weight

PL = prism earth load (lb/ft) PL w H 0.0089 DoDo

12PL 637.78

s 0.9s Ressistance factor for soil stiffness

Soiltype = Backfill type Soiltype "cl85"

Ms = Constrained soil modulus at 0.15ksf specified in Table 1(psi) Ms 130

R = Radius to centroid of culvert wall (in) RDm

2R 13.08

E = Initial or long-term modulus of elasticity as specified in Table 12.12.3.3-1 (psi) E 110000

Ap = Unit pipe area (in2/in)

SH = Hoop stiffness factor SHs Ms R

E Ap SH 0.04

VAF = Vertical arching factor VAF 0.76 0.71SH 1.17

SH 2.92VAF 1.03

We = Vertical earth load (lb/ft) We VAF PL( ) We 657.49



whspWt

12LLDF

Hint 3.77


Wt

12LLDF H

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H

Lt

12LLDF H H Hintif

ALL 12.43


H Hintif

2 LLALL

H HintifWLL 1287.32


12H .82if

Lt

12LLDF H otherwise




100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25

WL = Service Live Load (lb/ft) WL Mmpf 1 IM( ) WLL minDi

12Lt.gov WL 3854.25



Wtf LFd We LFl WL Wtf 8027Wtf = Total Factor Load (lb/ft)


Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160


CALCULATION BY: GL DATE

APPROVED BY DATE

OBJECT : Profile Wall-AASHTO Standard Design_cl85

SOURCE: AASHTO Standard Bridge Design Specifications; ASCE 15-98_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3













LLDF 1.75






Soil Unit Weight


12PL 637.78



Ms = Constrained soil modulus at 0.15ksf specified in Table 1 Ms 130


2R 13.08




E Ap SH 0.04


SH 2.92VAF 1.03




LLDFHint 3.43




H Hintif

2 LLALL



0.2 1 H 2if

0.1 2 H 3if

0 H 3if

I 0.2

WL = Service Live Load (lb/ft) WL 1 I( ) WLL minDi

12LLDF H WL 3134.69






Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Profile Wall - Proposed Simplified Design Eqation_cl85

SOURCE: NCHRP 15-29; ASCE 15-98_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3













LLDF 1.15






Soil Unit Weight


12PL 637.78



Ms = Constrained soil modulus at 0.15ksf specified in Table 1(psi) Ms 130


2R 13.08




E Ap SH 0.04


SH 2.92VAF 1.03




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

ALL 12.8


H Hintif

2 LLALL



12H .82if

Lt

12LLDF H otherwise




100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25


12Lt.gov WL 3741.07






2TD 641.05

F1.Lim = Limit value for factor F1 F1.lim max15Di

1.0 F1.lim 1

F1 = Correction factor

F1 max F1.lim 0.75

Di

12

Lt

12LLDF H( )

F1 1

F2 = Correction factor for soil typeF2

0.951 0.6 SH F2 0.927


2F1 F2

TL 3036.09




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : RCP AASHTO LRFD design method_type1


Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3



wc = unit weight of concrete (pcf) wc 150



h = wall thickness (in.) h 3

Do = outside diameter of pipe (in.) Do Di 2 h Do 30

Dm = mean diameter of pipe (in.) Dm Di h Dm 27

wf = unit weight of fluid (pcf) wf 62.4

Fe = soil-structure interaction factor for the specified installation as defined herein (table 12.10.2.1-3)

Fe 1.35

LL = total live load applied at surface (lb.)LL 16000




LLDF 1.15

whsp = wheel spacing (ft.) whsp 6

LFl = live load factor LFl 1.75

LFd = dead load factor LFd 1.3



Pipe Unit Weight

A = area of the pipe (in2) A14

Do2 Di

2 A 254.47

Wp = pipe unit weight (lb/ft) Wp wcA

144Wp 265

Soil Unit Weight


12PL 380.1

We = vertical earth load (lb/ft) We Fe PL We 513.13

Fluid Unit Weight

Wf = fluid load (lb/ft) Wf wf14

Di

12

2

Wf 196.04



whspWt

12LLDF

Hint 3.77


Wt

12LLDF H

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H

Lt

12LLDF H H Hintif

ALL 5.59


H Hintif

2 LLALL

H Hintif WLL 2864.1


12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.29


12Lt.gov WL 8784.85



Wts = Total Service Load (lb/ft) Wts Wp We Wf WL Wts 9759.1

Wtf LFd Wp We Wf LFl WL Wtf 16640Wtf = Total Factor Load (lb/ft)

Total Moment and Thrust and Shear Values AASHTO LRFDDi 24

Nondimensional Coefficients (Cmi, Cni,Cvi) H 1Installation Type 1 Coefficients; See Table C-3.1. InvertInstallation Type 2 Coefficients; See Table C-3.2.

Installation Type 3 Coefficients; See Table C-3.3.


Cmip 0.225 Cnip 0.077 Cvip 0.437

Cmie 0.091 Cnie 0.188 Cvie 0.143

Cmif 0.088 Cnif 0.445 Cvif 0.141

Cmil 0.165 Cnil 0.046 Cvil 0.15

Moment and Thrust and Shear Values

Factor Values

Mi LFd Cmip Wp Cmie We Cmif Wf LFl Cmil WLDm

2Mi 36413.41

Ni LFd Cnip Wp Cnie We Cnif Wf LFl Cnil WL Ni 668.64

Vi LFd Cvip Wp Cvie We Cvif Wf LFl Cvil WL Vi 2587.94

Service Values

Ms Cmip Wp Cmie We Cmif Wf Cmil WLDm

2Ms 21236.69

Ns Cnip Wp Cnie We Cnif Wf Cnil WL Ns 374.46

Vs Cvip Wp Cvie We Cvif Wf Cvil WL Vs 1534.58

Flexural Resistance at the Strength Limit State

Circumferential Reinforcement

As = Area of reinforcement per length of pipe (in2/ft)

fy = Specified yield strength of reinforcing (ksi) fy 65

d = Distance from compression face to centroid of tension reinforcement (in.) d h 1.5 d 1.5

Mu = Moment due to factored loads (kip-in/ft) MuMi

1000Mu 36.413

Nu = Thrust due to factored load, taken to be positive for compression (kip/ft)

NuNi

1000Nu 0.669

= Resistance factor for flexure specified in Article 12.5.5 ( =0.9, Type 1 installation; =1.0, Other type installations)

0.9

b = Length of reinforcement for flexural resistance provided (in) b 12SHEET 3 OF 5

Page 27 of 46

fc = Compressive strength of concrete (ksi) fc 4

g 0.85 b fc g 40.8

Asg d Nu g g d

2Nu 2 d h 2 Mu

fy As 0.744

Table 12.10.2.1-3

1 2 3 4VAF 1.35 1.4 1.4 1.45HAF 0.45 0.4 0.37 0.3

Installation Type

* Fe shall be taken as the vertical arching factor, VAF

Type Reinforcement C11 Smooth wire or plain bars 12 Welded smooth wire fabric

with 8.0 inch maximumspacing of longitudinals

3 Welded deformed wire fabric,deformed wire, bars, or anyreinforcement with stirrupsanchored thereto

1.5

1.9

Table 1


ASCE 15-98 SIDD Pressure Distribution

Location Load Type Location Load TypeCmi Cni Cvi Cmi Cni Cvi

Invert Wp 0.225 0.077 0.437 Invert Wp 0.227 0.077 0.437

We 0.091 0.188 0.143 We 0.122 0.169 0.198

Wf 0.088 -0.445 0.141 Wf 0.111 -0.137 0.193

WL1 0.075 0.25 0.15 WL1 0.107 0.205 0.188

WL2 0.165 -0.046 WL2 0.189 -0.035

Crown Wp 0.079 -0.077 0.083 Crown Wp 0.079 -0.077 0.088

We 0.083 0.157 0.117 We 0.094 0.126 0.136

Wf 0.057 -0.187 0.062 Wf 0.062 -0.204 0.074

WL1 0.068 0.2 0.1 WL1 0.08 0.171 0.137

WL2 0.236 0.046 WL2 0.241 0.035

Springline Wp -0.091 0.249 Springline Wp -0.091 0.249

We -0.077 0.5 We -0.09 0.5

Wf -0.064 -0.068 Wf -0.07 -0.068

WL1 -0.065 0.5 WL1 -0.078 0.513

WL2 -0.154 0.5 WL2 -0.16 0.5



We 0.15 0.163 0.249 We 0.191 0.128 0.309

Wf 0.133 -0.425 0.238 Wf 0.16 -0.403 0.284

WL1 0.136 0.199 0.224 WL1 0.185 0.152 0.305

WL2 0.211 -0.023 WL2 0.237 -0.004

Crown Wp 0.079 -0.077 0.094 Crown Wp 0.079 -0.077 0.1

We 0.103 0.107 0.15 We 0.118 0.079 0.169

Wf 0.068 -0.215 0.085 Wf 0.076 -0.232 0.096

WL1 0.091 0.149 0.124 WL1 0.11 0.114 0.152

WL2 0.247 0.023 WL2 0.255 0.004


We -0.103 0.5 We -0.127 0.504

Wf -0.081 -0.063 Wf -0.095 -0.057

WL1 -0.126 0.497 WL1 -0.121 0.495

WL2 -0.155 0.496 WL2 -0.168 0.492

Coefficients CoefficientsInstallation Type 1 Coefficients Installation Type 2 Coefficients

Installation Type 3 Coefficients Installation Type 4 CoefficientsCoefficients Coefficients

Table C-3.1. Table C-3.2.

Table C-3.3. Table C-3.4.SHEET 5 OF 5

Page 29 of 46


CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : RCP AASHTO Standard design method_type1

SOURCE: AASHTO standard Bridge Design Specifications; ASCE 15-98_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3











Fe 1.35





LLDF 1.75






Pipe Unit Weight


Do2 Di

2 A 2968.81


144Wp 3093

Soil Unit Weight


12PL 2296.64


Fluid Unit Weight


Di

12

2

Wf 3136.57



LLDFHint 3.43




H Hintif

2 LLALL



0.2 1 H 2if

0.1 2 H 3if

0 H 3if

I 0.3

WL = Service Live Load (lb/ft) WL 1 I( ) WLL minDi

12LLDF H WL 11885.71




Wtf LFd Wp We Wf LFl WL Wtf 37920.4Wtf = Total Factor Load (lb/ft)

Total Moment and Thrust and Shear Values AASHTO Standard

Di 96Nondimensional Coefficients (Cmi, Cni,Cvi) H 1

Installation Type 1 Coefficients; See Table C-3.1. CrownInstallation Type 2 Coefficients; See Table C-3.2.



Cmip 0.079 Cnip 0.077 Cvip 0.083

Cmie 0.083 Cnie 0.157 Cvie 0.117

Cmif 0.057 Cnif 0.187 Cvif 0.062

Cmil 0.236 Cnil 0.046 Cvil 0.1


Factor Values


2Mi 3.66 105



Service Values


2Ms 1.83 105









1000Mu 366.002


NuNi

1000Nu 0.747


= Resistance factor for flexure specified in Article 12.5.5 ( =0.9, Tpye 1 installation; =1.0, Other type installations)

0.9

b = Length of reinforcement for flexural resistance provided (in) b 12


g 0.85 b fc g 40.8

Asg d Nu g g d

2Nu 2 d h 2 Mu

fy As 0.931

Table 12.10.2.1-3

1 2 3 4VAF 1.35 1.4 1.4 1.45HAF 0.45 0.4 0.37 0.3

Installation Type





1.5

1.9

Table 1





We 0.091 0.188 0.143 We 0.122 0.169 0.198

Wf 0.088 -0.445 0.141 Wf 0.111 -0.137 0.193

WL1 0.075 0.25 0.15 WL1 0.107 0.205 0.188

WL2 0.165 -0.046 WL2 0.189 -0.035

Crown Wp 0.079 -0.077 0.083 Crown Wp 0.079 -0.077 0.088

We 0.083 0.157 0.117 We 0.094 0.126 0.136

Wf 0.057 -0.187 0.062 Wf 0.062 -0.204 0.074

WL1 0.068 0.2 0.1 WL1 0.08 0.171 0.137

WL2 0.236 0.046 WL2 0.241 0.035


We -0.077 0.5 We -0.09 0.5

Wf -0.064 -0.068 Wf -0.07 -0.068

WL1 -0.065 0.5 WL1 -0.078 0.513

WL2 -0.154 0.5 WL2 -0.16 0.5



We 0.15 0.163 0.249 We 0.191 0.128 0.309

Wf 0.133 -0.425 0.238 Wf 0.16 -0.403 0.284

WL1 0.136 0.199 0.224 WL1 0.185 0.152 0.305

WL2 0.211 -0.023 WL2 0.237 -0.004

Crown Wp 0.079 -0.077 0.094 Crown Wp 0.079 -0.077 0.1

We 0.103 0.107 0.15 We 0.118 0.079 0.169

Wf 0.068 -0.215 0.085 Wf 0.076 -0.232 0.096

WL1 0.091 0.149 0.124 WL1 0.11 0.114 0.152

WL2 0.247 0.023 WL2 0.255 0.004


We -0.103 0.5 We -0.127 0.504

Wf -0.081 -0.063 Wf -0.095 -0.057

WL1 -0.126 0.497 WL1 -0.121 0.495

WL2 -0.155 0.496 WL2 -0.168 0.492





Page 34 of 46


CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : RCP Proposed Simplified Equation method_type1


Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3











Fe 1.35





LLDF 1.15






Pipe Unit Weight


Do2 Di

2 A 2968.81


144Wp 3093

Soil Unit Weight


12PL 2296.64


Fluid Unit Weight


Di

12

2

Wf 3136.57


Di = Inside diameter of concrete pipe (in)

LLDFcp = Live load distribution factor for concrete pipe

LLDF 1.15 Di 24if

0.00833 Di 0.95 24 Di 96if

1.75 Di 96ifLLDF 1.75


whspWt

12

.06 Di

12LLDF

Hint 2.2


Wt

12LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

ALL 10.07


H Hintif

2 LLALL



12H .82if

Lt

12LLDF H otherwise




100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.29


12Lt.gov WL 6350.04



Wtf LFd Wp We Wf LFl WL Wtf 23241Wtf = Total Factor Load (lb/ft)

Total Moment and Thrust and Shear Values H 1

Di 96Nondimensional Coefficients (Cmi, Cni,Cvi)





Cmip 0.079 Cnip 0.077 Cvip 0.083

Cmie 0.083 Cnie 0.157 Cvie 0.117

Cmif 0.057 Cnif 0.187 Cvif 0.062

Cmil 0.236 Cnil 0.046 Cvil 0.1


Factor Values


2Mi 1.84 105



Service Values


2Ms 1.14 105










1000Mu 184.124


NuNi

1000Nu 0.072

= Resistance factor for flexure specified in Article 12.5.5 ( =0.9, Tpye 1 installation; =1.0, Other type installations)

0.9

b = Length of reinforcement for flexural resistance provided (in) b 12


g 0.85 b fc g 40.8

Asg d Nu g g d

2Nu 2 d h 2 Mu

fy As 0.442

Table 12.10.2.1-3

1 2 3 4VAF 1.35 1.4 1.4 1.45HAF 0.45 0.4 0.37 0.3

Installation Type





1.5

1.9

Table 1





We 0.091 0.188 0.143 We 0.122 0.169 0.198

Wf 0.088 -0.445 0.141 Wf 0.111 -0.137 0.193

WL1 0.075 0.25 0.15 WL1 0.107 0.205 0.188

WL2 0.165 -0.046 WL2 0.189 -0.035

Crown Wp 0.079 -0.077 0.083 Crown Wp 0.079 -0.077 0.088

We 0.083 0.157 0.117 We 0.094 0.126 0.136

Wf 0.057 -0.187 0.062 Wf 0.062 -0.204 0.074

WL1 0.068 0.2 0.1 WL1 0.08 0.171 0.137

WL2 0.236 0.046 WL2 0.241 0.035


We -0.077 0.5 We -0.09 0.5

Wf -0.064 -0.068 Wf -0.07 -0.068

WL1 -0.065 0.5 WL1 -0.078 0.513

WL2 -0.154 0.5 WL2 -0.16 0.5



We 0.15 0.163 0.249 We 0.191 0.128 0.309

Wf 0.133 -0.425 0.238 Wf 0.16 -0.403 0.284

WL1 0.136 0.199 0.224 WL1 0.185 0.152 0.305

WL2 0.211 -0.023 WL2 0.237 -0.004

Crown Wp 0.079 -0.077 0.094 Crown Wp 0.079 -0.077 0.1

We 0.103 0.107 0.15 We 0.118 0.079 0.169

Wf 0.068 -0.215 0.085 Wf 0.076 -0.232 0.096

WL1 0.091 0.149 0.124 WL1 0.11 0.114 0.152

WL2 0.247 0.023 WL2 0.255 0.004


We -0.103 0.5 We -0.127 0.504

Wf -0.081 -0.063 Wf -0.095 -0.057

WL1 -0.126 0.497 WL1 -0.121 0.495

WL2 -0.155 0.496 WL2 -0.168 0.492





Page 39 of 46


CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Corrugated Metal Pipe - AASHTO LRFD Design Diameter=8 Depth=1


Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3



wc = unit weight of steel (pcf) wc 490






Fe = soil-structure interaction factor for the specified installation as defined herein

Fe 1.0

Ap 0.968AP = unit pipe area (in2/ft.)





LLDF 1.15






Soil Unit Weight


12PL 1786.13




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H

Lt

12LLDF H H Hintif

ALL 5.59


H Hintif

2 LLALL

H Hintif WLL 2864.1


12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.29

WL = Service Live Load (lb/ft) WL Mmpf 1 IM( ) WLL minDm

12Lt.gov WL 8784.85


Wts = Total Service Load (lb/ft) Wts We WL Wts 10571

Wtf = Total Factor Load (lb/ft) Wtf LFd We LFl WL Wtf 18856.5


Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Corrugated Metal Pipe - AASHTO Standard Design Diameter= 8 Depth=1

SOURCE: AASHTO standard Bridge Design Specifications; ASCE 15-98_________________________________________________________________________________________________

Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3



ws = unit weight of concrete (pcf) ws 490







Fe 1.0

AP = unit pipe area (in2/ft.) Ap 0.968





LLDF 1.75






Soil Unit Weight


12PL 1786.13




LLDFHint 3.43




H Hintif

2 LLALL



0.2 1 H 2if

0.1 2 H 3if

0 H 3if

I 0.3

WL = Service Live Load (lb/ft) WL 1 I( ) WLL minDm

12LLDF H WL 11885.71





Wtf




CNAPhone: (612) 379-8805

Fax: (612) 379-8160




OBJECT : Corrugated Metal Pipe - Simplified Design Equation


Units

lb lbf psilb

in2kip 1000lbf ksi

kip

in2plf

lbfft

psflbf

ft2pcf

lbf

ft3



wc = unit weight of steel (pcf) wc 490







Fe 1.0

AP = unit pipe area (in2/ft.) Ap 0.968





LLDF 1.15






Soil Unit Weight


12PL 535.1




whspWt

12LLDF

Hint 3.77


Wt

12LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

Wt

12whsp LLDF H 0.06

Di

12

Lt

12LLDF H H Hintif

ALL 12.8


H Hintif

2 LLALL



12H .82if

Lt

12LLDF H otherwise



100

IM 331 0.125 H

100H 8if

0 H 8ifIM 0.25

WL = Service Live Load (lb/ft) WL Mmpf 1 IM( ) WLL minDm

12Lt.gov WL 3753.39







2TD 521.72

F1.Lim = Limit value for factor F1 F1.lim max15Di

1.0 F1.lim 1

F1 = Correction factor

F1 max F1.lim 0.75

Di

12

Lt

12LLDF H( )

F1 1


2F1

TL 3284.21



appendix d.1 parametric study mathcad calculation...

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