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{"sheet":"Circular Pipe - Cement.","index":0,"n_rows":85,"n_cols":34,"rows_kept":85,"cut":false,"hidden":false,"merged":[[1,28,1,32],[59,28,59,32],[45,2,45,6],[44,2,44,6],[43,2,43,6],[29,2,29,6],[30,2,30,6],[31,2,31,6],[38,2,38,6],[36,2,36,6],[56,2,56,6],[10,3,10,6],[7,3,7,6],[9,3,9,6],[11,3,11,6],[13,3,13,6],[42,2,42,6],[5,2,5,15],[12,3,12,6],[58,2,58,6],[59,2,59,6],[52,2,52,6],[53,2,53,6],[55,2,55,6],[32,2,32,6],[23,2,23,6],[21,2,21,6],[20,2,20,6],[33,2,33,6],[22,2,22,6],[8,3,8,6],[24,2,24,6],[25,2,25,6],[34,2,34,6],[26,2,26,6],[28,2,28,6],[27,2,27,6],[60,2,60,6],[62,2,62,6],[64,2,64,6],[63,2,63,6],[65,2,65,6],[61,2,61,6],[84,2,84,6],[84,9,84,14],[82,2,82,6],[66,2,66,6],[68,2,68,6],[81,2,81,6],[83,2,83,6],[75,2,75,6],[76,2,76,6],[77,9,77,14],[77,2,77,6],[67,2,67,6],[69,2,69,6],[74,2,74,6],[54,2,54,6],[47,2,47,6],[48,2,48,6],[2,27,2,34],[6,28,6,32],[7,28,7,32],[9,28,9,32],[37,26,37,27],[10,28,10,32],[17,28,17,32],[18,28,18,32],[19,28,19,32],[11,28,11,32],[12,28,12,32],[2,2,2,15],[4,2,4,15]]}
[]
[]
[null,null,"SAPL Design",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Circular Pipe - Cementitious"]
[]
[null,null,"Structural Design for Liner Thickness Using Cementitious Materials",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Live and Dead Loads Calculation:"]
[null,null,"Circular Corrugated Metal Pipe"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If impact factor = 1 + 0.33 [(96 – h)/96] ≥ 1.0",null,null,null,null,{"$f":"MAX((1+0.33*((96-'Circular Pipe - Cement.'!H23)/96)),1)","v":1.2475000000000001}]
[null,null,"Project:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"lw load width parallel to direction of travel (in)\n\n",null,null,null,null,{"$f":"AH62","v":37.599999999999994}]
[null,null,"Trial:"]
[null,null,"Location:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"hint (in)",null,null,null,null,{"$f":"('Circular Pipe - Cement.'!H27-'Circular Pipe - Cement.'!H26-0.06*'Circular Pipe - Cement.'!H29)/'Circular Pipe - Cement.'!H24","v":42.086956521739133}]
[null,null,"DOT:","Select DOT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ww  Load width perpendicular to direction of travel (in)",null,null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H23<'Circular Pipe - Cement.'!AH10,'Circular Pipe - Cement.'!H26+'Circular Pipe - Cement.'!H24*'Circular Pipe - Cement.'!H23+0.06*'Circular Pipe - Cement.'!H29,(('Circular Pipe - Cement.'!H26+'Circular Pipe - Cement.'!H27+'Circular Pipe - Cement.'!H24*'Circular Pipe - Cement.'!H23)+0.06*'Circular Pipe - Cement.'!H29))","v":51.199999999999996}]
[null,null,"Latitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H23/12<'Circular Pipe - Cement.'!H32,'Circular Pipe - Cement.'!H23/12,'Circular Pipe - Cement.'!H32)","v":2},null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - No groundwater",null,null,null,null,{"$f":"'Circular Pipe - Cement.'!H43*('Circular Pipe - Cement.'!H30*AA12-2*'Circular Pipe - Cement.'!H31)/144","v":0.61789412025085744}]
[null,null,"Longitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - With groundwater",null,null,null,null,{"$f":"(('Circular Pipe - Cement.'!H43*AA12-'Circular Pipe - Cement.'!H34)*'Circular Pipe - Cement.'!H30+'Circular Pipe - Cement.'!H34*('Circular Pipe - Cement.'!H30-62.4))/144","v":0.61789412025085744}]
[null,null,"Date:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"0.433*('Circular Pipe - Cement.'!H34+'Circular Pipe - Cement.'!H35)","v":2.165}]
[]
[null,null,"Input",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Design (Cementitious Liner):"]
[null,null,"Output"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi)",null,null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H34=0,'Circular Pipe - Cement.'!AH12,'Circular Pipe - Cement.'!AH13)","v":0.61789412025085744}]
[null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CL  live load distribution coefficient (in.), is equal to lw / S ≤ 1.0",null,null,null,null,{"$f":"MIN(AH8/'Circular Pipe - Cement.'!H70,1)","v":0.62666666666666659}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H34=0,0,'Circular Pipe - Cement.'!AH14)","v":0}]
[null,null,"Mp  Multiple Presence Factor, typically equal to 1.2                                                                                                                                                                                                                               Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.                                                                                                                                                                                                                Table 3.6.1.1.2.1.                                                                                                                              ",null,null,null,null,1.2]
[null,null,"P  Design Wheel Load                                                                                                                                                                                                                                                                                                                     Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                         Section 3.6.1.2.6b.                                                                                                                                                                                                                                                                                                      P Load is the weight an AASHTO design truck imposes on a single wheel (or pair of wheels in the case of dual wheels).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Typical HL-93 Design Truck has 3 axles, front axle load of 8 kips, and two rear axles with a load of 32 kips each (rear wheel load of 16 kips each)                                                         ",null,null,null,null,16000,"lb"]
[null,null,"h  Depth of Cover over Culvert                                                                                                                                                                                                                                                                                                                                                                                    Distance from top of the pipe to top of the soil",null,null,null,null,24,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Single Span",null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H59<='Circular Pipe - Cement.'!H78,IF('Circular Pipe - Cement.'!H78<='Circular Pipe - Cement.'!H60,1,0),0)","v":1}]
[null,null,"LLDF  Live Load Distribution Factor                                                                                                                                                                                                                                                                                                                       Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                                                                                                            Table 3.6.1.2.6a-1                                                                                                                                                                                                                                                                                                                         For Concrete Pipe with fill depth 2.0ft or greater, linearly interpolate between these limits:  \n1.15 for diameter 2.0ft or less\n1.75 for diameters 8.0ft or greater \nAll other culverts and buried structures: 1.15",null,null,null,null,1.1499999999999999,null,null,null,null,"Figure 8-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Multiple Span",null,null,null,{"$f":"IF('Circular Pipe - Cement.'!H59<='Circular Pipe - Cement.'!H85,IF('Circular Pipe - Cement.'!H85<='Circular Pipe - Cement.'!H60,1,0),0)","v":1}]
[null,null,"lt  Tire Patch Length                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,10,"in."]
[null,null,"Wt  Tire Patch Width                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,20,"in."]
[null,null,"Sw  Spacing between the Wheel Pairs on the Axle                                                                                                                                                                                                                                                                                                                                            Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,72,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Delaware Department of Transportation"]
[null,null,"Sa Axle Spacing                                                                                                                                                                                                                                                                                                                                 Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,48,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Florida Department of Transportation"]
[null,null,"Di  Inside Diameter or Clear Span of the Culvert",null,null,null,null,60,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minnesota Department of Transportation"]
[null,null,"δsoil   Soil Unit Weight",null,null,null,null,120,"pcf",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"New York State Department of Transportation"]
[null,null,"c  Soil Cohesion                                                                                                                                                                                                                                                                                                                                     Cohesion per ASCE Manual of Practice (MOP) 60. Standard values:                                                                                                                                                                                                                                         Clay, very soft:  40 psf\nClay, medium: 250 psf\nClay, hard: 1,000 psf\nSand, loose dry: 0 psf\nSand, silty: 100 psf\nSand, dense: 300 psf",null,null,null,null,0,"psf",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"North Carolina Department of Transportation"]
[null,null,"Bc O.D. or outside span length of the liner (ft)",null,null,null,null,{"$f":"H29/12","v":5},"ft",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ohio Department of Transportation"]
[null,null,"kµ'  Select kµ' - Refer to Figure 9-13 in ASCE MOP 60                                                                                                                                                                                                                                                                      kµ'=0.1924 min for granular material without cohesion                                                                                                                                                                                                                             kµ'=0.165 max for sand and gravel                                                                                                                                                                                                                                                                        kµ'=0.150 max for saturated top soil                                                                                                                                                                                                                                                                   kµ'=0.130 max for ordinary clay                                                                                                                                                                                                                                                                              kµ'=0.110 max for saturated clay                                                                                                                                                                                                                                                                                                                                                                                                                                                      ",null,null,null,null,0.19239999999999999,null,null,null,null,"Figure 8-2",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pennsylvania Department of Transportation"]
[null,null,"Hw  Height of the Groundwater above the Top of the Pipe                                                                                                                                                                                                                            See figure 8-2                                                                                                                                                                                                                                                                                                                   Hw = 0 if no groundwater                                                                                                                                                                                                                                                                                              ",null,null,null,null,0,"ft",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select DOT"]
[null,null,"Hr height of the vertical dimension of the pipe (ft).",null,null,null,null,{"$f":"H29/12","v":5}]
[]
[null,null,"Select if it is a Single Span culvert or Multiple Span culverts? ",null,null,null,null,"Single Span"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"-2kµ'H/Bc",null,{"$f":"-2*'Circular Pipe - Cement.'!H33*'Circular Pipe - Cement.'!H23/('Circular Pipe - Cement.'!H32*12)","v":-0.15391999999999997}]
[null,null,{"$f":"IF(H37=\"Single Span\",\"\",\"Specify the distance between inside faces of end walls perpendicular to roadway\")","v":""},null,null,null,null,0,{"$f":"IF(H37=\"Single Span\",\"\",\"ft\")","v":""},null,null,null,"Figure 8-3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select kµ'",null,{"$f":"IF(C48=\"Note: The effects of live load is neglected.\",0,1)","v":1}]
[null,null,"Live and Dead Loads Results:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19239999999999999]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16500000000000001]
[null,null,"Ct  Coefficient                                                                                                                                                                                                                                                           (Figure 9-13 in ASCE MOP 60)",null,null,null,null,{"$f":"(1-EXP('Circular Pipe - Cement.'!AC38))/(2*'Circular Pipe - Cement.'!H33)","v":0.37073647215051442},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.15,null,"Yes"]
[null,null,"PL  Live Load on Pipe",null,null,null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,(H21*H22*'Circular Pipe - Cement.'!AH7)/('Circular Pipe - Cement.'!AH8*'Circular Pipe - Cement.'!AH11),0),IF(H23<=(H39*12),(H21*H22*'Circular Pipe - Cement.'!AH7)/('Circular Pipe - Cement.'!AH8*'Circular Pipe - Cement.'!AH11),0))","v":12.441821808510642},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.13,null,"No"]
[null,null,"PE  Earth Load acting on the Horizontal Soil Plane at the Top of the Pipe",null,null,null,null,{"$f":"'Circular Pipe - Cement.'!AH18","v":0.61789412025085744},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.11]
[null,null,"Pw  External Hydrostatic Pressure acting on the Pipe",null,null,null,null,{"$f":"'Circular Pipe - Cement.'!AH20","v":0},"psi"]
[]
[null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,\"\",\"Note: The effects of live load is neglected.\"),IF(H23<=(H39*12),\"\",\"Note: The effects of live load is neglected.\"))","v":""}]
[null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For single-span culverts, the effects of live load may be neglected where the depth of fill is more than 8.0 ft. and exceeds the span length.\"),IF(H23<=(H39*12),\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For multiple span culverts, the effects of live load may be neglected where the depth of fill exceeds the distance between inside faces of end walls.\"))","v":""}]
[]
[null,null,"Design Assumptions (Cementitious Liner):"]
[]
[null,null,"r  top radius of the liner structure measured to the centroid of the liner's profile",null,null,null,null,{"$f":"H29*0.5","v":30},"in."]
[null,null,"t  Wall Thickness of the Liner - See figure 8-3                                                                                                                                                                                                                                                   Note: Wall thickness is above the corrugation crests.                                  ",null,null,null,null,1,"in."]
[null,null,"Assume only the liner above the corrugation crests is effective? Select Yes or No",null,null,null,null,"No"]
[null,null,{"$f":"IF(H55=\"No\",\"c  Distance from the Centroid of the Liner Pipe Wall Profile to the Interior Wall Surface - See figure 8-3\",\"\")","v":"c  Distance from the Centroid of the Liner Pipe Wall Profile to the Interior Wall Surface - See figure 8-3"},null,null,null,null,0.63700000000000001,{"$f":"IF(H55=\"No\",\"in.\",\"\")","v":"in."},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H55=\"Yes\",0.5*H54,H56)","v":0.63700000000000001},"in."]
[null,null,{"$f":"IF(H55=\"No\",\"I  SAPL Area Moment of Inertia of the Liner Wall Section\",\"\")","v":"I  SAPL Area Moment of Inertia of the Liner Wall Section"},null,null,null,null,0.18140000000000001,{"$f":"IF(H55=\"No\",\"in.4 /in.\",\"\")","v":"in.4 /in."},null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H55=\"Yes\",(H54^3)/12,H57)","v":0.18140000000000001},"in.4/in."]
[]
[null,null,"σCS  Compressive Stress Strength of the Liner Material                                                                                                                                                                                                                                                                                           Compressive strength value to be provided by manufacturer in accordance with Pipe Liner Special Provision.",null,null,null,null,-8390,"psi"]
[null,null,"σflex  Flexural Stress Strength (Modulus of Rupture) of the Liner Material                                                                                                                                                                                                                                                                                                                                                          Flexural strength value to be provided by manufacturer in accordance with Pipe Liner Special Provision.",null,null,null,null,1665,"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"H.in Parallel",null,null,null,null,{"$f":"(H28-H25)/H24","v":33.04347826086957}]
[null,null,"γEV  Load Factor for Soil Prism Load - Service, 1.0",null,null,null,null,1]
[null,null,"γEV  Load Factor for Soil Prism Load - Strength, 1.30",null,null,null,null,1.3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H23<AH60,H25+H24*H23,H25+H28+H24*H23)","v":37.599999999999994}]
[null,null,"γWA Load Factor for Groundwater Load, 1.0",null,null,null,null,1]
[null,null,"γLL  Load Factor for Live Load - Service, 1.0",null,null,null,null,1]
[null,null,"γLL  Load Factor for Live Load - Strength, 1.75",null,null,null,null,1.75]
[null,null,"ƞEV  Load Modifier for Soil Prism Load, use 1.0 per Article 1.3.2 of the BDS",null,null,null,null,1]
[null,null,"ƞR  Load Modifier for Redundancy, 1.05 for Strength Limit State under Earth Loads",null,null,null,null,1.05]
[null,null,"ƞR  Load Modifier for Redundancy, 1.0 for Strength Limit State under Live Loads",null,null,null,null,1]
[null,null,"ƞLL  Load Modifier for Live Load, use 1.0 per Article 1.3.2 of the BDS",null,null,null,null,1]
[null,null,"S  span of culvert (in)",null,null,null,null,{"$f":"H29","v":60}]
[]
[null,null,"Results (Cementitious Liner)"]
[]
[null,null,"Service"]
[null,null,"Tservice  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H61*H45+'Circular Pipe - Cement.'!AH19*'Circular Pipe - Cement.'!H44*H64)*'Circular Pipe - Cement.'!H53+H46","v":210.10837016354373},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H54","v":1},"in.2/in."]
[null,null,"Mservice  Moment",null,null,null,null,{"$f":"0.0062*'Circular Pipe - Cement.'!AH19*'Circular Pipe - Cement.'!H44*H64*(('Circular Pipe - Cement.'!H53)^2)","v":43.506562500000001},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Service)",null,null,null,null,{"$f":"(-(H75/H76))+((H77*U56)/U57)","v":-57.331742200478658},"psi",{"$f":"IF(H78>=H59,IF(H78<=H60,\"Stress within limits. The \"&H54&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H54&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H54&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]
[]
[]
[null,null,"Strength"]
[null,null,"Tstrength  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H66*H67*H62*H45+'Circular Pipe - Cement.'!AH19*'Circular Pipe - Cement.'!H44*H65*H69*H68)*'Circular Pipe - Cement.'!H53+H46*H63","v":361.74979144511218},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H54","v":1},"in.2/in."]
[null,null,"Mstrength  Moment",null,null,null,null,{"$f":"0.0062*'Circular Pipe - Cement.'!AH19*'Circular Pipe - Cement.'!H44*H65*H69*H68*(('Circular Pipe - Cement.'!H53)^2)","v":76.136484375000009},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Strength)",null,null,null,null,{"$f":"(-(H82/H83))+((H84*U56)/U57)","v":-94.390692509748305},"psi",{"$f":"IF(H85>=H59,IF(H85<=H60,\"Stress within limits. The \"&H54&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H54&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H54&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]

{"sheet":"Arch Pipe - Cement.","index":1,"n_rows":104,"n_cols":51,"rows_kept":104,"cut":false,"hidden":false,"merged":[[34,2,34,6],[64,28,64,32],[94,2,94,6],[95,2,95,6],[96,2,96,6],[40,2,40,6],[52,2,52,6],[60,2,60,6],[62,2,62,6],[63,2,63,6],[43,2,43,6],[45,2,45,6],[54,2,54,6],[55,2,55,6],[61,2,61,6],[84,9,84,14],[103,2,103,6],[103,9,103,14],[97,2,97,6],[97,9,97,14],[100,2,100,6],[101,2,101,6],[102,2,102,6],[4,2,4,15],[9,3,9,6],[10,3,10,6],[11,3,11,6],[12,3,12,6],[8,3,8,6],[66,2,66,6],[81,2,81,6],[82,2,82,6],[83,2,83,6],[84,2,84,6],[71,2,71,6],[72,2,72,6],[67,2,67,6],[68,2,68,6],[69,2,69,6],[70,2,70,6],[73,2,73,6],[75,2,75,6],[74,2,74,6],[38,2,38,6],[41,2,41,6],[50,2,50,6],[51,2,51,6],[2,2,2,15],[5,2,5,15],[27,2,27,6],[28,2,28,6],[29,2,29,6],[20,2,20,6],[22,2,22,6],[23,2,23,6],[24,2,24,6],[7,3,7,6],[13,3,13,6],[49,2,49,6],[39,2,39,6],[90,2,90,6],[90,9,90,14],[25,2,25,6],[21,2,21,6],[87,2,87,6],[88,2,88,6],[89,2,89,6],[37,2,37,6],[30,2,30,6],[31,2,31,6],[32,2,32,6],[33,2,33,6],[35,2,35,6],[36,2,36,6],[65,2,65,6],[37,26,37,27],[2,27,2,34],[6,28,6,32],[7,28,7,32],[9,28,9,32],[19,28,19,32],[10,28,10,32],[11,28,11,32],[12,28,12,32],[17,28,17,32],[18,28,18,32]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pipe Arch Size (in.)","Cross-sectional Area (ft2)","Springline Rise, B (in)","Top Radius (in)","Bottom Corner Radius (in)","Bottom Radius (in)"]
[null,null,"SAPL Design",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Arch Pipe - Cementitious",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"17 x 13",1.1000000000000001,4.125,8.625,3.5,25.625,null,17,13]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"21 x 15",1.6,4.875,10.75,4.125,33.125,null,21,15]
[null,null,"Structural Design for Liner Thickness Using Cementitious Materials",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,null,null,null,null,"20 x 16",1.7,5.125,10.25,5,27.5,null,20,16]
[null,null,"Arch Corrugated Metal Pipe",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"23 x 19",2.2999999999999998,5.875,11.625,5.375,34.25,null,23,19]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If impact factor = 1 + 0.33 [(96 – h)/96] ≥ 1.0",null,null,null,null,{"$f":"MAX((1+0.33*((96-'Arch Pipe - Cement.'!H30)/96)),1)","v":1.2475000000000001},null,null,null,null,null,1.2475000000000001,null,null,"24 x 18",2.2000000000000002,5.625,11.875,4.875,34.625,null,24,18]
[null,null,"Project:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"lw load width parallel to direction of travel (in)\n\n",null,null,null,null,{"$f":"AH67","v":37.599999999999994},null,null,null,null,null,37.599999999999994,null,null,"27 x 21",3,6.75,13.5,5.75,40.875,null,27,21]
[null,null,"Trial:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"28 x 20",2.9,6.5,14,5.5,42.25,null,28,20]
[null,null,"Location:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"hint (in)",null,null,null,null,{"$f":"('Arch Pipe - Cement.'!H34-'Arch Pipe - Cement.'!H33-0.06*'Arch Pipe - Cement.'!H36)/'Arch Pipe - Cement.'!H31","v":41.513043478260876},null,null,null,null,null,41.513043478260876,null,null,"33 x 26",4.7,8.75,16.625,7.125,51.375,null,33,26]
[null,null,"DOT:","Select DOT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ww  Load width perpendicular to direction of travel (in)",null,null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H30<'Arch Pipe - Cement.'!AH10,'Arch Pipe - Cement.'!H33+'Arch Pipe - Cement.'!H31*'Arch Pipe - Cement.'!H30+0.06*'Arch Pipe - Cement.'!H36,(('Arch Pipe - Cement.'!H33+'Arch Pipe - Cement.'!H34+'Arch Pipe - Cement.'!H31*'Arch Pipe - Cement.'!H30)+0.06*'Arch Pipe - Cement.'!H36))","v":51.859999999999992},null,null,null,null,null,51.859999999999992,null,null,"35 x 24",4.5,8.125,17.875,6.875,55.125,null,35,24]
[null,null,"Latitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H30/12<'Arch Pipe - Cement.'!H39,'Arch Pipe - Cement.'!H30/12,'Arch Pipe - Cement.'!H39)","v":2},null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - No groundwater",null,null,null,null,{"$f":"'Arch Pipe - Cement.'!H50*('Arch Pipe - Cement.'!H37*AA12-2*'Arch Pipe - Cement.'!H38)/144","v":0.52827823085194259},null,null,null,null,null,4.9305555555555554,null,null,"40 x 31",6.7,10.375,20.25,8.375,62.5,null,40,31]
[null,null,"Longitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - With groundwater",null,null,null,null,{"$f":"(('Arch Pipe - Cement.'!H50*AA12-'Arch Pipe - Cement.'!H41)*'Arch Pipe - Cement.'!H37+'Arch Pipe - Cement.'!H41*('Arch Pipe - Cement.'!H37-62.4))/144","v":0.52827823085194259},null,null,null,null,null,4.9305555555555554,null,null,"42 x 29",6.5,9.75,21.5,8.25,66.125,null,42,29]
[null,null,"Date:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"0.433*('Arch Pipe - Cement.'!H41+'Arch Pipe - Cement.'!H42)","v":1.6959166666666665},null,null,null,null,null,1.6959166666666665,null,null,"46 x 36",9.1999999999999993,12.375,23.25,9.75,73,null,46,36]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"49 x 33",8.9,11.375,25.125,9.625,77.25,null,49,33]
[null,null,"Input",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Design (Cementitious Liner):",null,null,null,null,null,null,null,null,null,null,null,null,null,"53 x 41",11.7,15.25,28.0625,10.1875,73.4375,null,53,41]
[null,null,"Output",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"57 x 38",11.6,13,28.625,11,88.25,null,57,38]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi)",null,null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H41=0,'Arch Pipe - Cement.'!AH12,'Arch Pipe - Cement.'!AH13)","v":0.52827823085194259},null,null,null,null,null,4.9305555555555554,null,null,"60 x 46",15.6,20.5,29.375,18.75,51.125,null,60,46]
[null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CL  live load distribution coefficient (in.), is equal to lw / S ≤ 1.0",null,null,null,null,{"$f":"MIN(AH8/'Arch Pipe - Cement.'!H25,1)","v":0.52957746478873235},null,null,null,null,null,0.62666666666666659,null,null,"64 x 43",14.7,14.625,32.25,12.375,99.25,null,64,43]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H41=0,0,'Arch Pipe - Cement.'!AH14)","v":0},null,null,null,null,null,0,null,null,"66 x 51",19.3,22.75,32.625,20.75,56.25,null,66,51]
[null,null,"Select Standard Pipe Arch Sizes",null,null,null,null,"71 x 47","in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"71 x 47",18.100000000000001,16.25,35.75,13.75,110.25,null,71,47]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"73 x 55",23.2,25.125,36.75,22.875,63.75,null,73,55]
[null,null,"Pipe Arch - Top Radius",null,null,null,null,{"$f":"VLOOKUP(H21,'Arch Pipe - Cement.'!AQ2:AV34,4,FALSE)","v":35.75},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Single Span",null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H66<='Arch Pipe - Cement.'!H85,IF('Arch Pipe - Cement.'!H85<='Arch Pipe - Cement.'!H67,1,0),0)","v":1},{"$f":"IF('Arch Pipe - Cement.'!H66<='Arch Pipe - Cement.'!H98,IF('Arch Pipe - Cement.'!H98<='Arch Pipe - Cement.'!H67,1,0),0)","v":1},null,null,null,null,null,null,null,null,"77 x 52",21.9,17.875,39.375,15.125,121.25,null,77,52]
[null,null,"Pipe Arch - Bottom Radius",null,null,null,null,{"$f":"VLOOKUP(H21,'Arch Pipe - Cement.'!AQ2:AV34,6,FALSE)","v":110.25},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Multiple Span",null,null,null,{"$f":"IF('Arch Pipe - Cement.'!H66<='Arch Pipe - Cement.'!H91,IF('Arch Pipe - Cement.'!H91<='Arch Pipe - Cement.'!H67,1,0),0)","v":1},{"$f":"IF('Arch Pipe - Cement.'!H66<='Arch Pipe - Cement.'!H104,IF('Arch Pipe - Cement.'!H104<='Arch Pipe - Cement.'!H67,1,0),0)","v":1},null,null,null,null,null,null,null,null,"81 x 59",27.4,23.75,39.5,20.875,82.625,null,81,59]
[null,null,"Pipe Arch - Span",null,null,null,null,{"$f":"VLOOKUP(H21,'Arch Pipe - Cement.'!AQ2:AX34,8,FALSE)","v":71},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(AG23:AG24)","v":2},null,null,null,null,null,null,null,null,null,"83 x 57",26,19.5,43,16.5,132.25,null,83,57]
[null,null,"Pipe Arch - Rise",null,null,null,null,{"$f":"VLOOKUP(H21,'Arch Pipe - Cement.'!AQ2:AY34,9,FALSE)","v":47},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"87 x 63",32.1,25.75,43.375,22.625,92.25,null,87,63]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Delaware Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"95 x 67",37,27.75,47,24.375,100.25,null,95,67]
[null,null,"Mp  Multiple Presence Factor, typically equal to 1.2                                                                                                                                                                                                                               Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.                                                                                                                                                                                                                Table 3.6.1.1.2.1.                                                                                                                              ",null,null,null,null,1.2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Florida Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"103 x 71",42.4,29.75,51.25,26.125,111.625,null,103,71]
[null,null,"P  Design Wheel Load                                                                                                                                                                                                                                                                                                                     Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                         Section 3.6.1.2.6b.                                                                                                                                                                                                                                                                                                      P Load is the weight an AASHTO design truck imposes on a single wheel (or pair of wheels in the case of dual wheels).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Typical HL-93 Design Truck has 3 axles, front axle load of 8 kips, and two rear axles with a load of 32 kips each (rear wheel load of 16 kips each)                                                         ",null,null,null,null,16000,"lb",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minnesota Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"112 x 75",48,31.625,54.875,27.75,120.25,null,112,75]
[null,null,"h  Depth of Cover over Culvert                                                                                                                                                                                                                                                                                                                                                                                    Distance from top of the pipe to top of the soil",null,null,null,null,24,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"New York State Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"117 x 79",54.2,33.625,59.375,29.5,131.75,null,117,79]
[null,null,"LLDF  Live Load Distribution Factor                                                                                                                                                                                                                                                                                                                       Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                                                                                                            table 3.6.1.2.6a-1                                                                                                                                                                                                                                                                                                                         For Concrete Pipe with fill depth 2.0ft or greater, linearly interpolate between these limits:  \n1.15 for diameter 2.0ft or less\n1.75 for diameters 8.0ft or greater \nAll other culverts and buried structures: 1.15",null,null,null,null,1.1499999999999999,null,null,null,null,"Figure 8-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"North Carolina Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"128 x 83",60.5,35.625,63.25,31.25,139.75,null,128,83]
[null,null,"lt  Tire Patch Length                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,10,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ohio Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"137 x 87",67.400000000000006,37.625,67.375,33,149.5,null,137,87]
[null,null,"Wt  Tire Patch Width                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,20,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pennsylvania Department of Transportation",null,null,null,null,null,null,null,null,null,null,null,null,null,"142 x 91",74.5,39.5,71.625,34.75,162.375,null,142,91]
[null,null,"Sw  Spacing between the Wheel Pairs on the Axle                                                                                                                                                                                                                                                                                                                                            Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,72,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select DOT"]
[null,null,"Sa Axle Spacing                                                                                                                                                                                                                                                                                                                                 Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,48,"in."]
[null,null,"Span  Clear span of the culvert (in)   See figure 8-2",null,null,null,null,{"$f":"H25","v":71}]
[null,null,"δsoil   Soil Unit Weight",null,null,null,null,120,"pcf"]
[null,null,"c  Soil Cohesion                                                                                                                                                                                                                                                                                                                                     Cohesion per ASCE Manual of Practice (MOP) 60. Standard values:                                                                                                                                                                                                                                         Clay, very soft:  40 psf\nClay, medium: 250 psf\nClay, hard: 1,000 psf\nSand, loose dry: 0 psf\nSand, silty: 100 psf\nSand, dense: 300 psf",null,null,null,null,0,"psf",null,null,null,"Figure 8-2",null,null,null,null,null,null,null,null,null,null,null,null,null,"-2kµ'H/Bc",null,{"$f":"-2*'Arch Pipe - Cement.'!H40*'Arch Pipe - Cement.'!H30/('Arch Pipe - Cement.'!H39*12)","v":-0.13007323943661969}]
[null,null,"Bc  outside span length of the liner (ft)",null,null,null,null,{"$f":"H36/12","v":5.916666666666667},null,null,null,null,"Figure 8-1"]
[null,null,"kµ'  Select kµ' - Refer to Figure 9-13 in ASCE MOP 60                                                                                                                                                                                                                                                                      kµ'=0.1924 min for granular material without cohesion                                                                                                                                                                                                                             kµ'=0.165 max for sand and gravel                                                                                                                                                                                                                                                                        kµ'=0.150 max for saturated top soil                                                                                                                                                                                                                                                                   kµ'=0.130 max for ordinary clay                                                                                                                                                                                                                                                                              kµ'=0.110 max for saturated clay                                                                                                                                                                                                                                                                                                                                                                                                                                                      ",null,null,null,null,0.19239999999999999]
[null,null,"Hw  Height of the Groundwater above the Top of the Pipe                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Hw = 0 if no groundwater                                                                                                                                                                                                                                                                                              ",null,null,null,null,0,"ft"]
[null,null,"Hr height of the vertical dimension of the pipe (ft).",null,null,null,null,{"$f":"H26/12","v":3.9166666666666665}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select kµ'",null,{"$f":"IF(C55=\"Note: The effects of live load is neglected.\",0,1)","v":1},null,"Yes"]
[null,null,"Select if it is a Single Span culvert or Multiple Span culverts? ",null,null,null,null,"Single Span",null,null,null,null,"Figure 8-3",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19239999999999999,null,null,null,"No"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16500000000000001]
[null,null,{"$f":"IF(H44=\"Single Span\",\"\",\"Specify the distance between inside faces of end walls perpendicular to roadway\")","v":""},null,null,null,null,0,{"$f":"IF(H44=\"Single Span\",\"\",\"ft\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.15]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.13]
[null,null,"Live and Dead Loads Results:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.11]
[]
[null,null,"Ct  Coefficient                                                                                                                                                                                                                                                           (Figure 9-13 in ASCE MOP 60)",null,null,null,null,{"$f":"(1-EXP('Arch Pipe - Cement.'!AC38))/(2*H40)","v":0.31696693851116553}]
[null,null,"PL  Live Load on Pipe",null,null,null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,(H28*H29*'Arch Pipe - Cement.'!AH7)/('Arch Pipe - Cement.'!AH8*'Arch Pipe - Cement.'!AH11),0),IF(H30<=(H46*12),(H28*H29*'Arch Pipe - Cement.'!AH7)/('Arch Pipe - Cement.'!AH8*'Arch Pipe - Cement.'!AH11),0))","v":12.283480073192148},"psi"]
[null,null,"PE  Earth Load acting on the Horizontal Soil Plane at the Top of the Pipe",null,null,null,null,{"$f":"'Arch Pipe - Cement.'!AH18","v":0.52827823085194259},"psi"]
[null,null,"Pw  External Hydrostatic Pressure acting on the Pipe",null,null,null,null,{"$f":"'Arch Pipe - Cement.'!AH20","v":0},"psi"]
[]
[null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,\"\",\"Note: The effects of live load is neglected.\"),IF(H30<=(H46*12),\"\",\"Note: The effects of live load is neglected.\"))","v":""}]
[null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For single-span culverts, the effects of live load may be neglected where the depth of fill is more than 8.0 ft. and exceeds the span length.\"),IF(H30<=(H46*12),\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For multiple span culverts, the effects of live load may be neglected where the depth of fill exceeds the distance between inside faces of end walls.\"))","v":""}]
[]
[]
[null,null,"Design Assumptions (Cementitious Liner):"]
[]
[null,null,"t  Wall Thickness of the Liner - See figure 8-3                                                                                                                                                                                                                                                   Note: Wall thickness is above the corrugation crests.                                  ",null,null,null,null,1,"in."]
[null,null,"Assume only the liner above the corrugation crests is effective? Select Yes or No",null,null,null,null,"No"]
[null,null,{"$f":"IF(H62=\"No\",\"c  Distance from the Centroid of the Liner Pipe Wall Profile to the Interior Wall Surface - See figure 8-3\",\"\")","v":"c  Distance from the Centroid of the Liner Pipe Wall Profile to the Interior Wall Surface - See figure 8-3"},null,null,null,null,0.63700000000000001,{"$f":"IF(H62=\"No\",\"in.\",\"\")","v":"in."},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H62=\"Yes\",0.5*H61,H63)","v":0.63700000000000001},"in."]
[null,null,{"$f":"IF(H62=\"No\",\"I  SAPL Area Moment of Inertia of the Liner Wall Section\",\"\")","v":"I  SAPL Area Moment of Inertia of the Liner Wall Section"},null,null,null,null,0.18140000000000001,{"$f":"IF(H62=\"No\",\"in.4/in\",\"\")","v":"in.4/in"},null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H62=\"Yes\",(H61^3)/12,H64)","v":0.18140000000000001},"in.4/in."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"H.in Parallel",null,null,null,null,{"$f":"(H35-H32)/H31","v":33.04347826086957}]
[null,null,"σCS  Compressive Stress Strength of the Liner Material                                                                                                                                                                                                                                                                                           Compressive strength value to be provided by manufacturer in accordance with Pipe Liner Special Provision.",null,null,null,null,-8390,"psi"]
[null,null,"σflex  Flexural Stress Strength (Modulus of Rupture) of the Liner Material                                                                                                                                                                                                                                                                                                                                                          Flexural strength value to be provided by manufacturer in accordance with Pipe Liner Special Provision.",null,null,null,null,1665,"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H30<AH65,H32+H31*H30,H32+H35+H31*H30)","v":37.599999999999994}]
[null,null,"γEV  Load Factor for Soil Prism Load - Service, 1.0",null,null,null,null,1]
[null,null,"γEV  Load Factor for Soil Prism Load - Strength, 1.30",null,null,null,null,1.3]
[null,null,"γWA Load Factor for Groundwater Load, 1.0",null,null,null,null,1]
[null,null,"γLL  Load Factor for Live Load - Service, 1.0",null,null,null,null,1]
[null,null,"γLL  Load Factor for Live Load - Strength, 1.75",null,null,null,null,1.75]
[null,null,"ƞEV  Load Modifier for Soil Prism Load, use 1.0 per Article 1.3.2 of the BDS",null,null,null,null,1]
[null,null,"ƞR  Load Modifier for Redundancy, 1.05 for Strength Limit State under Earth Loads",null,null,null,null,1.05]
[null,null,"ƞR  Load Modifier for Redundancy, 1.0 for Strength Limit State under Live Loads",null,null,null,null,1]
[null,null,"ƞLL  Load Modifier for Live Load, use 1.0 per Article 1.3.2 of the BDS",null,null,null,null,1]
[]
[null,null,"Results (Cementitious Liner)"]
[]
[null,null,"Service"]
[null,null,"Top Radius"]
[null,null,"Tservice  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H68*H52+'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H71*H51)*H23+H53","v":209.27487338308521},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H61","v":1},"in.2/in."]
[null,null,"Mservice  Moment",null,null,null,null,{"$f":"0.0062*'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H71*H51*(H23^2)","v":51.545968452442395},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Service)",null,null,null,null,{"$f":"(-(H82/H83))+((H84*T63)/T64)","v":-28.2672553885659},"psi",{"$f":"IF(H85>=H66,IF(H85<=H67,\"Stress within limits. The \"&H61&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]
[]
[null,null,"Bottom Radius"]
[null,null,"Tservice  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H23/H24)*(H68*H52+'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H71*H51)*H25*0.5+H53","v":67.385560136957139},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H61","v":1},"in.2/in."]
[null,null,"Mservice  Moment",null,null,null,null,{"$f":"0.0062*(H23/H24)*'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H71*H51*((H25*0.5)^2)","v":16.481501163519788},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Service)",null,null,null,null,{"$f":"(-(H88/H89))+((H90*T63)/T64)","v":-9.509505885787874},"psi",{"$f":"IF(H91>=H66,IF(H91<=H67,\"Stress within limits. The \"&H61&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]
[]
[null,null,"Strength"]
[null,null,"Top Radius"]
[null,null,"Tstrength  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H69*H73*H74*H52+'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H51*H72*H76*H75)*H23+H70*H53","v":360.179300629642},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H61","v":1},"in.2/in."]
[null,null,"Mstrengthe  moment",null,null,null,null,{"$f":"0.0062*'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H51*H72*H76*H75*(H23^2)","v":90.205444791774198},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Strength)",null,null,null,null,{"$f":"(-(H95/H96))+((H97*T63)/T64)","v":-43.415969139233141},"psi",{"$f":"IF(H98>=H66,IF(H98<=H67,\"Stress within limits. The \"&H61&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]
[]
[null,null,"Bottom Radius"]
[null,null,"Tstrength  Thrust in Liner",null,null,null,null,{"$f":"0.8323*(H23/H24)*(H69*H73*H74*H52+'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H51*H72*H76*H75)*H25*0.5+H70*H53","v":115.97610133652873},"lb/in."]
[null,null,"A  Area of the Cross-Section of the proposed Liner per linear inch",null,null,null,null,{"$f":"H61","v":1},"in.2/in."]
[null,null,"Mstrengthe  Moment",null,null,null,null,{"$f":"0.0062*(H23/H24)*'Arch Pipe - Cement.'!AH19*'Arch Pipe - Cement.'!H51*H72*H76*H75*((H25*0.5)^2)","v":28.84262703615963},"in.-lbs/in."]
[null,null,"σcrown  Normal Stress (Strength)",null,null,null,null,{"$f":"(-(H101/H102))+((H103*T63)/T64)","v":-14.693006396982497},"psi",{"$f":"IF(H104>=H66,IF(H104<=H67,\"Stress within limits. The \"&H61&\"-in. thick liner is sufficient.\",\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\"),\"Stress exceeds limits. The \"&H61&\"-in. thick liner is not sufficient.\")","v":"Stress within limits. The 1-in. thick liner is sufficient."}]

{"sheet":"Circular Pipe - Polym.","index":2,"n_rows":102,"n_cols":34,"rows_kept":102,"cut":false,"hidden":false,"merged":[[62,2,62,6],[58,2,58,6],[44,2,44,6],[43,2,43,6],[45,2,45,6],[59,2,59,6],[60,2,60,6],[56,2,56,6],[57,2,57,6],[2,2,2,15],[5,2,5,15],[31,2,31,6],[42,2,42,6],[33,2,33,6],[34,2,34,6],[36,2,36,6],[38,2,38,6],[23,2,23,6],[24,2,24,6],[25,2,25,6],[12,3,12,6],[13,3,13,6],[4,2,4,15],[7,3,7,6],[10,3,10,6],[8,3,8,6],[26,2,26,6],[55,2,55,6],[54,2,54,6],[47,2,47,6],[48,2,48,6],[27,2,27,6],[9,3,9,6],[28,2,28,6],[21,2,21,6],[22,2,22,6],[20,2,20,6],[11,3,11,6],[29,2,29,6],[32,2,32,6],[30,2,30,6],[97,8,97,13],[63,2,63,6],[80,2,80,6],[81,2,81,6],[82,2,82,6],[67,2,67,6],[64,2,64,6],[85,2,85,6],[75,2,75,6],[78,2,78,6],[76,2,76,6],[84,2,84,6],[83,2,83,6],[90,9,90,14],[101,2,101,6],[68,9,68,14],[65,2,65,6],[74,2,74,6],[68,2,68,6],[101,9,101,14],[88,9,88,14],[95,2,95,6],[96,2,96,6],[97,2,97,6],[100,2,100,6],[89,9,89,14],[89,2,89,6],[88,2,88,6],[77,2,77,6],[79,2,79,6],[54,26,54,27],[55,26,55,27],[2,27,2,34],[6,28,6,32],[7,28,7,32],[9,28,9,32],[10,28,10,32],[11,28,11,32],[20,28,20,32],[12,28,12,32],[18,28,18,32],[19,28,19,32],[23,28,23,32]]}
[]
[]
[null,null,"SAPL Design",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Circular Pipe - Polymeric"]
[]
[null,null,"Structural Design for Liner Thickness Using Flexible Polymeric Materials       ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Live and Dead Loads Calculation:"]
[null,null,"Circular Corrugated Metal Pipe"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If impact factor = 1 + 0.33 [(96 – h)/96] ≥ 1.0",null,null,null,null,{"$f":"MAX((1+0.33*((96-'Circular Pipe - Polym.'!H23)/96)),1)","v":1.2475000000000001}]
[null,null,"Project:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"lw load width parallel to direction of travel (in)\n\n",null,null,null,null,{"$f":"AH25","v":37.599999999999994}]
[null,null,"Trial:"]
[null,null,"Location:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"hint (in)",null,null,null,null,{"$f":"('Circular Pipe - Polym.'!H27-'Circular Pipe - Polym.'!H26-0.06*'Circular Pipe - Polym.'!H29)/'Circular Pipe - Polym.'!H24","v":42.086956521739133}]
[null,null,"DOT:","Select DOT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ww  Load width perpendicular to direction of travel (in)",null,null,null,null,{"$f":"IF('Circular Pipe - Polym.'!H23<'Circular Pipe - Polym.'!AH10,'Circular Pipe - Polym.'!H26+'Circular Pipe - Polym.'!H24*'Circular Pipe - Polym.'!H23+0.06*'Circular Pipe - Polym.'!H29,(('Circular Pipe - Polym.'!H26+'Circular Pipe - Polym.'!H27+'Circular Pipe - Polym.'!H24*'Circular Pipe - Polym.'!H23)+0.06*'Circular Pipe - Polym.'!H29))","v":51.199999999999996}]
[null,null,"Latitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF('Circular Pipe - Polym.'!H23/12<'Circular Pipe - Polym.'!H32,'Circular Pipe - Polym.'!H23/12,'Circular Pipe - Polym.'!H32)","v":2},null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - No groundwater",null,null,null,null,{"$f":"'Circular Pipe - Polym.'!H43*('Circular Pipe - Polym.'!H30*AA12-2*'Circular Pipe - Polym.'!H31)/144","v":0.61789412025085744}]
[null,null,"Longitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - With groundwater",null,null,null,null,{"$f":"(('Circular Pipe - Polym.'!H43*AA12-'Circular Pipe - Polym.'!H34)*'Circular Pipe - Polym.'!H30+'Circular Pipe - Polym.'!H34*('Circular Pipe - Polym.'!H30-62.4))/144","v":0.61789412025085744}]
[null,null,"Date:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"0.433*('Circular Pipe - Polym.'!H34+'Circular Pipe - Polym.'!H35)","v":2.165}]
[]
[null,null,"Input"]
[null,null,"Output",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Design (Cementitious Liner):"]
[]
[null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi)",null,null,null,null,{"$f":"IF('Circular Pipe - Polym.'!H34=0,'Circular Pipe - Polym.'!AH12,'Circular Pipe - Polym.'!AH13)","v":0.61789412025085744}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CL  live load distribution coefficient (in.), is equal to lw / S ≤ 1.0",null,null,null,null,{"$f":"MIN(AH8/'Circular Pipe - Polym.'!H65,1)","v":0.62666666666666659}]
[null,null,"Mp  Multiple Presence Factor, typically equal to 1.2                                                                                                                                                                                                                               Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.                                                                                                                                                                                                                Table 3.6.1.1.2.1.                                                                                                                              ",null,null,null,null,1.2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"IF('Circular Pipe - Polym.'!H34=0,0,'Circular Pipe - Polym.'!AH14)","v":0}]
[null,null,"P  Design Wheel Load                                                                                                                                                                                                                                                                                                                     Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                         Section 3.6.1.2.6b.                                                                                                                                                                                                                                                                                                      P Load is the weight an AASHTO design truck imposes on a single wheel (or pair of wheels in the case of dual wheels).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Typical HL-93 Design Truck has 3 axles, front axle load of 8 kips, and two rear axles with a load of 32 kips each (rear wheel load of 16 kips each)                                                      ",null,null,null,null,16000,"lb"]
[null,null,"h  Depth of Cover over Culvert                                                                                                                                                                                                                                                                                                                                                                                    Distance from top of the pipe to top of the soil",null,null,null,null,24,"in."]
[null,null,"LLDF  Live Load Distribution Factor                                                                                                                                                                                                                                                                                                                       Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                                                                                                            table 3.6.1.2.6a-1                                                                                                                                                                                                                                                                                                                         For Concrete Pipe with fill depth 2.0ft or greater, linearly interpolate between these limits:  \n1.15 for diameter 2.0ft or less\n1.75 for diameters 8.0ft or greater \nAll other culverts and buried structures: 1.15",null,null,null,null,1.1499999999999999,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"H.in Parallel",null,null,null,null,{"$f":"(H28-H25)/H24","v":33.04347826086957}]
[null,null,"lt  Tire Patch Length                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,10,"in.",null,null,null,"Figure 8-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H23<AH24,H25+H24*H23,H25+H28+H24*H23)","v":37.599999999999994}]
[null,null,"Wt  Tire Patch Width                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,20,"in."]
[null,null,"Sw  Spacing between the Wheel Pairs on the Axle                                                                                                                                                                                                                                                                                                                                            Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,72,"in."]
[null,null,"Sa Axle Spacing                                                                                                                                                                                                                                                                                                                                 Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,48,"in."]
[null,null,"Di  Inside Diameter or Clear Span of the Culvert",null,null,null,null,60,"in."]
[null,null,"δsoil   Soil Unit Weight",null,null,null,null,120,"pcf"]
[null,null,"c  Soil Cohesion                                                                                                                                                                                                                                                                                                                                     Cohesion per ASCE Manual of Practice (MOP) 60. Standard values:                                                                                                                                                                                                                                         Clay, very soft:  40 psf\nClay, medium: 250 psf\nClay, hard: 1,000 psf\nSand, loose dry: 0 psf\nSand, silty: 100 psf\nSand, dense: 300 psf",null,null,null,null,0,"psf"]
[null,null,"Bc O.D. or outside span length of the liner (ft)",null,null,null,null,{"$f":"H29/12","v":5}]
[null,null,"kµ'  Select kµ' - Refer to Figure 9-13 in ASCE MOP 60                                                                                                                                                                                                                                                                      kµ'=0.1924 min for granular material without cohesion                                                                                                                                                                                                                             kµ'=0.165 max for sand and gravel                                                                                                                                                                                                                                                                        kµ'=0.150 max for saturated top soil                                                                                                                                                                                                                                                                   kµ'=0.130 max for ordinary clay                                                                                                                                                                                                                                                                              kµ'=0.110 max for saturated clay                                                                                                                                                                                                                                                                                                                                                                                                                                                      ",null,null,null,null,0.19239999999999999,null,null,null,null,"Figure 8-2"]
[null,null,"Hw  Height of the Groundwater above the Top of the Pipe                                                                                                                                                                                                                            See figure 8-2                                                                                                                                                                                                                                                                                                                   Hw = 0 if no groundwater                                                                                                                                                                                                                                                                                              ",null,null,null,null,0,"ft"]
[null,null,"Hr height of the vertical dimension of the pipe (ft).",null,null,null,null,{"$f":"H29/12","v":5}]
[]
[null,null,"Select if it is a Single Span culvert or Multiple Span culverts? ",null,null,null,null,"Single Span"]
[]
[null,null,{"$f":"IF(H37=\"Single Span\",\"\",\"Specify the distance between inside faces of end walls perpendicular to roadway\")","v":""},null,null,null,null,0,{"$f":"IF(H37=\"Single Span\",\"\",\"ft\")","v":""},null,null,null,"Figure 8-3",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Single Span"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Multiple Span"]
[null,null,"Live and Dead Loads Results:"]
[]
[null,null,"Ct  Coefficient                                                                                                                                                                                                                                                           (Figure 9-13 in ASCE MOP 60)",null,null,null,null,{"$f":"(1-EXP('Circular Pipe - Polym.'!AC56))/(2*H33)","v":0.37073647215051442},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Delaware Department of Transportation"]
[null,null,"PL  Live Load on Pipe",null,null,null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,(H21*H22*'Circular Pipe - Polym.'!AH7)/('Circular Pipe - Polym.'!AH8*'Circular Pipe - Polym.'!AH11),0),IF(H23<=(H39*12),(H21*H22*'Circular Pipe - Polym.'!AH7)/('Circular Pipe - Polym.'!AH8*'Circular Pipe - Polym.'!AH11),0))","v":12.441821808510642},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Florida Department of Transportation"]
[null,null,"PE  Earth Load acting on the Horizontal Soil Plane at the Top of the Pipe",null,null,null,null,{"$f":"'Circular Pipe - Polym.'!AH19","v":0.61789412025085744},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minnesota Department of Transportation"]
[null,null,"Pw  External Hydrostatic Pressure Acting on the Pipe",null,null,null,null,{"$f":"'Circular Pipe - Polym.'!AH21","v":0},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"New York State Department of Transportation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"North Carolina Department of Transportation"]
[null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,\"\",\"Note: The effects of live load is neglected.\"),IF(H23<=(H39*12),\"\",\"Note: The effects of live load is neglected.\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ohio Department of Transportation"]
[null,null,{"$f":"IF(H37=\"Single Span\",IF(H23<=96,\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For single-span culverts, the effects of live load may be neglected where the depth of fill is more than 8.0 ft. and exceeds the span length.\"),IF(H23<=(H39*12),\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For multiple span culverts, the effects of live load may be neglected where the depth of fill exceeds the distance between inside faces of end walls.\"))","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pennsylvania Department of Transportation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select DOT"]
[null,null,"Design Assumptions (Flexible Polymeric Liner):"]
[]
[null,null,"Deflection Verification"]
[]
[null,null,"Do  outside diameter of liner (in)",null,null,null,null,{"$f":"H29","v":60}]
[null,null,"Di  inner diameter of the liner",null,null,null,null,{"$f":"H55","v":60},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"-2kµ'H/Bc",null,{"$f":"-2*'Circular Pipe - Polym.'!H33*'Circular Pipe - Polym.'!H23/('Circular Pipe - Polym.'!H32*12)","v":-0.15391999999999997}]
[null,null,"t  Wall Thickness of the Liner - See figure 8-3                                                                                                                                                                                                                                                   Note: Wall thickness is above the corrugation crests.                                  ",null,null,null,null,1.2,"in."]
[null,null,"ISAPL  Moment of Inertia of Liner Profile per unit length of Liner",null,null,null,null,4.5600000000000002E-2,"in4/in"]
[null,null,"DL  Deflection Lag Factor, a value of 1.0 is recommended for rehabilitation lining                                                                                                                                                                                                                                                                                                                                                                                                 Refer to AASHTO LRFD Bridge Design Manual, 8th Ed., Section 12.12.2.2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         ",null,null,null,null,1]
[null,null,"KB  Bedding Coefficient, a value of 0.083 is recommended for rehabilitation lining                                                                                                                                                                                                                                                                                                                                                        Refer to AASHTO LRFD Bridge Design Manual, 8th Ed., Section 12.12.2.2                                                                                                                                                                               ",null,null,null,null,8.3000000000000004E-2]
[null,null,"ESAPL  Short-Term Circumferential Flexural Modulus of Liner Material                                                                                                                                                                                                       For determining long term and short term modulus of elasticity, use ASTM D790 standard test methods for short term, and ASTM D2990  standard test methods for long term. In the absence of the ASTM D2990 standard tests, it is a common practice to use 50% of the short term modulus of elasticity as a value for the long term modulus of elasticity.",null,null,null,null,735,"ksi"]
[]
[null,null,"R  radius of liner measured to the centroid of liner profile",null,null,null,null,{"$f":"(H55-H57)*0.5","v":29.4},"in."]
[null,null,"Ms  Secant Constrained Soil Modulus, as specified in Article 12.12.3.5                                                                                                                                                                                                        A conservative value for Ms is 0.503, which assumes sandy soil at 85% compaction.                                                                                                                                                                                  Alternately, use the Pe value above to determine Ms from Table 12.12.3.5-1 of AASHTO LRFD Bridge Design Specifications.                                                          ",null,null,null,null,0.503,"ksi"]
[null,null,"S  span of culvert (in)",null,null,null,null,{"$f":"H55","v":60}]
[null,null,"ΔA  Maximum Percentage of the Allowable Deflection                                                                                                                                                                                                                                          [ ΔA = % x Di ]",null,null,null,null,0.05,"%"]
[null,null,"Results",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select kµ'",null,{"$f":"IF(C48=\"Note: The effects of live load is neglected.\",0,1)","v":1}]
[null,null,"ΔA  Total Allowable Deflection of Liner, Reduction in Vertical Diameter ",null,null,null,null,{"$f":"H66*H56","v":3},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19239999999999999]
[null,null,"Δt  Total Deflection of the Pipe, expressed as a Reduction of the Vertical Diameter",null,null,null,null,{"$f":"((H60*(H59*H45+'Circular Pipe - Polym.'!AH20*'Circular Pipe - Polym.'!H44)*'Circular Pipe - Polym.'!H55))/(1000*(((H61*H58/(H63^3))+0.061*H64)))","v":1.3094709030005571},"in.",{"$f":"IF(H69<=H68,\"Δt ≤ Δa - Deflection within limits\",\"Δt > Δa - Deflection exceeds limit\")","v":"Δt ≤ Δa - Deflection within limits"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16500000000000001]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.15]
[null,null,"Design Assumptions (Flexible Polymeric Liner):",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.13]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.11]
[null,null,"Strength limit state for global buckling"]
[]
[null,null,"γWA  Load Factor for Hydrostatic Pressure, as per Article 3.4.1, use 1.0",null,null,null,null,1]
[null,null,"γEV  Load Factor for Vertical Pressure from Dead Load of Earth Fill, recommend 1.3 for rehab                                                                                                                                                             See Table 3.4.1-2 of AASHTO LRFD Bridge Design Specifications for the range of possible values. Values range from 1.95 to 0.9 for Thermoplastic Pipe, with 1.95 being more conservative.                                                                                                     ",null,null,null,null,1.3]
[null,null,"γLL  Load Factor for Live Load , as specified in Article 3.4.1",null,null,null,null,1.75]
[null,null,"ƞEV  Load Modifier for Vertical Pressure from Dead Load of Earth Fill on a Buried  Structure per Article 1.3.2, recommend 1.0 for rehab",null,null,null,null,1]
[null,null,"ƞLL  Load Modifier as Specified in Article 1.3.2, as they apply to live loads on culverts                                                                                                                                                                          use 1.0 per Article 1.3.2                     \n",null,null,null,null,1]
[null,null,"RW  water buoyancy factor (0.67 minimum) = 1-0.33 (HW/H)",null,null,null,null,{"$f":"MAX(0.67,1-0.33*(H34/(H23/12)))","v":1}]
[null,null,"r  mean radius of liner = (OD-t)/2  (in)",null,null,null,null,{"$f":"(H55-H57)*0.5","v":29.4}]
[null,null,"Cn  Scalar Calibration Factor, 0.55",null,null,null,null,0.55000000000000004]
[null,null,"ϕs Resistance Factor of the Soil to account for variability, 0.9                                                                                                                                                                                                                           Refer to AASHTO LRFD Bridge Design Specifications 8th ed. Table 12.5.5-1.                                                     ",null,null,null,null,0.9]
[null,null,"ϕbck Resistance Factor for Global Buckling as defined in Table 12.5.5-1, use 0.70",null,null,null,null,0.7]
[null,null,"ESAPL  Long-Term Circumferential Flexural Modulus of Liner Material                                                                                                                                                                                                        For determining long term and short term modulus of elasticity, use ASTM D790 standard test methods for short term, and ASTM D2990  standard test methods for long term. In the absence of the ASTM D2990 standard tests, it is a common practice to use 50% of the short term modulus of elasticity as a value for the long term modulus of elasticity.",null,null,null,null,529,"ksi"]
[null,null,"ν  Poisson's Ratio of the Soil, 0.3",null,null,null,null,0.3]
[]
[null,null,"Results"]
[null,null,"εfb   Factored Buckling Strain Demand",null,null,null,null,{"$f":"((H75*H78*H34*0.433+H76*H78*H45*H80+H77*H79*'Circular Pipe - Polym.'!AH20*H44)*H81)/(1000*H85*H57)","v":6.6913221806236267E-4},"in./in."]
[null,null,"εbck   Nominal Strain Capacity for Buckling",null,null,null,null,{"$f":"(1.2*H82*((H85*H58)^(1/3))*(((H83*H64*(1-2*H86))/((1-H86)^2))^(2/3))*(11.4/(11+(H55/H23))))/(H57*H85)","v":1.3063750450690377E-3},"in./in.",{"$f":"IF(H89<=(H84*H90),\"The strength buckling limit state is satisfied by the \"&H57&\" inch-thick liner\",\"The strength buckling limit state is Not satisfied by the \"&H57&\" inch-thick liner\")","v":"The strength buckling limit state is satisfied by the 1.2 inch-thick liner"}]
[null,null,null,null,null,null,null,null,null,{"$f":"IF(H23<=2*H55,\"\",\"Note: depth of fill over top of pipe (H) = \"&H23&\" in. used to calculate εbck is greater than two times the OD\")","v":""}]
[null,null,"Design Assumptions (Flexible Polymeric Liner):"]
[]
[null,null,"Strength limit state for flexure"]
[]
[null,null,"ϕf  Resistance Factor for Flexure, 0.90 (Table 12.5.5-1, BDS)",null,null,null,null,0.9]
[null,null,"Sb  Long-Term Ring-Bending Strain for Product under Design per the Manufacturer's Testing                                                                                                                                                             Sb is obtained from manufacturer's ASTM D5365 test results.                              \n",null,null,null,null,1.2999999999999999E-2]
[null,null,"Df Shape Factor (dimensionless)                                                                                                                                                                                  See Table 12.12.3.10.2b-1 of AASHTO LRFD Bridge Design Specifications                                                                                                                                                                                                             A conservative value is 5.5 for poorly compacted gravel.\n\n",null,null,null,null,5.5]
[]
[null,null,"Results"]
[null,null,"εf  Factored Long-Term Strain due to Flexure",null,null,null,null,{"$f":"H76*H98*(H57/(H63*2))*(H68/(2*H63))","v":7.4448146605581023E-3}]
[null,null,"ϕf Sb",null,null,null,null,{"$f":"H96*H97","v":1.17E-2},null,{"$f":"IF(H101<=H102,\"εf ≤ ϕf Sb: The long-term strain due to the estimated deflection is acceptable\",\"εf > ϕf Sb: The long-term strain due to the estimated deflection is not acceptable\")","v":"εf ≤ ϕf Sb: The long-term strain due to the estimated deflection is acceptable"}]

{"sheet":"Arch Pipe - Polym.","index":3,"n_rows":88,"n_cols":47,"rows_kept":88,"cut":false,"hidden":false,"merged":[[68,28,68,32],[11,3,11,6],[12,3,12,6],[13,3,13,6],[23,2,23,6],[37,2,37,6],[24,2,24,6],[25,2,25,6],[27,2,27,6],[28,2,28,6],[29,2,29,6],[30,2,30,6],[31,2,31,6],[32,2,32,6],[33,2,33,6],[35,2,35,6],[2,2,2,15],[5,2,5,15],[20,2,20,6],[21,2,21,6],[22,2,22,6],[4,2,4,15],[7,3,7,6],[9,3,9,6],[10,3,10,6],[8,3,8,6],[36,2,36,6],[34,2,34,6],[63,2,63,6],[38,2,38,6],[49,2,49,6],[40,2,40,6],[41,2,41,6],[43,2,43,6],[45,2,45,6],[50,2,50,6],[51,2,51,6],[52,2,52,6],[60,2,60,6],[62,2,62,6],[39,2,39,6],[54,2,54,6],[55,2,55,6],[64,2,64,6],[65,2,65,6],[66,2,66,6],[79,2,79,6],[61,2,61,6],[80,2,80,6],[67,2,67,6],[68,2,68,6],[69,2,69,6],[70,2,70,6],[77,2,77,6],[85,2,85,6],[71,2,71,6],[72,2,72,6],[85,9,85,14],[87,9,87,14],[73,2,73,6],[86,2,86,6],[87,2,87,6],[83,9,83,14],[81,2,81,6],[82,2,82,6],[83,2,83,6],[80,9,80,14],[84,2,84,6],[78,9,78,14],[78,2,78,6],[2,27,2,34],[6,28,6,32],[7,28,7,32],[9,28,9,32],[10,28,10,32],[11,28,11,32],[20,28,20,32],[12,28,12,32],[18,28,18,32],[19,28,19,32],[52,26,52,27],[22,28,22,32],[23,28,23,32],[24,28,24,32],[25,28,25,32],[26,28,26,32],[32,28,32,32],[33,28,33,32],[27,28,27,32],[28,28,28,32],[29,28,29,32],[30,28,30,32],[31,28,31,32]]}
[]
[]
[null,null,"SAPL Design",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Arch Pipe - Polymeric",null,null,null,null,null,null,null,null,null,null,"Pipe Arch Size (in.)","Cross-sectional Area (ft2)","Springline Rise, B (in)","Top Radius (in)","Bottom Corner Radius (in)","Bottom Radius (in)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"17 x 13",1.1000000000000001,4.125,8.625,3.5,25.625,null,17,13]
[null,null,"Structural Design for Liner Thickness Using Flexible Polymeric Materials",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,"21 x 15",1.6,4.875,10.75,4.125,33.125,null,21,15]
[null,null,"Arch Corrugated Metal Pipe",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"20 x 16",1.7,5.125,10.25,5,27.5,null,20,16]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If impact factor = 1 + 0.33 [(96 – h)/96] ≥ 1.0",null,null,null,null,{"$f":"MAX((1+0.33*((96-'Arch Pipe - Polym.'!H30)/96)),1)","v":1.2475000000000001},null,null,null,null,"23 x 19",2.2999999999999998,5.875,11.625,5.375,34.25,null,23,19]
[null,null,"Project:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"lw load width parallel to direction of travel (in)\n\n",null,null,null,null,{"$f":"AH70","v":37.599999999999994},null,null,null,null,"24 x 18",2.2000000000000002,5.625,11.875,4.875,34.625,null,24,18]
[null,null,"Trial:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"27 x 21",3,6.75,13.5,5.75,40.875,null,27,21]
[null,null,"Location:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"hint (in)",null,null,null,null,{"$f":"('Arch Pipe - Polym.'!H34-'Arch Pipe - Polym.'!H33-0.06*'Arch Pipe - Polym.'!H36)/'Arch Pipe - Polym.'!H31","v":41.513043478260876},null,null,null,null,"28 x 20",2.9,6.5,14,5.5,42.25,null,28,20]
[null,null,"DOT:","Select DOT",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ww  Load width perpendicular to direction of travel (in)",null,null,null,null,{"$f":"IF('Arch Pipe - Polym.'!H30<'Arch Pipe - Polym.'!AH10,'Arch Pipe - Polym.'!H33+'Arch Pipe - Polym.'!H31*'Arch Pipe - Polym.'!H30+0.06*'Arch Pipe - Polym.'!H36,(('Arch Pipe - Polym.'!H33+'Arch Pipe - Polym.'!H34+'Arch Pipe - Polym.'!H31*'Arch Pipe - Polym.'!H30)+0.06*'Arch Pipe - Polym.'!H36))","v":51.859999999999992},null,null,null,null,"33 x 26",4.7,8.75,16.625,7.125,51.375,null,33,26]
[null,null,"Latitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF('Arch Pipe - Polym.'!H30/12<'Arch Pipe - Polym.'!H39,'Arch Pipe - Polym.'!H30/12,'Arch Pipe - Polym.'!H39)","v":2},null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - No groundwater",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!H50*('Arch Pipe - Polym.'!H37*AA12-2*'Arch Pipe - Polym.'!H38)/144","v":0.52827823085194259},null,null,null,null,"35 x 24",4.5,8.125,17.875,6.875,55.125,null,35,24]
[null,null,"Longitude:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi) - With groundwater",null,null,null,null,{"$f":"(('Arch Pipe - Polym.'!H50*AA12-'Arch Pipe - Polym.'!H41)*'Arch Pipe - Polym.'!H37+'Arch Pipe - Polym.'!H41*('Arch Pipe - Polym.'!H37-62.4))/144","v":0.52827823085194259},null,null,null,null,"40 x 31",6.7,10.375,20.25,8.375,62.5,null,40,31]
[null,null,"Date:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"0.433*('Arch Pipe - Polym.'!H41+'Arch Pipe - Polym.'!H42)","v":1.6959166666666665},null,null,null,null,"42 x 29",6.5,9.75,21.5,8.25,66.125,null,42,29]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"46 x 36",9.1999999999999993,12.375,23.25,9.75,73,null,46,36]
[null,null,"Input",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"49 x 33",8.9,11.375,25.125,9.625,77.25,null,49,33]
[null,null,"Output",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Design (Cementitious Liner):",null,null,null,null,null,null,null,null,null,"53 x 41",11.7,15.25,28.0625,10.1875,73.4375,null,53,41]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"57 x 38",11.6,13,28.625,11,88.25,null,57,38]
[null,null,"Live and Dead Loads Calculation:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"PE  earth load acting on the horizontal soil plane at the top of the pipe (psi)",null,null,null,null,{"$f":"IF('Arch Pipe - Polym.'!H41=0,'Arch Pipe - Polym.'!AH12,'Arch Pipe - Polym.'!AH13)","v":0.52827823085194259},null,null,null,null,"60 x 46",15.6,20.5,29.375,18.75,51.125,null,60,46]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CL  live load distribution coefficient (in.), is equal to lw / S ≤ 1.0",null,null,null,null,{"$f":"MIN(AH8/'Arch Pipe - Polym.'!H25,1)","v":0.52957746478873235},null,null,null,null,"64 x 43",14.7,14.625,32.25,12.375,99.25,null,64,43]
[null,null,"Select Standard Pipe Arch Sizes",null,null,null,null,"71 x 47","in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pw  external hydrostatic pressure acting on the pipe (psi)",null,null,null,null,{"$f":"IF('Arch Pipe - Polym.'!H41=0,0,'Arch Pipe - Polym.'!AH14)","v":0},null,null,null,null,"66 x 51",19.3,22.75,32.625,20.75,56.25,null,66,51]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"71 x 47",18.100000000000001,16.25,35.75,13.75,110.25,null,71,47]
[null,null,"Pipe Arch - Top Radius",null,null,null,null,{"$f":"VLOOKUP(H21,AM3:AR37,4,FALSE)","v":35.75},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P =  (0.433∙Hw ) + Rtop/Rbottom (PE/144+CL∙PL)     (psi)",null,null,null,null,{"$f":"0.433*'Arch Pipe - Polym.'!H41+('Arch Pipe - Polym.'!H23/'Arch Pipe - Polym.'!H24)*('Arch Pipe - Polym.'!H52+'Arch Pipe - Polym.'!AH20*'Arch Pipe - Polym.'!H51)","v":2.2806497568068509},null,null,null,null,"73 x 55",23.2,25.125,36.75,22.875,63.75,null,73,55]
[null,null,"Pipe Arch - Bottom Radius",null,null,null,null,{"$f":"VLOOKUP(H21,AM3:AR37,6,FALSE)","v":110.25},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"pcr = 0.60 ESAPL  t2.2 / (P2⁄5 Rbottom9⁄5 )  (psi)",null,null,null,null,{"$f":"(0.6*'Arch Pipe - Polym.'!H68*1000*('Arch Pipe - Polym.'!H61^2.2))/(('Arch Pipe - Polym.'!H65^0.4)*('Arch Pipe - Polym.'!H24^1.8))","v":11.429640510190815},null,null,null,null,"77 x 52",21.9,17.875,39.375,15.125,121.25,null,77,52]
[null,null,"Pipe Arch - Span",null,null,null,null,{"$f":"VLOOKUP(H21,AM3:AV37,8,FALSE)","v":71},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"dcr=0.5 Γ(d,g)  Rbottom/k(2⁄5)  ((t2 P)/(Rbottom )3 )(2⁄5)  (in)",null,null,null,null,{"$f":"(0.5*'Arch Pipe - Polym.'!H69*'Arch Pipe - Polym.'!H24*(((('Arch Pipe - Polym.'!H61^2)*'Arch Pipe - Polym.'!H65)/('Arch Pipe - Polym.'!H24^3))^0.4))/('Arch Pipe - Polym.'!H64^0.4)","v":1.5871531176318807},null,null,null,null,"81 x 59",27.4,23.75,39.5,20.875,82.625,null,81,59]
[null,null,"Pipe Arch - Rise",null,null,null,null,{"$f":"VLOOKUP(H21,AM3:AV37,9,FALSE)","v":47},"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"M_cr=0.1Γ_(M,g)  (E_SAPL (t)^3)/R_bottom   ()",null,null,null,null,{"$f":"(0.1*'Arch Pipe - Polym.'!H70*'Arch Pipe - Polym.'!H68*1000*('Arch Pipe - Polym.'!H61^3))/'Arch Pipe - Polym.'!H24","v":666.66666666666663},null,null,null,null,"83 x 57",26,19.5,43,16.5,132.25,null,83,57]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"N_cr=1.26p_cr R_bottom",null,null,null,null,{"$f":"1.26*AH24*'Arch Pipe - Polym.'!H24","v":1587.7485114731571},null,null,null,null,"87 x 63",32.1,25.75,43.375,22.625,92.25,null,87,63]
[null,null,"Mp  Multiple Presence Factor, typically equal to 1.2                                                                                                                                                                                                                               Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.                                                                                                                                                                                                                Table 3.6.1.1.2.1.                                                                                                                              ",null,null,null,null,1.2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"m_b=(2.56〖(α⁄α_cr )〗^2)/(1+4.35〖(α⁄α_cr )〗^5 )",null,null,null,null,{"$f":"(2.56*(('Arch Pipe - Polym.'!H67/'Arch Pipe - Polym.'!H80)^2))/(1+4.35*(('Arch Pipe - Polym.'!H67/'Arch Pipe - Polym.'!H80)^5))","v":0.61887466048639905},null,null,null,null,"95 x 67",37,27.75,47,24.375,100.25,null,95,67]
[null,null,"P  Design Wheel Load                                                                                                                                                                                                                                                                                                                     Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                         Section 3.6.1.2.6b.                                                                                                                                                                                                                                                                                                      P Load is the weight an AASHTO design truck imposes on a single wheel (or pair of wheels in the case of dual wheels).                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Typical HL-93 Design Truck has 3 axles, front axle load of 8 kips, and two rear axles with a load of 32 kips each (rear wheel load of 16 kips each)                                                 ",null,null,null,null,16000,"lb",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"M_u=(m_b (p⁄p_cr )M_cr)/(1-(1-m_b)〖(p⁄p_cr )〗^2 )",null,null,null,null,{"$f":"(AH28*(AH23/AH24)*AH26)/((1-(((1-AH28))*((AH23/AH24)^2))))","v":83.594607957028941},null,null,null,null,"103 x 71",42.4,29.75,51.25,26.125,111.625,null,103,71]
[null,null,"h  Depth of Cover over Culvert                                                                                                                                                                                                                                                                                                                                                                                    Distance from top of the pipe to top of the soil",null,null,null,null,24,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"N_u=p/p_cr  N_cr ",null,null,null,null,{"$f":"(AH23/AH24)*AH27","v":316.81646096682368},null,null,null,null,"112 x 75",48,31.625,54.875,27.75,120.25,null,112,75]
[null,null,"LLDF  Live Load Distribution Factor                                                                                                                                                                                                                                                                                                                       Refer to AASHTO Bridge Desgin Specifications, 8th Ed.,                                                                                                                                                                                                                                                                                                            table 3.6.1.2.6a-1                                                                                                                                                                                                                                                                                                                         For Concrete Pipe with fill depth 2.0ft or greater, linearly interpolate between these limits:  \n1.15 for diameter 2.0ft or less\n1.75 for diameters 8.0ft or greater \nAll other culverts and buried structures: 1.15",null,null,null,null,1.1499999999999999,null,null,null,null,"Figure 8-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ_(u,b)=(6M_u)/t^2 ",null,null,null,null,{"$f":"6*AH29/('Arch Pipe - Polym.'!H61^2)","v":501.56764774217368},null,null,null,null,"117 x 79",54.2,33.625,59.375,29.5,131.75,null,117,79]
[null,null,"lt  Tire Patch Length                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,10,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ_(u,d)=N_u/A  ",null,null,null,null,{"$f":"AH30/'Arch Pipe - Polym.'!H61","v":316.81646096682368},null,null,null,null,"128 x 83",60.5,35.625,63.25,31.25,139.75,null,128,83]
[null,null,"Wt  Tire Patch Width                                                                                                                                                                                                                                                                                                                                              Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.5.",null,null,null,null,20,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"σ_u=σ_(u,b)+σ_(u,d)",null,null,null,null,{"$f":"AH31+AH32","v":818.38410870899736},null,null,null,null,"137 x 87",67.400000000000006,37.625,67.375,33,149.5,null,137,87]
[null,null,"Sw  Spacing Between the Wheel Pairs on the Axle                                                                                                                                                                                                                                                                                                                                            Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,72,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"d_s=d_cr [1- (1-p/p_cr )^0.5 ]     (in)",null,null,null,null,{"$f":"AH25*(1-AJ34)","v":0.1671505314009174},null,{"$f":"(1-(AH23/AH24))^0.5","v":0.89468531451438338},null,null,"142 x 91",74.5,39.5,71.625,34.75,162.375,null,142,91]
[null,null,"Sa Axle Spacing                                                                                                                                                                                                                                                                                                                                 Refer to AASHTO LRFD Bridge Design Specifications, 8th Ed.  Section 3.6.1.2.3.",null,null,null,null,48,"in."]
[null,null,"Span  Clear span of the culvert (in)   See figure 8-2",null,null,null,null,{"$f":"H25","v":71}]
[null,null,"δsoil   Soil Unit Weight",null,null,null,null,120,"pcf"]
[null,null,"c  Soil Cohesion                                                                                                                                                                                                                                                                                                                                     Cohesion per ASCE Manual of Practice (MOP) 60. Standard values:                                                                                                                                                                                                                                         Clay, very soft:  40 psf\nClay, medium: 250 psf\nClay, hard: 1,000 psf\nSand, loose dry: 0 psf\nSand, silty: 100 psf\nSand, dense: 300 psf",null,null,null,null,0,"psf",null,null,null,"Figure 8-2"]
[null,null,"Bc  outside span length of the liner (ft)",null,null,null,null,{"$f":"H36/12","v":5.916666666666667},null,null,null,null,"Figure 8-1",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Single Span"]
[null,null,"kµ'  Select kµ' - Refer to Figure 9-13 in ASCE MOP 60                                                                                                                                                                                                                                                                      kµ'=0.1924 min for granular material without cohesion                                                                                                                                                                                                                             kµ'=0.165 max for sand and gravel                                                                                                                                                                                                                                                                        kµ'=0.150 max for saturated top soil                                                                                                                                                                                                                                                                   kµ'=0.130 max for ordinary clay                                                                                                                                                                                                                                                                              kµ'=0.110 max for saturated clay                                                                                                                                                                                                                                                                                                                                                                                                                                                      ",null,null,null,null,0.19239999999999999,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Multiple Span"]
[null,null,"Hw  Height of the Groundwater above the Top of the Pipe                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Hw = 0 if no groundwater                                                                                                                                                                                                                                                                                              ",null,null,null,null,0,"ft"]
[null,null,"Hr height of the vertical dimension of the pipe (ft).",null,null,null,null,{"$f":"H26/12","v":3.9166666666666665}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Delaware Department of Transportation"]
[null,null,"Select if it is a Single Span culvert or Multiple Span culverts? ",null,null,null,null,"Single Span",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Florida Department of Transportation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Minnesota Department of Transportation"]
[null,null,{"$f":"IF(H44=\"Single Span\",\"\",\"Specify the distance between inside faces of end walls perpendicular to roadway\")","v":""},null,null,null,null,0,{"$f":"IF(H44=\"Single Span\",\"\",\"ft\")","v":""},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"New York State Department of Transportation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"North Carolina Department of Transportation"]
[null,null,"Live and Dead Loads Results:",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Ohio Department of Transportation"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Pennsylvania Department of Transportation"]
[null,null,"Ct  Coefficient                                                                                                                                                                                                                                                           (Figure 9-13 in ASCE MOP 60)",null,null,null,null,{"$f":"(1-EXP('Arch Pipe - Polym.'!AC53))/(2*H40)","v":0.31696693851116553},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select DOT"]
[null,null,"PL  Live Load on Pipe",null,null,null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,(H28*H29*'Arch Pipe - Polym.'!AH7)/('Arch Pipe - Polym.'!AH8*'Arch Pipe - Polym.'!AH11),0),IF(H30<=(H46*12),(H28*H29*'Arch Pipe - Polym.'!AH7)/('Arch Pipe - Polym.'!AH8*'Arch Pipe - Polym.'!AH11),0))","v":12.283480073192148},"psi",null,null,null,"Figure 8-3"]
[null,null,"PE  Earth Load acting on the Horizontal Soil Plane at the Top of the Pipe",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH19","v":0.52827823085194259},"psi"]
[null,null,"Pw  External Hydrostatic Pressure acting on the Pipe",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH21","v":0},"psi",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"-2kµ'H/Bc",null,{"$f":"-2*'Arch Pipe - Polym.'!H40*'Arch Pipe - Polym.'!H30/('Arch Pipe - Polym.'!H39*12)","v":-0.13007323943661969}]
[]
[null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,\"\",\"Note: The effects of live load is neglected.\"),IF(H30<=(H46*12),\"\",\"Note: The effects of live load is neglected.\"))","v":""}]
[null,null,{"$f":"IF(H44=\"Single Span\",IF(H30<=96,\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For single-span culverts, the effects of live load may be neglected where the depth of fill is more than 8.0 ft. and exceeds the span length.\"),IF(H30<=(H46*12),\"\",\"Per AASHTO LRFD Bridge Design Specifications, 8th Ed, Section 3.6.1.2.6a: For multiple span culverts, the effects of live load may be neglected where the depth of fill exceeds the distance between inside faces of end walls.\"))","v":""},null,null,null,null,null,null,null,null,null,"Figure 8-4"]
[]
[]
[null,null,"Design Assumptions (Flexible Polymeric Materials):",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Select kµ'",null,{"$f":"IF(C55=\"Note: The effects of live load is neglected.\",0,1)","v":1}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.19239999999999999]
[null,null,"t  Thickness of the Liner - See figure 8-4                                                                                                                                                                                                                                                          Note: Wall thickness is above the corrugation crests.                                  ",null,null,null,null,1,"in.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.16500000000000001]
[null,null,"ISAPL  Moment of Inertia of Liner Profile per unit length of Liner",null,null,null,null,4.5600000000000002E-2,"in4/in",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.15]
[null,null,"Γ(α,g)  Amplification Factor for the Critical Angle due to Initial Gap, for SAPL = 1",null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.13]
[null,null,"k  Deformation Mode, k = 1 for a Pipe Arch Shape",null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.11]
[null,null,"P  Perimeter of the Lining",null,null,null,null,188.5,"in."]
[null,null,"R  radius of the arc where the blister develops, (in)",null,null,null,null,{"$f":"H24","v":110.25}]
[null,null,"α  Half Arc Angle where Blister Develops                                                                                                                                                                                                                                                                                               See figure 8-3                             ",null,null,null,null,13,"degree°"]
[null,null,"ESAPL  Short-Term Circumferential Flexural Modulus of Liner Material                                                                                                                                                                                                                                                For determining long term and short term modulus of elasticity, use ASTM D790 standard test methods for short term, and ASTM D2990  standard test methods for long term. In the absence of the ASTM D2990 standard tests, it is a common practice to use 50% of the short term modulus of elasticity as a value for the long term modulus of elasticity.",null,null,null,null,735,"ksi"]
[null,null,"Γ(d,g)  Amplification Factor for the Critical Deflection due to Initial Gap, for SAPL = 1",null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"H.in Parallel",null,null,null,null,{"$f":"(H35-H32)/H31","v":33.04347826086957}]
[null,null,"Γ(M,g)  Amplification Factor for the Critical Moment due to Initial Gap, for SAPL = 1",null,null,null,null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"IF(H30<AH69,H32+H31*H30,H32+H35+H31*H30)","v":37.599999999999994}]
[null,null,"ϕbck  Resistance Factor to Buckling, recommend a value of 0.5",null,null,null,null,0.5]
[null,null,"σR  Stress Strength of Material Corresponding to 95% Lower Confidence Limit",null,null,null,null,14000,"psi"]
[null,null,"ϕM  Strength Resistance Factor for Material, use 0.67 in absence of testing",null,null,null,null,0.66666666666666663]
[null,null,"Deflection Limit: Percentage of the Straight Section (flattest arc element)",null,null,null,null,0.03,"%"]
[]
[null,null,"Results (Flexible Polymeric Materials):"]
[]
[null,null,"Δt  Total Deflection of Liner",null,null,null,null,{"$f":"(H51*(H23^4))/(384*H68*1000*H62)","v":1.5589859602027452},"in."]
[null,null,"ΔA  Total Allowable Deflection of Liner (ΔA = 0.05 Rtop)",null,null,null,null,{"$f":"0.05*H23","v":1.7875000000000001},"in.",{"$f":"IF(H78<=H79,\"The \"&H61&\"-inch thickness is good for the deflection performance\",\"The \"&H61&\"-inch thickness is not sufficient for the deflection performance\")","v":"The 1-inch thickness is good for the deflection performance"}]
[null,null,"αcr  Calculated Half Blister Angle just before Buckling occurs",null,null,null,null,{"$f":"((1.55*H63*(H61^(2/5))*(H65^(1/5)))/((H64^(1/5))*(H66^(3/5))))*180/PI()","v":15.069173826700295},"degree°"]
[null,null,"αcr / α",null,null,null,null,{"$f":"H80/H67","v":1.1591672174384842},null,{"$f":"IF(H81<=1.5,\"Eq. 8-33 is satisfied: αcr / α ≤ 1.5\",\"Eq. 8-33 is not satisfied: αcr / α > 1.5\")","v":"Eq. 8-33 is satisfied: αcr / α ≤ 1.5"}]
[null,null,"p  Design Pressure",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH23","v":2.2806497568068509},"psi"]
[null,null,"pcr  Buckling Pressure of a Critical Lining",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH24","v":11.429640510190815},"psi"]
[null,null,"ϕbck pcr        ",null,null,null,null,{"$f":"H83*H71","v":5.7148202550954075},"psi",{"$f":"IF(H82<=H84,\"Condition of stability is verified: P ≤ (ϕbck Pcr )\",\"Condition of stability is not verified: P > (ϕbck Pcr)\")","v":"Condition of stability is verified: P ≤ (ϕbck Pcr )"}]
[null,null,"ϕM σR   ",null,null,null,null,{"$f":"H72*H73","v":9333.3333333333321},"psi"]
[null,null,"σu= σ(u,b)+σ(u,d)     ",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH33","v":818.38410870899736},"psi",{"$f":"IF(H86<=H85,\"Condition of strength is verified: σu ≤ (ϕM σR)\",\"Condition of strength is not verified: σu > (ϕM σR)\")","v":"Condition of strength is verified: σu ≤ (ϕM σR)"}]
[null,null,"ds  Maximum Deflection ",null,null,null,null,{"$f":"'Arch Pipe - Polym.'!AH34","v":0.1671505314009174},"in."]
[null,null,"dL  Permissible Deflection for Flexible Polymeric Liners",null,null,null,null,{"$f":"((H67*PI())/180)*H24*H74","v":0.75044794512626178},"in.",{"$f":"IF(H87<=H88,\"Deflection is within the suggested limit of \"&H74*100&\"%\",\"Deflection is not within the suggested limit of \"&H74*100&\"%\")","v":"Deflection is within the suggested limit of 3%"}]