{"text_format":"1","workbook":"xlsx","n_sheets":11,"sheets":["Introduction","LRFR Input","Output HL93, LA3S2, LA3, 3-3","Output HL93, LA6, LA8","Output HL93, NRL, SU4, SU5","Output HL93, NRL, SU6, SU7","Output HL93, OFRD1, 2 & 3","Reference tables","section property tables","seam strength tables","NCSPA Design Data Sheet No 19"],"not_rendered":{"charts":0,"images":19,"macros":1,"external_links":0,"defined_names":44,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Introduction","index":0,"n_rows":32,"n_cols":10,"rows_kept":32,"cut":false,"hidden":false,"merged":[[0,9,12,18],[21,0,21,8],[23,0,23,8],[25,0,25,8],[9,2,9,3],[9,4,9,5],[13,0,13,8],[15,0,15,8],[17,0,17,8],[19,0,19,8],[10,4,10,5],[11,4,11,5],[0,3,0,5],[2,4,2,5],[3,4,3,5],[5,2,5,3],[28,0,28,8],[29,0,29,8],[30,0,30,8],[31,0,31,8],[5,4,5,5],[7,2,7,3],[7,4,7,5],[6,1,6,3],[6,4,6,7]]}
[null,null,null,"INTRODUCTION",null,null,null,null,null,"DISCLAIMER: The Louisiana Department of Transportation and Development (LaDOTD) makes these documents and software available on an \"as is\" basis. All warranties and representations of any kind with regard to said documents and software are disclaimed, including the implied warranties of merchantability and fitness for a particular use. Under no circumstances will the LaDOTD, or any of its officers or employees be liable for any consequential, incidental, special or exemplary damages even if apprised of the likelihood of such damages occurring. The LaDOTD does not warrant the documents and software against deficiencies of any kind. The use of any of these documents and software for work that is under contract with the LaDOTD does not relieve the contractor from any obligations assumed by the contract, or from complete and proper fulfillment of the terms of the contract, nor does it entitle the contractor to compensation for damages or loss which could be attributed to such use.\n\nInformation on this web site is posted to aid in the efficient dissemination of information to designers. The data contained within this web site is periodically updated. Designers are responsible to be aware of any updates and incorporate significant changes into their final design."]
[]
[null,null,null,"Date:","2018-01-29"]
[null,null,null,"Version:","1.0"]
[]
[null,null,"Developed By:",null,"Ohio DOT"]
[null,"Modified By:",null,null,"CBC Engineers under LADOTD contract"]
[null,null,"Reviewed By:",null,"Qiming Chen",null," "]
[]
[null,null,"Maintained By:",null,"Qiming Chen"]
[null,null,null,"Email:","qiming.chen@la.gov"]
[null,null,null,"Phone:","225-379-1412"]
[]
["Genearl: This spreadsheet is designed to aid a qualified engineer in completing the bridge load rating analysis of a corrugated metal pipe cuvlert structure (DOTD culvert structure type: STLRCH, ALURCH, STLPIP, and ALUPIP with corrugation). Sound engineering judgement and familiariry with the analysis are required to choose appropriate input values and to recognize situations that may deviate from the standard case on which these spreadsheets based. This spreadsheet is comprised of six worksheets: Introduction; LRFR Input; Output HL93, LA3S2, LA3, 3-3; Output HL93, LA6, LA8; Output HL93, NRL, SU4, SU5; Output HL93, NRL, SU6, SU7; Output HL93, OFRD1, 2 & 3; Reference tables; section property table; seam strength table; and NCSPA Design Data Sheet No 19. The LRFR Input worksheet is protected. The passoword is \"Rating\"."]
[]
["LRFR Input Worksheet:  Yellow shaded cells are required input, please input a appropriate value or choose a appropriate option from the drop-down list."]
[]
["Output HL93, LA3S2, LA3, 3-3; Output HL93, LA6, LA8; Output HL93, NRL, SU4, SU5; Output HL93, NRL, SU6, SU7; Output HL93, OFRD1, 2 & 3; Worksheets: These worksheets will be updated automatically after inputing the appropriate values in the Input Worksheet. These worksheet contains rating facotrs of the structure defined in the Input Worksheet for different types of vehicles."]
[]
["Reference Tables Worksheet:  This worksheet contains tabulated values that are accessed using lookup funcions based on selections from the drop down cells in the LRFR input worksheet."]
[]
["Section Property Tables Worksheet:  This worksheet is a reference able that is reproduced from AASHTO LRFD Bridge Design Specs, Section 12, Appendix A12. This worksheet is used to determine the Area (As), Radius of Gyration (r) and Moment of Inertia (I)."]
[]
["Seam Strength Tables Worksheet:  This worksheet is a reference table that is reproduced from AASHTO LRFD Bridge Design Specs, Section 12, Appendix A12."]
[]
["NCSPA Design Data Sheet No 19Worksheet:  This worksheet is a full reproduction of the National Corrugated Steel Pipe Association data sheet for load rating and structural evaluation for in-service corrugated steel structures."]
[]
["References:"]
["AASHTO LRFD Bridge Design Specifications, Seventh Edition, Section 3, 4 & 12."]
["NCSPA Design Data Sheet No. 19."]
["LaDOTD Bridge Design & Evaluation Manual REV 7, Section 6."]
["AASHTO Manual for Bridge Evaluation, Second Edition."]

{"sheet":"LRFR Input","index":1,"n_rows":80,"n_cols":20,"rows_kept":80,"cut":false,"hidden":false,"merged":[[21,10,22,21],[60,3,62,3],[60,2,62,2],[56,4,58,8],[39,1,39,2],[39,3,39,7],[45,4,45,7],[45,1,50,2],[60,1,62,1],[60,4,62,8],[44,3,44,4],[44,1,44,2],[42,3,42,4],[42,1,42,2],[46,4,46,7],[43,1,43,2],[43,3,43,4],[55,1,55,8],[56,1,58,1],[48,5,50,8],[47,4,47,7],[52,3,52,4],[52,1,52,2],[51,3,51,4],[51,1,51,2],[72,14,75,14],[70,14,70,15],[70,13,71,13],[72,13,75,13],[64,1,67,1],[72,10,75,10],[72,11,75,11],[72,12,75,12],[70,10,71,10],[70,11,71,11],[70,12,71,12],[65,4,67,8],[65,2,67,2],[65,3,67,3],[1,4,1,7],[2,6,2,7],[3,6,3,7],[4,6,4,7],[7,1,27,8],[6,1,6,8],[28,1,28,8],[37,1,37,2],[37,3,37,7],[40,5,41,7],[31,1,31,8],[32,1,32,8],[33,1,33,8],[36,3,36,6],[35,1,35,7],[38,1,38,2],[41,1,41,2],[40,1,40,2],[41,3,41,4],[40,3,40,4],[38,3,38,7],[70,18,70,19],[71,18,71,19],[69,10,69,19],[69,1,77,1],[69,4,77,8],[76,15,79,15],[72,18,75,18],[76,16,79,16],[76,17,79,17],[72,19,75,19],[76,10,79,10],[76,11,79,11],[76,12,79,12],[76,13,79,13],[76,14,79,14],[72,15,75,15]]}
[]
[null,"Structure No:",null,"Bridge Name:","LADOTD"]
[null,"Route/Crossing:"," ","ADTT:",630]
[null,"Year Built:",1993,"Load Rated By:","D.N","Date:","2013-01-14"]
[null,"Structure Type:","Corrugated Metal Pipe Arch","Checked By:","M.H.","Date:","2013-01-14"]
[]
[null,"CORRUGATED METAL STRUCTURE (CIRCULAR & PIPE ARCH) & ARCHES "]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,"yellow shaded areas are required input."]
[null,null,null,null,null,null,null,null,null,null,"input a value or choose a option from a drop-down list"]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null," "]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null," "]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,"  "]
[]
[null,"* For unsymmetrical structures, structures deflected more than 5% from design shape, or those that show localized distortions require that the actual maximum radius be determined in those distorted areas as show above. Use two times the actual maximum radius rather than the span in structural design checks. Typically this provides a conservative evaluation of the structure. Calculate maximum existing top radius by taking measurements around the upper periphery of the culvert using a ruler of length \"P\" to obtain values of \"M\". This should be done at selected stations along length of culvert, particularly at locations with noticeable sag."]
[]
[]
[null,"LRFR of In-Service, Corrugated Metal Pipe Structures                                     "]
[]
[null,"(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
[null,"Structure Information (from existing bridge plans & field measurements):"]
[null,null,null,"  (\"←\" : choose from a drop-down list)"]
[null,"Structure Type (to determine Minimum Cover):",null,"Corrugated Metal Pipe",null,null,null,null,"←"]
[null,"Seam Type (to determine Seam Strength):",null,"Helical pipe w/ lock seam or fully welded seam",null,null,null,null,"←"]
[null,"Structure Category (based on NCSPA Design Data Sheet No. 19)",null,"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)",null,null,null,null,"←"]
[null,"Depth of Fill \"H\" (ft) =                                                                                       (the lowest cover over the structure in a traffic area)",null,2.6,null,{"$f":"IF(AND(D41>8,D41>D42),\"Based on AASHTO LRFD 3.6.1.2.6, The effects of live load maybe neglected when H>8' and H>Span Length, no need for LRFR.\",\"\")","v":""}]
[null,"Span Length \"S\" (ft) =",null,11.42]
[null,"Rise \"R\" (ft) =",null,7.25]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,70.5]
[null,"Determine Actual Top Radius \"Rt\" (ft) =                                  (can be determined by field measurements or hand calculations)",null,9.4149999999999991,null,null,null,null,null," "]
[null,"Metal Corrugation & Gage Information:",null,"Metal Type","Steel",null,null,null,"←"]
[null,null,null,"Corrugation (if known)","3 x 1 (corrugated steel pipe)",null,null,null,"←"]
[null,null,null,"Gage number (if known)",10,null,null,null,"←"]
[null,null,null,"c (in) =",null,"Note: if corrugation & gage number are known, leave the input cells for \"c\", \"d\" & \"t\" blank; if corrugation & gage number are unknown, field measurements of \"c\", \"d\" & \"t\" are required."]
[null,null,null,"d (in) ="]
[null,null,null,"t (in) ="]
[null,"Pipe Crown Deflection ** (if any) =",null,0.05]
[null,"Metal Loss based on materials field evaluation (if any) =",null,0]
[null,"** reduction in rise divided by the span length from design shape in the unit of percentage"]
[]
[null,"Load Rating Input Sheet"]
[null,"Pipe Cross-Section Properties","As (in2/ft) =",{"$f":"'section property tables'!I11","v":2.008},"input these values based on metal type, corrugation, gage number or pipe wall thickness, see tables in worksheet \"section property tables\". "]
[null,null,"r (in) =",{"$f":"'section property tables'!J11","v":0.34720000000000001}]
[null,null,"I x 10-3 (in4/in) =",{"$f":"'section property tables'!K11","v":20.183}]
[]
[null,"Pipe Seam Strength","Seam Strength (k/ft) =",0,"input the seam strength value based on metal type, corrugation, gage number or pipe wall thickness, see tables in worksheet \"seam strength tables\""]
[]
[]
[]
[null,"Backfill","δ = Soil density (k/ft3) =",0.12]
[null,null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6) ",1.1499999999999999,"1.15 used here for select granular backfill, change the factor φE to 1.0 for all other cases."]
[]
[]
[]
[null,"Load Factors","gDC (Dead Load)  =",1.25,"input the load factors based on the \"LRFR Load Factors\" table on the right",null,null,null,null,null,"LRFR Load Factors"]
[null,null,"gEV (Vertical Earth Pressure for CMPs)  =",1.95,null,null,null,null,null,null,"Bridge Type","Limit State","Dead Load gDC","Vertical Earth Pressure EV for CMPs","HL-93 Loading",null,"Legal Loads","Spec. Hauling Loads","Routine (Annual) Permit Loads"]
[null,null,"gLL   (HL-93 Loading - Inventory)  =",1.75,null,null,null,null,null,null,null,null,null,null,"Inventory gLL","Operating gLL","Operating gLL","Operating gLL","Operating gLL"]
[null,null,"gLL   (HL-93 Loading - Operating)  =",1.35,null,null,null,null,null,null,"Steel or Aluminum","Strength I",1.25,1.95,1.75,1.35,"Unknown ADTT - 1.80","Unknown ADTT - 1.60","-","-"]
[null,null,"gLL (Legal Loads - Operating - based on ADTT) =",1.8,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT ≥ 5000 - 1.80","ADTT ≥ 5000 - 1.60"]
[null,null,"gLL (Special Hauling Loads - Operating - based on ADTT) =",1.6,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT = 1000 - 1.65","ADTT = 1000 - 1.40"]
[null,null,"gLL (Routine Permit OFRD1 - Operating - based on ADTT) =",1.47,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT ≤ 100 - 1.40","ADTT ≤ 100 - 1.15"]
[null,null,"gLL (Routine Permit OFRD2 - Operating - based on ADTT) =",1.38,null,null,null,null,null,null,"Steel or Aluminum","Strength II",1.25,1.95,"-","-","-","-","Weight up to 100 kips","Weight ≥ 150 kips"]
[null,null,"gLL (Routine Permit OFRD3 - Operating - based on ADTT) =",1.3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT ≥ 5000 - 1.80","ADTT ≥ 5000 - 1.30"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT = 1000 - 1.60","ADTT = 1000 - 1.20"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ADTT ≤ 100 - 1.40","ADTT ≤ 100 - 1.10"]

{"sheet":"Output HL93, LA3S2, LA3, 3-3","index":2,"n_rows":238,"n_cols":9,"rows_kept":238,"cut":false,"hidden":false,"merged":[[10,0,10,1],[55,2,55,4],[54,0,54,1],[43,1,43,2],[44,1,44,2],[45,1,45,2],[46,1,46,2],[47,1,47,2],[14,0,15,5],[19,2,19,3],[21,2,21,3],[21,1,23,1],[37,2,37,4],[33,0,33,1],[49,5,50,6],[23,2,23,3],[6,0,6,6],[7,0,7,6],[8,0,8,6],[1,3,1,6],[2,5,2,6],[3,5,3,6],[4,5,4,6],[225,5,229,5],[221,0,221,4],[200,0,200,2],[11,0,11,5],[12,0,12,5],[13,0,13,5],[59,5,59,6],[119,0,128,6],[94,1,95,1],[135,3,135,4],[97,4,97,5],[98,1,98,2],[98,3,98,5],[99,2,99,5],[65,1,65,3],[82,2,82,4],[108,1,108,2],[81,2,81,4],[173,0,173,5],[190,0,190,5],[157,2,157,5],[174,0,174,5],[175,0,175,5],[172,0,172,5],[176,0,177,5],[179,0,179,6],[31,0,31,2],[139,1,139,2],[88,1,89,1],[109,1,109,2],[58,5,58,6],[62,1,62,3],[61,1,61,3],[58,1,58,3],[59,1,59,3],[39,1,39,3],[56,2,56,4],[57,1,57,3],[83,2,83,4],[81,1,83,1],[63,1,63,3],[64,1,64,3],[209,0,209,2],[223,0,224,0],[225,0,229,0],[32,0,32,2],[16,0,16,5],[17,0,17,5],[60,1,60,3],[138,1,138,2],[27,2,27,3],[24,1,25,4],[40,1,40,3],[38,1,38,3],[29,0,29,1],[29,2,29,5],[129,0,129,6],[22,2,22,3]]}
[]
["Structure No:",{"$f":"'LRFR Input'!C2","v":0},"Bridge Name:",{"$f":"'LRFR Input'!E2","v":"LADOTD"}]
["Route/Crossing:",{"$f":"'LRFR Input'!C3","v":" "},"ADTT:",{"$f":"'LRFR Input'!E3","v":630}]
["Year Built:",{"$f":"'LRFR Input'!C4","v":1993},"Load Rated By:",{"$f":"'LRFR Input'!E4","v":"D.N"},"Date:",{"$f":"'LRFR Input'!G4","v":"2013-01-14"}]
["Structure Type:",{"$f":"'LRFR Input'!C5","v":"Corrugated Metal Pipe Arch"},"Checked By:",{"$f":"'LRFR Input'!E5","v":"M.H."},"Date:",{"$f":"'LRFR Input'!G5","v":"2013-01-14"}]
[]
["LRFR of In-Service, Corrugated Metal Pipe Structures"]
["Based on AASHTO LRFD Bridge Design Specifications, Section 3, 4 & 12 & NCSPA Design Data Sheet No. 19 & ODOT Bridge Design Manual 2004 (effective 10-15-2010), Section 900 & 2008 AASHTO MBE"]
["(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
["A.   Design Dimensions"]
["   1.  For typical structures, use the actual field measured span for calculations."]
["   2.  For unsymmetrical structures or those deflected over 5%:"]
["       a. use 2 x the top radius (2 Rt) in lieu of span for calculations."]
["       b. base critical buckling stress calculations on the theoretical design span, reducing the resulting allowable buckling stress by the appropriate multiplier to account for deflection \" f \" (NCSPA Design Data Sheet No. 19, Figure B.1.1)."]
[]
["   3.  For all long span structures (horizontal ellipse, low and high profile arches, inverted pear shapes and pear arches), as well as other horizontal ellipses, use 2 x actual top radius (2Rt) in all cases."]
[]
[]
[null,"For typical structures :","Design Span = Actual Span \"S\" (ft) =",null,{"$f":"'LRFR Input'!D42","v":11.42}]
[]
[null,"For unsymmetrical or deflect more than 5% structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[null,null,"Pipe Crown Deflection =",null,{"$f":"'LRFR Input'!D52","v":0.05}]
[null,null,"Buckling Strength Reduction Factor, f * =",null,{"$f":"-5.6*E23+0.95","v":0.66999999999999993}]
[null,"* reduction factor f is based on NCSPA Design Data Sheet No 19, II Structural Evaluation A.2.b & Appendix B.1, Figure B.1.1 for Unsymmetrical structures or structures deflected over 5% only."]
[]
[]
[null,"long span structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[]
["Structure Category:",null,{"$f":"'LRFR Input'!D40","v":"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"}]
[]
["Then, Span Length used in Load Rating Calculation =",null,null,{"$f":"IF(C30 =\"Typical (NCSPA design data sheet no. 19, II. A. 1.)\", E20, E22)","v":18.829999999999998},"ft"]
["Then, Rt used in Load Rating Calculation =",null,null,{"$f":"'LRFR Input'!D45:E45","v":9.4149999999999991},"ft"]
["B.   Design Properties"]
[]
["Conduits Mechanical & Section Properties:"]
["Mechanical Properties:"]
[null,"Metal Type:",{"$f":"'LRFR Input'!E46","v":"Steel"}]
[null,"Fy = Minimum Yield Point of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,3,FALSE)","v":33},"ksi"]
[null,"Fu = Minimum Tensile Strength of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,2,FALSE)","v":45},"ksi"]
[null,"Em = Modulus of elasticity of metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,4,FALSE)","v":29000},"ksi"]
[]
["Section Properties:"]
["Corrugation:",{"$f":"'LRFR Input'!E47","v":"3 x 1 (corrugated steel pipe)"}]
["Gage Number:",{"$f":"'LRFR Input'!E48","v":10}]
["c (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E49, \"\")","v":""}]
["d (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E50, \"\")","v":""}]
["t (in) =",{"$f":"IF(B45=\"N/A\", 'LRFR Input'!E51, VLOOKUP(B45,'Reference tables'!B39:C48,2,FALSE))","v":0.13800000000000001}]
[]
["As (in2/ft) =",{"$f":"'LRFR Input'!D57","v":2.008}]
["r (in) =",{"$f":"'LRFR Input'!D58","v":0.34720000000000001}]
["I x 10-3 (in4/in) =",{"$f":"'LRFR Input'!D59","v":20.183}]
[]
[]
["C.   Design Calculations:"]
[null,"Structure Type:",{"$f":"'LRFR Input'!D38","v":"Corrugated Metal Pipe"}]
[null,"Seam Type:",{"$f":"'LRFR Input'!D39","v":"Helical pipe w/ lock seam or fully welded seam"}]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,null,{"$f":"'LRFR Input'!D44","v":70.5}]
[null,"AASHTO minimum cover, h (ft) =",null,null,{"$f":"E28/8","v":2.3537499999999998},{"$f":"IF(AND(C56=\"Long Span Structural Plate (AASHTO 12.7)\",B48<'Reference tables'!C17), \"see * below\", \"\")","v":""}]
[null,"Height of cover above crown \"H\" (ft) =    ",null,null,{"$f":"'LRFR Input'!D41","v":2.6},{"$f":"IF(E60>=E59, \"\", \"! H<h, cover not deep enough!\")","v":""}]
[null,"φloss = Section Properties reduction factor on the basis of metal loss from the materials field evaluation =    ",null,null,{"$f":"1-'LRFR Input'!D53","v":1}]
[null,"φ1 = Resistance Factor for wall area and buckling (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",0.67,1)","v":1}]
[null,"φ2 = Resistance Factor for seam strength (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", 0.67, IF('LRFR Input'!D39=\"Helical pipe w/ lock seam or fully welded seam\", 1, \"\"))","v":1}]
[null,"δ = Soil density (k/ft3)",null,null,{"$f":"'LRFR Input'!D65","v":0.12}]
[null,"k = soil stiffness factor =",null,null,0.22]
[null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6)=",null,null,{"$f":"'LRFR Input'!D66","v":1.1499999999999999}]
[]
[]
["Calculate the fcr (critical buckling stress) :",null,"(AASHTO LRFD 12.7.2.4)"]
[]
["if:"]
[]
["if:"]
[]
["Compare:","S (in) =",{"$f":"D32*12","v":225.95999999999998},{"$f":"IF(C75>F75, \">\", \"<\")","v":">"},null,{"$f":"(B51/E65)*(24*E41*1000/(E40*1000))^0.5","v":196.27066710499614}]
[]
["Therefore,","fcr =",{"$f":"IF(C75<F75, (E40*1000-((E40*1000)^2/(48*E41*1000))*(E65*C75/B51)^2)/1000, (12*E41*1000/(E65*C75/B51)^2)/1000)","v":16.97579738990796},"ksi"]
[]
["Calculate the Tcap (thrust capacity of the wall) :"]
[null,"Seam Strength (k/ft) =",{"$f":"'LRFR Input'!D61","v":0}]
[]
[null,"Tcap = less of:","1.  wall yield strength = φ1 φloss Fy A =",null,null,{"$f":"E39*B50*E62*E61","v":66.263999999999996}]
[null,null,"2.  wall buckling strength = f φ1 φloss fcr A =",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"N/A\", IF(C30=\"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)\", C77*B50*E62*E61*E24, C77*B50*E62*E61))","v":22.838558776486572},null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"buckling not applicable to long spans\", \"\")","v":""}]
[null,null,"3.  seam strength = φ2 x (seam strength) =",null,null,{"$f":"E63*C80","v":0}]
[]
["Therefore,","Tcap = ",{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", MIN(F82,F83,F84), MIN(F82,F83))","v":22.838558776486572},"k/ft"]
[]
["Calculate the TE (pipe wall thrust due to earth cover) :"]
[null,"TE = higher value of :","1.   δ H (S/2) =",{"$f":"E64*E60*D32/2","v":2.9374799999999999},"k/ft"]
[null,null,"2.   δ H Rt =",{"$f":"E64*E60*D33","v":2.9374799999999999},"k/ft"]
[]
["Therefore,","TE = ",{"$f":"MAX(D89,D90)","v":2.9374799999999999},"k/ft"]
[]
["Calculate the T(L+I) (pipe wall thrust due to live load plus impact) :"]
[null,"T(L+IM) = higher value of :","1.   ρ (L+IM)  (S/2) =","k/ft"]
[null,null,"2.   ρ (L+IM)  Rt =","k/ft"]
[]
[null,"Based on AASHTO LRFD 3.6.2.2:"]
[null,"Live load Dynamic Load Allowance,   IM =",null,"33(1.0-0.125 DE) ≥ 0%"]
[null,"where,","DE = the minimum depth of earth cover above the structure (ft)"]
[]
[null,null,"For this structure: Depth of Fill, DE = H=",{"$f":"E60","v":2.6},"ft"]
[null,null,"IM =",{"$f":"IF(33*(1-0.125*D102)/100>0,33*(1-0.125*D102)/100,0)","v":0.22275000000000003}]
[null,null,"(1+IM) =",{"$f":"1+D103","v":1.22275}]
[]
["Case A:","Depth of Fill, H < 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 4.6.2.10.1 & 2 (case 1: traffic travels parallel to span):"]
[null,"   When Depths of Fill of Culverts < 2.0 ft,"]
[null,"Eaxle= 96+1.44 S =",null,{"$f":"(96+1.44*D32)","v":123.1152},"in"]
[null,"Therefore,    Ewheel = ½ Eaxle =",null,{"$f":"D109/24","v":5.1298000000000004},"ft"]
[null,null,"Espan = LT + φE (H) =","same as case B, see calculations below"]
[null,"Where,"]
[null,null,"Ewheel = equivalent distribution width perpendicular to span, = WD"]
[null,null,"WD = Distributed load width/ per wheel load"]
[null,null,"Espan = equivalent distribution length parallel to span, = LD"]
[null,null,"LD = Distributed load length/ per wheel load"]
["Case B:","Depth of Fill, H ≥ 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 3.6.1.2.5 & 6:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Where, WT = Tire contact width, LT = Tire contact length, WD = Distributed load width, LD = Distributed load length"]
[]
["The surface tire contact area for HL-93 loading (per AASHTO LRFD 3.6.1.2.5):"]
["WT = 20\" =",{"$f":"20/12","v":1.6666666666666667},"ft"]
["LT = 10\" =",{"$f":"10/12","v":0.83333333333333337},"ft"]
["The surface tire contact area for LA3S2, LA3, 3-3  (per AASHTO LRFD C3.6.1.2.5 Guideline):"]
["WT (in) =","P/0.8  "]
["LT (in) =","6.4g(1+IM/100) "]
["where,","p = wheel load (kips)"]
[null,"g = Load Factor for Legal Loads gLL =",null,{"$f":"'LRFR Input'!D74","v":1.8}]
[null,"IM = dynamic load allowance percent"]
["So,",null,"HL-93 Tandem","LA Type 3-S2","LA Type 3","Type 3-3"]
[null,"P \"heavy axle\" wheel load (kips) =",12.5,8,8,7]
[null,"WT (ft) =",{"$f":"B133","v":1.6666666666666667},{"$f":"(D142/0.8)/12","v":0.83333333333333337},{"$f":"(E142/0.8)/12","v":0.83333333333333337},0.72916666666666663]
[null,"LT (ft) =",{"$f":"B134","v":0.83333333333333337},{"$f":"6.4*$D$104/12*$D$139","v":1.17384},{"$f":"6.4*$D$104/12*$D$139","v":1.17384},{"$f":"6.4*$D$104/12*$D$139","v":1.17384}]
[]
["Distribution of wheel loads through earth fills (per AASHTO LRFD 3.6.1.2.6):"]
[]
["for HL-93 Design Truck:"]
[null,"WD = 1.67+φEH=",{"$f":"20/12+E66*D102","v":4.6566666666666663},"ft"]
[null,"LD = 0.83 + φEH =",{"$f":"10/12+E66*D102","v":3.8233333333333333},"ft"]
["for HL-93 Tandem, LA3S2, LA3, 3-3 Trucks:"]
[null,null,"HL-93 Tandem","LA Type 3-S2","LA Type 3","Type 3-3"]
[null,"WD = WT + φEH =",{"$f":"C143+$E$66*$E$60","v":4.6566666666666663},3.8233333333333333,3.8233333333333333,3.7191666666666663]
[null,"LD = LT + φEH =",3.8233333333333333,4.1638399999999995,4.1638399999999995,4.1638399999999995]
[]
[null,null,"Fill depth, H =",{"$f":"D102","v":2.6},{"$f":"IF(D156<2, \"H<2', Case A applied\", IF(D156>=2, \"H>=2', Case B applied\", \"\"))","v":"H>=2', Case B applied"}]
[null,null,"Structure Total Length, L =",{"$f":"'LRFR Input'!D44","v":70.5},"ft "]
[null,null,"[ if WD (total) > L, use L = WD (total) in the calculations ]"]
[null,"HL-93 Truck","HL-93 Tandem","LA Type 3-S2","LA Type 3","Type 3-3"]
["Heavy Axle Load (lbs)",32000,25000,16000,16000,14000]
["P (1+ IM) (lbs) =",{"$f":"B160/2*$D$104","v":19564},{"$f":"C160/2*$D$104","v":15284.375},{"$f":"D160/2*$D$104","v":9782},{"$f":"E160/2*$D$104","v":9782},{"$f":"F160/2*$D$104","v":8559.25}]
["* Saxle 1 (ft) =",0,4,4,4,4]
["* Saxle 2 (ft) =",0,0,0,0,0]
["wheel spacing on axle",6,6,6,6,6]
["WD (ft) =",{"$f":"IF($D$156<2, $D$110, C149)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, C153)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, D153)","v":3.8233333333333333},{"$f":"IF($D$156<2, $D$110, E153)","v":3.8233333333333333},{"$f":"IF($D$156<2, $D$110, F153)","v":3.7191666666666663}]
["LD (ft) =",{"$f":"C150","v":3.8233333333333333},{"$f":"C154","v":3.8233333333333333},{"$f":"D154","v":4.1638399999999995},{"$f":"E154","v":4.1638399999999995},{"$f":"F154","v":4.1638399999999995}]
["WD (total) = ",{"$f":"IF(B165>B164, MIN(B165+B164,$D$157), MIN(B165,$D$157) )","v":4.6566666666666663},{"$f":"IF(C165>C164, MIN(C165+C164, $D$157), MIN(C165,$D$157))","v":4.6566666666666663},{"$f":"IF(D165>D164, MIN(D165+D164, $D$157), MIN(D165,$D$157))","v":3.8233333333333333},{"$f":"IF(E165>E164, MIN(E165+E164, D157), MIN(E165,D157))","v":3.8233333333333333},{"$f":"IF(F165>F164, MIN(F165+F164, D157), MIN(F165,D157))","v":3.7191666666666663}]
["LD (total) =",{"$f":"IF(B166>B162, B166+B162, B166)","v":3.8233333333333333},{"$f":"IF(C166>C162, C166+C162, C166)","v":3.8233333333333333},{"$f":"IF(D166>D162, D166+D162, D166)","v":8.1638400000000004},{"$f":"IF(E166>E162, E166+E162, E166)","v":8.1638400000000004},{"$f":"IF(F166>F162, F166+F162, F166)","v":8.1638400000000004}]
["* AD (ft2) =",{"$f":"B167*B168","v":17.803988888888888},{"$f":"C167*C168","v":17.803988888888888},{"$f":"D167*D168","v":31.213081600000002},{"$f":"E167*E168","v":31.213081600000002},{"$f":"F167*F168","v":30.362681599999998}]
["* PD (kips) =",{"$f":"IF(AND(B167>B165,B168>B166),4*B161/1000,IF(OR(B167>B165,B168>B166),2*B161/1000,B161/1000))","v":19.564},{"$f":"IF(AND(C167>C165,C168>C166),4*C161/1000,IF(OR(C167>C165,C168>C166),2*C161/1000,C161/1000))","v":15.284375000000001},{"$f":"IF(AND(D167>D165,D168>D166),4*D161/1000,IF(OR(D167>D165,D168>D166),2*D161/1000,D161/1000))","v":19.564},{"$f":"IF(AND(E167>E165,E168>E166),4*E161/1000,IF(OR(E167>E165,E168>E166),2*E161/1000,E161/1000))","v":19.564},{"$f":"IF(AND(F167>F165,F168>F166),4*F161/1000,IF(OR(F167>F165,F168>F166),2*F161/1000,F161/1000))","v":17.118500000000001}]
["ρ (L+IM) = PD/AD =",{"$f":"B170/B169","v":1.0988548758424299},{"$f":"C170/C169","v":0.8584803717518984},{"$f":"D170/D169","v":0.62678848089129391},{"$f":"E170/E169","v":0.62678848089129391},{"$f":"F170/F169","v":0.56380066245532157}]
["T(L+IM) (k/ft) =",{"$f":"MAX(B171*$D$32/2, B171*$D$33)","v":10.345718656056476},{"$f":"MAX(C171*$D$32/2, C171*$D$33)","v":8.0825927000441222},{"$f":"MAX(D171*$D$32/2, D171*$D$33)","v":5.9012135475915315},{"$f":"MAX(E171*$D$32/2, E171*$D$33)","v":5.9012135475915315},{"$f":"MAX(F171*$D$32/2, F171*$D$33)","v":5.308183237016852}]
["*   Saxle 1 = distance to the 1st adjacent heavy axle load, if the spacing is > 4', Saxle1 = 0.  "]
["     Saxle 2 = distance to the 2nd adjacent heavy axle load, if the spacing is > 4', Saxle2 = 0.  "]
["     AD = Total Load Distributed Area "]
["     PD = Total Load being Distributed"]
["Transverse pressure overlaps are considered.  Longitudinal pressure overlaps are considered for two adjacent heavy axle loads when the Saxle is ≤ 4 feet."]
[]
[]
["D.   Load Rating Factors for Ring Compression Structures:"]
["      1.  Operating Load Rating Factor (RFO):"]
["               a. RFO based on wall strength"]
[]
[]
["               b. RFO based on minimum cover requirements"]
[]
[]
[null,"         Where, ",null,{"$f":"IF((2.36*E60/D32+0.528)>1, 1, 2.36*E60/D32+0.528)","v":0.85386298459904419}]
[null,"So,   RFO-C =",{"$f":"E60^2/(D188*(E59)^2)","v":1.429018472478925}]
[]
["Operating Load Rating Factors, RFO"]
[null,"HL-93 Truck","HL-93 Tandem","LA Type 3-S2","LA Type 3","Type 3-3"]
["Tcap",{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},22.838558776486572,22.838558776486572,22.838558776486572]
["TE ",{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},2.9374799999999999,2.9374799999999999,2.9374799999999999]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B172","v":10.345718656056476},{"$f":"C172","v":8.0825927000441222},5.9012135475915315,5.9012135475915315,5.308183237016852]
["gLL ",{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D74","v":1.8},{"$f":"'LRFR Input'!D74","v":1.8},{"$f":"'LRFR Input'!D74","v":1.8}]
["RFO-W",{"$f":"(B193-B195*B194)/(B196*B197)","v":1.2250888217861231},{"$f":"(C193-C195*C194)/(C196*C197)","v":1.5681136918862377},1.6108243046108417,1.6108243046108417,{"$f":"(F193-F195*F194)/(F196*F197)","v":1.7907856199970569}]
["RFO-C",{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
["RFO",{"$f":"MIN(B198,$B$199)","v":1.2250888217861231},{"$f":"MIN(C198,$B$199)","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
[]
[]
["      2.  Inventory Load Rating Factor (RFi):"]
["               a. RFi based on wall strength"]
[]
[]
["               b. RFi based on minimum cover requirements"]
[]
[]
["Inventory Load Rating Factor, RFi"]
[null,"HL-93 Truck","HL-93 Tandem"]
["Tcap",{"$f":"B193","v":22.838558776486572},{"$f":"C193","v":22.838558776486572}]
["TE ",{"$f":"B194","v":2.9374799999999999},{"$f":"C194","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B196","v":10.345718656056476},{"$f":"C196","v":8.0825927000441222}]
["gLL ",{"$f":"'LRFR Input'!D72","v":1.75},{"$f":"'LRFR Input'!D72","v":1.75}]
["RFi-w",{"$f":"(B212-B213*B214)/(B215*B216)","v":0.94506851966358085},{"$f":"(C212-C213*C214)/(C215*C216)","v":1.2096877051693835}]
["RFi-c",{"$f":"E60^2/E59^2","v":1.220185977958022},{"$f":"E60^2/E59^2","v":1.220185977958022}]
["RFi",{"$f":"MIN(B217,$B$218)","v":0.94506851966358085},{"$f":"MIN(C217,$B$218)","v":1.2096877051693835}]
[]
[]
["Load Rating Summary:"]
[null,"Load","GVW","Rating Factor","Safe Load"]
["Inventory",{"$f":"B211","v":"HL-93 Truck"},36,{"$f":"B219","v":0.94506851966358085},{"$f":"C224*D224","v":34.02246670788891}]
[null,{"$f":"C211","v":"HL-93 Tandem"},25,{"$f":"C219","v":1.2096877051693835},30.242192629234587]
["Operating",{"$f":"B192","v":"HL-93 Truck"},36,{"$f":"B200","v":1.2250888217861231},44.103197584300432]
[null,{"$f":"C192","v":"HL-93 Tandem"},25,{"$f":"C200","v":1.429018472478925},35.725461811973126]
[null,{"$f":"D192","v":"LA Type 3-S2"},36.5,{"$f":"D200","v":1.429018472478925},{"$f":"C228*D228","v":52.159174245480763}]
[null,{"$f":"E192","v":"LA Type 3"},20.5,{"$f":"E200","v":1.429018472478925},29.294878685817963]
[null,{"$f":"F192","v":"Type 3-3"},40,{"$f":"F200","v":1.429018472478925},57.160738899156996]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null," "]

{"sheet":"Output HL93, LA6, LA8","index":3,"n_rows":238,"n_cols":9,"rows_kept":238,"cut":false,"hidden":false,"merged":[[14,0,15,5],[1,3,1,6],[2,5,2,6],[3,5,3,6],[4,5,4,6],[6,0,6,6],[7,0,7,6],[8,0,8,6],[10,0,10,1],[11,0,11,5],[12,0,12,5],[13,0,13,5],[16,0,16,5],[17,0,17,5],[19,2,19,3],[21,1,23,1],[21,2,21,3],[22,2,22,3],[23,2,23,3],[43,1,43,2],[24,1,25,4],[27,2,27,3],[29,0,29,1],[29,2,29,5],[31,0,31,2],[32,0,32,2],[33,0,33,1],[37,2,37,4],[38,1,38,3],[39,1,39,3],[40,1,40,3],[59,1,59,3],[59,5,59,6],[44,1,44,2],[45,1,45,2],[46,1,46,2],[47,1,47,2],[49,5,50,6],[54,0,54,1],[55,2,55,4],[56,2,56,4],[57,1,57,3],[58,1,58,3],[58,5,58,6],[94,1,95,1],[60,1,60,3],[61,1,61,3],[62,1,62,3],[63,1,63,3],[64,1,64,3],[65,1,65,3],[81,1,83,1],[81,2,81,4],[82,2,82,4],[83,2,83,4],[88,1,89,1],[157,2,157,5],[97,4,97,5],[98,1,98,2],[98,3,98,5],[99,2,99,5],[108,1,108,2],[109,1,109,2],[119,0,128,6],[129,0,129,6],[135,3,135,4],[138,1,138,2],[139,1,139,2],[225,0,229,0],[225,5,229,5],[172,0,172,5],[173,0,173,5],[174,0,174,5],[175,0,175,5],[176,0,177,5],[179,0,179,6],[190,0,190,5],[200,0,200,2],[209,0,209,2],[221,0,221,4],[223,0,224,0]]}
[]
["Structure No:",{"$f":"'LRFR Input'!C2","v":0},"Bridge Name:",{"$f":"'LRFR Input'!E2","v":"LADOTD"}]
["Route/Crossing:",{"$f":"'LRFR Input'!C3","v":" "},"ADTT:",{"$f":"'LRFR Input'!E3","v":630}]
["Year Built:",{"$f":"'LRFR Input'!C4","v":1993},"Load Rated By:",{"$f":"'LRFR Input'!E4","v":"D.N"},"Date:",{"$f":"'LRFR Input'!G4","v":"2013-01-14"}]
["Structure Type:",{"$f":"'LRFR Input'!C5","v":"Corrugated Metal Pipe Arch"},"Checked By:",{"$f":"'LRFR Input'!E5","v":"M.H."},"Date:",{"$f":"'LRFR Input'!G5","v":"2013-01-14"}]
[]
["LRFR of In-Service, Corrugated Metal Pipe Structures                                     "]
["Based on AASHTO LRFD Bridge Design Specifications, Section 3, 4 & 12 & NCSPA Design Data Sheet No. 19 & ODOT Bridge Design Manual 2004 (effective 10-15-2010), Section 900 & 2008 AASHTO MBE"]
["(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
["A.   Design Dimensions"]
["   1.  For typical structures, use the actual field measured span for calculations."]
["   2.  For unsymmetrical structures or those deflected over 5%:"]
["       a. use 2 x the top radius (2 Rt) in lieu of span for calculations."]
["       b. base critical buckling stress calculations on the theoretical design span, reducing the resulting allowable buckling stress by the appropriate multiplier to account for deflection \" f \" (NCSPA Design Data Sheet No. 19, Figure B.1.1)."]
[]
["   3.  For all long span structures (horizontal ellipse, low and high profile arches, inverted pear shapes and pear arches), as well as other horizontal ellipses, use 2 x actual top radius (2Rt) in all cases."]
[]
[]
[null,"For typical structures :","Design Span = Actual Span \"S\" (ft) =",null,{"$f":"'LRFR Input'!D42","v":11.42}]
[]
[null,"For unsymmetrical or deflect more than 5% structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[null,null,"Pipe Crown Deflection =",null,{"$f":"'LRFR Input'!D52","v":0.05}]
[null,null,"Buckling Strength Reduction Factor, f * =",null,{"$f":"'Output HL93, LA3S2, LA3, 3-3'!E24","v":0.66999999999999993}]
[null,"* reduction factor f is based on NCSPA Design Data Sheet No 19, II Structural Evaluation A.2.b & Appendix B.1, Figure B.1.1 for Unsymmetrical structures or structures deflected over 5% only."]
[]
[]
[null,"long span structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[]
["Structure Category:",null,{"$f":"'LRFR Input'!D40","v":"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"}]
[]
["Then, Span Length used in Load Rating Calculation =",null,null,{"$f":"IF(C30 =\"Typical (NCSPA design data sheet no. 19, II. A. 1.)\", E20, E22)","v":18.829999999999998},"ft"]
["Then, Rt used in Load Rating Calculation =",null,null,{"$f":"'LRFR Input'!D45:E45","v":9.4149999999999991},"ft"]
["B.   Design Properties"]
[]
["Conduits Mechanical & Section Properties:"]
["Mechanical Properties:"]
[null,"Metal Type:",{"$f":"'LRFR Input'!E46","v":"Steel"}]
[null,"Fy = Minimum Yield Point of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,3,FALSE)","v":33},"ksi"]
[null,"Fu = Minimum Tensile Strength of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,2,FALSE)","v":45},"ksi"]
[null,"Em = Modulus of elasticity of metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,4,FALSE)","v":29000},"ksi"]
[]
["Section Properties:"]
["Corrugation:",{"$f":"'LRFR Input'!E47","v":"3 x 1 (corrugated steel pipe)"}]
["Gage Number:",{"$f":"'LRFR Input'!E48","v":10}]
["c (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E49, \"\")","v":""}]
["d (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E50, \"\")","v":""}]
["t (in) =",{"$f":"IF(B45=\"N/A\", 'LRFR Input'!E51, VLOOKUP(B45,'Reference tables'!B39:C48,2,FALSE))","v":0.13800000000000001}]
[]
["As (in2/ft) =",{"$f":"'LRFR Input'!D57","v":2.008}]
["r (in) =",{"$f":"'LRFR Input'!D58","v":0.34720000000000001}]
["I x 10-3 (in4/in) =",{"$f":"'LRFR Input'!D59","v":20.183}]
[]
[]
["C.   Design Calculations:"]
[null,"Structure Type:",{"$f":"'LRFR Input'!D38","v":"Corrugated Metal Pipe"}]
[null,"Seam Type:",{"$f":"'LRFR Input'!D39","v":"Helical pipe w/ lock seam or fully welded seam"}]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,null,{"$f":"'LRFR Input'!D44","v":70.5}]
[null,"AASHTO minimum cover, h (ft) =",null,null,{"$f":"E28/8","v":2.3537499999999998},{"$f":"IF(AND(C56=\"Long Span Structural Plate (AASHTO 12.7)\",B48<'Reference tables'!C17), \"see * below\", \"\")","v":""}]
[null,"Height of cover above crown \"H\" (ft) =    ",null,null,{"$f":"'LRFR Input'!D41","v":2.6},{"$f":"IF(E60>=E59, \"\", \"! H<h, cover not deep enough!\")","v":""}]
[null,"φloss = Section Properties reduction factor on the basis of metal loss from the materials field evaluation =    ",null,null,{"$f":"1-'LRFR Input'!D53","v":1}]
[null,"φ1 = Resistance Factor for wall area and buckling (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",0.67,1)","v":1}]
[null,"φ2 = Resistance Factor for seam strength (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", 0.67, IF('LRFR Input'!D39=\"Helical pipe w/ lock seam or fully welded seam\", 1, \"\"))","v":1}]
[null,"δ = Soil density (k/ft3)",null,null,{"$f":"'LRFR Input'!D65","v":0.12}]
[null,"k = soil stiffness factor =",null,null,0.22]
[null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6)=",null,null,{"$f":"'LRFR Input'!D66","v":1.1499999999999999}]
[]
[]
["Calculate the fcr (critical buckling stress) :",null,"(AASHTO LRFD 12.7.2.4)"]
[]
["if:"]
[]
["if:"]
[]
["Compare:","S (in) =",{"$f":"D32*12","v":225.95999999999998},{"$f":"IF(C75>F75, \">\", \"<\")","v":">"},null,{"$f":"(B51/E65)*(24*E41*1000/(E40*1000))^0.5","v":196.27066710499614}]
[]
["Therefore,","fcr =",{"$f":"IF(C75<F75, (E40*1000-((E40*1000)^2/(48*E41*1000))*(E65*C75/B51)^2)/1000, (12*E41*1000/(E65*C75/B51)^2)/1000)","v":16.97579738990796},"ksi"]
[]
["Calculate the Tcap (thrust capacity of the wall) :"]
[null,"Seam Strength (k/ft) =",{"$f":"'LRFR Input'!D61","v":0}]
[]
[null,"Tcap = less of:","1.  wall yield strength = φ1 φloss Fy A =",null,null,{"$f":"E39*B50*E62*E61","v":66.263999999999996}]
[null,null,"2.  wall buckling strength = f φ1 φloss fcr A =",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"N/A\", IF(C30=\"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)\", C77*B50*E62*E61*E24, C77*B50*E62*E61))","v":22.838558776486572},null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"buckling not applicable to long spans\", \"\")","v":""}]
[null,null,"3.  seam strength = φ2 x (seam strength) =",null,null,{"$f":"E63*C80","v":0}]
[]
["Therefore,","Tcap = ",{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", MIN(F82,F83,F84), MIN(F82,F83))","v":22.838558776486572},"k/ft"]
[]
["Calculate the TE (pipe wall thrust due to earth cover) :"]
[null,"TE = higher value of :","1.   δ H (S/2) =",{"$f":"E64*E60*D32/2","v":2.9374799999999999},"k/ft"]
[null,null,"2.   δ H Rt =",{"$f":"E64*E60*D33","v":2.9374799999999999},"k/ft"]
[]
["Therefore,","TE = ",{"$f":"MAX(D89,D90)","v":2.9374799999999999},"k/ft"]
[]
["Calculate the T(L+I) (pipe wall thrust due to live load plus impact) :"]
[null,"T(L+IM) = higher value of :","1.   ρ (L+IM)  (S/2) =","k/ft"]
[null,null,"2.   ρ (L+IM)  Rt =","k/ft"]
[]
[null,"Based on AASHTO LRFD 3.6.2.2:"]
[null,"Live load Dynamic Load Allowance,   IM =",null,"33(1.0-0.125 DE) ≥ 0%"]
[null,"where,","DE = the minimum depth of earth cover above the structure (ft)"]
[]
[null,null,"For this structure: Depth of Fill, DE = H=",{"$f":"E60","v":2.6},"ft"]
[null,null,"IM =",{"$f":"IF(33*(1-0.125*D102)/100>0,33*(1-0.125*D102)/100,0)","v":0.22275000000000003}]
[null,null,"(1+IM) =",{"$f":"1+D103","v":1.22275}]
[]
["Case A:","Depth of Fill, H < 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 4.6.2.10.1 & 2 (case 1: traffic travels parallel to span):"]
[null,"   When Depths of Fill of Culverts < 2.0 ft,"]
[null,"Eaxle= 96+1.44 S =",null,{"$f":"(96+1.44*D32)","v":123.1152},"in"]
[null,"Therefore,    Ewheel = ½ Eaxle =",null,{"$f":"D109/24","v":5.1298000000000004},"ft"]
[null,null,"Espan = LT + φE (H) =","same as case B, see calculations below"]
[null,"Where,"]
[null,null,"Ewheel = equivalent distribution width perpendicular to span, = WD"]
[null,null,"WD = Distributed load width/ per wheel load"]
[null,null,"Espan = equivalent distribution length parallel to span, = LD"]
[null,null,"LD = Distributed load length/ per wheel load"]
["Case B:","Depth of Fill, H ≥ 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 3.6.1.2.5 & 6:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Where, WT = Tire contact width, LT = Tire contact length, WD = Distributed load width, LD = Distributed load length"]
[]
["The surface tire contact area for HL-93 loading (per AASHTO LRFD 3.6.1.2.5):"]
["WT = 20\" =",{"$f":"20/12","v":1.6666666666666667},"ft"]
["LT = 10\" =",{"$f":"10/12","v":0.83333333333333337},"ft"]
["The surface tire contact area for LA6, LA8  (per AASHTO LRFD C3.6.1.2.5 Guideline):"]
["WT (in) =","P/0.8  "]
["LT (in) =","6.4g(1+IM/100) "]
["where,","p = wheel load (kips)"]
[null,"g = Load Factor for Legal Loads gLL =",null,{"$f":"'LRFR Input'!D74","v":1.8}]
[null,"IM = dynamic load allowance percent"]
["So,",null,"HL-93 Tandem","LA Type 6","LA Type 8"]
[null,"P \"heavy axle\" wheel load (kips) =",12.5,9.25,9.25]
[null,"WT (ft) =",{"$f":"B133","v":1.6666666666666667},{"$f":"(D142/0.8)/12","v":0.96354166666666663},{"$f":"(E142/0.8)/12","v":0.96354166666666663}]
[null,"LT (ft) =",{"$f":"B134","v":0.83333333333333337},{"$f":"6.4*$D$104/12*$D$139","v":1.17384},{"$f":"6.4*$D$104/12*$D$139","v":1.17384}]
[]
["Distribution of wheel loads through earth fills (per AASHTO LRFD 3.6.1.2.6):"]
[]
["for HL-93 Design Truck:"]
[null,"WD = 1.67+φEH=",{"$f":"20/12+E66*D102","v":4.6566666666666663},"ft"]
[null,"LD = 0.83 + φEH =",{"$f":"10/12+E66*D102","v":3.8233333333333333},"ft"]
["for HL-93 Tandem, LA6, LA8 Trucks:"]
[null,null,"HL-93 Tandem","LA Type 6","LA Type 8"]
[null,"WD = WT + φEH =",{"$f":"C143+$E$66*$E$60","v":4.6566666666666663},3.9535416666666663,3.9535416666666663]
[null,"LD = LT + φEH =",3.8233333333333333,4.1638399999999995,4.1638399999999995]
[]
[null,null,"Fill depth, H =",{"$f":"D102","v":2.6},{"$f":"IF(D156<2, \"H<2', Case A applied\", IF(D156>=2, \"H>=2', Case B applied\", \"\"))","v":"H>=2', Case B applied"}]
[null,null,"Structure Total Length, L =",{"$f":"'LRFR Input'!D44","v":70.5},"ft "]
[null,null,"[ if WD (total) > L, use L = WD (total) in the calculations ]"]
[null,"HL-93 Truck","HL-93 Tandem","LA Type 6","LA Type 8"]
["Heavy Axle Load (lbs)",32000,25000,18500,18500]
["P (1+ IM) (lbs) =",{"$f":"B160/2*$D$104","v":19564},{"$f":"C160/2*$D$104","v":15284.375},{"$f":"D160/2*$D$104","v":11310.4375},{"$f":"E160/2*$D$104","v":11310.4375}]
["* Saxle 1 (ft) =",0,4,4,4]
["* Saxle 2 (ft) =",0,0,0,0]
["wheel spacing on axle",6,6,6,6]
["WD (ft) =",{"$f":"IF($D$156<2, $D$110, C149)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, C153)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, D153)","v":3.9535416666666663},{"$f":"IF($D$156<2, $D$110, E153)","v":3.9535416666666663}]
["LD (ft) =",{"$f":"C150","v":3.8233333333333333},{"$f":"C154","v":3.8233333333333333},{"$f":"D154","v":4.1638399999999995},{"$f":"E154","v":4.1638399999999995}]
["WD (total) = ",{"$f":"IF(B165>B164, MIN(B165+B164,$D$157), MIN(B165,$D$157) )","v":4.6566666666666663},{"$f":"IF(C165>C164, MIN(C165+C164, $D$157), MIN(C165,$D$157))","v":4.6566666666666663},{"$f":"IF(D165>D164, MIN(D165+D164, $D$157), MIN(D165,$D$157))","v":3.9535416666666663},{"$f":"IF(E165>E164, MIN(E165+E164, D157), MIN(E165,D157))","v":3.9535416666666663}]
["LD (total) =",{"$f":"IF(B166>B162, B166+B162, B166)","v":3.8233333333333333},{"$f":"IF(C166>C162, C166+C162, C166)","v":3.8233333333333333},{"$f":"IF(D166>D162, D166+D162, D166)","v":8.1638400000000004},{"$f":"IF(E166>E162, E166+E162, E166)","v":8.1638400000000004}]
["* AD (ft2) =",{"$f":"B167*B168","v":17.803988888888888},{"$f":"C167*C168","v":17.803988888888888},{"$f":"D167*D168","v":32.276081599999998},{"$f":"E167*E168","v":32.276081599999998}]
["* PD (kips) =",{"$f":"IF(AND(B167>B165,B168>B166),4*B161/1000,IF(OR(B167>B165,B168>B166),2*B161/1000,B161/1000))","v":19.564},{"$f":"IF(AND(C167>C165,C168>C166),4*C161/1000,IF(OR(C167>C165,C168>C166),2*C161/1000,C161/1000))","v":15.284375000000001},{"$f":"IF(AND(D167>D165,D168>D166),4*D161/1000,IF(OR(D167>D165,D168>D166),2*D161/1000,D161/1000))","v":22.620875000000002},{"$f":"IF(AND(E167>E165,E168>E166),4*E161/1000,IF(OR(E167>E165,E168>E166),2*E161/1000,E161/1000))","v":22.620875000000002}]
["ρ (L+IM) = PD/AD =",{"$f":"B170/B169","v":1.0988548758424299},{"$f":"C170/C169","v":0.8584803717518984},{"$f":"D170/D169","v":0.70085567635942536},{"$f":"E170/E169","v":0.70085567635942536}]
["T(L+IM) (k/ft) =",{"$f":"MAX(B171*$D$32/2, B171*$D$33)","v":10.345718656056476},{"$f":"MAX(C171*$D$32/2, C171*$D$33)","v":8.0825927000441222},{"$f":"MAX(D171*$D$32/2, D171*$D$33)","v":6.5985561929239891},{"$f":"MAX(E171*$D$32/2, E171*$D$33)","v":6.5985561929239891}]
["*   Saxle 1 = distance to the 1st adjacent heavy axle load, if the spacing is > 4', Saxle1 = 0.  "]
["     Saxle 2 = distance to the 2nd adjacent heavy axle load, if the spacing is > 4', Saxle2 = 0.  "]
["     AD = Total Load Distributed Area "]
["     PD = Total Load being Distributed"]
["Transverse pressure overlaps are considered.  Longitudinal pressure overlaps are considered for two adjacent heavy axle loads when the Saxle is ≤ 4 feet."]
[]
[]
["D.   Load Rating Factors for Ring Compression Structures:"]
["      1.  Operating Load Rating Factor (RFO):"]
["               a. RFO based on wall strength"]
[]
[]
["               b. RFO based on minimum cover requirements"]
[]
[]
[null,"         Where, ",null,{"$f":"IF((2.36*E60/D32+0.528)>1, 1, 2.36*E60/D32+0.528)","v":0.85386298459904419}]
[null,"So,   RFO-C =",{"$f":"E60^2/(D188*(E59)^2)","v":1.429018472478925}]
[]
["Operating Load Rating Factors, RFO"]
[null,"HL-93 Truck","HL-93 Tandem","LA Type 6","LA Type 8"]
["Tcap",{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572}]
["TE ",{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B172","v":10.345718656056476},{"$f":"C172","v":8.0825927000441222},6.5985561929239891,6.5985561929239891]
["gLL ",{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D74","v":1.8},{"$f":"'LRFR Input'!D74","v":1.8}]
["RFO-W",{"$f":"(B193-B195*B194)/(B196*B197)","v":1.2250888217861231},{"$f":"(C193-C195*C194)/(C196*C197)","v":1.5681136918862377},1.4405906278941509,1.4405906278941509]
["RFO-C",{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925}]
["RFO",{"$f":"MIN(B198,$B$199)","v":1.2250888217861231},{"$f":"MIN(C198,$B$199)","v":1.429018472478925},1.429018472478925,1.429018472478925]
[]
[]
["      2.  Inventory Load Rating Factor (RFi):"]
["               a. RFi based on wall strength"]
[]
[]
["               b. RFi based on minimum cover requirements"]
[]
[]
["Inventory Load Rating Factor, RFi"]
[null,"HL-93 Truck","HL-93 Tandem"]
["Tcap",{"$f":"B193","v":22.838558776486572},{"$f":"C193","v":22.838558776486572}]
["TE ",{"$f":"B194","v":2.9374799999999999},{"$f":"C194","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B196","v":10.345718656056476},{"$f":"C196","v":8.0825927000441222}]
["gLL ",{"$f":"'LRFR Input'!D72","v":1.75},{"$f":"'LRFR Input'!D72","v":1.75}]
["RFi-w",{"$f":"(B212-B213*B214)/(B215*B216)","v":0.94506851966358085},{"$f":"(C212-C213*C214)/(C215*C216)","v":1.2096877051693835}]
["RFi-c",{"$f":"E60^2/E59^2","v":1.220185977958022},{"$f":"E60^2/E59^2","v":1.220185977958022}]
["RFi",{"$f":"MIN(B217,$B$218)","v":0.94506851966358085},{"$f":"MIN(C217,$B$218)","v":1.2096877051693835}]
[]
[]
["Load Rating Summary:"]
[null,"Load","GVW","Rating Factor","Safe Load"]
["Inventory",{"$f":"B211","v":"HL-93 Truck"},36,{"$f":"B219","v":0.94506851966358085},{"$f":"C224*D224","v":34.02246670788891}]
[null,{"$f":"C211","v":"HL-93 Tandem"},25,{"$f":"C219","v":1.2096877051693835},30.242192629234587]
["Operating",{"$f":"B192","v":"HL-93 Truck"},36,{"$f":"B200","v":1.2250888217861231},44.103197584300432]
[null,{"$f":"C192","v":"HL-93 Tandem"},25,{"$f":"C200","v":1.429018472478925},35.725461811973126]
[null,{"$f":"D192","v":"LA Type 6"},40,{"$f":"D200","v":1.429018472478925},{"$f":"C228*D228","v":57.160738899156996}]
[null,{"$f":"E192","v":"LA Type 8"},44,{"$f":"E200","v":1.429018472478925},62.876812789072702]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null," "]

{"sheet":"Output HL93, NRL, SU4, SU5","index":4,"n_rows":238,"n_cols":9,"rows_kept":238,"cut":false,"hidden":false,"merged":[[14,0,15,5],[1,3,1,6],[2,5,2,6],[3,5,3,6],[4,5,4,6],[6,0,6,6],[7,0,7,6],[8,0,8,6],[10,0,10,1],[11,0,11,5],[12,0,12,5],[13,0,13,5],[16,0,16,5],[17,0,17,5],[19,2,19,3],[21,1,23,1],[21,2,21,3],[22,2,22,3],[23,2,23,3],[43,1,43,2],[24,1,25,4],[27,2,27,3],[29,0,29,1],[29,2,29,5],[31,0,31,2],[32,0,32,2],[33,0,33,1],[37,2,37,4],[38,1,38,3],[39,1,39,3],[40,1,40,3],[59,1,59,3],[59,5,59,6],[44,1,44,2],[45,1,45,2],[46,1,46,2],[47,1,47,2],[49,5,50,6],[54,0,54,1],[55,2,55,4],[56,2,56,4],[57,1,57,3],[58,1,58,3],[58,5,58,6],[94,1,95,1],[60,1,60,3],[61,1,61,3],[62,1,62,3],[63,1,63,3],[64,1,64,3],[65,1,65,3],[81,1,83,1],[81,2,81,4],[82,2,82,4],[83,2,83,4],[88,1,89,1],[157,2,157,5],[97,4,97,5],[98,1,98,2],[98,3,98,5],[99,2,99,5],[108,1,108,2],[109,1,109,2],[119,0,128,6],[129,0,129,6],[135,3,135,4],[138,1,138,2],[139,1,139,2],[225,0,229,0],[225,5,229,5],[172,0,172,5],[173,0,173,5],[174,0,174,5],[175,0,175,5],[176,0,177,5],[179,0,179,6],[190,0,190,5],[200,0,200,2],[209,0,209,2],[221,0,221,4],[223,0,224,0]]}
[]
["Structure No:",{"$f":"'LRFR Input'!C2","v":0},"Bridge Name:",{"$f":"'LRFR Input'!E2","v":"LADOTD"}]
["Route/Crossing:",{"$f":"'LRFR Input'!C3","v":" "},"ADTT:",{"$f":"'LRFR Input'!E3","v":630}]
["Year Built:",{"$f":"'LRFR Input'!C4","v":1993},"Load Rated By:",{"$f":"'LRFR Input'!E4","v":"D.N"},"Date:",{"$f":"'LRFR Input'!G4","v":"2013-01-14"}]
["Structure Type:",{"$f":"'LRFR Input'!C5","v":"Corrugated Metal Pipe Arch"},"Checked By:",{"$f":"'LRFR Input'!E5","v":"M.H."},"Date:",{"$f":"'LRFR Input'!G5","v":"2013-01-14"}]
[]
["LRFR of In-Service, Corrugated Metal Pipe Structures                                     "]
["Based on AASHTO LRFD Bridge Design Specifications, Section 3, 4 & 12 & NCSPA Design Data Sheet No. 19 & ODOT Bridge Design Manual 2004 (effective 10-15-2010), Section 900 & 2008 AASHTO MBE"]
["(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
["A.   Design Dimensions"]
["   1.  For typical structures, use the actual field measured span for calculations."]
["   2.  For unsymmetrical structures or those deflected over 5%:"]
["       a. use 2 x the top radius (2 Rt) in lieu of span for calculations."]
["       b. base critical buckling stress calculations on the theoretical design span, reducing the resulting allowable buckling stress by the appropriate multiplier to account for deflection \" f \" (NCSPA Design Data Sheet No. 19, Figure B.1.1)."]
[]
["   3.  For all long span structures (horizontal ellipse, low and high profile arches, inverted pear shapes and pear arches), as well as other horizontal ellipses, use 2 x actual top radius (2Rt) in all cases."]
[]
[]
[null,"For typical structures :","Design Span = Actual Span \"S\" (ft) =",null,{"$f":"'LRFR Input'!D42","v":11.42}]
[]
[null,"For unsymmetrical or deflect more than 5% structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[null,null,"Pipe Crown Deflection =",null,{"$f":"'LRFR Input'!D52","v":0.05}]
[null,null,"Buckling Strength Reduction Factor, f * =",null,{"$f":"'Output HL93, LA3S2, LA3, 3-3'!E24","v":0.66999999999999993}]
[null,"* reduction factor f is based on NCSPA Design Data Sheet No 19, II Structural Evaluation A.2.b & Appendix B.1, Figure B.1.1 for Unsymmetrical structures or structures deflected over 5% only."]
[]
[]
[null,"long span structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[]
["Structure Category:",null,{"$f":"'LRFR Input'!D40","v":"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"}]
[]
["Then, Span Length used in Load Rating Calculation =",null,null,{"$f":"IF(C30 =\"Typical (NCSPA design data sheet no. 19, II. A. 1.)\", E20, E22)","v":18.829999999999998},"ft"]
["Then, Rt used in Load Rating Calculation =",null,null,{"$f":"'LRFR Input'!D45:E45","v":9.4149999999999991},"ft"]
["B.   Design Properties"]
[]
["Conduits Mechanical & Section Properties:"]
["Mechanical Properties:"]
[null,"Metal Type:",{"$f":"'LRFR Input'!E46","v":"Steel"}]
[null,"Fy = Minimum Yield Point of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,3,FALSE)","v":33},"ksi"]
[null,"Fu = Minimum Tensile Strength of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,2,FALSE)","v":45},"ksi"]
[null,"Em = Modulus of elasticity of metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,4,FALSE)","v":29000},"ksi"]
[]
["Section Properties:"]
["Corrugation:",{"$f":"'LRFR Input'!E47","v":"3 x 1 (corrugated steel pipe)"}]
["Gage Number:",{"$f":"'LRFR Input'!E48","v":10}]
["c (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E49, \"\")","v":""}]
["d (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E50, \"\")","v":""}]
["t (in) =",{"$f":"IF(B45=\"N/A\", 'LRFR Input'!E51, VLOOKUP(B45,'Reference tables'!B39:C48,2,FALSE))","v":0.13800000000000001}]
[]
["As (in2/ft) =",{"$f":"'LRFR Input'!D57","v":2.008}]
["r (in) =",{"$f":"'LRFR Input'!D58","v":0.34720000000000001}]
["I x 10-3 (in4/in) =",{"$f":"'LRFR Input'!D59","v":20.183}]
[]
[]
["C.   Design Calculations:"]
[null,"Structure Type:",{"$f":"'LRFR Input'!D38","v":"Corrugated Metal Pipe"}]
[null,"Seam Type:",{"$f":"'LRFR Input'!D39","v":"Helical pipe w/ lock seam or fully welded seam"}]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,null,{"$f":"'LRFR Input'!D44","v":70.5}]
[null,"AASHTO minimum cover, h (ft) =",null,null,{"$f":"E28/8","v":2.3537499999999998},{"$f":"IF(AND(C56=\"Long Span Structural Plate (AASHTO 12.7)\",B48<'Reference tables'!C17), \"see * below\", \"\")","v":""}]
[null,"Height of cover above crown \"H\" (ft) =    ",null,null,{"$f":"'LRFR Input'!D41","v":2.6},{"$f":"IF(E60>=E59, \"\", \"! H<h, cover not deep enough!\")","v":""}]
[null,"φloss = Section Properties reduction factor on the basis of metal loss from the materials field evaluation =    ",null,null,{"$f":"1-'LRFR Input'!D53","v":1}]
[null,"φ1 = Resistance Factor for wall area and buckling (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",0.67,1)","v":1}]
[null,"φ2 = Resistance Factor for seam strength (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", 0.67, IF('LRFR Input'!D39=\"Helical pipe w/ lock seam or fully welded seam\", 1, \"\"))","v":1}]
[null,"δ = Soil density (k/ft3)",null,null,{"$f":"'LRFR Input'!D65","v":0.12}]
[null,"k = soil stiffness factor =",null,null,0.22]
[null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6)=",null,null,{"$f":"'LRFR Input'!D66","v":1.1499999999999999}]
[]
[]
["Calculate the fcr (critical buckling stress) :",null,"(AASHTO LRFD 12.7.2.4)"]
[]
["if:"]
[]
["if:"]
[]
["Compare:","S (in) =",{"$f":"D32*12","v":225.95999999999998},{"$f":"IF(C75>F75, \">\", \"<\")","v":">"},null,{"$f":"(B51/E65)*(24*E41*1000/(E40*1000))^0.5","v":196.27066710499614}]
[]
["Therefore,","fcr =",{"$f":"IF(C75<F75, (E40*1000-((E40*1000)^2/(48*E41*1000))*(E65*C75/B51)^2)/1000, (12*E41*1000/(E65*C75/B51)^2)/1000)","v":16.97579738990796},"ksi"]
[]
["Calculate the Tcap (thrust capacity of the wall) :"]
[null,"Seam Strength (k/ft) =",{"$f":"'LRFR Input'!D61","v":0}]
[]
[null,"Tcap = less of:","1.  wall yield strength = φ1 φloss Fy A =",null,null,{"$f":"E39*B50*E62*E61","v":66.263999999999996}]
[null,null,"2.  wall buckling strength = f φ1 φloss fcr A =",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"N/A\", IF(C30=\"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)\", C77*B50*E62*E61*E24, C77*B50*E62*E61))","v":22.838558776486572},null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"buckling not applicable to long spans\", \"\")","v":""}]
[null,null,"3.  seam strength = φ2 x (seam strength) =",null,null,{"$f":"E63*C80","v":0}]
[]
["Therefore,","Tcap = ",{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", MIN(F82,F83,F84), MIN(F82,F83))","v":22.838558776486572},"k/ft"]
[]
["Calculate the TE (pipe wall thrust due to earth cover) :"]
[null,"TE = higher value of :","1.   δ H (S/2) =",{"$f":"E64*E60*D32/2","v":2.9374799999999999},"k/ft"]
[null,null,"2.   δ H Rt =",{"$f":"E64*E60*D33","v":2.9374799999999999},"k/ft"]
[]
["Therefore,","TE = ",{"$f":"MAX(D89,D90)","v":2.9374799999999999},"k/ft"]
[]
["Calculate the T(L+I) (pipe wall thrust due to live load plus impact) :"]
[null,"T(L+IM) = higher value of :","1.   ρ (L+IM)  (S/2) =","k/ft"]
[null,null,"2.   ρ (L+IM)  Rt =","k/ft"]
[]
[null,"Based on AASHTO LRFD 3.6.2.2:"]
[null,"Live load Dynamic Load Allowance,   IM =",null,"33(1.0-0.125 DE) ≥ 0%"]
[null,"where,","DE = the minimum depth of earth cover above the structure (ft)"]
[]
[null,null,"For this structure: Depth of Fill, DE = H=",{"$f":"E60","v":2.6},"ft"]
[null,null,"IM =",{"$f":"IF(33*(1-0.125*D102)/100>0,33*(1-0.125*D102)/100,0)","v":0.22275000000000003}]
[null,null,"(1+IM) =",{"$f":"1+D103","v":1.22275}]
[]
["Case A:","Depth of Fill, H < 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 4.6.2.10.1 & 2 (case 1: traffic travels parallel to span):"]
[null,"   When Depths of Fill of Culverts < 2.0 ft,"]
[null,"Eaxle= 96+1.44 S =",null,{"$f":"(96+1.44*D32)","v":123.1152},"in"]
[null,"Therefore,    Ewheel = ½ Eaxle =",null,{"$f":"D109/24","v":5.1298000000000004},"ft"]
[null,null,"Espan = LT + φE (H) =","same as case B, see calculations below"]
[null,"Where,"]
[null,null,"Ewheel = equivalent distribution width perpendicular to span, = WD"]
[null,null,"WD = Distributed load width/ per wheel load"]
[null,null,"Espan = equivalent distribution length parallel to span, = LD"]
[null,null,"LD = Distributed load length/ per wheel load"]
["Case B:","Depth of Fill, H ≥ 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 3.6.1.2.5 & 6:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Where, WT = Tire contact width, LT = Tire contact length, WD = Distributed load width, LD = Distributed load length"]
[]
["The surface tire contact area for HL-93 loading (per AASHTO LRFD 3.6.1.2.5):"]
["WT = 20\" =",{"$f":"20/12","v":1.6666666666666667},"ft"]
["LT = 10\" =",{"$f":"10/12","v":0.83333333333333337},"ft"]
["The surface tire contact area for NRL, SU4, SU5  (per AASHTO LRFD C3.6.1.2.5 Guideline):"]
["WT (in) =","P/0.8  "]
["LT (in) =","6.4g(1+IM/100) "]
["where,","p = wheel load (kips)"]
[null,"g = Load Factor for Special Hauling Loads gLL =",null,{"$f":"'LRFR Input'!D75","v":1.6}]
[null,"IM = dynamic load allowance percent"]
["So,",null,"HL-93 Tandem","NRL","SU4","SU5"]
[null,"P \"heavy axle\" wheel load (kips) =",12.5,8.5,8.5,8.5]
[null,"WT (ft) =",{"$f":"B133","v":1.6666666666666667},{"$f":"(D142/0.8)/12","v":0.88541666666666663},{"$f":"(E142/0.8)/12","v":0.88541666666666663},0.88541666666666663]
[null,"LT (ft) =",{"$f":"B134","v":0.83333333333333337},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333}]
[]
["Distribution of wheel loads through earth fills (per AASHTO LRFD 3.6.1.2.6):"]
[]
["for HL-93 Design Truck:"]
[null,"WD = 1.67+φEH=",{"$f":"20/12+E66*D102","v":4.6566666666666663},"ft"]
[null,"LD = 0.83 + φEH =",{"$f":"10/12+E66*D102","v":3.8233333333333333},"ft"]
["for HL-93 Tandem, NRL, SU4, SU5 Trucks:"]
[null,null,"HL-93 Tandem","NRL","SU4","SU5"]
[null,"WD = WT + φEH =",{"$f":"C143+$E$66*$E$60","v":4.6566666666666663},3.8754166666666663,3.8754166666666663,3.8754166666666663]
[null,"LD = LT + φEH =",3.8233333333333333,4.0334133333333329,4.0334133333333329,4.0334133333333329]
[]
[null,null,"Fill depth, H =",{"$f":"D102","v":2.6},{"$f":"IF(D156<2, \"H<2', Case A applied\", IF(D156>=2, \"H>=2', Case B applied\", \"\"))","v":"H>=2', Case B applied"}]
[null,null,"Structure Total Length, L =",{"$f":"'LRFR Input'!D44","v":70.5},"ft "]
[null,null,"[ if WD (total) > L, use L = WD (total) in the calculations ]"]
[null,"HL-93 Truck","HL-93 Tandem","NRL","SU4","SU5"]
["Heavy Axle Load (lbs)",32000,25000,17000,17000,17000]
["P (1+ IM) (lbs) =",{"$f":"B160/2*$D$104","v":19564},{"$f":"C160/2*$D$104","v":15284.375},{"$f":"D160/2*$D$104","v":10393.375},{"$f":"E160/2*$D$104","v":10393.375},{"$f":"F160/2*$D$104","v":10393.375}]
["* Saxle 1 (ft) =",0,4,4,4,4]
["* Saxle 2 (ft) =",0,0,0,0,0]
["wheel spacing on axle",6,6,6,6,6]
["WD (ft) =",{"$f":"IF($D$156<2, $D$110, C149)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, C153)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, D153)","v":3.8754166666666663},{"$f":"IF($D$156<2, $D$110, E153)","v":3.8754166666666663},{"$f":"IF($D$156<2, $D$110, F153)","v":3.8754166666666663}]
["LD (ft) =",{"$f":"C150","v":3.8233333333333333},{"$f":"C154","v":3.8233333333333333},{"$f":"D154","v":4.0334133333333329},{"$f":"E154","v":4.0334133333333329},{"$f":"F154","v":4.0334133333333329}]
["WD (total) = ",{"$f":"IF(B165>B164, MIN(B165+B164,$D$157), MIN(B165,$D$157) )","v":4.6566666666666663},{"$f":"IF(C165>C164, MIN(C165+C164, $D$157), MIN(C165,$D$157))","v":4.6566666666666663},{"$f":"IF(D165>D164, MIN(D165+D164, $D$157), MIN(D165,$D$157))","v":3.8754166666666663},{"$f":"IF(E165>E164, MIN(E165+E164, D157), MIN(E165,D157))","v":3.8754166666666663},{"$f":"IF(F165>F164, MIN(F165+F164, D157), MIN(F165,D157))","v":3.8754166666666663}]
["LD (total) =",{"$f":"IF(B166>B162, B166+B162, B166)","v":3.8233333333333333},{"$f":"IF(C166>C162, C166+C162, C166)","v":3.8233333333333333},{"$f":"IF(D166>D162, D166+D162, D166)","v":8.033413333333332},{"$f":"IF(E166>E162, E166+E162, E166)","v":8.033413333333332},{"$f":"IF(F166>F162, F166+F162, F166)","v":8.033413333333332}]
["* AD (ft2) =",{"$f":"B167*B168","v":17.803988888888888},{"$f":"C167*C168","v":17.803988888888888},{"$f":"D167*D168","v":31.132823922222215},{"$f":"E167*E168","v":31.132823922222215},{"$f":"F167*F168","v":31.132823922222215}]
["* PD (kips) =",{"$f":"IF(AND(B167>B165,B168>B166),4*B161/1000,IF(OR(B167>B165,B168>B166),2*B161/1000,B161/1000))","v":19.564},{"$f":"IF(AND(C167>C165,C168>C166),4*C161/1000,IF(OR(C167>C165,C168>C166),2*C161/1000,C161/1000))","v":15.284375000000001},{"$f":"IF(AND(D167>D165,D168>D166),4*D161/1000,IF(OR(D167>D165,D168>D166),2*D161/1000,D161/1000))","v":20.786750000000001},{"$f":"IF(AND(E167>E165,E168>E166),4*E161/1000,IF(OR(E167>E165,E168>E166),2*E161/1000,E161/1000))","v":20.786750000000001},{"$f":"IF(AND(F167>F165,F168>F166),4*F161/1000,IF(OR(F167>F165,F168>F166),2*F161/1000,F161/1000))","v":20.786750000000001}]
["ρ (L+IM) = PD/AD =",{"$f":"B170/B169","v":1.0988548758424299},{"$f":"C170/C169","v":0.8584803717518984},{"$f":"D170/D169","v":0.6676795542842705},{"$f":"E170/E169","v":0.6676795542842705},{"$f":"F170/F169","v":0.6676795542842705}]
["T(L+IM) (k/ft) =",{"$f":"MAX(B171*$D$32/2, B171*$D$33)","v":10.345718656056476},{"$f":"MAX(C171*$D$32/2, C171*$D$33)","v":8.0825927000441222},{"$f":"MAX(D171*$D$32/2, D171*$D$33)","v":6.2862030035864063},{"$f":"MAX(E171*$D$32/2, E171*$D$33)","v":6.2862030035864063},{"$f":"MAX(F171*$D$32/2, F171*$D$33)","v":6.2862030035864063}]
["*   Saxle 1 = distance to the 1st adjacent heavy axle load, if the spacing is > 4', Saxle1 = 0.  "]
["     Saxle 2 = distance to the 2nd adjacent heavy axle load, if the spacing is > 4', Saxle2 = 0.  "]
["     AD = Total Load Distributed Area "]
["     PD = Total Load being Distributed"]
["Transverse pressure overlaps are considered.  Longitudinal pressure overlaps are considered for two adjacent heavy axle loads when the Saxle is ≤ 4 feet."]
[]
[]
["D.   Load Rating Factors for Ring Compression Structures:"]
["      1.  Operating Load Rating Factor (RFO):"]
["               a. RFO based on wall strength"]
[]
[]
["               b. RFO based on minimum cover requirements"]
[]
[]
[null,"         Where, ",null,{"$f":"IF((2.36*E60/D32+0.528)>1, 1, 2.36*E60/D32+0.528)","v":0.85386298459904419}]
[null,"So,   RFO-C =",{"$f":"E60^2/(D188*(E59)^2)","v":1.429018472478925}]
[]
["Operating Load Rating Factors, RFO"]
[null,"HL-93 Truck","HL-93 Tandem","NRL","SU4","SU5"]
["Tcap",{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},22.838558776486572,22.838558776486572,22.838558776486572]
["TE ",{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},2.9374799999999999,2.9374799999999999,2.9374799999999999]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B172","v":10.345718656056476},{"$f":"C172","v":8.0825927000441222},6.2862030035864063,6.2862030035864063,6.2862030035864063]
["gLL ",{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D75","v":1.6},{"$f":"'LRFR Input'!D75","v":1.6},{"$f":"'LRFR Input'!D75","v":1.6}]
["RFO-W",{"$f":"(B193-B195*B194)/(B196*B197)","v":1.2250888217861231},{"$f":"(C193-C195*C194)/(C196*C197)","v":1.5681136918862377},1.7011931493785577,1.7011931493785577,{"$f":"(F193-F195*F194)/(F196*F197)","v":1.7011931493785577}]
["RFO-C",{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
["RFO",{"$f":"MIN(B198,$B$199)","v":1.2250888217861231},{"$f":"MIN(C198,$B$199)","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
[]
[]
["      2.  Inventory Load Rating Factor (RFi):"]
["               a. RFi based on wall strength"]
[]
[]
["               b. RFi based on minimum cover requirements"]
[]
[]
["Inventory Load Rating Factor, RFi"]
[null,"HL-93 Truck","HL-93 Tandem"]
["Tcap",{"$f":"B193","v":22.838558776486572},{"$f":"C193","v":22.838558776486572}]
["TE ",{"$f":"B194","v":2.9374799999999999},{"$f":"C194","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B196","v":10.345718656056476},{"$f":"C196","v":8.0825927000441222}]
["gLL ",{"$f":"'LRFR Input'!D72","v":1.75},{"$f":"'LRFR Input'!D72","v":1.75}]
["RFi-w",{"$f":"(B212-B213*B214)/(B215*B216)","v":0.94506851966358085},{"$f":"(C212-C213*C214)/(C215*C216)","v":1.2096877051693835}]
["RFi-c",{"$f":"E60^2/E59^2","v":1.220185977958022},{"$f":"E60^2/E59^2","v":1.220185977958022}]
["RFi",{"$f":"MIN(B217,$B$218)","v":0.94506851966358085},{"$f":"MIN(C217,$B$218)","v":1.2096877051693835}]
[]
[]
["Load Rating Summary:"]
[null,"Load","GVW","Rating Factor","Safe Load"]
["Inventory",{"$f":"B211","v":"HL-93 Truck"},36,{"$f":"B219","v":0.94506851966358085},{"$f":"C224*D224","v":34.02246670788891}]
[null,{"$f":"C211","v":"HL-93 Tandem"},25,{"$f":"C219","v":1.2096877051693835},30.242192629234587]
["Operating",{"$f":"B192","v":"HL-93 Truck"},36,{"$f":"B200","v":1.2250888217861231},44.103197584300432]
[null,{"$f":"C192","v":"HL-93 Tandem"},25,{"$f":"C200","v":1.429018472478925},35.725461811973126]
[null,{"$f":"D192","v":"NRL"},40,{"$f":"D200","v":1.429018472478925},{"$f":"C228*D228","v":57.160738899156996}]
[null,{"$f":"E192","v":"SU4"},27,{"$f":"E200","v":1.429018472478925},38.583498756930972]
[null,{"$f":"F192","v":"SU5"},31,{"$f":"F200","v":1.429018472478925},44.299572646846677]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null," "]

{"sheet":"Output HL93, NRL, SU6, SU7","index":5,"n_rows":238,"n_cols":9,"rows_kept":238,"cut":false,"hidden":false,"merged":[[14,0,15,5],[1,3,1,6],[2,5,2,6],[3,5,3,6],[4,5,4,6],[6,0,6,6],[7,0,7,6],[8,0,8,6],[10,0,10,1],[11,0,11,5],[12,0,12,5],[13,0,13,5],[16,0,16,5],[17,0,17,5],[19,2,19,3],[21,1,23,1],[21,2,21,3],[22,2,22,3],[23,2,23,3],[43,1,43,2],[24,1,25,4],[27,2,27,3],[29,0,29,1],[29,2,29,5],[31,0,31,2],[32,0,32,2],[33,0,33,1],[37,2,37,4],[38,1,38,3],[39,1,39,3],[40,1,40,3],[59,1,59,3],[59,5,59,6],[44,1,44,2],[45,1,45,2],[46,1,46,2],[47,1,47,2],[49,5,50,6],[54,0,54,1],[55,2,55,4],[56,2,56,4],[57,1,57,3],[58,1,58,3],[58,5,58,6],[94,1,95,1],[60,1,60,3],[61,1,61,3],[62,1,62,3],[63,1,63,3],[64,1,64,3],[65,1,65,3],[81,1,83,1],[81,2,81,4],[82,2,82,4],[83,2,83,4],[88,1,89,1],[157,2,157,5],[97,4,97,5],[98,1,98,2],[98,3,98,5],[99,2,99,5],[108,1,108,2],[109,1,109,2],[119,0,128,6],[129,0,129,6],[135,3,135,4],[138,1,138,2],[139,1,139,2],[225,0,229,0],[225,5,229,5],[172,0,172,5],[173,0,173,5],[174,0,174,5],[175,0,175,5],[176,0,177,5],[179,0,179,6],[190,0,190,5],[200,0,200,2],[209,0,209,2],[221,0,221,4],[223,0,224,0]]}
[]
["Structure No:",{"$f":"'LRFR Input'!C2","v":0},"Bridge Name:",{"$f":"'LRFR Input'!E2","v":"LADOTD"}]
["Route/Crossing:",{"$f":"'LRFR Input'!C3","v":" "},"ADTT:",{"$f":"'LRFR Input'!E3","v":630}]
["Year Built:",{"$f":"'LRFR Input'!C4","v":1993},"Load Rated By:",{"$f":"'LRFR Input'!E4","v":"D.N"},"Date:",{"$f":"'LRFR Input'!G4","v":"2013-01-14"}]
["Structure Type:",{"$f":"'LRFR Input'!C5","v":"Corrugated Metal Pipe Arch"},"Checked By:",{"$f":"'LRFR Input'!E5","v":"M.H."},"Date:",{"$f":"'LRFR Input'!G5","v":"2013-01-14"}]
[]
["LRFR of In-Service, Corrugated Metal Pipe Structures                                     "]
["Based on AASHTO LRFD Bridge Design Specifications, Section 3, 4 & 12 & NCSPA Design Data Sheet No. 19 & ODOT Bridge Design Manual 2004 (effective 10-15-2010), Section 900 & 2008 AASHTO MBE"]
["(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
["A.   Design Dimensions"]
["   1.  For typical structures, use the actual field measured span for calculations."]
["   2.  For unsymmetrical structures or those deflected over 5%:"]
["       a. use 2 x the top radius (2 Rt) in lieu of span for calculations."]
["       b. base critical buckling stress calculations on the theoretical design span, reducing the resulting allowable buckling stress by the appropriate multiplier to account for deflection \" f \" (NCSPA Design Data Sheet No. 19, Figure B.1.1)."]
[]
["   3.  For all long span structures (horizontal ellipse, low and high profile arches, inverted pear shapes and pear arches), as well as other horizontal ellipses, use 2 x actual top radius (2Rt) in all cases."]
[]
[]
[null,"For typical structures :","Design Span = Actual Span \"S\" (ft) =",null,{"$f":"'LRFR Input'!D42","v":11.42}]
[]
[null,"For unsymmetrical or deflect more than 5% structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[null,null,"Pipe Crown Deflection =",null,{"$f":"'LRFR Input'!D52","v":0.05}]
[null,null,"Buckling Strength Reduction Factor, f * =",null,{"$f":"'Output HL93, LA3S2, LA3, 3-3'!E24","v":0.66999999999999993}]
[null,"* reduction factor f is based on NCSPA Design Data Sheet No 19, II Structural Evaluation A.2.b & Appendix B.1, Figure B.1.1 for Unsymmetrical structures or structures deflected over 5% only."]
[]
[]
[null,"long span structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[]
["Structure Category:",null,{"$f":"'LRFR Input'!D40","v":"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"}]
[]
["Then, Span Length used in Load Rating Calculation =",null,null,{"$f":"IF(C30 =\"Typical (NCSPA design data sheet no. 19, II. A. 1.)\", E20, E22)","v":18.829999999999998},"ft"]
["Then, Rt used in Load Rating Calculation =",null,null,{"$f":"'LRFR Input'!D45:E45","v":9.4149999999999991},"ft"]
["B.   Design Properties"]
[]
["Conduits Mechanical & Section Properties:"]
["Mechanical Properties:"]
[null,"Metal Type:",{"$f":"'LRFR Input'!E46","v":"Steel"}]
[null,"Fy = Minimum Yield Point of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,3,FALSE)","v":33},"ksi"]
[null,"Fu = Minimum Tensile Strength of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,2,FALSE)","v":45},"ksi"]
[null,"Em = Modulus of elasticity of metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,4,FALSE)","v":29000},"ksi"]
[]
["Section Properties:"]
["Corrugation:",{"$f":"'LRFR Input'!E47","v":"3 x 1 (corrugated steel pipe)"}]
["Gage Number:",{"$f":"'LRFR Input'!E48","v":10}]
["c (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E49, \"\")","v":""}]
["d (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E50, \"\")","v":""}]
["t (in) =",{"$f":"IF(B45=\"N/A\", 'LRFR Input'!E51, VLOOKUP(B45,'Reference tables'!B39:C48,2,FALSE))","v":0.13800000000000001}]
[]
["As (in2/ft) =",{"$f":"'LRFR Input'!D57","v":2.008}]
["r (in) =",{"$f":"'LRFR Input'!D58","v":0.34720000000000001}]
["I x 10-3 (in4/in) =",{"$f":"'LRFR Input'!D59","v":20.183}]
[]
[]
["C.   Design Calculations:"]
[null,"Structure Type:",{"$f":"'LRFR Input'!D38","v":"Corrugated Metal Pipe"}]
[null,"Seam Type:",{"$f":"'LRFR Input'!D39","v":"Helical pipe w/ lock seam or fully welded seam"}]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,null,{"$f":"'LRFR Input'!D44","v":70.5}]
[null,"AASHTO minimum cover, h (ft) =",null,null,{"$f":"E22/8","v":2.3537499999999998},{"$f":"IF(AND(C56=\"Long Span Structural Plate (AASHTO 12.7)\",B48<'Reference tables'!C17), \"see * below\", \"\")","v":""}]
[null,"Height of cover above crown \"H\" (ft) =    ",null,null,{"$f":"'LRFR Input'!D41","v":2.6},{"$f":"IF(E60>=E59, \"\", \"! H<h, cover not deep enough!\")","v":""}]
[null,"φloss = Section Properties reduction factor on the basis of metal loss from the materials field evaluation =    ",null,null,{"$f":"1-'LRFR Input'!D53","v":1}]
[null,"φ1 = Resistance Factor for wall area and buckling (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",0.67,1)","v":1}]
[null,"φ2 = Resistance Factor for seam strength (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", 0.67, IF('LRFR Input'!D39=\"Helical pipe w/ lock seam or fully welded seam\", 1, \"\"))","v":1}]
[null,"δ = Soil density (k/ft3)",null,null,{"$f":"'LRFR Input'!D65","v":0.12}]
[null,"k = soil stiffness factor =",null,null,0.22]
[null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6)=",null,null,{"$f":"'LRFR Input'!D66","v":1.1499999999999999}]
[]
[]
["Calculate the fcr (critical buckling stress) :",null,"(AASHTO LRFD 12.7.2.4)"]
[]
["if:"]
[]
["if:"]
[]
["Compare:","S (in) =",{"$f":"D32*12","v":225.95999999999998},{"$f":"IF(C75>F75, \">\", \"<\")","v":">"},null,{"$f":"(B51/E65)*(24*E41*1000/(E40*1000))^0.5","v":196.27066710499614}]
[]
["Therefore,","fcr =",{"$f":"IF(C75<F75, (E40*1000-((E40*1000)^2/(48*E41*1000))*(E65*C75/B51)^2)/1000, (12*E41*1000/(E65*C75/B51)^2)/1000)","v":16.97579738990796},"ksi"]
[]
["Calculate the Tcap (thrust capacity of the wall) :"]
[null,"Seam Strength (k/ft) =",{"$f":"'LRFR Input'!D61","v":0}]
[]
[null,"Tcap = less of:","1.  wall yield strength = φ1 φloss Fy A =",null,null,{"$f":"E39*B50*E62*E61","v":66.263999999999996}]
[null,null,"2.  wall buckling strength = f φ1 φloss fcr A =",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"N/A\", IF(C30=\"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)\", C77*B50*E62*E61*E24, C77*B50*E62*E61))","v":22.838558776486572},null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"buckling not applicable to long spans\", \"\")","v":""}]
[null,null,"3.  seam strength = φ2 x (seam strength) =",null,null,{"$f":"E63*C80","v":0}]
[]
["Therefore,","Tcap = ",{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", MIN(F82,F83,F84), MIN(F82,F83))","v":22.838558776486572},"k/ft"]
[]
["Calculate the TE (pipe wall thrust due to earth cover) :"]
[null,"TE = higher value of :","1.   δ H (S/2) =",{"$f":"E64*E60*D32/2","v":2.9374799999999999},"k/ft"]
[null,null,"2.   δ H Rt =",{"$f":"E64*E60*D33","v":2.9374799999999999},"k/ft"]
[]
["Therefore,","TE = ",{"$f":"MAX(D89,D90)","v":2.9374799999999999},"k/ft"]
[]
["Calculate the T(L+I) (pipe wall thrust due to live load plus impact) :"]
[null,"T(L+IM) = higher value of :","1.   ρ (L+IM)  (S/2) =","k/ft"]
[null,null,"2.   ρ (L+IM)  Rt =","k/ft"]
[]
[null,"Based on AASHTO LRFD 3.6.2.2:"]
[null,"Live load Dynamic Load Allowance,   IM =",null,"33(1.0-0.125 DE) ≥ 0%"]
[null,"where,","DE = the minimum depth of earth cover above the structure (ft)"]
[]
[null,null,"For this structure: Depth of Fill, DE = H=",{"$f":"E60","v":2.6},"ft"]
[null,null,"IM =",{"$f":"IF(33*(1-0.125*D102)/100>0,33*(1-0.125*D102)/100,0)","v":0.22275000000000003}]
[null,null,"(1+IM) =",{"$f":"1+D103","v":1.22275}]
[]
["Case A:","Depth of Fill, H < 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 4.6.2.10.1 & 2 (case 1: traffic travels parallel to span):"]
[null,"   When Depths of Fill of Culverts < 2.0 ft,"]
[null,"Eaxle= 96+1.44 S =",null,{"$f":"(96+1.44*D32)","v":123.1152},"in"]
[null,"Therefore,    Ewheel = ½ Eaxle =",null,{"$f":"D109/24","v":5.1298000000000004},"ft"]
[null,null,"Espan = LT + φE (H) =","same as case B, see calculations below"]
[null,"Where,"]
[null,null,"Ewheel = equivalent distribution width perpendicular to span, = WD"]
[null,null,"WD = Distributed load width/ per wheel load"]
[null,null,"Espan = equivalent distribution length parallel to span, = LD"]
[null,null,"LD = Distributed load length/ per wheel load"]
["Case B:","Depth of Fill, H ≥ 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 3.6.1.2.5 & 6:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Where, WT = Tire contact width, LT = Tire contact length, WD = Distributed load width, LD = Distributed load length"]
[]
["The surface tire contact area for HL-93 loading (per AASHTO LRFD 3.6.1.2.5):"]
["WT = 20\" =",{"$f":"20/12","v":1.6666666666666667},"ft"]
["LT = 10\" =",{"$f":"10/12","v":0.83333333333333337},"ft"]
["The surface tire contact area for NRL, SU6, SU7  (per AASHTO LRFD C3.6.1.2.5 Guideline):"]
["WT (in) =","P/0.8  "]
["LT (in) =","6.4g(1+IM/100) "]
["where,","p = wheel load (kips)"]
[null,"g = Load Factor for Special Hauling Loads gLL =",null,{"$f":"'LRFR Input'!D75","v":1.6}]
[null,"IM = dynamic load allowance percent"]
["So,",null,"HL-93 Tandem","NRL","SU6","SU7"]
[null,"P \"heavy axle\" wheel load (kips) =",12.5,8.5,8.5,8.5]
[null,"WT (ft) =",{"$f":"B133","v":1.6666666666666667},{"$f":"(D142/0.8)/12","v":0.88541666666666663},{"$f":"(E142/0.8)/12","v":0.88541666666666663},0.88541666666666663]
[null,"LT (ft) =",{"$f":"B134","v":0.83333333333333337},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333},{"$f":"6.4*$D$104/12*$D$139","v":1.0434133333333333}]
[]
["Distribution of wheel loads through earth fills (per AASHTO LRFD 3.6.1.2.6):"]
[]
["for HL-93 Design Truck:"]
[null,"WD = 1.67+φEH=",{"$f":"20/12+E66*D102","v":4.6566666666666663},"ft"]
[null,"LD = 0.83 + φEH =",{"$f":"10/12+E66*D102","v":3.8233333333333333},"ft"]
["for HL-93 Tandem, NRL, SU4, SU5 Trucks:"]
[null,null,"HL-93 Tandem","NRL","SU6","SU7"]
[null,"WD = WT + φEH =",{"$f":"C143+$E$66*$E$60","v":4.6566666666666663},3.8754166666666663,3.8754166666666663,3.8754166666666663]
[null,"LD = LT + φEH =",3.8233333333333333,4.0334133333333329,4.0334133333333329,4.0334133333333329]
[]
[null,null,"Fill depth, H =",{"$f":"D102","v":2.6},{"$f":"IF(D156<2, \"H<2', Case A applied\", IF(D156>=2, \"H>=2', Case B applied\", \"\"))","v":"H>=2', Case B applied"}]
[null,null,"Structure Total Length, L =",{"$f":"'LRFR Input'!D44","v":70.5},"ft "]
[null,null,"[ if WD (total) > L, use L = WD (total) in the calculations ]"]
[null,"HL-93 Truck","HL-93 Tandem","NRL","SU6","SU7"]
["Heavy Axle Load (lbs)",32000,25000,17000,17000,17000]
["P (1+ IM) (lbs) =",{"$f":"B160/2*$D$104","v":19564},{"$f":"C160/2*$D$104","v":15284.375},{"$f":"D160/2*$D$104","v":10393.375},{"$f":"E160/2*$D$104","v":10393.375},{"$f":"F160/2*$D$104","v":10393.375}]
["* Saxle 1 (ft) =",0,4,4,4,4]
["* Saxle 2 (ft) =",0,0,0,0,0]
["wheel spacing on axle",6,6,6,6,6]
["WD (ft) =",{"$f":"IF($D$156<2, $D$110, C149)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, C153)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, D153)","v":3.8754166666666663},{"$f":"IF($D$156<2, $D$110, E153)","v":3.8754166666666663},{"$f":"IF($D$156<2, $D$110, F153)","v":3.8754166666666663}]
["LD (ft) =",{"$f":"C150","v":3.8233333333333333},{"$f":"C154","v":3.8233333333333333},{"$f":"D154","v":4.0334133333333329},{"$f":"E154","v":4.0334133333333329},{"$f":"F154","v":4.0334133333333329}]
["WD (total) = ",{"$f":"IF(B165>B164, MIN(B165+B164,$D$157), MIN(B165,$D$157) )","v":4.6566666666666663},{"$f":"IF(C165>C164, MIN(C165+C164, $D$157), MIN(C165,$D$157))","v":4.6566666666666663},{"$f":"IF(D165>D164, MIN(D165+D164, $D$157), MIN(D165,$D$157))","v":3.8754166666666663},{"$f":"IF(E165>E164, MIN(E165+E164, D157), MIN(E165,D157))","v":3.8754166666666663},{"$f":"IF(F165>F164, MIN(F165+F164, D157), MIN(F165,D157))","v":3.8754166666666663}]
["LD (total) =",{"$f":"IF(B166>B162, B166+B162, B166)","v":3.8233333333333333},{"$f":"IF(C166>C162, C166+C162, C166)","v":3.8233333333333333},{"$f":"IF(D166>D162, D166+D162, D166)","v":8.033413333333332},{"$f":"IF(E166>E162, E166+E162, E166)","v":8.033413333333332},{"$f":"IF(F166>F162, F166+F162, F166)","v":8.033413333333332}]
["* AD (ft2) =",{"$f":"B167*B168","v":17.803988888888888},{"$f":"C167*C168","v":17.803988888888888},{"$f":"D167*D168","v":31.132823922222215},{"$f":"E167*E168","v":31.132823922222215},{"$f":"F167*F168","v":31.132823922222215}]
["* PD (kips) =",{"$f":"IF(AND(B167>B165,B168>B166),4*B161/1000,IF(OR(B167>B165,B168>B166),2*B161/1000,B161/1000))","v":19.564},{"$f":"IF(AND(C167>C165,C168>C166),4*C161/1000,IF(OR(C167>C165,C168>C166),2*C161/1000,C161/1000))","v":15.284375000000001},{"$f":"IF(AND(D167>D165,D168>D166),4*D161/1000,IF(OR(D167>D165,D168>D166),2*D161/1000,D161/1000))","v":20.786750000000001},{"$f":"IF(AND(E167>E165,E168>E166),4*E161/1000,IF(OR(E167>E165,E168>E166),2*E161/1000,E161/1000))","v":20.786750000000001},{"$f":"IF(AND(F167>F165,F168>F166),4*F161/1000,IF(OR(F167>F165,F168>F166),2*F161/1000,F161/1000))","v":20.786750000000001}]
["ρ (L+IM) = PD/AD =",{"$f":"B170/B169","v":1.0988548758424299},{"$f":"C170/C169","v":0.8584803717518984},{"$f":"D170/D169","v":0.6676795542842705},{"$f":"E170/E169","v":0.6676795542842705},{"$f":"F170/F169","v":0.6676795542842705}]
["T(L+IM) (k/ft) =",{"$f":"MAX(B171*$D$32/2, B171*$D$33)","v":10.345718656056476},{"$f":"MAX(C171*$D$32/2, C171*$D$33)","v":8.0825927000441222},{"$f":"MAX(D171*$D$32/2, D171*$D$33)","v":6.2862030035864063},{"$f":"MAX(E171*$D$32/2, E171*$D$33)","v":6.2862030035864063},{"$f":"MAX(F171*$D$32/2, F171*$D$33)","v":6.2862030035864063}]
["*   Saxle 1 = distance to the 1st adjacent heavy axle load, if the spacing is > 4', Saxle1 = 0.  "]
["     Saxle 2 = distance to the 2nd adjacent heavy axle load, if the spacing is > 4', Saxle2 = 0.  "]
["     AD = Total Load Distributed Area "]
["     PD = Total Load being Distributed"]
["Transverse pressure overlaps are considered.  Longitudinal pressure overlaps are considered for two adjacent heavy axle loads when the Saxle is ≤ 4 feet."]
[]
[]
["D.   Load Rating Factors for Ring Compression Structures:"]
["      1.  Operating Load Rating Factor (RFO):"]
["               a. RFO based on wall strength"]
[]
[]
["               b. RFO based on minimum cover requirements"]
[]
[]
[null,"         Where, ",null,{"$f":"IF((2.36*E60/D32+0.528)>1, 1, 2.36*E60/D32+0.528)","v":0.85386298459904419}]
[null,"So,   RFO-C =",{"$f":"E60^2/(D188*(E59)^2)","v":1.429018472478925}]
[]
["Operating Load Rating Factors, RFO"]
[null,"HL-93 Truck","HL-93 Tandem","NRL","SU6","SU7"]
["Tcap",{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},22.838558776486572,22.838558776486572,22.838558776486572]
["TE ",{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},2.9374799999999999,2.9374799999999999,2.9374799999999999]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B172","v":10.345718656056476},{"$f":"C172","v":8.0825927000441222},6.2862030035864063,6.2862030035864063,6.2862030035864063]
["gLL ",{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D75","v":1.6},{"$f":"'LRFR Input'!D75","v":1.6},{"$f":"'LRFR Input'!D75","v":1.6}]
["RFO-W",{"$f":"(B193-B195*B194)/(B196*B197)","v":1.2250888217861231},{"$f":"(C193-C195*C194)/(C196*C197)","v":1.5681136918862377},1.7011931493785577,1.7011931493785577,{"$f":"(F193-F195*F194)/(F196*F197)","v":1.7011931493785577}]
["RFO-C",{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
["RFO",{"$f":"MIN(B198,$B$199)","v":1.2250888217861231},{"$f":"MIN(C198,$B$199)","v":1.429018472478925},1.429018472478925,1.429018472478925,1.429018472478925]
[]
[]
["      2.  Inventory Load Rating Factor (RFi):"]
["               a. RFi based on wall strength"]
[]
[]
["               b. RFi based on minimum cover requirements"]
[]
[]
["Inventory Load Rating Factor, RFi"]
[null,"HL-93 Truck","HL-93 Tandem"]
["Tcap",{"$f":"B193","v":22.838558776486572},{"$f":"C193","v":22.838558776486572}]
["TE ",{"$f":"B194","v":2.9374799999999999},{"$f":"C194","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B196","v":10.345718656056476},{"$f":"C196","v":8.0825927000441222}]
["gLL ",{"$f":"'LRFR Input'!D72","v":1.75},{"$f":"'LRFR Input'!D72","v":1.75}]
["RFi-w",{"$f":"(B212-B213*B214)/(B215*B216)","v":0.94506851966358085},{"$f":"(C212-C213*C214)/(C215*C216)","v":1.2096877051693835}]
["RFi-c",{"$f":"E60^2/E59^2","v":1.220185977958022},{"$f":"E60^2/E59^2","v":1.220185977958022}]
["RFi",{"$f":"MIN(B217,$B$218)","v":0.94506851966358085},{"$f":"MIN(C217,$B$218)","v":1.2096877051693835}]
[]
[]
["Load Rating Summary:"]
[null,"Load","GVW","Rating Factor","Safe Load"]
["Inventory",{"$f":"B211","v":"HL-93 Truck"},36,{"$f":"B219","v":0.94506851966358085},{"$f":"C224*D224","v":34.02246670788891}]
[null,{"$f":"C211","v":"HL-93 Tandem"},25,{"$f":"C219","v":1.2096877051693835},30.242192629234587]
["Operating",{"$f":"B192","v":"HL-93 Truck"},36,{"$f":"B200","v":1.2250888217861231},44.103197584300432]
[null,{"$f":"C192","v":"HL-93 Tandem"},25,{"$f":"C200","v":1.429018472478925},35.725461811973126]
[null,{"$f":"D192","v":"NRL"},40,{"$f":"D200","v":1.429018472478925},{"$f":"C228*D228","v":57.160738899156996}]
[null,{"$f":"E192","v":"SU6"},34.75,{"$f":"E200","v":1.429018472478925},49.658391918642643]
[null,{"$f":"F192","v":"SU7"},38.75,{"$f":"F200","v":1.429018472478925},55.374465808558341]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null," "]

{"sheet":"Output HL93, OFRD1, 2 & 3","index":6,"n_rows":238,"n_cols":14,"rows_kept":238,"cut":false,"hidden":false,"merged":[[14,0,15,5],[1,3,1,6],[2,5,2,6],[3,5,3,6],[4,5,4,6],[6,0,6,6],[7,0,7,6],[8,0,8,6],[10,0,10,1],[11,0,11,5],[12,0,12,5],[13,0,13,5],[16,0,16,5],[17,0,17,5],[19,2,19,3],[21,1,23,1],[21,2,21,3],[22,2,22,3],[23,2,23,3],[43,1,43,2],[24,1,25,4],[27,2,27,3],[29,0,29,1],[29,2,29,5],[31,0,31,2],[32,0,32,2],[33,0,33,1],[37,2,37,4],[38,1,38,3],[39,1,39,3],[40,1,40,3],[59,1,59,3],[59,5,59,6],[44,1,44,2],[45,1,45,2],[46,1,46,2],[47,1,47,2],[49,5,50,6],[54,0,54,1],[55,2,55,4],[56,2,56,4],[57,1,57,3],[58,1,58,3],[58,5,58,6],[94,1,95,1],[60,1,60,3],[61,1,61,3],[62,1,62,3],[63,1,63,3],[64,1,64,3],[65,1,65,3],[81,1,83,1],[81,2,81,4],[82,2,82,4],[83,2,83,4],[88,1,89,1],[157,2,157,5],[97,4,97,5],[98,1,98,2],[98,3,98,5],[99,2,99,5],[108,1,108,2],[109,1,109,2],[119,0,128,6],[129,0,129,6],[135,3,135,4],[138,1,138,2],[139,1,139,2],[225,0,229,0],[225,5,229,5],[172,0,172,5],[173,0,173,5],[174,0,174,5],[175,0,175,5],[176,0,177,5],[179,0,179,6],[190,0,190,5],[200,0,200,2],[209,0,209,2],[221,0,221,4],[223,0,224,0]]}
[]
["Structure No:",{"$f":"'LRFR Input'!C2","v":0},"Bridge Name:",{"$f":"'LRFR Input'!E2","v":"LADOTD"}]
["Route/Crossing:",{"$f":"'LRFR Input'!C3","v":" "},"ADTT:",{"$f":"'LRFR Input'!E3","v":630}]
["Year Built:",{"$f":"'LRFR Input'!C4","v":1993},"Load Rated By:",{"$f":"'LRFR Input'!E4","v":"D.N"},"Date:",{"$f":"'LRFR Input'!G4","v":"2013-01-14"}]
["Structure Type:",{"$f":"'LRFR Input'!C5","v":"Corrugated Metal Pipe Arch"},"Checked By:",{"$f":"'LRFR Input'!E5","v":"M.H."},"Date:",{"$f":"'LRFR Input'!G5","v":"2013-01-14"}]
[]
["LRFR of In-Service, Corrugated Metal Pipe Structures                                     "]
["Based on AASHTO LRFD Bridge Design Specifications, Section 3, 4 & 12 & NCSPA Design Data Sheet No. 19 & ODOT Bridge Design Manual 2004 (effective 10-15-2010), Section 900 & 2008 AASHTO MBE"]
["(do not use this spreadsheet to load rate Structural Plate Box Culverts)"]
[]
["A.   Design Dimensions"]
["   1.  For typical structures, use the actual field measured span for calculations."]
["   2.  For unsymmetrical structures or those deflected over 5%:"]
["       a. use 2 x the top radius (2 Rt) in lieu of span for calculations."]
["       b. base critical buckling stress calculations on the theoretical design span, reducing the resulting allowable buckling stress by the appropriate multiplier to account for deflection \" f \" (NCSPA Design Data Sheet No. 19, Figure B.1.1)."]
[]
["   3.  For all long span structures (horizontal ellipse, low and high profile arches, inverted pear shapes and pear arches), as well as other horizontal ellipses, use 2 x actual top radius (2Rt) in all cases."]
[]
[]
[null,"For typical structures :","Design Span = Actual Span \"S\" (ft) =",null,{"$f":"'LRFR Input'!D42","v":11.42}]
[]
[null,"For unsymmetrical or deflect more than 5% structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[null,null,"Pipe Crown Deflection =",null,{"$f":"'LRFR Input'!D52","v":0.05}]
[null,null,"Buckling Strength Reduction Factor, f * =",null,{"$f":"'Output HL93, LA3S2, LA3, 3-3'!E24","v":0.66999999999999993}]
[null,"* reduction factor f is based on NCSPA Design Data Sheet No 19, II Structural Evaluation A.2.b & Appendix B.1, Figure B.1.1 for Unsymmetrical structures or structures deflected over 5% only."]
[]
[]
[null,"long span structures:","Design Span (ft) = 2Rt = ",null,{"$f":"2*'LRFR Input'!D45","v":18.829999999999998}]
[]
["Structure Category:",null,{"$f":"'LRFR Input'!D40","v":"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"}]
[]
["Then, Span Length used in Load Rating Calculation =",null,null,{"$f":"IF(C30 =\"Typical (NCSPA design data sheet no. 19, II. A. 1.)\", E20, E22)","v":18.829999999999998},"ft"]
["Then, Rt used in Load Rating Calculation =",null,null,{"$f":"'LRFR Input'!D45:E45","v":9.4149999999999991},"ft"]
["B.   Design Properties"]
[]
["Conduits Mechanical & Section Properties:"]
["Mechanical Properties:"]
[null,"Metal Type:",{"$f":"'LRFR Input'!E46","v":"Steel"}]
[null,"Fy = Minimum Yield Point of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,3,FALSE)","v":33},"ksi"]
[null,"Fu = Minimum Tensile Strength of the Metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,2,FALSE)","v":45},"ksi"]
[null,"Em = Modulus of elasticity of metal",null,null,{"$f":"VLOOKUP(C38,'Reference tables'!C32:F36,4,FALSE)","v":29000},"ksi"]
[]
["Section Properties:"]
["Corrugation:",{"$f":"'LRFR Input'!E47","v":"3 x 1 (corrugated steel pipe)"}]
["Gage Number:",{"$f":"'LRFR Input'!E48","v":10}]
["c (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E49, \"\")","v":""}]
["d (in) =",{"$f":"IF(B44=\"N/A\",'LRFR Input'!E50, \"\")","v":""}]
["t (in) =",{"$f":"IF(B45=\"N/A\", 'LRFR Input'!E51, VLOOKUP(B45,'Reference tables'!B39:C48,2,FALSE))","v":0.13800000000000001}]
[]
["As (in2/ft) =",{"$f":"'LRFR Input'!D57","v":2.008}]
["r (in) =",{"$f":"'LRFR Input'!D58","v":0.34720000000000001}]
["I x 10-3 (in4/in) =",{"$f":"'LRFR Input'!D59","v":20.183}]
[]
[]
["C.   Design Calculations:"]
[null,"Structure Type:",{"$f":"'LRFR Input'!D38","v":"Corrugated Metal Pipe"}]
[null,"Seam Type:",{"$f":"'LRFR Input'!D39","v":"Helical pipe w/ lock seam or fully welded seam"}]
[null,"Longitudinal Length of Structure \"L\" (ft) =",null,null,{"$f":"'LRFR Input'!D44","v":70.5}]
[null,"AASHTO minimum cover, h (ft) =",null,null,{"$f":"E22/8","v":2.3537499999999998},{"$f":"IF(AND(C56=\"Long Span Structural Plate (AASHTO 12.7)\",B48<'Reference tables'!C17), \"see * below\", \"\")","v":""}]
[null,"Height of cover above crown \"H\" (ft) =    ",null,null,{"$f":"'LRFR Input'!D41","v":2.6},{"$f":"IF(E60>=E59, \"\", \"! H<h, cover not deep enough!\")","v":""}]
[null,"φloss = Section Properties reduction factor on the basis of metal loss from the materials field evaluation =    ",null,null,{"$f":"1-'LRFR Input'!D53","v":1}]
[null,"φ1 = Resistance Factor for wall area and buckling (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",0.67,1)","v":1}]
[null,"φ2 = Resistance Factor for seam strength (Table 12.5.5-1)",null,null,{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", 0.67, IF('LRFR Input'!D39=\"Helical pipe w/ lock seam or fully welded seam\", 1, \"\"))","v":1}]
[null,"δ = Soil density (k/ft3)",null,null,{"$f":"'LRFR Input'!D65","v":0.12}]
[null,"k = soil stiffness factor =",null,null,0.22]
[null,"φE = Factor for Distribution of Live Load with Depth of Fill based on Backfill Type (per AASHTO LRFD 3.6.1.2.6)=",null,null,{"$f":"'LRFR Input'!D66","v":1.1499999999999999}]
[]
[]
["Calculate the fcr (critical buckling stress) :",null,"(AASHTO LRFD 12.7.2.4)"]
[]
["if:"]
[]
["if:"]
[]
["Compare:","S (in) =",{"$f":"D32*12","v":225.95999999999998},{"$f":"IF(C75>F75, \">\", \"<\")","v":">"},null,{"$f":"(B51/E65)*(24*E41*1000/(E40*1000))^0.5","v":196.27066710499614}]
[]
["Therefore,","fcr =",{"$f":"IF(C75<F75, (E40*1000-((E40*1000)^2/(48*E41*1000))*(E65*C75/B51)^2)/1000, (12*E41*1000/(E65*C75/B51)^2)/1000)","v":16.97579738990796},"ksi"]
[]
["Calculate the Tcap (thrust capacity of the wall) :"]
[null,"Seam Strength (k/ft) =",{"$f":"'LRFR Input'!D61","v":0}]
[]
[null,"Tcap = less of:","1.  wall yield strength = φ1 φloss Fy A =",null,null,{"$f":"E39*B50*E62*E61","v":66.263999999999996}]
[null,null,"2.  wall buckling strength = f φ1 φloss fcr A =",null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"N/A\", IF(C30=\"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)\", C77*B50*E62*E61*E24, C77*B50*E62*E61))","v":22.838558776486572},null,null,{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\", \"buckling not applicable to long spans\", \"\")","v":""}]
[null,null,"3.  seam strength = φ2 x (seam strength) =",null,null,{"$f":"E63*C80","v":0}]
[]
["Therefore,","Tcap = ",{"$f":"IF('LRFR Input'!D39=\"Annular pipe w/ spot welded, riveted or bolted seam\", MIN(F82,F83,F84), MIN(F82,F83))","v":22.838558776486572},"k/ft"]
[]
["Calculate the TE (pipe wall thrust due to earth cover) :"]
[null,"TE = higher value of :","1.   δ H (S/2) =",{"$f":"E64*E60*D32/2","v":2.9374799999999999},"k/ft"]
[null,null,"2.   δ H Rt =",{"$f":"E64*E60*D33","v":2.9374799999999999},"k/ft"]
[]
["Therefore,","TE = ",{"$f":"MAX(D89,D90)","v":2.9374799999999999},"k/ft"]
[]
["Calculate the T(L+I) (pipe wall thrust due to live load plus impact) :"]
[null,"T(L+IM) = higher value of :","1.   ρ (L+IM)  (S/2) =","k/ft"]
[null,null,"2.   ρ (L+IM)  Rt =","k/ft"]
[]
[null,"Based on AASHTO LRFD 3.6.2.2:"]
[null,"Live load Dynamic Load Allowance,   IM =",null,"33(1.0-0.125 DE) ≥ 0%"]
[null,"where,","DE = the minimum depth of earth cover above the structure (ft)"]
[]
[null,null,"For this structure: Depth of Fill, DE = H=",{"$f":"E60","v":2.6},"ft"]
[null,null,"IM =",{"$f":"IF(33*(1-0.125*D102)/100>0,33*(1-0.125*D102)/100,0)","v":0.22275000000000003}]
[null,null,"(1+IM) =",{"$f":"1+D103","v":1.22275}]
[]
["Case A:","Depth of Fill, H < 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 4.6.2.10.1 & 2 (case 1: traffic travels parallel to span):"]
[null,"   When Depths of Fill of Culverts < 2.0 ft,"]
[null,"Eaxle= 96+1.44 S =",null,{"$f":"(96+1.44*D32)","v":123.1152},"in"]
[null,"Therefore,    Ewheel = ½ Eaxle =",null,{"$f":"D109/24","v":5.1298000000000004},"ft"]
[null,null,"Espan = LT + φE (H) =","same as case B, see calculations below"]
[null,"Where,"]
[null,null,"Ewheel = equivalent distribution width perpendicular to span, = WD"]
[null,null,"WD = Distributed load width/ per wheel load"]
[null,null,"Espan = equivalent distribution length parallel to span, = LD"]
[null,null,"LD = Distributed load length/ per wheel load"]
["Case B:","Depth of Fill, H ≥ 2 ft"]
[null,"Calculations will be based on AASHTO LRFD 3.6.1.2.5 & 6:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Where, WT = Tire contact width, LT = Tire contact length, WD = Distributed load width, LD = Distributed load length"]
[]
["The surface tire contact area for HL-93 loading (per AASHTO LRFD 3.6.1.2.5):"]
["WT = 20\" =",{"$f":"20/12","v":1.6666666666666667},"ft"]
["LT = 10\" =",{"$f":"10/12","v":0.83333333333333337},"ft"]
["The surface tire contact area for OFRD #1, OFRD #2, OFRD #3  (per AASHTO LRFD C3.6.1.2.5 Guideline):"]
["WT (in) =","P/0.8  "]
["LT (in) =","6.4g(1+IM/100) "]
["where,","p = wheel load (kips)",null,"OFRD #1","OFRD #2","OFRD #3"]
[null,"g = Load Factor for Routine Permit Loads gLL =",null,{"$f":"'LRFR Input'!D76","v":1.47},{"$f":"'LRFR Input'!D77","v":1.38},{"$f":"'LRFR Input'!D78","v":1.3}]
[null,"IM = dynamic load allowance percent"]
["So,",null,"HL-93 Tandem","OFRD #1","OFRD #2","OFRD #3"]
[null,"P \"heavy axle\" wheel load (kips) =",12.5,18.100000000000001,14.25,13]
[null,"WT (ft) =",{"$f":"B133","v":1.6666666666666667},{"$f":"(D142/0.8)/12","v":1.8854166666666667},{"$f":"(E142/0.8)/12","v":1.484375},1.3541666666666667]
[null,"LT (ft) =",{"$f":"B134","v":0.83333333333333337},{"$f":"6.4*$D$104/12*$D$139","v":0.95863600000000004},{"$f":"6.4*$D$104/12*$E$139","v":0.89994399999999997},{"$f":"6.4*$D$104/12*$F$139","v":0.84777333333333338}]
[]
["Distribution of wheel loads through earth fills (per AASHTO LRFD 3.6.1.2.6):"]
[]
["for HL-93 Design Truck:"]
[null,"WD = 1.67+φEH=",{"$f":"20/12+E66*D102","v":4.6566666666666663},"ft"]
[null,"LD = 0.83 + φEH =",{"$f":"10/12+E66*D102","v":3.8233333333333333},"ft"]
["for HL-93 Tandem, OFRD #1, OFRD #2, OFRD #3 Trucks:"]
[null,null,"HL-93 Tandem","OFRD #1","OFRD #2","OFRD #3"]
[null,"WD = WT + φEH =",{"$f":"C143+$E$66*$E$60","v":4.6566666666666663},4.8754166666666663,4.4743750000000002,4.3441666666666663]
[null,"LD = LT + φEH =",3.8233333333333333,3.9486359999999996,3.8899439999999998,3.8377733333333333]
[]
[null,null,"Fill depth, H =",{"$f":"D102","v":2.6},{"$f":"IF(D156<2, \"H<2', Case A applied\", IF(D156>=2, \"H>=2', Case B applied\", \"\"))","v":"H>=2', Case B applied"}]
[null,null,"Structure Total Length, L =",{"$f":"'LRFR Input'!D44","v":70.5},"ft "]
[null,null,"[ if WD (total) > L, use L = WD (total) in the calculations ]"]
[null,"HL-93 Truck","HL-93 Tandem","OFRD #1","OFRD #2","OFRD #3"]
["Heavy Axle Load (lbs)",32000,25000,36200,28500,26000]
["P (1+ IM) (lbs) =",{"$f":"B160/2*$D$104","v":19564},{"$f":"C160/2*$D$104","v":15284.375},{"$f":"D160/2*$D$104","v":22131.775000000001},{"$f":"E160/2*$D$104","v":17424.1875},{"$f":"F160/2*$D$104","v":15895.75}]
["* Saxle 1 (ft) =",0,4,4.5,5.4,5.4]
["* Saxle 2 (ft) =",0,0,0,0,5.4]
["wheel spacing on axle",6,6,6,6,6]
["WD (ft) =",{"$f":"IF($D$156<2, $D$110, C149)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, C153)","v":4.6566666666666663},{"$f":"IF($D$156<2, $D$110, D153)","v":4.8754166666666663},{"$f":"IF($D$156<2, $D$110, E153)","v":4.4743750000000002},{"$f":"IF($D$156<2, $D$110, F153)","v":4.3441666666666663}]
["LD (ft) =",{"$f":"C150","v":3.8233333333333333},{"$f":"C154","v":3.8233333333333333},{"$f":"D154","v":3.9486359999999996},{"$f":"E154","v":3.8899439999999998},{"$f":"F154","v":3.8377733333333333}]
["WD (total) = ",{"$f":"IF(B165>B164, MIN(B165+B164,$D$157), MIN(B165,$D$157) )","v":4.6566666666666663},{"$f":"IF(C165>C164, MIN(C165+C164, $D$157), MIN(C165,$D$157))","v":4.6566666666666663},{"$f":"IF(D165>D164, MIN(D165+D164, $D$157), MIN(D165,$D$157))","v":4.8754166666666663},{"$f":"IF(E165>E164, MIN(E165+E164, D157), MIN(E165,D157))","v":4.4743750000000002},{"$f":"IF(F165>F164, MIN(F165+F164, D157), MIN(F165,D157))","v":4.3441666666666663}]
["LD (total) =",{"$f":"IF(B166>B162, B166+B162, B166)","v":3.8233333333333333},{"$f":"IF(C166>C162, C166+C162, C166)","v":3.8233333333333333},{"$f":"IF(D166>D162, D166+D162, D166)","v":3.9486359999999996},{"$f":"IF(E166>E162, E166+E162, E166)","v":3.8899439999999998},{"$f":"IF(F166>F162, F166+F162+F163, F166)","v":3.8377733333333333}]
["* AD (ft2) =",{"$f":"B167*B168","v":17.803988888888888},{"$f":"C167*C168","v":17.803988888888888},{"$f":"D167*D168","v":19.251245764999997},{"$f":"E167*E168","v":17.405068185000001},{"$f":"F167*F168","v":16.671926988888888}]
["* PD (kips) =",{"$f":"IF(AND(B167>B165,B168>B166),4*B161/1000,IF(OR(B167>B165,B168>B166),2*B161/1000,B161/1000))","v":19.564},{"$f":"IF(AND(C167>C165,C168>C166),4*C161/1000,IF(OR(C167>C165,C168>C166),2*C161/1000,C161/1000))","v":15.284375000000001},{"$f":"IF(AND(D167>D165,D168>D166),4*D161/1000,IF(OR(D167>D165,D168>D166),2*D161/1000,D161/1000))","v":22.131775000000001},{"$f":"IF(AND(E167>E165,E168>E166),4*E161/1000,IF(OR(E167>E165,E168>E166),2*E161/1000,E161/1000))","v":17.424187499999999},{"$f":"IF(AND(F167>F165,F168>F166),6*F161/1000,IF(F168>F166,3*F161/1000,IF(F167>F165,2*F161/1000,F161/1000)))","v":15.89575}]
["ρ (L+IM) = PD/AD =",{"$f":"B170/B169","v":1.0988548758424299},{"$f":"C170/C169","v":0.8584803717518984},{"$f":"D170/D169","v":1.1496281991390391},{"$f":"E170/E169","v":1.0010984912438594},{"$f":"F170/F169","v":0.95344407461679881}]
["T(L+IM) (k/ft) =",{"$f":"MAX(B171*$D$32/2, B171*$D$33)","v":10.345718656056476},{"$f":"MAX(C171*$D$32/2, C171*$D$33)","v":8.0825927000441222},{"$f":"MAX(D171*$D$32/2, D171*$D$33)","v":10.823749494894052},{"$f":"MAX(E171*$D$32/2, E171*$D$33)","v":9.4253422950609362},{"$f":"MAX(F171*$D$32/2, F171*$D$33)","v":8.9766759625171595}]
["*   Saxle 1 = distance to the 1st adjacent heavy axle load, if the spacing is > 4', Saxle1 = 0.  "]
["     Saxle 2 = distance to the 2nd adjacent heavy axle load, if the spacing is > 4', Saxle2 = 0.  "]
["     AD = Total Load Distributed Area "]
["     PD = Total Load being Distributed"]
["Transverse pressure overlaps are considered.  Longitudinal pressure overlaps are considered for two adjacent heavy axle loads when the Saxle is ≤ 4 feet."]
[]
[]
["D.   Load Rating Factors for Ring Compression Structures:"]
["      1.  Operating Load Rating Factor (RFO):"]
["               a. RFO based on wall strength"]
[]
[]
["               b. RFO based on minimum cover requirements"]
[]
[]
[null,"         Where, ",null,{"$f":"IF((2.36*E60/D32+0.528)>1, 1, 2.36*E60/D32+0.528)","v":0.85386298459904419}]
[null,"So,   RFO-C =",{"$f":"E60^2/(D188*(E59)^2)","v":1.429018472478925}]
[]
["Operating Load Rating Factors, RFO"]
[null,"HL-93 Truck","HL-93 Tandem","OFRD #1","OFRD #2","OFRD #3"]
["Tcap",{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572},{"$f":"$C$86","v":22.838558776486572}]
["TE ",{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999},{"$f":"$C$92","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B172","v":10.345718656056476},{"$f":"C172","v":8.0825927000441222},10.823749494894052,9.4253422950609362,8.9766759625171595]
["gLL ",{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D73","v":1.35},{"$f":"'LRFR Input'!D76","v":1.47},{"$f":"'LRFR Input'!D77","v":1.38},{"$f":"'LRFR Input'!D78","v":1.3}]
["RFO-W",{"$f":"(B193-B195*B194)/(B196*B197)","v":1.2250888217861231},{"$f":"(C193-C195*C194)/(C196*C197)","v":1.5681136918862377},1.075392349431346,1.3154846718714803,{"$f":"(F193-F195*F194)/(F196*F197)","v":1.4662334020652517}]
["RFO-C",{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925},{"$f":"$C$189","v":1.429018472478925}]
["RFO",{"$f":"MIN(B198,$B$199)","v":1.2250888217861231},{"$f":"MIN(C198,$B$199)","v":1.429018472478925},1.075392349431346,1.3154846718714803,1.429018472478925]
[]
[]
["      2.  Inventory Load Rating Factor (RFi):"]
["               a. RFi based on wall strength"]
[]
[]
["               b. RFi based on minimum cover requirements"]
[]
[]
["Inventory Load Rating Factor, RFi"]
[null,"HL-93 Truck","HL-93 Tandem"]
["Tcap",{"$f":"B193","v":22.838558776486572},{"$f":"C193","v":22.838558776486572}]
["TE ",{"$f":"B194","v":2.9374799999999999},{"$f":"C194","v":2.9374799999999999}]
["gEV ",{"$f":"'LRFR Input'!D71","v":1.95},{"$f":"'LRFR Input'!D71","v":1.95}]
["T(L+IM)",{"$f":"B196","v":10.345718656056476},{"$f":"C196","v":8.0825927000441222},null,null,null,null,null,null,null,null,72,0.21,{"$f":"M215*L215","v":15.12}]
["gLL ",{"$f":"'LRFR Input'!D72","v":1.75},{"$f":"'LRFR Input'!D72","v":1.75},null,null,null,null,null,null,null,null,50,0.27,{"$f":"M216*L216","v":13.5}]
["RFi-w",{"$f":"(B212-B213*B214)/(B215*B216)","v":0.94506851966358085},{"$f":"(C212-C213*C214)/(C215*C216)","v":1.2096877051693835},null,null,null,null,null,null,null,null,72,0.27,19.440000000000001]
["RFi-c",{"$f":"E60^2/E59^2","v":1.220185977958022},{"$f":"E60^2/E59^2","v":1.220185977958022},null,null,null,null,null,null,null,null,50,0.35,17.5]
["RFi",{"$f":"MIN(B217,$B$218)","v":0.94506851966358085},{"$f":"MIN(C217,$B$218)","v":1.2096877051693835},null,null,null,null,null,null,null,null,73,0.36,26.279999999999998]
[null,null,null,null,null,null,null,null,null,null,null,41,0.36,14.76]
[null,null,null,null,null,null,null,null,null,null,null,80,0.4,32]
["Load Rating Summary:",null,null,null,null,null,null,null,null,null,null,80,0.32,25.6]
[null,"Load","GVW","Rating Factor","Safe Load",null,null,null,null,null,null,88,0.32,28.16]
["Inventory",{"$f":"B211","v":"HL-93 Truck"},36,{"$f":"B219","v":0.94506851966358085},{"$f":"C224*D224","v":34.02246670788891},null,null,null,null,null,null,80,0.38,30.4]
[null,{"$f":"C211","v":"HL-93 Tandem"},25,{"$f":"C219","v":1.2096877051693835},30.242192629234587,null,null,null,null,null,null,54,0.38,20.52]
["Operating",{"$f":"B192","v":"HL-93 Truck"},36,{"$f":"B200","v":1.2250888217861231},44.103197584300432,null,null,null,null,null,null,62,0.38,23.56]
[null,{"$f":"C192","v":"HL-93 Tandem"},25,{"$f":"C200","v":1.429018472478925},35.725461811973126,null,null,null,null,null,null,69.5,0.38,26.41]
[null,{"$f":"D192","v":"OFRD #1"},66.349999999999994,{"$f":"D200","v":1.075392349431346},{"$f":"C228*D228","v":71.352282384769794},null,null,null,null,null,null,77.5,0.38,29.45]
[null,{"$f":"E192","v":"OFRD #2"},71.25,{"$f":"E200","v":1.3154846718714803},93.728282870842975,null,null,null,null,null,null,132.6,0.24,31.823999999999998]
[null,{"$f":"F192","v":"OFRD #3"},104.5,{"$f":"F200","v":1.429018472478925},149.33243037404768,null,null,null,null,null,null,142.5,0.28999999999999998,41.324999999999996]
[null,null,null,null,null,null,null,null,null,null,null,209,0.33,68.97]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null," "]

{"sheet":"Reference tables","index":7,"n_rows":65,"n_cols":6,"rows_kept":65,"cut":false,"hidden":false,"merged":[[1,1,5,1],[7,1,8,1],[50,1,64,1],[31,1,35,1],[10,1,12,1]]}
[null,null,null,"Minimum Cover (ft.)","←AASHTO DEFINED MINIMUM COVER (AASHTO LRFD table 12.6.6.3-1 & table 12.8.3.1.1-1 for long-span)"]
[null,"Structure Type:","Corrugated Metal Pipe"]
[null,null,"Spiral Rib Steel Pipe",{"$f":"MAX('Output HL93, LA3S2, LA3, 3-3'!D32/4,1)","v":4.7074999999999996}]
[null,null,"Spiral Rib Aluminum Pipe",{"$f":"IF('Output HL93, LA3S2, LA3, 3-3'!D32*12<=48,MAX('Output HL93, LA3S2, LA3, 3-3'!D32/2,1),MAX('Output HL93, LA3S2, LA3, 3-3'!D32/2.75,1))","v":6.8472727272727267}]
[null,null,"Structural Plate Pipe",{"$f":"MAX('Output HL93, LA3S2, LA3, 3-3'!D32/8,1)","v":2.3537499999999998}]
[null,null,"Long Span Structural Plate",{"$f":"IF('LRFR Input'!D38=\"Long Span Structural Plate\",VLOOKUP('Output HL93, LA3S2, LA3, 3-3'!B48,B22:C28,2),\"\")","v":""}]
[]
[null,"Seam Type:","Annular pipe w/ spot welded, riveted or bolted seam"]
[null,null,"Helical pipe w/ lock seam or fully welded seam"]
[]
[null,"Structure Category:","Typical (NCSPA design data sheet No. 19, II. A. 1.)"]
[null,null,"Unsymmetrical  or deflect over 5% (NCSPA design data sheet No. 19, II. A. 2.)"]
[null,null,"Long span (NCSPA design data sheet No. 19, II. A. 3.)"]
[]
[null,"Long Span Structural Plate Structures Minimum Top Arc Thickness Chart (in) (AASHTO LRFD Table 12.8.3.1.1-1)"]
[null,null,"6 x 2 corrugated steel plates"]
[null,"Min. =",{"$f":"IF(C21=\">= 15'\",0.109,IF(C21=\"15'-17'\",0.138,IF(C21=\"17'-20'\",0.168,IF(C21=\"20'-23'\",0.218,IF(C21=\"23'-25'\",0.249,\"\")))))","v":0.109},"in"]
[]
[null,"Long Span Structural Plate Structures Minimum Cover Chart (ft.) (AASHTO LRFD Table 12.8.3.1.1-1)"]
[null,"Rt = ",{"$f":"'Output HL93, LA3S2, LA3, 3-3'!D33","v":9.4149999999999991},"ft"]
[null,"Steel Thickness",{"$f":"IF(C20<=15,\">= 15'\", IF(C20<17,\"15'-17'\",IF(C20<20,\"17'-20'\",IF(C20<23,\"20'-23'\",\"23'-25'\"))))","v":">= 15'"},"← Rt range"]
[null,0.109,{"$f":"IF(C21=\">= 15'\",2.5,\"\")","v":2.5}]
[null,0.13800000000000001,{"$f":"IF(C21=\">= 15'\",2.5,IF(C21=\"15'-17'\",3, \"\"))","v":2.5}]
[null,0.16800000000000001,{"$f":"IF(C21=\">= 15'\",2.5,IF(C21=\"15'-17'\",3,IF(C21=\"17'-20'\",3,\"\")))","v":2.5}]
[null,0.188,{"$f":"IF(C21=\">= 15'\",2.5,IF(C21=\"15'-17'\",3,IF(C21=\"17'-20'\",3,\"\")))","v":2.5}]
[null,0.218,{"$f":"IF(C21=\">= 15'\",2,IF(C21=\"15'-17'\",2.5,IF(C21=\"17'-20'\",2.5,IF(C21=\"20'-23'\",3,\"\"))))","v":2}]
[null,0.249,{"$f":"IF(C21=\">= 15'\",2,IF(C21=\"15'-17'\",2,IF(C21=\"17'-20'\",2.5,IF(C21=\"20'-23'\",3,4))))","v":2}]
[null,0.28000000000000003,{"$f":"IF(C21=\">= 15'\",2,IF(C21=\"15'-17'\",2,IF(C21=\"17'-20'\",2.5,IF(C21=\"20'-23'\",3,4))))","v":2}]
[]
[]
[null,null,"From AASHTO LRFD SECTION 12, APPENDIX A12","Fu (ksi)","Fy (ksi)","E (ksi)"]
[null,"Metal Type:","Steel",45,33,29000]
[null,null,"Aluminum-structural plate (thickness 0.100\" - 0.175\")",35,24,10000]
[null,null,"Aluminum-structural plate (thickness 0.176\" - 0.250\")",34,24,10000]
[null,null,"Aluminum-corrugated metal (Grade 3004-H34)",31,24,10000]
[null,null,"Aluminum-corrugated metal (Grade 3004-H32)",27,20,10000]
[]
[null,"Gage Number","Metal Thickness (in)"]
[null,16,6.4000000000000001E-2]
[null,14,7.9000000000000001E-2]
[null,12,0.109]
[null,10,0.13800000000000001]
[null,8,0.16800000000000001]
[null,7,0.188]
[null,5,0.218,null," "]
[null,3,0.249]
[null,1,0.28000000000000003]
[null,"N/A",{"$f":"'LRFR Input'!E51","v":0},"←from field measurement"]
[]
[]
[null,"corrugation","1½ x ¼ (corrugated steel pipe)"]
[null,null,"2⅔ x ½ (corrugated steel pipe)"]
[null,null,"3 x 1 (corrugated steel pipe)"]
[null,null,"5 x 1 (corrugated steel pipe)"]
[null,null,"¾ x ¾ x 7½ (spiral rib steel pipe)"]
[null,null,"¾ x 1 x 11½ (spiral rib steel pipe)"]
[null,null,"6 x 2 (steel structural plate pipe)"]
[null,null,"1½ x ¼ (corrugated aluminum pipe)"]
[null,null,"2⅔ x ½ (corrugated aluminum pipe)"]
[null,null,"3 x 1 (corrugated aluminum pipe)"]
[null,null,"6 x 1 (corrugated aluminum pipe)"]
[null,null,"¾ x ¾ x 7½ (aluminum spiral rib pipe)"]
[null,null,"¾ x 1 x 11½ (aluminum spiral rib pipe)"]
[null,null,"9 x 2½ (aluminum structural plate pipe)"]
[null,null,"N/A"]

{"sheet":"section property tables","index":8,"n_rows":35,"n_cols":24,"rows_kept":35,"cut":false,"hidden":false,"merged":[[1,0,1,1],[0,0,0,2],[20,2,20,4],[20,5,20,7],[20,8,20,10],[1,2,1,4],[1,5,1,7],[1,8,1,10],[1,12,1,14],[20,11,20,14],[1,15,1,17],[1,18,1,20],[1,21,1,23],[20,15,20,17],[20,18,20,20],[20,21,20,23]]}
["Cross-Section Properties",null,null,null,null,null,null,"From AASHTO LRFD SECTION 12, APPENDIX A12"]
["Steel",null,"1½ x ¼ (corrugated steel pipe)",null,null,"2⅔ x ½ (corrugated steel pipe)",null,null,"3 x 1 (corrugated steel pipe)",null,null,null,"5 x 1 (corrugated steel pipe)",null,null,"¾ x ¾ x 7½ (spiral rib steel pipe)",null,null,"¾ x 1 x 11½ (spiral rib steel pipe)",null,null,"6 x 2 (steel structural plate pipe)"]
["Gage #","Thickness (in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)",null,"As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)"]
[null,2.8000000000000001E-2,0.30399999999999999]
[null,3.4000000000000002E-2,0.38]
[null,0.04,0.45600000000000002,8.1600000000000006E-2,{"$f":"0.253","v":0.253},0.46500000000000002,0.17019999999999999,1.121]
[null,5.1999999999999998E-2,0.60799999999999998,8.2400000000000001E-2,0.34399999999999997,0.61899999999999999,0.17069999999999999,1.5]
[16,6.4000000000000001E-2,0.76100000000000001,8.3199999999999996E-2,0.439,0.77500000000000002,0.17119999999999999,1.8919999999999999,0.89,0.3417,8.6590000000000007,null,0.79400000000000004,0.36570000000000003,8.85,0.50900000000000001,0.25800000000000001,2.8210000000000002,0.374,0.38300000000000001,4.58]
[14,7.9000000000000001E-2,0.95,8.4599999999999995E-2,0.56699999999999995,0.96799999999999997,0.1721,2.3919999999999999,1.113,0.3427,10.882999999999999,null,0.99199999999999999,0.36630000000000001,11.092000000000001,0.71199999999999997,0.25,3.7010000000000001,0.52400000000000002,0.373,6.08]
[12,0.109,1.331,8.7900000000000006E-2,0.85699999999999998,1.3560000000000001,0.1741,3.4249999999999998,1.56,0.3448,15.459,null,1.39,0.36770000000000003,15.65,1.1839999999999999,0.23699999999999999,5.5369999999999999,0.88300000000000001,0.35499999999999998,9.26,1.556,0.68200000000000005,60.411000000000001]
[10,0.13800000000000001,1.712,9.1899999999999996E-2,1.2050000000000001,1.744,0.17660000000000001,4.5330000000000004,2.008,0.34720000000000001,20.183,null,1.788,0.36930000000000002,20.317,1.7170000000000001,0.22800000000000001,7.4329999999999998,null,null,null,2.0030000000000001,0.68400000000000005,78.174999999999997]
[8,0.16800000000000001,2.0979999999999999,9.6699999999999994E-2,1.635,2.133,0.17949999999999999,5.7249999999999996,2.4580000000000002,0.34989999999999999,25.091000000000001,null,2.1859999999999999,0.37109999999999999,25.091999999999999,null,null,null,null,null,null,2.4489999999999998,0.68600000000000005,96.162999999999997]
[7,0.188,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7389999999999999,0.68799999999999994,108]
[5,0.218,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.1989999999999998,0.69,126.922]
[3,0.249,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.65,0.69199999999999995,146.172]
[1,0.28000000000000003,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.1189999999999998,0.69499999999999995,165.83600000000001]
[null,0.318,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,4.6710000000000003,0.69799999999999995,190]
[null,0.38,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,5.6130000000000004,0.70399999999999996,232]
[]
[]
[null,"Aluminum","1½ x ¼ (corrugated aluminum pipe)",null,null,"2⅔ x ½ (corrugated aluminum pipe)",null,null,"3 x 1 (corrugated aluminum pipe)",null,null,"6 x 1 (corrugated aluminum pipe)",null,null,null,"¾ x ¾ x 7½ (aluminum spiral rib pipe)",null,null,"¾ x 1 x 11½ (aluminum spiral rib pipe)",null,null,"9 x 2½ (aluminum structural plate pipe)"]
[null,"Thickness (in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","Effective As","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)","As (in2/ft)","r (in)","I x 10-3(in4/in)"]
[null,4.8000000000000001E-2,0.60799999999999998,8.2400000000000001E-2,0.34399999999999997]
[null,0.06,0.76100000000000001,8.3199999999999996E-2,0.34899999999999998,0.77500000000000002,0.17119999999999999,1.8919999999999999,0.89,0.3417,8.6590000000000007,0.77500000000000002,0.38700000000000001,0.3629,8.5050000000000008,0.41499999999999998,0.27200000000000002,2.5579999999999998,0.312,0.39600000000000002,4.08]
[null,7.4999999999999997E-2,null,null,null,0.96799999999999997,0.1721,2.3919999999999999,1.1180000000000001,0.3427,10.882999999999999,0.96799999999999997,0.48399999999999999,0.36299999999999999,10.631,0.56899999999999995,0.26700000000000002,3.3719999999999999,0.42699999999999999,0.39100000000000001,5.45]
[null,0.105,null,null,null,1.3560000000000001,0.1741,3.4249999999999998,1.56,0.3448,15.459,1.3560000000000001,0.67800000000000005,0.36359999999999998,14.34,0.91400000000000003,0.25800000000000001,5.0730000000000004,0.69699999999999995,0.38,8.39]
[null,0.13500000000000001,null,null,null,1.7450000000000001,0.17660000000000001,4.5330000000000004,2.0880000000000001,0.34720000000000001,20.183,1.744,0.872,0.36459999999999998,19.318999999999999,1.29,0.252,6.8259999999999996,1.0089999999999999,0.36899999999999999,11.48]
[null,0.16400000000000001,null,null,null,2.13,0.17949999999999999,5.7249999999999996,2.4580000000000002,0.34989999999999999,25.091000000000001,2.133,1.0660000000000001,0.36559999999999998,23.76]
[null,0.1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.4039999999999999,0.84379999999999999,83.064999999999998]
[null,0.125,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,1.75,0.84440000000000004,103.991]
[null,0.15,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.1,0.84489999999999998,124.883]
[null,0.17499999999999999,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.4489999999999998,0.84540000000000004,145.89500000000001]
[null,0.2,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2.7989999999999999,0.84599999999999997,166.959]
[null,0.22500000000000001,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.149,0.8468,188.179]
[null,0.25,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3.5009999999999999,0.84730000000000005,209.434]

{"sheet":"seam strength tables","index":9,"n_rows":30,"n_cols":12,"rows_kept":30,"cut":false,"hidden":false,"merged":[[23,9,29,9],[16,1,17,1],[16,2,17,2],[16,3,17,3],[16,4,17,4],[16,5,17,5],[16,6,17,6],[16,7,17,7],[16,8,17,8],[18,7,22,7],[16,9,17,9],[15,5,15,6],[18,2,19,2],[18,5,19,5],[20,2,22,2],[20,5,22,5],[0,0,0,4],[15,14,15,16],[15,17,15,19],[1,7,1,10],[1,0,1,1],[1,2,1,4],[1,5,1,6],[5,7,11,7],[12,7,13,7],[5,2,7,2],[3,2,4,2],[3,5,4,5],[5,5,7,5],[15,9,15,11],[15,7,15,8],[15,2,15,4]]}
["Minimum Longitudinal Seam Strength",null,null,null,null,"From AASHTO LRFD SECTION 12, APPENDIX A12"]
["Steel",null,"2 x ½ & 2⅔ x ½  (corrugated steel pipe) - Riveted or Spot Welded",null,null,"3 x 1 (corrugated steel pipe) - Riveted or Spot Welded",null,"6 x 2 (steel structural plate pipe)"]
["Gage #","Thickness (in)","Rivet Size                   (in)","Single Rivets (k/ft)","Double Rivets (k/ft)","Rivet Size                   (in)","Double Rivets (k/ft)","Diameter      (in)","4 Bolts/ft (k/ft)","6 Bolts/ft (k/ft)","8 Bolts/ft (k/ft)"]
[16,6.4000000000000001E-2,0.3125,16.7,21.6,"⅜",28.7]
[14,7.9000000000000001E-2,null,18.2,29.8,null,35.700000000000003]
[12,0.109,"⅜",23.4,46.8,0.4375,53,"¾",43]
[10,0.13800000000000001,null,24.5,49,null,63.7,null,62]
[8,0.16800000000000001,null,25.6,51.3,null,70.7,null,81]
[7,0.188,null,null,null,null,null,null,93]
[5,0.218,null,null,null,null,null,null,112]
[3,0.249,null,null,null,null,null,null,132]
[1,0.28000000000000003,null,null,null,null,null,null,144,180,194]
[null,0.318,null,null,null,null,null,"⅞",null,null,235]
[null,0.38,null,null,null,null,null,null,null,null,285]
[]
[null,"Aluminum","2 x ½ & 2⅔ x ½  (corrugated aluminum pipe) - Riveted",null,null,"3 x 1 (corrugated aluminum pipe) - Riveted",null,"6 x 1 (corrugated aluminum pipe) - Riveted",null,"9 x 2½ (aluminum structural plate pipe)"]
[null,"Thickness (in)","Rivet Size                   (in)","Single Rivets (k/ft)","Double Rivets             (k/ft)","Rivet Size                   (in)","Double Rivets (k/ft)","Rivet Size                   (in)","Double Rivets                (k/ft)","Diameter                    (in)","steel bolts","aluminum bolts"]
[null,null,null,null,null,null,null,null,null,null,"5⅓ Bolts/ft (k/ft)","5⅓ Bolts/ft               (k/ft)"]
[null,0.06,0.3125,9,14,"⅜",16.5,0.5,16]
[null,7.4999999999999997E-2,null,9,18,null,20.5,null,19.899999999999999]
[null,0.105,"⅜",15.6,31.5,0.5,28,null,27.9]
[null,0.13500000000000001,null,16.2,33,null,42,null,35.9]
[null,0.16400000000000001,null,16.8,34,null,54.5,null,43.5]
[null,0.1,null,null,null,null,null,null,null,"¾",28,26.4]
[null,0.125,null,null,null,null,null,null,null,null,41,34.799999999999997]
[null,0.15,null,null,null,null,null,null,null,null,54.1,44.4]
[null,0.17499999999999999,null,null,null,null,null,null,null,null,63.7,52.8]
[null,0.2,null,null,null,null,null,null,null,null,73.400000000000006,52.8]
[null,0.22500000000000001,null,null,null,null,null,null,null,null,83.2,52.8]
[null,0.25,null,null,null,null,null,null,null,null,93.1,52.8]

{"sheet":"NCSPA Design Data Sheet No 19","index":10,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}