insulators 101 panel final a

84
IEEE T&D – Insulators 101 Insulators 101” Insulators 101” Section A – Introduction Section A – Introduction Presented by Andy Schwalm Presented by Andy Schwalm IEEE Chairman, Lightning and Insulator IEEE Chairman, Lightning and Insulator Subcommittee Subcommittee IEEE/PES 2010 Transmission and Distribution IEEE/PES 2010 Transmission and Distribution Conference and Exposition Conference and Exposition New Orleans, Louisiana New Orleans, Louisiana April 20, 2010 April 20, 2010

Upload: redscorp123

Post on 02-Oct-2015

219 views

Category:

Documents


0 download

DESCRIPTION

Insulators 101 Panel Final A

TRANSCRIPT

  • Insulators 101Section A Introduction

    Presented by Andy SchwalmIEEE Chairman, Lightning and Insulator Subcommittee

    IEEE/PES 2010 Transmission and Distribution Conference and Exposition New Orleans, Louisiana April 20, 2010

  • What Is an Insulator?An insulator is a dam*** poor conductor!

    And more, technically speaking!

    An insulator is a mechanical support!Primary function - support the line mechanicallySecondary function electricalAir is the insulatorOuter shells/surfaces are designed to increase leakage distance and strike distance

  • What Does an Insulator Do?Maintains an Air GapSeparates Line from Groundlength of air gap depends primarily on system voltage, modified by desired safety margin, contamination, etc.Resists Mechanical Stresseseveryday loads, extreme loadsResists Electrical Stressessystem voltage/fields, overvoltagesResists Environmental Stressesheat, cold, UV, contamination, etc.

  • Basically grew out of the needs of the telegraph industry starting in the late 1700s, early 1800s

    Early history centers around what today we would consider very low DC voltages

    Gradually technical needs increased as AC voltages grew with the development of the electric power industryWhere Did Insulators Come From?

  • HistoryGlass plates used to insulate telegraph line DC to Baltimore

    Glass insulators became the norm soon thereafter typical collectors items today

    Many, many trials with different materials wood cement porcelain - beeswax soaked rag wrapped around the wire, etc.

    Ultimately porcelain and glass prevailed

  • History Wet process porcelain developed for high voltage applications Porcelain insulator industry started

    Application voltages increased Insulator designs became larger, more complexCeramics (porcelain, glass) still only choices at high voltages

  • History US trials of first NCIs cycloaliphatic based Not successful, but others soon became interested and a new industry started up

    Europeans develop modern style NCI fiberglass rod with various polymeric sheds Now considered First generation

  • History NCI insulator industry really begins in US with field trials of insulators Since that time - new manufacturers, new designs, new materialsNCIs at generation X there have been so many improvements in materials, end fitting designs, etc.Change in materials have meant changes in line design practices, maintenance practices, etc.Ceramic manufacturers have not been idle either with development of higher strength porcelains, RG glazes, etc.

  • History Domestic manufacturing of insulators decreases, shift to offshore (all types)

    Engineers need to develop knowledge and skills necessary to evaluate and compare suppliers and products from many different countries

    An understanding of the basics of insulator manufacturing, design and application is more essential than ever before

  • Insulator Types For simplicity will discuss in terms of three broad applications:

    Distribution lines (thru 69 kV)

    Transmission lines (69 kV and up)

    Substations (all voltages)

  • Insulator Types Distribution lines

    Pin type insulators -mainly porcelain, growing use of polymeric (HDPE high density polyethylene), limited use of glass (in US at least)Line post insulators porcelain, polymericDead end insulators polymeric, porcelain, glassSpool insulators porcelain, polymericStrain insulators, polymeric, porcelain

  • Types of Insulators Distribution

  • Insulator Types Transmission lines

    Suspension insulators - new installations mainly NCIs, porcelain and glass now used less frequently

    Line post insulators mainly NCIs for new lines and installations, porcelain much less frequent now

  • Types of Insulators Transmission

  • Insulator Types Substations

    Post insulators porcelain primarily, NCIs growing in use at lower voltages (~161 kV and below)

    Suspension insulators NCIs (primarily), ceramic

    Cap and Pin insulators legacy type

  • Types of Insulators Substation

  • Insulator Types - ComparisonsCeramic Porcelain or toughened glass Metal components fixed with cementANSI Standards C29.1 through C29.10Non Ceramic Typically fiberglass rod with rubber (EPDM or Silicone) sheath and weather shedsHDPE line insulator applicationsCycloaliphatic (epoxies) station applications, some line applicationsMetal components normally crimpedANSI Standards C29.11 C29.19

  • Insulator Types - ComparisonsCeramic Materials very resistant to UV, contaminant degradation, electric field degradation Materials strong in compression, weaker in tensionHigh modulus of elasticity - stiffBrittle, require more careful handlingHeavier than NCIsNon Ceramic Hydrophobic materials improve contamination performanceStrong in tension, weaker in compressionDeflection under load can be an issueLighter easier to handleElectric field stresses must be considered

  • Insulator Types - ComparisonsCeramic Generally designs are matureLimited flexibility of dimensionsProcess limitations on sizes and shapesApplications/handling methods generally well understood Non Ceramic Material properties have been improved UV resistance much improved for exampleStandardized product lines now existBalancing act - leakage distance/field stress take advantage of hydrophobicityApplication parameters still being developedLine design implications (lighter weight, improved shock resistance)

  • Insulators 101Section B - Design Criteria

    Presented by Al BernstorfIEEE Chairman, Insulator Working Group

    IEEE/PES 2010 Transmission and Distribution Conference and Exposition New Orleans, Louisiana April 20, 2010

  • Design Criteria - MechanicalAn insulator is a mechanical support!

    Its primary function is to support the line mechanically

    Electrical Characteristics are an afterthought.

    Will the insulator support your line?

    Determine The Maximum Load the Insulator Will Ever See Including NESC Overload Factors.

  • Design Criteria - MechanicalSuspension Insulators

    PorcelainM&E (Mechanical & Electrical) RatingRepresents a mechanical test of the unit while energized.When the porcelain begins to crack, it electrically punctures.Average ultimate strength will exceed the M&E Rating when new.Never Exceed 50% of the M&E Rating

    NCIs (Polymer Insulators)S.M.L. Specified Mechanical Load Guaranteed minimum ultimate strength when new.R.T.L. Routine Test Load Proof test applied to each NCI.Never Load beyond the R.T.L.

  • Design Criteria - MechanicalLine Post insulators

    PorcelainCantilever Rating Represents the Average Ultimate Strength in Cantilever when new.Minimum Ultimate Cantilever of a single unit may be as low as 85%.Never Exceed 40% of the Cantilever Rating Proof Test Load

    NCIs (Polymer Insulators)S.C.L. (Specified Cantilever Load)Not based upon lot testingBased upon manufacturer testingR.C.L. (Rated Cantilever Load) or MDC or MDCL (Maximum Design Cantilever Load) or MCWL or WCL (Working Cantilever Load)Never Exceed RCL or MDC or MDCL or MCWL or WCLS.T.L. (Specified Tensile Load) Tensile Proof Test=(STL/2)

  • Design Criteria - MechanicalOther Considerations

    Suspensions and Deadends Only apply tension loads

    Line Posts Cantilever is only one loadTransverse (tension or compression) on line post loading transverse to the direction of the line.Longitudinal in the direction of travel of the lineCombined Loading Curve Contour curves representing various Longitudinal loadsAvailable Vertical load as a function of Transverse loadingManufacturers have different safety factors!!!

  • Design Criteria - Mechanical

    Data Input

    Parameter InputValue

    Nominal Rod Diameter of Post, Inches2.5

    Nominal Section Length of Post43

    Post Upsweep Angle/Angle to Horizontal12

    Post's MWL (RCL)2245

    Post's Top Cap Tension Rating (Working Load)2500

    Post's Top Cap Compression Rating (Working Load)2500

    Nominal Bottom Cap Section Length8See Values Below

    Catalog Number of Assembly69 kV Post - 2.5" Rod

    Post Cap Attachment Point Working Load2500Usually the Same as the Tension and Compression Ratings Above.

    Young's Modulus6000000

    Target Stress56000

    TYPICAL END FITTING LENGTHS

    SERIES 150 LINE POST3.5

    SERIES 175 LINE POST3.5

    SERIES 250 LINE POST8

    SERIES 300 LINE POST8.8

    SERIES 350 LINE POST10

    VERTICAL LOAD, LBF

    TRANSVERSE LOAD, LBF

    &L&F&C&A&R&D

    &LERM 99-5&CPage &P&Rrab

    Chart1

    00000

    00000

    497.49371855330000

    700489.8979485566000

    852.9361054616691.0137480543000

    979.7958971133842.6149773176000

    1089.7247358852968.2458365519433.012701892200

    1187.43420870381077.0329614269640.312423743300

    1275.73508221731173.6694594306792.148975887700

    1356.4659966251260.9520212918916.515138991200

    1430.90880212541340.70876777921023.474474522900

    15001414.21356237311118.033988749900

    1564.44878471621482.39670803741203.1209415516444.40972086580

    1624.80768092721545.9624833741280.6248474866624.49979983980

    1681.517172081605.45943580021351.8505834596759.93420767850

    1734.93515728981661.32477258361417.7446878758871.77978870810

    1785.35710713571713.91365010031479.0199457749968.24583655190

    1833.03027798231763.51920885481536.22914957371053.56537528530

    1878.16399709931810.38669902321589.81130955851130.26545554570

    1920.93727122981854.72369909911640.121946685712000

    1961.50452459331896.70767383911687.45370306861263.92246597640

    20001936.49167310371732.05080756891322.87565553230

    2036.54118544161974.208702241774.1194999211377.4977313956384.0572873934

    2071.23151772082009.97512422421813.83571472171428.2856857086538.5164807134

    2104.16254125012043.8933435971851.35085815741475.6354563374653.8348415311

    2135.41565040632076.05394920271886.79622641131519.8684153571748.3314773548

    2165.06350946112106.53744329411920.28643696721561.2494995996829.1561975888

    2193.17121994612135.41565040631951.92212959431600900

    2219.79728804232162.75287538821981.79211826061636.3068171954963.0680142129

    2244.99443206442188.60686282392009.97512422421670.3293088491019.8039027186

    22452213.02959763312036.54118544161702.20445305491071.2142642814

    22452236.06797749982061.55281280881732.05080756891118.0339887499

    224522452085.06594619931759.97159067981128.9151526446

    224522452107.13075057061786.05710994921118.287333806

    224522452127.79228309531810.38669902321107.6595149674

    224522452147.09105535841809.66991217751097.0316961289

    224522452158.12806373071799.04209333891086.4038772903

    224522452147.50024489211788.41427450041075.7760584517

    224522452136.87242605351777.78645566181065.1482396132

    224522452126.2446072151767.15863682321054.5204207746

    224522452115.61678837641756.53081798471043.892601936

    224522452104.98896953781745.90299914611033.2647830974

    224522452094.36115069931735.27518030751022.6369642589

    224522452083.73333186071724.6473614691012.0091454203

    224522452073.10551302211714.01954263041001.3813265817

    224522452062.47769418361703.3917237918990.7535077432

    22452239.16973136922051.8498753451692.7639049532980.1256889046

    22452228.54191253062041.22205650641682.1360861147969.497870066

    22452217.9140936922030.59423766781671.5082672761958.8700512275

    22452207.28627485342019.96641882931660.8804484376948.2422323889

    22452196.65845601492009.33859999071650.252629599937.6144135503

    22452186.03063717631998.71078115221639.6248107604926.9865947118

    2234.36420356532175.40281833771988.08296231361628.9969919218916.3587758732

    2223.7127552872164.77499949921977.4551434751618.3691730833905.7309570346

    2213.04610766122154.14718066061966.82732463641607.7413542447895.103138196

    2202.3647097642143.5193618221956.19950579791597.1135354061884.4753193575

    2191.66900718812132.89154298351945.57168695931586.4857165676873.8475005189

    2180.95944198252122.26372414491934.94386812071575.857897729863.2196816803

    2170.23645259192111.63590530631924.31604928221565.2300788904852.5918628418

    2159.50047379822101.00808646781913.68823044361554.6022600519841.9640440032

    2148.7519366632090.38026762921903.0604116051543.9744412133831.3362251646

    2137.99126847172079.75244879061892.43259276651533.3466223747820.7084063261

    2127.21889267852069.1246299521881.80477392791522.7188035362810.0805874875

    2116.43522885332058.49681111351871.17695508931512.0909846976799.4527686489

    2105.64069262952047.86899227491860.54913625081501.463165859788.8249498104

    2094.83569565332037.24117343631849.92131741221490.8353470204778.1971309718

    2084.02064553492026.61335459781839.29349857361480.2075281819767.5693121332

    2073.19594579992015.98553575921828.6656797351469.5797093433756.9414932947

    2062.36199584352005.35771692061818.03786089651458.9518905047746.3136744561

    2051.51919088481994.72989808211807.41004205791448.3240716662735.6858556175

    2040.66792192361984.10207924351796.78222321931437.6962528276725.0580367789

    2029.80857569811973.47426040491786.15440438081427.068433989714.4302179404

    2018.94153464361962.84644156641775.52658554221416.4406151505703.8023991018

    2008.06717685371952.21862272781764.89876670361405.8127963119693.1745802632

    1997.18587604171941.59080388921754.27094786511395.1849774733682.5467614247

    1986.29800150421930.96298505061743.64312902651384.5571586348671.9189425861

    1975.40391808621920.33516621211733.01531018791373.9293397962661.2911237475

    1964.50398614671909.70734737351722.38749134941363.3015209576650.663304909

    1953.59856152691899.0795285351711.75967251081352.673702119640.0354860704

    1942.68799551891888.45170969641701.13185367221342.0458832805538.5164807134

    1931.77263483611877.82389085781690.50403483361331.4180644419384.0572873934

    1920.85282158531867.19607201921679.87621599511320.79024560330

    1909.92889323961856.56825318071669.24839715651263.92246597640

    1899.00118261321845.94043434211640.121946685712000

    1878.16399709931810.38669902321589.81130955851130.26545554570

    1833.03027798231763.51920885481536.22914957371053.56537528530

    1785.35710713571713.91365010031479.0199457749968.24583655190

    1734.93515728981661.32477258361417.7446878758871.77978870810

    1681.517172081605.45943580021351.8505834596759.93420767850

    1624.80768092721545.9624833741280.6248474866624.49979983980

    1564.44878471621482.39670803741203.1209415516444.40972086580

    15001414.21356237311118.033988749900

    1430.90880212541340.70876777921023.474474522900

    1356.4659966251260.9520212918916.515138991200

    1275.73508221731173.6694594306792.148975887700

    1187.43420870381077.0329614269640.312423743300

    1089.7247358852968.2458365519433.012701892200

    979.7958971133842.6149773176000

    852.9361054616691.0137480543000

    700489.8979485566000

    497.49371855330000

    00000

    &A

    Page &P

    LINE POST APPLICATION CURVES9-12-05

    Compression

    Tension

    0 Longitudinal

    500 Longitudinal

    1000 Longitudinal

    1500 Longitudinal

    2000 Longitudinal

    TRANSVERSE LOAD, LBF

    VERTICAL LOAD, LBF

    69 kV Post - 2.5" Rod

    Loading 1

    Longitudinal Load - Graph 10Load Att.MomentsMomentsWorkingLesser of

    TLLowPointTestTestRootRootMomentVert 1 and

    Rod's Radius1.25TranverseLong.VerticalSummaryabcb^2-4acroot1root2root1root2OneTwoRemainderVert 2

    Vertical10Vertical2

    -250000

    Moment of Inertia1.9174743652-25000001882.16550446111965083.7032514-8796892384.980570090383534651.81702.0066125351-2746.06129242051882647596.9458514510.2545982240063375.3735283294133885.925176946-2746.06129242052746.06129242050

    Section Length43-24500497.4937185533497.49371855331880.85215048441925782.02918637-8817568093.0452770046804063326.21712.9509209097-2736.83896478939182.206530352714202.35342486670063980.2470365416133121.02779353-2736.83896478932736.8389647893497.4937185533

    Upsweep Angle0.2094393333-240007007001879.56532891141886480.35512134-8837826110.0380370003894287758.81723.8966200082-2727.57567606639059.093713205413894.58890432720064587.6937661052132356.267062932-2727.57567606632727.5756760663700

    Upsweep9.1399242012-23500852.9361054616852.93610546161878.30503974181847178.68105631-8857666435.9587769961667107802.71734.8434637116-2718.27194948638933.514880954813587.00052175670065197.7049467856131591.682470303-2718.27194948632718.2719494863852.9361054616

    Cap Attachment Loading Limit2500-23000979.7958971133979.79589711331877.07128297591807877.00699128-8877089070.8075699201351573351745.7912010076-2708.92830900558805.457514656413279.62755610065810.2715104867130827.313294588-2708.92830900552708.9283090055979.7958971133

    Compression Limit12282.1080350872-225001089.72473588521089.72473588521875.86405861351768575.33292626-8896094014.5842169879310804255.91756.739575994-2699.5452792148674.908975383812972.50907543440066425.3840885326130063.198603864-2699.5452792142699.5452792141089.7247358852

    Transverse Compression Load Limit-2500-220001187.43420870381187.43420870381874.68336665471729273.65886123-8914681267.288969839206150489.61767.688327882-2690.12338524698541.856507225812665.6839323490067043.0330089942129299.37725072-2690.12338524692690.12338524691187.4342087038

    Transverse Tension Load Limit2500-215001275.73508221731275.73508221731873.52920709941689971.9847962-8932850828.9215869799833031983.91778.637191001-2680.66315269538406.287240335112359.19075936840067663.2082940616128535.887867681-2680.66315269532680.66315269531275.7350822173

    Overall Transverse Range5000-210001356.4659966251356.4659966251872.40157994781650670.31073117-8950602699.4822469761203018710.21789.5858948051-2671.16510751728268.188194030812053.06796442160068285.8996574643127772.768862676-2671.16510751722671.16510751721356.465996625

    -205001430.90880212541430.90880212541871.30048519961611368.63666614-8967936878.9708969723327414663.51800.5341638802-2661.62977594828127.546279951311747.35372635880068911.0965019411127010.058414555-2661.62977594822661.62977594821430.9088021254

    C10.00230358-20000150015001870.22592285511572066.96260112-8984853367.3875269686217257862.51811.4817179522-2652.05768441147984.348305261711442.08599051870069538.7879167614126247.794468656-2652.05768441142652.05768441141500

    -195001564.44878471621564.44878471621869.17789291411532765.28853609-9001352164.7321469649883320349.61822.4282718969-2642.44935942777838.58097591111137.30246434760070168.9626752989125486.014732427-2642.44935942772642.44935942771564.4487847162

    Post's RTL2500-190001624.80768092721624.80768092721868.15639537671493463.61447106-9017433271.0047469614336108190.81833.373535751-2632.80532752557690.230899942610833.04061307280070801.6092326595124724.756671093-2632.80532752552632.80532752551624.8076809272

    Post's Moment Rating96535-185001681.517172081681.517172081867.16143024291454161.94040603-9033096686.2053269579585861475.61844.317214724-2623.12611515037539.284590855910529.33765543270071436.715723366123964.057503395-2623.12611515032623.12611515031681.51717208

    Post's Cantilever Working Load Rating2245-180001734.93515728981734.93515728981866.19299751261414860.26634101-9048342410.3338969545642554317.51855.2590092118-2613.41224857497385.728471019110226.23055946460072074.2699590996123203.954197368-2613.41224857492613.41224857491734.9351572898

    Longitudinal Load0-175001785.35710713571785.35710713571865.25109718591375558.59227598-9063170443.3904569512515894853.21866.1986148115-2603.66425380847229.54887513369923.75603835370072714.2594265011122444.483466199-2603.66425380842603.66425380841785.3571071357

    Deflection Constant0.00230358-170001833.03027798231833.03027798231864.33572926281336256.91821095-9077580785.3749869480215325243.41877.1357223371-2593.88265650627070.73205374819621.95054634310073356.6712850329121685.68176413-2593.88265650622593.88265650621833.0302779823

    Deflection due to Longitudinal0-165001878.16399709931878.16399709931863.44689374331296955.24414592-9091573436.2875169448750021672.31888.0700178372-2584.06798187936909.26417682379320.85027470960074001.4923649032120927.585282438-2584.06798187932584.06798187931878.1639970993

    K Factor for Buckling4-160001920.93727122981920.93727122981862.58459062731257653.57008089-9105148396.1280169418128894347.81899.0011826132-2574.22075460446745.13133734869020.49114780360074648.7091650542120170.229945473-2574.22075460442574.22075460441920.9372712298

    -155001961.50452459331961.50452459331861.74881991481218351.89601587-9118305664.896569388360587501.31909.9288932396-2564.34149873366578.31955500148720.90881915880075298.3078512155119413.65140677-2564.34149873362564.34149873361961.5045245933

    -15000200020001860.9395816061179050.22195084-9131045242.59298693594534793881920.8528215853-2554.43073760416408.81477986418422.13866766970075950.2742540254118657.885045222-2554.43073760412554.43073760412000

    Calculations for longitudinal load561-145002036.54118544162036.54118544161860.15687570071139748.54788581-9143367129.2174469331415682286.81931.7726348361-2544.48899374886236.60289618228124.21579384180076604.5938672194117902.965961336-2544.48899374882544.48899374882036.5411854416

    Logic500-140002071.23151772082071.23151772081859.4007021991100446.87382078-9155271324.76988693042550425001942.6879955189-2534.51678880666061.6697261737827.17501611360077261.2518458894117148.928973549-2534.51678880662534.51678880662071.2315177208

    Loading 10-135002104.16254125012104.16254125011858.67106110091061145.19975575-9166757829.2503169277979140353.81953.5985615269-2524.51464343295884.00103387997531.05086725460077920.2330048146116395.808614632-2524.51464343292524.51464343292104.1625412501

    Loading 2500-130002135.41565040632135.41565040631857.96795240631021843.52569073-9177826642.6587369252595290197.91964.5039861467-2514.48307721095703.58252907367235.87759083770078581.5218168642115643.639128157-2514.48307721092514.48307721092135.4156504063

    Loading 31000-125002165.06350946112165.06350946111857.2913761153982541.851625698-9188477764.9951269228110540405.71975.4039180862-2504.42260856265520.39987119736941.68913779130079245.1024114756114892.454465052-2504.42260856262504.42260856262165.0635094611

    Loading 41500-120002193.17121994612193.17121994611856.6413322278943240.17756067-9198711196.2595169204531673374.31986.2980015042-2494.33375466125334.43867335776648.51916302890079910.958573207114142.288280231-2494.33375466122494.33375466122193.1712199461

    Loading 52000-115002219.79728804232219.79728804231856.017820744903938.503495642-9208526936.4518769181865205524.21997.1858760417-2484.21703134245145.68450635816356.40102216040080579.0737403677113393.173929304-2484.21703134242484.21703134242219.7972880423

    LONGITUDINAL52500-110002244.99443206442244.99443206441855.4208416637864636.829430614-9217924985.5722369160117387299.82008.0671768537-2474.07295301784954.12290277516065.36776828470081249.4310037269112645.14446537-2474.07295301782474.07295301782244.9944320644

    -1050022452268.81026090771854.8503949869825335.155365587-9226905343.6205669139294203169.12018.9415346436-2463.90203258794759.73936107635775.45214886650081922.0131053008111898.232635893-2463.90203258792463.90203258792268.8102609077

    -1000022452291.28784747791854.3064807138786033.481300559-9235468010.5968869119401371623.82029.8085756981-2453.70478135554562.51934977915486.68660269640082596.8024372221111152.470879664-2453.70478135552453.70478135552291.2878474779

    Miscellaneous Calculations-950022452312.46621596941853.7890988442746731.807235531-9243612986.5011869100444345178.92040.6679219236-2443.48170894024362.44831164855199.10325693810083273.7810406903110407.891323848-2443.48170894022443.48170894022312.4662159694

    -900022452332.38075793811853.2982493782707430.133170503-9251340271.3334769082428310373.62051.5191908848-2433.23332319344159.51166793384912.73392426140083952.9306050056109664.525781113-2433.23332319342433.23332319342332.3807579381

    -850022452351.06358910181852.8339323157668128.459105475-9258649865.0937569065358187770.32062.3619958435-2422.96013011363953.69482264224627.61010006440084634.2324666878108922.405746857-2422.96013011362422.96013011362351.0635891018

    -800022452368.54385646541852.3961476568628826.785040447-9265541767.78269049238631955.22073.1959457999-2412.66263376293744.98316684934343.76295978370085317.6676086789108181.562396518-2412.66263376292412.66263376292368.5438564654

    -750022452384.84800354241851.9848954015589525.110975419-9272015979.3982469034074031538.12084.0206455349-2402.34133618373533.36208304334061.22335629510086003.2166596344107442.026582971-2402.34133618372402.34133618372384.8480035424

    -7000224524001851.6001755498550223.436910391-9278072499.9424769019868509152.72094.8356956533-2391.99673731673318.81694950393780.02181740560086690.8598933003106703.828834023-2391.99673731672391.99673731672391.9967373167

    -650022452414.02154091471851.2419881016510921.762845363-9283711329.4146869006625921455.92105.6406926295-2381.62933491893101.3331447133500.18854343650087380.5772279794105966.999349995-2381.62933491892381.62933491892381.6293349189

    -600022452426.93221990231850.910333057471620.088780335-9288932467.8148868994349859128.52116.4352288533-2371.23962448352880.89605179693221.75340490088072.3482260873105231.5680014-2371.23962448352371.23962448352371.2396244835

    -550022452438.74967965141850.6052104159432318.414715307-9293735915.1430668983043646875.12127.2188926785-2360.82809915982657.4910629972944.74594026840088766.152093798104497.56432671-2360.82809915982360.82809915982360.8280991598

    -500022452449.48974278321850.3266201784393016.740650279-9298121671.3992268972710343423.62137.9912684717-2350.39524967392431.10358417012669.19535383790089461.9676807812103765.017530221-2350.39524967392350.39524967392350.3952496739

    -450022452459.16652547161850.0745623445353715.066585251-9302089736.5833768963352741525.92148.751936663-2339.94156425132201.71903931472395.1305136870090159.7734800313103033.956480012-2339.94156425132339.94156425132339.9415642513

    -400022452467.79253585061849.8490369142314413.392520223-9305640110.695568954973367957.12159.5004737982-2329.46752853941969.32287512212122.57994972980090859.5476277893102304.409705996-2329.46752853942329.46752853942329.4675285394

    -350022452475.37875889731849.6500438874275111.718455195-9308772793.7356268947574483516.52170.2364525919-2318.97362553141733.90056555241851.57185186580091561.2679035577101576.405398074-2318.97362553142318.97362553142318.9736255314

    -300022452481.93472919821849.4775832642235810.044390168-9311487785.7037268941158083026.52180.9594419825-2308.4603354911495.43761643141582.13406822470092264.9117302104100849.971404374-2308.4603354912308.4603354912308.460335491

    -250022452487.46859276661849.3316550446196508.37032514-9313785086.5998168935725895333.62191.6690071881-2297.92813587881253.91957006911314.29410350940092970.4561741957100125.135229601-2297.92813587882297.92813587882297.9281358788

    -200022452491.98715887541849.2122592286157206.696260112-9315664696.4238868931279383307.62202.364709764-2287.37750127861009.3320098961048.07911743450093677.877945836599401.9240334672-2287.37750127862287.37750127862287.3775012786

    -150022452495.49594269361849.1193958161117905.022195084-9317126615.1759368927819743842.22213.0461076612-2276.808903326761.660565118783.51592326260094387.15339972498680.3646292369-2276.8089033262276.8089033262276.808903326

    -100022452497.99919935941849.053064807178603.3481300558-9318170842.8559768925347907854.62223.712755287-2266.222810637510.8909153859520.63098643810095098.258535209597960.4834823538-2266.2228106372266.2228106372266.222810637

    -50022452499.499949991849.013266201839301.6740650279-9318797379.4639968923864540285.72234.3642035653-2255.6196887386257.0087954787259.45042331780095811.168996991297242.306709175-2255.61968873862255.61968873862255.6196887386

    002245250018490-9319006225689233700401002245-2245000096525.860075798896525.8600757988-224522452245

    5002234.36420356532499.499949991849.0132662018-39301.6740650279-9318797379.4639968923864540285.72255.6196887386-2234.3642035653-260.1496119164-257.69486874920097242.30670917595811.1689969912-2234.36420356532234.36420356532234.3642035653

    10002223.7127552872497.99919935941849.0530648071-78603.3481300558-9318170842.8559768925347907854.62266.222810637-2223.712755287-523.4541118915-513.60912047240097960.483482353895098.2585352095-2223.7127552872223.7127552872223.712755287

    15002213.04610766122495.49594269361849.1193958161-117905.022195084-9317126615.1759368927819743842.22276.808903326-2213.0461076612-789.9274975799-767.71804589940098680.364629236994387.153399724-2213.04610766122213.04610766122213.0461076612

    20002202.3647097642491.98715887541849.2122592286-157206.696260112-9315664696.4238868931279383307.62287.3775012786-2202.364709764-1059.5836879434-1019.99728972850099401.924033467293677.8779458365-2202.3647097642202.3647097642202.364709764

    25002191.66900718812487.46859276661849.3316550446-196508.37032514-9313785086.5998168935725895333.62297.9281358788-2191.6690071881-1332.4365185216-1270.422851310800100125.13522960192970.4561741957-2191.66900718812191.66900718812191.6690071881

    30002180.95944198252481.93472919821849.4775832642-235810.044390168-9311487785.7037268941158083026.52308.460335491-2180.9594419825-1608.4997367014-1518.971085237700100849.97140437492264.9117302104-2180.95944198252180.95944198252180.9594419825

    35002170.23645259192475.37875889731849.6500438874-275111.718455195-9308772793.7356268947574483516.52318.9736255314-2170.2364525919-1887.7869969873-1765.618701831900101576.40539807491561.2679035577-2170.23645259192170.23645259192170.2364525919

    40002159.50047379822467.79253585061849.8490369142-314413.392520223-9305640110.695568954973367957.12329.4675285394-2159.5004737982-2170.311856274-2010.342767541900102304.40970599690859.5476277893-2159.50047379822159.50047379822159.5004737982

    45002148.7519366632459.16652547161850.0745623445-353715.066585251-9302089736.5833768963352741525.92339.9415642513-2148.751936663-2456.0877691241-2253.120705241300103033.95648001290159.7734800313-2148.7519366632148.7519366632148.751936663

    50002137.99126847172449.48974278321850.3266201784-393016.740650279-9298121671.3992268972710343423.62350.3952496739-2137.9912684717-2745.1280830517-2493.93029443300103765.01753022189461.9676807812-2137.99126847172137.99126847172137.9912684717

    55002127.21889267852438.74967965141850.6052104159-432318.414715307-9293735915.1430668983043646875.12360.8280991598-2127.2188926785-3037.4460338151-2732.749671357700104497.5643267188766.152093798-2127.21889267852127.21889267852127.2188926785

    60002116.43522885332426.93221990231850.910333057-471620.088780335-9288932467.8148868994349859128.52371.2396244835-2116.4352288533-3333.0547407192-2969.5573290100105231.568001488072.3482260873-2116.43522885332116.43522885332116.4352288533

    65002105.64069262952414.02154091471851.2419881016-510921.762845363-9283711329.4146869006625921455.92381.6293349189-2105.6406926295-3631.9672019308-3204.332117059400105966.99934999587380.5772279794-2105.64069262952105.64069262952105.6406926295

    70002094.835695653324001851.6001755498-550223.436910391-9278072499.9424769019868509152.72391.9967373167-2094.8356956533-3934.1962898083-3437.053241680100106703.82883402386690.8598933003-2094.83569565332094.83569565332094.8356956533

    75002084.02064553492384.84800354241851.9848954015-589525.110975419-9272015979.3982469034074031538.12402.3413361837-2084.0206455349-4239.7547462472-3667.700265287400107442.02658297186003.2166596344-2084.02064553492084.02064553492084.0206455349

    80002073.19594579992368.54385646541852.3961476568-628826.785040447-9265541767.78269049238631955.22412.6626337629-2073.1959457999-4548.6551780441-3896.253106184500108181.56239651885317.6676086789-2073.19594579992073.19594579992073.1959457999

    85002062.36199584352351.06358910181852.8339323157-668128.459105475-9258649865.0937569065358187770.32422.9601301136-2062.3619958435-4860.9100522817-4122.692038117200108922.40574685784634.2324666878-2062.36199584352062.36199584352062.3619958435

    90002051.51919088482332.38075793811853.2982493782-707430.133170503-9251340271.3334769082428310373.62433.2333231934-2051.5191908848-5176.531691735-4346.997689740800109664.52578111383952.9306050056-2051.51919088482051.51919088482051.5191908848

    95002040.66792192362312.46621596941853.7890988442-746731.807235531-9243612986.5011869100444345178.92443.4817089402-2040.6679219236-5495.5322703023-4569.151043997800110407.89132384883273.7810406903-2040.66792192362040.66792192362040.6679219236

    100002029.80857569812291.28784747791854.3064807138-786033.481300559-9235468010.5968869119401371623.82453.7047813555-2029.8085756981-5817.9238084626-4789.133437407400111152.47087966482596.8024372221-2029.80857569812029.80857569812029.8085756981

    105002018.94153464362268.81026090771854.8503949869-825335.155365587-9226905343.6205669139294203169.12463.9020325879-2018.9415346436-6143.7181687608-5006.926559270300111898.23263589381922.0131053008-2018.94153464362018.94153464362018.9415346436

    110002008.06717685372244.99443206441855.4208416637-864636.829430614-9217924985.5722369160117387299.82474.0729530178-2008.0671768537-6472.9270513235-5222.512450785700112645.1444653781249.4310037269-2008.06717685372008.06717685372008.0671768537

    115001997.18587604172219.79728804231856.017820744-903938.503495642-9208526936.4518769181865205524.22484.2170313424-1997.1858760417-6805.5619894062-5435.873504086400113393.17392930480579.0737403677-1997.18587604171997.18587604171997.1858760417

    120001986.29800150422193.17121994611856.6413322278-943240.17756067-9198711196.2595169204531673374.32494.3337546612-1986.2980015042-7141.6343449758-5646.992461188700114142.28828023179910.958573207-1986.29800150421986.29800150421986.2980015042

    125001975.40391808622165.06350946111857.2913761153-982541.851625698-9188477764.9951269228110540405.72504.4226085626-1975.4039180862-7481.1553043278-5855.852412861600114892.45446505279245.1024114756-1975.40391808621975.40391808621975.4039180862

    130001964.50398614672135.41565040631857.9679524063-1021843.52569073-9177826642.6587369252595290197.92514.4830772109-1964.5039861467-7824.1358737421-6062.436797414600115643.63912815778581.5218168642-1964.50398614671964.50398614671964.5039861467

    135001953.59856152692104.16254125011858.6710611009-1061145.19975575-9166757829.2503169277979140353.82524.5146434329-1953.5985615269-8170.5868751792-6266.729399405700116395.80861463277920.2330048146-1953.59856152691953.59856152691953.5985615269

    140001942.68799551892071.23151772081859.400702199-1100446.87382078-9155271324.76988693042550425002534.5167888066-1942.6879955189-8520.5189420169-6468.714348272400117148.92897354977261.2518458894-1942.68799551891942.68799551891942.6879955189

    145001931.77263483612036.54118544161860.1568757007-1139748.54788581-9143367129.2174469331415682286.82544.4889937488-1931.7726348361-8873.9425148312-6668.37611688400117902.96596133676604.5938672194-1931.77263483611931.77263483611931.7726348361

    150001920.852821585320001860.939581606-1179050.22195084-9131045242.59298693594534793882554.4307376041-1920.8528215853-9230.8678372235-6865.699520019500118657.88504522275950.2742540254-1920.85282158531920.85282158531920.8528215853

    155001909.92889323961961.50452459331861.7488199148-1218351.89601587-9118305664.896569388360587501.32564.3414987336-1909.9288932396-9591.3049516934-7060.669712770900119413.6514067775298.3078512155-1909.92889323961909.92889323961909.9288932396

    160001899.00118261321920.93727122981862.5845906273-1257653.57008089-9105148396.1280169418128894347.82574.2207546044-1899.0011826132-9955.2636955624-7253.272188873800120170.22994547374648.7091650542-1899.00118261321899.00118261321899.0011826132

    165001878.16399709931878.16399709931863.4468937433-1296955.24414592-9091573436.2875169448750021672.32584.0679818793-1888.0700178372-10322.753696947-7443.492778966300120927.58528243874001.4923649032-1888.07001783721888.07001783721878.1639970993

    170001833.03027798231833.03027798231864.3357292628-1336256.91821095-9077580785.3749869480215325243.42593.8826565062-1877.1357223371-10693.7843707858-7631.317648778100121685.6817641373356.6712850329-1877.13572233711877.13572233711833.0302779823

    175001785.35710713571785.35710713571865.2510971859-1375558.59227598-9063170443.3904569512515894853.22603.6642538084-1866.1986148115-11068.3649149197-7816.733297251500122444.48346619972714.2594265011-1866.19861481151866.19861481151785.3571071357

    180001734.93515728981734.93515728981866.1929975126-1414860.26634101-9048342410.3338969545642554317.52613.4122485749-1855.2590092118-11446.5043062294-7999.726554594600123203.95419736872074.2699590996-1855.25900921181855.25900921181734.9351572898

    185001681.517172081681.517172081867.1614302429-1454161.94040603-9033096686.2053269579585861475.62623.1261151503-1844.317214724-11828.21129683-8180.284580269600123964.05750339571436.715723366-1844.3172147241844.3172147241681.51717208

    190001624.80768092721624.80768092721868.1563953767-1493463.61447106-9017433271.0047469614336108190.82632.8053275255-1833.373535751-12213.4944103253-8358.394860917700124724.75667109370801.6092326595-1833.3735357511833.3735357511624.8076809272

    195001564.44878471621564.44878471621869.1778929141-1532765.28853609-9001352164.7321469649883320349.62642.4493594277-1822.4282718969-12602.361938123-8534.045208219800125486.01473242770168.9626752989-1822.42827189691822.42827189691564.4487847162

    20000150015001870.2259228551-1572066.96260112-8984853367.3875269686217257862.52652.0576844114-1811.4817179522-12994.8219358127-8707.223756698800126247.79446865669538.7879167614-1811.48171795221811.48171795221500

    205001430.90880212541430.90880212541871.3004851996-1611368.63666614-8967936878.9708969723327414663.52661.6297759482-1800.5341638802-13390.882219608-8877.918961460700127010.05841455568911.0965019411-1800.53416388021800.53416388021430.9088021254

    210001356.4659966251356.4659966251872.4015799478-1650670.31073117-8950602699.4822469761203018710.22671.1651075172-1789.5858948051-13790.5503628543-9046.11959587900127772.76886267668285.8996574643-1789.58589480511789.58589480511356.465996625

    215001275.73508221731275.73508221731873.5292070994-1689971.9847962-8932850828.9215869799833031983.92680.6631526953-1778.637191001-14193.8336926038-9211.814749223200128535.88786768167663.2082940616-1778.6371910011778.6371910011275.7350822173

    220001187.43420870381187.43420870381874.6833666547-1729273.65886123-8914681267.288969839206150489.62690.1233852469-1767.688327882-14600.7392862594-9374.993824232200129299.3772507267043.0330089942-1767.6883278821767.6883278821187.4342087038

    225001089.72473588521089.72473588521875.8640586135-1768575.33292626-8896094014.5842169879310804255.92699.545279214-1756.739575994-15011.2739682879-9535.646534635400130063.19860386466425.3840885326-1756.7395759941756.7395759941089.7247358852

    23000979.7958971133979.79589711331877.0712829759-1807877.00699128-8877089070.8075699201351573352708.9283090055-1745.7912010076-15425.4443070051-9693.762902622800130827.31329458865810.2715104867-1745.79120100761745.7912010076979.7958971133

    23500852.9361054616852.93610546161878.3050397418-1847178.68105631-8857666435.9587769961667107802.72718.2719494863-1734.8434637116-15843.2566114338-9849.333256265400131591.68247030365197.7049467856-1734.84346371161734.8434637116852.9361054616

    240007007001879.5653289114-1886480.35512134-8837826110.0380370003894287758.82727.5756760663-1723.8966200082-16264.716928235-10002.348226887300132356.26706293264587.6937661052-1723.89662000821723.8966200082700

    24500497.4937185533497.49371855331880.8521504844-1925782.02918637-8817568093.0452770046804063326.22736.8389647893-1712.9509209097-16689.831038715-10152.798746392500133121.0277935363980.2470365416-1712.95092090971712.9509209097497.4937185533

    25000001882.1655044611-1965083.7032514-8796892384.980570090383534651.82746.0612924205-1702.0066125351-17118.6044559084-10300.67604454620133885.92517694663375.3735283294-1702.00661253511702.00661253510

    &L&F&C&A&R&D

    &LERM 99-5&CPage &P&Rrab

    Allen Bernstorf:Changed Equation denominator from 5 to 4 - rev. 2

    Load 2

    Longitudinal Load - Graph 1500Load Att.Trans.WorkingLesser of

    LowPointDeflectionTestTestMomentVert 1 and

    Rod's Radius1.25TranverseVerticalSummaryConstantabcb^2-4acroot1root2root1root2RemainderVert 2

    Vertical1ZVertical2

    -25000

    Moment of Inertia1.9174743652-25005000018491965083.7032514-8313757831.3797265350106881668.61654.6396952479-2717.4215791048000064788.8688755599134450.997091124-2717.42157910482717.42157910480

    Section Length43-24505000018491925782.02918637-8334433539.4444965350106881668.61665.2675140864-2706.7937602662000065357.0440692801133628.603716419-2706.79376026622706.79376026620

    Upsweep Angle0.2094393333-2400500489.8979485566489.897948556618491886480.35512134-8354691556.4372565350106881668.61675.895332925-2696.1659414276000065927.8984751774132808.716765832-2696.16594142762696.1659414276489.8979485566

    Upsweep9.1399242012-2350500691.0137480543691.013748054318491847178.68105631-8374531882.3579965350106881668.61686.5231517636-2685.538122589000066501.4280820029131991.336907553-2685.5381225892685.538122589691.0137480543

    Cap Attachment Loading Limit2500-2300500842.6149773176842.614977317618491807877.00699128-8393954517.2067265350106881668.61697.1509706021-2674.9103037505000067077.6289688335131176.464819948-2674.91030375052674.9103037505842.6149773176

    Compression Limit12282.1080350872-2250500968.2458365519968.245836551918491768575.33292626-8412959460.9834365350106881668.61707.7787894407-2664.2824849119000067656.4973026015130364.101191749-2664.28248491192664.2824849119968.2458365519

    Transverse Compression Load Limit-2500-22005001077.03296142691077.032961426918491729273.65886123-8431546713.6881265350106881668.61718.4066082793-2653.6546660733000068238.0293357028129554.246722253-2653.65466607332653.65466607331077.0329614269

    Transverse Tension Load Limit2500-21505001173.66945943061173.669459430618491689971.9847962-8449716275.320865350106881668.61729.0344271178-2643.0268472348000068822.2214036817128746.902121522-2643.02684723482643.02684723481173.6694594306

    Overall Transverse Range5000-21005001260.95202129181260.952021291818491650670.31073117-8467468145.8814665350106881668.61739.6622459564-2632.3990283962000069409.069922988127942.06811059-2632.39902839622632.39902839621260.9520212918

    -20505001340.70876777921340.708767779218491611368.63666614-8484802325.3701165350106881668.61750.290064795-2621.7712095576000069998.5713888052127139.745421674-2621.77120955762621.77120955761340.7087677792

    -20005001414.21356237311414.213562373118491572066.96260112-8501718813.7867465350106881668.61760.9178836336-2611.1433907191000070590.7223729456126339.934798389-2611.14339071912611.14339071911414.2135623731

    -19505001482.39670803741482.396708037418491532765.28853609-8518217611.1313665350106881668.61771.5457024721-2600.5155718805000071185.5195218126125542.636995968-2600.51557188052600.51557188051482.3967080374

    Post's RTL2500-19005001545.9624833741545.96248337418491493463.61447106-8534298717.4039665350106881668.61782.1735213107-2589.8877530419000071782.9595544247124747.852781488-2589.88775304192589.88775304191545.962483374

    Post's Moment Rating96535-18505001605.45943580021605.459435800218491454161.94040603-8549962132.6045465350106881668.61792.8013401493-2579.2599342034000072383.0392605014123955.582934102-2579.25993420342579.25993420341605.4594358002

    Post's Cantilever Working Load Rating2245-18005001661.32477258361661.324772583618491414860.26634101-8565207856.7331165350106881668.61803.4291589878-2568.6321153648000072985.7554986077123165.828245275-2568.63211536482568.63211536481661.3247725836

    Longitudinal Load500-17505001713.91365010031713.913650100318491375558.59227598-8580035889.7896765350106881668.61814.0569778264-2558.0042965262000073591.1051943556122378.589519022-2558.00429652622558.00429652621713.9136501003

    Deflection Constant0.00230358-17005001763.51920885481763.519208854818491336256.91821095-8594446231.774265350106881668.61824.684796665-2547.3764776876000074199.0853386603121593.867572163-2547.37647768762547.37647768761763.5192088548

    Deflection due to Longitudinal1.1517899889-16505001810.38669902321810.386699023218491296955.24414592-8608438882.6867365350106881668.61835.3126155035-2536.7486588491000074809.6929860497120811.663234566-2536.74865884912536.74865884911810.3866990232

    K Factor for Buckling4-16005001854.72369909911854.723699099118491257653.57008089-8622013842.5272365350106881668.61845.9404343421-2526.1208400105000075422.9252530244120031.977349418-2526.12084001052526.12084001051854.7236990991

    -15505001896.70767383911896.707673839118491218351.89601587-8635171111.2957265350106881668.61856.5682531807-2515.493021172000076038.779316468119254.810773479-2515.4930211722515.4930211721896.7076738391

    -15005001936.49167310371936.491673103718491179050.22195084-8647910688.992265350106881668.61867.1960720192-2504.8652023334000076657.2524121044118480.164377361-2504.86520233342504.86520233341936.4916731037

    Calculations for longitudinal load561-14505001974.208702241974.2087022418491139748.54788581-8660232575.6166665350106881668.61877.8238908578-2494.2373834948000077278.3418330013117708.039045804-2494.23738349482494.23738349481974.20870224

    Logic500-14005002009.97512422422009.975124224218491100446.87382078-8672136771.1691165350106881668.61888.4517096964-2483.6095646562000077902.0449281186116938.435677961-2483.60956465622483.60956465622009.9751242242

    Loading 10-13505002043.8933435972043.89334359718491061145.19975575-8683623275.6495365350106881668.61899.079528535-2472.9817458177000078528.3591008995116171.355187686-2472.98174581772472.98174581772043.893343597

    Loading 2500-13005002076.05394920272076.053949202718491021843.52569073-8694692089.0579565350106881668.61909.7073473735-2462.3539269791000079157.2818079031115406.798503841-2462.35392697912462.35392697912076.0539492027

    Loading 31000-12505002106.53744329412106.53744329411849982541.851625698-8705343211.3943465350106881668.61920.3351662121-2451.7261081405000079788.8105574773114644.766570592-2451.72610814052451.72610814052106.5374432941

    Loading 41500-12005002135.41565040632135.41565040631849943240.17756067-8715576642.6587365350106881668.61930.9629850506-2441.098289302000080422.942908471113885.260347728-2441.0982893022441.0982893022135.4156504063

    Loading 52000-11505002162.75287538822162.75287538821849903938.503495642-8725392382.8510965350106881668.61941.5908038892-2430.4704704634000081059.6764689828113128.280810982-2430.47047046342430.47047046342162.7528753882

    LONGITUDINAL52500-11005002188.60686282392188.60686282391849864636.829430614-8734790431.9714565350106881668.61952.2186227278-2419.8426516248000081699.0088951469112373.828952358-2419.84265162482419.84265162482188.6068628239

    -10505002213.02959763312213.02959763311849825335.155365587-8743770790.0197865350106881668.61962.8464415664-2409.2148327863000082340.9378899537111621.905780467-2409.21483278632409.21483278632213.0295976331

    -10005002236.06797749982236.06797749981849786033.481300559-8752333456.996165350106881668.61973.4742604049-2398.5870139477000082985.4612021045110872.512320876-2398.58701394772398.58701394772236.0679774998

    Miscellaneous Calculations-95050022452257.76438097511849746731.807235531-8760478432.900465350106881668.61984.1020792435-2387.9591951091000083632.576624899110125.649616457-2387.95919510912387.95919510912257.7643809751

    -90050022452278.15714997891849707430.133170503-8768205717.7326965350106881668.61994.7298980821-2377.3313762706000084282.2819951546109381.318727751-2377.33137627062377.33137627062278.1571499789

    -85050022452297.2810015321849668128.459105475-8775515311.4929765350106881668.62005.3577169206-2366.703557432000084934.5751921559108639.520733342-2366.7035574322366.7035574322297.281001532

    -80050022452315.1673805581849628826.785040447-8782407214.1812265350106881668.62015.9855357592-2356.0757385934000085589.4541366352107900.256730236-2356.07573859342356.07573859342315.167380558

    -75050022452331.84476327221849589525.110975419-8788881425.7974665350106881668.62026.6133545978-2345.4479197548000086246.9167897803107163.527834249-2345.44791975482345.44791975482331.8447632722

    -70050022452347.33891886111849550223.436910391-8794937946.3416965350106881668.62037.2411734363-2334.8201009163000086906.961152271106429.335180411-2334.82010091632334.82010091632334.8201009163

    -65050022452361.67313572391849510921.762845363-8800576775.813965350106881668.62047.8689922749-2324.1922820777000087569.5852633426105697.679923374-2324.19228207772324.19228207772324.1922820777

    -60050022452374.86841740761849471620.088780335-8805797914.214165350106881668.62058.4968111135-2313.5644632391000088234.787199875104968.563237834-2313.56446323912313.56446323912313.5644632391

    -55050022452386.9436524561849432318.414715307-8810601361.5422865350106881668.62069.124629952-2302.9366444006000088902.5650755077104241.986318962-2302.93664440062302.93664440062302.9366444006

    -50050022452397.91576165641849393016.740650279-8814987117.7984465350106881668.62079.7524487906-2292.308825562000089572.9170397784103517.950382845-2292.3088255622292.3088255622292.308825562

    -45050022452407.79982556691849353715.066585251-8818955182.9825965350106881668.62090.3802676292-2281.6810067234000090245.8412772864102796.456666944-2281.68100672342281.68100672342281.6810067234

    -40050022452416.60919471891849314413.392520223-8822505557.0947265350106881668.62101.0080864678-2271.0531878849000090921.3360068777102077.506430555-2271.05318788492271.05318788492271.0531878849

    -35050022452424.35558448011849275111.718455195-8825638240.1348465350106881668.62111.6359053063-2260.4253690463000091599.3994808538101361.100955289-2260.42536904632260.42536904632260.4253690463

    -30050022452431.04915622861849235810.044390168-8828353232.1029465350106881668.62122.2637241449-2249.7975502077000092280.0299842006100647.241545563-2249.79755020772249.79755020772249.7975502077

    -2505002239.16973136922436.69858620221849196508.37032514-8830650532.9990365350106881668.62132.8915429835-2239.1697313692000092963.22583383999935.9295291013-2239.16973136922239.16973136922239.1697313692

    -2005002228.54191253062441.31112314671849157206.696260112-8832530142.823165350106881668.62143.519361822-2228.5419125306000093648.985377895699227.1662574506-2228.54191253062228.54191253062228.5419125306

    -1505002217.9140936922444.89263567951849117905.022195084-8833992061.5751565350106881668.62154.1471806606-2217.914093692000094337.306994993198520.9531065132-2217.9140936922217.9140936922217.914093692

    -1005002207.28627485342447.4476501041184978603.3481300558-8835036289.2551965350106881668.62164.7749994992-2207.2862748534000095028.189093559297817.2914770876-2207.28627485342207.28627485342207.2862748534

    -505002196.65845601492448.9793792517184939301.6740650279-8835662825.8632165350106881668.62175.4028183377-2196.6584560149000095721.630111154297116.1827954281-2196.65845601492196.65845601492196.6584560149

    05002186.03063717632449.489742783218490-8835871671.3992265350106881668.62186.0306371763-2186.0306371763000096417.628513817296417.6285138172-2186.03063717632186.03063717632186.0306371763

    505002175.40281833772448.97937925171849-39301.6740650279-8835662825.8632165350106881668.62196.6584560149-2175.4028183377000097116.182795428195721.6301111542-2175.40281833772175.40281833772175.4028183377

    1005002164.77499949922447.44765010411849-78603.3481300558-8835036289.2551965350106881668.62207.2862748534-2164.7749994992000097817.291477087695028.1890935592-2164.77499949922164.77499949922164.7749994992

    1505002154.14718066062444.89263567951849-117905.022195084-8833992061.5751565350106881668.62217.914093692-2154.1471806606000098520.953106513294337.3069949931-2154.14718066062154.14718066062154.1471806606

    2005002143.5193618222441.31112314671849-157206.696260112-8832530142.823165350106881668.62228.5419125306-2143.519361822000099227.166257450693648.9853778956-2143.5193618222143.5193618222143.519361822

    2505002132.89154298352436.69858620221849-196508.37032514-8830650532.9990365350106881668.62239.1697313692-2132.8915429835000099935.929529101392963.225833839-2132.89154298352132.89154298352132.8915429835

    3005002122.26372414492431.04915622861849-235810.044390168-8828353232.1029465350106881668.62249.7975502077-2122.26372414490000100647.24154556392280.0299842006-2122.26372414492122.26372414492122.2637241449

    3505002111.63590530632424.35558448011849-275111.718455195-8825638240.1348465350106881668.62260.4253690463-2111.63590530630000101361.10095528991599.3994808538-2111.63590530632111.63590530632111.6359053063

    4005002101.00808646782416.60919471891849-314413.392520223-8822505557.0947265350106881668.62271.0531878849-2101.00808646780000102077.50643055590921.3360068777-2101.00808646782101.00808646782101.0080864678

    4505002090.38026762922407.79982556691849-353715.066585251-8818955182.9825965350106881668.62281.6810067234-2090.38026762920000102796.45666694490245.8412772864-2090.38026762922090.38026762922090.3802676292

    5005002079.75244879062397.91576165641849-393016.740650279-8814987117.7984465350106881668.62292.308825562-2079.75244879060000103517.95038284589572.9170397784-2079.75244879062079.75244879062079.7524487906

    5505002069.1246299522386.9436524561849-432318.414715307-8810601361.5422865350106881668.62302.9366444006-2069.1246299520000104241.98631896288902.5650755077-2069.1246299522069.1246299522069.124629952

    6005002058.49681111352374.86841740761849-471620.088780335-8805797914.214165350106881668.62313.5644632391-2058.49681111350000104968.56323783488234.787199875-2058.49681111352058.49681111352058.4968111135

    6505002047.86899227492361.67313572391849-510921.762845363-8800576775.813965350106881668.62324.1922820777-2047.86899227490000105697.67992337487569.5852633426-2047.86899227492047.86899227492047.8689922749

    7005002037.24117343632347.33891886111849-550223.436910391-8794937946.3416965350106881668.62334.8201009163-2037.24117343630000106429.33518041186906.961152271-2037.24117343632037.24117343632037.2411734363

    7505002026.61335459782331.84476327221849-589525.110975419-8788881425.7974665350106881668.62345.4479197548-2026.61335459780000107163.52783424986246.9167897803-2026.61335459782026.61335459782026.6133545978

    8005002015.98553575922315.1673805581849-628826.785040447-8782407214.1812265350106881668.62356.0757385934-2015.98553575920000107900.25673023685589.4541366352-2015.98553575922015.98553575922015.9855357592

    8505002005.35771692062297.2810015321849-668128.459105475-8775515311.4929765350106881668.62366.703557432-2005.35771692060000108639.52073334284934.5751921559-2005.35771692062005.35771692062005.3577169206

    9005001994.72989808212278.15714997891849-707430.133170503-8768205717.7326965350106881668.62377.3313762706-1994.72989808210000109381.31872775184282.2819951546-1994.72989808211994.72989808211994.7298980821

    9505001984.10207924352257.76438097511849-746731.807235531-8760478432.900465350106881668.62387.9591951091-1984.10207924350000110125.64961645783632.576624899-1984.10207924351984.10207924351984.1020792435

    10005001973.47426040492236.06797749981849-786033.481300559-8752333456.996165350106881668.62398.5870139477-1973.47426040490000110872.51232087682985.4612021045-1973.47426040491973.47426040491973.4742604049

    10505001962.84644156642213.02959763311849-825335.155365587-8743770790.0197865350106881668.62409.2148327863-1962.84644156640000111621.90578046782340.9378899537-1962.84644156641962.84644156641962.8464415664

    11005001952.21862272782188.60686282391849-864636.829430614-8734790431.9714565350106881668.62419.8426516248-1952.21862272780000112373.82895235881699.0088951469-1952.21862272781952.21862272781952.2186227278

    11505001941.59080388922162.75287538821849-903938.503495642-8725392382.8510965350106881668.62430.4704704634-1941.59080388920000113128.28081098281059.6764689828-1941.59080388921941.59080388921941.5908038892

    12005001930.96298505062135.41565040631849-943240.17756067-8715576642.6587365350106881668.62441.098289302-1930.96298505060000113885.26034772880422.942908471-1930.96298505061930.96298505061930.9629850506

    12505001920.33516621212106.53744329411849-982541.851625698-8705343211.3943465350106881668.62451.7261081405-1920.33516621210000114644.76657059279788.8105574773-1920.33516621211920.33516621211920.3351662121

    13005001909.70734737352076.05394920271849-1021843.52569073-8694692089.0579565350106881668.62462.3539269791-1909.70734737350000115406.79850384179157.2818079031-1909.70734737351909.70734737351909.7073473735

    13505001899.0795285352043.8933435971849-1061145.19975575-8683623275.6495365350106881668.62472.9817458177-1899.0795285350000116171.35518768678528.3591008995-1899.0795285351899.0795285351899.079528535

    14005001888.45170969642009.97512422421849-1100446.87382078-8672136771.1691165350106881668.62483.6095646562-1888.45170969640000116938.43567796177902.0449281186-1888.45170969641888.45170969641888.4517096964

    14505001877.82389085781974.208702241849-1139748.54788581-8660232575.6166665350106881668.62494.2373834948-1877.82389085780000117708.03904580477278.3418330013-1877.82389085781877.82389085781877.8238908578

    15005001867.19607201921936.49167310371849-1179050.22195084-8647910688.992265350106881668.62504.8652023334-1867.19607201920000118480.16437736176657.2524121044-1867.19607201921867.19607201921867.1960720192

    15505001856.56825318071896.70767383911849-1218351.89601587-8635171111.2957265350106881668.62515.493021172-1856.56825318070000119254.81077347976038.779316468-1856.56825318071856.56825318071856.5682531807

    16005001845.94043434211854.72369909911849-1257653.57008089-8622013842.5272365350106881668.62526.1208400105-1845.94043434210000120031.97734941875422.9252530244-1845.94043434211845.94043434211845.9404343421

    16505001810.38669902321810.38669902321849-1296955.24414592-8608438882.6867365350106881668.62536.7486588491-1835.31261550350000120811.66323456674809.6929860497-1835.31261550351835.31261550351810.3866990232

    17005001763.51920885481763.51920885481849-1336256.91821095-8594446231.774265350106881668.62547.3764776876-1824.6847966650000121593.86757216374199.0853386603-1824.6847966651824.6847966651763.5192088548

    17505001713.91365010031713.91365010031849-1375558.59227598-8580035889.7896765350106881668.62558.0042965262-1814.05697782640000122378.58951902273591.1051943556-1814.05697782641814.05697782641713.9136501003

    18005001661.32477258361661.32477258361849-1414860.26634101-8565207856.7331165350106881668.62568.6321153648-1803.42915898780000123165.82824527572985.7554986077-1803.42915898781803.42915898781661.3247725836

    18505001605.45943580021605.45943580021849-1454161.94040603-8549962132.6045465350106881668.62579.2599342034-1792.80134014930000123955.58293410272383.0392605014-1792.80134014931792.80134014931605.4594358002

    19005001545.9624833741545.9624833741849-1493463.61447106-8534298717.4039665350106881668.62589.8877530419-1782.17352131070000124747.85278148871782.9595544247-1782.17352131071782.17352131071545.962483374

    19505001482.39670803741482.39670803741849-1532765.28853609-8518217611.1313665350106881668.62600.5155718805-1771.54570247210000125542.63699596871185.5195218126-1771.54570247211771.54570247211482.3967080374

    20005001414.21356237311414.21356237311849-1572066.96260112-8501718813.7867465350106881668.62611.1433907191-1760.91788363360000126339.93479838970590.7223729456-1760.91788363361760.91788363361414.2135623731

    20505001340.70876777921340.70876777921849-1611368.63666614-8484802325.3701165350106881668.62621.7712095576-1750.2900647950000127139.74542167469998.5713888052-1750.2900647951750.2900647951340.7087677792

    21005001260.95202129181260.95202129181849-1650670.31073117-8467468145.8814665350106881668.62632.3990283962-1739.66224595640000127942.0681105969409.069922988-1739.66224595641739.66224595641260.9520212918

    21505001173.66945943061173.66945943061849-1689971.9847962-8449716275.320865350106881668.62643.0268472348-1729.03442711780000128746.90212152268822.2214036817-1729.03442711781729.03442711781173.6694594306

    22005001077.03296142691077.03296142691849-1729273.65886123-8431546713.6881265350106881668.62653.6546660733-1718.40660827930000129554.24672225368238.0293357028-1718.40660827931718.40660827931077.0329614269

    2250500968.2458365519968.24583655191849-1768575.33292626-8412959460.9834365350106881668.62664.2824849119-1707.77878944070000130364.10119174967656.4973026015-1707.77878944071707.7787894407968.2458365519

    2300500842.6149773176842.61497731761849-1807877.00699128-8393954517.2067265350106881668.62674.9103037505-1697.15097060210000131176.46481994867077.6289688335-1697.15097060211697.1509706021842.6149773176

    2350500691.0137480543691.01374805431849-1847178.68105631-8374531882.3579965350106881668.62685.538122589-1686.52315176360000131991.33690755366501.4280820029-1686.52315176361686.5231517636691.0137480543

    2400500489.8979485566489.89794855661849-1886480.35512134-8354691556.4372565350106881668.62696.1659414276-1675.8953329250000132808.71676583265927.8984751774-1675.8953329251675.895332925489.8979485566

    2450500001849-1925782.02918637-8334433539.4444965350106881668.62706.7937602662-1665.26751408640000133628.60371641965357.0440692801-1665.26751408641665.26751408640

    2500500001849-1965083.7032514-8313757831.3797265350106881668.62717.4215791048-1654.6396952479000134450.99709112464788.8688755599-1654.63969524791654.63969524790

    &L&F&C&A&R&D

    &LERM 99-5&CPage &P&Rrab

    Allen Bernstorf:Changed Equation denominator from 5 to 4 - rev. 2

    Loading 3

    Longitudinal Load - Graph 11000Load Att.Trans.WorkingLesser of

    LowPointDeflectionTestTestMomentVert 1 and

    Rod's Radius1.25TranverseVerticalSummaryConstantabcb^2-4acroot1root2root1root2RemainderVert 2

    Vertical1ZVertical2

    -25000

    Moment of Inertia1.9174743652-250010000018491965083.7032514-6864354170.5773854630317406374.51467.3198392237-2530.1017230806000067894.7338561834131545.41648643-2530.10172308062530.10172308060

    Section Length43-245010000018491925782.02918637-6885029878.6421554630317406374.51477.9476580623-2519.473904242000068381.8250244248130769.137780288-2519.4739042422519.4739042420

    Upsweep Angle0.2094393333-240010000018491886480.35512134-6905287895.6349154630317406374.51488.5754769008-2508.8460854035000068872.2191458017129995.551131749-2508.84608540352508.84608540350

    Upsweep9.1399242012-235010000018491847178.68105631-6925128221.5556554630317406374.51499.2032957394-2498.2182665649000069365.9036813895129224.659225549-2498.21826656492498.21826656490

    Cap Attachment Loading Limit2500-230010000018491807877.00699128-6944550856.4043854630317406374.51509.831114578-2487.5904477263000069862.8663092639128456.464784387-2487.59044772632487.59044772630

    Compression Limit12282.1080350872-22501000433.0127018922433.012701892218491768575.33292626-6963555800.1810954630317406374.51520.4589334165-2476.9626288878000070363.094920552127690.970569567-2476.96262888782476.9626288878433.0127018922

    Transverse Compression Load Limit-2500-22001000640.3124237433640.312423743318491729273.65886123-6982143052.8857854630317406374.51531.0867522551-2466.3348100492000070866.5776155451126928.179381652-2466.33481004922466.3348100492640.3124237433

    Transverse Tension Load Limit2500-21501000792.1489758877792.148975887718491689971.9847962-7000312614.5184654630317406374.51541.7145710937-2455.7069912106000071373.3026998736126168.094061133-2455.70699121062455.7069912106792.1489758877

    Overall Transverse Range5000-21001000916.5151389912916.515138991218491650670.31073117-7018064485.0791254630317406374.51552.3423899322-2445.079172372000071883.258680743125410.717489109-2445.0791723722445.079172372916.5151389912

    -205010001023.47447452291023.474474522918491611368.63666614-7035398664.5677754630317406374.51562.9702087708-2434.4513535335000072396.4342632313124656.052587978-2434.45135353352434.45135353351023.4744745229

    -200010001118.03398874991118.033988749918491572066.96260112-7052315152.984454630317406374.51573.5980276094-2423.8235346949000072912.8183466483123904.102322149-2423.82353469492423.82353469491118.0339887499

    -195010001203.12094155161203.120941551618491532765.28853609-7068813950.3290254630317406374.51584.225846448-2413.1957158563000073432.4000209541123154.86969876-2413.19571585632413.19571585631203.1209415516

    Post's RTL2500-190010001280.62484748661280.624847486618491493463.61447106-7084895056.6016254630317406374.51594.8536652865-2402.5678970178000073955.1685632396122408.357768411-2402.56789701782402.56789701781280.6248474866

    Post's Moment Rating96535-185010001351.85058345961351.850583459618491454161.94040603-7100558471.802254630317406374.51605.4814841251-2391.9400781792000074481.1134342654121664.569625917-2391.94007817922391.94007817921351.8505834596

    Post's Cantileve Working Load Rating2245-180010001417.74468787581417.744687875818491414860.26634101-7115804195.9307754630317406374.51616.1093029637-2381.3122593406000075010.2242750612120923.508411069-2381.31225934062381.31225934061417.7446878758

    Longitudinal Load1000-175010001479.01994577491479.019945774918491375558.59227598-7130632228.9873254630317406374.51626.7371218022-2370.6844405021000075542.4909035841120185.177309414-2370.68444050212370.68444050211479.0199457749

    Deflection Constant0.00230358-170010001536.22914957371536.229149573718491336256.91821095-7145042570.9718654630317406374.51637.3649406408-2360.0566216635000076077.9033114342119449.579553047-2360.05662166352360.05662166351536.2291495737

    Deflection due to Longitudinal2.3035799777-165010001589.81130955851589.811309558518491296955.24414592-7159035221.8843954630317406374.51647.9927594794-2349.4288028249000076616.4516606294118716.718421424-2349.42880282492349.42880282491589.8113095585

    K Factor for Buckling4-160010001640.12194668571640.121946685718491257653.57008089-7172610181.7248954630317406374.51658.6205783179-2338.8009839864000077158.1262804369117986.597242183-2338.80098398642338.80098398641640.1219466857

    -155010001687.45370306861687.453703068618491218351.89601587-7185767450.4933854630317406374.51669.2483971565-2328.1731651478000077702.9176642609117259.219391989-2328.17316514782328.17316514781687.4537030686

    -150010001732.05080756891732.050807568918491179050.22195084-7198507028.1898654630317406374.51679.8762159951-2317.5453463092000078250.8164665868116534.58829739-2317.54534630922317.54534630921732.0508075689

    Calculations for longitudinal load561-145010001774.1194999211774.11949992118491139748.54788581-7210828914.8143254630317406374.51690.5040348336-2306.9175274706000078801.8134999808115812.707435692-2306.91752747062306.91752747061774.119499921

    Logic500-140010001813.83571472171813.835714721718491100446.87382078-7222733110.3667754630317406374.51701.1318536722-2296.2897086321000079355.8997321433115093.580335852-2296.28970863212296.28970863211813.8357147217

    Loading 10-135010001851.35085815741851.350858157418491061145.19975575-7234219614.8471954630317406374.51711.7596725108-2285.6618897935000079913.0662830178114377.210579389-2285.66188979352285.66188979351851.3508581574

    Loading 2500-130010001886.79622641131886.796226411318491021843.52569073-7245288428.2556154630317406374.51722.3874913494-2275.0340709549000080473.304421951113663.601801308-2275.03407095492275.03407095491886.7962264113

    Loading 31000-125010001920.28643696721920.28643696721849982541.851625698-7255939550.59254630317406374.51733.0153101879-2264.4062521164000081036.6055649073112952.75769105-2264.40625211642264.40625211641920.2864369672

    Loading 41500-120010001951.92212959431951.92212959431849943240.17756067-7266172981.8563954630317406374.51743.6431290265-2253.7784332778000081602.9612717338112244.681993455-2253.77843327782253.77843327781951.9221295943

    Loading 52000-115010001981.79211826061981.79211826061849903938.503495642-7275988722.0487554630317406374.51754.2709478651-2243.1506144392000082172.363243477111539.378509747-2243.15061443922243.15061443921981.7921182606

    LONGITUDINAL52500-110010002009.97512422422009.97512422421849864636.829430614-7285386771.169154630317406374.51764.8987667036-2232.5227956007000082744.8033197497110836.851098536-2232.52279560072232.52279560072009.9751242242

    -105010002036.54118544162036.54118544161849825335.155365587-7294367129.2174454630317406374.51775.5265855422-2221.8949767621000083320.2734761471110137.103676843-2221.89497676212221.89497676212036.5411854416

    -100010002061.55281280882061.55281280881849786033.481300559-7302929796.1937654630317406374.51786.1544043808-2211.2671579235000083898.7658217124109440.140221143-2211.26715792352211.26715792352061.5528128088

    Miscellaneous Calculations-95010002085.06594619932085.06594619931849746731.807235531-7311074772.0980654630317406374.51796.7822232193-2200.639339085000084480.2725964497108745.964768431-2200.6393390852200.6393390852085.0659461993

    -90010002107.13075057062107.13075057061849707430.133170503-7318802056.9303554630317406374.51807.4100420579-2190.0115202464000085064.7861688846108054.581417305-2190.01152024642190.01152024642107.1307505706

    -85010002127.79228309532127.79228309531849668128.459105475-7326111650.6906354630317406374.51818.0378608965-2179.3837014078000085652.2990336715107365.994329077-2179.38370140782179.38370140782127.7922830953

    -80010002147.09105535842147.09105535841849628826.785040447-7333003553.3788854630317406374.51828.665679735-2168.7558825692000086242.8038092462106680.207728901-2168.75588256922168.75588256922147.0910553584

    -75010002158.12806373072165.06350946111849589525.110975419-7339477764.9951254630317406374.51839.2934985736-2158.1280637307000086836.2932355239105997.225906924-2158.12806373072158.12806373072158.1280637307

    -70010002147.50024489212181.74242292711849550223.436910391-7345534285.5393554630317406374.51849.9213174122-2147.5002448921000087432.7601716414105317.053219465-2147.50024489212147.50024489212147.5002448921

    -65010002136.87242605352197.1572542721849510921.762845363-7351173115.0115654630317406374.51860.5491362508-2136.8724260535000088032.1975937427104639.694090208-2136.87242605352136.87242605352136.8724260535

    -60010002126.2446072152211.33443874961849471620.088780335-7356394253.4117654630317406374.51871.1769550893-2126.244607215000088634.5985928078103965.153011431-2126.2446072152126.2446072152126.244607215

    -55010002115.61678837642224.29764195351849432318.414715307-7361197700.7399454630317406374.51881.8047739279-2115.6167883764000089239.9563725228103293.434545249-2115.61678837642115.61678837642115.6167883764

    -50010002104.98896953782236.06797749981849393016.740650279-7365583456.996154630317406374.51892.4325927665-2104.9889695378000089848.2642471918102624.543324887-2104.98896953782104.98896953782104.9889695378

    -45010002094.36115069932246.66419386611849353715.066585251-7369551522.1802554630317406374.51903.060411605-2094.3611506993000090459.5156396898101958.484055979-2094.36115069932094.36115069932094.3611506993

    -40010002083.73333186072256.10283453571849314413.392520223-7373101896.2923854630317406374.51913.6882304436-2083.7333318607000091073.7040794545101295.261517892-2083.73333186072083.73333186072083.7333318607

    -35010002073.10551302212264.39837484481849275111.718455195-7376234579.332554630317406374.51924.3160492822-2073.1055130221000091690.8232005178100634.880565074-2073.10551302212073.10551302212073.1055130221

    -30010002062.47769418362271.56333832011849235810.044390168-7378949571.300654630317406374.51934.9438681207-2062.4776941836000092310.866739575799977.3461284338-2062.47769418362062.47769418362062.4776941836

    -25010002051.8498753452277.60839478611849196508.37032514-7381246872.1966854630317406374.51945.5716869593-2051.849875345000092933.828534096299322.6632167459-2051.8498753452051.8498753452051.849875345

    -20010002041.22205650642282.54244210271849157206.696260112-7383126482.0207554630317406374.51956.1995057979-2041.2220565064000093559.702520463198670.8369180824-2041.22205650642041.22205650642041.2220565064

    -15010002030.59423766782286.37267303471849117905.022195084-7384588400.7728154630317406374.51966.8273246364-2030.5942376678000094188.48273215898021.8724012764-2030.59423766782030.59423766782030.5942376678

    -10010002019.96641882932289.1046284519184978603.3481300558-7385632628.4528554630317406374.51977.455143475-2019.9664188293000094820.163297975897375.7749174129-2019.96641882932019.96641882932019.9664188293

    -5010002009.33859999072290.7422377911184939301.6740650279-7386259165.0608754630317406374.51988.0829623136-2009.3385999907000095454.738440277396732.5498013509-2009.33859999072009.33859999072009.3385999907

    010001998.71078115222291.287847477918490-7386468010.5968854630317406374.51998.7107811522-1998.7107811522000096092.202473274696092.2024732746-1998.71078115221998.71078115221998.7107811522

    5010001988.08296231362290.74223779111849-39301.6740650279-7386259165.0608754630317406374.52009.3385999907-1988.0829623136000096732.549801350995454.7384402773-1988.08296231361988.08296231361988.0829623136

    10010001977.4551434752289.10462845191849-78603.3481300558-7385632628.4528554630317406374.52019.9664188293-1977.455143475000097375.774917412994820.1632979758-1977.4551434751977.4551434751977.455143475

    15010001966.82732463642286.37267303471849-117905.022195084-7384588400.7728154630317406374.52030.5942376678-1966.8273246364000098021.872401276494188.482732158-1966.82732463641966.82732463641966.8273246364

    20010001956.19950579792282.54244210271849-157206.696260112-7383126482.0207554630317406374.52041.2220565064-1956.1995057979000098670.836918082493559.7025204631-1956.19950579791956.19950579791956.1995057979

    25010001945.57168695932277.60839478611849-196508.37032514-7381246872.1966854630317406374.52051.849875345-1945.5716869593000099322.663216745992933.8285340962-1945.57168695931945.57168695931945.5716869593

    30010001934.94386812072271.56333832011849-235810.044390168-7378949571.300654630317406374.52062.4776941836-1934.9438681207000099977.346128433892310.8667395757-1934.94386812071934.94386812071934.9438681207

    35010001924.31604928222264.39837484481849-275111.718455195-7376234579.332554630317406374.52073.1055130221-1924.31604928220000100634.88056507491690.8232005178-1924.31604928221924.31604928221924.3160492822

    40010001913.68823044362256.10283453571849-314413.392520223-7373101896.2923854630317406374.52083.7333318607-1913.68823044360000101295.26151789291073.7040794545-1913.68823044361913.68823044361913.6882304436

    45010001903.0604116052246.66419386611849-353715.066585251-7369551522.1802554630317406374.52094.3611506993-1903.0604116050000101958.48405597990459.5156396898-1903.0604116051903.0604116051903.060411605

    50010001892.43259276652236.06797749981849-393016.740650279-7365583456.996154630317406374.52104.9889695378-1892.43259276650000102624.54332488789848.2642471918-1892.43259276651892.43259276651892.4325927665

    55010001881.80477392792224.29764195351849-432318.414715307-7361197700.7399454630317406374.52115.6167883764-1881.80477392790000103293.43454524989239.9563725228-1881.80477392791881.80477392791881.8047739279

    60010001871.17695508932211.33443874961849-471620.088780335-7356394253.4117654630317406374.52126.244607215-1871.17695508930000103965.15301143188634.5985928078-1871.17695508931871.17695508931871.1769550893

    65010001860.54913625082197.1572542721849-510921.762845363-7351173115.0115654630317406374.52136.8724260535-1860.54913625080000104639.69409020888032.1975937427-1860.54913625081860.54913625081860.5491362508

    70010001849.92131741222181.74242292711849-550223.436910391-7345534285.5393554630317406374.52147.5002448921-1849.92131741220000105317.05321946587432.7601716414-1849.92131741221849.92131741221849.9213174122

    75010001839.29349857362165.06350946111849-589525.110975419-7339477764.9951254630317406374.52158.1280637307-1839.29349857360000105997.22590692486836.2932355239-1839.29349857361839.29349857361839.2934985736

    80010001828.6656797352147.09105535841849-628826.785040447-7333003553.3788854630317406374.52168.7558825692-1828.6656797350000106680.20772890186242.8038092462-1828.6656797351828.6656797351828.665679735

    85010001818.03786089652127.79228309531849-668128.459105475-7326111650.6906354630317406374.52179.3837014078-1818.03786089650000107365.99432907785652.2990336715-1818.03786089651818.03786089651818.0378608965

    90010001807.41004205792107.13075057061849-707430.133170503-7318802056.9303554630317406374.52190.0115202464-1807.41004205790000108054.58141730585064.7861688846-1807.41004205791807.41004205791807.4100420579

    95010001796.78222321932085.06594619931849-746731.807235531-7311074772.0980654630317406374.52200.639339085-1796.78222321930000108745.96476843184480.2725964497-1796.78222321931796.78222321931796.7822232193

    100010001786.15440438082061.55281280881849-786033.481300559-7302929796.1937654630317406374.52211.2671579235-1786.15440438080000109440.14022114383898.7658217124-1786.15440438081786.15440438081786.1544043808

    105010001775.52658554222036.54118544161849-825335.155365587-7294367129.2174454630317406374.52221.8949767621-1775.52658554220000110137.10367684383320.2734761471-1775.52658554221775.52658554221775.5265855422

    110010001764.89876670362009.97512422421849-864636.829430614-7285386771.169154630317406374.52232.5227956007-1764.89876670360000110836.85109853682744.8033197497-1764.89876670361764.89876670361764.8987667036

    115010001754.27094786511981.79211826061849-903938.503495642-7275988722.0487554630317406374.52243.1506144392-1754.27094786510000111539.37850974782172.363243477-1754.27094786511754.27094786511754.2709478651

    120010001743.64312902651951.92212959431849-943240.17756067-7266172981.8563954630317406374.52253.7784332778-1743.64312902650000112244.68199345581602.9612717338-1743.64312902651743.64312902651743.6431290265

    125010001733.01531018791920.28643696721849-982541.851625698-7255939550.59254630317406374.52264.4062521164-1733.01531018790000112952.7576910581036.6055649073-1733.01531018791733.01531018791733.0153101879

    130010001722.38749134941886.79622641131849-1021843.52569073-7245288428.2556154630317406374.52275.0340709549-1722.38749134940000113663.60180130880473.304421951-1722.38749134941722.38749134941722.3874913494

    135010001711.75967251081851.35085815741849-1061145.19975575-7234219614.8471954630317406374.52285.6618897935-1711.75967251080000114377.21057938979913.0662830178-1711.75967251081711.75967251081711.7596725108

    140010001701.13185367221813.83571472171849-1100446.87382078-7222733110.3667754630317406374.52296.2897086321-1701.13185367220000115093.58033585279355.8997321433-1701.13185367221701.13185367221701.1318536722

    145010001690.50403483361774.1194999211849-1139748.54788581-7210828914.8143254630317406374.52306.9175274706-1690.50403483360000115812.70743569278801.8134999808-1690.50403483361690.50403483361690.5040348336

    150010001679.87621599511732.05080756891849-1179050.22195084-7198507028.1898654630317406374.52317.5453463092-1679.87621599510000116534.5882973978250.8164665868-1679.87621599511679.87621599511679.8762159951

    155010001669.24839715651687.45370306861849-1218351.89601587-7185767450.4933854630317406374.52328.1731651478-1669.24839715650000117259.21939198977702.9176642609-1669.24839715651669.24839715651669.2483971565

    160010001640.12194668571640.12194668571849-1257653.57008089-7172610181.7248954630317406374.52338.8009839864-1658.62057831790000117986.59724218377158.1262804369-1658.62057831791658.62057831791640.1219466857

    165010001589.81130955851589.81130955851849-1296955.24414592-7159035221.8843954630317406374.52349.4288028249-1647.99275947940000118716.71842142476616.4516606294-1647.99275947941647.99275947941589.8113095585

    170010001536.22914957371536.22914957371849-1336256.91821095-7145042570.9718654630317406374.52360.0566216635-1637.36494064080000119449.57955304776077.9033114342-1637.36494064081637.36494064081536.2291495737

    175010001479.01994577491479.01994577491849-1375558.59227598-7130632228.9873254630317406374.52370.6844405021-1626.73712180220000120185.17730941475542.4909035841-1626.73712180221626.73712180221479.0199457749

    180010001417.74468787581417.74468787581849-1414860.26634101-7115804195.9307754630317406374.52381.3122593406-1616.10930296370000120923.50841106975010.2242750612-1616.10930296371616.10930296371417.7446878758

    185010001351.85058345961351.85058345961849-1454161.94040603-7100558471.802254630317406374.52391.9400781792-1605.48148412510000121664.56962591774481.1134342654-1605.48148412511605.48148412511351.8505834596

    190010001280.62484748661280.62484748661849-1493463.61447106-7084895056.6016254630317406374.52402.5678970178-1594.85366528650000122408.35776841173955.1685632396-1594.85366528651594.85366528651280.6248474866

    195010001203.12094155161203.12094155161849-1532765.28853609-7068813950.3290254630317406374.52413.1957158563-1584.2258464480000123154.8696987673432.4000209541-1584.2258464481584.2258464481203.1209415516

    200010001118.03398874991118.03398874991849-1572066.96260112-7052315152.984454630317406374.52423.8235346949-1573.59802760940000123904.10232214972912.8183466483-1573.59802760941573.59802760941118.0339887499

    205010001023.47447452291023.47447452291849-1611368.63666614-7035398664.5677754630317406374.52434.4513535335-1562.97020877080000124656.05258797872396.4342632313-1562.97020877081562.97020877081023.4744745229

    21001000916.5151389912916.51513899121849-1650670.31073117-7018064485.0791254630317406374.52445.079172372-1552.34238993220000125410.71748910971883.258680743-1552.34238993221552.3423899322916.5151389912

    21501000792.1489758877792.14897588771849-1689971.9847962-7000312614.5184654630317406374.52455.7069912106-1541.71457109370000126168.09406113371373.3026998736-1541.71457109371541.7145710937792.1489758877

    22001000640.3124237433640.31242374331849-1729273.65886123-6982143052.8857854630317406374.52466.3348100492-1531.08675225510000126928.17938165270866.5776155451-1531.08675225511531.0867522551640.3124237433

    22501000433.0127018922433.01270189221849-1768575.33292626-6963555800.1810954630317406374.52476.9626288878-1520.45893341650000127690.97056956770363.094920552-1520.45893341651520.4589334165433.0127018922

    23001000001849-1807877.00699128-6944550856.4043854630317406374.52487.5904477263-1509.8311145780000128456.46478438769862.8663092639-1509.8311145781509.8311145780

    23501000001849-1847178.68105631-6925128221.5556554630317406374.52498.2182665649-1499.20329573940000129224.65922554969365.9036813895-1499.20329573941499.20329573940

    24001000001849-1886480.35512134-6905287895.6349154630317406374.52508.8460854035-1488.57547690080000129995.55113174968872.2191458017-1488.57547690081488.57547690080

    24501000001849-1925782.02918637-6885029878.6421554630317406374.52519.473904242-1477.94765806230000130769.13778028868381.8250244248-1477.94765806231477.94765806230

    25001000001849-1965083.7032514-6864354170.5773854630317406374.52530.1017230806-1467.3198392237000131545.4164864367894.7338561834-1467.31983922371467.31983922370

    &L&F&C&A&R&D

    &LERM 99-5&CPage &P&Rrab

    Allen Bernstorf:Changed Equation denominator from 5 to 4 - rev. 2

    Loading 4

    Longitudinal Load - Graph 11500Load Att.Trans.WorkingLesser of

    LowPointDeflectionTestTestMomentVert 1 and

    Rod's Radius1.25TranverseVerticalSummaryConstantabcb^2-4acroot1root2root1root2RemainderVert 2

    Vertical1ZVertical2

    -25000

    Moment of Inertia1.9174743652-250015000018491965083.7032514-4448681402.5734836764001614217.71108.233868832-2171.0157526888000073803.1045376097125962.389280818-2171.01575268882171.01575268880

    Section Length43-245015000018491925782.02918637-4469357110.6382536764001614217.71118.8616876705-2160.3879338503000074143.1695893348125276.668652328-2160.38793385032160.38793385030

    Upsweep Angle0.2094393333-240015000018491886480.35512134-4489615127.6310136764001614217.71129.4895065091-2149.7601150117000074487.3504577467124593.996903639-2149.76011501172149.76011501170

    Upsweep9.1399242012-235015000018491847178.68105631-4509455453.5517536764001614217.71140.1173253477-2139.1322961732000074835.6302189229123914.380051223-2139.13229617322139.13229617320

    Cap Attachment Loading Limit2500-230015000018491807877.00699128-4528878088.4004836764001614217.71150.7451441862-2128.5044773346000075187.9920772954123237.824182246-2128.50447733462128.50447733460

    Compression Limit12282.1080350872-225015000018491768575.33292626-4547883032.1771936764001614217.71161.3729630248-2117.876658496000075544.4193668641122564.335455417-2117.8766584962117.8766584960

    Transverse Compression Load Limit-2500-220015000018491729273.65886123-4566470284.8818836764001614217.71172.0007818634-2107.2488396574000075904.8955523106121893.920101849-2107.24883965742107.24883965740

    Transverse Tension Load Limit2500-215015000018491689971.9847962-4584639846.5145636764001614217.71182.6286007019-2096.6210208189000076269.4042300191121226.58442593-2096.62102081892096.62102081890

    Overall Transverse Range5000-210015000018491650670.31073117-4602391717.0752236764001614217.71193.2564195405-2085.9932019803000076637.9291290036120562.334806199-2085.99320198032085.99320198030

    -205015000018491611368.63666614-4619725896.5638736764001614217.71203.8842383791-2075.3653831417000077010.4541117468119901.177696232-2075.36538314172075.36538314170

    -200015000018491572066.96260112-4636642384.980536764001614217.71214.5120572176-2064.7375643032000077386.9631749519119243.119625534-2064.73756430322064.73756430320

    -19501500444.4097208658444.409720865818491532765.28853609-4653141182.3251236764001614217.71225.1398760562-2054.1097454646000077767.4404502109118588.167200437-2054.10974546462054.1097454646444.4097208658

    Post's RTL2500-19001500624.4997998398624.499799839818491493463.61447106-4669222288.5977236764001614217.71235.7676948948-2043.481926626000078151.870204591117936.327105012-2043.4819266262043.481926626624.4997998398

    Post's Moment Rating96535-18501500759.9342076785759.934207678518491454161.94040603-4684885703.798336764001614217.71246.3955137334-2032.8541077875000078540.2368411429117287.606101981-2032.85410778752032.8541077875759.9342076785

    Post's Cantilever Working Load Rating2245-18001500871.7797887081871.779788708118491414860.26634101-4700131427.9268736764001614217.71257.0233325719-2022.2262889489000078932.5248993329116642.01103364-2022.22628894892022.2262889489871.7797887081

    Longitudinal Load1500-17501500968.2458365519968.245836551918491375558.59227598-4714959460.9834336764001614217.71267.6511514105-2011.5984701103000079328.7190554008115999.548822788-2011.59847011032011.5984701103968.2458365519

    Deflection Constant0.00230358-170015001053.56537528531053.565375285318491336256.91821095-4729369802.9679636764001614217.71278.2789702491-2000.9706512718000079728.8041226477115360.226473666-2000.97065127182000.97065127181053.5653752853

    Deflection due to Longitudinal3.4553699666-165015001130.26545554571130.265455545718491296955.24414592-4743362453.8804936764001614217.71288.9067890876-1990.3428324332000080132.7650516548114724.051072898-1990.34283243321990.34283243321130.2654555457

    K Factor for Buckling4-160015001200120018491257653.57008089-4756937413.7209936764001614217.71299.5346079262-1979.7150135946000080540.5869304358114091.029790441-1979.71501359461979.71501359461200

    -155015001263.92246597641263.922465976418491218351.89601587-4770094682.4894836764001614217.71310.1624267648-1969.087194756000080952.2549845264113461.169880546-1969.0871947561969.0871947561263.9224659764

    -150015001322.87565553231322.875655532318491179050.22195084-4782834260.1859636764001614217.71320.7902456033-1958.4593759175000081367.7545770111112834.478682715-1958.45937591751958.45937591751322.8756555323

    Calculations for longitudinal load561-145015001377.49773139561377.497731395618491139748.54788581-4795156146.8104236764001614217.71331.4180644419-1947.8315570789000081787.0712084924112210.963622678-1947.83155707891947.83155707891377.4977313956

    Logic500-140015001428.28568570861428.285685708618491100446.87382078-4807060342.3628736764001614217.71342.0458832805-1937.2037382403000082210.1905170016111590.632213361-1937.20373824031937.20373824031428.2856857086

    Loading 10-135015001475.63545633741475.635456337418491061145.19975575-4818546846.8432936764001614217.71352.673702119-1926.5759194018000082637.0982778567110973.49205587