Download - Insulators 101 Panel Final A
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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
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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
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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.
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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?
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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
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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
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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
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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.
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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
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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)
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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
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Types of Insulators Distribution
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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
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Types of Insulators Transmission
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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
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Types of Insulators Substation
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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
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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
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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)
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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
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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.
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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.
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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)
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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!!!
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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
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497.49371855330000
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2244.99443206442188.60686282392009.97512422421670.3293088491019.8039027186
22452213.02959763312036.54118544161702.20445305491071.2142642814
22452236.06797749982061.55281280881732.05080756891118.0339887499
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224522452107.13075057061786.05710994921118.287333806
224522452127.79228309531810.38669902321107.6595149674
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224522452158.12806373071799.04209333891086.4038772903
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22452217.9140936922030.59423766781671.5082672761958.8700512275
22452207.28627485342019.96641882931660.8804484376948.2422323889
22452196.65845601492009.33859999071650.252629599937.6144135503
22452186.03063717631998.71078115221639.6248107604926.9865947118
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2202.3647097642143.5193618221956.19950579791597.1135354061884.4753193575
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2170.23645259192111.63590530631924.31604928221565.2300788904852.5918628418
2159.50047379822101.00808646781913.68823044361554.6022600519841.9640440032
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2073.19594579992015.98553575921828.6656797351469.5797093433756.9414932947
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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
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497.49371855330000
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&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
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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
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-1505002217.9140936922444.89263567951849117905.022195084-8833992061.5751565350106881668.62154.1471806606-2217.914093692000094337.306994993198520.9531065132-2217.9140936922217.9140936922217.914093692
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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