pylon vector solution.pdf

7/27/2015 pylonvectorsolution

http://designtechnologyinstem.x10.mx/02%20structures/StructuresDesignProblems/PylonProblem/pylonsolutions/pylonvectorsolution.html 1/5

FollowUpSolutionstoPylonProblem

Thefollowingspacediagramsandvectordiagramsoffersomealternativesolutionstothisdesignproblem.DesignA

Becausetheframeworkandtheloadingarebothsymmetrical,itispossibletoassumethatthesupportreactionsare10Neach.Theanglesbetweenthemembersareeitherat90,60or30degrees,whichenablestouseofstandarddrawingboardtriangles(setsquares).

Thevectordiagramcanbedrawnasfollows.(refertostepladdersforanexplanationofBowsNotationmethodofvectoranalysis)

Drawatobbtocctod,dtoa(useasuitablescalesay5mm(or2/10thofaninch)represents1Newton)

LookingatthelefthandendofthespacediagramAandBhavebeenestablishedasaandbonthevectordiagram,HisbetweenAandBsothevectorpositionofhcanbedeterminedbytriangulation.HencedrawalinefrombparalleltoHBtointersectwithalinedrawnfromaparalleltoAH.

Thepositionofecanbedeterminedinthesamewayash(aeparalleltoAEanddeparalleltoDE)

DeterminefbydrawingfromatofparalleltoAFandintersectwithaline,fromeparalleltoEF.

Thepositionofgcanbedeterminedinthesamewayasf.

fandgarebothatthesamelocationwhichindicatesthatthememberFGistechnicallyredundant,howeverastheframeworkisassumedtobepinjointed,FGisrequiredtomaintainrigidityintheframework.

Thenatureandmagnitudeforeachmembercanbemeasuredfromthevectordiagram.

MemberNatureofreactionMagnitudeAEtension20NAFtension17.32NAHtension20NBHcompression17.32NCGcompression17.32NDEcompression17.32NEFcompression20NFGredundant0GHcompression20N

7/27/2015 pylonvectorsolution

http://designtechnologyinstem.x10.mx/02%20structures/StructuresDesignProblems/PylonProblem/pylonsolutions/pylonvectorsolution.html 2/5

ThevectordiagramforDesignBcanbedrawnisasimilarmanner.ThereisanobviousdifferenceinEFandGHastheyareredundantinthissolution.FGremainsredundantbutallthreeredundantmemberswillberequiredtomaintainrigidity.

DesignB

Thenatureandmagnitudeofthereactionsinmembersareshownbelow.

MemberNatureofreactionMagnitudeAEtension17.32NAFtension17.32NAHtension17.32NBHcompression20NCGcompression17.32NDEcompression20NEFredundant0FGredundant0GHredundant0

Itisalsopossibletousetrigonometrytoobtainaccuratevalues..

Inbothvectordiagramsabis5Nsoahandbhcanbedeterminedasfollows

x=10x=10Sin30Tan30=20N=17.32N

IfthearmsareextendedandtheanglesbetweenthearmsarereducedasintheDesignCtheinternalreactionsinmembersareincreased,ascanbeseeninthediagramsbelow.

ThevectordiagramfordesignCisdrawninasimilarmanner.

WhenthisdesigniscomparedwithdesignAyouwillseethatthemagnitudeoftheforcesinseveralmembersisincreasedbecauseofthechangeinanglebetweenthemembers.

DesignC

7/27/2015 pylonvectorsolution

http://designtechnologyinstem.x10.mx/02%20structures/StructuresDesignProblems/PylonProblem/pylonsolutions/pylonvectorsolution.html 3/5

Athreedimensionaldesignsolution

Alltheaboveanalysisassumesthatthestructureispurelytwodimensional,whichofcourseisnotthecase.

Belowisasketchofapossible3dimensionalsolutiontotheproblem.Thisrequiresadditionalmemberstobeanalysed,whicharedrawninathickerline.

Astherearenow4verticalsupportpositionsthereactionateachisnowonly5Newtons

Threeseparateviewsareshownbelowofthe3dimensionaldesign.Thealtered/additionalmembersaredrawninathickerline.

7/27/2015 pylonvectorsolution

http://designtechnologyinstem.x10.mx/02%20structures/StructuresDesignProblems/PylonProblem/pylonsolutions/pylonvectorsolution.html 4/5

Todeterminetheforcesinthenewhorizontalmembers,usetheprojectionviewfromP.Theoriginaltwodimensionalvectordiagramsolutiongaveacompressionforceof17.32Ninthesinglehorizontalmember.Thisforceof17.32NewtonsisnowopposedbytwonewmembersshowninthespacediagramKLJ.

Fromthespacediagram,drawthevectordiagramklj,fromwhichthevaluesofljandjkare8.94N,bothinCompression.

Thevaluesforthetwomembersontheoppositesideofthepylonwithhavethesamenatureandmagnitude.

TodeterminetheforcesinthethreenewmembersformingthetrianglesatthetopofthetowerconsidertheviewfromEEanddrawthespaceandvectordiagrams..

Remembertheanglesbetweenthetriangleframemembersare60degrees.

Thenatureandmagnitudeofthereactionsinmembersareshownbelow.

7/27/2015 pylonvectorsolution

http://designtechnologyinstem.x10.mx/02%20structures/StructuresDesignProblems/PylonProblem/pylonsolutions/pylonvectorsolution.html 5/5

MemberNatureofreactionMagnitudeNQcompression5.77NPQtension2.88N``MQcompression5.77N

Alloftheabovedrawingshavebeencompletedusingacomputerdrawingprogram.Theaccuracyofthevectorvalueshavebeenconfirmedbytrigonometricalcalculations.

LongSlendermembers

Longslendermembersarelikelytobuckleundercompressionbeforethemembersundertensionfail.Itisadvantageoustobracetheframewithdiagonalsatanoptimalangleof45degrees.Asshownintheillustrationsshownbelow.

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