Frames and Distributed Loads - Assignment PDF

Preview

Summary

Frames and Distributed Loads - Assignment...

Description

OREGONSTATEUNIVERSITY CollegeofEngineering

ENGR211 Instructor:K.Martin

ENGR211:Statics Frames&Machines,DistributedLoads Completeeachproblemonengineeringpaper.YoudonotneedtousetheGiven/Find/Solutionformat,but yoursolutionsmustbefullydevelopedandpresentedprofessionally.Showallyourwork,includingequations used,andpertinentsketches.Finalanswersshallbeboxedorcircled,mustincludecorrectunits,andshow concernforsignificantdigits(usually3or4).Yourworkistobecompletedandsubmittedindividually.

Problem1:Youwanttohoisttheengineasshownbelow.Theenginehasaweightof 2250lbs.ThehydraulicjackatHhasacapacityof2.5tons.ThepinatDcanonly carry5kips,tensionorcompression.Canyoulifttheenginetotheposition shown?Note:pointHisusedonlytoidentifythejack,considermemberBFasa singlemember.

 a. Howmanypoundsareinaton?Hint:Seethetopofpage9inyourtextbook b. Whichmemberforcesdoyouneedtofindinordertoanswerthequestion(thereare twoofthem)?



c. Identifythetwo‐forcemembersintheframe(ignorethechain) 

Page1of4

OREGONSTATEUNIVERSITY CollegeofEngineering

ENGR211 Instructor:K.Martin

d. DrawFBD’sofmembersEGandCE. BeawarethatjointCshouldhavetwounknownforcesonyourFBD.Itistruethereisa rolleratC,butthereisalsoanothermemberthatattachesthere(memberAC). Therefore,jointC“feels”morethanjustaverticalcomponentofforce.ShowCxandCy onyourFBD. Also,resolveeachtwo‐forcememberintooneunknown,therebyreducingthenumberof unknowns(andclutter)inyoursystem. e. Solveforthetwodesiredmemberforces.Youcandothiswithasfewasthree equilibriumequations.LookatyourFBD’sandseeifyoucanstrategizehowtodoso. It’sokayifyouusemorethanthreeequations.Thepointistoteachyouthatyou shouldn’timpulsivelywritelotsofequationsjustbecauseyoucan.Comeupwitha planfirst,thensolvefortherequiredunknowns.Expressanswersusing3significant figuresandunitsofkips. f. Canyouhoisttheengineasshown?Youmustchecktwocriteria–thejackcapacityand thepincapacity.Showthesechecksasinequalities. g. WhataretheexternalreactionsatAandCforthepositionshown?Hint:Considerthe overallframeasawholetoanswerthisquestion.Onlyexternalforcesareshownonthe overallFBD. 

Whatdoesthismeanforthehoist?



Isthissafe?



Whatwouldyoudotomakethedesignbetter?

h. Ifyouweregiventheweightsofallthemembersandyouassumedtheweightactedat themidpointofeachpiece,wouldwehaveanytwo‐forcemembers(again,ignorethe chain)?



Page2of4

OREGONSTATEUNIVERSITY CollegeofEngineering

ENGR211 Instructor:K.Martin

Problem2:Threecolumnsaresupportedbyafooting.Duetothemagnitudeofthecolumn loadsandthespacingofthecolumns,thesoilpressurebeneaththefootinghasa trapezoidalshapeasshown.Thegeotechnicalengineer(i.e.soilexpert)has stipulatedthatw1shouldequal25kN/mandw2shouldbe10kN/minordernot toexceedthebearingcapacityofthesoil.Whatthenistheallowable magnitudeofthethirdcolumnload,F3,anditslocation,x,fromthesecond column? Don’tdoanythingwiththe“kern”forthisproblem;justfollowthestepsgivenbelow.

 Given: w1=25kN/m



Find: F3(kN)

w2=10kN/m







x(m) 

a. DrawaFBDofthesystem  

Breakthetrapezoidaldistributedloadintoarectangleandatriangle Showtheresultantforcesforthetwodistributedloadshapes

b. UseFy=0tosolvefortheunknownforce,F 3 c. UseM A=0tosolvefortheunknowndistance,x





Page3of4

OREGONSTATEUNIVERSITY CollegeofEngineering

ENGR211 Instructor:K.Martin

Problem3:WhatistheforceinmemberBDoftheframe?ThereisapinatEandaroller supportatA. 

Figurenotnecessarily drawntoscale.

  Hints: 

Withanyframeproblem,trytoidentifythetwo‐forcemembersfirst.Thereisoneinthis frame.



Aswithallframeproblems,disassembletheframeanddrawFBD’softhemain components.



Youneedtosolveforatleastoneexternalreactiontoavoidsolvingasystemof simultaneousequations.UseaFBDoftheoverallframewithappliedloadstosolveforone externalreactionforce.



YoudoNOTneedtofindthecentroidoftheentiredistributedloadshape.Instead,breakit upintotwopieces–arectangleandatriangle.Thenyouonlyneedtofindtheresultant force(area)ofeachpieceandapplytheresultantthroughthecentroidofthatpiece. Youwouldgetthesameanswerifyoulocatedthecentroidoftheentiredistributedload shape,butitismoretimeconsumingtosolvetheproblemthisway.  Page4of4...