Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 163

P.5.12 Intheplanepin-jointedframeworkshowninFig.P.5.12,bars25,35,15,and45arelinearlyelasticwith
modulusofelasticityE.Theremainingthreebarsobeyanonlinearelasticstress–strainlawgivenby

ε=

τ

E

[

1 +

(

τ

τ 0

)n]

whereτisthestresscorrespondingtostrainε.Bars15,45,and23eachhaveacross-sectionalareaA,andeachof
theremainderhasanareaofA/

√
3.Thelengthofmember12isequaltothelengthofmember34= 2 L.
IfaverticalloadP 0 isappliedatjoint5asshown,showthattheforceinthemember23,thatis,F 23 ,isgiven
bytheequation

αnxn+^1 +3.5x+0.8= 0

Fig. P.5.12

where

x=F 23 /P 0 and α=P 0 /Aτ 0

P.5.13 Figure P.5.13 shows a plan view of two beams, AB 9150mm long and DE 6100mm long. The simply
supportedbeamABcarriesaverticalloadof100000NappliedatF,adistanceone-thirdofthespanfromB.This
beamissupportedatContheencastrébeamDE.Thebeamsareofuniformcrosssectionandhavethesamesecond
momentofarea83.5× 106 mm^4 .E=200000N/mm^2 .CalculatethedeflectionofC.

Ans. 5.6mm

Fig. P.5.13