Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 289

Fig. P.8.6

P.8.7 Therelationbetweenstressσandstrainεincompressionforacertainmaterialis

10.5× 106 ε=σ+ 21000

( σ

49000

) 16

Assumingthetangentmodulusequationtobevalidforauniformstrutofthismaterial,plotthegraphofσbagainst
l/r,whereσbistheflexuralbucklingstress,ltheequivalentpin-endedlength,andrtheleastradiusofgyrationof
thecrosssection.
Estimatetheflexuralbucklingloadforatubularstrutofthismaterial,of1.5unitsoutsidediameterand0.08
unitswallthicknesswitheffectivelength20units.

Ans. 14 454forceunits.

P.8.8 ArectangularportalframeABCDisrigidlyfixedtoafoundationatAandDandissubjectedtoacom-
pressionloadPappliedateachendofthehorizontalmemberBC(seeFig.P.8.8).Ifthemembersallhavethesame
bendingstiffnessEI,showthatthebucklingloadsformodeswhicharesymmetricalabouttheverticalcenterline
aregivenbythetranscendentalequation

λa

2

=−

1

2

(a

b

)

tan

(

λa

2

)

where

λ^2 =P/EI

Fig. P.8.8

P.8.9 Acompressionmember(Fig.P.8.9)ismadeofcircularsectiontube,diameterd,thicknesst.Themember
isnotperfectlystraightwhenunloaded,havingaslightlybowedshapewhichmayberepresentedbytheexpression

v=δsin

(πz

l

)

ShowthatwhentheloadPisapplied,themaximumstressinthemembercanbeexpressedas

σmax=

P

πdt

[

1 +

1

1 −α

4 δ

d

]