322 CHAPTER 9 Thin Plates
Ans. 613.8N/mm,844.7N/mm.Fig. P.9.4P.9.5 Asimplysupportedbeamhasaspanof2.4mandcarriesacentralconcentratedloadof10kN.Theflanges
of the beam each have a cross-sectional area of 300mm^2 , while that of the vertical web stiffeners is 280mm^2.
Ifthedepthofthebeam,measuredbetweenthecentroidsofareaoftheflanges,is350mmandthestiffenersare
symmetrically arranged about the web and spaced at 300mm intervals, determine the maximum axial load in a
flangeandthecompressiveloadinastiffener.
Itmaybeassumedthatthebeamweb,ofthickness1.5mm,iscapableofresistingdiagonaltensiononly.
Ans. 19.9kN,3.9kN.
P.9.6 Thesparofanaircraftistobedesignedasanincompletediagonaltensionbeam,theflangesbeingparallel.
Thestiffenerspacingwillbe250mm,theeffectivedepthofwebwillbe750mm,andthedepthbetweenweb-to-
flangeattachmentsis725mm.
Thesparistocarryanultimateshearforceof100000N.Themaximumpermissibleshearstressis165N/mm^2 ,
butitisalsorequiredthattheshearstressshouldnotexceed15timesthecriticalshearstressforthewebpanel.
Assumingαtobe40◦andusingthefollowingrelationships:
(i) Selectthesmallestsuitablewebthicknessfromthefollowingrangeofstandardthicknesses.(TakeYoung’s
modulusEas70 000N/mm^2 .)
0.7mm,0.9mm,1.2mm,1.6mm(ii) Calculate the stiffener end load and the secondary bending moment in the flanges (assume stiffeners to be
symmetricalabouttheweb).
Theshearstressbucklingcoefficientforthewebmaybecalculatedfromtheexpression
K=7.70[1+0.75(b/d)^2 ]banddhavingtheirusualsignificance.
Therelationshipbetweenthediagonaltensionfactorandthebucklingstressratiois
τ/τCR 579111315
k 0.37 0.40 0.42 0.48 0.51 0.53Note thatαis the angle of diagonal tension measured from the spanwise axis of the beam, as in the usual
notation.
Ans. 1.2mm,130AS/( 1 +0.0113AS),238910Nmm.P.9.7 The main compressive wing structure of an aircraft consists of stringers, having the section shown in
Fig.P.9.7(b),bondedtoathinskin(Fig.P.9.7(a)).FindsuitablevaluesforthestringerspacingbandribspacingL