304 CHAPTER 9 Thin Plates
Fig.9.7
Determination ofgfor two types of stiffener/skin combinations.
numberofequivalentflangesoftheskinareincluded.Acuttotheleftofastiffenerisnotcounted,since
itisregardedasbelongingtothestiffenertotheleftofthatcut.Thecalculationofgfortwotypesof
skin/stiffenercombinationisillustratedinFig.9.7.Equation(9.13)isapplicabletoeithermonolithicor
built-uppanelswhen,inthelattercase,interrivetbucklingandwrinklingstressesaregreaterthanthe
localfailurestress.
ThevaluesoffailurestressgivenbyEqs.(9.11),(9.12),and(9.13)areassociatedwithlocalorsec-
ondaryinstabilitymodes.Consequently,theyapplywhenle/r≤20.Intheintermediaterangebetween
thelocalandprimarymodes,failureoccursthroughacombinationofboth.Atthemoment,thereisno
theorythatpredictssatisfactorilyfailureinthisrange,andwerelyontestdataandempiricalmethods.
The NACA (now NASA) have produced direct reading charts for the failure of “top hat,” Z-, and
Y-sectionstiffenedpanels;abibliographyoftheresultsisgivenbyGerard[Ref.10].
It must be remembered that research into methods of predicting the instability and postbuckling
strength of the thin-walled types of structure associated with aircraft construction is a continuous
process. Modern developments include the use of the computer-based finite element technique (see
Chapter6)andthestudyofthesensitivityofthin-walledstructurestoimperfectionsproducedduring
fabrication;muchusefulinformationandanextensivebibliographyarecontainedinthestudyofMurray
[Ref.2].
9.7 TensionFieldBeams................................................................................
Thesparsofaircraftwingsusuallycompriseanupperandalowerflangeconnectedbythin,stiffened
webs. Thesewebsareoftenofsuchathicknessthattheybuckleundershearstressesatafractionof
theirultimateload.TheformofthebuckleisshowninFig.9.8(a),wherethewebofthebeambuckles
undertheactionofinternaldiagonalcompressivestressesproducedbyshear,leavingawrinkledweb
capableofsupportingdiagonaltensiononlyinadirectionperpendiculartothatofthebuckle;thebeam
isthensaidtobeacompletetensionfieldbeam.