Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

292 CHAPTER 8 Columns Fig. P.8.14 Fig. P.8.15 P.8.16 Apin-endedcolumnoflength1.0mhasthecrosssectionshowninFig.P.8.16.Iftheendsof ...

CHAPTER 9 Thin Plates................................................................................ We shall see in Chapter 11 ...

294 CHAPTER 9 Thin Plates Fig.9.1 Buckling of a thin flat plate. andthatthesearesmallcomparedwiththethicknessoftheplate.Theseres ...

9.1 Buckling of Thin Plates 295 andforanontrivialsolution Nx,CR=π^2 a^2 D 1 m^2 ( m^2 a^2 + n^2 b^2 ) 2 (9.3) Exactlythesameresu ...

296 CHAPTER 9 Thin Plates Fig.9.2 Buckling coefficientkfor simply supported plates. In general, the critical stress for a unifor ...

9.2 Inelastic Buckling of Plates 297 Fig.9.3 (a) Buckling coefficients for flat plates in compression; (b) buckling coefficients ...

298 CHAPTER 9 Thin Plates whereEandνareelasticvaluesofYoung’smodulusandPoisson’sratio.Inthelinearlyelasticregion, η=1, which mea ...

9.4 Local Instability 299 9.4 LocalInstability.................................................................................. ...

300 CHAPTER 9 Thin Plates 9.5 InstabilityofStiffenedPanels...................................................................... ...

9.5 Instability of Stiffened Panels 301 actingasacolumnisle,thentheEulercriticalstressis σCR,E= π^2 E (le/r)^2 asinEq.(8.8).Inad ...

302 CHAPTER 9 Thin Plates 9.6 FailureStressinPlatesandStiffenedPanels...................................................... Thep ...

9.6 Failure Stress in Plates and Stiffened Panels 303 Gerard[Refs.9–12]extendedtheprecedingmethodtothepredictionoflocalfailurest ...

304 CHAPTER 9 Thin Plates Fig.9.7 Determination ofgfor two types of stiffener/skin combinations. numberofequivalentflangesofthes ...

9.7Tension Field Beams 305 Fig.9.8 Diagonal tension field beam. 9.7.1 Complete Diagonal Tension ThetheorypresentedhereisduetoWag ...

306 CHAPTER 9 Thin Plates whichgives σz=σtcos^2 α or,substitutingforσtfromEq.(9.15), σz= τ tanα (9.17) or,forthisparticularbeam, ...

9.7Tension Field Beams 307 Now,resolvingforceshorizontally, FB−FT+σztd= 0 whichgives,onsubstitutingforσzandFTfromEqs.(9.18)and(9 ...

308 CHAPTER 9 Thin Plates compressiveloadPinastiffenerisgivenby P=σytb whichbecomes,fromEq.(9.22), P= Wb d tanα (9.23) Iftheload ...

9.7Tension Field Beams 309 45 ◦,usuallyoftheorderof40◦and,inthetypeofbeamcommontoaircraftstructures,rarelybelow 38 ◦. For beams ...

310 CHAPTER 9 Thin Plates Fig.9.12 Beam of Example 9.1. thatis, FT=17.7kN Hence,thedirectstressinthetopflangeproducedbytheextern ...

9.7Tension Field Beams 311 InEqs.(9.28)and(9.29),itisimplicitlyassumedthatastiffenerisfullyeffectiveinresistingaxial load. This ...