Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

152 CHAPTER 5 Energy Methods Fig.5.26 Linearly elastic body subjected to loadsP 1 ,P 2 ,P 3 ,...,Pn. thecompletesystemofloadsare ...

5.10 The Reciprocal Theorem 153 P 2 followedbyP 1 ,wehave U 2 = P 2 2 (a 22 P 2 )+ P 1 2 (a 11 P 1 )+P 2 (a 21 P 1 ) (5.27) Byth ...

154 CHAPTER 5 Energy Methods Fig.5.27 (a) Given deflected shape of propped cantilever; (b) determination of the deflection of C. ...

5.10 The Reciprocal Theorem 155 Fig.5.28 Model analysis of a fixed beam. or θA(c),2= W M δ 1 (ii) whereθA(c),2is the rotation at ...

156 CHAPTER 5 Energy Methods 5.11 TemperatureEffects............................................................................ ...

5.11 Temperature Effects 157 Fig.5.31 (a) Linear temperature gradient applied to beam element; (b) bending of beam element due t ...

158 CHAPTER 5 Energy Methods Fig.5.32 Beam of Example 5.14. Example 5.14 Determine the deflection of the tip of the cantilever i ...

Problems 159 Fig. P.5.1 P.5.2 Arigidtriangularplateissuspendedfromahorizontalplanebythreeverticalwiresattachedtoitscorners. Thew ...

160 CHAPTER 5 Energy Methods (a) Deriveaformulaforthecentraldeflectionofthebeam,duetoP,whensimplysupportedateachendofthe span. ( ...

Problems 161 Fig. P.5.8 Under some system of loading, member 14 carries a tensile stress of 0.7N/mm^2. Calculate the change in t ...

162 CHAPTER 5 Energy Methods P.5.10 TheplaneframeABCDofFig.P.5.10consistsofthreestraightmemberswithrigidjointsatBandC,freely hin ...

Problems 163 P.5.12 Intheplanepin-jointedframeworkshowninFig.P.5.12,bars25,35,15,and45arelinearlyelasticwith modulusofelasticity ...

164 CHAPTER 5 Energy Methods P.5.14 TheplanestructureshowninFig.P.5.14consistsofauniformcontinuousbeamABCpinnedtoafixture atAand ...

Problems 165 Fig. P.5.16 Takingintoaccountonlystrainsduetobending,calculatethedistributionofbendingmomentaroundtheframe intermso ...

166 CHAPTER 5 Energy Methods TheframeisloadedinitsownplanebyasystemofpointloadsPwhicharebalancedbyaconstantshearflowq aroundtheo ...

Problems 167 P.5.21 FigureP.5.21showstwocantilevers,theendofonebeingverticallyabovetheotherandconnectedtoitby aspringAB.Initiall ...

168 CHAPTER 5 Energy Methods Fig. P.5.24 giventhat (a) thetemperaturedistributionis θ=θ 0 cos2ψ for−π/ 4 <ψ<π/ 4 θ=0 for−π ...

CHAPTER 6 Matrix Methods........................................................................... Actualaircraftstructurescons ...

170 CHAPTER 6 Matrix Methods Amoredifficulttypeofstructuretoidealizeisthecontinuumstructure;inthiscategoryaredams, plates,shells ...

6.2 Stiffness Matrix for an Elastic Spring 171 where[K]isasymmetricmatrixoftheform [K]= ⎡ ⎢ ⎢ ⎣ k 11 k 12 ··· k 1 n k 21 k 22 ·· ...