Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

112 CHAPTER 5 Energy Methods Fig.5.1 (a) Strain energy of a member subjected to simple tension; (b) load–deflection curve for a ...

5.2 The Principle of the Stationary Value 113 Fig.5.2 Load–deflection curve for a linearly elastic member. Hence, dU dy =P dU dP ...

114 CHAPTER 5 Energy Methods Thefirsttermintheprecedingexpressionisthenegativevirtualworkdonebytheparticlesintheelastic body,whi ...

5.3Application to Deflection Problems 115 Fig.5.3 Determination of the deflection of a point on a framework by the method of com ...

116 CHAPTER 5 Energy Methods We note that the support reactions do not appear in Eq. (5.9). This convenient absence derives from ...

5.3Application to Deflection Problems 117 Fig.5.4 (a) Actual loading of framework; (b) determination of vertical deflection of B ...

118 CHAPTER 5 Energy Methods andthehorizontalmovementofDis (^) D,h= 880 × 106 1800 × 200000 =2.44mm whichagreewiththevirtualwork ...

5.3Application to Deflection Problems 119 mechanicsofthesolutionarethesameineithercase.WechoosethereforealinearM–θrelationshipas ...

120 CHAPTER 5 Energy Methods where the symbols take their previous meanings and is the vertical deflection of any point on the b ...

5.3Application to Deflection Problems 121 Fig.5.7 Deflection of a simply supported beam by the method of complementary energy. a ...

122 CHAPTER 5 Energy Methods FromCtoD, M= ( 1 4 PB,f+ 1 2 PC,f+ wL 2 ) (L−z)− w 2 (L−z)^2 sothat ∂M ∂PB,f = 1 4 (L−z) ∂M ∂PC,f = ...

5.4Application to the Solution of Statically Indeterminate Systems 123 Fig.5.8 Analysis of a statically indeterminate framework ...

124 CHAPTER 5 Energy Methods Table 5.2 ① ② ③ ④ ⑤ Member Length F ∂F/∂R FL∂F/∂R AB L −R/ √ 2 − 1 / √ 2 RL/ 2 BC L −R/√ 2 − 1 /√ 2 ...

5.4Application to the Solution of Statically Indeterminate Systems 125 Example 5.3 Calculatetheloadsinthemembersofthesinglyredun ...

126 CHAPTER 5 Energy Methods Fig.5.10 Framework of Example 5.4. Example 5.4 Aplane,pin-jointedframeworkconsistsofsixbarsforminga ...

5.4Application to the Solution of Statically Indeterminate Systems 127 Table 5.4Tension positive ① ② ③ ④ ⑤ ⑥ Member L(mm) F(N) ∂ ...

128 CHAPTER 5 Energy Methods whereRjand (^) jarethereactionandknowndeflection(atleastintermsofRj)ofthejthsupportpoint inatotalof ...

5.4Application to the Solution of Statically Indeterminate Systems 129 Weobservethatifthebeamwereonlycapableofsupportingdirectlo ...

130 CHAPTER 5 Energy Methods betweenFandBitis M= P 4 (L−z)− √ 3 2 Rz hence ∂M ∂R =− √ 3 2 z andbetweenBandCthebendingmomentis M= ...

5.4Application to the Solution of Statically Indeterminate Systems 131 Atwo-dimensionalringhasredundanciesofdirectload,bendingmo ...