170_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 170_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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164 CHAPTER 2 Axially Loaded Members Solution 2.5-16 With gap s closed due to ± T, structure is one-degree statically-indeterminate; select internal force (Q) at juncture of bar & spring as the redundant; use superpo- sition of two released structures in the solution ² rel1 ³ relative displ. between end of bar at C & end of spring due to ± T rel1 ³ ´ ± T µ (L 1 L 2 ) rel1 is greater than gap length s rel2 ³ relative displ. between ends of bar & spring due to pair of forces Q, one on end of bar at C & the other on end of spring d rel2 ³ Q a L 1 EA 1 + L 2 E A 2 + 1 k 3 b d rel2 ³ Q a L 1 E A 1 + L 2 E A 2 b + Q k 3 compatibility: rel1 rel2 ³ s rel2 ³ s · rel1 rel2 ³ s · ± T(L 1 L 2 ) (a) R EACTIONS AT A & D statics: R A ³· QR D ³ Q R D R A ; ; R A ³ · s + a ¢ T 1 L 1 + L 2 2 L 1 E A 1 + L 2 E A 2 + 1 k 3 [ s · a ¢ T 1 L 1 + L 2 2 ] Q ³ E A 1 A 2 k 3 L 1 A 2 k 3 + L 2 A 1 k 3 + EA 1 A 2 Q ³ s · a ¢ T 1 L 1 + L 2 2 L 1 E A 1 + L 2 E A 2 + 1 k 3 (c) max. shear stress in pipe 1 or 2 when either P 1 or P 2 is applied ¸
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