164CHAPTER 2Axially Loaded MembersSolution 2.5-16With gap s closed due to ±T, structure is one-degreestatically-indeterminate; select internal force (Q) atjuncture of bar & spring as the redundant; use superpo-sition of two released structures in the solution²rel1³relative displ. between end of bar at C & end ofspring due to ±Trel1³´±Tµ(L1¶L2)rel1is greater than gaplength srel2³relative displ. between ends of bar & spring dueto pair of forces Q, one on end of bar at C &the other on end of springdrel2³Q aL1EA1+L2E A2+1k3bdrel2³Q aL1E A1+L2E A2b+Qk3compatibility:rel1¶rel2³srel2³s·rel1rel2³s·±T(L1¶L2)(a) REACTIONS ATA & Dstatics:RA³·QRD³QRDRA;;RA³·s+a¢T1L1+L22L1E A1+L2E A2+1k3[ s·a¢T1L1+L22]Q³E A1A2 k3L1A2 k3+L2A1k3+EA1A2Q³s·a¢T1L1+L22L1E A1+L2E A2+1k3(c) max. shear stress in pipe 1 or 2 when either P1or P2is applied ¸
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