180_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

180_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 174 3:00 PM Page 174 CHAPTER 2 Axially Loaded Members Solution 2.5-23 solve for redundant Q The figure shows a section through the tube, cap and spring Q d + ¢ T ( a kL1 + a tL) f + ft Properties & dimensions Fk 0.174 kips (b) Ft force in tube 6 in. At p [d2 4o L1 1 in. 8 t do L At 0 L t 80 1 k ft 0.125 in. Lf L Lf 2 0.1875 kips c1 c2 Qft t( T)L i.e., add displacements for the two released structures to initial tube length L Lf 12.01 in. ; (d) Set Q 0 to find T required to reduce spring force to zero L EtAt ¢ T reqd Treqd rel. displ. across cut spring due to precompres1 sion and T k TL1 t TL 1 L (10 6)/ F rel. displ. across cut spring due to redundant Q(f ft) compatibility: k (c) Final length of tube redundant Q f Flexibilities compressive force in spring (Fk) & also tensile force in tube ; Q NOTE: if tube is rigid, Fk note that Q result below is for zero temp. (until part(d)) (a) Force in spring Fk 2 kip 1.5 in L1 6.5(10 6)/ F T 2.307 in2 k 12 in. spring is 1/8 in. longer than tube k 100 ksi 2 t)2] ( do 12.125 in. Et ; Fk ( d a k L1 + a tL) 141.9 F since t k, a temp. increase is req’d to expand tube so that spring force goes to zero 0 Steel wires Problem 2.5-24 Prestressed concrete beams are sometimes manufactured in the following manner. High-strength steel wires are stretched by a jacking mechanism that applies a force Q, as represented schematically in part (a) of the figure. Concrete is then poured around the wires to form a beam, as shown in part (b). After the concrete sets properly, the jacks are released and the force Q is removed [see part (c) of the figure]. Thus, the beam is left in a prestressed condition, with the wires in tension and the concrete in compression. Let us assume that the prestressing force Q produces in the steel wires an initial stress 0 620 MPa. If the moduli of elasticity of the steel and concrete are in the ratio 12:1 and the cross-sectional areas are in the ratio 1:50, what are the final stresses s and c in the two materials? Q Q (a) Concrete Q Q (b) (c) ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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