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02-03ChapGere.0016 - A s 5 total area of steel wires A c 5...

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SECTION 2.5 Misfits and Prestrains 121 Problem 2.5-20 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? Solution 2.5-20 Prestressed concrete beam Q Q Q Q (a) (b) (c) Steel wires Concrete
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Unformatted text preview: A s 5 total area of steel wires A c 5 area of concrete 5 50 A s E s 5 12 E c P s 5 final tensile force in steel wires P c 5 final compressive force in concrete 5 Q A s 5 620 MPa E QUILIBRIUM EQUATION P s 5 P c (Eq. 1) C OMPATIBILITY EQUATION AND FORCE-DISPLACEMENT RELATIONS d 1 5 initial elongation of steel wires d 2 5 final elongation of steel wires d 3 5 shortening of concrete (Eq. 2, Eq. 3) Solve simultaneously Eqs. (1) and (3): P s 5 P c 5 s 0 A s 1 1 E s A s E c A c d 1 2 d 2 5 d 3 Ê or Ê s 0 L E s 2 P s L E s A s 5 P c L E c A c 5 P c L E c A c 5 P s L E s A s 5 QL E s A s 5 s L E s S TRESSES S UBSTITUTE NUMERICAL VALUES : s c 5 620 MPa 50 1 12 5 10 MPa (Compression) s s 5 620 MPa 1 1 12 50 5 500 MPa (Tension) s 5 620 MPa Ê E s E c 5 12 Ê A s A c 5 1 50 s c 5 P c A c 5 s A c A s 1 E s E c s s 5 P s A s 5 s 1 1 E s A s E c A c A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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