181_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

181_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 3:00 PM Page 175 SECTION 2.5 Thermal Effects Solution 2.5-24 Prestressed concrete beam L 0 length initial stress in wires Q As 620 MPa As total area of steel wires Ac area of concrete 50 As Es Ps Ps Pc COMPATIBILITY EQUATION AND FORCE-DISPLACEMENT RELATIONS 1 STRESSES (Eq. 1) final elongation of steel wires 1 s0 EsAs 1+ EcAc Pc Ac s0 Ac Es + As Ec 0 shortening of concrete ss 2 3 PsL EsAs or PcL EcAc Solve simultaneously Eqs. (1) and (3): Ps Ps As Pc s0As EsAs 1+ EcAc ; ; SUBSTITUTE NUMERICAL VALUES: Pc L Ec Ac s0L Es ss sc s0L Es PsL EsAs 3 final compressive force in concrete initial elongation of steel wires QL EsAs 2 final tensile force in steel wires Pc EQUILIBRIUM EQUATION 12 Ec sc (Eq. 2, Eq. 3) 620 MPa 620 MPa 12 1+ 50 620 MPa 50 + 12 Es Ec 12 As Ac 1 50 500 MPa (Tension) 10 MPa (Compression) ; ; 175 ...
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