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nter of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia IiyuyiIx=Ai(yuyi)^2Moment of inertia Istage 1ASAOC+05+02+08+11+00+07 TAON+03+03+06+00+03+09 AORP+04+03+07+00+02+09 NSA+05+02+08+11 +09+11stage 2ASAOC+05+02+08+11+01+08 TAON+03+03+06+00+03+09 TAOP+04+03+07+00+02+09 NSA+05+02+08+11 +10+11stage 3ASAOC+05+02+08+11+01+08 TAON+03+03+06+00+03+09 TAOP+04+03+07+00+02+09 NSA+05+02+08+11 +10+11Support Sectionstage The name of the PartitionePartitioned area AiDistance of center of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia IiyuyiIx=Ai(yuyi)^2Moment of inertia Istage 1ASAOC+06+02+08+11+00+06 TAON+03+03+06+00+03+03 AORP+04+02+06+00+02+08 NSA+06+02+08+11 +08+11stage 2ASAOC+06+02+08+11+00+07 TAON+03+03+06+00+03+09 TAOP+04+02+07+00+02+08 NCA+06+02+08+11 +09+11stage 3ASAOC+06+02+08+11+00+07 TAON+03+03+06+00+03+09 TAOP+04+02+07+00+02+08 NSA+06+02+08+11 +09+11 Summary table of control section at different stages of cross section geometric characteristicsstagesectionarea of blockYuYb IWuWbWpstage 1L/2 L/4 CPS SS stage 2L/2 L/4 CPS SS stage 3L/2 L/4 CPS SS ASAOC means all section area of concrete,TAON means transfer area of nonprestress,AORP means area of reserve piple,NSA means net section area,TAOP means transfer area of means changed point section,SS means support section.7. Calculation of carrying capacity from ultimate limit state in long term.1) Calculation of carrying capacity from normal section.As for midspan section,which subbjected Mmax.(1) calculate depth of pression that the beam is type ? of T shape beam. X=(fpdAp+fsdAs)/fcdbf ?=(12602520+330509)/(2200)=68mmhf ?=228mmAssumption is correct.(2) Calculation of carrying capacity from normal section. Distance between action point of resultant force with prestressed rebar and nonprestressed rebar and bottom of section a is a =(fpdApap+fsdAsas)/(fsdAs+fpdAp)=(12602520100+33050945)/(12602520+330509)=97mmh0=ha=180097=1703mmAooording to Load Table ,we can know that Md=m Mu=fcdbf ?x(hox/2)=220068(170368/2) =mγ0Md=1m=m OK!!!From calculation of Excel ,we can get carrying capacity of other sections, Carrying capacity of normal sectionsectiondesign valueaXh0Mumidspan1001700OKL/42371563OKchanged point section2231577OK2) Calculation of carrying capacity from diagonal section. According to the formula 103 ftdα2bh0=γ0Vd=(fcu,k)^ bho,check upper limit and down limit of +Vcs+Vpb .From Excel calculation ,we can get, Flexural bearing capacity for diagnoal sectionSection checkDesign valueah0Upper limitDown limitVCSVPDVcs+VpdpPSVfsvResultL/44742371563280OKchanged point section5051295280OKsupport section831969280OK For the steel cable is anchored in the beam end, its number has no change and the bend up angle is little, its inclined flexural bearing capacity does not control the design, so the check is neglected.8. Estimation of prestress losses from steel cable.1)The control stress in tensioning of prestressed reinforcement.2)Stress losses of steel cable.(1)Prestress losses from friction berween prestressed reinforcement and pipeline: As for midspan section: 。 d is the distance from anchor point to bearing central line。 is the friction coefficient of reinforcement and pipe and is the local deviation of pipe per meter length’s influence on the friction coefficient, we know 。 is the pipe rolls angle from tensioned place to the midspan, only N1 is a siphon standpipe,so , N2, N3 is not only a siphon but also a flat bend pipe, the siphon angle is: 。 and the flat bend angle is , so the space angle is .midspan sectionθ(0)θ(rad)μθxkxβσconσl1N18 1395 N2 1395 N3 1395 mean L/4θ(0)θ(rad)μθxkxβσconσl1N1000 1395 N28 1395 N3 1395 mean changed point sectionθ(0)θ(rad)μθxkxβσconσl1N1000 1395 N2000 1395 N38 1395 mean support sectionθ(0)θ(rad)μθxkxβσconσl1N1000 1395 N2000 1395 N3000 1395 mean mean of each control sectionMidspan sectionL/4 sectionChange point sectionSupport section (2)Anchorage deformation、steel retraction causes stress lossesPost tensioned structure should consider the influence