后张法预应力钢绞线的理论伸长量计算书

后张法预应力钢绞线的理论伸长量计算书计算依据：《公路桥涵施工技术规范》（JTJ041-2000）及《施工图纸》计算公式：△L=PpL/AyEg式中：△L—理论伸长值Pp—平均张拉力（N）L—预应力钢材长度（cm）Eg—预应力钢材弹性模量（N/mm2）Ay—预应力钢材截面面积（mm2）平均张拉力Pp的计算公式Pp=P[1-e-（kx+μθ）]/（kx+μθ）式中：P—预应力钢材张拉端张拉力x—从张拉端至计算截面的孔道长度（m）θ—从张拉端至计算截面曲线孔道部分切线的夹角之和（rad）μ—预应力钢筋与孔道壁的摩擦系数。见（JTJ041-2000）附表11.4k—孔道每米局部偏差对摩擦的影响系数。见（JTJ041-2000）附表11.4三、计算参数的选取：Eg=1.95×105（实验数据），Ay=140mm2。k=0.0015，μ=0.25(图纸给定)每根预应力钢绞线端部计算长度增加45cm。正弯矩钢绞线伸长量计算16m端跨空心板预应力钢材伸长量：钢绞线束N1的θ值：左θ1=0.038144、右θ1’=0.038144钢绞线束N2的θ值：左θ2=0.039055、右θ2’=0.039055将钢绞线束按直线段、圆曲线段、直线段分为三段：直线段：N1：P1=1357.8×140=190092（N），X1=45+264.8=309.8，X1=45+253=298左Pp1=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×3.098+0.25×0）］/0.0015×3.098+0.25×0=189651.00（N）右Pp1’=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×2.98+0.25×0）］/0.0015×2.98+0.25×0=189667.78（N）左△L1=189651.00×309.8/1.95×105×140=2.1522cm右△L1’=189667.78×298/1.95×105×140=2.0704cm圆曲线段：P2=189651.00×2-190092=189210.01(N)P2’=189667.78×2-190092=189243.55(N)左Pp2=P[1-e-（kx+μθ）]/（kx+μθ）=189210.01×［1-e-（0.0015×2.397+0.25×0.038144）］/0.0015×2.397+0.25×0.038144=188849.35（N）右Pp2’=P[1-e-（kx+μθ）]/（kx+μθ）=189243.55×［1-e-（0.0015×2.454+0.25×0.039055）］/0.0015×2.454+0.25×0.039055=188819.84（N）左△L2=188849.35×276.8/1.95×105×140=1.6581cm右△L2’=188819.84×265/1.95×105×140=1.6973cm直线段：P3=188849.35×2-189210.01=188488.69(N)P3’=188819.84×2-189243.55=188396.12(N)左Pp3=P[1-e-（kx+μθ）]/（kx+μθ）=188488.69×［1-e-（0.0015×3.1137+0.25×0）］/0.0015×3.1137+0.25×0=188049.2（N）右Pp3’=P[1-e-（kx+μθ）]/（kx+μθ）=188396.12×［1-e-（0.0015×2.4583+0.25×0）］/0.0015×2.4583+0.25×0=188049.2（N）左△L3=188049.2×311.37/1.95×105×140=2.1448cm右△L3’=188049.2×245.83/1.95×105×140=1.6933cm左△L=5.955cm右△L=5.461cm全板△L=11.416钢绞线束N1的θ值：左θ1=0.024783、右θ1’=0.024783钢绞线束N2的θ值：左θ2=0.025594、右θ2’=0.025594N2：P1=1357.8×140=190092（N），X1=45+205=217，X1=45+193.4=217左Pp1=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×2.50+0.25×0）］/0.0015×2.50+0.25×0=189736.02（N）右Pp1’=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×2.384+0.25×0）］/0.0015×2.384+0.25×0=189752.52（N）左△L1=189736.02×250/1.95×105×140=1.7375cm右△L1’=189752.52×238.4/1.95×105×140=1.6570cm圆曲线段：P2=189736.02×2-190092=189380.05(N)P2’=189752.52×2-190092=189413.04(N)左Pp2=P[1-e-（kx+μθ）]/（kx+μθ）=189380.05×［1-e-（0.0015×1.557+0.25×0.024783）］/0.0015×1.557+0.25×0.024783=189283.44（N）右Pp2’=P[1-e-（kx+μθ）]/（kx+μθ）=189413.04×［1-e-（0.0015×1.608+0.25×0.025594）］/0.0015×1.608+0.25×0.025594=189257.05（N）左△L2=189283.44×155.7/1.95×105×140=1.0795cm右△L2’=189257.05×160.8/1.95×105×140=1.1147cm直线段：P3=189283.44×2-189380.05=189186.83(N)P3’=189257.05×2-189413.04=189101.06(N)左Pp3=P[1-e-（kx+μθ）]/（kx+μθ）=189186.83×［1-e-（0.0015×4.51065+0.25×0）］/0.0015×4.51065+0.25×0=188548.26（N）右Pp3’=P[1-e-（kx+μθ）]/（kx+μθ）=187386.8×［1-e-（0.0015×3.90535+0.25×0）］/0.0015×3.90535+0.25×0=188548.26（N）左△L3=188548.26×451.065/1.95×105×140=3.1153cm右△L3’=186973.2507×390.535/1.95×105×140=2.6972cm左△L=5.932cm右△L=5.469cm全板△L=11.40116m中跨边板预应力钢材伸长量：钢绞线束N1的θ值：左θ1=0.030627、右θ1’=0.030627钢绞线束N2的θ值：左θ2=0.030627、右θ2’=0.030627将钢绞线束按直线段、圆曲线段、直线段分为三段：直线段：N1：P1=1357.8×140=190092（N），X1=45+323.4=323.4X2=45+323.4=323.4左Pp1=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×3.234+0.25×0）］/0.0015×3.234+0.25×0=189631.68（N）右Pp1’=P[1-e-（kx+μθ）]/（kx+μθ）=190092×［1-e-（0.0015×3.234+0.25×0）］/0.0015×3.234+0.25×0=189631.68N）左△L1=189631.68×323.4/1.95×105×140=1.3334cm右△L1’=189631.68×323.4/1.95×105×140=1.3334cm圆曲线段：P2=189631.68×2-190092=189171.35(N)P2’=189631.68×2-190092=189171.35(N)左Pp2=P[1-e-（kx+μθ）]/（kx+μθ）=189171.35×［1-e-（0.0015×1.925+0.25×0.030627）］/0.0015×1.925+0.25×0.030627=189093.32（N）右Pp2’=P[1-e-（kx+μθ）]/（kx+μθ）=189171.35×［1-e-（0.0015×1.925+0.25×0.030627）］/0.0015×1.925+0.25×0.030627=189093.32（N）左△L2=189093.32×192.5/1.95×105×140=1.322cm右△L2’=189093.32×192.5/1.95×105×140=1.322cm直线段：P3=189093.32×2-189171.35=189015.30(N)P3’=189093.32×2-189171.35=189015.30(N)左Pp3=P[1-e-（kx+μθ）]/（kx+μθ）=189015.30×［1-e-（0.0015×3.027+0.25×0）］/0.0015×3.027+0.25×0=188586.83（N）右Pp3’=P[1-e-（kx+μθ）]/（kx+μθ）=189015.30×［1-e-（0.0015×3.027+0.25×0）］/0.0015×3.027+0.25×0=188586.83（N）左△L3=188586.83×302.700/1.95×105×140=2.091cm右△L3’=188586.83×302.700/1.95×105×140=2.091cm左L=5.671cm右L=5.671cm全板△L=11.34216m中跨边板预应力钢材伸长量：钢绞线束N1的θ值：左θ1=0.018633、右θ1’=0.018633钢绞线束N2的θ值：左θ2=0.018633、右θ2’=0.018633将钢绞线束按直直线段、圆圆曲线段、直直线段分为为三段：直线段：N2：P1=13577.8×1140=11900992（N），X1=45+214.9=259..9X1=45+214.9=259..9左Pp1=P[[1-e--（kx+μθ）]/（kx+μθ）=190092××［1-e-（0.00015×22.5999+0.225×0）］/0.00015××2.5999+0..25×00=18897211.94（N）右Pp1’=PP[1-ee-（kx+μθ）]/（kx+μθ）=190092××［1-e-（0.00015×22.5999+0.225×0）］/0.00015××2.5999+0..25×00=18897211.94（N）左△L1=1897721.994×259..9/1..95×1105×1400=1.88062ccm右△L1’=189721..94×259..9/1..95×1105×1400=1.88062ccm圆曲线段：P2=1897721.994×2--1900092=11893551.899(N)P2’=189721..94×22-1900092==1893351.889(N)左Pp2=P[[1-e--（kx+μθ）]/（kx+μθ）=189351..89×［1-e-（0.00015×11.1711+0.225×0）］/0.00015××1.1771+0..25×00=1894483.661（N）右Pp2’=PP[1-ee-（kx+μθ）]/（kx+μθ）=189351..89×［1-e-（0.00015×11.1711+0.225×0）］/0.00015××1.1771+0..25×00=18894833.61（N）左△L2=1894483.661×117..1/1..95×1105×1400=0.81228cm右△L2’=189483..61×117..1/1..95×1105×1400=0.81228cm直线段：P3=1894483.661×2--1893351.889=1896615.332(N)P3’=1894833.61××2-18893511.89==1896615.332(N)左Pp3=1899615..32×［1-e-（0.00015×44.41445+0..25×00）］/0.00015××4.41145+00.25××0=11889888.911（N）右Pp3’=18896155.32××［1-e-（0.00015×44.41445+0..25×00）］/0.00015××4.41145+00.25××0=11889888.911（N）左△L3=1889988.991×441..45/11.95××105×1400=3.0056cm右△L3’=188988..91×441..45/11.95××105×1400=3.0056cm左△L=5.6755cm右△L=5.6755cm，全板△L=111.350016m中跨跨中板预应力力钢材伸长长量：钢绞线束N1的的θ值：左θ1=0.02297833、右θ1’=0.0297883钢绞线束N2的的θ值：左θ1=0.02297833、右θ1’=0.0297883将钢绞线束按直直线段、圆圆曲线段、直直线段分为为三段：直线段：N1：P1=13577.8×1140=11900992（N），X1=45+281=326X1=45+281==326左Pp1=1900092××［1-e-（0.00015×33.26++0.255×0）］/0.00015××3.266+0.225×0=1899627..98（N）右Pp1’=19900922×［1-e-（0.00015×33.26++0.255×0）］/0.00015××3.266+0.225×0=1899627..98（N）左△L1=1896627.998×326/11.95××105×1400=2.22644ccm右△L1’=189627..98×326/11.95××105×1400=2.22644ccm圆曲线段：P2=1896627.998×2--1900092=11891663.966(N)P2’=189627..98×22-1900092==1891163.996(N)左Pp2=1899163..96×［1-e-（0.00015×11.8711+0.225×0..0297783）］/0.00015××1.8771+0..25×00.0299783=1899120..89（N）右Pp2’=18891633.96××［1-e-（0.00015×11.8711+0.225×0..0297783）］/0.00015××1.8771+0..25×00.0299783==1891120.889（N）左△L2=1891120.889×187..1/1..95×1105×1400=1.22961ccm右△L2’=189120..89×1187.11/1.995×1005×1400=1.22961ccm直线段：P3=1891120.889×2--1891163.996=1890077.881(N)P3’=189120..89×22-1899163..96=1890077.881(N)左Pp3=1899077..81×［1-e-（0.00015×33.06335+0..25×00）］/0.00015××3.06635+00.25××0=11886444.044（N）右Pp3’=18890777.81××［1-e-（0.00015×33.06335+0..25×00）］/0.00015××3.06635+00.25××0=11886444.044（N）左△L3=1886644.004×306..350//1.955×1055×1400=2.11169ccm右△L3’=188644..04×306..350//1.955×1055×1400=2.11169ccm左L=5.6777cm右L=5.6777cm16m中跨跨中板预应力力钢材伸长长量：钢绞线束N1的的θ值：左θ1=0.0111316、右θ1’=0.01113166钢绞线束N2的的θ值：左θ2=0.01113166、右θ2’=0.01113166将钢绞线束按直直线段、圆圆曲线段、直直线段分为为三段：直线段：N2：P1=13577.8×1140=11900992（N），X1=45+232.9=277..9X2=45+232.9=277..9左Pp1=1900092××［1-e-（0.00015×22.7799+0.225×0）］/0.00015××2.7779+0..25×00=18896966.35（N）右Pp1’=19900922×［1-e-（0.00015×22.779+0.225×0）］/0.00015××2.7779+0..25×00=18896966.35（N）左△L1=1896696.335×277.9//1.955×1055×1400=1.9311cm右△L1’=1896966.35××277.9//1.955×1055×1400=1.9311cm圆曲线段：P2=1896696.335×2--1900092=11893000.7(N)P2’=1896966.35××2-19900922=1899300..7（N)左Pp2=1899300..7×［1-e-（0.00015×11.1711+0.225×0）］/0.00015××1.1771+0..25×00=1899708..86（N）右Pp2’=18893000.7×［1-e-（0.00015×11.1711+0.225×0）］/0.00015××1.1771+0..25×00=18897088.86（N）左△L2=1897708.886×80.55/1.995×1005×1400=0.55594cm右△L2’=1897088.86××80.55/1.995×1005×1400=0.55594cm直线段：P3=1897708.886×2--1893300.77=1885537.662（N)P3’=1897088.86××2-18893000.7=1885537.662(N)左Pp3=1888537..62×［1-e-（0.00015×44.5977+0.225×0）］/0.00015××4.5977+0.225×0=1877889..08（N）右Pp3’=18885377.62××［1-e-（0.00015×44.5977+0.225×0）］/0.00015××4.5997+0..25×00=18878899.08（N）左△L3=1878889.008×459..7/1..95×1105×1400=3.11638ccm右△L3’=187889..08×4459.77/1.995×1005×1400=3.11638cmm左△L=5.6522cm右△L=5.6522cm全板△L=11.3304cmm控制应力达到110%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..1=199.00992y11=0.00343xx-0.11=0.00343××19.00092--0.1==0.5552y22=0.00352xx-0.44=0.00352××19.00092--0.4==0.2552控制应力力达到20%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..2=388.01884y11=0.00343xx-0.11=0.00343××38.00184--0.1==1.2004y22=0.00352xx-0.44=0.00352××38.00184--0.4==0.9338控制应力力达到40%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..4=766.15668y11=0.00343xx-0.11=0.00343××76.11568--0.1==2.5112y22=0.00352xx-0.44=0.00352××76.11568--0.4==2.2881控制应力力达到60%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..6=388.01884y11=0.00343xx-0.11=0.00343××38.00184--0.1==3.8112y22=0.00352xx-0.44=0.00352××38.00184--0.4==3.6115控制应力力达到80%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..8=1552.07736y11=0.00343xx-0.11=0.00343××152..07366-0.11=5.1116y22=0.00352xx-0.44=0.00352××152..07366-0.44=4.9953控制应力力达到100%时，油表30366#、302448#读数：x==1900092N==190..092KKN×1==190..092y11=0.00343xx-0.11=0.00343××190..092--0.1==6.422y22=0.00352xx-0.44=0.00352××190..092--0.4==6.2991控制应力达到110%时，油表30366#、302448#读数：(3根)x==1900092N==190..092KKN×0..1=199.00992y11=0.00343xx-0.11=0.00343××19.00092××3-0..1=1..856y22=0.00352xx-0.44=0.00352××19.00092××3-0..4=1..556控制应力力达到20%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..2=388.01884y11=0.00343xx-0.11=0.00343××38.00184××3-0..1=3..812y22=0.00352xx-0.44=0.00352××38.00184××3-0..4=3..614控制应力力达到40%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..4=766.15668y11=0.00343xx-0.11=0.00343××76.11568××3-0..1=7..736y22=0.00352xx-0.44=0.00352××76.11568××3-0..4=7..643控制应力力达到60%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..6=388.01884y11=0.00343xx-0.11=0.00343××38.00184××3-0..1=111.6366y22=0.00352xx-0.44=0.00352××38.00184××3-0..4=111.6455控制应力力达到80%时，油表30366#、302448#读数：x==1900092N==190..092KKN×0..8=1552.07736y11=0.00343xx-0.11=0.00343××152..07366×3-00.1=115.5488y22=0.00352xx-0.44=0.00352××152..07366×3-00.4=115.6559控制应力力达到100%时，油表30366#、302448#读数：x==1900092N==190..092KKN×1==190..092y11=0.00343xx-0.11=0.00343××190..092××3-0..1=199.46y22=0.00352xx-0.44=0.00352××19