t梁预应力钢绞线的理论伸长量计算书1

'T梁预应力钢绞线理论伸长值分段计算T梁预应力钢绞线理论伸长值计算书一、计算依据《T形梁上部构造通用图》YQT-SLT240ZQ-30-1，K0+936浸长1#桥、K2+317浸长2#桥、K4+953马料河桥设计图纸及《公路桥涵施工技术规范》（JTJ041-2000），《混凝土弯梁桥》。二、计算公式1、预应力钢绞线理论伸长值计算公式预应力钢绞线伸长值：ΔL＝(Pp×L)/(Ap×Ep),其中：ΔL－预应力钢绞线伸长值（mm）L－预应力钢绞线计算长度（mm），包括千斤顶工作段长度Ap－预应力钢绞线的截面面积（mm2）Ep－预应力钢绞线的弹性模量（N/mm2）Pp－预应力钢绞线的平均张拉力（N）；按JTJ041－2000《公路桥涵施工技术规范》附录G-8预应力筋平均张拉力的计算2、预应力钢绞线平均张拉力计算公式Pp=P×（1-e-(kx+μθ)）/（kx+μθ）；其中：P－预应力钢束张拉端的张拉力（N）k－孔道每米局部偏差对摩擦的影响系数x－从张拉端至计算截面的孔道长度（m）μ－预应力钢绞线与孔道壁的摩擦系数θ－从张拉端至计算截面的孔道部分切线的夹角之和(rad)3、预应力钢绞线伸长值修正计算公式ΔL’＝(Ap×Ep)/(Ap’×Ep’)×ΔL,其中：Ap－预应力钢绞线的截面面积（mm2）Ep－预应力钢绞线的弹性模量（N/mm2）Ap’－预应力钢绞线的实测截面面积（mm2）Ep’－预应力钢绞线的实测弹性模量（N/mm2）三、设计参数及计算参数的选取预应力筋为φs15.20(7φ5)高强度低松弛预应力钢绞线，设计公称面积Ap＝139mm2安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算，弹性模量为：Ep＝1.95×105Mpa，锚下张拉控制应力：σk＝1395Mpa。N1钢束α竖=7.2890°；N2钢束α竖=7.2890°，α平=8.1301°；N3钢束α竖=6.0542°，α平=8.1301°。采用两端同时对称张拉技术张拉。实测钢绞线公称面积Ap’＝140mm2，弹性模量为：Ep’＝1.923×105Mpa，计算k=0.0015，μ=0.16（设计给定），锚环夹片至张拉工具夹片长度46cm，采用有效张拉力进行计算。四、预应力伸长值计算钢绞线束按无孔道壁的摩擦系数直线段、有孔道局部偏差对摩擦的影响系数及孔道壁摩擦系数圆曲线段两种类型计算（以下计算均以一根钢绞线计算，如下图一端简支一端连续，直线及曲线长度根据设计图纸端点坐标、曲线起点坐标、终点坐标计算）。以K2+317浸长2#桥右1-4(A型)T梁为例计算，梁长L=2936.1cm。1、各段长度计算①N1各段长度计算LA-B锚环夹片至张拉工具夹片长度=460mmLB-C=(((L/2-21)-(L/2-1136.9))2+(162.4-19.7)2)0.5=(((2936.1/2-21)-(2936.1/2-1136.9))2+(162.4-19.7)2)0.5=1125cm=11250mmLD-E=L/2-1289.2=2936.1/2-1289.2=178.85cm=1788.5mmLE-F=L/2-1289.2=2936.1/2-1289.2=178.85cm=1788.5mmLG-H=(((L/2-6.2)-(L/2-1136.9))2+(164.3-19.7)2)0.5=(((2936.1/2-6.2)-(2936.1/2-1136.9))2+(164.3-19.7)2)0.5=1139.9cm=11399mmLH-I锚环夹片至张拉工具夹片长度=460mmLC-D=LF-G=((L-8)×10-LB-C-LD-E-LE-F-LG-H)/2安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算=((2936.1-8)×10-11250-1788.8-1788.5-11399)/2=1528mm②N2各段长度计算LA-B锚环夹片至张拉工具夹片长度=460mmLB-C=(((L/2-19.6)-(L/2-710.5))2+(122.6-34.2)2)0.5=(((2936.1/2-19.6)-(2936.1/2-710.5))2+(122.6-34.2)2)0.5=696.5cm=6965mmLD-E=L/2-1143.5=2936.1/2-1143.5=322.75cm=3227.5mmLE-F=L/2-1143.5=2936.1/2-1143.5=322.75cm=3227.5mmLG-H=(((L/2-4.8)-(L/2-710.5))2+(124.5-34.2)2)0.5=(((2936.1/2-4.8)-(2936.1/2-710.5))2+(124.5-34.2)2)0.5=711.5cm=7115mmLH-I锚环夹片至张拉工具夹片长度=460mmLC-D=LF-G=((L-7)×10-LB-C-LD-E-LE-F-LG-H)/2=((2936.1-7)×10-6965-3227.5-3227.5-7115)/2=4378mm③N3各段长度计算LA-B锚环夹片至张拉工具夹片长度=460mmLB-C=(((L/2-18.4)-(L/2-542.2))2+(82.3-26.7)2)0.5=(((2936.1/2-18.4)-(2936.1/2-542.2))2+(82.3-26.7)2)0.5=526.7cm=5267mmLD-E=L/2-858.6=2936.1/2-858.6=609.45cm=6094.5mmLE-F=L/2-858.6=2936.1/2-858.6=609.45cm=6094.5mmLG-H=(((L/2-3.6)-(L/2-542.2))2+(83.9-26.7)2)0.5=(((2936.1/2-3.6)-(2936.1/2-542.2))2+(83.9-26.7)2)0.5=541.6cm=5416mmLH-I锚环夹片至张拉工具夹片长度=460mmLC-D=LF-G=((L-11)×10-LB-C-LD-E-LE-F-LG-H)/2=((2936.1-11)×10-5267-6094.5-6094.5-5416)/2=3190mm2、N1钢绞线理论伸长值计算①A-C段直线预应力钢绞线理论伸长值计算张拉端A点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LA-B=460mm，LB-C=11250mm，PpA=P=Pp。ΔLA-C＝(Pp×L)/(Ap×Ep)=(193905×(460+11250))/(139×1.95×105)=83.77mm安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算②C-D段曲线预应力钢绞线理论伸长值计算C点有效张拉力：PpC=PpA=193905NLC-D=1528mm，k=0.0015，μ=0.16，x=1.528m，θ=α竖=7.2890°=0.1272170492rad。平均PpC-D=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×1.528+0.16×0.1272170492）］/(0.0015×1.528+0.16×0.1272170492)=191725.82NΔLC-D＝(Pp×L)/(Ap×Ep)=(191725.82×1528)/(139×1.95×105)=10.81mm③D-E段直线预应力钢绞线理论伸长值计算D点有效张拉力：PpD=PpC×e-（kx+μθ）=193905×e-（0.0015×1.528+0.16×0.1272170492）=189563.04NLD-E=1788.5mmΔLD-E＝(Pp×L)/(Ap×Ep)=(189563.04×1788.5)/(139×1.95×105)=12.51mm④G-I段直线预应力钢绞线理论伸长值计算张拉端I点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LH-I=460mm，LG-H=11399mm，PpI=P=Pp。ΔLG-I＝(Pp×L)/(Ap×Ep)=(193905×(460+11399))/(139×1.95×105)=84.84mm⑤F-G段曲线预应力钢绞线理论伸长值计算G点有效张拉力：PpG=PpI=193905NLF-G=1528mm，k=0.0015，μ=0.16，x=1.528m，θ=α竖=7.2890°=0.1272170492rad。平均PpF-G=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×1.528+0.16×0.1272170492）］/(0.0015×1.528+0.16×0.1272170492)=191725.82NΔLF-G＝(Pp×L)/(Ap×Ep)=(191725.82×1528)/(139×1.95×105)=10.81mm⑥E-F段直线预应力钢绞线理论伸长值计算F点有效张拉力：PpF=PpG×e-（kx+μθ）=193905×e-（0.0015×1.528+0.16×0.1272170492）=189563.04NLE-F=1788.5mmΔLE-F＝(Pp×L)/(Ap×Ep)=(189563.04×1788.5)/(139×1.95×105)=12.51mm合计伸长值：ΔL1＝ΔLA-C+ΔLC-D+ΔLD-E+ΔLE-F+ΔLF-G+ΔLG-I=83.77+10.81+12.51+125.51+10.81+84.84=215.25mmN1一端伸长值ΔL=ΔL1/2=215.25/2=107.63mm安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算N1钢绞线伸长值修正ΔL’＝(Ap×Ep)/(Ap’×Ep’)×ΔL＝(139×1.95×105)/(140×1.933×105)×107.63＝107.8（mm）3、N2钢绞线理论伸长值计算①A-C段直线预应力钢绞线理论伸长值计算张拉端A点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LA-B=460mm，LB-C=6965mm，PpA=P=Pp。ΔLA-C＝(Pp×L)/(Ap×Ep)=(193905×(460+6965))/(139×1.95×105)=53.12mm②C-D段曲线预应力钢绞线理论伸长值计算C点有效张拉力：PpC=PpA=193905NLC-D=4378mm，k=0.0015，μ=0.16，x=4.378m，α竖=7.2890°，α平=8.1301°。θ=三维空间曲线包角β=(7.28902+（8.1301×2）2)0.5=0.3110035810rad。平均PpC-D=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×4.378+0.16×0.3110035810）］/(0.0015×4.378+0.16×0.3110035810)=188545.01NΔLC-D＝(Pp×L)/(Ap×Ep)=(188545.01×4378)/(139×1.95×105)=30.45mm③D-E段直线预应力钢绞线理论伸长值计算D点有效张拉力：PpD=PpC×e-（kx+μθ）=193905×e-（0.0015×4.378+0.16×0.3110035810）=183284.72NLD-E=3227.5mmΔLD-E＝(Pp×L)/(Ap×Ep)=(183284.72×3227.5)/(139×1.95×105)=21.82mm④G-I段直线预应力钢绞线理论伸长值计算张拉端I点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LH-I=460mm，LG-H=7115mm，PpI=P=Pp。ΔLG-I＝(Pp×L)/(Ap×Ep)=(193905×(460+7115))/(139×1.95×105)=54.19mm⑤F-G段曲线预应力钢绞线理论伸长值计算G点有效张拉力：PpG=PpI=193905NLF-G=4378mm，k=0.0015，μ=0.16，x=4.378m，α竖=7.2890°，α平=8.1301°。θ=三维空间曲线包角β=(7.28902+（8.1301×2）2)0.5=0.3110035810rad。平均PpF-G=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×4.378+0.16×0.3110035810）］/(0.0015×4.378+0.16×0.3110035810)=188545.01N安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算ΔLF-G＝(Pp×L)/(Ap×Ep)=(188545.01×4378)/(139×1.95×105)=30.45mm⑥E-F段直线预应力钢绞线理论伸长值计算F点有效张拉力：PpF=PpG×e-（kx+μθ）=193905×e-（0.0015×4.378+0.16×0.3110035810）=183284.72NLE-F=3227.5mmΔLE-F＝(Pp×L)/(Ap×Ep)=(183284.72×3227.5)/(139×1.95×105)=21.82mm合计伸长值：ΔL2＝ΔLA-C+ΔLC-D+ΔLD-E+ΔLE-F+ΔLF-G+ΔLG-I=53.12+30.45+21.82+21.82+30.45+54.19=211.85mmN2一端伸长值ΔL=ΔL2/2=211.85/2=105.93mmN2钢绞线伸长值修正ΔL’＝(Ap×Ep)/(Ap’×Ep’)×ΔL＝(139×1.95×105)/(140×1.933×105)×105.93＝106.1（mm）4、N3钢绞线理论伸长值计算①A-C段直线预应力钢绞线理论伸长值计算张拉端A点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LA-B=460mm，LB-C=5267mm，PpA=P=Pp。ΔLA-C＝(Pp×L)/(Ap×Ep)=(193905×(460+5267))/(139×1.95×105)=40.97mm②C-D段曲线预应力钢绞线理论伸长值计算C点有效张拉力：PpC=PpA=193905NLC-D=3190mm，k=0.0015，μ=0.16，x=3.190m，α竖=6.0542°，α平=8.1301°。θ=三维空间曲线包角β=(6.05422+（8.1301×2）2)0.5=0.3028271700rad。平均PpC-D=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×3.190+0.16×0.3028271700）］/(0.0015×3.190+0.16×0.3028271700)=188833.89NΔLC-D＝(Pp×L)/(Ap×Ep)=(188833.89×3190)/(139×1.95×105)=22.22mm③D-E段直线预应力钢绞线理论伸长值计算D点有效张拉力：PpD=PpC×e-（kx+μθ）=193905×e-（0.0015×3.190+0.16×0.3028271700）=183851.98NLD-E=6094.5mmΔLD-E＝(Pp×L)/(Ap×Ep)=(183851.98×6094.5)/(139×1.95×105)=41.34mm安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算④G-I段直线预应力钢绞线理论伸长值计算张拉端I点张拉力：P=σk×Ap=1395×139=193905N锚环夹片至张拉工具夹片长度LH-I=460mm，LG-H=5416mm，PpI=P=Pp。ΔLG-I＝(Pp×L)/(Ap×Ep)=(193905×(460+5416))/(139×1.95×105)=42.04mm⑤F-G段曲线预应力钢绞线理论伸长值计算G点有效张拉力：PpG=PpI=193905NLF-G=3190mm，k=0.0015，μ=0.16，x=3.190m，α竖=6.0542°，α平=8.1301°。θ=三维空间曲线包角β=(6.05422+（8.1301×2）2)0.5=0.3028271700rad。平均PpF-G=P[1-e-（kx+μθ）]/（kx+μθ）=193905×［1-e-（0.0015×3.190+0.16×0.3028271700）］/(0.0015×3.190+0.16×0.3028271700)=188833.89NΔLF-G＝(Pp×L)/(Ap×Ep)=(188833.89×3190)/(139×1.95×105)=22.22mm⑥E-F段直线预应力钢绞线理论伸长值计算F点有效张拉力：PpF=PpG×e-（kx+μθ）=193905×e-（0.0015×3.190+0.16×0.3028271700）=183851.98NLE-F=6094.5mmΔLE-F＝(Pp×L)/(Ap×Ep)=(183851.98×6094.5)/(139×1.95×105)=41.34mm合计伸长值：ΔL3＝ΔLA-C+ΔLC-D+ΔLD-E+ΔLE-F+ΔLF-G+ΔLG-I=40.97+22.22+41.34+41.34+22.22+42.04=210.13mmN3一端伸长值ΔL=ΔL3/2=210.13/2=105.07mmN3钢绞线伸长值修正ΔL’＝(Ap×Ep)/(Ap’×Ep’)×ΔL＝(139×1.95×105)/(140×1.933×105)×105.07＝105.2（mm）5、T梁15%控制张拉预应力钢绞线理论伸长值计算张拉端15%张拉力：P=σk×Ap×0.15=1395×139×0.15=29085.75N，其余计算方法步骤同2～4，结果为：N1△L15%＝12.57+1.62+1.88+1.88+1.62+12.73=16.15mm修正ΔL’＝(139×1.95×105)/(140×1.933×105)×16.15＝16.2（mm）N2△L15%＝7.97+4.57+3.27+3.27+4.57+8.13=15.89mm修正ΔL’＝(139×1.95×105)/(140×1.933×105)×15.89＝15.9（mm）N3△L15%＝6.15+3.33+6.20+6.20+3.33+6.31＝15.76mm安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算修正ΔL’＝(139×1.95×105)/(140×1.933×105)×15.76＝15.8（mm）6、T梁60%控制张拉预应力钢绞线理论伸长值计算张拉端60%张拉力：P=σk×Ap×0.60=1395×139×0.60=116343N，其余计算方法步骤同3，结果为：N2△L60%==31.87+18.27+13.09+13.09+18.27+32.51=63.55mm修正ΔL’＝(139×1.95×105)/(140×1.933×105)×63.55＝63.7（mm）五、压力表读数计算N1钢绞线根数：n=6，N2钢绞线根数：n=7，N3钢绞线根数：n=7。1、压力表1计算千斤顶编号:20432压力表编号:08.01.17.2588Y=0.021009X-0.18097①钢绞线15%压力表读数计算张拉端15%张拉力：P=193905×0.15=29085.75N。N1Y=0.021009×29085.75×6/1000-0.18097=3.49MpaN2Y=0.021009×29085.75×7/1000-0.18097=4.10MpaN3Y=0.021009×29085.75×7/1000-0.18097=4.10Mpa②钢绞线60%压力表读数计算张拉端60%张拉力：P=193905×0.60=116343N。N2Y=0.021009×116343×7/1000-0.18097=19.23Mpa③钢绞线100%压力表读数计算张拉端100%张拉力：P=193905N。N1Y=0.021009×193905×6/1000-0.18097=24.26MpaN2Y=0.021009×193905×7/1000-0.18097=28.34MpaN3Y=0.021009×193905×7/1000-0.18097=28.34Mpa2、压力表2计算千斤顶编号:20486压力表编号:08.01.12.1144Y=0.021109X-0.65668①钢绞线15%压力表读数计算张拉端15%张拉力：P=193905×0.15=29085.75N。N1Y=0.021109×29085.75×6/1000-0.65668=3.03MpaN2Y=0.021109×29085.75×7/1000-0.65668=3.64Mpa安宁至晋宁高速公路土建一合同段-9- T梁预应力钢绞线理论伸长值分段计算N3Y=0.021109×29085.75×7/1000-0.65668=3.64Mpa②钢绞线60%压力表读数计算张拉端60%张拉力：P=193905×0.60=116343N。N2Y=0.021109×116343×7/1000-0.65668=16.53Mpa③钢绞线100%压力表读数计算张拉端100%张拉力：P=193905N。N1Y=0.021109×193905×6/1000-0.65668=23.90MpaN2Y=0.021109×193905×7/1000-0.65668=28.00MpaN3Y=0.021109×193905×7/1000-0.65668=28.00Mpa安宁至晋宁高速公路土建一合同段-9-'