30m箱梁预应力张拉计算书

一、张拉设计

预应力钢束为φ高强度低松弛钢绞线，横载面积140mm2，有单束5根、4根两种形式，锚具型号分别为OVM15-5型、OVM15-4、锚下控制应力N1～N3为1340Mpa，N4为1320Mpa，T1为1395Mpa，T2为1340MPa。 二、张拉设备选用

1、张拉设备能力计算（以单束5根为例，边跨N1～N3） P=σ控×A×n

=1340×106 N/m2×140×10-6 m2×5

=938KN=

为了抵消夹片锚固回缩时的预应力损失（按一端回缩6mm计），超张拉3%σ控：

Pmax=P×103%=

2、张拉设备行程（以最长钢束拉力无磨阻损失为例） ΔL=σ控×L/Ep

=1340×106××103/×1011) =

张拉时为两侧张拉,单侧伸长量为2=

所选用QYC150型穿心式液压千斤顶,其张拉力T=150T，行程ls=400mm。

3、压力表选用

150T千斤顶活塞面积为290cm2。

由式Pn=P/An（式中Pn —计算压力表读数；P—张拉力；An—张

拉设备工作液压面积），得：

Pn =×104N/29000mm2 =mm2

所选用最大读数为60MPa的压力表。 三、分级张拉段划分

为了便于伸长量测量和控制两端张拉的同步进行，把张拉段分为10%σ控、20%σ控、100%σ控、103%σ控四个阶段，各阶段张拉力分别为：

张拉力 张拉阶段 10%σ控（KN） 20%σ控（KN） 100%σ控（KN） 103%σ控（KN） 5φs 938 4φ 四、应力张拉操作程序

初张拉至δk（准确测量伸长量），持荷3分钟，然后张拉至δk，持荷3分钟，再张拉直接到位δk，持荷3分钟，进油张拉到δk锚固。不再采用超张拉工艺。

五、理论伸长量计算

根据公路桥规12.8.3款和附录G-8规定，对预应力钢铰线理论伸长量进行计算：

1、计算公式：

ΔL=PpL/（ApEp）（公式1）

Pp= {P×[1-e-（kx+μθ）]}/ （kx+μθ）（公式2） 式中，ΔL—理论伸长量，cm；

Pp—预应力钢铰线平均张拉力，N； L—预应力钢铰线长度，cm；

Ep—弹性模量，N/mm2，取Ep =×105 N/mm2； Ap— 一束预应力钢铰线总面积，单根截面140 mm2； P—预应力钢铰线张拉端张拉力，N； 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轨道部分切线的夹角和，rad； k—管道偏差系数，取k=； μ—管道磨阻系数，取μ=；

锚具变形、钢筋回缩取6mm（一端）； 2、分段方法：

根据图所示分AB、BC、CD、DE共4段进行计算，不考虑工作长度。

3、计算方法：

(1)计算每一段的起点和终点力。每一段的终点力就是下一段的起点力，例如靠近张拉端第一段BC的终点C点力即为第二段CD的起点力，每段的终点力与起点力的关系如下式：

Pz=Pq×e-(KX+μθ)（公式3） Pz—分段终点力（N）

Pq—分段的起点力（N）

各段的起终点力可以根据公式3从张拉端开始进行逐步的计算。 (2)根据每一段起点力Pq代入公式2求出每一段平均张拉力Pp。 (3)根据Pp代入公式1计算出每一段的伸长值ΔL，相加后得出全长钢绞线伸长量。

4、计算数据：

单根钢绞线千斤顶张拉力N1～N3P=Δk×Ap=1340×140=187600(N)，N4P=Δk×Ap=1320×140=184800(N)，T1P=Δk×Ap=1395×140=195300(N)，T2P=Δk×Ap=1340×140=187600(N)，根据以上各计算方法编程求得各钢束伸长量数据如下：

Ⅰ.边跨引申量计算表

N1钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.996160.959310.99602Pq(N)187600187155.21185751.83185037.80177509.00Pz(N)187155.21185751.83185037.80177509.00176802.15Pp(N)187377.521852.185394.59181247.34177155.34△L(mm)10.94.517.448.717.3197.46.50.02620.007532567.600.003857330.40.12220.041266000.00399合计14795N2钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.997790.961070.99255Pq(N)187600187155.21185751.83185340.66178125.67Pz(N)187155.21185751.83185340.66178125.67176799.49Pp(N)187377.521852.1856.17181709.29177461.75△L(mm)10.94.510.040.732.4196.86.50.02620.007531477.300.002226108.70.12220.03971498200.00747合计14805

N3钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.999430.962830.910Pq(N)187600187155.21185751.831855.96178746.36Pz(N)187155.21185751.831855.96178746.36176798.17Pp(N)187377.521852.185698.182174.38177770.48△L(mm)10.94.52.632.7.6196.26.50.02620.00753380.0800.000574886.90.12220.03787730600.01096合计14810N4钢束计算表分段L1L2L3x(mm)θ(rad)kx+μθ101600.00152e-(kx+μθ)0.998480.992820.98069Pq(N)184800.00184518.59183193.32Pz(N)184518.59183193.32179655.39Pp(N)184659.26183855.16181418.61△L(mm)6.94.986.4196.4733.040.02440.007211300100.01950合计14750T1钢束计算表分段L1L2L3合计x(mm)θ(rad)kx+μθ100300.00150e-(kx+μθ)0.998500.987010.99536Pq(N)195300.00195006.39192472.68Pz(N)195006.39192472.68191580.05Pp(N)195153.16193736.78192026.02△L(mm)7.22.821.863.6399.330.04990.013083099450100.00465T2钢束计算表分段L1L2L3合计x(mm)θ(rad)kx+μθ100300.00150e-(kx+μθ)0.998500.987010.99015Pq(N)187600.00187317.97184884.15Pz(N)187317.97184884.15183063.11Pp(N)187458.95186098.41183972.13△L(mm)6.92.744.5108.2399.330.04990.013086599800100.00990

边跨钢束张拉力与油表读数对应表1#千斤顶编号拉力级张拉力（KN）表号：12.8.4.1252#千斤顶表号：12.8.4.104表号：12.8.4.1表号：12.8.4.194油表读数伸长量油表读数伸长量油表读数伸长量油表读数（MPa)(mm)（MPa)(mm)（MPa)(mm)（MPa)5.179.5044.095.179.5044.095.179.5044.094.257.6634.925.359.85.865.179.5044.09204019820391972040198203919561311221083.798.13.133.798.13.133.798.13.132.866.3133.873.978.5244.923.798.13.13204019820391972040198203919561311221083.948.2242.443.948.2242.443.948.2242.443.046.4133.374.128.5744.203.948.2242.44204019820391972040198203919561311221083.337.7342.923.337.7342.923.337.7342.922.405.8633.603.518.0944.733.337.7342.92伸长量(mm)20401982039197204019820391956131122108初始张拉10%20%100%10%20%100%10%20%100%10%20%93.8187.6933.8187.6933.8187.693873.92147.8N1持荷3min终张初始张拉N2持荷3min终张初始张拉N3持荷3min终张初始张拉N4持荷3min终张初始张拉100%739.210%20%97.65195.3T1持荷3min终张初始张拉100%976.510%20%100%93.8187.6938T2持荷3min终张

Ⅱ.中跨引申量计算表

N1钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.993110.959310.99915Pq(N)187600187155.21185751.83184472.17176966.38Pz(N)187155.21185751.83184472.17176966.38176815.41Pp(N)187377.521852.185111.27180693.301760.88△L(mm)10.94.531.248.53.7197.66.50.02620.007534608.600.006917330.40.12220.04156900.00085合计14745N2钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.994280.961070.99610Pq(N)187600187155.21185751.83184688.48177498.88Pz(N)187155.21185751.83184688.48177498.88176807.45Pp(N)187377.521852.185219.65181069.177152.94△L(mm)10.94.526.040.516.9197.46.50.02620.007533827.300.005746108.70.12220.03971260200.00390合计14775N3钢束计算表分段x(mm)θ(rad)kx+μθL1L2L3L4L51582.500.00237e-(kx+μθ)0.997630.992500.9950.962830.99307Pq(N)187600187155.21185751.83184906.43178034.31Pz(N)187155.21185751.83184906.43178034.31176800.82Pp(N)187377.521852.185328.81181448.68177416.85△L(mm)10.94.520.632.530.1197.26.50.02620.007533041.100.0045886.90.12220.03787463500.00695合计14800

N4钢束计算表分段L1L2L3x(mm)θ(rad)kx+μθ107100.00161e-(kx+μθ)0.998390.992820.98083Pq(N)184800.00184503.37183178.21Pz(N)184503.37183178.21179667.52Pp(N)184651.183839.99181417.20△L(mm)7.24.985.7195.8733.040.02440.007211290100.01935合计14705

T1钢束计算表分段L1L2L3合计x(mm)θ(rad)kx+μθ100300.00150e-(kx+μθ)0.998500.987010.99536Pq(N)195300.00195006.39192472.68Pz(N)195006.39192472.68191580.05Pp(N)195153.16193736.78192026.02△L(mm)7.22.821.863.6399.330.04990.013083099450100.00465

T2钢束计算表分段L1L2L3合计x(mm)θ(rad)kx+μθ100300.00150e-(kx+μθ)0.998500.987010.99015Pq(N)187600.00187317.97184884.15Pz(N)187317.97184884.15183063.11Pp(N)187458.95186098.41183972.13△L(mm)6.92.744.5108.2399.330.04990.013086599800100.00990

中跨钢束张拉力与油表读数对应表1#千斤顶编号拉力级张拉力（KN）表号：12.8.4.1252#千斤顶表号：12.8.4.104表号：12.8.4.1表号：12.8.4.194油表读数伸长量油表读数伸长量油表读数伸长量油表读数（MPa)(mm)（MPa)(mm)（MPa)(mm)（MPa)4.317.7735.444.317.7735.444.317.7735.444.257.6634.925.359.85.865.179.5044.09204019820391972040198203919561311221082.926.4134.392.926.4134.392.926.4134.392.866.3133.873.978.5244.923.798.13.13204019820391972040198203919561311221083.096.5133.883.096.5133.883.096.5133.883.046.4133.374.128.5744.203.948.2242.44204019820391972040198203919561311221082.455.9734.122.455.9734.122.455.9734.122.405.8633.603.518.0944.733.337.7342.92伸长量(mm)20401982039197204019820391956131122108初始张拉10%20%75.04150.1N1持荷3min终张初始张拉100%750.410%20%75.04150.1N2持荷3min终张初始张拉100%750.410%20%75.04150.1N3持荷3min终张初始张拉100%750.410%20%73.92147.8N4持荷3min终张初始张拉100%739.210%20%97.65195.3T1持荷3min终张初始张拉100%976.510%20%100%93.8187.6938T2持荷3min终张