温度场和温度应力计算

1、附计算书3：温度场和温度应力计算一、温度场计算计算以本工程1.2m厚底板为例，用差分法计算底板28d水化热温升曲线。计算中各参数的取值如下：每m3胶凝材料用量，440kg/ m3； Q胶凝材料水化热总量（kJ/kg）；，本例采用实测值260kJ/kg；混凝土的比热，取1.0kJ/ (kg)； 混凝土的质量密度，取2400kg/ m3；导温系数，取0.0035m2/h；m，取0.5。混凝土的入模温度取10，地基温度为18，大气温度为18。温度场计算差分公式如下： （B.4.2-1）试算、，确定。取 = 0.5天 = 12小时， = 0.4m，即分3层则，可行。代入该值得出相应的差分法公式为画出相

2、应的计算示意图，并进行计算。底板厚1.2m，分3层，每层0.4m，相应的计算示意如下图。从上至下各层混凝土的温度分别用、表示，相应时刻各层的温度即为、。混凝土与大气接触的上表面边界温度用表示，与地基接触的下表面边界温度用表示。 = 0，即第天，上表面边界，取大气温度， = 18各层混凝土温度取入模温度，即= = = 10下表面边界，取地基温度，= 18； = 1，即第天，温升10.544上表面边界温度，散热温升为0，始终保持不变， = 18 第一层混凝土温度，见计算图示中方框1，的边界为和，在的基础上考虑温升，即第二层混凝土温度，见计算图示中方框2，的边界为和，在的基础上考虑温升，即第三层混凝

3、土温度，见计算图示中方框3，的边界为和，在的基础上考虑温升，即下表面边界温度，需要考虑散热温升，所以需每一步都需进行修正。见计算图示中方框6，的边界为和地基温度18，在的基础上考虑温升，即以上即完成了一遍 = 1时，各温度计算。同理 = 2，即第天，温升 = 8.212，上表面 = 18，同理可计算 = 356，即第1.528天的各层温度值，本算例中不再进行详细计算，最终计算结果如表1。表1 不同混凝土龄期下各层混凝土温度值（单位：）混凝土龄期上表面第一层第二层第三层底界边层018101010180.51822.64420.54422.64426.44411829.08529.85831.30

4、231.4411.51832.77336.42937.35434.27121834.83640.69341.28335.7902.51835.83343.18943.56536.44131836.10344.37844.61736.4913.51835.87644.62144.77436.12341835.31144.19844.29535.4694.51834.52743.31843.38034.62751833.60742.13842.17733.6715.51832.61540.77440.79932.65661831.59439.31339.32931.6206.51830.57737

5、.81637.82630.59471829.58536.32736.33429.5957.51828.63234.87834.88228.63981827.72933.48733.49027.7338.51826.88032.16932.17126.88291826.08830.93230.93326.0899.51825.35329.77729.77825.354101824.67628.70828.70824.67610.51824.05327.72027.72124.053111823.48226.81326.81323.48211.51822.96025.98225.98222.961

6、121822.48525.22225.22222.48512.51822.05224.53024.53022.052131821.65923.90023.90021.65913.51821.30323.32823.32821.303141820.98022.80822.80820.98014.51820.68722.33822.33820.687151820.42321.91221.91220.42315.51820.18321.52721.52720.183161819.96821.17921.17919.96816.51819.77320.86420.86419.773171819.597

7、20.58120.58119.59717.51819.43820.32420.32419.438181819.29520.09320.09319.29518.51819.16619.88519.88519.166191819.05019.69719.69719.05019.51818.94519.52819.52818.945201818.85119.37619.37618.85120.51818.76619.23819.23818.766211818.68919.11519.11518.68921.51818.62019.00319.00318.620221818.55818.90318.9

8、0318.55822.51818.50218.81318.81318.502231818.45218.73118.73118.45223.51818.40718.65818.65818.407241818.36618.59218.59218.36624.51818.32918.53318.53318.329251818.29618.48018.48018.29625.51818.26718.43118.43118.267261818.24018.38818.38818.24026.51818.21618.34918.34918.216271818.19418.31418.31418.19427

9、.51818.17518.28318.28318.175281818.15718.25418.25418.157二、温度应力计算示例以下计算示例按照步长为1天进行。1、里表温差T1计算公式如下 （B.5.1）计算结果见表2 各龄期混凝土收缩当量温差计算根据公式 （B.2.1） （B.2.2）其中 取4.0×10-4石家庄市内年平均气温值取14.5计算结果见表3 综合降温差T2计算公式如下 （B.5.2）计算结果见表2表2 综合温差计算结果混凝土龄期第一层(Tb)第三层（Tm）第三层（Td）T1（Tm- Tb）T2*T1*T201010100.0000.000/-8.6610.522.

10、64422.64422.6440.0008.6612.217 -8.803129.08531.30231.3022.21717.4652.365 -6.1711.532.77337.35437.3544.58123.6361.866 -4.127234.83641.28341.2836.44727.7631.285 -2.5522.535.83343.56543.5657.73230.3150.781 -1.422336.10344.61744.6178.51431.7370.384 -0.2693.535.87644.77444.7748.89832.0060.086 0.043435.31

11、144.29544.2958.98431.963-0.131 0.9394.534.52743.38043.3808.85331.024-0.283 0.763533.60742.17742.1778.57030.261-0.385 0.9235.532.61540.79940.7998.18429.337-0.450 1.007631.59439.32939.3297.73528.330-0.485 1.0366.530.57737.82637.8267.24927.295-0.500 1.720729.58536.33436.3346.74925.575-0.500 1.0347.528.

12、63234.88234.8826.25024.541-0.488 0.977827.72933.49033.4905.76123.563-0.470 0.9098.526.88032.17132.1715.29122.654-0.446 0.834926.08830.93330.9334.84521.820-0.420 0.7569.525.35329.77829.7784.42521.064-0.393 -1.0121024.67628.70828.7084.03222.075-0.364 0.52210.524.05327.72127.7213.66821.554-0.337 0.4481

13、123.48226.81326.8133.33121.105-0.310 0.37911.522.96025.98225.9823.02120.726-0.284 0.3131222.48525.22225.2222.73720.413-0.260 0.25212.522.05224.53024.5302.47820.161-0.237 0.1961321.65923.90023.9002.24119.965-0.216 0.14313.521.30323.32823.3282.02519.822-0.196 0.4621420.98022.80822.8081.82919.360-0.178

14、 0.06414.520.68722.33822.3381.65119.296-0.161 0.0241520.42321.91221.9121.49019.273-0.146 -0.01215.520.18321.52721.5271.34319.285-0.132 -0.0451619.96821.17921.1791.21119.330-0.119 -0.07516.519.77320.86420.8641.09219.405-0.108 -0.1021719.59720.58120.5810.98419.507-0.097 -0.12617.519.43820.32420.3240.8

15、8619.633-0.088 -0.1481819.29520.09320.0930.79919.780-0.079 -0.16718.519.16619.88519.8850.71919.947-0.072 -0.1841919.05019.69719.6970.64820.132-0.064 -0.20019.518.94519.52819.5280.58320.332-0.058 -0.2142018.85119.37619.3760.52520.546-0.052 -0.22620.518.76619.23819.2380.47320.772-0.047 -0.2372118.6891

16、9.11519.1150.42521.010-0.042 -0.24721.518.62019.00319.0030.38321.257-0.038 -0.2562218.55818.90318.9030.34521.512-0.034 -0.26322.518.50218.81318.8130.31021.776-0.031 -0.2702318.45218.73118.7310.27922.046-0.028 -0.27623.518.40718.65818.6580.25122.322-0.025 -0.2812418.36618.59218.5920.22622.603-0.023 -

17、0.28624.518.32918.53318.5330.20322.888-0.020 -0.2892518.29618.48018.4800.18323.178-0.018 -0.29325.518.26718.43118.4310.16523.471-0.017 -0.2962618.24018.38818.3880.14823.766-0.015 -0.29826.518.21618.34918.3490.13324.064-0.013 -0.3002718.19418.31418.3140.12024.364-0.012 -0.30127.518.17518.28318.2830.1

18、0824.665-0.011 -0.3032818.15718.25418.2540.09724.968-0.097 /注：表中*T1和*T2列中括号内数值为按照以下公式计算结果，其值在计算自约束应力和外约束应力时使用。 （B.6.1-2） （B.6.2-2） 表3各龄期混凝土收缩当量温差计算结果混凝土龄期y(t)(10-4)Ty(t)Ty(t)00.000 0.000 0.517 0.50.052 0.517 0.515 10.103 1.032 0.512 1.50.154 1.545 0.510 20.205 2.054 0.484 2.50.254 2.539 0.500 30.304

19、 3.039 0.176 3.50.321 3.215 0.450 40.367 3.665 -0.046 4.50.362 3.619 0.392 50.401 4.012 0.390 5.50.440 4.402 0.388 60.479 4.790 0.386 6.50.518 5.177 -0.311 70.487 4.866 0.335 7.50.520 5.201 0.333 80.553 5.534 0.331 8.50.587 5.865 0.330 90.619 6.195 0.328 9.50.652 6.523 2.017 100.854 8.539 0.405 10.5

20、0.894 8.944 0.403 110.935 9.347 0.401 11.50.975 9.748 0.399 121.015 10.147 0.397 12.51.054 10.544 0.395 131.094 10.939 0.393 13.51.133 11.332 0.025 141.136 11.357 0.377 14.51.173 11.734 0.375 151.211 12.109 0.373 15.51.248 12.482 0.371 161.285 12.853 0.369 16.51.322 13.223 0.368 171.359 13.590 0.366

21、 17.51.396 13.956 0.364 181.432 14.320 0.362 18.51.468 14.682 0.360 191.504 15.042 0.359 19.51.540 15.401 0.357 201.576 15.758 0.355 20.51.611 16.113 0.353 211.647 16.466 0.351 21.51.682 16.817 0.350 221.717 17.167 0.348 22.51.751 17.515 0.346 231.786 17.861 0.344 23.51.821 18.206 0.343 241.855 18.5

22、48 0.341 24.51.889 18.889 0.339 251.923 19.229 0.338 25.51.957 19.567 0.336 261.990 19.902 0.334 26.52.024 20.237 0.333 272.057 20.569 0.331 27.52.090 20.900 0.329 282.123 21.230 1、 各龄期的混凝土弹性模量基础混凝土浇灌初期，处于升温阶段，呈塑性状态，混凝土的弹性模量很小，由变形变化引起的应力也很小，温度应力一般可忽略不计。经过数日，弹性模量随时间迅速上升，此时由变形变化引起的应力状态（即混凝土降温引起拉应力）随着弹性模量的上升显著增加，因此必需考虑弹性模量的变化规律，一般按下