溫度場(chǎng)和溫度應(yīng)力計(jì)算

1、附計(jì)算書(shū)3：溫度場(chǎng)和溫度應(yīng)力計(jì)算一、溫度場(chǎng)計(jì)算計(jì)算以本工程1.2m厚底板為例，用差分法計(jì)算底板28d水化熱溫升曲線。計(jì)算中各參數(shù)的取值如下：每m3膠凝材料用量，440kg/ m3； Q膠凝材料水化熱總量（kJ/kg）；，本例采用實(shí)測(cè)值260kJ/kg；混凝土的比熱，取1.0kJ/ (kg)； 混凝土的質(zhì)量密度，取2400kg/ m3；導(dǎo)溫系數(shù)，取0.0035m2/h；m，取0.5?；炷恋娜肽囟热?0，地基溫度為18，大氣溫度為18。溫度場(chǎng)計(jì)算差分公式如下： （B.4.2-1）試算、，確定。取 = 0.5天 = 12小時(shí)， = 0.4m，即分3層則，可行。代入該值得出相應(yīng)的差分法公式為畫(huà)出相

2、應(yīng)的計(jì)算示意圖，并進(jìn)行計(jì)算。底板厚1.2m，分3層，每層0.4m，相應(yīng)的計(jì)算示意如下圖。2 / 20從上至下各層混凝土的溫度分別用、表示，相應(yīng)時(shí)刻各層的溫度即為、?；炷僚c大氣接觸的上表面邊界溫度用表示，與地基接觸的下表面邊界溫度用表示。 = 0，即第天，上表面邊界，取大氣溫度， = 18各層混凝土溫度取入模溫度，即= = = 10下表面邊界，取地基溫度，= 18； = 1，即第天，溫升10.544上表面邊界溫度，散熱溫升為0，始終保持不變， = 18 第一層混凝土溫度，見(jiàn)計(jì)算圖示中方框1，的邊界為和，在的基礎(chǔ)上考慮溫升，即第二層混凝土溫度，見(jiàn)計(jì)算圖示中方框2，的邊界為和，在的基礎(chǔ)上考慮溫升，

3、即第三層混凝土溫度，見(jiàn)計(jì)算圖示中方框3，的邊界為和，在的基礎(chǔ)上考慮溫升，即下表面邊界溫度，需要考慮散熱溫升，所以需每一步都需進(jìn)行修正。見(jiàn)計(jì)算圖示中方框6，的邊界為和地基溫度18，在的基礎(chǔ)上考慮溫升，即以上即完成了一遍 = 1時(shí)，各溫度計(jì)算。同理 = 2，即第天，溫升 = 8.212，上表面 = 18，同理可計(jì)算 = 356，即第1.528天的各層溫度值，本算例中不再進(jìn)行詳細(xì)計(jì)算，最終計(jì)算結(jié)果如表1。表1 不同混凝土齡期下各層混凝土溫度值（單位：）混凝土齡期上表面第一層第二層第三層底界邊層018101010180.51822.64420.54422.64426.44411829.08529.85

4、831.30231.4411.51832.77336.42937.35434.27121834.83640.69341.28335.7902.51835.83343.18943.56536.44131836.10344.37844.61736.4913.51835.87644.62144.77436.123混凝土齡期上表面第一層第二層第三層底界邊層41835.31144.19844.29535.4694.51834.52743.31843.38034.62751833.60742.13842.17733.6715.51832.61540.77440.79932.65661831.59439.3

5、1339.32931.6206.51830.57737.81637.82630.59471829.58536.32736.33429.5957.51828.63234.87834.88228.63981827.72933.48733.49027.7338.51826.88032.16932.17126.88291826.08830.93230.93326.0899.51825.35329.77729.77825.354101824.67628.70828.70824.67610.51824.05327.72027.72124.053111823.48226.81326.81323.48211.

6、51822.96025.98225.98222.961121822.48525.22225.22222.48512.51822.05224.53024.53022.052131821.65923.90023.90021.65913.51821.30323.32823.32821.303141820.98022.80822.80820.98014.51820.68722.33822.33820.687151820.42321.91221.91220.42315.51820.18321.52721.52720.183161819.96821.17921.17919.96816.51819.7732

7、0.86420.86419.773171819.59720.58120.58119.59717.51819.43820.32420.32419.438181819.29520.09320.09319.29518.51819.16619.88519.88519.166191819.05019.69719.69719.05019.51818.94519.52819.52818.945201818.85119.37619.37618.85120.51818.76619.23819.23818.766211818.68919.11519.11518.68921.51818.62019.00319.00

8、318.620221818.55818.90318.90318.55822.51818.50218.81318.81318.502231818.45218.73118.73118.45223.51818.40718.65818.65818.407241818.36618.59218.59218.36624.51818.32918.53318.53318.329混凝土齡期上表面第一層第二層第三層底界邊層251818.29618.48018.48018.29625.51818.26718.43118.43118.267261818.24018.38818.38818.24026.51818.216

9、18.34918.34918.216271818.19418.31418.31418.19427.51818.17518.28318.28318.175281818.15718.25418.25418.157二、溫度應(yīng)力計(jì)算示例以下計(jì)算示例按照步長(zhǎng)為1天進(jìn)行。1、里表溫差T1計(jì)算公式如下 （B.5.1）計(jì)算結(jié)果見(jiàn)表2 各齡期混凝土收縮當(dāng)量溫差計(jì)算根據(jù)公式 （B.2.1） （B.2.2）其中 取4.010-4石家莊市內(nèi)年平均氣溫值取14.5計(jì)算結(jié)果見(jiàn)表3 綜合降溫差T2計(jì)算公式如下 （B.5.2）計(jì)算結(jié)果見(jiàn)表2表2 綜合溫差計(jì)算結(jié)果混凝土齡期第一層(Tb)第三層（Tm）第三層（Td）T1（Tm-

10、 Tb）T2*T1*T201010100.0000.000/-8.6610.522.64422.64422.6440.0008.6612.217 -8.803混凝土齡期第一層(Tb)第三層（Tm）第三層（Td）T1（Tm- Tb）T2*T1*T2129.08531.30231.3022.21717.4652.365 -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 -1.422336.1

11、0344.61744.6178.51431.7370.384 -0.2693.535.87644.77444.7748.89832.0060.086 0.043435.31144.29544.2958.98431.963-0.131 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.

12、57737.82637.8267.24927.295-0.500 1.720729.58536.33436.3346.74925.575-0.500 1.0347.528.63234.88234.8826.25024.541-0.488 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 -1.012102

13、4.67628.70828.7084.03222.075-0.364 0.52210.524.05327.72127.7213.66821.554-0.337 0.4481123.48226.81326.8133.33121.105-0.310 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

14、.14313.521.30323.32823.3282.02519.822-0.196 0.4621420.98022.80822.8081.82919.360-0.178 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

15、.405-0.108 -0.1021719.59720.58120.5810.98419.507-0.097 -0.12617.519.43820.32420.3240.88619.633-0.088 -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 -0.2142018.85119.37

16、619.3760.52520.546-0.052 -0.22620.518.76619.23819.2380.47320.772-0.047 -0.2372118.68919.11519.1150.42521.010-0.042 -0.247混凝土齡期第一層(Tb)第三層（Tm）第三層（Td）T1（Tm- Tb）T2*T1*T221.518.62019.00319.0030.38321.257-0.038 -0.2562218.55818.90318.9030.34521.512-0.034 -0.26322.518.50218.81318.8130.31021.776-0.031 -0.27

17、02318.45218.73118.7310.27922.046-0.028 -0.27623.518.40718.65818.6580.25122.322-0.025 -0.2812418.36618.59218.5920.22622.603-0.023 -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 -0.2962618.24018.38818.3880.14823.7

18、66-0.015 -0.29826.518.21618.34918.3490.13324.064-0.013 -0.3002718.19418.31418.3140.12024.364-0.012 -0.30127.518.17518.28318.2830.10824.665-0.011 -0.3032818.15718.25418.2540.09724.968-0.097 /注：表中*T1和*T2列中括號(hào)內(nèi)數(shù)值為按照以下公式計(jì)算結(jié)果，其值在計(jì)算自約束應(yīng)力和外約束應(yīng)力時(shí)使用。 （B.6.1-2） （B.6.2-2） 表3各齡期混凝土收縮當(dāng)量溫差計(jì)算結(jié)果混凝土齡期y(t)(10-4)Ty(t)T

19、y(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 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 混凝土齡期y(t)(10-4

20、)Ty(t)Ty(t)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 10.50.894 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 0.0

21、25 141.136 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 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

22、.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 18.548 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 混凝土齡期y(t)(10-4)Ty(t)Ty(t)282.123 21.230 1、 各齡期的混凝土彈性模量基礎(chǔ)混凝土澆灌初期，處于升溫階段，呈塑性狀態(tài)，混凝土的彈性模量很小，由變形變化引起的應(yīng)力也很小，溫度應(yīng)力一般可忽略不計(jì)。經(jīng)過(guò)數(shù)日，彈性模量隨時(shí)間迅速上升，此時(shí)由變形變化引起的應(yīng)力狀態(tài)（即混凝土降溫引起拉應(yīng)力）隨著彈性模量的上升顯著增加，因此必需考慮彈性模量的變化規(guī)律，一般按下列公式計(jì)算：式中 任意齡期的彈性模量； 最終的彈性模量，一般