(整理)溫度場(chǎng)和溫度應(yīng)力計(jì)算

1、精品文檔附計(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：W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；C混凝土的比熱，取1.0kJ/(kg.。C)；P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。C，地基溫度為18。C，大氣溫度為18。C。溫度場(chǎng)計(jì)算差分公式如下：T+TAtAt、T=k十2a-T(2a-1)+AT(B.4.2-1)n,k+12Ax2n,kAx2n,k試算At、

2、Ax，確定u。Ax2取At=0.5天=12小時(shí)，Ax=0.4m，即分3層貝yu竺=0.0035X旦=0.2625沁1，可行。Ax20.424代入該值得出相應(yīng)的差分法公式為T(mén)+TT二0.525-n,k+12n,kk畫(huà)出相應(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。從上至下各層混凝土的溫度分別用T、T、T表示，相應(yīng)k時(shí)刻各層的溫度即為T(mén)、1231kT2,k、T3,k?；炷僚c大氣接觸的上表面邊界溫度用T表示，與地基接觸的下表面邊界溫度用T0表示。k=0，即第k-At二0-0.5二0天，上表面邊界T，取大氣溫度，T=18。C00各層混凝土溫度取入模溫度，即

3、T1,0=T2,0=T30=10。C下表面邊界T0，取地基溫度，T0=18。C；k=1，即第k-At二1-0.5二0.5天，溫升AT=T1max(e一m-(k-1)-Ate一m-k-At)二440-260-(e-0，(1-1).0.5-e-0，1.0.5)二1.0-240010.544。C上表面邊界溫度T，散熱溫升為0,始終保持不變，T=18。C00第一層混凝土溫度，見(jiàn)計(jì)算圖示中方框1，的邊界為T(mén)0和，在的基礎(chǔ)上考慮溫升AT,即T+TT二0.525-0辺+0.475-T+AT二22.644。C1,121,01第二層混凝土溫度，見(jiàn)計(jì)算圖示中方框2,的邊界為一,0和一,0，在的基礎(chǔ)上考慮溫升AT，

4、即1T+TT二0.525-丄辺+0.475-T+AT二20.544。C2,122,01第三層混凝土溫度T3,1，見(jiàn)計(jì)算圖示中方框3,T3,1的邊界為T(mén)2,0和丁，在T3,0的基礎(chǔ)上考慮溫升AT,即1T+TT=0.525t+0.475-T+AT=22.644C23,01下表面邊界溫度T0，需要考慮散熱溫升AT/2，所以需每一步都需進(jìn)行修正。見(jiàn)計(jì)算01圖示中方框6，T0的邊界為T(mén)30和地基溫度18。C，在T0的基礎(chǔ)上考慮溫升AT/2，即03,001,T+18,ATT=0.525亠+0.475-T+1=26.444C0202以上即完成了一遍k=1時(shí)，各溫度計(jì)算。同理k=2，即第k-At二2-0.5二

5、1天，溫升AT=8.212。C，2上表面T0=18oC，T+TT=0.525亠21+0.475-T+AT=29.085C21,12T+TT=0.525+31+0.475-T+AT=29.858C22,12T+TT=0.525亠0+0.475-T+AT=31.302C23,12T+18ATT=0.525亠+0.475T+2=31.441C0202同理可計(jì)算k=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：。C）混凝土齡期上表面第一層第二層第三層底界邊層018101010180.51822.64420.54422.6

6、4426.44411829.08529.85831.30231.4411.51832.77336.42937.35434.27121834.83640.69341.28335.7902.51835.83343.18943.56536.44131836.10344.37844.61736.4913.51835.87644.62144.77436.12341835.31144.19844.29535.469混凝土齡期上表面第一層第二層第三層底界邊層4.51834.52743.31843.38034.62751833.60742.13842.17733.6715.51832.61540.77440.

7、79932.65661831.59439.31339.32931.6206.51830.57737.81637.82630.59471829.58536.32736.33429.5957.51828.63234.87834.88228.63981827.72933.48733.49027.7338.51826.88032.16932.17126.88291826.08830.93230.93326.0899.51825.35329.77729.77825.354101824.67628.70828.70824.67610.51824.05327.72027.72124.053111823.48

8、226.81326.81323.48211.51822.96025.98225.98222.961121822.48525.22225.22222.48512.51822.05224.53024.53022.052131821.65923.90023.90021.65913.51821.30323.32823.32821.303141820.98022.80822.80820.98014.51820.68722.33822.33820.687151820.42321.91221.91220.42315.51820.18321.52721.52720.183161819.96821.17921.

9、17919.96816.51819.77320.86420.86419.773171819.59720.58120.58119.59717.51819.43820.32420.32419.438181819.29520.09320.09319.29518.51819.16619.88519.88519.166191819.05019.69719.69719.05019.51818.94519.52819.52818.945201818.85119.37619.37618.85120.51818.76619.23819.23818.766211818.68919.11519.11518.6892

10、1.51818.62019.00319.00318.620221818.55818.90318.90318.55822.51818.50218.81318.81318.502231818.45218.73118.73118.452混凝土齡期上表面第一層第二層第三層底界邊層23.51818.40718.65818.65818.407241818.36618.59218.59218.36624.51818.32918.53318.53318.329251818.29618.48018.48018.29625.51818.26718.43118.43118.267261818.24018.38818

11、.38818.24026.51818.21618.34918.34918.216271818.19418.31418.31418.19427.51818.17518.28318.28318.175281818.15718.25418.25418.157二、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4T1計(jì)算公式如下AT(t)二T(t)-T(t)(B.5.1)1mb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8(t)=8o(1e-o.oit)-M-M-MM(B.2.1)yy12311T(t)=8(t)/a(B.2.2)yy其中80取4.0X10-4y石家莊市內(nèi)年平均氣溫值

12、取14.5C計(jì)算結(jié)果見(jiàn)表3綜合降溫差t2計(jì)算公式如下AT(t)=-4T(tT(細(xì)T(t卡T)T他/)26mbmdmyw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-Tb)T2*T1*T2混凝土齡期第一層(Tb)第三層(Tm)第三層(Td)T1(Tm-Tb)T2*T1*T201010100.0000.000/-8.6610.522.64422.64422.6440.0008.6612.217-8.803129.08531.30231.3022.21717.4652.365-6.1711.532.77337.35437.3544.58123.63

13、61.866-4.127234.83641.28341.2836.44727.7631.285-2.5522.535.83343.56543.5657.73230.3150.781-1.422336.10344.61744.6178.51431.7370.384-0.2693.535.87644.77444.7748.89832.0060.0860.043435.31144.29544.2958.98431.963-0.1310.9394.534.52743.38043.3808.85331.024-0.2830.763533.60742.17742.1778.57030.261-0.3850

14、.9235.532.61540.79940.7998.18429.337-0.4501.007631.59439.32939.3297.73528.330-0.4851.0366.530.57737.82637.8267.24927.295-0.5001.720729.58536.33436.3346.74925.575-0.5001.0347.528.63234.88234.8826.25024.541-0.4880.977827.72933.49033.4905.76123.563-0.4700.9098.526.88032.17132.1715.29122.654-0.4460.8349

15、26.08830.93330.9334.84521.820-0.4200.7569.525.35329.77829.7784.42521.064-0.393-1.0121024.67628.70828.7084.03222.075-0.3640.52210.524.05327.72127.7213.66821.554-0.3370.4481123.48226.81326.8133.33121.105-0.3100.37911.522.96025.98225.9823.02120.726-0.2840.3131222.48525.22225.2222.73720.413-0.2600.25212

16、.522.05224.53024.5302.47820.161-0.2370.1961321.65923.90023.9002.24119.965-0.2160.14313.521.30323.32823.3282.02519.822-0.1960.4621420.98022.80822.8081.82919.360-0.1780.06414.520.68722.33822.3381.65119.296-0.1610.0241520.42321.91221.9121.49019.273-0.146-0.01215.520.18321.52721.5271.34319.285-0.132-0.0

17、451619.96821.17921.1791.21119.330-0.119-0.07516.519.77320.86420.8641.09219.405-0.108-0.1021719.59720.58120.5810.98419.507-0.097-0.12617.519.43820.32420.3240.88619.633-0.088-0.1481819.29520.09320.0930.79919.780-0.079-0.16718.519.16619.88519.8850.71919.947-0.072-0.1841919.05019.69719.6970.64820.132-0.

18、064-0.20019.518.94519.52819.5280.58320.332-0.058-0.2142018.85119.37619.3760.52520.546-0.052-0.226混凝土齡期第一層(Tb)第三層(Tm)第三層(Td)T1(Tm-Tb)T2*T1*T220.518.76619.23819.2380.47320.772-0.047-0.2372118.68919.11519.1150.42521.010-0.042-0.24721.518.62019.00319.0030.38321.257-0.038-0.2562218.55818.90318.9030.34521

19、.512-0.034-0.26322.518.50218.81318.8130.31021.776-0.031-0.2702318.45218.73118.7310.27922.046-0.028-0.27623.518.40718.65818.6580.25122.322-0.025-0.2812418.36618.59218.5920.22622.603-0.023-0.28624.518.32918.53318.5330.20322.888-0.020-0.2892518.29618.48018.4800.18323.178-0.018-0.29325.518.26718.43118.4

20、310.16523.471-0.017-0.2962618.24018.38818.3880.14823.766-0.015-0.29826.518.21618.34918.3490.13324.064-0.013-0.3002718.19418.31418.3140.12024.364-0.012-0.30127.518.17518.28318.2830.10824.665-0.011-0.3032818.15718.25418.2540.09724.968-0.097/注：表中*4片和*4T2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。AT(t)=AT(t

21、)-AT(t-j)(B.6.1-2)1i11AT(t)二AT(t-j)-AT(t)(B.6.2-2)2i22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)Ty(t)00.0000.0000.5170.50.0520.5170.51510.1031.0320.5121.50.1541.5450.51020.2052.0540.4842.50.2542.5390.50030.3043.0390.1763.50.3213.2150.45040.3673.665-0.0464.50.3623.6190.39250.4014.0120.3905.50.4404.4020.3

22、8860.4794.7900.386混凝土齡期8y(t)(10-4)Ty(t)Ty(t)6.50.5185.177-0.31170.4874.8660.3357.50.5205.2010.33380.5535.5340.3318.50.5875.8650.33090.6196.1950.3289.50.6526.5232.017100.8548.5390.40510.50.8948.9440.403110.9359.3470.40111.50.9759.7480.399121.01510.1470.39712.51.05410.5440.395131.09410.9390.39313.51.1

23、3311.3320.025141.13611.3570.37714.51.17311.7340.375151.21112.1090.37315.51.24812.4820.371161.28512.8530.36916.51.32213.2230.368171.35913.5900.36617.51.39613.9560.364181.43214.3200.36218.51.46814.6820.360191.50415.0420.35919.51.54015.4010.357201.57615.7580.35520.51.61116.1130.353211.64716.4660.35121.

24、51.68216.8170.350221.71717.1670.34822.51.75117.5150.346231.78617.8610.34423.51.82118.2060.343241.85518.5480.34124.51.88918.8890.339251.92319.2290.33825.51.95719.5670.336261.99019.9020.33426.52.02420.2370.333272.05720.5690.331混凝土齡期&y(t)(10-4)Ty(t)Ty(t)27.52.09020.9000.329282.12321.2301、各齡期的混凝土彈性模量基礎(chǔ)混

25、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：E二E(1一e-o.09t)(t)(0)式中E任意齡期的彈性模量；(t)Eo最終的彈性模量，一般取成齡的彈性模量，取3.15x104N/mm2；t混凝土澆灌后到計(jì)算時(shí)的天數(shù)。各階段彈性模量：E=0.271x104N/mm2(1)E=0.519x104N/mm2(2)E=0.745x104N/mm2(3)E=1.314

26、x104N/mm2(6)E=1.749x104N/mm2(9)E=2.080 x104N/mm2(12)E=2.333x104N/mm2(15)E=2.527x104N/mm2(18)E=2.674x104N/mm2(21)E=2.787x104N/mm2(24)E=2.873x104N/mm2(27)E=2.938x104N/mm2(30)2、自約束應(yīng)力計(jì)算根據(jù)公式(XnB.6.1-1)o(t)=AT(t)E(t)H(t,t)z21iiii=1o(1)=1.0X10-42X4.581X2710X1=0.62Mpao(2)=1.0X10-42X(4.581X2710X1+3.151x5190

27、x1)=1.44Mpao=1.0X10-4x(4.581x2710 x0.278+3.151x5190 x0.278+1.166x7450 x1)=0.83Mpa2根據(jù)表2中計(jì)算結(jié)果，3.5天后AT(t)變?yōu)樨?fù)值，同時(shí)由于徐變效應(yīng)，自約束應(yīng)力計(jì)算值將減小，本算例中不再計(jì)算。3、外約束應(yīng)力的計(jì)算公式如下Xno(t)=AT(t)E(t)H(t)xR(t)(B.6.2-1)x1H2iii1ii=1式中L底板長(zhǎng)度，考慮單組底板最長(zhǎng)為27000mm；|CHE其中H基礎(chǔ)底板厚度，本例為1200mm；C總阻力系數(shù)(地基水平剪切剛度)，N/mm3，本工程采用鋼制模版加支撐x鋼結(jié)構(gòu)，考慮成型混凝土結(jié)構(gòu)要滿足驗(yàn)收標(biāo)準(zhǔn)，近似將混凝土外側(cè)結(jié)構(gòu)看做高強(qiáng)度混凝土阻力系數(shù)取0.01N/mm3。前期升溫外約束應(yīng)力為壓應(yīng)力，由于早期彈性模量較小且徐變時(shí)間較長(zhǎng)，其值不大，實(shí)際應(yīng)用中可將這部分壓應(yīng)力作為安全儲(chǔ)備。外約束應(yīng)力計(jì)算時(shí)從降溫階段開(kāi)始。1)9天(第1臺(tái)階降溫)自第9天至第30天的徐變應(yīng)力：0=001=2.183x10-51200 x1.749xl04pL=2.183x10-5x27000=0.294722chp查表得（9）=1749x104x