全預(yù)應(yīng)力混凝土梁設(shè)計

1、全預(yù)應(yīng)力混凝土梁設(shè)計一設(shè)計題目預(yù)應(yīng)力混凝土簡支 T梁設(shè)計二設(shè)計資料1. 橋梁跨徑與橋?qū)挊藴士鐝剑?0m (墩中心距離)主梁全長：39.96m計算跨徑：39.0m橋面凈空：凈 14+2 X 1.75m=17.5m2. 設(shè)計荷載：城一A級車輛荷載，人群荷載 3.0kN/m，結(jié)構(gòu)重要性指數(shù)0=：1.1。3. 材料性能參數(shù)(1) 混凝土強度等級為C50,主要強度指標為：強度標準值 fck =32.4Mpa, ftk =2.65Mpa強度設(shè)計值 憶=22.4Mpa,酩=1.83Mpa強度模量Ec =3.45 104MPa(2) 預(yù)應(yīng)力鋼筋采用1 X 7標準型一15.2 186011 GB/T522419

2、95鋼絞線，其強度 指標為：抗拉強度標準值fpk =1860MPa抗拉強度設(shè)計值fpd = 1260Mpa彈性模量Ec=1.95 1 05MPa相對界限受壓區(qū)高度I =0.4, =0.2563(3 )預(yù)應(yīng)力錨具采用 OVM錨具(4 )普通鋼筋1 )縱向抗拉普通鋼筋采用HRB400鋼筋，其強度指標為抗拉強度標準值fsk =400MPa抗拉強度設(shè)計值fsd =330MPa彈性模量Es =2.0 105MPa相對界限受壓區(qū)高度0.53, p 0.19852 )箍筋及構(gòu)造鋼筋采用 HRB335鋼筋，其強度指標為抗拉強度標準值fsk =335MPa抗拉強度設(shè)計值 fsd =280MPa彈性模量Es =2

3、.0 105MPa4. 主要結(jié)構(gòu)構(gòu)造尺寸主梁高度 h = 2300mm，主梁間距 S = 2500mm，其中主梁上翼緣預(yù)制部分寬為 1600mm，現(xiàn)澆段寬為900mm，全橋由7片梁組成，設(shè)7道橫隔梁。5. 內(nèi)力計算結(jié)果摘錄預(yù)制主梁(包括橫隔梁)的自重=24.46kN/m主梁現(xiàn)澆部分的自重g1m =4.14kN/m二期恒載(包括橋面鋪裝、人行道及欄桿)g2p =8.16kN/m(1)恒載內(nèi)力：恒載內(nèi)力計算結(jié)果表1截面位置距支點截面的距離x ( mm預(yù)置梁自重現(xiàn)澆段自重二期恒載彎矩剪力彎矩剪力彎矩剪力M G1PK(kN m)VG1 PK(kN)M G1MK(kN m)VG1MK(kN)M G2K(

4、kN m)VG2K(kN)支點00.00476.970.0080.730.00159.12變截面2000905.02428.05153.1872.45301.92142.80L/497503487.84238.49590.3440.371163.5779.56跨中195004650.460787.1201551.420(2)活載內(nèi)力:活載內(nèi)力計算結(jié)果表2截面位置距支點截 面的距離x(mmA級車道荷載人群何載取大彎矩最大剪力最大彎矩最大剪力M Q1K(kN m)對應(yīng)V(kN)VQ1K(kN)對應(yīng)M(kN m)M Q2K(kN m)對應(yīng)V(kN)VQ2K(kN)對應(yīng)M(kN m)支點00251.9

5、3251.930032.6932.690變截面2000472.44235.79215.711335.6559.8632.5637.13135.65L/497501762.50173.23175.321675.25230.6732.4617.74183.68跨中195002427.6621.6890.431724.75307.5714.267.89155.26(3 )內(nèi)力計算組合:1) 基本組合M d =1.2( M GK 1P + M GK1m + M GK2 )+1.4 Mqik+1.12 M Q2KVd =1.2( VGK1P+VGK1m+VGK2 )+14 VQ1K+1.12 VQ2K2

6、) 短期組合M Q1KMs=( M GK1P + M GK1m + M gk 2)+.7+ M Q2K1 + A3) 長期組合M Q1KM L =( M GK1P+ M GK1m + M GK2 )+0.4(- + M Q2K )1 +卩荷載內(nèi)力計算結(jié)果表3截面位置項目基本組合Sd短期組合Ss長期組合SlMdVdMsVsM LVl(kN? m)(kN)(kN? m)(kN)(kN? m)(kN)支點取大彎矩0.001249.500.00907.140.00819.97最大剪力0.001249.500.00907.140.00819.97、-M、7取大彎矩2360.601138.531715.5

7、7823.391552.97740.63變截面最大剪力3653.981115.542331.45815.391891.91735.27L/4最大彎矩9015.95708.986572.16499.265964.16433.34最大剪力8841.17695.426473.58485.855914.17428.20跨中最大彎矩12130.0046.328815.4827.827979.9813.46最大剪力10975.34135.448223.3864.477667.7535.49設(shè)計內(nèi)容:(一) 預(yù)應(yīng)力鋼筋數(shù)量的確定及布置首先，根據(jù)跨中截面正截面抗裂要求，確定預(yù)應(yīng)力鋼筋數(shù)量。為滿足抗裂要求，所需

8、的有效預(yù)加力為N Ms.W1 ep0.85( p)A WMs為短期效應(yīng)彎矩組合設(shè)計值，由表3查得Ms = 8815.48 kN? m估算鋼筋數(shù)量時，可近似采用毛截面幾何性質(zhì)。按跨中截面尺寸圖給定的截面尺寸計算：6 2Ac =0.968750 10 mm ， y =1610.71mm， yc -689.29mm，JC =0.2649 10 mm4 , Wx =0.1645 109mm3ep為預(yù)應(yīng)力鋼筋重心至毛截面重心的距離，ep二ycx-ap假設(shè) ap =150mm則 ep =1610.71-150 =1460.71mm由此得到pe68815.48 10 164468286.80.85 (968

9、7501460.71)164468286.8)-6360782.9N擬采用j15.2鋼絞線，單根鋼絞線的公稱截面面積Ap1 =139mm2，抗拉強度標準值fpk =1860MPa，張拉控制應(yīng)力取 on =0.75fpk =0.75 1860 = 1395MPa，預(yù)應(yīng)力損失按張拉控制力的20%估算。npNpe(二con d)Ap6360782.9(1 -0.2) 1395 139= 41.0045,取 48 根。采用4束12 j15.2預(yù)應(yīng)力鋼筋束，OVM-12型錨具，供給的預(yù)應(yīng)力筋截面面積Ap =48 139 = 6672mm2，采用 80金屬波紋管成孔，預(yù)留管道直徑為85mm。預(yù)應(yīng)力筋束曲線

10、要素表表4鋼束編號起彎點距跨中(mm曲線水平長度(mm曲線方程1019980_6 2y = 250 + 4.80961X0 x2400015980y =150 + 6.46146x10x23、4120007980y =150 + 7.066540x2各計算截面預(yù)應(yīng)力鋼筋束的位置和傾角面錨固截面支點截面變截面點L/4截面跨屮截面截面距離跨中(mr)199801950017500975001號束21702078.91722.9638.8250鋼束到梁2號束18001652.41277.6313.6100底的距離（mm3、4號束600497.5331.9100100合力點1292.51181.691

11、6.8288.1137.5鋼束與水 平線夾角（度）1號束12.087911.804210.61715.953302號束12.964512.585310.99584.721803、4號束7.14976.72294.938600平均值9.83809.45887.87252.66880累計角度（度）1號束00.28371.47086.134612.08792號束00.37921.96878.242712.96453、4號束00.42682.21117.14977.1497（二）截面幾何性質(zhì)計算部分預(yù)應(yīng)力各階段截面幾何性質(zhì)表6階段截面A106 mmys(mmyx(mn)ep(mm)I10 mmW(x

12、109 mm3)WH %Wp = l/ep階段1：鋼束 灌漿、錨固刖支點1.432301010.741289.26107.660.730560.566650.722800.67858變截面0.991831083.951216.05299.250.642660.528480.592890.21476L/40.81105926.681373.321084.970.543920.396060.586960.51386跨中0.81105926.931373.071235.570.534520.389290.576810.43261階段2:現(xiàn)澆600mm連接 段支點1.478121021.281278.

13、7297.120.760220.594520.744380.78276變截面1.037511096.841203.16286.360.675120.561120.615510.23576L/40.85674992.831307.171019.090.612650.468680.617070.60119跨中0.85674992.751307.251169.750.613240.469120.617720.52452階段3:二期 何載、活載支點1.61313937.581362.42180.820.874520.641890.868750.48364變截面1.17251979.791320.214

14、03.410.801920.607420.818461.98785L/40.99174874.831425.171137.070.721430.506210.824650.63446跨中0.99174867.851432.151294.650.726300.507130.836900.56100（三）承載能力極限狀態(tài)計算1.跨中截面正截面承載力計算150 匯3+250 一ap175mmp4hp = h - ap = 2300 -175 = 2125mmb = 200mm,上翼板厚度為150mm，考慮承托影響，其平均厚度為hf =150 2 0.5 500 100 (2500-200) = 17

15、1.74mm上翼緣有效寬度取下列數(shù)值較小者(1) bf _s = 2500(2)bflL 3 =39003=13000mm(3)bf b 12hf,因承托坡度hbh =100500 = 0.2 ： 1.3故不計承托影響，hf按上翼緣平均厚度計算 bf 200 12 171.74 = 2260mm綜上，hf取2260 mm首先按公式fpdAp豈fcdbfhf判斷截面類型，代入數(shù)據(jù)計算得fpdAp=1260 6672 =8406720Nfcdbfhf =22.4 2260 171.7 =8692140.8N因為84067208692140.8,滿足上式要求，屬于第一類T型，應(yīng)按寬度為bf的矩形截面

16、計算其承載力。由a X = 0的條件，計算混凝土受壓區(qū)高度X 二fcdbf1260 667222.4 2260=166.1mm 乞 171.7mm乞 bho =0.4 2125 = 850mm將x二166.1mm代入下式計算截面承載能力Mdu = Qbfx(h0 -仝)=171700Md = 12130kN2計算結(jié)果表明，跨中截面的抗彎承載力滿足要求。2.斜截面抗剪承載力計算(1 )距支點h/2截面斜截面抗剪承載力計算首先進行截面抗剪強度上下限復(fù)核0.5M0%2ftdbho JVd 蘭0.510jf7bhoVd為驗算截面處剪力組合設(shè)計值，按內(nèi)插法得距支點h2 =1150mm處，V為1192.4

17、預(yù)應(yīng)力：2取1.25 ； 驗算截面距支點1150處的截面腹板寬度 b = 550mm，取h 2125mm求得：1336.8 0Vd =1311.64kN : 4214.8kN斜截面抗剪承載力計算0Vd Vcs VpdVd = 1192.4kN,=1.0,2 = 1.25,-3 = 1.1, b = 550mmApb十宀100( pb 3=0.5709bh。 A =0.001829 bSvVcs： 3 0.45 10bh (2 0.6 J fcu,kfsd,v =2106.24kN-p1 =10.01，邛2 =10.51 ,齊3,4 =5.13Vpb =0.75 10” fpApd sinp=8

18、43.39kNVdu =VCs Vpd =2949.6CkN0Vd =1311.64kN說明截面抗剪承載力是足夠的。(2)變截面點處斜截面抗剪承載力計算首先進行抗剪強度上、下限復(fù)核：0.5 10： 2ftdbh Vd 乞0.51 10* fcu,kbh。其中 Vj T065.28kN,b = 200mm,ho 仍取 2125求得：486.09kN ： 0Vd -1171.81kN ：1502.60kN計算表明，承載尺寸滿足要求，但需配置抗剪鋼筋斜截面抗剪承載力按下式計算0Vd -Vcs VpdVcs=：1：2：3 0.45 10bh,(2 0.6 沉 fcu,ksvfsd,v忙=100(弘 A

19、) =1.57bh0 = Asv -0.00503bSvVcs2： 3 0.45 10訕。(2 0.6 汎 fcu,kSfsd,v =1423.41kN鮎=10.6171 p2 =10.9958 戶p34 =4.9386Vpb =0.75 10- fpd Apdsinrp =862.46kNVdu 二Vcs Vpd =2285.87kNVd =1171.81kN說明截面抗剪承載力滿足要求。(四)預(yù)應(yīng)力損失計算1.摩阻損失6二沏1 d摩擦損失計算表表7截面鋼束號1234總計支點x(mm)0.480.480.480.480（弧度）0.004250.004750.005710.00571CJ12.4

20、82.652.992.9911.11x(mm)2.482.482.482.48變截面e（弧度）0.21960.02450.029490.0294912.7913.6715.3915.3914.31L/4截面x(mm)10.2310.2310.2310.23e（弧度）0.090610.10120.12160.1216Oi52.0155.5662.3862.3858.08跨中x(mm)19.9819.9819.9819.98e（弧度）0.17700.19760.23760.2376Oi99.79106.44119.26119.26111.192.錨具變形損失2反摩擦的影響長度計算表表8鋼束號123

21、4 0 = con1395139513951395鋁巧11295.211288.561275.741275.74也 =（氏叩/L0.0049940.0053270.0059690.005969l f ( mm1249.7512100.611431.311431.3錨具變形損失計算表表9截面鋼束號1234總計支點x( mm480480480480Act ( MPa124.83128.92136.47136.47a |2 ( MPa120.04123.81130.07130.07505.32x( mm2480248024802480變截面g ( MPa124.83128.92136.47136.4

22、7a 12 ( MPa100.06102.50106.86106.86416.28L/4x( mm10230102301023010230g ( MPa124.83128.92136.47136.47a 12 ( MPa22.6519.9314.3414.3471.28跨中x( mm199801998019980199803 ( MPa124.83128.92136.47136.47a 12 ( MPa0.000.000.000.000.003.分批張拉損失二|4 -Ep 厶；pc : Ep = Ep. Ec = 5.65預(yù)應(yīng)力鋼筋束的張拉順序為：4321. Npe為張拉控制力減去摩擦損失和錨

23、具變形損失后的張拉力。預(yù)應(yīng)力分批張拉損失的計算見表。分批張拉損失計算表表10截 面張 拉 束 號有效張拉力NpeC103N)張拉鋼束偏心距ey(mm)計算鋼束偏心距ey(mm)個各鋼束應(yīng)力損失 | 4(MPa支占八、32130.800.00.0791.760.00.0791.760.00.018.4422115.920.0-363.14-363.140.0791.76791.760.03.643.6412122.50-789.6-789.64-789.64-363791.76791.7613.08-1.89-1.89總計13.081.7520.49變截面32122.950.00.0884.15

24、0.00.0884.150.00.026.6822133.090.0-61.55-61.550.0884.15884.150.011.1311.1312138.63-506.8-506.85-506.85-61884.15884.1512.773.763.76總計12.7714.9941.67L/432198.890.00.01273.320.00.01273.320.00.052.3522200.940.01059.721059.720.01273.31273.30.041.0141.0112202.33734.52734.52734.5210591273.31273.333.1536.74

25、36.74總計33.1577.75130.1跨 中32127.930.00.01273.070.00.01273.070.00.051.2822149.320.01273.071273.070.01273.01273.00.051.7951.7912160.411123.11123.071123.0711231273.01273.043.8543.8543.85總計43.8595.64146.924.鋼筋應(yīng)力松弛損失=屮上(0.52 Hfpk0.26) ；pe鋼筋應(yīng)力松弛損失計算表表11鋼束ape( MPa5( MPa截面12341234支點1272.51255.51223.51204.813

26、6.5534.2830.1227.77變截面1282.21266.11221.81195.137.8835.6927.1726.57L/41320.31286.41240.51152.243.2238.4532.3121.47跨中1259.21208.71180.11048.834.7728.2524.7510.455.混凝土收縮、徐變損失二160.9Ep ；cs(t,t。)： Ep；pc (t,t。)peNpAnNpMgkepepJnps2e ps.2 ，I二 Jn . An混凝土收縮、徐變損失計算表表12截面e Ps(mmPP PsNpe(kN)M自重(kN -口預(yù)(MPa自重(MPaG

27、PC(MPal6(MPa支點106.70.004141.0218568.20.005.990.005.9967.1變截面299.90.005691.1328505.51260.128.58-0.827.7674.9L/41085.20.006732.6199473.45241.7510.46-8.22.2637.4跨中1198.10.006732.9203290.66989.0010.32-3.72-2.4916.876.預(yù)應(yīng)力損失組合應(yīng)力損失組合表13截面坊 iii1 +12+14(MPaa ma 15+ i 6( MPa1234平均1234平均支點122.52140.26135.48154

28、.22138.12105.44103.1799.01196.66101.07變截面112.85128.94137.24163.92135.74160.47158.28149.73149.16154.41L/474.66108.64154.47206.82136.15161.84157.07150.93140.09152.48跨中136.15150.29214.90266.18191.88152.19145.67142.17127.87141.98(五)正常使用極限狀態(tài)計算1.全預(yù)應(yīng)力混凝土構(gòu)件抗裂性驗算正截面抗裂性驗算以跨中截面受拉邊的正應(yīng)力控制。在荷載短期效應(yīng)組合作用下應(yīng)滿足:J -085匚

29、乞0二St為在荷載短期荷載效應(yīng)組合作用下，截面受拉邊的應(yīng)力:M G1PK丁n1m Mg2K 嘰：Mq2KJ0yox由表6查得J n1 J y n1 x二 0.3892910 9 mm 3二 0.46911109mm3J0/y0x 二 0.5071210 9 mm 3彎矩設(shè)計值由表1和2查得:MG1Pk =4650kN m,MGmK =787.12kN m,MG2K =1551.42kN mMQ1K = 2427.66kN m,MQ2K = 307.57kN m,1T.1188 將上述數(shù)值代入公式得：宀 ，4650.47 丄 787.12 1551.42 +0.7 漢 2427.66 1.118

30、8 + 307.57、；-st=()=25.25MPa0.389290.469110.27630匚pc為截面下邊緣的有效預(yù)應(yīng)壓力:pcAnN penxJnynxN p =stAp =(con -si sII ) Ap= (1395 -191.88 -141.98) 6672,1000= 7080.13kN7080.13 7080.13x1.23557、小 得二 pc =() 1000得0.81105= 31.20MPa0.38929；st 0.85pc - -1MPa : 0計算結(jié)果表明，正截面抗裂性滿足要求。(2)斜截面抗裂性驗算斜截面抗裂性驗算以主拉應(yīng)力控制，一般取變截面點分別計算截面上梗

31、肋、在荷載短期效應(yīng)組合作用下的主拉應(yīng)力，應(yīng)滿足二tp乞.6ftk的要求。形心軸和下肋處二tp為荷載短期效應(yīng)組合作用下的主拉應(yīng)力Jex2-,2M G1PK二cx _ _ 二 pc _Jn1yn1M G1mKJyn2Jn2M G2K * 0.7M Q1K ./ (1 + 4) + M JQ2Ky。VG1PKHSn1塔S2Vg2K0.7VQ1K (1)Vq2k sJOba A sin 日pe pep (Si1J mb上述公式中車輛荷載和人群荷載產(chǎn)生的內(nèi)力值，按最大剪力布置荷載， 即取最大剪力對應(yīng)的彎矩值，其數(shù)值由表 3差得。恒載內(nèi)力值：MG1PK =905.02kN mMG1mK =153.18kN

32、 mVG1PK = 428.05kN m，MG2K =301.92kN mVGimK =72.45kN mVG2K =142.8kN m活載內(nèi)力值:Mq1k =472.44kN mM Q2 k = 59.86kN m11.1188VQ1K =215.71kN mVQ2K =37.13kN m截面點處的主要截面幾何性質(zhì)由表6差得：計算點幾何性質(zhì)表14計算點受力階段6 2A| (x 10 mm )yx1 (mr)d (mm93S1 (x 10 mm )上梗肋處階段10.4450001008.95933.950.31277階段20.3100001021.84946.840.31677階段30.310

33、000904.79829.790.40263形心位置階段10.49679920.841000.45746階段20.49937804.79850.40189階段30.61096846.8400.51739下梗肋處階段10.193751016.05816.050.19686階段20.25011003.16803.160.25089階段30.25011120.2920.210.28016變截面處的有效預(yù)應(yīng)力陽=0.99183 106mm2&2 =1.03751 106mm26 2A =1.17251 10 mm124J n1 =0.64266 10 mmJn2 =0.67512 10 mm4J0 =

34、 0.80192 1012mm4yn1s =1083.95 mmyn2s = 1096.84mmy0s 二 979.79mmpe5on 一6 Fi =1395 135.74 154.41 = 1104.85MPaNP = ；peAp =1104.85 6672 1000 = 7371.6kNepn = ypn = 299.25mm預(yù)應(yīng)力筋彎起角度分別為：常=10.6171 % =10.9958兔3,4 =4.9386將上述數(shù)值代入，分別計算上梗肋、形心軸和下梗肋處的主拉應(yīng)力。 a）上梗肋CX/ 7371.60.99183= 4.23MPa= 4.237371.6 O.29925 0.93395

35、) 10000.64266905.020.64266 10000.93395153.180.67512 10000.9468430192 7 472.44 1.1188 5986 0.829790.80192 1000= 4.23 1.32 0.21 0.32 =6.08MPa428.05 0.3127772.45 0.31677142.820.7 215.71 1.1188 37.13) 0.402630.64266 0.2 10000.67512 0.2 10000.80192 0.2 10001104.85 6672 sin 7.87250.31277-0.64266 x 0.2。06=

36、1.04 0.17 0.37 _2.21 - _0.63MPa6.086.08 22Gp(一)2 (一0.63)2 0.06MPab)形心軸處1000 =7.78MPa“7371.67371.60.29925 門八二 pc =(0.1)p 0.991830.64266905.02153.18匚cx =7.78 -浜 0.1-沁 0.0850.64266 10000.67512 1000= 7.74于 _ 428.05 漢 0.45746 丄 72.45 漢 0.40189+ (142.8+0.7 漢 215.71. 1.1188+37.13)漢 0.40263-0.64266 0.2 1000

37、0.67512 0.2 10000.80192 0.2 10001104.85 6672 sin 7.87250.517390.64266 0.2 1000-1.55MPa7 47/ 7 47 22W_K-y-)2 +(_1.55)2 =_0.31MPaC)下梗肋處z 7371.6 丄 7371.6X0.299250.81605) .1000 =10.23MPaCT =( +pc 0.991830.64266905.02153.18二cx =10.23 -0.81605 -0.803160.64266 10000.67512 1000= 8.9MPa亍 _ 428.05X0.19686 *72

38、.45 漢 0.25089 十(142.8 +0.7 匯 215.711.1188 + 37.13)匯 0.280160.64266 0.2 10000.67512 0.2 10000.80192 0.2 10001104.85 6672 sin 7.8723 0.1968660.64266 0.2 10=-0.4MPa；tp - Q02MPa變截面處不同計算點主應(yīng)力匯總表表15計算點位置正應(yīng)力 cx( MPa剪應(yīng)力t( MPa主壓應(yīng)力ercp( MPa上梗肋處6.08-0.63-0.06形心位置7.47-1.55-0.31下梗肋處8.9-0.4-0.02計算結(jié) 果表明，形心 處主 拉應(yīng)力最

39、大，其數(shù) 值為 tp,max =.31MPa，小于限制值0.7ftk =2.65 0.7 =1.855MPa2.變形計算(1)使用階段的撓度計算十對C50混凝使用階段的撓度值，按短期荷載效應(yīng)組合計算，并考慮撓度長期影響系數(shù)土， 于1.425，剛度 B0 =0.95EcJ0 =0.95 3.45 104 0.72630 1012= 2.38 1016N mm2荷載短期效應(yīng)組合作用下的撓度值，可簡化為按等效均布荷載作用情況計算:5L2 Msfs-48B。539.962 8815.48=61.6mmX480.95 3.45 0.72630 104自重產(chǎn)生的撓度值按等效均布荷載作用情況計算:空L2 g

40、48 B02539.96(4650.46787.12 1551.42)=480.95 3.45 0.72630 104二 48.8mm消除自重產(chǎn)生的撓度，并考慮撓度長期影響系數(shù)后，使用階段撓度值為,fs _fG) =1.425 (61.6 -48.8) =18.24mm:L 600 = 66.6mm計算結(jié)果表明，使用階段的撓度值滿足規(guī)范要求。(2)預(yù)加力引起的反拱計算及預(yù)拱度的設(shè)置預(yù)加力引起的反拱近似地按等截面梁計算，截面剛度按跨中截面凈截面確定，即取412122B0 =0.95 Ec Jn =0.95 3.45 100.53452 10 =1.75 10 N mm反拱長期系數(shù)采用二=2.0預(yù)

41、加力引起的跨中撓度為B。MP-M12為跨中截面作用單位力 P=1時，所產(chǎn)生的 M1圖在半跨范圍內(nèi)的面積:：；M1 2 = 16M p為半跨范圍 M 1圖重心（距支點L 3處）所對應(yīng)的預(yù)加應(yīng)力引起的彎矩圖縱坐標M p = NpepNp =（ %n - ；L1 -匚 lii ） Ap =（1395-136.15 -152.48） 6672. 1000 = 7381.7N ep為距支點L 3處的預(yù)應(yīng)力束偏心距ep _ yxo _ apMP = 7381.7 103 （1424.17-294.6）=8338.15 106N m由預(yù)加力產(chǎn)生的跨中反拱為2 62 39960 16 8838.15 1016

42、1.75 10= 201.61 認425 616.6=89.32mm由于預(yù)加力產(chǎn)生的長期反拱值大于按荷載短期效應(yīng)組合計算的長期撓度，所以可以不設(shè)預(yù)拱度。（六）持久狀況應(yīng)力驗算（1）跨中截面混凝土法向正應(yīng)力驗算kcNpWsm-conpep epn1M G1PK . MG1PK MG1mK M Q1K M Q2KWsn1Wsn2WosJ 一 ；-1395 191.88 141.98 = 1061.14MPa-0.5fckNp =：；peAp =1061.14 6672 1000 =7079.9kN由表六查得：epn1 = ypn1 = 1235.57mm* r 7079.97079.9 勺.23557 丄 4650.46 丄 787.12-kc 二一0.811050.389290.389290.469121000 =8.33 ： 0.5 fck =0.5 32.