橋梁工程課程設(shè)計預(yù)應(yīng)力混凝土簡支小箱梁橋設(shè)計計算書姓 名： 學(xué) 號： 班 級： 指導(dǎo)教師： 成 績： 二一二年七月第一章 設(shè)計依據(jù)1公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范（JTG D62-2004）（以下簡稱公預(yù)規(guī)）2公路橋涵設(shè)計通用規(guī)范（JTG D60-2004）（以下簡稱橋規(guī))3公路工程技術(shù)標準（JTG B012003）第二章 設(shè)計資料及上部結(jié)構(gòu)主要尺寸2.1 設(shè)計資料1. 橋梁跨徑及橋?qū)挊藴士鐝剑?5 m；主梁全長：34.94 m；計算跨徑：34.19 m；橋面寬度：0.5 m （防撞欄桿）+15.9（凈行車道寬度）m + 0.5 m（防撞欄桿） = 16.9 m。分幅：單幅行車方向：單向行車2. 設(shè)計荷載公路-I級，無人群荷載，單側(cè)防撞護欄重7.8 kN/m。3. 材料及工藝混凝土：小箱梁梁的預(yù)制部分及現(xiàn)澆接縫部分均采用C50（容重為26 kN/m3）；鋪裝層為10cm厚瀝青混凝土混凝土（容重為24kN/m3）；瀝青鋪裝層下設(shè)置8cm厚的C40防水混凝土調(diào)平層（容重為25kN/m3）。預(yù)應(yīng)力鋼筋：鋼絞線，MPa，單根面積140mm2。普通鋼筋：直徑12 mm采用HRB335鋼筋；直徑0.5377 2號梁圖2-6按照2車道加載0.67*0.862=0.57750.4744 3號梁按照2車道加載0.67*0.8163=0.54690.3948根據(jù)對稱性關(guān)系3.2.2 支座處用杠桿原理法1號梁圖2-72號梁圖2-83號梁圖2-9根據(jù)對稱性關(guān)系表3-4 各梁橫向分布系數(shù)梁號跨中支座10.88591.078920.8621.132330.81631.132340.8621.132350.88591.07893.2.2 活載計算 荷載值 折減系數(shù) 0.671號梁 彎矩橫向分布系數(shù)圖2-10剪力橫向分布系數(shù)圖2-11支座處 彎矩M=0 剪力圖2-12Q=1.143*1.0789*300*0.67+1.143*（0.5*（1.0789*1+0.8859*0.8571）*34.19/7+0. 8859*0.5*6*34.19/7）*10.5*0.67=388.35kN1/8跨處 彎矩圖2-13 M=1.143*0.8859*3.74*300*0.67+1.143*0.8859*0.5*3.74*34.19*10.5*0.67=1216.64剪力圖2-14 Q=1.143*0.91*300*0.67+1.143*（0.5*（0.91*0.875+0.8859*0.8571）*0.61+0.8859*0.5*6*34.19/7）*10.5*0.67=317.26kN1/4跨處彎矩圖2-15M=1.143*0.8859*6.41*300*0.67+1.143*0.8859*0.5*6.41*34.19*10.5*0.67=2085.21剪力圖2-16Q=1.143*0.75*300*0.8859*0.67+1.143*0.8859*0.5*0.75*0.75*34.19*10.5*0.67=221.05Kn3/8跨處彎矩圖2-17M=1.143*0.8859*8.013*300*0.67+1.143*0.8859*0.5*8.013*34.19*10.5*0.67=2606.67 剪力圖2-18Q=1.143*0.625*300*0.8859*0.67+1.143*0.8859*0.5*0.625*0.625*34.19*10.5*0.67=174.77kN跨中處彎矩圖2-19 M=1.143*300*8.5475*0.8859*0.67+1.143*0.5*34.19*8.5475*10.5*0.8859*0.67=2780.55剪力圖2-20Q=129.37kN2號梁彎矩橫向分布系數(shù)圖2-21剪力橫向分布系數(shù)圖2-22支座處M=0Q=398.45kN1/8跨處M=1183.82Q=311.84kN1/4跨處M=2028.96Q=215.18kN3/8跨處M=2536.35Q=170.06kN 跨中處 M=2705.54 Q=128.64kN3號梁彎矩橫向分布系數(shù)圖2-23剪力橫向分布系數(shù)支座處M=0Q=392.29kN1/8跨處M=1121.06Q=296.35kN1/4跨處M=1923.91Q=203.75kN3/8跨處M=2401.88Q=161.04kN 跨中處 M=2561.79 Q=121.82kN4,5號梁活載內(nèi)力分別于2，1號梁相同表3-5 各梁活載內(nèi)力值 梁號 支座處 1/8跨處 1/4跨處 3/8跨處 跨中處M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)M(kN.m)Q(kN)10388.351216.64317.262085.21221.052606.67174.772780.55129.3720398.451183.82311.842028.96215.182536.35170.062705.54128.6430392.291121.06296.351923.91203.752401.88161.042561.79121.8240398.451183.82311.842028.96215.182536.35170.062705.54128.6450388.351216.64317.262885.21221.052606.67174.772780.55129.37 3.3內(nèi)力組合表3-6 1號梁內(nèi)力組合 1號梁 序號 荷載類別 支座處 1/8跨處 1/4跨處 3/8跨處 跨中處 Q M Q M Q M Q M Q kN kN.m kN kN.m kN kN.m kN kN.m kN 1 自重 662.77742479497.084248.38331.3925310.8188.8885665.0502 二期恒載 292.49731094219.371874.9146.252343.7783.36022500.103 恒載 955.27483573716.456123.27477.6427654.57272.2488165.1504 活載 388.351216.64317.262085.21221.052606.67174.772780.55129.375 承載力極限狀態(tài)組合 1,690.005,990.901,303.9010,267.20882.612,834.80571.413,691.00181.16 正常使用短期組合 1,193.104,318.10910.77,400.306139,251.00379.39,868.0079.27 正常使用長期組合 1,091.203,998.80827.56,853.005558,566.80333.49,138.2045.38 正常使用標準組合 1,343.604,789.601,033.708,208.50698.710,261.2044710,945.70129.4表3-7 2號梁內(nèi)力組合 2號梁 序號 荷載類別 支座處 1/8跨處 1/4跨處 3/8跨處 跨中處 Q M Q M Q M Q M Q kN kN.m kN kN.m kN kN.m kN kN.m kN 1 自重 671.662512.02503.7464305.36335.8385382.04191.4185741.0402 二期恒載 292.51093.93219.3711874.9146.2512343.7783.35872500.103 恒載 964.163605.95723.1186180.25482.0897725.81274.7778241.1404 活載 398.451183.82311.842028.96215.182536.35170.062705.54128.645 承載力極限狀態(tài)組合 1,714.805,984.501,304.3010,256.80879.812,821.90567.813,677.10180.16 正常使用短期組合 1,208.204,330.90914.17,422.80613.99,279.10378.99,898.1078.87 正常使用長期組合 1,103.604,020.20832.26,890.30557.48,613.40334.39,188.00458 正常使用標準組合 1,362.604,789.801,035.008,209.20697.310,262.20444.810,946.70128.6表3-8 3號梁內(nèi)力組合 3號梁 序號 荷載類別 支座處 1/8跨處 1/4跨處 3/8跨處 跨中處 Q M Q M Q M Q M Q kN kN.m kN kN.m kN kN.m kN kN.m kN 1 自重 671.662512.02503.7464305.36335.8385382.04191.4185741.0402 二期恒載 292.51093.93219.3711874.9146.2512343.7783.35872500.103 恒載 964.163605.95723.1186180.25482.0897725.81274.7778241.1404 活載 392.291121.06296.351923.91203.752401.88161.042561.79121.825 承載力極限狀態(tài)組合 1,706.205,896.601,282.6010,109.80863.812,633.60555.213,475.90170.56 正常使用短期組合 1,204.404,292.50904.67,358.50606.99,196.80373.49,810.0074.67 正常使用長期組合 1,101.403,998.30826.86,853.50553.48,566.40331.19,137.7042.68 正常使用標準組合 1,356.504,727.001,019.508,104.20685.810,127.70435.810,802.90121.8第四章 預(yù)應(yīng)力鋼筋估束和布置4.1 預(yù)應(yīng)力鋼束的估束 由于邊梁的內(nèi)力最大，所以預(yù)應(yīng)力鋼筋的布置一邊梁為準，其他梁預(yù)應(yīng)力布置和邊梁相同。對于預(yù)應(yīng)力鋼筋混凝土簡支梁橋，控制結(jié)構(gòu)設(shè)計的通常是抗裂性驗算。因而，可按照抗裂性驗算原則完成估束工作。根據(jù)公路鋼筋混凝土及預(yù)應(yīng)力混凝土橋涵設(shè)計規(guī)范JTG D62-2004的第6.3.1條(P58)規(guī)定：全預(yù)應(yīng)力混凝土構(gòu)件，在作用(或荷載) 短期效應(yīng)組合下預(yù)制構(gòu)件： (4-1)式中，為作用(或荷載) 短期效應(yīng)組合下構(gòu)件抗裂驗算邊緣混凝土的拉應(yīng)力，為扣除全部預(yù)應(yīng)力損失后預(yù)加力在構(gòu)件抗裂驗算邊緣產(chǎn)生的預(yù)壓應(yīng)力。本課程設(shè)計，抗裂驗算邊緣為截面下邊緣。根據(jù)材料力學(xué)知識，作用(或荷載) 短期效應(yīng)組合下構(gòu)件抗裂驗算邊緣混凝土的拉應(yīng)力按下式求得 (4-2)其中，是彎矩短期效應(yīng)組合值，是毛截面抗彎慣性矩，是下邊緣距截面中性軸的距離。 預(yù)加力在構(gòu)件抗裂驗算邊緣產(chǎn)生的預(yù)壓應(yīng)力的計算按如下方式計算。將預(yù)加力等效為作用在截面中性軸位置處的軸力和一外加彎矩，如圖4-1所示。圖4-1 預(yù)加力等效則，預(yù)加力在構(gòu)件抗裂驗算邊緣產(chǎn)生的預(yù)壓應(yīng)按下式計算 (4-3)上式中，是毛截面面積，是預(yù)應(yīng)力鋼絞線合力作用點距截面中性軸的距離，和的定義和式(4-2)一致，是預(yù)加力，按下式計算 (4-4)其中，和分別為預(yù)應(yīng)力鋼束的有效預(yù)應(yīng)力和面積。將式(4-2)(4-4)代入式(4-1)，并將式(4-1)取等號，得到預(yù)應(yīng)力鋼束面積估算公式 (4-5)上式中，預(yù)應(yīng)力鋼束的有效預(yù)應(yīng)力及預(yù)應(yīng)力鋼絞線合力作用點距截面中性軸的距離需要預(yù)先假定。一般而言，對于的預(yù)應(yīng)力鋼絞線的控制張拉應(yīng)力取，在估束階段，根據(jù)經(jīng)驗，考慮25%的預(yù)應(yīng)力損失，則有效預(yù)應(yīng)力的估計值為。對于跨中截面，可假設(shè)預(yù)應(yīng)力鋼絞線合力作用點距截面下邊緣18cm進行試算。代入4-5得選配12束5f15.2的鋼束實際 圖4-1 預(yù)應(yīng)力鋼束布置圖表4-1 鋼束尺寸鋼束號長度（cm）半徑（m）彎起角度（） 鋼束中心到梁底距離支座處1/8截面處1/4截面處3/8截面處跨中處N11738.043000212.59999N21739.98300075211.02999N31740.34450077429.32202020N41740.69600079649.7231.093131N51741.067500711870.4145.074242N61741.429000714091.6861.725353表4-2 截面特性計算點截面積（）截面重心至底面（mm）Wn()梁自重彎矩（kN.m）In（）I（）截面重心至到鋼束質(zhì)心距離（mm）跨中1372504.51418645.71188.61158.84.526*1085665.055.38*10115.76*1011915.6885.81/8跨1372504.51418645.71188.61158.84.526*1085310.85.38*10115.76*1011915.6885.81/4跨1372504.51418645.71188.21159.14.545*1084248.385.40*10115.76*1011895.2866.13/8跨1372504.51418645.71185.31160.84.606*10824795.46*10115.72*1011750725.5支點1599504.51645645.711051097.35.620*10806.21*10116.17*1011284276.34.2 預(yù)應(yīng)力損失計算4.2.1磨阻損失表4-3 計算表計算點鋼束 x （）（rad）mMPa跨中N130.0523617.380.0375890.03689151.46314N270.1221717.380.0529470.0515771.94013N370.1221717.380.0529470.0515771.94013N470.1221717.380.0529470.0515771.94013N570.1221717.380.0529470.0515771.94013N670.1221717.380.0529470.0515771.940131/8跨N130.0523613.0050.0310260.0305542.61719N270.1221713.0050.0463850.04532563.229N370.1221713.0050.0463850.04532563.229N470.1221713.0050.0463850.04532563.229N570.1221713.0050.0463850.04532563.229N670.1221713.0050.0463850.04532563.2291/4跨N130.052368.630.0244640.02416733.71299N270.122178.630.0398220.0390454.46051N370.122178.630.0398220.0390454.46051N46.680.116598.630.0385940.03785852.81241N55.360.093558.630.0335250.0329745.99255N64.480.078198.630.0301460.02969741.426743/8跨N130.052364.630.0184640.01829425.52072N24.930.086044.630.0258740.02554235.63166N33.310.057774.630.0196540.01946227.14981N42.590.04524.630.016890.01674823.36313N52.010.035084.630.0146630.01455620.30513N61.670.029154.630.0133570.01326818.50933支點N1000.120.000180.000180.251077N2000.120.000180.000180.251077N3000.120.000180.000180.251077N4000.120.000180.000180.251077N5000.120.000180.000180.251077N6000.120.000180.000180.2510774.2.2 由錨具變形及鋼束回縮引起的預(yù)應(yīng)力損失按公預(yù)規(guī)計算公式如下反向摩擦影響長度：其中 為預(yù)應(yīng)力鋼筋扣除磨阻損失后錨固端應(yīng)力 l 為張拉端至錨固端的距離 在反影響長度內(nèi)，距張拉端x處的錨具變形、鋼筋回縮損失：；在反影響長度外，錨具變形、鋼筋回縮損失：表4-4 計算表計算點鋼束影響長度xMPammmmMPa跨中N10.00296119877.861738014.79261N20.00413916812.5173800N30.00413916812.5173800N40.00413916812.5173800N50.00413916812.5173800N60.00413916812.51738001/8跨N10.00327718895.381300538.6054N20.00486215512.791300524.38526N30.00486215512.791300524.38526N40.00486215512.791300524.38526N50.00486215512.791300524.38526N60.00486215512.791300524.385261/4跨N10.00390617306.12863067.78631N20.00631113616.25863062.93248N30.00631113616.25863062.93248N40.0061213827.08863063.60836N50.00532914816.81863065.94368N60.004815611.98863067.031433/8跨N1k0.00551214569.244630109.5709N20.00769612330.074630118.5167N30.00586414125.384630111.3597N40.00504615227.134630106.9469N50.00438616333.554630102.6532N60.00399817107.56463099.76298支點N10.00209223647.212098.45247N20.00209223647.212098.45247N30.00209223647.212098.45247N40.00209223647.212098.45247N50.00209223647.212098.45247N60.00209223647.212098.452474.2.3 鋼筋松弛引起的預(yù)應(yīng)力損失 表4-5 計算表計算點鋼束平均cosMPaMPaMPa/mm跨中N11328.74412.75E-061.061,255.6873.07N21323.0612.75E-061.061,250.3072.76N31323.0612.75E-061.061,250.3072.76N41323.0612.75E-061.061,250.3072.76N51323.0612.75E-061.061,250.3072.76N61323.0612.75E-061.061,250.3072.761/8跨N11313.77712.75E-061.061,241.5372.25N21307.38612.75E-061.061,235.4971.89N31307.38612.75E-061.061,235.4971.89N41307.38612.75E-061.061,235.4971.89N51307.38612.75E-061.061,235.4971.89N61307.38612.75E-061.061,235.4971.891/4跨N11293.5010.99982.70E-061.061,223.6969.81N21277.6070.99982.70E-061.061,208.6568.95N31277.6070.99982.70E-061.061,208.6568.95N41278.5790.99982.70E-061.061,209.5769.01N51283.0640.99982.70E-061.061,213.8169.25N61286.5420.99982.70E-061.061,217.1069.443/8跨N11259.9080.99772.36E-061.051,200.2259.69N21240.8520.99772.36E-061.051,182.0758.78N31256.4910.99772.36E-061.051,196.9759.52N41264.690.99772.36E-061.051,204.7859.91N51272.0420.99772.36E-061.051,211.7860.26N61276.7280.99772.36E-061.051,216.2460.48支點N11296.2960.99361.13E-061.021,266.2230.08N21296.2960.99361.13E-061.021,266.2230.08N31296.2960.99361.13E-061.021,266.2230.08N41296.2960.99361.13E-061.021,266.2230.08N51296.2960.99361.13E-061.021,266.2230.08N61296.2960.99361.13E-061.021,266.2230.084.2.4 由鋼筋應(yīng)力松弛引起的預(yù)應(yīng)力損失公預(yù)規(guī)規(guī)定，鋼絞線由松弛引起的預(yù)應(yīng)力損失的終極值，按下式計算：表4-6 計算表計算點鋼束跨中N11,255.6834.3N21,250.3033.59N31,250.3033.59N41,250.3033.59N51,250.3033.59N61,250.3033.591/8跨N11,241.5332.44N21,235.4931.66N31,235.4931.66N41,235.4931.66N51,235.4931.66N61,235.4931.661/4跨N11,223.6930.14N21,208.6528.25N31,208.6528.25N41,209.5728.36N51,213.8128.89N61,217.1029.313/8跨N11,200.2227.2N21,182.0724.99N31,196.9726.8N41,204.7827.77N51,211.7828.64N61,216.2429.2支點N11,266.2235.71N21,266.2235.71N31,266.2235.71N41,266.2235.71N51,266.2235.71N61,266.2235.714.2.5 混凝土收縮徐變引起的預(yù)應(yīng)力損失 根據(jù)公預(yù)規(guī)規(guī)定，由混凝土收縮徐變引起的預(yù)應(yīng)力損失可按下式計算：其中支座處跨中處 表4-7 計算表計算點鋼束MPaMPa跨中N127.07259.872.87206.55N226.94258.852.87205.74N326.94258.852.87205.74N426.94258.852.87205.74N526.94258.852.87205.74N626.94258.852.87205.741/8跨N126.74257.22.87204.43N226.6256.062.87203.52N326.6256.062.87203.52N426.6256.062.87203.52N526.6256.062.87203.52N626.6256.062.87203.521/4跨N125.82249.722.79199.66N225.48246.932.79197.43N325.48246.932.79197.43N425.5247.12.79197.57N525.6247.892.79198.19N625.67248.52.79198.683/8跨N122.13219.542.26182.4N221.77216.612.26179.97N322.07219.012.26181.97N422.22220.282.26183.01N522.36221.412.26183.95N622.45222.132.26184.55支點N111.46125.51.2113.29N211.46125.51.2113.99N311.46125.51.2113.99N411.46125.51.2113.29N511.46125.51.2113.29N611.46125.51.2113.29 表4-8 鋼束預(yù)應(yīng)力損失一覽表 計算點鋼束 預(yù)加應(yīng)力階段 正常使用階段錨固前的預(yù)應(yīng)力損失錨固時的預(yù)應(yīng)力損失錨固后的預(yù)應(yīng)力損失鋼束有效應(yīng)力12456跨中N151.4631414.7926173.071,255.6834.3206.551,014.83N271.94013072.761,250.3033.59205.741,010.97N371.94013072.761,250.3033.59205.741,010.97N471.94013072.761,250.3033.59205.741,010.97N571.94013072.761,250.3033.59205.741,010.97N671.94013072.761,250.3033.59205.741,010.971/8跨N142.6171938.605472.251,241.5332.44204.431,004.66N263.22924.3852671.891,235.4931.66203.521,000.31N363.22924.3852671.891,235.4931.66203.521,000.31N463.22924.3852671.891,235.4931.66203.521,000.31N563.22924.3852671.891,235.4931.66203.521,000.31N663.22924.3852671.891,235.4931.66203.521,000.311/4跨N133.7129967.7863169.811,223.6930.14199.66993.89N254.4605162.9324868.951,208.6528.25197.43982.97N354.4605162.9324868.951,208.6528.25197.43982.97N452.8124163.6083669.011,209.5728.36197.57983.64N545.9925565.9436869.251,213.8128.89198.19986.73N641.4267467.0314369.441,217.1029.31198.68989.113/8跨N125.52072109.570959.691,200.2227.2182.4990.62N235.63166118.516758.781,182.0724.99179.97977.11N327.