1、橋梁工程課程設計預應力混凝土簡支小箱梁橋設計計算書姓 名： 學 號： 班 級： 指導教師： 成 績： 二一二年七月第一章 設計依據1公路鋼筋混凝土及預應力混凝土橋涵設計規范（JTG D62-2004）（以下簡稱公預規）2公路橋涵設計通用規范（JTG D60-2004）（以下簡稱橋規)3公路工程技術標準（JTG B012003）第二章 設計資料及上部結構主要尺寸2.1 設計資料1. 橋梁跨徑及橋寬標準跨徑：35 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：

2、單向行車2. 設計荷載公路-I級，無人群荷載，單側防撞護欄重7.8 kN/m。3. 材料及工藝混凝土：小箱梁梁的預制部分及現澆接縫部分均采用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）；瀝青鋪裝層下設置8cm厚的C40防水混凝土調平層（容重為25kN/m3）。預應力鋼筋：鋼絞線，MPa，單根面積140mm2。普通鋼筋：直徑12 mm采用HRB335鋼筋；直徑<12 mm采用R235鋼筋。工藝：主梁按后張法施工工藝制作，采用內徑55 mm的預埋波紋管和夾片式錨具。2.1、基本尺寸圖2-1圖2-2中梁截面特性： A=1.38m；=0.548；中

3、心點到底面的距離 y=1.16m。圖2-3圖2-4邊梁截面特性： A=1.401m；=0.552；中心點到底面的距離 y=1.17m。第三章 內力計算3.1 恒載計算1號梁 一期恒載 梁體自重及橫隔板：二期恒載防撞欄桿 ：鋪裝層：總恒載：2號梁 防撞欄桿 ：鋪裝層：梁體自重及橫隔板： 表3-1 1號梁恒載表 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

4、.0502 二期恒載 292.49731094219.371874.9146.252343.7783.36022500.103 恒載 955.27483573716.456123.27477.6427654.57272.2488165.150表3-2 2號梁恒載表 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 292.5109

5、3.93219.3711874.9146.2512343.7783.35872500.103 恒載 964.163605.95723.1186180.25482.0897725.81274.7778241.140表3-3 3號梁恒載表 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

6、.9146.2512343.7783.35872500.103 恒載 964.163605.95723.1186180.25482.0897725.81274.7778241.1403.2 活載計算3.2.1 橫向分布系數計算3.2.1.1 跨中處用剛接板法1號梁活載計算圖2-5按照2車道加載0.67*0.936>0.5377 2號梁圖2-6按照2車道加載0.67*0.862=0.5775>0.4744 3號梁按照2車道加載0.67*0.8163=0.5469>0.3948根據對稱性關系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根據對稱性關系表3

7、-4 各梁橫向分布系數梁號跨中支座10.88591.078920.8621.132330.81631.132340.8621.132350.88591.07893.2.2 活載計算 荷載值 折減系數 0.671號梁彎矩橫向分布系數圖2-10剪力橫向分布系數圖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*0.6

8、7+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

9、.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2-19M=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

10、剪力圖2-20Q=129.37kN2號梁彎矩橫向分布系數圖2-21剪力橫向分布系數圖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圖2-23剪力橫向分布系數支座處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

11、梁活載內力分別于2，1號梁相同表3-5 各梁活載內力值 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)10388.351216.64317.262085.21221.052606.67174.772780.55129.3720398.451183.82311.842028.96215.182536.35170.062705.54128.6430392.291121.06296.351923.91203.752401.88161.042561.79121.824039

12、8.451183.82311.842028.96215.182536.35170.062705.54128.6450388.351216.64317.262885.21221.052606.67174.772780.55129.37 3.3內力組合表3-6 1號梁內力組合 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 292.497

13、31094219.371874.9146.252343.7783.36022500.103 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 1,193.104,318.10910.77,400.306139,251.00379.3

14、9,868.0079.27 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 671.662512.02503.7464305.36335.838538

15、2.04191.4185741.0402 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 1,208.20

16、4,330.90914.17,422.80613.99,279.10378.99,898.1078.87 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

17、 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 承載力極限狀態組合 1,706.205,896.601,282.6010,109.80863.812,633

18、.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 預應力鋼筋估束和布置4.1 預應力鋼束的估束 由于邊梁的內力最大，所以預應力鋼筋的布置一邊梁為準，其他梁預應力布置與

19、邊梁相同。對于預應力鋼筋混凝土簡支梁橋，控制結構設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。根據公路鋼筋混凝土及預應力混凝土橋涵設計規范JTG D62-2004的第條(P58)規定：全預應力混凝土構件，在作用(或荷載) 短期效應組合下預制構件： (4-1)式中，為作用(或荷載) 短期效應組合下構件抗裂驗算邊緣混凝土的拉應力，為扣除全部預應力損失后預加力在構件抗裂驗算邊緣產生的預壓應力。本課程設計，抗裂驗算邊緣為截面下邊緣。根據材料力學知識，作用(或荷載) 短期效應組合下構件抗裂驗算邊緣混凝土的拉應力按下式求得 (4-2)其中，是彎矩短期效應組合值，是毛截面抗彎慣性矩，是下邊

20、緣距截面中性軸的距離。 預加力在構件抗裂驗算邊緣產生的預壓應力的計算按如下方式計算。將預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 預加力等效則，預加力在構件抗裂驗算邊緣產生的預壓應按下式計算 (4-3)上式中，是毛截面面積，是預應力鋼絞線合力作用點距截面中性軸的距離，和的定義與式(4-2)一致，是預加力，按下式計算 (4-4)其中，和分別為預應力鋼束的有效預應力和面積。將式(4-2)(4-4)代入式(4-1)，并將式(4-1)取等號，得到預應力鋼束面積估算公式 (4-5)上式中，預應力鋼束的有效預應力及預應力鋼絞線合力作用點距截面中性軸的距離需要預先假定。一

21、般而言，對于的預應力鋼絞線的控制張拉應力取，在估束階段，根據經驗，考慮25%的預應力損失，則有效預應力的估計值為。對于跨中截面，可假設預應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 預應力鋼束布置圖表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N11738.043000212.59999N21739.98300075211.02999N31740.34450077429.32202020N41740.69600079649.7231.09313

22、1N51741.067500711870.4145.074242N61741.429000714091.6861.725353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1372504.514186

23、45.71188.21159.14.545*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 預應力損失計算磨阻損失表4-3 計算表計算點鋼束 x （°）（rad）mMPa跨中N130.0523617.380.0375890.03689151.46314N270.1221717

24、.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N130.0523613.0050.0310260.0305542.61719N270.1221713.0050.0463850.04532563.229N370.1221713.0050.0463850.04532563.229N47

25、0.1221713.0050.0463850.04532563.229N570.1221713.0050.0463850.04532563.229N670.1221713.0050.0463850.04532563.2291/4跨N130.052368.630.0244640.02416733.71299N270.122178.630.0398220.0390454.46051N370.122178.630.0398220.0390454.46051N46.680.116598.630.0385940.03785852.81241N55.360.093558.630.0335250.03297

26、45.99255N64.480.078198.630.0301460.02969741.426743/8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N100

27、0.120.000180.000180.251077N2000.120.000180.000180.251077N3000.120.000180.000180.251077N4000.120.000180.000180.251077N5000.120.000180.000180.251077N6000.120.000180.000180.251077 由錨具變形及鋼束回縮引起的預應力損失按公預規計算公式如下反向摩擦影響長度：其中 為預應力鋼筋扣除磨阻損失后錨固端應力 l 為張拉端至錨固端的距離 在反影響長度內，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

28、-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N10.00327718895.381300538.6054N20.00486215512.791300524.38526N30.00486215512.791300524.38526N40.00486215512.791300524.3852

29、6N50.00486215512.791300524.38526N60.00486215512.791300524.385261/4跨N10.00390617306.12863067.78631N20.00631113616.25863062.93248N30.00631113616.25863062.93248N40.0061213827.08863063.60836N50.00532914816.81863065.94368N60.004815611.98863067.031433/8跨N1k0.00551214569.244630109.5709N20.00769612330.07463

30、0118.5167N30.00586414125.384630111.3597N40.00504615227.134630106.9469N50.00438616333.554630102.6532N60.00399817107.56463099.76298支點N10.00209223647.212098.45247N20.00209223647.212098.45247N30.00209223647.212098.45247N40.00209223647.212098.45247N50.00209223647.212098.45247N60.00209223647.212098.45247

31、鋼筋松弛引起的預應力損失 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-061.061,241.5372.25N213

32、07.38612.75E-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

33、.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.

34、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.

35、13E-061.021,266.2230.08 由鋼筋應力松弛引起的預應力損失公預規規定，鋼絞線由松弛引起的預應力損失的終極值，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.

36、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N11,266.2235.71N21,266.2235.71N31,266.2235.71N41,266.2235.71N51,266.2235.71N61,266.2235.71 混凝土收縮徐變引起的預應力損失 根據公預規規定，由混凝土收縮徐變引起的預應力損失可按下式計算：其中支座處跨中

37、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

38、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N111.46125.51.2113.29N

39、211.46125.51.2113.99N311.46125.51.2113.99N411.46125.51.2113.29N511.46125.51.2113.29N611.46125.51.2113.29 表4-8 鋼束預應力損失一覽表 計算點鋼束 預加應力階段 正常使用階段錨固前的預應力損失錨固時的預應力損失錨固后的預應力損失鋼束有效應力12456跨中N151.4631414.7926173.071,255.6834.3206.551,014.83N271.94013072.761,250.3033.59205.741,010.97N371.94013072.761,250.3033.5

40、9205.741,010.97N471.94013072.761,250.3033.59205.741,010.97N571.94013072.761,250.3033.59205.741,010.97N671.94013072.761,250.3033.59205.741,010.971/8跨N142.6171938.605472.251,241.5332.44204.431,004.66N263.22924.3852671.891,235.4931.66203.521,000.31N363.22924.3852671.891,235.4931.66203.521,000.31N463.22

41、924.3852671.891,235.4931.66203.521,000.31N563.22924.3852671.891,235.4931.66203.521,000.31N663.22924.3852671.891,235.4931.66203.521,000.311/4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N125.52072109.570959.691,200.2227.2182.4990.62N235.63166118.516758.781,182.0724.99179.97977.11N327.14981111.359759.521,196.9726.8181.97988.2N423.36313106.946