空腹式懸鏈線拱橋設計

1、 橋梁工程課程設計 專 業(yè)： 交通工程 學 號： 1804100433 姓 名： 汪鋒 指 導 教 師： 邢世玲 時 間 ： 2013年6月 南京工業(yè)大學交通學院二O一三年六月橋梁工程課程設計任務書一、 設計題目空腹式等截面懸鏈線箱形無鉸拱橋設計二、 設計資料1. 設計標準設計荷載：公路I級，人群荷載3.5橋面凈空 凈人行道+安全帶凈跨徑；凈失高；凈跨比 2. 材料數(shù)據(jù)與結構布置要求拱頂填料平均厚度（包括路面，以下稱路面）；材料容重主拱圈材料容重（包括橫隔板、施工超重） 拱上立柱（墻）材料容重 腹空拱圈材料容重 腹孔拱上填料容重鋼筋混凝土簡支板材料容重主拱圈實腹段填料容重人行道板及欄桿重混凝土

2、材料：強度等級為C40，主要強度指標為：強度標準值 強度設計值 彈性模量 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 抗拉強度設計值 彈性模量 相對界限受壓區(qū)高度 2)箍筋及構造鋼筋采用HRB335鋼筋，其強度指標為抗拉強度標準值 抗拉強度設計值 彈性模量 本橋采用支架現(xiàn)澆施工方法。主拱圈為單箱六室截面的鋼筋混凝土拱圈，由 C30混凝土現(xiàn)場澆筑而成。拱上建筑可采用簡支板形式或圓弧拱形式，凈跨為57m左右，拱腳至拱頂布置46跨左右 (主拱圈的具體幾何參照指導書實例修改自定)。3設計計算依據(jù)交通部部頒標準公路橋涵設計通用規(guī)范(JTG D602004) 交通人民出

3、版社 交通部部頒標準公路鋼筋混凝土及預應力混凝土橋涵設計規(guī)范(JTG D622004) 交通人民出版社 交通部部頒標準公路圬工橋涵設計規(guī)范(JTG D61-2005) 交通人民出版社 公路設計手冊-拱橋(上) 人民交通出版社，2000.7三、 主拱圈截面幾何要素的計算（一） 主拱圈橫截面設計 拱圈截面高度按經驗公式估算 拱圈由6個各為1.5m寬的拱箱組成，全寬 （二） 箱形拱圈截面幾何性質截面積 繞箱底邊緣的靜面矩 主拱圈截面重心軸： 主拱圈截面繞重心軸的慣性矩： 拱圈截面繞重心軸的回轉半徑： 四、 確定拱軸系數(shù)（一） 上部結構構造布置1. 主拱圈假定,相應的,查拱橋（上冊）表-20（6）得：

4、 主拱圈的計算跨徑和計算失高： 拱鉸截面的水平投影和豎向投影： 將拱軸沿跨徑24等分，每等分長,每等分點拱軸線的縱坐標，相應的拱背面坐標：,拱腹曲面坐標，具體數(shù)值見下表：截面號035.443846114.175130.730570.8897160.88971613.2854132515.06484575132.490192170.81792911.594250.775040.8386660.83866610.7555831112.43291589229.536538330.6594589.3479030.816220.7963540.7963548.55154862610.1442564732

5、6.58288450.5222847.4034430.853470.7615970.7615976.641846568.165040111423.629230670.4044165.7326490.886390.7333120.7333124.999337656.465960694520.675576830.304144.3112240.91480.7105380.7105383.6006860645.021761709617.7219230.223.1185280.938720.6924320.6924322.4260962423.810960738714.768269170.1507742

6、.1372410.95830.6782840.6782841.4589565132.815525437811.814615330.0954561.3531010.97380.6674880.6674880.6856129712.02058935298.86096150.0532430.7547260.985490.659570.659570.0951560541.414296786105.9073076670.0235210.3334130.993630.6541670.654167-0.320753820.987580265112.9536538330.0058590.0830520.998

7、420.6510290.651029-0.567976540.7340807091200010.650.65-0.650.652.拱上腹孔布置從主拱兩端起拱線起向外延伸3m后向跨中對稱布置5對圓弧小拱，腹拱圈厚d'=0.35m，凈跨徑l'0=4.8m，凈矢高f'0=0.8m，座落在寬為 0.5m的鋼筋混凝土排架式腹拱墩支承的寬為 0.6m的鋼筋混凝土蓋梁上。腹拱拱頂?shù)墓氨澈椭鞴肮绊數(shù)墓氨吃谕粯烁摺８构岸斩罩芯€的橫坐標lx，以及各墩中線自主拱拱背到腹拱起拱線的高度 h=y1+y上×(1-1/cos) - (d'+f'0)，分別計算如表項目1號立

8、柱32.50.916943381.32553311.602180.8155831.29041710.263410072號立柱27.10.764589711.105297.7232510.6268611.1802356.4560981673號立柱21.70.612236040.8850484.7772190.4686691.1043783.5593734994號橫墻16.30.459882370.6648062.6206050.3333031.0540831.4354510285號腹拱座11.0950.313030360.4525161.1905360.2182571.0235410.02523

9、4161空、實腹段分界線10.990.310067930.4482341.1677340.2160551.0230740.002736639由f'0/l'0=1/8，查拱橋(上冊)表3-2得 sin0=0.6，cos0=0.8，0=36.870腹拱拱腳的水平投影和豎向投影 x'=d'×sin0=0.35×0.6=0.21m； y'=d'×cos0=0.35×0.8=0.28m（二）上部恒載計算1、橋面系欄桿：g=52kN/m2、主拱圈恒載3、拱上空腹段恒載腹拱圈外弧跨徑 腹拱圈內弧半徑腹拱圈重 腹拱側墻護拱

10、重填料及路面重兩腹拱之間起拱線以上部分重力一個腹拱重力： 腹孔下部蓋梁重力底梁重力1號立柱重力2號立柱重力3號立柱重力4號橫墻重力5號腹拱座重力腹孔集中力拱上實腹段的荷載拱頂填料及橋面系重懸鏈線曲邊三角形腹拱推力靠近主拱拱頂一側的腹拱，一般多做成兩平鉸拱，在較大的恒載作用下和考慮到周圍的填料等構造的作用，可以折中地按無鉸圓弧拱計算其推力，而不計彎矩的影響。 腹拱拱腳的水平推力 查拱橋(上冊)表(I)-4得 腹拱拱腳推力作用線的縱坐標如圖所示，其距x軸的偏心距為： 腹拱推力對各截面重心產生的力矩：驗算拱軸系數(shù)恒載對l/4截面和拱腳截面的力矩見下表：項目集中力編號重力l/4截面拱腳截面力臂力矩力臂

11、力矩主拱圈P0-125281.0196321411.4988790.26橫隔板P1-14P15P0 中接頭拱腳段拱上空腹段P131876.91266002.9438465525.342P141781.72986008.34384614866.48P151709.311740013.7438523492.52P161655.268951.4219232353.66519.1438531688.21P17720.5573176.6269234775.07824.3488517544.74實腹段P181625.640812.2269219876.5829.9488548686.07P19827.14

12、39859.4702497833.2627.1921722491.84腹拱推力F799.3023742.7585282204.89813.8151311042.4715147.0515477.584958454.97264127.9五、拱圈彈性中心及彈性壓縮系數(shù)1 彈性中心 彈性壓縮系數(shù) 六、主拱圈截面內力計算(一)結構自重內力計算 (1)假載內力a.求假載 b.假載內力假載產生的內力可以將其直接布置在內力影響線上求得。不考慮彈性壓縮的假載內力見下表項目影響線面積力或力矩表值乘數(shù)拱頂截面M0.001985025.0659.949628183.1262H0.12742354.498745.170

13、22831.373l/4M-0.001245025.065-6.23108-114.685H0.12742354.498745.17022831.373拱腳截面M0.00445025.06522.11029406.9472H0.12742354.498745.17022831.373V0.270.8876914.17754260.9423計入彈性壓縮的假載內力計入彈性壓縮的假載內力計算見下表項目拱頂截面l/4拱腳截面 10.938720.73057 00.3446810.682838831.3730275831.373831.373 260.9423 9.7158817469.7158829.

14、715882 821.6571458875.2952778.4593 183.1262302-114.685406.9472 4.80810471.689576-9.36702 229.8412069-98.2694315.9383(2)“拱軸線恒載”內力 a.推力 b.考慮彈性壓縮的內力考慮彈性壓縮的“拱軸線恒載”內力見下表項目拱頂截面l/4拱腳截面 10.938720.7305717817.6096417018.3117018.3117609.3832716819.4216819.42 17817.6096418129.2723294.56 208.2263708186.6976145.2

15、996 17609.3832717942.5723149.26 4.80810471.689576-9.36702 1001.174192336.0318-1862.96(3)考慮確定m系數(shù)偏差影響的恒載內力考慮m系數(shù)偏差影響的恒載內力等于“拱軸線m的恒載”內力加上“假載”的內力，計算結果見下表拱頂截面l/4拱腳截面拱軸線恒載假載合計拱軸線恒載假載合計拱軸線恒載假載合計水平力17817.60964831.37302818648.9817018.30727831.373027517849.6817018.31831.37317849.68軸力17609.38327821.65714618431.

16、0417942.57127875.29523818817.8723149.26778.459323927.72彎矩1001.174192229.8412071231.015336.0318449-98.26939119237.7625-1862.96315.9383-1547.032.“恒載壓力線”偏離拱軸線的影響 “恒載壓力線”(指空腹式無鉸拱橋不考慮拱軸線的偏離和恒載彈性壓縮影響的恒載壓力線，也就是人們所說的“三鉸拱恒載壓力線”)與拱軸線在“五點”以外的偏離影響可以用一般力學原理進行計算，參見圖13。 (1)“恒載壓力線”偏離拱軸線的偏離彎矩Mp計算恒載偏離彎矩Mp，首先要計算出橋跨結構沿

17、跨徑各等分段的分塊恒載對各截面的力矩，再算各截面壓力線的縱坐標，然后才能求得Mp。下面按主拱圈、拱上實腹段和各集中力三部分計算各分塊恒載對各截面的力矩。 a.主拱圈自重對各截面產生的力矩Ml在這里，對于所要求的每一等分點而言，積分上限為常數(shù)，并不計等式前面的負號，則上式為：式中：可根據(jù)值從拱橋(例集)附表1-1查得； 可根據(jù)值從拱橋(例集)附表1-2查得 主拱圈對各截面的力矩M1的值見下表截面號S1S2*S1-S2M11200000110.0833333330.083870.0037570.003233548.2189100.1666666670.167043330.0142830.01355

18、82299.390.250.251210.031480.0313235312.16980.3333333330.336296670.57574-0.46364-78631.770.4166666670.422546670.091570.08449114329.3960.50.510310.12890.12625521412.3450.5833333330.60030.1779702740.6666666670.749440.235840.26378744737.1530.750.788460.30330.28804548851.2620.8333333330.8884

19、53330.382830.35754860638.6510.9166666670.993206670.4745870.43585373918.86011.103670.580130.5235488790.26b.拱上實腹段恒載對各截面產生的彎矩M2 計算拱上實腹段的恒載時，必須將拱頂填料及面層的矩形板塊和其下面的懸鏈線曲邊三角形塊分開才能準確計算，否則只能是近似的。 (a)矩形板塊從拱頂?shù)矫總€截面的矩形板塊的重力： 對實腹段里每個截面的力矩： 對空腹段里每個截面的力矩： 各截面的力矩見下表區(qū)間截面號懸鏈線曲邊三角形矩形塊M2kP M實腹段12000000000110.083333330.120

20、46715.908170.750060.73823511.743965820.003472222645.2323656.9763100.166666670.240933127.54270.7502421.475399188.17636390.0138888892580.9292769.10690.250.3614432.02070.7505432.210427954.95030620.031255807.0916762.041分界點0.310067930.448234827.1440.750835l/2*0空腹段80.33333333827.1440.7508353.5629422947.06

21、56490.05528491610273.4213220.4970.41666667827.1440.7508356.5165955390.1626520.081123911507520465.1760.5827.1440.7508359.4702497833.2596550.10696290519876.5827709.8450.58333333827.1440.75083512.423910276.356660.13280189924678.1734954.5240.66666667827.1440.75083515.3775612719.453660.15864089329479.754

22、2199.230.75827.1440.75083518.3312115162.550660.18447988734281.3349443.8820.83333333827.1440.75083521.2848617605.647670.21031888239082.9156688.5510.91666667827.1440.75083524.2385220048.744670.23615787643884.4963933.2301827.1440.75083527.1921722491.841670.2619968748686.0771177.91 (b)懸鏈線曲邊三角形塊從拱頂?shù)饺我饨孛娴?/p>

23、重力(參見上表) 每一塊Pi的重心的橫坐標： 在實腹段里，截面重心到任意截面的力臂為，在空腹段里，整塊曲邊三角形面積的重心到每個截面的力臂為。每個截面的力矩見上表c.各集中力對各截面的力矩M3拱上空腹段的腹孔和橫隔板等各集中力及其相應的橫坐標lx。在前面已經求出，各豎向集中力到截面的力臂，產生的力矩；腹拱水平推力H'g作用在第7與第8截面之間，對07截面產生的力矩 。具體計算見下表。截面號豎向力P17P16P15P14P13腹拱推力合力P720.5573171655.2691709.3121781.731876.913F1015.919212lx11.09516.321.727.132

24、.5e0.172603474MMMMMy1MM3120000000110.083333333000000100.16666666700000090.2500000080.333333333518.5240940000518.524170.4166666672646.8009800002.1372409751420.5529314067.35460.54775.077862353.6650003.118528492204.8983719333.64150.5833333336903.354747242.7560004.3112238863158.22263217304.3340.66666666

25、79031.6316212131.853297.657005.7326491724294.37123828755.5130.7511159.908517020.948346.372007.4034433365629.84097942157.0620.83333333313288.185421910.0313395.094341.25309.347902557184.05184560118.6110.91666666715416.462326799.1218443.89603.866011.59424958979.56229379242.820117544.739231688.2123492.5

26、214866.485525.34214.175129511042.46581104159.8d.計算偏離彎矩Mp上部結構恒載對拱圈各截面重心的彎矩：壓力線的縱坐標： 式中，Hg為不計彈性壓縮的恒載水平推力： 各截面上“恒載壓力線”偏離拱軸線的值：i偏離彎矩具體數(shù)值見下表截面號主拱圈拱上實腹段集中力合計恒載壓力線拱軸線偏心偏離彎矩M1M2M3Myiy1yMp120000000011548.2188748656.97625501205.1950.064680.0830520.018371989342.3288137102299.3003812769.1055205068.4060.272010.3

27、334070.0613974791144.03107195312.1688186762.0409012074.210.6479950.7547130.1067183311988.5032478-78631.7335413220.4902518.5241-64892.7-3.482641.3530774.83571786490104.86413714329.393720465.16744067.35438861.912.0856282.1372030.05157468961.0009636621412.3353527709.84459333.64158455.823.1371883.118474

28、-0.01871356-348.6932838529205.2687834954.521717304.3381464.124.371994.311148-0.06084152-1133.671713444737.1475942199.198928755.51115691.96.2089125.732548-0.47636392-8876.180808348851.2624249443.876142157.06140452.27.5377427.403313-0.13442889-2504.839449260638.6513256688.553360118.61177445.89.5231039

29、.347738-0.17536483-3267.606796173918.8613863933.230579242.82217094.911.6509811.59405-0.05692724-1060.736273088790.2582271177.9076104159.8264127.914.1751314.17488-0.0002495-4.648981647(2)偏離彎矩Mp在彈性中心產生的贅余力贅余力各項的計算見下表。 截面 12010.504.808020110.0183719890.998421.0015830.0184014.7250530.086946100.061397479

30、0.993631.0064110.0617914.4746980.27649690.1067183310.985491.0147240.108294.0533920.4389484.8357178640.97381.0269054.9658223.45502817.1570570.051574680.95831.0435150.0538192.6709020.1437456-0.0187135550.938721.06528-0.019941.689631-0.033685-0.0608415160.91481.093135-0.066510.496957-0.033054-0.4763639

31、180.886391.128172-0.53742-0.924440.4968153-0.134428890.853471.171687-0.15751-2.595210.4087682-0.1753648340.816221.22516-0.21485-4.539630.975341-0.0569272410.775041.290256-0.07345-6.785950.4984330-0.00024950.730570.684397-0.00017-9.366780.00159913.251224.1382820.4174由上表1得 (3)“恒載壓力線”偏離拱軸線的附加內力“恒載壓力線”偏

32、離拱軸線在拱圈任意截面中產生的附加內力為 拱頂、l/4截面、拱腳三個截面的附加內力見下表。項目拱頂截面l/4拱腳截面 10.938720.73057 00.3446810.682838 4.80810471.689576-9.367021564.4309821468.5631142.9260539.22911068.2530-348.693-4.64898-5819.037087-5819.04-5819.04 -13340.98504-8810.968830.378 (4)空腹式無鉸拱的恒載壓力線空腹式無鉸拱橋在恒載作用下考慮壓力線與拱軸線的偏離以及恒載彈性壓縮的影響之后，拱中任意截面存在三

33、個內力這三個力的合力作用點的偏心距為 所以，空腹式無鉸拱橋恒載壓力線的縱坐標空腹式無鉸拱恒載壓力線的縱坐標值見下表截面 1204.808104700.04508410.9936650.045371572-0.045371572110.0830524.72505270.0183720.062930.998420.9952580.0632298650.019722074100.3334074.47469770.0613970.1043690.993631.0001160.1043573630.22838061990.7547134.05339170.1067180.1470210.985491.0

34、084810.1457850280.60678148681.3530773.45502774.8357184.872230.97381.0207364.773252643-3.54859956972.1372032.67090170.0515750.083120.95831.0374440.0801196632.05359696563.1184741.6896307-0.018710.0066150.938721.0593340.0062445443.1118218154.3111480.4969567-0.06084-0.043070.91481.08734-0.039609054.3544

35、460445.732548-0.9244433-0.47636-0.46760.886391.122556-0.416545236.20248248537.403313-2.5952083-0.13443-0.136240.853471.166281-0.116819867.54018934829.347738-4.5396333-0.17536-0.18950.816221.219989-0.155328119.538039775111.59405-6.7859453-0.05693-0.085290.775041.285346-0.0663567611.67966721014.17488-

36、9.3667753-0.00025-0.044960.730571.364166-0.0329602314.219995773.空腹無鉸拱的實際恒載內力空腹式無鉸拱的實際恒載內力等于計人拱軸系數(shù)m的偏差影響的內力與“壓力線”及拱軸線偏離的附加內力之和，其結果見下表截面項目拱頂截面l/4拱腳截面拱軸線恒載假載合計拱軸線恒載假載合計拱軸線恒載假載合計水平力Hg18648.982671564.4309820213.4117849.680291564.43098219414.1117849.681564.43119414.11軸力Ng18431.040421564.4309819995.4718817

37、.866511468.56265120286.4323927.721142.92625070.65彎矩Mg1231.015399-13340.985-12110237.7624538-8810.955741-8573.19-1547.038830.3787283.353(二)活載內力計算1.公路-I級和人群荷載內力車道荷載的均布荷載標準值采用10.5KN/m，計算剪力時，所加集中力荷載P采用360KN人群荷載 橋梁基頻：不計彈性壓縮的公路-I級及人群荷載內力見下表截面項目公路I級人群荷載影響線面積車道荷載集中荷載表值乘數(shù)面積拱頂截面Mmax10.53605.250.00665025.06487

38、733.16543相應H110.53605.250.06536354.498692723.17003Mmin10.53605.25-0.004965025.064877-24.9243相應H110.53605.250.06167354.498692721.86193L/4截面Mmax10.53605.250.008975025.06487745.07483相應H110.53605.250.04054354.498692714.37138Mmin10.53605.25-0.0015025.064877-5.02506相應H110.53605.250.0865354.498692730.66414

39、拱腳Mmax10.53605.250.018615025.06487793.51646相應H110.53605.250.08977354.498692731.82335相應V汽10.53600.1640170.88769211.6262911.62608人0.1640170.88769211.6262911.62608Mmin10.53605.25-0.014945025.064877-75.0745相應H110.53605.250.03726354.498692713.20862相應V汽10.53600.3359970.88769223.8175623.81713人0.3359970.887

40、69223.8175623.81713接上表：影響線縱坐標汽車力或力矩人群力或力矩表值乘數(shù)0.051770.887691750.979174.11850.232435.00085694.817121.6427-0.012270.88769-601.696-130.8530.12195.00085471.458114.77520.0595870.887692093.429236.64290.136325.00085416.13375.44973-0.0286370.88769-822.558-26.38160.206395.00085728.2155160.98670.0513970.88769

41、2408.042490.96140.197315.00085723.8317167.07260.707141448.93860.70714161.03802-0.0613170.88769-2470.53-394.1410.062875.00085264.469569.345260.938261688.18330.938261125.0422計人彈性壓縮的公路-I級及人群荷載內力見下表項目拱頂截面人群L/4MmaxMminMmaxMminMmaxMmincos11110.938720.93872sin00000.3446810.344681與M相應的H1694.8169837471.45797

42、9121.6427114.7752416.133728.2155與M相應的VN694.8169837471.457979121.6427114.7752390.6324683.5905H8.1200128295.509716841.4215831.3413254.8631598.510326N8.1200128295.509716841.4215831.3413254.5651457.988813Np686.6969709465.948262120.2211113.4338386.0672675.6016M1750.978655-601.69633174.1185-130.8532093.42

43、9-822.558y4.80810474.80810474.8081054.8081051.6895761.689576M39.0418718526.49129546.8351216.4492338.21667814.37884Mp1790.020527-575.20503180.9536-124.4032101.645-808.179接上表人群拱腳截面人群MmaxMminMmaxMmin0.938720.938720.730570.730570.730570.730570.3446806660.3446806660.6828380.6828380.6828380.68283875.44972

44、927160.9867188723.8317264.4695167.072669.34526448.9386688.183361.03802125.042270.82616986151.1214527835.3619663.1311163.7373136.04510.8817469691.8813792028.4590953.0907361.9525020.8104070.8277135151.7660882846.1799612.2579991.4264390.59205969.99845634149.3553644829.182660.8731162.3108135.453236.6428

45、677-26.38159062408.042-2470.53490.9614-394.1411.689576211.68957621-9.36702-9.36702-9.36702-9.367021.4897787033.178733542-79.2365-28.951-18.2891-7.5911238.1326464-23.202857062328.806-2499.48472.6723-401.732(三)溫度變化、混凝土收縮、徐變的內力計算溫度變化為其它可變荷載，混凝土收縮、徐變?yōu)橛谰煤奢d，似乎要分項計算，但考慮到習慣和可能，還是將三者一起計算。拱圈合攏溫度7 月平均最低氣溫2 月平均最高氣溫30 拱圈材料彈性模量 拱圈材料線脹縮系數(shù) 混凝土收縮作用按下降10溫度的影響計入?；炷列熳冏饔玫挠绊懀?當計算溫度內力時以；當計算混凝土收縮內力時以的系數(shù)計入。 因此，計算降低溫度時 計算升高溫度時 溫度變化、混凝土徐變和收縮在彈性中心產生的水平力 溫度變化、混凝土徐變和收