下部結(jié)構(gòu)鉆孔灌注樁雙柱式橋墩的計(jì)算

1、表 3-153. 2下部結(jié)構(gòu)鉆孔灌注樁、雙柱式橋墩的計(jì)算3.2.1設(shè)計(jì)資料1、設(shè)計(jì)標(biāo)準(zhǔn)及上部構(gòu)造設(shè)計(jì)荷載：公路-II級(jí)；橋面凈空：凈-8+2 x 1m標(biāo)準(zhǔn)跨徑：Lb =13m ,梁長12.96m；上部構(gòu)造：預(yù)應(yīng)力簡支空心板。2、水文地質(zhì)條件沖刷深度：最大沖刷線為河床線下 6.88m處；按無橫橋向的水平力（漂流物、沖擊力、水流壓力等）計(jì)算。3、材料鋼筋：蓋梁主筋用HRB33屋岡筋，其它均用R235鋼筋混凝土：蓋梁、墩柱用C3Q系梁及鉆孔灌注樁用 C254、橋墩尺寸 5.5m蓋梁融而標(biāo)高咫 7 -0.7rn撕標(biāo)商1 I-1 JI II 1靠歹二3.2巾最大沖隧牖圖3-17 :尺寸單位 cm5、設(shè)計(jì)

2、依據(jù)公路橋涵地基與基礎(chǔ)設(shè)計(jì)規(guī)范（JTG D63-2007）3.2.2 蓋梁計(jì)算（一）荷載計(jì)算1、上部結(jié)構(gòu)永久荷載見表3-15:每片邊板自重（KN/m）每片中板自重（KN/m）一孔上部構(gòu)造自重與一個(gè)支座恒載反力（KN）1、9號(hào)28號(hào)(KN)邊板1、9號(hào)中板28號(hào)12.7499.513248.49292.86259.632、蓋梁自重及作用效應(yīng)計(jì)算（1/2蓋梁長度）圖 3-18表3-16:蓋梁自重產(chǎn)生的彎矩、剪力效應(yīng)計(jì)算截回編R自重（KN）彎矩(KN m)剪力（KN）V左V右1-1q1=0.7 X 0.625 X 1.5“5+叵 X0.2X 21.5 X 25=18.75M1 =-0.7 X 0.6

3、25 X 1.5 X 25 X0.625 0.625 X 0.2 X 1.5 X 25 X0625 =-5.61 3-18.75-18.752-21 ,、q2 = (0.9+1.1 ) X 20.625 X 1.5 X 25=23.44M 2=-0.7 X 1.25 X 1.5 X 25 X1.25 0.625- X 0.4 X 1.5 X 25 X21.25 0 =-24.413-42.19-42.19C967/E3-3q3 =0.75 X 1.1 X 1.5 X25=30.94M 3=-0.7 X 1.25 X 1.5 X 25 X1 251 251.375- X0.4X1.5X25X (

4、230 75 +0.75 ) -30.94 X u =-69.61-73.13116.944-4q4 =0.65 X 1.1 X 1.5 x25=26.81M 4 =190.07 X 0.65- (30.94+26.81 ) X0.7-0.7 X 1.25 X1.5 X 25X 1251252.025- X 0.4 X 1.5 X 25X (+231.4) =-0.3690.1390.135-5q5 =2.185 X 1.1 X 1.5X 25=90.13M 5=190.07 X 2.835- (30.94+26.81 +90.13 ) X 1.7925-0.7 X 1.25 X 1.5 X2

5、51.25 X4.21X 0.4 X 1.5 X25X21 25 +3.585 ) =98.12300q1+q2+q3 + q4 +q5=190.07KN3、可變荷載計(jì)算(1)可變荷載橫向分布系數(shù)計(jì)算：荷載對(duì)稱布置時(shí)用杠桿法，非對(duì)稱布置 用偏心受壓法。公路-I級(jí)單車列，對(duì)稱布置(圖3-19)時(shí):圖 3-191=6=012 = 50.088 =0.0442 5213 = 4 = 0.912 =0.4562b、雙車列，對(duì)稱布置（圖3-20）時(shí):圖 3-20P/2P/2P/2P/2一0儂板 板 板 板 板 板 號(hào) 號(hào) 號(hào) 號(hào) 號(hào) 號(hào)1 2 3 4 5 S11 =*0.093 =0.047212 =

6、50.907 =0.45425213 = 4 =-0.925 0.075 = 0.500c、單車列，非對(duì)稱布置（圖3-21）時(shí):318;5 O 1 8T-I AL PP/2P/2P/2130 I 180 P/2501P/2180 228,51SS153153153圖 3-21事 1由i二一士eai/（2 a2）,已知 n=6, e = 3.185,22222、a = 2 （0.7652.2953.955 ） = 42.99貝 U 1 3.185 3.955 = 1 0.2930 =0.460642.991 3.185 2.2952 -642.9913.185 0.7653 = 642.9916

7、1= 0.1700 =0.33761=1 0.0567 =0.22364 =1 -0.0567 =0.110615 0.1700 -0.003616 = - -0.290 = -0.126 6d、雙車列，非對(duì)稱布置（圖3-21）時(shí)：已知：n=6, e = 1.635, 2Z a2 =42.99二1 6=1 .1.635 3.95542.991.635 2.29542.991.635 0.76542.991=0.1504 = 0.31761二一 0.0873 =0.25461-0.0291 =0.19661 一 一40.0291 =0.1386160.1504 =0.0166(2)按順橋向可變荷

8、載移動(dòng)情況，求得支座可變荷載反力的最大值(圖3-22)23BKN圖 3-2210.5KN/m公路-I級(jí)雙孔布載單列車時(shí):-19.5 2 10.5B 二238 = 442.75 KN雙孔布載雙列車時(shí):2B=2 442.75 = 885.5KN單孔布置單列車時(shí)：195 105B = 238=340.375KN2單孔布載雙列車時(shí)：2B=2 340.375 = 680.75KNRi = B),見(3)可變荷載橫向分布后各梁支點(diǎn)反力(計(jì)算的一般公式為表 3-17表3-17 :各板支點(diǎn)反力計(jì)算何載橫向分布情況公路-I級(jí)荷載(KN計(jì)算方法橫向分布系 數(shù)11單孔雙孔BB對(duì)稱仰按單列行車公“1=0343.890

9、.00447.880.00杠桿法算路-I級(jí)“2=0.04415.1319.71n 3=0.456156.81204.231=0.456156.81204.230 5 =0.04415.1319.7150.000.00雙列行車公路-I級(jí)10.047687.7832.33895.7642.10% =0.454312.25406.68“3 =0.5343.89447.88“4 =0.5343.89447.88n 5 =0.454312.25406.68n 6=0.04732.3342.10非對(duì)稱磯J 按偏心受壓 法算單列行車公路-I級(jí)10.46343.89158.19447.88206.02n 2=

10、0.337115.89150.94“3=0.22376.6999.88“4=0.1137.8349.27“5 =-0.003-1.03-1.34n6 =-0.126-43.33-56.43雙列行車公路-I級(jí)10.319687.78219.40895.76285.75n 2=0.254174.70227.52“3=0.196134.80175.57“4=0.13894.91123.61n 5 =0.07954.3370.77=0.01611.0014.33(4)各板永久荷載、可變荷載反力組合：計(jì)算見表3-18,表中均取用各板的最大值，其中沖擊系數(shù)為:1 =1 0.2868 =1.2868表3-1

11、8 :各板永久荷載、可變荷載基本組合計(jì)算表(單位：KN)編R荷載情況1號(hào)板R12號(hào)板3號(hào)板4號(hào)板5號(hào)板6號(hào)板R2R3R4R5R6恒載585.73519.26519.26519.26519.26585.73公路-I級(jí)雙列對(duì)稱54.18523.31576.33576.33523.3154.18公路-I級(jí)雙列非對(duì)稱367.70292.78225.92159.0791.0618.44（4）+(2639.911042.571095.591095.591042.57639.91（5+卷953.43812.04745.18678.3610.32604.174、雙柱反力Gi計(jì)算（圖3-23）所引起的各梁反力表

12、3-19:圖3-23 :尺寸單位 cm表3-19 :雙柱反力 G1計(jì)算何載組反力G1計(jì)算式合情(KNJ)況組合1(639.91 6,79 +1042.57父5.13 +1095.593.6 +1095.59父 2.07(6公5.672778.07路-I+ 1042.57 0.54-639.911,12) =2778.07級(jí)雙列對(duì)稱組合。公路-I1 (953.43父6.79 +812.65 父 5.13 +745.18 父 3.6+ 678.33父 2.075.672536.57級(jí)雙+ 610.02 M0.54 -604.17父1.12) = 2536.57列非對(duì)稱由上表知應(yīng)取組合U控制設(shè)計(jì)，止

13、匕時(shí)G1 = G2 = 2778.07KN（二）內(nèi)力計(jì)算1、包載加活載作用下各截面的內(nèi)力（1）彎矩計(jì)算（圖3-23）截面位置見圖3-23,為求得最大彎矩值，支點(diǎn)負(fù)彎矩取用非對(duì)稱布置時(shí)的 數(shù)值，跨中彎矩取用對(duì)稱布置時(shí)數(shù)值。各截面彎矩計(jì)算式為：M11 =0M22 =-R 0.37M3L-R1 1.12M44 - -R1 1.77 - R2 0.11 G1 0.65M5s=R 3.955 - R2 2.30 - R3 0.77 G1 2.835各種荷載組合下的各截面彎矩計(jì)算見表 3-20表3-20 :各截面彎矩計(jì)算荷載組合情況墩柱反力（KN）板支座反力（KN）各截回號(hào)矩（KN m ）G1R1R2R3

14、截回2-2截回3-3截回4-4截回5-5組合C5公路-I級(jí)2778.07639.911042.571095.59-236.77-716.70558.422103.47雙列對(duì)稱組合Q公路-I級(jí)雙列非對(duì)稱2536.57953.43812.65745.18-352.77-1067.84-128.19977.48（2）相應(yīng)于最大彎矩時(shí)的剪力計(jì)算一般計(jì)算公式為：截面 1-1 : V左=0, V右=-R1；截面2-2 : V左=V右=-R1;截面 3-3 : V左=-R , V右=Gi - Ri ;截面 4-4 :V左=Y右=Gi- R- R2 ;截面 5-5 :V左=7右=G1- R1- R2 - R3

15、。計(jì)算值見表3-21 :表3-21 ：各截面剪力計(jì)算荷載組合情況墩柱反力G（KNJ）板支座反力（KNJ)各截回男力（KNJ）R2R3截回1-1截回2-2截回3-3截回4-4截回5-5V左V右V左V右V左V右V左V右V左V右組合6公2778.639104210950-639-63-639-63921381095109500路一級(jí)07.91.57.59.919.9.91.91.16.59.59組合7公2536.953812.745.0-953-95-953-9531583770.770.25.25.路一級(jí)57.436518.433.4.43.43蓋梁內(nèi)力匯總（表3-22）

16、表中各截面內(nèi)力取表3-20和表3-21中的最大值，按表3-22可繪制內(nèi)力計(jì)算的包絡(luò)圖表3-22 :蓋梁內(nèi)力匯總表內(nèi)力截回1-1截回2-2截回3-3截回4-4截回5-5彎矩(KN m)M自重-5.61-24.41-69.61-0.3698.12M荷載0.00-352.77-1067.84558.42977.48M計(jì)算-5.61-377.18-1137.45558.061075.60剪力（KN ）V自重左-18.75-42.19-73.1390.130.00右-18.75-42.19116.9490.130.00V荷載左0.00-953.43-953.431095.5925.31右-953.43-

17、953.432138.161095.5925.31V計(jì)算左-18.75-995.62-1026.561185.7225.31右-972.18-995.622255.101185.7225.31（三）截面配筋設(shè)計(jì)與承載力核算采用C30混凝土，主筋選用HRB335422,保護(hù)層5cm （鋼筋中心至混凝 土邊緣）。fcd =13.8MPa , fsd =280MPa。1.正截面抗彎承載力驗(yàn)算0M d - fcdbx ho -x2fsd As = fcd bX八fcdbxAs 二fsd以下取3-3截面作配筋設(shè)計(jì)，其它截面雷同。已知：bh =150 110cm, M d =-1137.45KN m ,取

18、 ?0=1.1, h0 =110-5 = 105cm即：、，、，6 j, XX )1.1 1137.45106 工13.8父1500Mx 1050 |2j化簡后為:x2 -2100x 112522.85 =0解方程得x = 59mmAs =2=4379 mmfcdbx _ 13.8 1500 59fT =280A.4379用(|)22鋼筋，其根數(shù)n= -3-9 = 11.5根，實(shí)際選用12根，配筋率：N =一As1 380.14561.21500 1050父100% =0.290%。該截面實(shí)際承載力Mu為:Mu=fsdAs h。59、=280 m 4561.2 m 1050 I2 J= 130

19、3.32KN m . 0Md =1137.45 1.1 =1251.20KN m就正截面承載能力與配筋率而言，配筋設(shè)計(jì)滿足公預(yù)規(guī)要求。其它截面的配筋設(shè)計(jì)如表3-23表3-23 :各截面鋼筋量計(jì)算表截卸號(hào)MKN m所需鋼筋面積As(mm2 )所需企22(根數(shù))實(shí)際選用含筋率(%根數(shù)As(mm2 )1-1-5.61830410.1932-2-377.1814243.71038010.2413-3-1137.45437911.51239080.2904-4558.0621175.61038010.2415-51075.6413410.91239080.2902 .斜截面按公預(yù)規(guī)5.2.10條要求,當(dāng)

20、截面符合：與Vd W0.50M10%2ftdbh0(KN河不進(jìn)行斜截面抗剪承載力計(jì)算，僅需按公預(yù)規(guī) 9.3.13條構(gòu)造要求配置箍筋。式中：Ct-預(yù)應(yīng)力提高系數(shù)，本例取口2=1.0；fsd 混凝土抗拉設(shè)計(jì)強(qiáng)度，本例取fsd=1.39MPa對(duì)于1-1截面：0.5 1Q-：2ftdbho0.5 1Q-1.0 1.391500850 =886.13KN對(duì)于2-2截面5-5截面：0.5 10&：2ftdbh0=0.5 10工1.0 1.3915001050 = 1094.63KN按公預(yù)規(guī)規(guī)定：0Vd M 0.51 10, Jfcu-kbh0 =0.51 10* 30 1500 1050 = 4399.5

21、8KN對(duì)照表3-23,可按構(gòu)造要求設(shè)置斜筋與箍筋，見圖 3-23。圖 3-233 .全梁承載力校核已知h0 =1050mm ,仃s =280MPa , 一根主筋企22所能承受的彎矩值為：M i =as x As x z , 其 中 z = 0.92% = 966mm, 代 入后得Mi =280 380.1 996 =102.83-24所示。(KN m),據(jù)此繪制彎矩包絡(luò)圖和全梁承載力校核圖，如圖122Z3.2.3橋墩墩柱計(jì)算墩柱直徑為130 cm,用30號(hào)混凝土，R235級(jí)鋼筋。尺寸見圖3-25.(一)荷載計(jì)算1 .恒載計(jì)算：(1)上部構(gòu)造恒載，一孔總重：3248.49KN(2)蓋梁自重(半根

22、梁重)：190.069KN(3)橫系梁重：72.976KN(4) 一根墩柱自重：169.23KN作用墩柱底面的包載垂直力為：1N橫=一父 3248.49+169.23 = 1793.475 KN 22 .汽車荷載計(jì)算荷載布置及行駛情況見前述圖3-19至圖3-21 ,由蓋梁計(jì)算得知：(1)公路I級(jí)單孔荷載單列車時(shí)：B1 -0, B2 =343.89KN,B1 B2 =343.89KN相應(yīng)的制動(dòng)力：T =343.89 2 0.1 =68.78KN按照公預(yù)規(guī)4.3.6條規(guī)定公路I級(jí)汽車制動(dòng)力不小于 165,故取制動(dòng)力165KN雙孔荷載單列車時(shí)：B B2 = 447.88KN相應(yīng)的制動(dòng)力:T =447

23、.88x2x0.1 =89.6KN 165KN ,故制動(dòng)力取 165KN汽車荷載中雙孔荷載產(chǎn)生支點(diǎn)處最大反力值，即產(chǎn)生最大墩柱垂直力；汽車 荷載中單孔荷載產(chǎn)生最大偏心彎矩，即產(chǎn)生最大墩柱低彎矩。3 .雙柱反力橫向分布系數(shù)計(jì)算（汽車荷載位置見圖3-25）:二318,52瓜 5I 283,5TRiRi圖3-25 :尺寸單位cm單列車時(shí):318.5 238.5, “八=1.062567=1 -1.062-0.062雙列車時(shí):163.5 238.5 = 0.7885672 =1 -0.788 = 0.2124 .荷載組合（1）最大最小垂直反力計(jì)算，見下表表3-24 :可變荷載組合垂直反力計(jì)算（雙孔）編

24、號(hào)荷載狀況最人垂直反力（KN最小垂直反力（KN）”1BT(1+u)“2B1 + u )1公路I級(jí)單列車1.0621224.13-0.062-71.472雙列車0.788908.30.212244.36表中汽車荷載已經(jīng)乘以沖擊系數(shù)(1 + =1.2868)(2)最大彎矩時(shí)計(jì)算(單孔)表3-25 :可變荷載組合最大彎矩計(jì)算(單孔)編號(hào)荷載情況墩柱頂反力計(jì)算式B”1+u)垂直力(KN水平力H (KN)對(duì)柱頂中心彎矩(KN，m)B1B2B1 +B20.25 B1 - B2 )1.14H1上部與蓋梁-1814.31002單孔雙列車687.78 X0.788 X1.2868697.410697.4182.

25、5174.35127.88表內(nèi)水平力由兩墩柱平均分配(二)截面配筋計(jì)算及應(yīng)力驗(yàn)算5 .作用于墩柱頂?shù)耐饬?圖3-26)(1)垂直力：最大垂直力：Nmax =1814.31 1224.13 =3038.44KN最小垂直力：(需要考慮與最大彎矩值相適應(yīng))Nmin =1814.31 697.41 =2511.72KN(2)彎矩：Mmax =174.35 127.88 = 302.23KN m(3)水平力:H =82.5KN2、作用于墩柱底的外力Nmax =3038.44 169.23 =3207.67KNNmin =2511.72 169.23 =2680.95KNM max =225.65 82.

26、5 5.1 =646.4KN3、截面配筋計(jì)算已知墩柱選用C30混凝土，采用20苴16HRB335I岡筋，Ag =40.22 cm2,則縱A 4022.向鋼筋配筋率 P=*=2=0.3%,由于 l0/(2r )=5.1/(2父0.65)=3.97,二 r 二 650故不計(jì)偏心增大系數(shù)：取=中=1.0；(1)雙孔荷載，按最大垂直力時(shí)，墩柱頂按軸心受壓構(gòu)件驗(yàn)算，根據(jù)公預(yù)規(guī)5.3.1條：”Nd W0.9巴qA+fsdAs ) . _ * * k-一 一一一一.一一七0.9 1A fsdAs .尸0.9 113.8 1327323 280 4022= 17498.89 KN 0Nd= 3038.44 1

27、.1 =3342.28滿足規(guī)范要求。(2)單孔荷載，最大彎矩時(shí)，墩柱頂按小偏心受壓構(gòu)件驗(yàn)算:Nd = 2511.72KNMd =225.65KN me0 = = 0.090 = 90mm Ndl0/ 2r =3.9 :二 7=1 .0 , e0 = 90mm根據(jù)公預(yù)規(guī)5.3.9條偏心受壓構(gòu)件承載力計(jì)算應(yīng)符合下列規(guī)定:22 _ 0Nd Ar fcdC r fsd與山， 2.5,可按彈性樁計(jì)算。3 .地面以下深度Z處樁身截面上的彎矩MZ與水平壓應(yīng)力(7ZX的計(jì)算 已知作用于地面處樁頂上的外力為：N0 =2717.44KN , H0 =84.507 KN , M0 =911.20KN m(1)樁身彎

28、矩MzH0Mz =0 Am MBma式中的無量綱系數(shù)Am,Bm可由表格查得，計(jì)算見表3-26，分布圖見圖3-29表3-26 :樁身彎矩 M z計(jì)算(單位：KM- mZZ =sZh =othAmBm蟲Am aMBmMz0.330.104.000.09960.9997427.69910.96938.650.660.204.000.196960.9980654.75909.43964.181.320.404.000.377390.98617104.91898.601003.511.970.604.000.529380.95861147.16873.491020.642.630.804.000.645

29、610.91324179.47832.141011.613.291.004.000.723050.85089201.00775.33976.334.281.304.000.767610.73161213.38666.64880.034.931.504.000.754660.68694209.78625.94835.726.582.004.000.614130.40658170.72370.48541.198.222.504.000.398960.14763110.90134.52245.429.873.004.000.193050.0759553.6669.21122.8711.513.504

30、.000.050810.0135414.1212.3426.4613.164.004.000.000050.000090.010.080.10(2)樁身水平壓應(yīng)力zx二 Ho二 zx二 一0zBx式中無量綱系數(shù)Ax,Bx可由表格查得,z為換算深度,z =A乙計(jì)算見表bi3-27,樁身的水平壓應(yīng)力分布示于圖3-29.最大沖刷線M(KNe)10,z(n)z(n)圖 3-29表3-27 :水平壓力 仃zx計(jì)算（單位：KM/I- m）ZZ =ZAxBx也zAx b1a2M -D zBxb1鼠0.000.000.000.000.000.660.202.117791.290884.849.6614.501

31、.320.401.802731.000648.2314.9823.212.300.701.360240.6388510.8716.7427.612.960.901.093610.4448111.2414.9826.223.621.100.854410.2860610.7311.7822.514.931.500.466140.062887.983.5311.516.582.000.14696-0.075723.36-5.67-2.319.873.00-0.08741-0.09471-2.99-10.63-13.6313.164.00-0.10788-0.01487-4.93-2.23-7.15（

32、四）樁身截面配筋與承載力驗(yàn)算（圖 3-30）圖 3-30驗(yàn)算最大彎矩值z(mì)=1.97m處的截面強(qiáng)度，該處內(nèi)力值為：M =1020.64KN mN = 2717.44KN樁內(nèi)豎向鋼筋按0.2%配置，則 ：22As1,50.2% =35.34 cm選用 2016, As = 40.22cm2 , P = 0.23%, n = Eg/Ec=6.7樁的換算面積為： - -2_42A。=Ah nAs = 1,56.7 40,22 101,794m4樁的換算截面模量Wo為：2二 3 nAsrs3W0 = R =0.331m 42R0 = 750mms = 0 - - - 0 f 2 0.05 0 = 675

33、mme0 = 90mm4 0取 lp =0.7 =9.21m a根據(jù)公預(yù)規(guī)5.3.9條和5.3.10條相關(guān)規(guī)定：e0 =M0/N0 =911.2/2717.44 = 335mme01 =0.2 2.7- = 0.835 ro rsJ =1.150.01 = 1.0886 1 ,取，2=1 2r偏心增大系數(shù)：=1 1 E 12 =1.0961400e0 / r rs 2r貝Ue0 =367mmit 370mm。按橋墩墩柱的計(jì)算方法，查公預(yù)規(guī)附錄C相關(guān)表格，可得到相關(guān)系數(shù)。經(jīng)試算，當(dāng) ”0.59時(shí)，從表格中查得：A=1.4589,B=0.6635,C=0.4485,D=1.8052另設(shè) g=0.88,因 p =0.23%