下部結(jié)構(gòu)鉆孔灌注樁雙柱式橋墩的計(jì)算

1、3. 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(zhǎng)12.96m；上部構(gòu)造：預(yù)應(yīng)力簡(jiǎn)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(wú)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C30,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 圖3-17 ：尺寸單位 cm5、設(shè)計(jì)依據(jù)?公路橋涵地基與根底設(shè)計(jì)標(biāo)準(zhǔn)?JTG

2、 D63-20223.2.2 蓋梁計(jì)算一荷載計(jì)算1、上部結(jié)構(gòu)永久荷載見(jiàn)表3-15:靠歹二3.2巾最大沖隧牖C967/E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KN1、9號(hào)2-8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(zhǎng)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KNV左V右1-1q1=0.7 X 0.625 X 1.5X 25+0.625 X0.2X21.5 X 25=18.75M1 =-0.7 X 0.625 X

3、 1.5 X 25 X0.625 0.625 X 0.2 X 1.5 X 25X06型=-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 =-24.413-42.19-42.193-3q3 =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 (230 75 +0.75

4、) -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 X251.25 X4.21X

5、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板 板 板 板 板 板 號(hào) 號(hào) 號(hào) 號(hào) 號(hào) 號(hào)1 2 3 4 5 S11 = .60.093 -0.047212 = 50.907 =0.454252

6、13 = 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eaj/2 a2 , n=6, e = 3.185,22222、a = 2 0.7652.2953.955 = 42.99貝 U1 3.185 3.955 = 6 1 0.2930 =0.460642.991 3.185 2.2952 -642.9913.185 0.7653 = 642.99161= 0.1700 =0.33761=1 0.

7、0567 =0.22364 - -0.0567 =0.1106150.1700 -0.003616 = - -0.290 = -0.126 6d、雙車列,非對(duì)稱布置圖3-21時(shí)：n=6, e = 1.635, 2Z a2 =42.99211.635 3.955T 642.991=0.1504 = 0.317611.635 2.295十642.991二一 0.0873 =0.254611.635 0.765 r 1-0.0291 =0.19661 一 一40.0291 =0.1386160.1504 =0.0166(2)按順橋向可變荷載移動(dòng)情況,求得支座可變荷載反力的最大值(圖3-22)23BK

8、N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 = 680.75KNR =B),見(jiàn)(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=0343.890.00447.880.00杠桿法算路-I級(jí)“2=0.04415.1

9、319.71“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“2 =0.454312.25406.68“3 =0.5343.89447.88“4 =0.5343.89447.88n 5 =0.454312.25406.68“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=0.337115.89150.94“3=0.22376.6999.8

10、8“4=0.1137.8349.27“5 =-0.003-1.03-1.346 =-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(jiàn)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3-18 :各板永久荷載、可變荷載根本組合計(jì)算表(單位：KN)編R荷載情況1

11、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367.70292.78225.92159.0791.0618.444+(2639.911042.571095.591095.591042.57639.91+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G

12、1計(jì)算式合情(KN)況組合1(639.91 6,79 +1042.57 父 5.13 +1095.59 父 3.6 +1095.59 父 2.076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 m6.79 +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限制設(shè)計(jì),止匕時(shí)G1 =G2 =2778.07KN二內(nèi)力計(jì)算1、包載加活載作用下各截面

13、的內(nèi)力1彎矩計(jì)算圖3-23截面位置見(jiàn)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：M14 =0M22 =-Ri 0.37M33R1 1.12M44 - -R1 1.77 - R2 0.11 G1 0.65M5s=R1 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(jiàn)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)2778.07639.911042.571

14、095.59-236.77-716.70558.422103.47雙列對(duì)稱組合Q公路-I級(jí)雙列非對(duì)稱2536.57953.43812.65745.18-352.77-1067.84-128.19977.482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=-R;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.計(jì)算值見(jiàn)表3-21 :表3-21 ：各截面剪力計(jì)算荷載組合情況墩柱反力GKN板支座反力KN)各截回男力KN

15、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

16、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-953.43-953.432138.161095.5925.31V計(jì)算左-18.75-995.62-1026.561185.7225.31右-97

17、2.18-995.622255.101185.7225.31三截面配筋設(shè)計(jì)與承載力核算采用C30混凝土,主筋選用HRB335 i 22,保護(hù)層5cm (鋼筋中央至混凝 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 bXfcdbxAs =d fsd以下取3-3截面作配筋設(shè)計(jì),其它截面雷同.：bh =150 110cm, M d =-1137.45KN m ,取 0=11,h0=110-5 = 105cm即：、,“6 j “ J X )1.1 1137.45106 13.8父1500Mx 10

18、50 |2)化簡(jiǎn)后為:x2 -2100x 112522.85 =0解方程得x = 59mm2=4379 mmfcdbx _ 13.8 1500 59280A.4379用(|)22鋼筋,其根數(shù)n= -39 = 11.5根,實(shí)際選用12根,配筋率：N =一As1 380.14561.21500 1050100% =0.290%該截面實(shí)際承載力Mu為:Mu=fsdAs ho59、=280 m 4561.2 m 1050 I2 J= 1303.32KN m . 0Md =1137.45 1.1 =1251.20KN m就正截面承載水平與配筋率而言,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

19、-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)截面符合： 皿 0.50M0J32ftdbh0(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：2預(yù)應(yīng)力提升系數(shù),本

20、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 10-：2ftdbh00.5 10-1.01.391500850 =886.13KN對(duì)于2-2截面5-5截面：0.5 10&:2ftdbh0=0.5 10-1.01.3915001050 =1094.63KN按?公預(yù)規(guī)?規(guī)定：0Vd M 0.51 10,fcukbh0 =0.51 10* 30 1500 1050 = 4399.58KN對(duì)照表3-23,可按構(gòu)造要求設(shè)置斜筋與箍筋,見(jiàn)圖 3-23.圖 3-233.全梁承載力校核h0 =1050mm, 0s =280MPa , 一根主筋企22所能承受的

21、彎矩值為：M l =as x As x z , 其 中z = 0.92h = 966mm, 代 入后得Ml =280 380.1 996 =102.8(KN m),據(jù)此繪制彎矩包絡(luò)圖和全梁承載力校核圖,如圖 3-24所示.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(jiàn)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 = 17

22、93.475 KN 22 .汽車荷載計(jì)算荷載布置及行駛情況見(jiàn)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根據(jù)?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)：B1 B2 = 447.88KN相應(yīng)的制動(dòng)力:T =447.88x2x0.1 =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

23、,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(jiàn)圖3-25:二318,5RiRi圖3-25 :尺寸單位cm單列車時(shí):318.5 238.5 彳“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(jiàn)下表表3-24 :可變荷載組合垂直反力計(jì)算雙孔編號(hào)荷載狀況最人垂直反力KN最小垂直反力KN1BT(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

24、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B1+u)垂直力(KN水平力H (KN)對(duì)柱頂中央彎矩(KN,m)BiB2B1 +B20.25 B1-B2 )1.14H1上部與蓋梁-1814.31002單孔雙列車687.78 X0.788 X1.2868697.410697.4182.5174.35127.88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1 .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

25、：(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 = 268Q95KNM max =225.65 82.5 5.1 =646.4KN3、截面配筋計(jì)算墩柱選用C30混凝土,采用20苴16HRB335I岡筋,Ag =40.22 cm2,那么縱向鋼筋配筋率P=Ag4022二 r2二 6502= 0.3%,由于 l0/(2r )

26、=5.1/(2父0.65)=3.97,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:0Nd 0.9 : fcdAfsdAs A J _. _ * * k一一 一一一一.一一七0.9 fcdA fsdAs 尸0.9 113.8 1327323 280 4022= 17498.89 KN 0Nd= 3038.44 1.1 =3342.28滿足標(biāo)準(zhǔn)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 m e0 = = 0.090 = 90mmNdl0/ 2r =3

27、.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)符合以下規(guī)定:22 _ 0Nd 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M與水平壓應(yīng)力(7ZX的計(jì)算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)樁身彎矩MzH0Mz =0 Am MBma式中的無(wú)量綱系數(shù)Am,Bm可由表格查得,計(jì)算見(jiàn)表3-26,分布圖見(jiàn)圖3-29表3-26 :樁身彎矩 M z計(jì)算(單位：KM- mZZ =sZh =othAmBm蟲(chóng)Am aMBmMz0.330.104.000.099

28、60.9997427.69910.96938.650.660.204.000.196960.9980654.75909.43964.181.320.404.000.377390.98617104.91898.601003.511.970.604.000.529380.95861147.16873.491020.642.630.804.000.645610.91324179.47832.141011.613.291.004.000.723050.85089201.00775.33976.334.281.304.000.767610.73161213.38666.64880.034.931.504

29、.000.754660.68694209.78625.94835.726.582.004.000.614130.40658170.72370.48541.198.222.504.000.398960.14763110.90134.52245.429.873.004.000.193050.0759553.6669.21122.8711.513.504.000.050810.0135414.1212.3426.4613.164.004.000.000050.000090.010.080.10(2)樁身水平壓應(yīng)力zx-zBx式中無(wú)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(jiàn)表二 H

30、o二 zx二 一bi3-27,樁身的水平壓應(yīng)力分布示于圖3-29.最大沖刷線M(KN,n)1U,z(n)z(n)圖 3-29表3-27 :水平壓力 仃zx計(jì)算單位：KM/I- RZZ =ZAxBx也1Ax b1a2MO -D zBxb1鼠0.000.000.000.000.000.660.202.117791.290884.849.6614.501.320.401.802731.000648.2314.9823.212.300.701.360240.6388510.8716.7427.612.960.901.093610.4448111.2414.9826.223.621.100.854410

31、.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,那么 ：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_42Ao =Ah nAs = 1.56.7 40.22 101.794m4樁的換算截面模量Wo為：2二 3 nAsrs3Wo = R =0.331m 42R0 = 750mms = 0