箱梁上緣懸臂計(jì)算

1、=V-臂天津三號(hào)線箱梁上緣懸臂計(jì)算書2006年7月7日 TOC o 1-5 h z HYPERLINK l bookmark4 o Current Document 天津三號(hào)線箱梁上緣懸臂計(jì)算書0I、最大線間距的懸臂處強(qiáng)度計(jì)算2II、4.4m線間距的懸臂處強(qiáng)度計(jì)算12II、4.4m線間距的懸臂處強(qiáng)度計(jì)算18I、最大線間距的懸臂處強(qiáng)度計(jì)算一、結(jié)構(gòu)簡(jiǎn)況等截面連續(xù)箱梁，梁高1.7m，橋面寬度隨線間距變化，箱梁底寬為4.2m, 雙線線間距為3.65m。運(yùn)營(yíng)狀態(tài)最大線間距為5m,在R=450m時(shí)，曲線加寬 為：內(nèi)側(cè)為0.31m，外為0.05m?，F(xiàn)對(duì)最大線間距和曲線加寬為0.31m的箱梁上 翼緣懸臂強(qiáng)度、

2、上翼緣懸臂裂縫寬及脫軌狀態(tài)下上翼緣懸臂強(qiáng)度、箱梁梁的穩(wěn)定 性進(jìn)行檢算。箱梁截面如圖1，計(jì)算時(shí)按承托處為固定端的懸臂梁計(jì)算。圖1箱梁截面圖二、計(jì)算米用規(guī)范鐵路橋涵設(shè)計(jì)基本規(guī)范TB 10002.1-2005鐵路橋涵鋼筋混凝土和預(yù)應(yīng)力混凝土結(jié)構(gòu)設(shè)計(jì)規(guī)范TB 10002.3-2005天津市地下鐵道二期工程施工圖設(shè)計(jì)技術(shù)要求城市軌道交通設(shè)計(jì)規(guī)范DGJ08-109-2004三、材料（一）砼箱梁砼 C50（二）鋼筋箱梁懸臂上緣受力鋼筋采用HRB335鋼筋，用6表示。四、荷載（一）恒載結(jié)構(gòu)自重箱梁砼容重Y =26kN/m3。二期恒載橋面鋪裝厚100mm，容重Y =25kN/m3。承軌臺(tái)及鋼軌按15kN/m-線

3、計(jì)算。疏散平臺(tái)結(jié)構(gòu)砼容重：Y =25kN/m3聲屏障按3.4kN/m計(jì)算，聲屏障高為從軌頂3.5m。電纜重按2.5kN/m計(jì)算（每側(cè)）。（二）活載1 .人群活載取4kN/m2風(fēng)載，按最不利的風(fēng)載計(jì)算。天津風(fēng)壓20m高之內(nèi)為基本風(fēng)壓為 叫=600Pa計(jì)算，聲屏障高3.5+0.52 =4.02m計(jì)算。列車活載1）活載軸重如圖2,列車荷載沖擊系數(shù)采用：1+. =1 + 0.8x6史30 + L有5 一. 有5 一. T W2-J有5 一. T H巖二 菖一二 苞2-JS3|114310.3Z. 34.6N10.3+.3+-1 5 4-3x(2.3+LO.：i+2.3 + 1.6Z)2.3ID.3N.

4、335圖2列車活載圖式（長(zhǎng)度單位：米）2）車輪分布寬度列車活載橫橋向布置如圖3。圖3列車活載橫橋向布置 b1= b2+2X0.344=0.15+0.688=0.838m2.3m(車輪荷載重疊但小于4.62m)所以按軸距為2.3m的二軸重計(jì)算：a= (a1+2h)+2c=(2.3+2X0.52)+2X1.24=5.88m五、計(jì)算簡(jiǎn)圖J I I I 一 J I I I 一 112100圖5箱梁上翼緣懸臂板受力示意圖i（Xi計(jì)算簡(jiǎn)圖見圖5。疏散平臺(tái)、聲屏障及電纜重：W1 = A0 xy 0 + 3.4 + 2.5 = 0.471 X 25 + 3.4 + 2.5 = 17.7 kN人行道板重 W2

5、= A0 xy 0 = 0.09 x 25 = 2.25 kN承軌臺(tái)及鋼軌重：W3 = 15/2 = 7.5 kN按等效集中力計(jì)算：人活載：P = 4x0.6 = 2.4 kN列車活載計(jì)算：a = 4 x （1 h） = 4 取a = 2按跨度為28m計(jì)算沖擊系數(shù)目=0.8 xa （一） = 0.8 x 2 x （一6一） = 0.16630 + L30 + 28列車活載 P2 = (1 + r ) X 2X：p軸重 /a = 1.166X 140/5.88 = 27.76 kN風(fēng)活載 W風(fēng)=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa風(fēng)活載對(duì)懸臂梁的彎矩

6、為：M風(fēng)=W風(fēng)x3.5x 1 x3.5/2 = 4.631kN-m、計(jì)算2-2時(shí)：截面懸臂自重及鋪裝(按等效集中力計(jì)算)箱梁懸臂自重W4 = A0 xy = 0.2X 1.21 X26 = 6.292kN橋面鋪裝W5 = A0 xy = 0.1 x 1.21 x 25 = 3.025kN集中力作用點(diǎn)均作用在1-1截面左0.605m處、計(jì)算3-3時(shí)：截面懸臂自重及鋪裝(按等效集中力計(jì)算)箱梁懸臂自重與= xy = 0.752 x 26 = 19.552 kN經(jīng)計(jì)算，集中力作用點(diǎn)在2-2截面左1.254m處橋面鋪裝W5 = A0 xy = 0.1 x 2.91 x 25 = 7.566kN集中力作

7、用點(diǎn)在2-2截面左1.455m處六、結(jié)構(gòu)計(jì)算截面配筋見圖5，受拉筋中16100+16200，受壓筋中12100，取一米寬計(jì) 算受拉筋為1016+516，受壓筋為1012。*16鴕伽*16鴕伽圖6箱梁上翼緣懸臂板截面配筋圖1、內(nèi)力計(jì)算1-1截面活載彎矩：M1 =-P x0.3-M=-2.4 x 0.3 - 4.63 M1 =-P x0.3-M恒載彎矩：M2 =* X0.15-. X0.3=17.7 x 0.15 2.25 x 0.3 = 1.995(kN - m)總彎矩 M = M1 + M2 = -3.355(kN - m)2-2截面活載引起的彎矩：M1 = Pj 0.61 + M風(fēng)=2.4

8、x 0.61 + 4.63 = 6.094(kN - m)恒載引起的彎矩：M2 =嗎x1.06+嗎x0.61+ W4 +Wpx0.605=17.7 x 1.06 + 2.25 x 0.61 + (6.292 + 3.025) x 0.605 = 25.8(kN - m)總彎矩 M = M1 + M2 = 31.9(kN - m)Q = P + 叫 + 乙 + W4 + W5 = 2.4 +17.7 + 2.25 + 6.292 + 3.025 = 31.67( kN)3-3截面活載引起的彎矩：M1 = P x 2.31 + P x 0.85 + M風(fēng)=2.4 x 2.31 + 27.76 x

9、0.85 + 4.63 = 33.8kN - m)恒載引起的彎矩：M2 = W1 x 2.76 + W2 x 2.31 + W3 x 0.85 + W4 x 1.254 + W5 x 1.455=17.7 x 2.76 + 2.25 x 2.31 + 7.5 x 0.85 +19.552 x 1.254 + 7.566 x 1.455 = 96.0(kN - m)總彎矩M = M1 + M2 = 33.8 + 96.0 = 129.8(kN - m)Q = p + P + 咯 + 乙 + W3 + W4 + W5 = 2.4 + 27.76 +17.7 + 2.25 + 7.5 +19.552

10、 + 7.566 = 84.7(kN)2、強(qiáng)度檢算1-1截面(本截面的彎矩和剪力都比2-2截面小，所以強(qiáng)度及裂縫寬不檢算)(2)2-2截面bx 20 + nA (x - a) - nA (h - x ) = 0 TOC o 1-5 h z 2s 0 ss 00-n(A + A ) + :n2(A + A )2 + 2nb(A a + A h )S X = ssss ss_00b-10 x (1130+ 2010) + 匕：102 x (1130+ 2010)2 + 2 x 10 x 1000 x (1130 x 45 + 2010 x 155)=59.34mm1000bh 3 、I =+ nA

11、 (x 一a)2 + nA (h 一 x )203s o ss o 01000 X1553 +10 X1130 X (59.34 - 45)2 +10 x 2010 x (155 - 59.34)2 = 2.56 x 108 mm 4=0=2.56 x 108 + 59.34 = 4.31 x 106 mm 3=0=2.56 x 108 - (155 - 59.34) = 2.68 x 106 mm3bcbc31.9x 103)/(4.31 x 106 x 10-9) = 7.4x 106Pa = 7.4Mpa b= 16.8Mpa=n=n -10 x (31.9 x 103)/(2.68 x

12、 106 x 10-9) = 119.0 x 106Pa = 119.0Mpa 155 - 45 = 110mm 取 z = 110mm中性軸剪應(yīng)力T = %=31.67 x 10 x 0 11) = 0.29 x 106 Pa = 0.29Mpa 1.55Mpa(3)3-3截面bx 20 + nA ( x - a) - nA (h - x ) = 0 TOC o 1-5 h z 2s 0 ss 00-n(A + A ) + Mn2(A + A )2 + 2nb(A a + A h )=sssssss 00b10 x (1130+ 3014.4) +.102 x (1130+ 3014.4)2

13、 + 2x 10 x 1000 x (1130 x45 + 3014.4x355) % = 113.9mm1000I =a + nA (x 一 a)2 + nA (h 一 X )2 03s o ss o 01000 x 3553 +10 x 1130 x (113.9 - 45)2 +10 x 3014.4 x (355 -113.9)2 = 2.3 x 109 mm 4w =、= 2.3 x 109 +113.9 = 2.017 x 107 mm 30 X0L = 2.3x 109 - (355 -113.9) = 9.5x 106mm3 (h0 -X0)bcbc=(129.8 x 103)

14、 /(2.017 x 107 x 10-9) = 6.44 x 106 Pa = 6.44Mpa b， = 16.8Mpab = nb = n -=10 x (129.8 x 103)/(9.5 x 106 x 10-9) = 136.6x 106Pa = 136.6Mpa 355 - 45 = 310mm 取 z = 299.2mmt =男乙=84 x 1% x 0 2992) = 0.283 x 106 Pa = 0.283Mpa 1.55Mpa3、裂縫寬度驗(yàn)算(1)2-2截面K1 = 0.8(P n(P n + P n + P n ) A /=1 12 23 3 sF(2ba ).s(p

15、 n +p n H 1 12 2(p n +p n H 1 12 2_(1 x 10) x=0.0223x 1000 x 45) w = K K r 土 (80 + 8 + 04) TOC o 1-5 h z f 1 2 E 職 s z=0.8 x 1.46 x 1.1 x 119 x (80 + 8 + 回次16) / 200000 = 0.135mm = w = 0.20mm 0.0223f(2)3-3截面K1 = 0.8=1 + 0.3 x231 + 0.5 x 969 = 1.45129.8129.8_ (p n + p n + p n )A / _ (p n + p n R =1 1

16、2 23 3sia =1 12 21 d+ p3n3)As/(2+ p3n3)As/(2ba )X1000 X 45) = 0.03028 + 0如=0.8 x 1.45 x 1.1 x 129“8 (80 + 8 + 0.4 次16) = 0.134mm 2.3m不計(jì)沖擊系數(shù)P2= ：p軸重/a = 70kN活載引起的彎矩：M1 = P x 0.5 = 35(kN m)恒載引起的彎矩：M2 =捋X1.06+.X0.61+叱+=)x0.605=17.7 x 1.06 + 2.25 x 0.61 + (6.292 + 3.025) x 0.605 = 25.8(kN m)總彎矩 M = M1 +

17、 M2 = 60.8(kN - m)Q = P2 + 叫 + % + W4 + W5 = 70 +17.7 + 2.25 + 6.292 + 3.025 = 99.27(kN)b = Mw = (60.8X 103)/(4.31 X106 X10-9)= 14.1 x 106Pa = 14.1Mpa ” = 16.8MpaC0b = n - MW - s10 X (60.8 X103)/(2.68 X106 X10-9) - 227 x 106Pa - 227Mpa 1.4b - 252Mpa s中性軸剪應(yīng)力T -侃-99.27.4 X10 X 0 11)- 0.902 x 106 Pa -

18、0.902Mpa 2.3m (車輪荷載重疊但小于 4.62m)所以按軸距為2.3m的二軸重計(jì)算：a= (a1+2h)+2c=2.3+2X2. 2=6.4m不計(jì)沖擊系數(shù)P2 - 2x ：p軸重/a -140/6.4 - 21.88求P2c=0.7m懸臂板的荷載有效分布寬度：a= (a1+2h)+2c=2X0.7=1.42.3m不計(jì)沖擊系數(shù)P2 - !p /a - 70/1.4 - 502 軸重活載引起的彎矩：M1 - P2 x 2.2 + P 2 x 0.7 - 21.88 x 2.2 + 50 x 0.7 - 83.14(kN - m)恒載引起的彎矩：M2 -叫 x 2.76 + W2 x 2

19、.31 + W3 x 0.82 + W4 x 1.254 + W5 x 1.455-17.7 x 2.76 + 2.25 x 2.31 + 7.5 x 0.82 +19.552 x 1.254 + 7.566 x 1.455 - 96.0(kN - m) 總彎矩 M = M 1 + M2 = 83.14 + 96.00 = 179.14(kN - m)Q = P + P + W + W + W + W + W = 21.88 + 50+17.7 + 2.25 + 7.5 +19.552+7.566 = 126.4(kN) 2212345a = M/c ，- w0=(179.14x 103)/(

20、2.017 x 107 x 10-9) = 8.88x 106Pa = 8.88Mpa a=6.8Mpaa =n M，ws=10 x (179.14x 103)/(9.5x 106 x 10-9) = 188.5x 106Pa = 188.5Mpa 1.4xa = 252Mpat =冗=126.4 x 1% x 0 299)= 0.43 x 106 Pa = 0.43Mpa 1.2M = 1713kN - mII、4.4m線間距的懸臂處強(qiáng)度計(jì)算一、結(jié)構(gòu)簡(jiǎn)況線間距為4.4m、曲線加寬為0.31m的箱梁?，F(xiàn)對(duì)其上翼緣懸臂強(qiáng)度、上緣翼懸 臂裂縫寬及脫軌狀態(tài)下上翼緣懸臂強(qiáng)度、箱梁總體穩(wěn)定性進(jìn)行檢算。截

21、面圖見 圖8。圖8箱梁截面圖二、計(jì)算采用規(guī)范同I三、材料同I四、荷載（一）恒載材料自重見I（二）活載人群活載同I。風(fēng)載，按最不利的風(fēng)載計(jì)算，同I。列車活載活載軸重如圖2,列車荷載沖擊系數(shù)采用：按跨28米計(jì)算1+=1 + 0.8x6L30 + L1)車輪分布寬度(列車活載橫橋向布置見圖9)圖9列車活載橫橋向布置c=0.55 +0.838/2=0.97m懸臂板的荷載有效分布寬度：a= (a1+2h)+2c=2X0.52+2X0.97=2.78m2.3m (車輪荷載重疊但小于 4.62m)所以按軸距為2.3m的二軸重計(jì)算：a= (a1+2h)+2c=(2.3+2X0.52)+2X0.97=5.28m

22、五、計(jì)算簡(jiǎn)圖圖10箱梁上翼緣懸臂板受力示意圖計(jì)算簡(jiǎn)圖見圖10。疏散平臺(tái)、聲屏障及電纜重：W1 = A0 xy 0 + 3.4 + 4 = 0.471 x 25 + 3.4 + 2.5 = 17.7kN人行道板重 W2 = A0 xy 0 = 0.09 x 25 = 2.25 kN承軌臺(tái)及鋼軌重：W3 = 15/2 = 7.5 kN按等效集中力計(jì)算：人活載：P = 4x0.6 = 2.4 kN列車活載計(jì)算：a = 4 x （1 h） = 4 取a = 2目=0.8 xa （一） = 0.8 x 2 x （一6一） = 0.16630 + L30 + 28列車活載 P2 = (1 +r ) X 2

23、X：p軸重 /a = 1.166X 140/5.28 = 30.91 kN風(fēng)活載 W風(fēng)=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa風(fēng)活載對(duì)懸臂梁的彎矩為：M風(fēng)=W風(fēng)x3.5x 1 x3.5/2 = 4.631kN-m懸臂自重與= xy = 0.692x26 = 17.992kN經(jīng)計(jì)算，集中力作用點(diǎn)在2-2截面左1.123m處鋪裝W5 = A0 xy = 0.1 x 2.61 x 25 = 6.525kN集中力作用點(diǎn)在2-2截面左1.305m處六、結(jié)構(gòu)計(jì)算截面配筋見圖11，受拉筋中16100，受壓筋中12100，取一米寬計(jì)算受拉筋為1016，受壓筋為101

24、2。圖11箱梁上翼緣懸臂板截面配筋圖5、內(nèi)力計(jì)算1-1截面活載引起的彎矩：M1 = P x 2.01 + P x 0.55 + M風(fēng)=2.4 x 2.01 + 30.91 x 0.55 + 4.63 = 26.45kN - m)恒載引起的彎矩：M2 =叫 x 2.46 + W2 x 2.01 + W3 x 0.55 + W4 x 1.123 + W5 x 1.305=17.7 x 2.46 + 2.25 x 2.01 + 7.5 x 0.55 +17.992 x 1.123 + 6.525 x 1.305 = 80.9(kN - m)總彎矩 M = M1 + M2 = 107.4(kN - m

25、)Q = P + P + 嗎 + W2 + W3 + W4 + W5 = 2.4 + 30.91 +17.7 + 2.25 + 7.5 +17.992 + 6.525 = 85.3(kN) 6、強(qiáng)度檢算 bx 20 + nA (x - a) - nA (h - x ) = 0 TOC o 1-5 h z 2S 0 ss 00-n(A + A ) +、.n2(A + A )2 + 2nb(A a + A h )n x =*sss一ss 00b=96.16mmI =0 + nA (x -a)2 + nA (h - x )2 03 s o ss o 0=1.67 x 109 mm 4w = = 1.

26、74 x 107 mm 30 x0w =0= 6.5 x 106 mm 3s ( h0 - x 0 )ccc=(107.4 x 103)/(1.74 x 107 x 10-9) = 6.2 x 106 Pa = 6.2Mpa c b = 16.8Mpa=10 x (107.4 x 103)/(6.5 x 106 x 10-9) = 165.2 x 106Pa = 165.2Mpa 355-45 = 310mm 取 z = 307mm=為乙=85.3 x 1% x 0 307) = 0.28 x 106Pa = 0.28Mpa 1.55Mpa 7、裂縫寬度驗(yàn)算K1 = 0.8=1 + 0.3 x

27、 空 + 0.5 x 竺=1.45107.6107.6,_ (P n + P n + P n )A / _ (p n + P n + P n )A /口s=112 23 3 sLA = 1 12 23 3s1(2ba )- c1-s=(1 x 10) x 200.96(2 x 1000 x 45) = 0-223w = K K r 土 (80 + 8 + 014d)f 1 2 E 職 s z=0.185mm 2.3m (車輪荷載重疊但小于 4.62m)所以按軸距為2.3m的二軸重計(jì)算：a= (a1+2h)+2c=2.3+2X1.9=6.1m不計(jì)沖擊系數(shù) P 2 = 2 x !p/ a = 14

28、0/6.1 = 22.952軸重求P2c=0.4m懸臂板的荷載有效分布寬度：a= (a1+2h)+2c=2X0.4=0.80m2.3m不計(jì)沖擊系數(shù)P2 = ：P軸重/a = 87.5kN活載引起的彎矩：M 1 = pjx0.4 + P x 1.9 = 78.6(kN m)恒載引起的彎矩：M 2 =咯 x 2.46 + W2 x 2.31 + W3 x 0.82 + W4 x 1.254 + W5 x 1.455=17.7 x 2.46 + 2.25 x 2.01 + 7.5 x 0.55 +19.552 x 1.123 + 6.525 x 1.305 = 82.66(kN m)總彎矩 M =

29、M 1 + M2 = 78.6 + 82.66 = 161.3(kN m)Q = P + P + W + W + W + W + W = 22.95 + 87.5 +17.7 + 2.25 + 7.5 +19.552 + 6.525 = 164(kN) 2212345a = M/c / w,0=(161.3x 103)/(2.017 x 107 x 10-9)= 8.0 x 106Pa = 8.0Mpa a=6.8Mpaa =n M/ws=10 x (161.3 x 103)/(9.5 x 106 x 10-9) = 169.8 x 106 Pa = 169.8Mpa 1.4 x a = 25

30、2Mpat =冗=164 x 1% x 0 299) = 0.55 x 106 Pa = 0.55Mpa 2.3m （車輪荷載重疊但小于 4.62m）所以按軸距為2.3m的二軸重計(jì)算：a= （a1+2h）+2c=（2.3+2X0.52）+2X1.07=5.48m五、計(jì)算簡(jiǎn)圖圖10箱梁上翼緣懸臂板受力示意圖計(jì)算簡(jiǎn)圖見圖10。疏散平臺(tái)、聲屏障及電纜重：W1 = A0 xy 0 + 3.4 + 4 = 0.471 x 25 + 3.4 + 2.5 = 17.7kN人行道板重 W2 = A0 xy 0 = 0.09 x 25 = 2.25 kN承軌臺(tái)及鋼軌重：W3 = 15/2 = 7.5 kN按等效

31、集中力計(jì)算：人活載：P = 4x0.6 = 2.4 kN列車活載計(jì)算：a = 4 x （1 h） = 4 取a = 2目=0.8 xa （一） = 0.8 x 2 x （一6一） = 0.16630 + L30 + 28列車活載 P2 = (1 + H) X 2X ：p軸重 /a = 1.166X 140/5.48 = 29.8 kN風(fēng)活載 W風(fēng)=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa風(fēng)活載對(duì)懸臂梁的彎矩為：M風(fēng)=W風(fēng)x 4.02x 1 x 4.02/2 = 6.11kN - m懸臂自重與= xy = 0.65x26 = 16.9kN經(jīng)計(jì)算，集中力作

32、用點(diǎn)在2-2截面左1.034m處鋪裝W5 = A0 xy = 0.1 x 2.4x 25 = 6.0kN集中力作用點(diǎn)在2-2截面左1.2m處六、結(jié)構(gòu)計(jì)算截面配筋見圖11，受拉筋中16100，受壓筋中12100，取一米寬計(jì)算受拉筋為1016，受壓筋為1012。圖11圖11箱梁上翼緣懸臂板截面配筋圖9、內(nèi)力計(jì)算1-1截面活載引起的彎矩：M1 = P x 1.8 + P x 0.65 + M風(fēng)=2.4 x 1.8 + 29.8 x 0.65 + 6.11 = 29.8kN - m)恒載引起的彎矩：M2 =叫 x 2.25 + W2 x 1.8 + W3 x 0.65 + W4 x 1.034 + W

33、5 x 1.2=17.7 x 2.25 + 2.25 x 1.8 + 7.5 x 0.65 +16.9 x 1.034 + 6.0 x 1.2 = 73.42(kN - m)總彎矩M = M1 + M2 = 103.2(kN - m)Q = P + P2 + 叫 + W2 + W3 + W4 + W5 = 2.4 + 29.8 +17.7 + 2.25 + 7.5 +16.9 + 6.0 = 82.55(kN) bx 210、10、強(qiáng)度檢算0 + nA (x - a) - nA (h - x ) = 0 TOC o 1-5 h z 2S 0 ss 00-n(A + A ) +、.n2(A + A )2 + 2nb(A a + A h )n x =*sss一ss 00b=96.16mmI =0 + nA (x -a)2 + nA (h - x )2 03 s o ss o 0=1.67 x 109 mm 4w = = 1.74 x 107 mm 30w =0= 6.5 x 106 mm 3s ( h0 - x 0 )cccc=(103.2x 103)/(1.74x 107 x 10-9) = 5.94x 106Pa = 5.94Mpa cb = 16.8Mpa=10 x (103.2 x 103)/(6.5 x 1