箱梁上缘悬臂计算

1、=V-臂天津三号线箱梁上缘悬臂计算书2006年7月7日 TOC o 1-5 h z HYPERLINK l bookmark4 o Current Document 天津三号线箱梁上缘悬臂计算书0I、最大线间距的悬臂处强度计算2II、4.4m线间距的悬臂处强度计算12II、4.4m线间距的悬臂处强度计算18I、最大线间距的悬臂处强度计算一、结构简况等截面连续箱梁，梁高1.7m，桥面宽度随线间距变化，箱梁底宽为4.2m, 双线线间距为3.65m。运营状态最大线间距为5m,在R=450m时，曲线加宽 为：内侧为0.31m，外为0.05m。现对最大线间距和曲线加宽为0.31m的箱梁上 翼缘悬臂强度、

2、上翼缘悬臂裂缝宽及脱轨状态下上翼缘悬臂强度、箱梁梁的稳定 性进行检算。箱梁截面如图1，计算时按承托处为固定端的悬臂梁计算。图1箱梁截面图二、计算米用规范铁路桥涵设计基本规范TB 10002.1-2005铁路桥涵钢筋混凝土和预应力混凝土结构设计规范TB 10002.3-2005天津市地下铁道二期工程施工图设计技术要求城市轨道交通设计规范DGJ08-109-2004三、材料（一）砼箱梁砼 C50（二）钢筋箱梁悬臂上缘受力钢筋采用HRB335钢筋，用6表示。四、荷载（一）恒载结构自重箱梁砼容重Y =26kN/m3。二期恒载桥面铺装厚100mm，容重Y =25kN/m3。承轨台及钢轨按15kN/m-线

3、计算。疏散平台结构砼容重：Y =25kN/m3声屏障按3.4kN/m计算，声屏障高为从轨顶3.5m。电缆重按2.5kN/m计算（每侧）。（二）活载1 .人群活载取4kN/m2风载，按最不利的风载计算。天津风压20m高之内为基本风压为 叫=600Pa计算，声屏障高3.5+0.52 =4.02m计算。列车活载1）活载轴重如图2,列车荷载冲击系数采用：1+. =1 + 0.8x6史30 + L有5 一. 有5 一. T W2-J有5 一. T H岩二 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图2列车活载图式（长度单位：米）2）车轮分布宽度列车活载横桥向布置如图3。图3列车活载横桥向布置 b1= b2+2X0.344=0.15+0.688=0.838m2.3m(车轮荷载重叠但小于4.62m)所以按轴距为2.3m的二轴重计算：a= (a1+2h)+2c=(2.3+2X0.52)+2X1.24=5.88m五、计算简图J I I I 一 J I I I 一 112100图5箱梁上翼缘悬臂板受力示意图i（Xi计算简图见图5。疏散平台、声屏障及电缆重：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承轨台及钢轨重：W3 = 15/2 = 7.5 kN按等效集中力计算：人活载：P = 4x0.6 = 2.4 kN列车活载计算：a = 4 x （1 h） = 4 取a = 2按跨度为28m计算冲击系数目=0.8 xa （一） = 0.8 x 2 x （一6一） = 0.16630 + L30 + 28列车活载 P2 = (1 + r ) X 2X：p轴重 /a = 1.166X 140/5.88 = 27.76 kN风活载 W风=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa风活载对悬臂梁的弯矩

6、为：M风=W风x3.5x 1 x3.5/2 = 4.631kN-m、计算2-2时：截面悬臂自重及铺装(按等效集中力计算)箱梁悬臂自重W4 = A0 xy = 0.2X 1.21 X26 = 6.292kN桥面铺装W5 = A0 xy = 0.1 x 1.21 x 25 = 3.025kN集中力作用点均作用在1-1截面左0.605m处、计算3-3时：截面悬臂自重及铺装(按等效集中力计算)箱梁悬臂自重与= xy = 0.752 x 26 = 19.552 kN经计算，集中力作用点在2-2截面左1.254m处桥面铺装W5 = A0 xy = 0.1 x 2.91 x 25 = 7.566kN集中力作

7、用点在2-2截面左1.455m处六、结构计算截面配筋见图5，受拉筋中16100+16200，受压筋中12100，取一米宽计 算受拉筋为1016+516，受压筋为1012。*16鸵伽*16鸵伽图6箱梁上翼缘悬臂板截面配筋图1、内力计算1-1截面活载弯矩：M1 =-P x0.3-M=-2.4 x 0.3 - 4.63 M1 =-P x0.3-M恒载弯矩：M2 =* X0.15-. X0.3=17.7 x 0.15 2.25 x 0.3 = 1.995(kN - m)总弯矩 M = M1 + M2 = -3.355(kN - m)2-2截面活载引起的弯矩：M1 = Pj 0.61 + M风=2.4

8、x 0.61 + 4.63 = 6.094(kN - m)恒载引起的弯矩：M2 =吗x1.06+吗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)总弯矩 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截面活载引起的弯矩：M1 = P x 2.31 + P x 0.85 + M风=2.4 x 2.31 + 27.76 x

9、0.85 + 4.63 = 33.8kN - m)恒载引起的弯矩：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)总弯矩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、强度检算1-1截面(本截面的弯矩和剪力都比2-2截面小，所以强度及裂缝宽不检算)(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中性轴剪应力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、裂缝宽度验算(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 职 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不计冲击系数P2= ：p轴重/a = 70kN活载引起的弯矩：M1 = P x 0.5 = 35(kN m)恒载引起的弯矩：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)总弯矩 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中性轴剪应力T -侃-99.27.4 X10 X 0 11)- 0.902 x 106 Pa -

18、0.902Mpa 2.3m (车轮荷载重叠但小于 4.62m)所以按轴距为2.3m的二轴重计算：a= (a1+2h)+2c=2.3+2X2. 2=6.4m不计冲击系数P2 - 2x ：p轴重/a -140/6.4 - 21.88求P2c=0.7m悬臂板的荷载有效分布宽度：a= (a1+2h)+2c=2X0.7=1.42.3m不计冲击系数P2 - !p /a - 70/1.4 - 502 轴重活载引起的弯矩：M1 - P2 x 2.2 + P 2 x 0.7 - 21.88 x 2.2 + 50 x 0.7 - 83.14(kN - m)恒载引起的弯矩：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) 总弯矩 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线间距的悬臂处强度计算一、结构简况线间距为4.4m、曲线加宽为0.31m的箱梁。现对其上翼缘悬臂强度、上缘翼悬 臂裂缝宽及脱轨状态下上翼缘悬臂强度、箱梁总体稳定性进行检算。截

21、面图见 图8。图8箱梁截面图二、计算采用规范同I三、材料同I四、荷载（一）恒载材料自重见I（二）活载人群活载同I。风载，按最不利的风载计算，同I。列车活载活载轴重如图2,列车荷载冲击系数采用：按跨28米计算1+=1 + 0.8x6L30 + L1)车轮分布宽度(列车活载横桥向布置见图9)图9列车活载横桥向布置c=0.55 +0.838/2=0.97m悬臂板的荷载有效分布宽度：a= (a1+2h)+2c=2X0.52+2X0.97=2.78m2.3m (车轮荷载重叠但小于 4.62m)所以按轴距为2.3m的二轴重计算：a= (a1+2h)+2c=(2.3+2X0.52)+2X0.97=5.28m

22、五、计算简图图10箱梁上翼缘悬臂板受力示意图计算简图见图10。疏散平台、声屏障及电缆重：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承轨台及钢轨重：W3 = 15/2 = 7.5 kN按等效集中力计算：人活载：P = 4x0.6 = 2.4 kN列车活载计算：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列车活载 P2 = (1 +r ) X 2

23、X：p轴重 /a = 1.166X 140/5.28 = 30.91 kN风活载 W风=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa风活载对悬臂梁的弯矩为：M风=W风x3.5x 1 x3.5/2 = 4.631kN-m悬臂自重与= xy = 0.692x26 = 17.992kN经计算，集中力作用点在2-2截面左1.123m处铺装W5 = A0 xy = 0.1 x 2.61 x 25 = 6.525kN集中力作用点在2-2截面左1.305m处六、结构计算截面配筋见图11，受拉筋中16100，受压筋中12100，取一米宽计算受拉筋为1016，受压筋为101

24、2。图11箱梁上翼缘悬臂板截面配筋图5、内力计算1-1截面活载引起的弯矩：M1 = P x 2.01 + P x 0.55 + M风=2.4 x 2.01 + 30.91 x 0.55 + 4.63 = 26.45kN - m)恒载引起的弯矩：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)总弯矩 M = M1 + M2 = 107.4(kN - m

25、)Q = P + P + 吗 + W2 + W3 + W4 + W5 = 2.4 + 30.91 +17.7 + 2.25 + 7.5 +17.992 + 6.525 = 85.3(kN) 6、强度检算 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=为乙=85.3 x 1% x 0 307) = 0.28 x 106Pa = 0.28Mpa 1.55Mpa 7、裂缝宽度验算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 职 s z=0.185mm 2.3m (车轮荷载重叠但小于 4.62m)所以按轴距为2.3m的二轴重计算：a= (a1+2h)+2c=2.3+2X1.9=6.1m不计冲击系数 P 2 = 2 x !p/ a = 14

28、0/6.1 = 22.952轴重求P2c=0.4m悬臂板的荷载有效分布宽度：a= (a1+2h)+2c=2X0.4=0.80m2.3m不计冲击系数P2 = ：P轴重/a = 87.5kN活载引起的弯矩：M 1 = pjx0.4 + P x 1.9 = 78.6(kN m)恒载引起的弯矩：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)总弯矩 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 （车轮荷载重叠但小于 4.62m）所以按轴距为2.3m的二轴重计算：a= （a1+2h）+2c=（2.3+2X0.52）+2X1.07=5.48m五、计算简图图10箱梁上翼缘悬臂板受力示意图计算简图见图10。疏散平台、声屏障及电缆重：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承轨台及钢轨重：W3 = 15/2 = 7.5 kN按等效

31、集中力计算：人活载：P = 4x0.6 = 2.4 kN列车活载计算：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列车活载 P2 = (1 + H) X 2X ：p轴重 /a = 1.166X 140/5.48 = 29.8 kN风活载 W风=K1K 2 K 3W0 = 1.4 x 1 x 0.9 x 600 = 756Pa风活载对悬臂梁的弯矩为：M风=W风x 4.02x 1 x 4.02/2 = 6.11kN - m悬臂自重与= xy = 0.65x26 = 16.9kN经计算，集中力作

32、用点在2-2截面左1.034m处铺装W5 = A0 xy = 0.1 x 2.4x 25 = 6.0kN集中力作用点在2-2截面左1.2m处六、结构计算截面配筋见图11，受拉筋中16100，受压筋中12100，取一米宽计算受拉筋为1016，受压筋为1012。图11图11箱梁上翼缘悬臂板截面配筋图9、内力计算1-1截面活载引起的弯矩：M1 = P x 1.8 + P x 0.65 + M风=2.4 x 1.8 + 29.8 x 0.65 + 6.11 = 29.8kN - m)恒载引起的弯矩：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)总弯矩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、强度检算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