斜拉桥有限元模拟

目 录一工程概况2二建模过程32.1 截面几何特性计算32.1.1 主梁截面简化及计算32.1.2 主塔截面简化及计算42.2 拉索初始应变计算及弹模修正值计算6三模型建立113.1 不考虑垂度效应建模113.1.1无初始应变建模113.1.2改变拉索实常数233.1.3成桥状态模态分析243.2 考虑垂度效应建模263.2.1 无初始应变状态建模263.2.2 更改拉索实常数58四总结分析59一工程概况1. 桥型：三塔四跨分离式双主梁斜拉桥2. 跨径：两主跨跨径1500m，两边跨分别设置两个过渡墩，跨径408+244=652m3. 桥宽：60.5m4. 主梁：分离式双主梁，单根主梁宽23.25m4. 桥塔：中塔为空间钻石型造型，塔高460m，分叉点距塔顶121m，分叉点距桥面239m，分叉点距塔身连接横梁250m，塔身连接横梁距塔底89m，横梁纵桥向长64m，横桥向长71m，塔底塔柱横桥向间距32m，纵桥向间距40m；边塔为平面钻石型造型，塔高386m，分叉点距塔顶101m，分叉点距桥面204m，分叉点距塔身连接横梁215m，塔身连接横梁距塔底70m，连接横梁横桥向长54.3m，塔底两塔柱横桥向间距40m。7. 塔底距桥面距离：此处考虑纵坡影响，假设塔底同一水平线上，中塔处桥面距塔底，边塔处桥面距塔底，第一过渡墩处桥面距塔底，第二过渡墩处桥面距塔底。8. 拉索：边跨有两种索距，分别为12m和16m，652m=82（两端距离）+1213（14根间距为12m的拉索）+1630（30根间距为16m的拉索），一幅边跨共计44根拉索，编号A0-A43；主跨只有16m一种索距，1500m=82（两端距离）+1643（44根间距为16m的拉索，锚于边塔上，编号J0-J43）+12+1649（50根间距为16m的拉索，锚于主塔上，编号Z0-1，Z0-2，Z1-Z48）。9. 梁间横梁：主梁间横梁布置与与拉索布置方式相对应。10. 约束条件：左桥端第一及第二过渡墩仅给予主梁竖向及横向的平移自由度约束， 右桥端第一及第二过渡墩处仅给予主梁竖向的及横向的平移自由度约束；边塔处刚横梁仅给予主梁横向和竖向约束，中塔处刚横梁给予主梁横向、纵向及竖向约束；索塔底部完全固结，索单元和梁单元给予全铰约束；10. 材料：1. 主梁： 2. 刚性鱼刺横梁和主塔连接横梁： 3. 斜拉索： 3. 索塔：11. 目标任务：利用大型有限元软件ANSYS建立斜拉桥全桥模型，分析重力作用下的结构响应并对结构进行动力特性分析，比较是否考虑几何非线性（P-效应及大位移）对结果的影响。建模过程中，主梁及主塔使用BEAM4单元模拟，拉索使用LINK180单元模拟。12.斜拉桥非线性的主要影响因素13.利用ANSYS进行斜拉桥建模步骤斜拉桥设计，施工过程中，结构分析一般需考虑几何非线性，如：斜拉桥垂度效应，大位移效应以及梁塔的组合效应，二建模过程2.1 截面几何特性计算2.1.1 主梁截面简化及计算主梁采用空间鱼刺双梁模型，使用BEAM4单元建模，所有截面几何特性以及质量集中于两根纵梁上，纵梁取标准断面，建模时节点建于截面形心处；横梁取真实横梁截面，鱼骨梁相对为刚性构件，无质量，只起传递力流的作用，截面可随意指定。图2.1 主梁标准断面简化图（顶板30mm，底板24mm）图2.2 横梁标准断面图（顶底板及腹板14mm，加劲肋10mm）表2.1 纵梁及横梁截面几何特性表格（m）面积IxIyCx(+)Cx(-)Cy(+)Cy(-)J主梁1.676.1876.1112.1311.131.603.439.18横梁0.270.990.511.611.612.512.510.87鱼骨梁1/31/31/31/31/31/31/31/32.1.2 主塔截面简化及计算（1）中塔截面简化 图2.3 中塔锚索段标准断面图（顶底板及腹板14mm，加劲肋10mm）上述四个截面分别记做ZMSD-1，ZMSD-2，ZMSD-3，ZMSD-4。 图2.4 中塔上塔柱 图2.5 中塔下塔柱（钢混组合截面） 图2.6 中塔横梁截面上述三个截面分别记做ZSTZ，ZXTZ，ZHL（2）边塔截面简化 图2.7 边塔锚索段标准断面图（顶底板及腹板14mm，加劲肋10mm）上述四个截面分别记做BMSD-1，BMSD-2，BMSD-3，BMSD-4。 图2.8 边塔上塔柱 图2.9 边塔下塔柱（钢混组合截面） 图2.10 边塔横梁截面上述三个截面分别记做BSTZ，BXTZ，BHL2.2 拉索初始应变计算及弹模修正值计算不考虑几何非线性进行静力分析时，可不考虑垂度效应，即拉索弹模不需进行修正；考虑非线性进行静力分析时，需考虑垂度效应，此时斜拉桥的拉索模拟采用等效弹性模量法。等效弹性模量方法用直弦杆代替实际的曲线索，直弦杆的弹性模量为考虑垂度变化影响的有效弹性模量。等效弹性模量计算如下：式中：Eeff 拉索等效弹模；E拉索材料有效模量；T拉索初张力；l拉索水平投影长度；w拉索单位长度重量；A拉索横截面面积；考虑垂度效应的拉索弹模修正计算见下表。表2.3 拉索成桥状态拉索应变及弹模修正计算编号索力T（N）规格(PES7-)面积A(mm2)应力(MPa)应变索长投影(m)单位长度拉索重量(kg/m)弹性模量(MPa)修正弹性模量（MPa）A4328310885.6 727 0.0038 64484.9 1.90E+05 A4228310885.6 717 0.0038 63284.9 1.90E+05 A4128310885.6 777 0.0041 62084.9 1.90E+05 A4030111578.0 785 0.0041 60890.3 1.90E+05 A3930111578.0 774 0.0041 59690.3 1.90E+05 A3831312039.5 794 0.0042 58493.9 1.90E+05 A3730111578.0 812 0.0043 57290.3 1.90E+05 A3630111578.0 799 0.0042 56090.3 1.90E+05 A3530111578.0 816 0.0043 54890.3 1.90E+05 A3430111578.0 803 0.0042 53690.3 1.90E+05 A3328310885.6 839 0.0044 52484.9 1.90E+05 A3228310885.6 854 0.0045 51284.9 1.90E+05 A3128310885.6 862 0.0045 50084.9 1.90E+05 A3028310885.6 846 0.0045 48884.9 1.90E+05 A2926510193.2 812 0.0043 47279.5 1.90E+05 A282419270.1 795 0.0042 45672.3 1.90E+05 A271997654.5 786 0.0041 44059.7 1.90E+05 A261997654.5 769 0.0040 42459.7 1.90E+05 A251997654.5 752 0.0040 40859.7 1.90E+05 编号索力T（N）规格(PES7-)面积A(mm2)应力(MPa)应变索长投影(m)单位长度拉索重量(kg/m)弹性模量(MPa)修正弹性模量（MPa）A241997654.5 735 0.0039 39259.7 1.90E+05 A232238577.7 768 0.0040 37666.9 1.90E+05 A222419270.1 752 0.0040 36072.3 1.90E+05 A212419270.1 733 0.0039 34472.3 1.90E+05 A202419270.1 769 0.0040 32872.3 1.90E+05 A192539731.6 764 0.0040 31275.9 1.90E+05 A182419270.1 781 0.0041 29672.3 1.90E+05 A172238577.7 762 0.0040 28066.9 1.90E+05 A162118116.1 782 0.0041 26463.3 1.90E+05 A151997654.5 805 0.0042 24859.7 1.90E+05 A141997654.5 782 0.0041 23259.7 1.90E+05 A131997654.5 758 0.0040 21659.7 1.90E+05 A121997654.5 735 0.0039 20059.7 1.90E+05 A111997654.5 712 0.0037 18459.7 1.90E+05 A101997654.5 690 0.0036 16859.7 1.90E+05 A92118116.1 631 0.0033 15263.3 1.90E+05 A82118116.1 612 0.0032 13663.3 1.90E+05 A71877193.0 515 0.0027 12056.1 1.90E+05 A6187 7193.0 501 0.0026 10456.1 1.90E+05 A5187 7193.0 455 0.0024 8856.1 1.90E+05 A4187 7193.0 444 0.0023 7256.1 1.90E+05 A3187 7193.0 435 0.0023 5656.1 1.90E+05 A2199 7654.5 395 0.0021 4059.7 1.90E+05 A1187 7193.0 423 0.0022 2456.1 1.90E+05 A01877193.0 428 0.0023 856.1 1.90E+05 J01877193.0 331 0.0017 856.1 1.90E+05 J1187 7193.0 333 0.0018 2456.1 1.90E+05 J2199 7654.5 316 0.0017 4059.7 1.90E+05 J3187 7193.0 342 0.0018 5656.1 1.90E+05 J4187 7193.0 349 0.0018 7256.1 1.90E+05 J5187 7193.0 358 0.0019 8856.1 1.90E+05 J6187 7193.0 367 0.0019 10456.1 1.90E+05 J71877193.0 378 0.0020 12056.1 1.90E+05 J81877193.0 389 0.0020 13656.1 1.90E+05 J91877193.0 402 0.0021 15256.1 1.90E+05 J101877193.0 414 0.0022 16856.1 1.90E+05 编号索力T（N）规格(PES7-)面积A(mm2)应力(MPa)应变索长投影(m)单位长度拉索重量(kg/m)弹性模量(MPa)修正弹性模量（MPa）J111997654.5 402 0.0021 18459.7 1.90E+05 J121997654.5 415 0.0022 20059.7 1.90E+05 J131997654.5 428 0.0023 21659.7 1.90E+05 J141997654.5 441 0.0023 23259.7 1.90E+05 J151997654.5 454 0.0024 24859.7 1.90E+05 J161997654.5 468 0.0025 26459.7 1.90E+05 J171997654.5 482 0.0025 28059.7 1.90E+05 J181997654.5 495 0.0026 29659.7 1.90E+05 J191997654.5 509 0.0027 31259.7 1.90E+05 J201997654.5 523 0.0028 32859.7 1.90E+05 J212118116.1 506 0.0027 34463.3 1.90E+05 J222118116.1 519 0.0027 36063.3 1.90E+05 J232419270.1 508 0.0027 37672.3 1.90E+05 J242419270.1 520 0.0027 39272.3 1.90E+05 J252419270.1 532 0.0028 40872.3 1.90E+05 J262419270.1 544 0.0029 42472.3 1.90E+05 J272419270.1 556 0.0029 44072.3 1.90E+05 J2826510193.2 556 0.0029 45679.5 1.90E+05 J2926510193.2 556 0.0029 47279.5 1.90E+05 J3026510193.2 582 0.0031 48879.5 1.90E+05 J3126510193.2 594 0.0031 50479.5 1.90E+05 J3226510193.2 605 0.0032 52079.5 1.90E+05 J3330111578.0 601 0.0032 53690.3 1.90E+05 J3431312039.5 588 0.0031 55293.9 1.90E+05 J3530111578.0 570 0.0030 56890.3 1.90E+05 J3630111578.0 609 0.0032 58490.3 1.90E+05 J3728310885.6 598 0.0031 60084.9 1.90E+05 J3828310885.6 608 0.0032 61684.9 1.90E+05 J3928310885.6 586 0.0031 63284.9 1.90E+05 J4028310885.6 595 0.0031 64884.9 1.90E+05 J4128310885.6 604 0.0032 66484.9 1.90E+05 J4228310885.6 580 0.0031 68084.9 1.90E+05 J4330111578.0 553 0.0029 69690.3 1.90E+05 Z4828310885.6 620 0.0033 79284.9 1.90E+05 Z4730111578.0 583 0.0031 77690.3 1.90E+05 Z4630111578.0 628 0.0033 76090.3 1.90E+05 编号索力T（N）规格(PES7-)面积A(mm2)应力(MPa)应变索长投影(m)单位长度拉索重量(kg/m)弹性模量(MPa)修正弹性模量（MPa）Z4530111578.0 622 0.0033 74490.3 1.90E+05 Z4430111578.0 622 0.0033 72890.3 1.90E+05 Z4330111578.0 622 0.0033 71290.3 1.90E+05 Z4230111578.0 622 0.0033 69690.3 1.90E+05 Z4128310885.6 653 0.0034 68084.9 1.90E+05 Z4028310885.6 643 0.0034 66484.9 1.90E+05 Z3926510193.2 677 0.0036 64879.5 1.90E+05 Z3826510193.2 667 0.0035 63279.5 1.90E+05 Z3726510193.2 657 0.0035 61679.5 1.90E+05 Z3626510193.2 647 0.0034 60079.5 1.90E+05 Z3526510193.2 636 0.0033 58479.5 1.90E+05 Z342539731.6 668 0.0035 56875.9 1.90E+05 Z332539731.6 657 0.0035 55275.9 1.90E+05 Z322539731.6 645 0.0034 53675.9 1.90E+05 Z312539731.6 634 0.0033 52075.9 1.90E+05 Z302419270.1 653 0.0034 50472.3 1.90E+05 Z292419270.1 640 0.0034 48872.3 1.90E+05 Z282419270.1 628 0.0033 47272.3 1.90E+05 Z272238577.7 665 0.0035 45666.9 1.90E+05 Z262238577.7 651 0.0034 44066.9 1.90E+05 Z252238577.7 637 0.0034 42466.9 1.90E+05 Z242118116.1 658 0.0035 40863.3 1.90E+05 Z232118116.1 643 0.0034 39263.3 1.90E+05 Z222118116.1 628 0.0033 37663.3 1.90E+05 Z211997654.5 650 0.0034 36059.7 1.90E+05 Z201997654.5 634 0.0033 34459.7 1.90E+05 Z191997654.5 618 0.0033 32859.7 1.90E+05 Z181997654.5 602 0.0032 31259.7 1.90E+05 Z171997654.5 585 0.0031 29659.7 1.90E+05 Z161877193.0 606 0.0032 28056.1 1.90E+05 Z151877193.0 589 0.0031 26456.1 1.90E+05 Z141877193.0 571 0.0030 24856.1 1.90E+05 Z131997654.5 573 0.0030 23259.7 1.90E+05 Z122419270.1 542 0.0029 21672.3 1.90E+05 Z112539731.6 578 0.0030 20075.9 1.90E+05 Z102419270.1 588 0.0031 18472.3 1.90E+05 Z92419270.1 570 0.0030 16872.3 1.90E+05 Z82118116.1 631 0.0033 15263.3 1.90E+05 Z71997654.5 649 0.0034 13659.7 1.90E+05 Z6199 7654.5 629 0.0033 12059.7 1.90E+05 Z5199 7654.5 612 0.0032 10459.7 1.90E+05 Z4199 7654.5 596 0.0031 8859.7 1.90E+05 Z3199 7654.5 582 0.0031 7259.7 1.90E+05 Z2199 7654.5 570 0.0030 5659.7 1.90E+05 Z1187 7193.0 391 0.0021 4056.1 1.90E+05 Z0_21395346.6 529 0.0028 2441.7 1.90E+05 Z0_11395346.6 696 0.0037 841.7 1.90E+05 三模型建立主梁采用空间鱼骨双梁模型，使用BEAM4单元建模，所有截面几何特性以及质量集中于两根纵梁上，纵梁取标准断面，建模时节点建于截面形心处；横梁取真实横梁截面，鱼骨梁相对为刚性构件，无质量，只起传递力流的作用。边塔使用BEAM4单元建模，塔顶（A）到分叉点（B）划分为4段共5个节点，用于锚固拉索单元，除锚固段外，上塔柱、下塔柱及塔身横梁均采用单一截面的梁单元建模。中塔使用BEAM4单元建模，塔顶（A）到分叉点（B）划分为4段共5个节点，用于锚固拉索单元，除锚固段外，上塔柱、下塔柱及塔身横梁均采用单一截面梁单元建模。拉索使用LINK10单元建模。边界约束条件如下处理，左桥端第一及第二过渡墩仅给予主梁竖向及横向的平移自由度约束，右桥端第一及第二过渡墩处仅给予主梁竖向的及横向的平移自由度约束；索塔底部完全固结，索单元和梁单元给予全铰约束；主梁完全漂浮体系。3.1 不考虑垂度效应建模3.1.1无初始应变建模/PREP7ET,1,4 ET,2,10MP,EX,1,3.5E10 MP,PRXY,1,0.17MP,DENS,1,2500MP,EX,2,10E15MP,PRXY,2,0MP,DENS,2,0MP,EX,3,1.9E11MP,PRXY,3,0.25MP,DENS,3,7800MP,EX,4,2.1E11MP,PRXY,4,0.31MP,DENS,4,7800R,1,109.3,3457.1,2555.4,14.2,15.4RMORE,4520.9R,2,124.6,4834.5,3045.9,14.2,19.0RMORE,5618.9R,3,135.4,7448.1,3488.7,14.2,22.6RMORE,7191.9R,4,151.1,11218.0,4509.0,15.0,26.2RMORE,9755.6R,5,79.5,956.0,2628.8,9.4,17.2RMORE,2280.0R,6,95.6,993.0,3685.1,9.0,19.0RMORE,5618.9R,7,200,8000,8000,19.0,14.2RMORE,5618.9R,8,184.4,7267.9,7304.7,18.0,18.4RMORE,11879.6R,9,227.5,11251.6,11683.2,21.8,22.2RMORE,16234.0R,10,273.3,18596.3,19713.1,25.6,26RMORE,26560.8R,11,301.2,27115.4,24081.9,29.2,27.2RMORE,35320.1R,12,68.8,1178.3,1849.9,11.2,14.6RMORE,2312.3R,13,58.4,603.3,1814.3,9.0,15.2RMORE,1427.0R,14,200,8000,8000,19.0,14.2RMORE,5618.9R,15,1.67,76.11,7.18,5.0,23.3RMORE,15.08R,16,2.67,124.60,10.13,5.0,23.3 RMORE,26.03R,17,2.20,124.60,10.13,5.0,23.3 RMORE,26.03R,19,0.27,0.99,0.51,3.2,5.0 RMORE,0.87R,20,1,1/12,1/12,1,1 RMORE,1/3R,21,0.0072 R,22,0.0077R,23,0.0081R,24,0.0086R,25,0.0093R,26,0.0097R,27,0.0102R,28,0.0053R,29,0.0109R,30,0.0116R,31,0.0120finish/PREP7*do,i,1,14x=-2144+(i-1)*12y1=-30.25y2=-18y3=18y4=30.25N,4*(i-1)+1,x,y1,0+0.169*(i-1)N,4*(i-1)+2,x,y2,0+0.169*(i-1)N,4*(i-1)+3,x,y3,0+0.169*(i-1)N,4*(i-1)+4,x,y4,0+0.169*(i-1)*enddo*do,i,1,30x=-1972+(i-1)*16y1=-30.25y2=-18y3=18y4=30.25N,56+4*(i-1)+1,x,y1,2.41+0.215*(i-1)N,56+4*(i-1)+2,x,y2,2.41+0.215*(i-1)N,56+4*(i-1)+3,x,y3,2.41+0.215*(i-1)N,56+4*(i-1)+4,x,y4,2.41+0.215*(i-1)*enddo*do,i,1,44x=-1492+(i-1)*16y1=-30.25y2=-18y3=18y4=30.25N,176+4*(i-1)+1,x,y1,9.02+0.21*(i-1)N,176+4*(i-1)+2,x,y2,9.02+0.21*(i-1)N,176+4*(i-1)+3,x,y3,9.02+0.21*(i-1)N,176+4*(i-1)+4,x,y4,9.02+0.21*(i-1)*enddo*do,i,1,50x=-792+(i-1)*16y1=-30.25y2=-18y3=18y4=30.25N,352+4*(i-1)+1,x,y1,18.26+0.2106*(i-1)N,352+4*(i-1)+2,x,y2,18.26+0.2106*(i-1)N,352+4*(i-1)+3,x,y3,18.26+0.2106*(i-1)N,352+4*(i-1)+4,x,y4,18.26+0.2106*(i-1)*enddo/PREP7Type,1$Real,15$Mat,4*do,i,1,5$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,16$Mat,4*do,i,6,15$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,15$Mat,4*do,i,16,25$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,17$Mat,4*do,i,26,45$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,16$Mat,4*do,i,46,55$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,15$Mat,4*do,i,56,120$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoType,1$Real,16$Mat,4*do,i,121,137$j2=4*(i-1)+2$j3=4*(i-1)+3$E,j2,j2+4$E,j3,j3+4$*enddoFinish/PREP7Type,1Real,20Mat,2*do,i,1,14j1=4*(i-1)+1j2=4*(i-1)+2j3=4*(i-1)+3j4=4*(i-1)+4E,j1,j2E,j4,j3*enddo*do,i,1,30j1=56+4*(i-1)+1j2=56+4*(i-1)+2j3=56+4*(i-1)+3j4=56+4*(i-1)+4E,j1,j2E,j4,j3*enddo*do,i,1,44j1=176+4*(i-1)+1j2=176+4*(i-1)+2j3=176+4*(i-1)+3j4=176+4*(i-1)+4E,j1,j2E,j4,j3*enddo*do,i,1,50j1=352+4*(i-1)+1j2=352+4*(i-1)+2j3=352+4*(i-1)+3j4=352+4*(i-1)+4E,j1,j2E,j4,j3*enddoFinish/PREP7Type,1Real,19Mat,4*do,i,1,138j2=4*(i-1)+2j3=4*(i-1)+3E,j2,j3*enddo/PREP7i=552N,i+1,-1500,-20,-77.8N,i+2,-1500,-35,-3.8N,i+3,-1500,20,-77.8N,i+4,-1500,35,-3.8N,i+5,-1500,0,208.2N,i+6,-1500,0,233.2N,i+7,-1500,0,258.2N,i+8,-1500,0,283.2N,i+9,-1500,0,308.2Finish/PREP7Type,1Mat,1Real,1E,i+8,i+9Real,2E,i+7,i+8Real,3E,i+6,i+7Real,4E,i+5,i+6Real,4E,i+5,i+6Real,5E,i+2,i+5E,i+4,i+5Real,7E,i+1,i+2E,i+3,i+4Real,6E,i+2,i+4/PREP7i=561N,i+1,-17,-20,-77.8N,i+2,17,-20,-77.8N,i+3,-17,20,-77.8N,i+4,17,20,-77.8N,i+5,-26.7,-34.0,14.9N,i+6,26.7,-34.0,14.9N,i+7,-26.7,34.0,14.9N,i+8,26.7,34.0,14.9N,i+9,0,0,264.2N,i+10,0,0,294.2N,i+11,0,0,314.2N,i+12,0,0,344.2N,i+13,0,0,374.2/PREP7Type,1Mat,1Real,14E,i+1,i+5Real,14E,i+2,i+6Real,14E,i+3,i+7Real,14E,i+4,i+8Real,12E,i+5,i+9E,i+6,i+9E,i+7,i+9E,i+8,i+9Real,11E,i+9,i+10Real,10E,i+10,i+11Real,9E,i+11,i+12Real,8E,i+12,i+13Real,13E,i+5,i+6E,i+7,i+8E,i+5,i+7E,i+6,i+8finish/PREP7$Type, 2$Real,29$Mat,3$E,561,1$E,561,4$finish/PREP7$Type, 2$Real,29$Mat,3$E,561,5$E,561,8$finish/PREP7$Type, 2$Real,29$Mat,3$E,561,9$E,561,12$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,13$E,561,16$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,17$E,561,20$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,21$E,561,24$Finish/PREP7$Type, 2$Real,31$Mat,3$E,561,25$E,561,28$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,29$E,561,32$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,33$E,561,36$Finish/PREP7$Type, 2$Real,30$Mat,3$E,561,37$E,561,40$Finish/PREP7$Type, 2$Real,31$Mat,3$E,560,41$E,560,44$Finish/PREP7$Type, 2$Real,29$Mat,3$E,560,45$E,560,48$Finish/PREP7$Type, 2$Real,29$Mat,3$E,560,49$E,560,52$Finish/PREP7$Type, 2$Real,29$Mat,3$E,560,53$E,560,56$Finish/PREP7$Type, 2$Real,27$Mat,3$E,560,57$E,560,60$Finish/PREP7$Type, 2$Real,25$Mat,3$E,560,61$E,560,63$Finish/PREP7$Type, 2$Real,22$Mat,3$E,560,65$E,560,68$Finish/PREP7$Type, 2$Real,22$Mat,3$E,560,69$E,560,72$Finish/PREP7$Type, 2$Real,22$Mat,3$E,560,73$E,560,76$Finish/PREP7$Type, 2$Real,22$Mat,3$E,560,77$E,560,80$Finish/PREP7$Type, 2$Real,24$Mat,3$E,559,81$E,559,84$Finish/PREP7$Type, 2$Real,25$Mat,3$E,559,85$E,559,88$Finish/PREP7$Type, 2$Real,25$Mat,3$E,559,89$E,559,92$Finish/PREP7$Type, 2$Real,25$Mat,3$E,559,93$E,559,96$Finish/PREP7$Type, 2$Real,26$Mat,3$E,559,97$E,559,100$Finish/PREP7$Type, 2$Real,25$Mat,3$E,559,101$E,559,104$Finish/PREP7$Type, 2$Real,24$Mat,3$E,559,105$E,559,108$Finish/PREP7$Type, 2$Real,23$Mat,3$E,559,109$E,559,112$Finish/PREP7$Type, 2$Real,22$Mat,3$E,559,113$E,559,116$Finish/PREP7$Type, 2$Real,22$Mat,3$E,559,117$E,559,120$Finish/PREP7$Type, 2$Real,22$Mat,3$E,558,121$E,558,124$Finish/PREP7$Type, 2$Real,22$Mat,3$E,558,125$E,558,128$Finish/PREP7$Type, 2$Real,22$Mat,3$E,558,129$E,558,132$Finish/PREP7$Type, 2$Real,22$Mat,3$E,558,133$E,558,136$Finish/PREP7$Type, 2$Real,23$Mat,3$E,558,137$E,558,140$Finish/PREP7$Type, 2$Real,23$Mat,3$E,558,141$E,558,144$Finish/PREP7$Type, 2$Real,21$Mat,3$E,558,145$E,558,148$Finish/PREP7$Type, 2$Real,21$Mat,3$E,558,149$E,558,