后张法预应力钢绞线的理论伸长量计算书共15页word资料

1、后张法预应力钢绞线的理论伸长量计算书1、 计算依据： 公路桥涵施工技术规范 （ JTJ041-2000 ）及施工图纸2、 计算公式： L=PpL/AyEg式中： L理论伸长值Pp 平均张拉力（N）L 预应力钢材长度（cm）Eg 预应力钢材弹性模量（N/mm2）Ay 预应力钢材截面面积（mm2）平均张拉力 Pp的计算公式 Pp=P1-e- （kx+B） / （kx+医0）式中： P 预应力钢材张拉端张拉力x 从张拉端至计算截面的孔道长度（m）9一从张拉端至计算截面曲线孔道部分切线的夹角之和（ rad ）医一预应力钢筋与孔道壁的摩擦系数。见（JTJ041-2000）附表 11.4k 孔道每米局部偏

2、差对摩擦的影响系数。见（ JTJ041-2000 ）附表 11.4三、计算参数的选取：Eg=1.95 X 105 （实验数据），Ay=140mm2。k=0.0015 , = =0.25（图纸给定 ）每根预应力钢绞线端部计算长度增加45cm。1 、 正弯矩钢绞线伸长量计算16m 端跨空心板预应力钢材伸长量：钢绞线束 N1 的 8 值：左 8 1=0.038144、右 8 1' =0.038144钢绞线束 N2 的 8 值：左 8 2=0.039055、右 8 2' =0.039055将钢绞线束按直线段、圆曲线段、直线段分为三段：直线段：N1 : P1=1357.8X 140=19

3、0092 ( N), X1=45+264.8=309.8 ,X1=45+253=298左 Pp1= P1-e- (kx+B) / (kx+dB)= 190092 X 1-e- (0.0015 X 3.098+0.25 X0) /0.0015 X 3.098+0.25X 0 =189651.00 (N)右 Pp1' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=190092 X 1-e- (0.0015 X 2.98+0.25 X 0) /0.0015 X2.98+0.25 X0 =189667.78 ( N)左4L1 =189651.00 X 309.8/1.95 X

4、 10右L1' =189667.78 X 298/1.95 X1055X 140=2.1522cm140=2.0704cm圆曲线段：P2=189651.00X 2 -190092=189210.01(N)P2 ' =189667.78 X 2-190092=189243.55(N) 左 Pp2= P1-e- (kx+ 医0 ) / (kx+(10)= 189210.01X 1-e- (0.0015 X2.397+0.25 X 0.038144 ) /0.0015 X2.397+0.25 X 0.038144 =188849.35 (ND右 Pp2' = P1-e-(kx

5、+ d 8 ) / ( kx+ d 8 )=189243.55 X 1-e- (0.0015 X 2.454+0.25 X 0.039055 ) /0.0015 X2.454+0.25 X 0.039055 =188819.84 ( N)左4L2 =188849.35 X 276.8/1.95 X 10右ALZ' =188819.84 X265/1.95 X1055X 140=1.6581cm X140=1.6973cm 直线段：P3=188849.35X 2 -189210.01=18848 8.69(N) P3 ' =1 88819.84 X2-189243.55=1883

6、96.12(N) 左 Pp3= P1-e- (kx+ d 8 ) / (kx+ d 9 )=188488.69 X 1-e- (0.0015 X 3.1137+0.25 X0) /0.0015 X3.1137+0.25 X0 =188049.2 ( N)右 Pp3' = P1-e-(kx+ d 8) / ( kx+ d 8 )=188396.12 X 1-e- (0.0015 X 2.4583+0.25 X0) /0.0015 X2.4583+ 0.25 X 0 =1880 49.2 ( N)左4L3 =188049.2 X 311.37/1.95 X 105X 140=2.1448c

7、m5 右4 13' =188049.2 X 245.83/1.95 X10X 140=1.6933cm左& L =5.955cm右/ L =5.461cm全板 L =11.416钢绞线束 N1 的 8 值：左 8 1=0.024783、右 8 1' =0.024783钢绞线束 N2 的 8 值：左 8 2=0.025594、右 8 2' =0.025594N2 : P1=1357.8X 140=190092 ( N), X1=45+205=217,X1=45+193.4=217左 Pp1= P1-e- (kx+B) / (kx+dB)= 190092 X 1-e

8、- (0.0015 X2.50+0.25 X 0) /0.0015 X 2.50+0.25 X0 =189736.02 ( N)右 Pp1' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=190092 X 1-e- (0.0015 X2.384+0.25 X0) /0.0015 X2 .384+0.25 X 0 =189752.52 ( N)左4L1 =189736.02 X 250/1.95 X 105X 140=1.7375cm5 右4L1' =189752.52 X 238.4/1.95 X10X 140=1.6570cm圆曲线段：P2=189736.0

9、2X 2 -190092=189380.05(N)P2' =189752.52X2 -190092=189413.04(N)左 Pp2= P1-e- (kx+B) / (kx+dB)=189380.05 X 1-e- (0.0015 X 1.557+0.25 X 0.024783 ) /0.0015 X1.557+0.25 X 0.024783 =189283.44(N)右 Pp2' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=189413.04 X 1-e- (0.0015 X 1.608+0.25 X 0.025594 ) /0.0015 X1.608+

10、0.25 X 0.025594 =189257.05 ( N)左4L2 =189283.44 X 155.7/1.95 X 105X 140=1.0795cm5 右ALZ' =189257.05X160.8/1.95 X 10X 140=1.1147cm直线段：P3=189283.44 X 2-189380.05=189186.83(N) P3 ' =189257.05 X2-189413.04=189101.06(N) 左 Pp3= P1-e- (kx+ d 8 ) / (kx+ d 8 )= 189186.83 X 1-e- (0.0015 X4.51065+0.25 X0

11、) /0.0015 X4.51065+0.25 X 0 =188548.26 ( N)右 Pp3' = P1-e-(kx+ d 8) / ( kx+ d 8 )=187386.8 X 1-e- (0.0015 X 3.90535+0.25 X0) /0.0015 X3.90535+0.25 X 0 =188548.26 ( N)左4L3 =188548.26 X 451.065/1.95 X 105X 140=3.1153cm5 右4 13' =186973.2507 X 390.535/1.95 X 10X140=2.6972cm左 L =5.932cm右/ L =5.469

12、cm全板L=11.40116m 中跨边板预应力钢材伸长量：钢绞线束 N1 的 e 值：左 e 1=0.030627、右 e 1' =0.030627钢绞线束 N2 的 8 值：左 8 2=0.030627、右 8 2' =0.030627将钢绞线束按直线段、圆曲线段、直线段分为三段： 直线段：N1 : P1=1357.8X 140=190092 ( N), X1=45+323.4=323.4X2=45+323.4=323.4左 Pp1= P1-e- (kx+B) / (kx+dB)=190092 X 1-e- (0.0015 X 3.234+0.25 X0) /0.0015 X

13、 3.234+0.25X0 =189631.68 (N)右 Pp1' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=190092 X 1-e- (0.0015 X 3.234+0.25 X0) /0.0015 X3.234+0.25 X 0 =189631.68N )左 L1 =189631.68 X 323.4/1.95 X 105X 140=1.3334cm5 右4L1' =189631.68X323.4/1.95 X 10X 140=1.3334cm圆曲线段：P2=189631.68X 2 -190092=189171.35(N)P2' =189

14、631.68X2 -190092=189171.35(N)左 Pp2= P1-e- (kx+B) / (kx+dB)=189171.35 X 1-e- (0.0015 X 1.925+0.25 X 0.030627 ) /0.0015 X1.925+0.25 X 0.030627 =189093.32(N)右 Pp2' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=189171.35 X 1-e- (0.0015 X 1.925+0.25 X 0.030627) /0.0015X 1.925+0.25 X 0.030627 =189093.32 ( N)左4L2 =1

15、89093.32 X 192.5/1.95 X 105X 140=1.322cm5 AL2' =189093.32 X 192.5/1.95 X10X 140=1.322cm直线段：P3=189093.32X 2 -189171.35=189015.30(N)P3' =189093.32X2 -189171.35=189015.30(N)左 Pp3= P1-e- (kx+B) / (kx+dB)= 189015.30 X 1-e- (0.0015 X 3.027+0.25 X 0) /0.0015 X3.027+0.25 X 0 =188586.83 ( N)右 Pp3'

16、; = P1-e-(kx+ d 8) / ( kx+ d 8 )= 189015.30 X 1-e- (0.0015 X 3.027+0.25 X 0) /0.0015 X3.027+0.25 X 0=188586.83 (N)左4L3 =188586.83 X 302.700/1.95 X 105X 140=2.091cm5 右4 13' =188586.83 X302.700/1.95 X 10X 140=2.091cm左 L=5.671cm右 L=5.671cm全板 L=11.34216m 中跨边板预应力钢材伸长量：钢绞线束N1的e值：左e 1=0.018633、右e 1 =0.

17、018633钢绞线束N2的 8 值：左 8 2=0.018633、右 8 2' =0.018633将钢绞线束按直线段、圆曲线段、直线段分为三段：直线段：N2 : P1=1357.8X 140=190092 ( N), X1=45+214.9=259.9X1=45+214.9=259.9左 Pp1= P1-e- (kx+B) / (kx+dB)=190092 X 1-e- (0.0015 X 2.599+0.25 X0) /0.0015 X2.599+0.25 X0 =189721.94 (W右 Pp1' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=19009

18、2 X 1-e- (0.0015 X 2.599+0.25 X0) /0.0015 X2.599+0.25 X0 =189721.94 (W左4L1 =189721.94 X 259.9/1.95 X 105 X 140=1.8062cm5 右L1' =189721.94 X 259.9/1.95 X10X 140=1.8062cm圆曲线段：P2=189721.94X - -190092=189351.89(N)P2' =189721.94X2 -190092=189351.89(N)左 Pp2= P1-e- (kx+B) / (kx+dB)=189351.89 X 1-e-

19、(0.0015 X 1.171+0.25 X 0) /0.0015 X1.171+0.25 X 0=189483.61 ( N)右 Pp2' = P1-e-(kx+ d 8 ) / ( kx+ d 8 )=189351.89 X 1-e- (0.0015 X 1.171+0.25 X 0) /0.0015 X1.171+0.25 X0 =189483.61 ( N)左4L2 =189483.61 X 117.1/1.95 X 105X 140=0.8128cm5 右 ALZ' =189483.61 X 117.1/1.95 X10X 140=0.8128cm直线段：P3=189

20、483.61 X 2 -189351.89=189615.32(N)P3' =189483.61 X2 -189351.89=189615.32(N)左 Pp3=189615.32X 1-e- (0.0015 X4.4145+0.25 X0) /0.0015 X4.4145+0.25 X0 =188988.91 (N)右 Pp3' =189615.32 X 1-e- (0.0015 X 4.4145+0.25 X 0) /0.0015X4.4145+0.25 X0 =188988.91 (N)左4L3 =188988.91 X 441.45/1.95 X 105X 140=3.

21、056cm5 AL3' =188988.91 X 441.45/1.95 X 10X 140=3.056cm左& L =5.675cm右/ L =5.675cm ,全板 L=11.35016m 中跨中板预应力钢材伸长量：钢绞线束N1的8值：左8 1=0.029783、右 8 1' =0.029783钢绞线束N2的8值：左8 1=0.029783、右 8 1' =0.029783将钢绞线束按直线段、圆曲线段、直线段分为三段： 直线段：N1 : P1=1357.8X 140=190092 ( N), X1=45+281=326X1=45+281=326左 Pp1=1

22、90092X 1-e- (0.0015 X 3.26+0.25 X 0) /0.0015 X 3.26+0.25X 0 =189627.98 ( N)右 Pp1' =190092X 1-e- (0.0015 X 3.26+0.25 X 0) /0.0015 X3.26+0.25 X0 =189627.98 ( N)左4L1 =189627.98 X 326/1.95 X 105X 140=2.2644cm5 右L1' =189627.98 X326/1.95 X 10X 140=2.2644cm圆曲线段：P2=189627.98X 2 -190092=189163.96(N)P

23、2' =189627.98X2 -190092=189163.96(N)左 Pp2=189163.96X 1-e- (0.0015 X1.871+0.25 X 0.029783 )/0.0015 X1.871+0.25 X 0.029783 =189120.89 (N)右 Pp2' =189163.96 X 1-e- (0.0015 X 1.871+0.25 X 0.029783 ) /0.0015X 1.871+0.25 X 0.029783=189120.89 (N)左4L2 =189120.89 X 187.1/1.95 X 105X 140=1.2961cm5 右ALZ

24、' =189120.89 X 187.1/1.95 X10X 140=1.2961cm直线段：P3=189120.89X 2 -189163.96=189077.81(N)P3' =189120.89X2 -189163.96=189077.81(N)左 Pp3=189077.81 X 1-e- (0.0015 X 3.0635+0.25 X 0) /0.0015 X3.0635+0.25 X 0 =188644.04 ( N)右 Pp3' =189077.81 X 1-e- (0.0015 X 3.0635+0.25 X 0) /0.00153.0635+0.25 X

25、 0 =188644.04 ( N)左4L3 =188644.04 X 306.350/1.95 X 105X 140=2.1169cm5 右4 13' =188644.04 X306.350/1.95 X 10X 140=2.1169cm左 L=5.677cm右 L=5.677cm16m 中跨中板预应力钢材伸长量：钢绞线束 N1 的 e 值：左 e 1=0.011316、右 e 1' =0.011316钢绞线束 N2 的 e 值：左 e 2=0.011316、右 e 2' =0.011316将钢绞线束按直线段、圆曲线段、直线段分为三段： 直线段：N2 : P1=135

26、7.8X 140=190092 ( N), X1=45+232.9=277.9X2=45+232.9=277.9(0.0015 X 2.779+0.25 X 0)左 Pp1=190092X 1-e- /0.0015 X2.779+0.25第 11 页X 0 =189696.35 (NJ)右 Pp1' =190092X 1-e- (0.0015 X 2.779+0.25 X 0) /0.0015 X2.779+0.25 X 0 =189696.35 ( N)左口 =189696.35 X 277.9/1.95 X 105X 140=1.931cm5 右!_1' =189696.3

27、5 X277.9/1.95 X10X 140=1.931cm圆曲线段：P2=189696.35X 2 -190092=189300.7(N)P2 ' =189696.35 X 2-190092=189300.7 ( N)左 Pp2=189300.7X 1-e- (0.0015 X 1.171+0.25 X 0) /0.0015 X1.171+0.25 X 0=189708.86 ( N)右 Pp2' =189300.7 X 1-e- (0.0015 X 1.171+0.25 X 0) /0.0015 X1.171+0.25 X 0 =189708.86 ( N)左4L2 =18

28、9708.86 X 80.5/1.95 X105X 140=0.5594cm5 右412' =189708.86 X 80.5/1.95 X 10 X 140=0.5594cm直线段：P3=189708.86 X 2-189300.7=188537.62 (N)P3' =189708.86X2 -189300.7=188537.62(N)左 Pp3=188537.62X 1-e- (0.0015 X4.597+0.25 X0) /0.0015 X4.597+0.25 X 0 =187889.08 ( N)右 Pp3' =188537.62 X 1-e- (0.0015

29、X 4.597+0.25 X 0) /0.00154.597+0.25 X 0 =187889.08 ( N)左4L3 =187889.08 X 459.7/1.95 X 105X 140=3.1638cm5 AL3' =187889.08 X459.7/1.95 X10X 140=3.1638cm左 L =5.652cm右/ L =5.652cm全板L=11.304cm控制应力达到10%时，油表3036#、 30248#读数：x=190092N=190 .092KNX 0.1=19.0092y1=0.0343x-0.1=0.0343 X 19.0092 -0.1=0.552y2=0.

30、0352x-0.4=0.0352 X 19.0092 -0.4=0.252控制应力达到20%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.2=38.0184y1=0.0343x-0.1=0.0343 X 38.0184 -0.1=1.204y2=0.0352x-0.4=0.0352 X 38.01 84-0.4=0.938控制应力达到40%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.4=76.1568y1=0.0343x-0.1=0.0343 X 76.1568 -0.1=2.512y2=0.0352x-0.4=

31、0.0352 X 76.1568 -0.4=2.281控制应力达到60%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.6=38.0184y1=0.0343x-0.1=0.0343 X 38.0184 -0.1=3.812y2=0.0352x-0.4=0.0352 X 38.0184 -0.4=3.615控制应力达到80%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.8=152.0736y1=0.0343x-0.1=0.0343 X 152.0736 -0.1=5.116y2=0.0352x-0.4=0.0352 X

32、 152.0736 -0.4=4.953控制应力达到100%时，油表3036#、 30248#读数：x=190092N=190.092KNX 1=190.092y1=0.0343x-0.1=0.0343 X 190.092 -0.1=6.42y2=0.0352x-0.4=0.0352 X 190.092 -0.4=6.291控制应力达到10%时，油表3036#、 30248#读数：（3 根 ）x=190092N=190.092KN< 0.1 = 19.0092y1=0.0343x-0.1=0.0343 X 19.0092 X3 -0.1=1.856y2=0.0352x-0.4=0.035

33、2 X 19.0092 X 3 -0.4=1.556控制应力达到20%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.2=38.0184y1=0.0343x-0.1=0.0343 X 38.0184 X3 -0.1=3.812y2=0.0352x-0.4=0.0352 X 38.0184 X3 -0.4=3.614控制应力达到40%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.4=76.1568y1=0.0343x-0.1=0.0343 X 76.1568 X3 -0.1=7.736y2=0.0352x-0.4=0.

34、0352 X 76.1568 X 3 -0.4=7.643控制应力达到60%时，油表3036#、 30248#读数：x=190092N=190.092KNX 0.6=38.0184y1=0.0343x-0.1=0.0343 X 38.0184 X3 -0.1=11.636y2=0.0352x-0.4=0.0352 X 38.0184 X 3 -0.4=11.645控制应力达到80%时，油表3036#、 30248#读数： x=190092N=190.092KNX 0.8=152.0736y1=0.0343x-0.1=0.0343X 152.0736X3 -0.1=15.548y2=0.0352x-0.4=0.0352X 152.0736X3 -0.4=15.659控制应力达到100%时，油表3036#、 30248#读数：x=1