1、T梁預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算書一、計(jì)算依據(jù)T形梁上部構(gòu)造通用圖YQT-SLT240ZQ-30-1，K0+936浸長1#橋、K2+317浸長2#橋、K4+953馬料河橋設(shè)計(jì)圖紙及公路橋涵施工技術(shù)規(guī)范（JTJ041-2000），混凝土彎梁橋。二、計(jì)算公式1、預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算公式預(yù)應(yīng)力鋼絞線伸長值：L(Pp×L)/(Ap×Ep), 其中：L預(yù)應(yīng)力鋼絞線伸長值（mm）L預(yù)應(yīng)力鋼絞線計(jì)算長度（mm），包括千斤頂工作段長度Ap預(yù)應(yīng)力鋼絞線的截面面積（mm2）Ep預(yù)應(yīng)力鋼絞線的彈性模量（N/ mm2）Pp預(yù)應(yīng)力鋼絞線的平均張拉力（N）；按JTJ0412000公路橋涵施工技術(shù)規(guī)

2、范附錄G-8預(yù)應(yīng)力筋平均張拉力的計(jì)算2、預(yù)應(yīng)力鋼絞線平均張拉力計(jì)算公式Pp =P×（1-e-(kx+)）/（kx+）；其中：P預(yù)應(yīng)力鋼束張拉端的張拉力（N）k孔道每米局部偏差對摩擦的影響系數(shù)x從張拉端至計(jì)算截面的孔道長度（m）預(yù)應(yīng)力鋼絞線與孔道壁的摩擦系數(shù)從張拉端至計(jì)算截面的孔道部分切線的夾角之和(rad)3、預(yù)應(yīng)力鋼絞線伸長值修正計(jì)算公式L(Ap×Ep)/(Ap×Ep) ×L, 其中：Ap預(yù)應(yīng)力鋼絞線的截面面積（mm2）Ep預(yù)應(yīng)力鋼絞線的彈性模量（N/ mm2）Ap預(yù)應(yīng)力鋼絞線的實(shí)測截面面積（mm2）Ep預(yù)應(yīng)力鋼絞線的實(shí)測彈性模量（N/ mm2）三、設(shè)

3、計(jì)參數(shù)及計(jì)算參數(shù)的選取預(yù)應(yīng)力筋為s15.20(75)高強(qiáng)度低松弛預(yù)應(yīng)力鋼絞線，設(shè)計(jì)公稱面積Ap139 mm2，彈性模量為：Ep1.95×105Mpa，錨下張拉控制應(yīng)力：k1395 Mpa。N1鋼束豎=7.2890°；N2鋼束豎=7.2890°，平=8.1301°；N3鋼束豎=6.0542°，平=8.1301°。采用兩端同時(shí)對稱張拉技術(shù)張拉。實(shí)測鋼絞線公稱面積Ap140 mm2，彈性模量為：Ep1.923×105Mpa，計(jì)算k=0.0015，=0.16（設(shè)計(jì)給定），錨環(huán)夾片至張拉工具夾片長度46cm，采用有效張拉力進(jìn)行計(jì)算。

4、四、預(yù)應(yīng)力伸長值計(jì)算鋼絞線束按無孔道壁的摩擦系數(shù)直線段、有孔道局部偏差對摩擦的影響系數(shù)及孔道壁摩擦系數(shù)圓曲線段兩種類型計(jì)算（以下計(jì)算均以一根鋼絞線計(jì)算，如下圖一端簡支一端連續(xù)，直線及曲線長度根據(jù)設(shè)計(jì)圖紙端點(diǎn)坐標(biāo)、曲線起點(diǎn)坐標(biāo)、終點(diǎn)坐標(biāo)計(jì)算）。以K2+317浸長2#橋右1-4 (A型)T梁為例計(jì)算，梁長L=2936.1cm。1、各段長度計(jì)算N1各段長度計(jì)算LA-B錨環(huán)夾片至張拉工具夾片長度=460mmLB-C=(L/2-21)-(L/2-1136.9)2+(162.4-19.7)2)0.5=(2936.1/2-21)-(2936.1/2-1136.9)2+(162.4-19.7)2)0.5=11

5、25cm=11250mmLD-E=L/2-1289.2=2936.1/2-1289.2=178.85cm=1788.5mmLE-F=L/2-1289.2=2936.1/2-1289.2=178.85cm=1788.5mmLG-H=(L/2-6.2)-(L/2-1136.9)2+(164.3-19.7)2)0.5=(2936.1/2-6.2)-(2936.1/2-1136.9)2+(164.3-19.7)2)0.5=1139.9cm=11399mmLH-I錨環(huán)夾片至張拉工具夾片長度=460mmLC-D=LF-G=(L-8)×10- LB-C- LD-E- LE-F- LG-H)/2=

6、(2936.1-8)×10-11250-1788.8-1788.5-11399)/2=1528mmN2各段長度計(jì)算LA-B錨環(huán)夾片至張拉工具夾片長度=460mmLB-C=(L/2-19.6)-(L/2-710.5)2+(122.6-34.2)2)0.5=(2936.1/2-19.6)-(2936.1/2-710.5)2+(122.6-34.2)2)0.5=696.5cm=6965mmLD-E=L/2-1143.5=2936.1/2-1143.5=322.75cm=3227.5mmLE-F= L/2-1143.5=2936.1/2-1143.5=322.75cm=3227.5mm LG

7、-H=(L/2-4.8)-(L/2-710.5)2+(124.5-34.2)2)0.5=(2936.1/2-4.8)-(2936.1/2-710.5)2+(124.5-34.2)2)0.5=711.5cm=7115mmLH-I錨環(huán)夾片至張拉工具夾片長度=460mmLC-D=LF-G=(L-7)×10- LB-C- LD-E- LE-F- LG-H)/2= (2936.1-7)×10-)/2=4378mmN3各段長度計(jì)算LA-B錨環(huán)夾片至張拉工具夾片長度=460mmLB-C=(L/2-18.4)-(L/2-542.2)2+(82.3-26.7)2)0.5=(2936.1/2-

8、18.4)-(2936.1/2-542.2)2+(82.3-26.7)2)0.5=526.7cm=5267mmLD-E=L/2-858.6=2936.1/2-858.6=609.45cm=6094.5mmLE-F= L/2-858.6=2936.1/2-858.6=609.45cm=6094.5mmLG-H=(L/2-3.6)-(L/2-542.2)2+(83.9-26.7)2)0.5=(2936.1/2-3.6)-(2936.1/2-542.2)2+(83.9-26.7)2)0.5=541.6cm=5416mmLH-I錨環(huán)夾片至張拉工具夾片長度=460mmLC-D=LF-G=(L-11)&#

9、215;10- LB-C- LD-E- LE-F- LG-H)/2= (2936.1-11)×10-5267-6094.5-6094.5-5416)/2=3190mm2、N1鋼絞線理論伸長值計(jì)算A-C段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端A點(diǎn)張拉力：P=k×Ap =1395×139=193905N錨環(huán)夾片至張拉工具夾片長度LA-B=460mm，LB-C=11250mm ，PpA =P= Pp。LA-C(Pp×L)/(Ap×Ep)=( 193905×(460+11250)/ (139×1.95×105)=83.77m

10、mC-D段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算C點(diǎn)有效張拉力：PpC =PpA =193905NLC-D=1528mm，k=0.0015，=0.16，x=1.528m，=豎=7.2890°=0.1272170492 rad。平均PpC-D= P1-e-（kx+）/（kx+）=193905×1-e-（0.0015×1.528+0.16×0.1272170492）/(0.0015×1.528+0.16×0.1272170492) =191725.82NLC-D(Pp×L)/(Ap×Ep)=( 191725.82×1

11、528)/ (139×1.95×105)=10.81mmD-E段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算D點(diǎn)有效張拉力： PpD= PpC×e-（kx+）= 193905×e-（0.0015×1.528+0.16×0.1272170492）=189563.04NLD-E=1788.5mmLD-E(Pp×L)/(Ap×Ep)=( 189563.04×1788.5)/ (139×1.95×105)=12.51mmG-I段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端I點(diǎn)張拉力：P=k×Ap =139

12、5×139=193905N錨環(huán)夾片至張拉工具夾片長度LH-I=460mm，LG-H=11399mm ，PpI =P= Pp。LG-I(Pp×L)/(Ap×Ep)=( 193905×(460+11399)/ (139×1.95×105)=84.84mmF-G段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算G點(diǎn)有效張拉力：PpG =PpI =193905NLF-G=1528mm，k=0.0015，=0.16，x=1.528m，=豎=7.2890°=0.1272170492 rad。平均PpF-G= P1-e-（kx+）/（kx+）=193905

13、×1-e-（0.0015×1.528+0.16×0.1272170492）/(0.0015×1.528+0.16×0.1272170492) =191725.82NLF-G(Pp×L)/(Ap×Ep)=( 191725.82×1528)/ (139×1.95×105)=10.81mmE-F段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算F點(diǎn)有效張拉力： PpF= PpG×e-（kx+）= 193905×e-（0.0015×1.528+0.16×0.1272170492）=

14、189563.04NLE-F=1788.5mmLE-F(Pp×L)/(Ap×Ep)=( 189563.04×1788.5)/ (139×1.95×105)=12.51mm合計(jì)伸長值：L1LA-C+LC-D+LD-E+LE-F+LF-G+LG-I=83.77+10.81+12.51+125.51+10.81+84.84=215.25mmN1一端伸長值L =L1/2=215.25/2=107.63mmN1鋼絞線伸長值修正L(Ap×Ep)/(Ap ×Ep) ×L(139×1.95×105)/( 140

15、×1.933×105) ×107.63107.8（mm）3、N2鋼絞線理論伸長值計(jì)算A-C段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端A點(diǎn)張拉力：P=k×Ap =1395×139=193905N錨環(huán)夾片至張拉工具夾片長度LA-B=460mm，LB-C=6965mm ，PpA =P= Pp。LA-C(Pp×L)/(Ap×Ep)=( 193905×(460+6965)/ (139×1.95×105)=53.12mmC-D段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算C點(diǎn)有效張拉力：PpC =PpA =193905NLC

16、-D=4378mm，k=0.0015，=0.16，x=4.378m，豎=7.2890°，平=8.1301°。=三維空間曲線包角=(7.28902+（8.1301×2）2)0.5=0.3110035810 rad。平均PpC-D= P1-e-（kx+）/（kx+）=193905×1-e-（0.0015×4.378+0.16×0.3110035810）/(0.0015×4.378+0.16×0.3110035810) =188545.01NLC-D(Pp×L)/(Ap×Ep)=( 188545.01

17、×4378)/ (139×1.95×105)=30.45mmD-E段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算D點(diǎn)有效張拉力： PpD= PpC×e-（kx+）= 193905×e-（0.0015×4.378+0.16×0.3110035810）=183284.72NLD-E=3227.5mmLD-E(Pp×L)/(Ap×Ep)=( 183284.72×3227.5)/ (139×1.95×105)=21.82mmG-I段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端I點(diǎn)張拉力：P=k×

18、Ap =1395×139=193905N錨環(huán)夾片至張拉工具夾片長度LH-I=460mm，LG-H=7115mm ，PpI =P= Pp。LG-I(Pp×L)/(Ap×Ep)=( 193905×(460+7115)/ (139×1.95×105)=54.19mmF-G段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算G點(diǎn)有效張拉力：PpG =PpI =193905NLF-G=4378mm，k=0.0015，=0.16，x=4.378m，豎=7.2890°，平=8.1301°。=三維空間曲線包角=(7.28902+（8.1301

19、5;2）2)0.5=0.3110035810 rad。平均PpF-G= P1-e-（kx+）/（kx+）=193905×1-e-（0.0015×4.378+0.16×0.3110035810）/(0.0015×4.378+0.16×0.3110035810) =188545.01NLF-G(Pp×L)/(Ap×Ep)=( 188545.01×4378)/ (139×1.95×105)=30.45mmE-F段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算F點(diǎn)有效張拉力： PpF= PpG×e-（kx+）

20、= 193905×e-（0.0015×4.378+0.16×0.3110035810）=183284.72NLE-F=3227.5mmLE-F(Pp×L)/(Ap×Ep)=( 183284.72×3227.5)/ (139×1.95×105)=21.82mm合計(jì)伸長值：L2LA-C+LC-D+LD-E+LE-F+LF-G+LG-I=53.12+30.45+21.82+21.82+30.45+54.19=211.85mmN2一端伸長值L =L2/2=211.85/2=105.93mmN2鋼絞線伸長值修正L(Ap

21、15;Ep)/(Ap ×Ep) ×L(139×1.95×105)/( 140×1.933×105) ×105.93106.1（mm）4、N3鋼絞線理論伸長值計(jì)算A-C段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端A點(diǎn)張拉力：P=k×Ap =1395×139=193905N錨環(huán)夾片至張拉工具夾片長度LA-B=460mm，LB-C=5267mm ，PpA =P= Pp。LA-C(Pp×L)/(Ap×Ep)=( 193905×(460+5267)/ (139×1.95×

22、105)=40.97mmC-D段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算C點(diǎn)有效張拉力：PpC =PpA =193905NLC-D=3190mm，k=0.0015，=0.16，x=3.190m，豎=6.0542°，平=8.1301°。=三維空間曲線包角=(6.05422+（8.1301×2）2)0.5=0.3028271700 rad。平均PpC-D= P1-e-（kx+）/（kx+）=193905×1-e-（0.0015×3.190+0.16×0.3028271700）/(0.0015×3.190+0.16×0.30282

23、71700) =188833.89NLC-D(Pp×L)/(Ap×Ep)=( 188833.89×3190)/ (139×1.95×105)=22.22mmD-E段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算D點(diǎn)有效張拉力： PpD= PpC×e-（kx+）= 193905×e-（0.0015×3.190+0.16×0.3028271700）=183851.98NLD-E=6094.5mmLD-E(Pp×L)/(Ap×Ep)=( 183851.98×6094.5)/ (139×1

24、.95×105)=41.34mmG-I段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端I點(diǎn)張拉力：P=k×Ap =1395×139=193905N錨環(huán)夾片至張拉工具夾片長度LH-I=460mm，LG-H=5416mm ，PpI =P= Pp。LG-I(Pp×L)/(Ap×Ep)=( 193905×(460+5416)/ (139×1.95×105)=42.04mmF-G段曲線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算G點(diǎn)有效張拉力：PpG =PpI =193905NLF-G=3190mm，k=0.0015，=0.16，x=3.190m，豎=

25、6.0542°，平=8.1301°。=三維空間曲線包角=(6.05422+（8.1301×2）2)0.5=0.3028271700 rad。平均PpF-G= P1-e-（kx+）/（kx+）=193905×1-e-（0.0015×3.190+0.16×0.3028271700）/(0.0015×3.190+0.16×0.3028271700) =188833.89NLF-G(Pp×L)/(Ap×Ep)=( 188833.89×3190)/ (139×1.95×105

26、)=22.22mmE-F段直線預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算F點(diǎn)有效張拉力： PpF= PpG×e-（kx+）= 193905×e-（0.0015×3.190+0.16×0.3028271700）=183851.98NLE-F=6094.5mmLE-F(Pp×L)/(Ap×Ep)=( 183851.98×6094.5)/ (139×1.95×105)=41.34mm合計(jì)伸長值：L3LA-C+LC-D+LD-E+LE-F+LF-G+LG-I=40.97+22.22+41.34+41.34+22.22+42.04

27、=210.13mmN3一端伸長值L =L3/2=210.13/2=105.07mmN3鋼絞線伸長值修正L(Ap×Ep)/(Ap ×Ep) ×L(139×1.95×105)/( 140×1.933×105) ×105.07105.2（mm）5、T梁15%控制張拉預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端15%張拉力：P=k×Ap ×0.15=1395×139×0.15=29085.75N，其余計(jì)算方法步驟同24，結(jié)果為：N1L15%12.57+1.62+1.88+1.88+1.62+12

28、.73=16.15mm修正L (139×1.95×105)/( 140×1.933×105) ×16.1516.2（mm）N2L15%7.97+4.57+3.27+3.27+4.57+8.13=15.89mm修正L (139×1.95×105)/( 140×1.933×105) ×15.8915.9（mm）N3L15%6.15+3.33+6.20+6.20+3.33+6.3115.76mm修正L (139×1.95×105)/( 140×1.933×105

29、) ×15.7615.8（mm）6、T梁60%控制張拉預(yù)應(yīng)力鋼絞線理論伸長值計(jì)算張拉端60%張拉力：P=k×Ap ×0.60=1395×139×0.60=116343N，其余計(jì)算方法步驟同3，結(jié)果為：N2L60%=31.87+18.27+13.09+13.09+18.27+32.51=63.55mm修正L (139×1.95×105)/( 140×1.933×105) ×63.5563.7（mm）五、壓力表讀數(shù)計(jì)算N1鋼絞線根數(shù)：n=6，N2鋼絞線根數(shù)：n=7，N3鋼絞線根數(shù)：n=7。1、壓力表1計(jì)算千斤頂編號:20432 壓力表編號:.2588 Y=0.021009X-0.18097鋼絞線15%壓力表讀數(shù)計(jì)算張拉端15%張拉力：P=193905×0.15=29085.75N。N1 Y=0.021009×29085.75×6/1000-0.18097=3.49