预应力钢筋混凝土T型梁结构设计.doc

Project of Principles of Structural Design预应力钢筋混凝土T型梁结构设计1. Known:Span of SSB: 29m；Computed span L=27.66m；Design load：Vehicular Load -；Pedestrian Load=3.0kN/m2；Coefficient of Importance 0=1.0；Environment：Bridge locates in a common field, environment ; Relative humidity (average of per year)= 75；Materials：Tendon: low relaxation strands(17)；Standard value of tension strength ；design value of tension strength；nominal area= 140mm2 ,nominal diameter15.2mm;elastic modulus ；Strand tapered of group anchors.Nonprestressed reinforcement:HRB400,fsk=400MPa,fsd=330MPa.HRB335：(d=(Ms/W-0.7ftk)/(1/A+ep/W)=(3823106/239.927106-0.72.65)/(1/876000+1156/239927000) =2372946(N)The control stress of pre-stressed rebar is .The pre-stress losses are estimated as 20% , so we can get the area of pre-stressed reinforcement is:Ap=Npe/(1-0.2)con=2372946/(0.81395)=2126(mm2)To use 3 bundle 6s15.24 strands, the area of pre-stressed reinforcement is :Ap=36140=2520(mm2). And use the strand tapered group anchors, metal corrugated pipe into the hole.2) : Lay out pre-stressed reinforcement.(1)Arrangement of prestressed rebar in mid-span section:According to the requirement of The Road Bridge Gauge,arrangement of prestressed reinforcement in midspan section shwon Figure 3.(2)Lay out steel cable of anchor cross-section:unit:mm Fig1. End of prestressed beam Fig.2 anchor position in the end Fig.3 cable position in mid-spanIn order to be convenient for construction,three steel cables anchor end of beam,which fits principle of homogeneous disperse and requirement of tension.It will offer much preshear force by bending more depth of N1 and N2 in end of beam. The all shown Fig1 and Fig2.3) :Location and angle of steel cable from other sections.(1)Bending shape、angle and radius of bending.Obtain interpolate curve between straight lines.In order to make preapplied force be perpendicular to anchor bearing plate,bending angle of N1, N2, N3 are . Radius of each steel cable is: ; .(2)calculating location of steel stable control points. unit:mmFigure4Calculation step can be shown example of N3,arrangement figure of bending shown Figure4.Calculating horizontal distance between lead point and anchoring point,According to the formula Ld=ccot0,we can have Ld=400cot80=2846mmCalculating horizontal distance between lead point and bending point,According to the formula Lb2=Rtan(0/2),we can have Lb2=15000tan40=1049mmThe horizontal diatance between bending point and anchoring point isLw=Ld+Lb2=2846+1049=3895mmThe horizontal distance between bending point and midspan section isXk=27660/2+312-Lw=10247mmThe horizontal distance between bending end point lead point isLb1=Lb2cos0=1049cos80=1039mmThe horizontal distance between bending end point and midspan section.X=Xk+Lb1+Lb2=10247+1049+1039=12335mmAccording to the same theory,we can get location of control point from N1 and N2,shown following table.List of control element form steel cableNumber of steel cableDepth C(mm)Angle 0 (0)Radius R (mm)Distance d(mm) LdLb2LwXkLb1XN1151084500015610744 3147 13891 95 3116 6358 N28008300002565692 2098 7790 6296 2077 10471 N34008150003122846 1049 3895 10247 1039 12335 (3)Calculating location and angle of steel cable from all kinds of sections.According to the Figure4,the distance point i to bottom of beam ai=a+ci,angle is i.c=100mm.when0，0， 100mm；0when0， 8， Position and angle of steel table from all cross sectionSectionNo.steelxixkLb1+Lb2xi-xkResultRangleCia+Cimidspan sectionN10 95 6263 -95 No bending45000 0 0 100 N20 6269 4175 -6269 No bending30000 0 0 100 N30 10247 2088 -10247 No bending15000 0 0 100 1/4 span sectionN16915 95 6263 6820 30000 1 0 100 N36915 10247 2088 -3332 No bending15000 0 0 100 changed point sectionN110130 95 6263 10035 30000 7 249 349 N310130 10247 2088 -117 No bending15000 0 0 100 support sectionN113830 95 6263 13735 45000 8 1488 1588 N213830 6269 4175 7561 30000 8 768 868 N313830 10247 2088 3583 15000 8 356 456 (4)The position and angle in flat bend zone N1, N2, N3 are in the same plane at the middle span, but at anchor terminal they are all in the middle lane, to get this result, N2、N3 must be bend from both sides to the middle line in the main beam lab. N2、N3 are take the same modus to bend up, and the position in flat bend as Fig. Shows. There are two curve arc, each angle is . unit:mm3)Requirement for non-prestressed reinforcement(location and area of rebar section)To satisfied with the ultimate limit state, the number of non-prestressed reinforcement are:After deciding the reinforcement number, non- prestressed reinforcement is decided according to the normal cross-sections ultimate limit state.Assume the distance from prestressed and non-prestressed reinforcements resultant force point to the cross-section bottom is a=80mm,so Assume first kind of T shape beam, according to , we can get the depth of compressive zone x1.05554.8106=22.42200X(1720-X/2) x= 67mmSo,As=(fcdbf - fpdAp)/fsd=384mm2Select 218mm HRB440 As=509mm2 ,lay out one line,space is 264mm. as = 45mm,shown following Figure.unit:mmRoad,Bridge&civil Engineering,Bilingual program class 1Page 546.Calculation of geometric features of main beam cross-section . Midspan Sectionstage The name of the PartitionePartitioned area AiDistance of center of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia Iiyu-yiIx=Ai(yu-yi)2Moment of inertia Istage 1ASAOC8.0400E+055.8400E+024.6954E+082.8502E+11-1.1865E+011.1318E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1829E+034.1192E+09AORP-1.1545E+041.7000E+03-1.9627E+070.0000E+00-1.1279E+03-1.4687E+10NSA7.9540E+055.7214E+024.5508E+082.8502E+11-1.0454E+102.7457E+11stage 2ASAOC8.0400E+055.8400E+024.6954E+082.8502E+112.6045E+015.4541E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1450E+033.8594E+09TAOP1.6120E+041.7000E+032.7404E+070.0000E+00-1.0900E+031.9150E+10NSA8.2306E+056.1005E+025.0211E+082.8502E+112.3555E+103.08579E+11stage 3ASAOC8.7600E+055.4300E+024.7567E+083.0138E+112.4824E+015.3980E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1872E+034.1492E+09TAOP1.6120E+041.7000E+032.7404E+070.0000E+00-1.1322E+032.0663E+10NSA8.9506E+055.6782E+025.0824E+083.0138E+112.5352E+103.26736E+11 1/4 span sectionstage The name of the PartitionePartitioned area AiDistance of center of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia Iiyu-yiIx=Ai(yu-yi)2Moment of inertia Istage 1ASAOC8.0400E+055.8400E+024.6954E+082.8502E+11-9.8762E+007.8421E+07TANO2.9440E+031.7550E+035.1667E+060.0000E+00-1.1809E+034.1053E+09AORP-1.1545E+041.5630E+03-1.8045E+070.0000E+00-9.8888E+02-1.1290E+10NSA7.9540E+055.7412E+024.5666E+082.8502E+11-7.1062E+092.77918E+11stage 2ASAOC8.0400E+055.8400E+024.6954E+082.8502E+112.3362E+014.3882E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1476E+033.8775E+09TAOP1.6120E+041.5630E+032.5195E+070.0000E+00-9.5564E+021.4721E+10NSA8.2306E+056.0736E+024.9990E+082.8502E+111.9038E+103.04062E+11stage 3ASAOC8.7600E+055.4300E+024.7567E+083.0138E+112.2356E+014.3783E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1896E+034.1665E+09TAOP1.6120E+041.5630E+032.5195E+070.0000E+00-9.9764E+021.6044E+10NSA8.9506E+055.6536E+025.0603E+083.0138E+112.0648E+103.22032E+11 Changed Point Sectionstage The name of the PartitionePartitioned area AiDistance of center of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia Iiyu-yiIx=Ai(yu-yi)2Moment of inertia Istage 1ASAOC8.0400E+055.8400E+024.6954E+082.8502E+11-5.9861E+002.8810E+07TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1770E+034.0783E+09AORP-1.1545E+041.2950E+03-1.4951E+070.0000E+00-7.1699E+02-5.9351E+09NSA7.9540E+055.7801E+024.5975E+082.8502E+11-1.8280E+092.83196E+11stage 2ASAOC8.0400E+055.8400E+024.6954E+082.8502E+111.8114E+012.6379E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1529E+033.9130E+09TAOP1.6120E+041.2950E+032.0875E+070.0000E+00-6.9289E+027.7390E+09NSA8.2306E+056.0211E+024.9558E+082.8502E+111.1916E+102.9694E+11stage 3ASAOC8.7600E+055.4300E+024.7567E+083.0138E+111.7530E+012.6919E+08TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1945E+034.2004E+09TAOP1.6120E+041.2950E+032.0875E+070.0000E+00-7.3447E+028.6958E+09NSA8.9506E+055.6053E+025.0171E+083.0138E+111.3165E+103.14549E+11Support Sectionstage The name of the PartitionePartitioned area AiDistance of center of gravity to the beam top yiBeam top edge of the area moments Si=Aiyiitself moment of inertia Iiyu-yiIx=Ai(yu-yi)2Moment of inertia Istage 1ASAOC1.0560E+066.5300E+026.8957E+083.3502E+111.1354E+001.3613E+06TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1009E+032.9440E+03AORP-1.1545E+048.3100E+02-9.5942E+060.0000E+00-1.7686E+02-3.6115E+08NSA1.0474E+066.5414E+026.8514E+083.3502E+11-3.5979E+083.34656E+11stage 2ASAOC1.0560E+066.5300E+026.8957E+083.35015E+115.6867E+003.4150E+07TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.0963E+033.5384E+09TAOP1.6120E+048.3100E+021.3396E+070.0000E+00-1.7231E+024.7863E+08NCA1.0751E+066.5869E+027.0813E+083.3502E+114.0512E+093.39067E+11stage 3ASAOC1.1280E+066.1700E+026.9598E+083.5661E+115.9281E+003.9641E+07TAON2.9440E+031.7550E+035.1667E+060.0000E+00-1.1321E+033.7730E+09TAOP1.6120E+048.3100E+021.3396E+070.0000E+00-2.0807E+026.9789E+08NSA1.1471E+066.2293E+027.1454E+083.5661E+114.5105E+093.6112E+11 Summary table of control section at different stages of cross section geometric characteristicsstagesectionarea of blockYuYbIWuWbWpstage 1L/2792454.65 567.74 1232.26 1123.18 270435278367.57 476335749.53 219462996.32 240775641.24 L/4792454.65 569.74 1230.26 984.20 273797245341.38 480567907.80 222551772.79 278191841.41 CPS792454.65 573.64 1226.36 712.33 279102550227.11 486545367.45 227586403.33 391817283.05 SS1044454.65 651.03 1148.97 173.55 334645640106.56 514023022.53 291257681.27 1928203250.34 stage 2L/2820119.78 605.94 1194.06 1088.92 304705868718.60 502868548.83 255183744.28 279823169.86 L/4820119.78 603.24 1196.76 954.18 300170187369.55 497594448.77 250819586.84 314583920.73 CPS820119.78 597.97 1202.03 690.60 293012718956.35 490008318.16 243765908.71 424287176.67 SS1072119.78 655.68 1144.32 169.50 335518546648.49 511713696.60 293202481.60 1979467856.16 stage 3L/2892119.78 563.91 1236.09 1131.20 322572823081.89 572033045.38 260961385.85 285160225.84 L/4892119.78 561.43 1238.57 996.28 317851984911.95 566146668.86 256628291.53 319040216.93 CPS892119.78 556.59 1243.41 732.34 310335087408.35 557567027.74 249583464.08 423758891.60 SS1144119.78 620.02 1179.98 205.42 357337657639.91 576337025.80 302832398.19 1739587062.15 ASAOC means all section area of concrete,TAON means transfer area of nonprestress,AORP means area of reserve piple,NSA means net section area,TAOP means transfer area of prestress.CPS means changed point section,SS means support section.7. Calculation of carrying capacity from ultimate limit state in long term.1) Calculation of carrying capacity from normal section.As for midspan section,which subbjected Mmax.(1) calculate depth of compression zone.Assume that the beam is type of T shape beam. X=(fpdAp+fsdAs)/fcdbf =(12602520+330509)/(22.42200)=68mm0Md=15554.8KNm=5554.8KNm OK!From calculation of Excel ,we can get carrying capacity of other sections, Carrying capacity of normal sectionsectiondesign valueaXh0Mumidspan5554.810088.5937517007228.634273OKL/44166.123788.5937515637228.634273OKchanged point section2574.622359.062515774862.066344OK2) Calculation of carrying