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BANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANH
03 Calculation I-Beam_I33m.xls【Input_material】 SHEET NO : / 1.MATERIAL DATA 1.1 General Thickness of Slab (mm) Width of Slab (mm) Beam numbers Strand type Nominal area of strands No of strands 1.2 Material strength & Stress Limits: 1.2.1 Prestressing steel (low-relaxation) Ultimate strength of prestressing steel Yield strength Elastic Modulus Limit of tensile stress after immediate losses Limit of tensile stress at service state 1.2.2 Reinforcement Yield strength Limit of tensile stress at service Elastic Modulus : : : : : : TS BS Nd = = = 200 2350 12.7 98.7 12 mm mm Nos mm mm2 Nos : : : : : f'pu = fpy=0.9f'pu Ep 0.9f'py f'pe=0.8f'py = 1860 1674 1.97E+05 1506.6 1339.2 MPa MPa MPa MPa MPa : : : f'sy = f'sa=0.6fsy = Es = 400 MPa 240 MPa 2.00E+05 MPa 1.2.3 Concrete Density gc Thermal coefficient EXP a) Girder Concrete Compresive strength at 28 days : Compresive strength at time of initial prestress : Limit of compresive stress at time of initial prestress: Limit of tensile stress at time of initial prestress : Limit of compresive stress at service * Prestress + permanent load : * Live load +1/2(prestress + permanent load) : Limit of tensile stress at service : Elastic Modulus : 0.043gc1.5(f'c)0.5 : b) Slab Concrete Compresive strength at 28 days : Limit of compresive stress at service * Prestress + permanent load : * Live load +1/2(prestress + permanent load) : Limit of tensile stress at service : Elastic Modulus : 0.043gc1.5(f'c)0.5 : Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung = = f'c f'ci = 0.9f'c 0.6 f'ci 0.58(f'ci)0.5 2500 kg/m3 1.08E-05 1/0C = = = = 40 36 21.6 3.48 MPa MPa MPa MPa 0.45 f'c 0.4 f'c 0.5(f'c)0.5 = Ec1 = 18 16 3.16 33990 MPa MPa MPa MPa f'c = 0.45 f'c 0.4 f'c 0.5 = 0.5(f'c) Ec2 = 35 MPa 15.75 14 2.96 31800 MPa MPa MPa MPa 03 Calculation I-Beam_I33m.xls【Input_section】 SHEET NO : / SECTION PROPERTIES 2.1 1-1 1-1 2-2 - 2, - - 4, - 3-3,4-4,5-5 Section Input Section SEC-1 SEC-2 SEC-3 SEC-4 SEC-5 B1 (mm) 650 650 650 650 650 B2 (mm) 850 850 850 850 850 B3 (mm) 650 479 285 200 200 B4 (mm) H1 (mm) 80 80 80 80 80 650 650 650 650 H2 (mm) 120 120 120 120 120 H3 (mm) 34 63 96 110 110 H4 (mm) 1416 1061 942 890 890 H5 (mm) 76 162 200 200 H6 (mm) 250 250 250 250 Section Properties (Origin) Section SEC-1 SEC-2 SEC-3 SEC-4 SEC-5 H Area (mm2) 1,099,900 909,485 715,185 637,250 637,250 (mm) 1650 1650 1650 1650 1650 Extreme fibre Top y' Bottom y (mm) (mm) 808 809 816 823 823 Cross Section Properties (PS steel included) Ns/c = E.steel/E.con Nslap/con = E.slab/E.con Area of strand Equivalent diameter of strand Diameter of strand Area of hole Inertia of hole Section Row of cable No of cable (No) R1 R2 R3 R4 R5 R6 all 1 1 Distance from bottom of fibre (at) 1311 1041 770 503 236 Area of steel equivale n 6864.57 6864.57 6864.57 6864.57 6864.57 772.2 Included Oval holes Section Properties area inc holes (mm2) 1083308 Yt inc holes (mm) 807 Yb inc holes (mm) 843 Ix inc holes (mm4) 253098489400 No of cable (No) 1 1 = = = = = 5.796 0.9356 1184.4 38.83 65.00 3318.31 876241 Section Section Distance from bottom of fibre (at) 1084 848 613 407 202 Distance from bottom of fibre (at) 884 679 474 323 172 Distance from bottom of fibre (at) 576 418 261 194 126 Area of steel equivale n 6864.57 6864.57 6864.57 6864.57 6864.57 630.8 Section 892893 805 845 235016567141 Section 1117631 809 841 258224779130 Section Sevice stage Properties area sv (mm2) Ytslab sv (mm) Yt sv (mm) Yb sv (mm) Ix sv (mm4) Section 1557349 753 553 1097.469 520584277806 Section 927216 813 837 239877558319 1366933 719 519 1131 489837344600 Inertia Ix (mm4) 255,582,195,288 235,851,995,578 219,345,544,100 213,600,768,818 213,600,768,818 Iy (mm4) (mm2) (mm) (mm) (mm2) (mm4) Section Included PS steel Properties area inc st (mm2) Yt inc st (mm) Yb inc st (mm) Ix inc st (mm4) Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 842 841 834 827 827 Bending Modulus Top W' Bottom W (mm3) (mm3) 316,253,451 303,598,130 291,632,395 280,352,466 268,682,488 263,122,417 259,451,852 258,370,452 259,451,852 258,370,452 No of cable (No) 1 1 Area of steel equivale n 6864.57 6864.57 6864.57 6864.57 6864.57 506.4 Section 698593 809 841 218345913703 Section 732916 824 826 224206328760 Section 1172634 678 478 1172 460464040308 No of cable (No) 1 1 Section Area of steel equivale n 6864.57 6864.57 6864.57 6864.57 6864.57 315 Section 620658 810 840 211928353289 Section 654981 837 813 221812772633 Section 1094699 661 461 1189 454329536894 No of cable (No) 1 1 Distance from bottom of fibre (at) 330 210 90 90 90 162 Area of steel equivale n 6864.57 6864.57 6864.57 6864.57 6864.57 Section 620658 806 844 210988404916 Section 654981 841 809 226454382532 Section 1094699 663 463 1187 461018064311 03 Calculation I-Beam_I33m.xls【sectionpro】 SHEET NO : / 2.2 Sumary of Section Properties 2.2.1 Cross Section Properties (Oval holes included) Cross section Section Area mm2 2.2.2 Top y' Bottom y mm mm Bending Modulus Top W' mm Inertia Bottom W mm Ix mm Iy mm4 SEC-1 1,083,308 807 843 313,594,046 300,267,367 253,098,489,400 SEC-2 892,893 805 845 292,011,507 278,066,731 235,016,567,141 SEC-3 698,593 809 841 270,028,583 259,504,022 218,345,913,703 SEC-4 620,658 810 840 261,769,972 252,174,869 211,928,353,289 SEC-5 620,658 806 844 261,932,224 249,840,510 210,988,404,916 Tranformed Section Properties for initial stage at tranfer (Prestressing steel included) Area Section 2.2.3 Extreme fibre mm2 Extreme fibre Top y2' Bottom y2 mm mm Bending Modulus Top W2' mm Bottom W2 mm Inertia Ix mm Iy mm4 SEC-1 1,117,631 809 841 319,087,090 307,140,289 258,224,779,130 SEC-2 927,216 813 837 295,141,184 286,508,300 239,877,558,319 SEC-3 732,916 824 826 271,998,982 271,531,913 224,206,328,760 SEC-4 654,981 837 813 264,968,067 272,876,141 221,812,772,633 SEC-5 654,981 841 809 269,180,888 280,013,086 226,454,382,532 Composite Section Properties for final stage (service stage) Area Section mm2 Extreme fibre Top y3' Bottom y3 mm mm Bending Modulus Top W3' mm Bottom W3 mm Inertia Ix mm Iy mm4 SEC-1 1,557,349 753 1,097 691,777,677 474,349,952 520,584,277,806 SEC-2 1,366,933 719 1,131 681,144,612 433,154,161 489,837,344,600 SEC-3 1,172,634 678 1,172 679,453,361 392,786,123 460,464,040,308 SEC-4 1,094,699 661 1,189 687,643,897 382,015,742 454,329,536,894 SEC-5 1,094,699 663 1,187 695,159,776 388,449,120 461,018,064,311 Area Section mm2 SEC-1 SEC-2 SEC-3 SEC-4 SEC-5 1,557,349 1,366,933 1,172,634 1,094,699 1,094,699 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Deck slab fibre S_Top y3' mm 753 719 678 661 663 Bending Modulus S_Top W3' mm3 691,777,677 681,144,612 679,453,361 687,643,897 695,159,776 Inertia Ix mm4 520,584,277,806 489,837,344,600 460,464,040,308 454,329,536,894 461,018,064,311 Iy mm4 03 Calculation I-Beam_I33m.xls【Internal force】 SHEET NO : / 3.1 Internal forces Due to S.W of Girder (DL1) A B 1650 34 250 1166 120 1650 80 40 8100 650 800 46 50 A 28 75 225 20 22 A -A B -B 850 850 100 100 650 100 890 1650 1166 1650 22 200 225 110120 80 650 34 120 80 100 735 B 250 250 200 225 200 225 650 650 1900 L2= L1= Fsec1= 1083308.464 Fsec2= W = Σ(FsecixLix0.0000025x9.8066)/ΣLi = 10650 890950.964 18.01 N/mm W= L3= Fsec3= 20450 620658.4638 18.01 N/mm Ltt= 32.20 m Bending Moment and Shear forces due to S.W of Girder (DL1) Component Unit Sec - Sec - Sec - Sec - Sec - Section Location 0Ltt 0.0625Ltt 0.125Ltt 0.25Ltt 0.5Ltt Distance from section to left bearing mm 2,013 4,025 8,050 16,100 Distance from section to right bearing mm 32,200 30,188 28,175 24,150 16,100 Moment M N.mm 547,014,790 1,021,094,274 1,750,447,327 2,333,929,769 Shear V N 289,929 253,688 217,447 144,965 Due to S.W of Deck Slab and S.W of longitudinal gider (DL2) Bb Tw Tb 3.2 Bb= 2350 mm Tb= 200 mm Fb=Bb*Tb = 470000 mm2 Wb= Fbx0.0000025x9.8066= 11.523 N/mm W= Bw= 1700 mm Tw= 80 mm Fw=Bw*Tw = 136000 mm2 Ww= Fwx0.0000025x9.8066= 3.334 N/mm 14.857 N/mm Ltt=32.20 m W = Wb+Ww = 14.857 N / mm Bending Moment and Shear forces due to S.W of deck slab (DL2) Component Unit Sec - Sec - Sec - Sec - Sec - Distance from section to left bearing mm 2,013 4,025 8,050 16,100 Distance from section to right bearing mm 32,200 30,188 28,175 24,150 16,100 Moment M N.mm 451,298,755 842,424,343 1,444,156,017 1,925,541,355 Shear V N 239,198 209,298 179,398 119,599 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 03 Calculation I-Beam_I33m.xls【Internal force】 SHEET NO : / 3.3 Due to S.W of Railing, Parapet and Barrier (DL3) CROSS SECTION 12000 11000 500 500 Bending Moment and Shear forces due to S.W of Railing , Parapet and Barrier (DL3) Flc= SF=2*Flc= Nd= W =(SFx0.0000025x9.8066 + 0.5x2)/Nd= 361000 722000 3.740 W= mm2 mm2 Nos N/mm 3.740 N/mm Ltt=32.20 m Bending Moment and Shear forces due to S.W of Railing , Parapet and Barrier (DL3) Component Unit Sec - Sec - Sec - Sec - Space from section to left bearing mm 2,013 4,025 8,050 Space from section to right bearing mm 32,200 30,188 28,175 24,150 Moment M N.mm 113,612,430 212,076,535 363,559,774 Shear V N 60,217 52,690 45,163 30,108 3.4 Sec - 16,100 16,100 484,746,366 Due to S.W of surface (DW) W= 0.248 Ltt= 32.20 Tlp= Bdeck= Nd W = (Bdesk xTlp * 0.0000023*9.8066)/Nd = 50 1100 0.248 N/mm m mm mm Nos N / mm Bending Moment and Shear forces due to S.W of Surface (DW) Component Unit Sec - Sec - Sec - Section Location 0L 0.0625L 0.125L Space from section to left bearing mm 2,013 4,025 Space from section to right bearing mm 32,200 30,188 28,175 Moment M N.mm 7,536,540 14,068,209 Shear V N 3,995 3,495 2,996 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Sec - 0.25L 8,050 24,150 24,116,929 1,997 Sec - 0.50L 16,100 16,100 32,155,905 03 Calculation I-Beam_I33m.xls【Internal force】 SHEET NO : / 3.5 3.5.1 Due to Live Load plus Impact (LL+IM) Calculation distribution of live load on cross beam Calculation span length (6000mm~73000mm) Area of beam Distance between the centers of gravity of beam and slab Moment of inertia of beam Number of beams (Nb≥3) L = A = eg = I = Nb = 32200.00 654981 923.00 2.3.E+11 5.00 Spacing of beams (1100mm~4900mm) S= thickness of concrete slab (450mm~1700mm) t= Distance from exterior web of exterior beam and the interior edge of curb or traffic barrier de = Skew angle θ= Correction factor for Moment e = Correction factor for Shear e = Impact factor IM = Longitudinal stiffness parameter factor Kg = Correction factors for load distribution factors for support shear of the obtuse corner Distribution of live loads per Lane for Moment in + Interior beams g = + Exterior beams Distribution of live loads per Lane for Shear in + Interior beams + Exterior beams mm mm mm mm4 Nos 2350.00 mm 200.00 mm 810.00 mm 0.00 Deg 1.06 0.87 1.25 8.38E+11 mm4 1.00 0.6626 g = 0.7019 g = g = 0.2149 0.1870 VEHICULAR LIVE LOADING DATA Unit Standard load Truck Tandem Lane Load 3.6.2 Axle concentrated load P1 Axle concentrated load P2 Axle concentrated load P3 Axle concentrated load P4 Axle concentrated load P5 N N N N N 35,000 145,000 145,000 110,000 110,000 Uniform distributed load W N / mm 9.30 axle 4300 4300 1200 Calculation value of influence line Xi P1 Xi 4.3 4.3 P2 MY1 Ltt P4 P3 MY2 MY3 MY4 4.3 4.3 P1 1.2 P5 Ltt MY5 1.2 P2 P3 VY1 VY2 P4 VY3 VY4 Ltt Iterm Section Location Distance from calculated section to left bearing Distance from calculated section to right bearing Area of Moment influence line MA Area of Shear influence line VA1 > Area of Shear influence line VA2 < Value of Moment influence line MY1 Value of Moment influence line MY2 Value of Moment influence line MY3 Value of Moment influence line MY4 Value of Moment influence line MY5 Value of Shear influence line VY1 Value of Shear influence line VY2 Value of Shear influence line VY3 Value of Shear influence line VY4 Value of Shear influence line VY5 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung P5 Unit mm mm mm2 mm2 mm2 Sec - 0L 32,200 16,100 0 0 0 1.00 0.87 0.73 1.00 0.96 Sec - 0.02L 2,013 30,188 30,376,172 14,150 -63 1887 1618 1324 1849 0.94 0.80 0.67 0.94 0.90 Sec - 0.25L 4,025 28,175 56,702,188 12,327 -252 3522 2984 2997 3447 0.88 0.74 0.61 0.88 0.84 VY5 Ltt Sec - 0.50L 8,050 24,150 97,203,750 9,056 -1,006 2813 6038 4963 5588 5888 0.75 0.62 0.48 0.75 0.71 Sec - 0.50L 16,100 16,100 129,605,000 4,025 -4,025 5900 8050 5900 7750 7750 0.50 0.37 0.23 0.50 0.46 03 Calculation I-Beam_I33m.xls【Internal force】 SHEET NO : / Forces P1 By P2 Truck P3 Total P1 P2 P3 Total By P4 Tandem P5 Total By lane load W Total Forces P1 P2 P3 Total By P4 Tandem P5 Total By lane load W Total By Truck Bending Moment due to Live Load plus Impact M = IM*g*MY(i)*P(i) for concentrated load or M = g*MA*W for uniform load Sec - Sec - Sec - Sec - 2,013 4025 8,050 X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) -4,300 -2,288 -275 3,750 123,046,875 0 2,013 341,967,773 4,025 638,339,844 8,050 1,094,296,875 4,300 6,313 293,256,836 8,325 540,917,969 12,350 899,453,125 -4,300 4,300 0 -0.6 0.6 0 635,224,609 -2,288 2,013 6,313 341,967,773 70,786,133 2,012 2,013 182,080,078 254,267,578 0 1,200 638,339,844 130,566,406 4,024 4,026 412,070,313 473,945,313 412,753,906 11,800 16,100 20,400 1,069,375,000 1,459,062,500 258,125,000 16,099 16,101 1,065,625,000 1,065,625,000 2,116,796,875 3,750 8,050 12,350 768,906,250 509,765,625 1,094,296,875 217,109,375 2,786,562,500 1,821,171,875 8,049 8,051 768,281,250 809,531,250 2,786,562,500 436,347,656 886,015,625 1,577,812,500 2,131,250,000 282,498,398 527,330,344 903,994,875 1,205,326,500 644,156,255 1,197,866,269 2,120,315,045 2,801,935,057 Sec - X(mm) V(N) 8,600 4,300 1,179,257,813 -275 4,025 8,325 X(mm) 11,800 16,100 20,400 Sec - 16100 M(N.mm) 258,125,000 1,459,062,500 1,069,375,000 18,005 101,777 119,782 77,210 77,210 149,730 57,922 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Shear forces due to Live Load plus Impact V = IM*g*VY(i)*P(i) for concentrated load or V = g*VA(i)*W for uniform load Sec - Sec - Sec - 2,013 4025 8050 X(mm) V(N) X(mm) V(N) X(mm) V(N) 10,613 6,313 2,013 2,013 3,213 29,331 145,718 169,922 344,970 128,906 123,782 252,688 131,599 102,422 12,625 8,325 4,025 4,025 5,225 26,596 134,390 158,594 319,580 120,313 115,188 235,501 114,637 93,320 16,650 12,350 8,050 8,050 9,250 21,128 111,733 135,938 268,799 103,125 98,001 201,126 84,223 75,870 Sec - 16100 X(mm) V(N) 24,700 20,400 16,100 10,190 66,421 90,625 167,236 68,750 63,626 132,376 37,433 43,986 16,100 17,300 03 Calculation I-Beam_I33m.xls【Prestress_1】 SHEET NO : / 3.6 Due to prestressing 3.6.1 Stress Loses (22TCN272-05, 5.9.5) Specified strength of Prestressing steel Yield strength of Prestressing steel Stress in Prestressing steel immediately prior to transfer Stress in Prestressing steel at service limit state after all losses Area of strand (at section 5) fpu fpy = 0.9fpu fpt = 0.75fpu fpe = 0.8fpy Aps1 1860 1674 1395 1339 5922.0 MPa MPa MPa MPa mm2 The number of identical n 5.0 Density of concrete yc 2500 Kg/m Specified compressive strength of Concrete f'c 40 MPa Specified compressive strength of Concrete at time of stress transfer f'ci = 0.9f'c 36 MPa 1.97E+05 MPa Elastic modulus of Prestressing Steel Ep Elastic modulus of Concrete Ec 33990 MPa Stress in Prestressing steel at jacking fpj = 0.72fpu 1339 MPa Friction and anchor set: Loss due to Friction and Anchor set Unit Sec - Sec - Sec - Sec - Sec - 2012.5 4025 8050 16100 T1 249 232 217 186 134 N/mm2 T2 249 232 217 186 134 N/mm2 T3 249 232 217 186 134 N/mm2 T4 249 232 217 186 134 N/mm2 T5 249 232 217 186 134 N/mm2 Average 248.67 232.05 216.80 185.69 133.95 N/mm2 Loss due to Elastic shortening ∆fpES =(n-1)*Ep*fcgp/(2*n*Eci) Eci Modulus of elasticity of concrete at transfer Eci = 0.043*yc(1.5)*(fci')(0.5) = 32250 MPa n is the number of identical tendon fcgp Sum of concrete stresses at the center of gravity of prestressing tendons due to prestressing force at trasfer and the self-weight of the member at the section of maximum moment fcgp = fo + fp 26.0 MPa fo due to self - weight of girder fo = Mo*e / Ix = 0.00 MPa Mo Moment due to self-weight of girder fp due to prestressing steel : f p = N/ A + N*e*e/Ix 26.01 MPa 7710444 N = 0.7*fpu*Aps1 = e : Distance from CGS to center of gravity of girder -647 mm Unit Sum of concrete stress at CGS f cgp Loss due to elastic shortening ∆fpES N/mm2 N/mm2 Sec - 26.0 66.2 Sec - 26.0 66.2 Sec - 26.0 66.2 Sec - 26.0 66.2 Sec - 26.0 66.2 Sec - 80 34.6 Sec - 80 34.6 Sec - 80 34.6 Sec - 80 34.6 Sec - 26.0 -6.98 263.3 Sec - 26.0 -6.98 263.3 Loss due to Shrinkage ∆fpSR = (117-1.03*H) The average annual ambient relative humidity H Loss due to Shrinkage ∆fpSR Unit % N/mm2 Sec - 80 34.6 Loss due to Creep ∆fpCR = 12.0 *fcgp - 7.0*∆fcdp ≥ ∆fcdp change in concrete stress at center of gravity of prestressing steel due to permanent loads, with the exception of the load acting at the time the prestressing force is applied ∆fcdp = Msw *e/Ix -6.98 MPa Msw : Moment due to self - weight of deck slab , surface, railing and parapet Msw = 2,442,443,626 N.mm Sum of concrete stress at CGS f cgp Change in concrete stress at CGS ∆fcdp Loss due to Creep ∆fpCR Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Unit N/mm2 N/mm2 N/mm2 Sec - 26.0 -6.98 263.3 Sec - 26.0 -6.98 263.3 Sec - 26.0 -6.98 263.3 03 Calculation I-Beam_I33m.xls【Prestress_1】 SHEET NO : / Loss due to relaxation Loss due to relaxation at transfer (Initial stage) ∆fpR1 = log(24.0*t) / 40.0*[fpj / fpy - 0.55]*fpj fpj : initial stress in strand at the end of prestressing = 0.75*fpu Loss due to relaxation at after transfer (final stage) ∆fpR2 = (138 - 0.4*∆fpES - 0.2*(∆fpSR + ∆fpCR))*30% Unit Sec - Sec - Time estimated in day from stressing to transfer (t) Day 14 14 Loss due to relaxation at transfer ∆fpR1 25.0 25.0 N/mm2 Loss due to relaxation after transfer ∆fpR2 15.6 15.6 N/mm2 3.6.2 Sec - 14 25.0 15.6 Sec - 14 25.0 15.6 Sec - 14 25.0 15.6 Internal forces due to prestressing Bending moment, shear force and normal force due to prestressing INITIAL STAGE AT TRANSFER Initial prestress σi = Jacking stress σj - (prestress losses due to relaxation at transfer and Elastic shortening) Jacking stress σj = stress in prestressing steel immidiately prior to transfer f pt σj = fpt Normal force N = σi1*Aps1 (A'ps1) + σi2*Aps2 Shear force V = Moment M = σi1*Aps1(A'ps1)*d1 - σi2*Aps2*d2 d1 Distance from CGS at bottom fibre to neutral axles d2 Distance from CGS at top fibre to neutral axles A'ps1 for Section and Section Unit Number of bottom fiber strands Area of bottom fiber strands Aps1 Total of Losses due to relaxation + ES+ FR+AS Jacking stress at bottom fibre σj1 Initial stress at bottom fibre σi1 Distance from CGS at bottom fibre to neutral axles d mm2 N/mm2 N/mm2 N/mm2 mm Sec - 5922 340 1395 1055 69 Sec - 5922 323 1395 1072 206 Sec - 5922 308 1395 1087 319 Angle in vertical plan between tendon and reinforecement rad 0.09 0.08 0.07 Normal force N N 6.25E+06 6.35E+06 6.44E+06 Shear force V N -530497 -519877 -452818 Moment M N.mm 0.00E+00 -1.31E+09 -2.06E+09 FINAL STAGE AT SERVICE Prestress σi = Jacking stress σj - (total losses of prestress) Sec - 5922 277 1395 1118 498 Sec - 5 5922 225 1395 1170 647 0.05 6.62E+06 -317054 -3.30E+09 6.93E+06 -4.48E+09 Sec - 590 1339 749 874 Sec - 539 1339 801 1025 0.05 4.43E+06 -212334 -3.88E+09 4.74E+06 -4.86E+09 Jacking stress sj = Stress in Prestressing steel at service limit state after all losses f pe σj = fpe Normal force N = σi1*Aps1 (A'ps1) + σi2*Aps2 Shear force V = M = σi1*Aps1(A'ps1)*d1 - σi2*Aps2*d2 Moment d1 Distance from CGS at bottom fibre to neutral axles d2 Distance from CGS at top fibre to neutral axles A'ps1 for Section and Section Total of Losses Jacking stress at bottom fibre σj1 Stress at bottom fibre σi1 Distance from CGS at bottom fibre to neutral axles d Unit N/mm2 N/mm2 N/mm2 mm Angle in vertical plan between tendon and reinforecement rad Normal force N N Shear force V N Moment M N.mm Where : CGS : Central gravity of strand Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Sec - 653 1339 686 325 0.09 4.06E+06 -344822 0.00E+00 Sec - 637 1339 702 500 Sec - 621 1339 718 666 0.08 0.07 4.16E+06 4.25E+06 -340740 -298977 -2.08E+09 -2.83E+09 03 Calculation I-Beam_I33m.xls【Summary】 SHEET NO : / 3.7 Summary of sectional forces 3.7.1 Summary of sectional forces for initial stage(at tranfer) Self - Weight of Girder (DL1) Initial prestress (Ps) Self - Weight of deck (DL2) N V M N V M N V M Unit N N N.mm N N N.mm N N N.mm Section - 289,929 6,248,657 -530,497 0 239,198 Section - Section - 0 253,688 217,447 547,014,790 1,021,094,274 6,347,076 6,437,393 -519,877 -452,818 -1,310,320,232 -2,055,517,122 0 209,298 179,398 451,298,755 842,424,343 Section - Section - 0 144,965 1,750,447,327 2,333,929,769 6,621,610 6,928,018 -317,054 -3,296,699,654 -4,480,542,171 0 119,599 1,444,156,017 1,925,541,355 3.7.2 Summary of sectional forces for final stage(service stage) N Self - Weight of deck (DL2) V M N Self-Weight of railing, parapet, Barrier(DL3) V M N Self - Weight of surface (DW) V M N Live load plus impact (LL + IM) V M N Prestress (Ps) V M Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Unit N N N.mm N N N.mm N N N.mm N N N.mm N N N.mm Section - 239,198 0 60,217 0 3,995 0 57,922 4,061,613 -344,822 Section - 209,298 451,298,755 52,690 113,612,430 3,495 7,536,540 102,422 Section - 179,398 842,424,343 45,163 212,076,535 2,996 14,068,209 93,320 Section - 119,599 1,444,156,017 30,108 363,559,774 1,997 24,116,929 75,870 Section - 0 1,925,541,355 0 484,746,366 0 32,155,905 43,986 644,156,255 1,197,866,269 2,120,315,045 2,801,935,057 4,160,032 4,250,349 -340,740 -298,977 -2,080,271,462 -2,830,316,585 4,434,566 4,740,974 -212,334 -3,877,120,207 -4,858,630,988 03 Calculation I-Beam_I33m.xls【Checking 1_1】 SHEET NO : / Checking for initial stage at transfer Specified compressive strength of Concrete at time of initial prestressing Compressive stress limit Tensile stresses limit f'c f'ci = 0.9*f'c [ f1 ] = 0.6*f'ci [ f2 ] = 0.25*(f'ci )0.5