BANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANH

BANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANH

02 Calculation I-Beam_I25.7m.xls【Input_material】 SHEET NO : / 1.MATERIAL DATA Girder length Thickness of Slab Width of Slab Beam numbers Strand type Nominal area of strands No of strands 1.4 Material strength & Stress Limits: 1.4.1 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 : : : : : : = 25700 200 2350 12.7 98.7 mm 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 1.4.2 Reinforcement Yield strength Limit of tensile stress at service Elastic Modulus : : : f'sy = f'sa=0.6fsy = Es = 400 MPa 240 MPa 2.00E+05 MPa 1.4.3 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 : 1.5 0.5 Elastic Modulus : 0.043gc (f'c) : 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 : 1.5 0.5 Elastic Modulus : 0.043gc (f'c) : Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Ld TS BS Nd 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(f'c)0.5 = Ec2 = 30 MPa 13.5 12 2.74 29440 MPa MPa MPa MPa 02 Calculation I-Beam_I25.7m.xls【Input_section】 SHEET NO : / SECTION PROPERTIES 2.1 1-1 1-1 - 2, 2-2 3-3 3-3,4-4,5-5 - 4, - Section Input Section SEC-1 SEC-2 SEC-3 SEC-4 SEC-5 B1 (mm) 600 600 600 600 600 B2 (mm) 800 800 800 800 800 B3 (mm) 600 460 293 200 200 B4 (mm) H1 (mm) 80 80 80 80 80 600 600 600 600 H2 (mm) 120 120 120 120 120 H3 (mm) 37 62 93 110 110 H4 (mm) 1213 867 754 690 690 H5 (mm) 70 153 200 200 H6 (mm) 250 250 250 250 Section Properties (Origin) Section SEC-1 SEC-2 SEC-3 SEC-4 SEC-5 H Area (mm2) 897,700 768,980 634,061 567,000 567,000 (mm) 1450 1449 1450 1450 1450 Extreme fibre Top y' Bottom y (mm) (mm) 707 707 712 718 718 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 hole Area of hole Inertia of hole Section Row of cable No of cable (No) R1 R2 R3 R4 R5 all 1 1 Distance from bottom of fibre (at) 1156 920 684 452 220 686.4 Area of steel equivale n 4004.33 4004.33 4004.33 4004.33 4004.33 Included Oval holes Section Properties area inc holes (mm2) 886249 Yt inc holes (mm) 707 Yb inc holes (mm) 743 Ix inc holes (mm4) 160070283812 No of cable (No) 1 1 = = = = = 5.796 0.8661 690.90 29.66 54.00 2290.22 417393 Section Section Distance from bottom of fibre (at) 962 755 548 368 189 564.4 Distance from bottom of fibre (at) 788 606 425 293 161 454.6 Distance from bottom of fibre (at) 519 378 236 178 119 286 Area of steel equivale n 4004.33 4004.33 4004.33 4004.33 4004.33 Section 757529 704 745 151694336504 Section 906271 708 742 162326736074 Section Sevice stage Properties area sv (mm2) Ytslab sv (mm) Yt sv (mm) Yb sv (mm) Ix sv (mm4) Section 1313355 657 457 992.598 346976886001 Section 777551 709 740 153828298534 1184635 631 431 1018 329944321913 Inertia Ix (mm4) 161,363,264,548 152,060,058,145 144,813,222,748 141,714,366,383 141,714,366,383 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 743 742 738 732 732 Bending Modulus Top W' Bottom W (mm3) (mm3) 228,156,873 217,250,236 215,146,747 204,870,204 203,304,088 196,303,312 197,302,365 193,667,610 197,302,365 193,667,610 No of cable (No) 1 1 Area of steel equivale n 4004.33 4004.33 4004.33 4004.33 4004.33 Section 622610 707 743 144372240969 Section 642632 716 734 146974772379 Section 1049716 600 400 1050 314303438731 No of cable (No) 1 1 Section Area of steel equivale n 4004.33 4004.33 4004.33 4004.33 4004.33 Section 555549 709 741 140974687562 Section 575571 725 725 145393896405 Section 982655 583 383 1067 308999693990 No of cable (No) 1 1 Distance from bottom of fibre (at) 305 195 85 85 85 151 Area of steel equivale n 4004.33 4004.33 4004.33 4004.33 4004.33 Section 555549 706 744 140555084180 Section 575571 727 723 147499185357 Section 982655 584 384 1066 311896727716 02 Calculation I-Beam_I25.7m.xls【sectionpro】 SHEET NO : / 2.2 Sumary of Section Properties 2.2.1 Cross Section Properties (Oval holes included) Cross section Section Area mm 2.2.2 Bending Modulus Inertia Top y' Bottom y Top W' Bottom W Ix Iy mm mm mm3 mm3 mm4 mm4 SEC-1 886,249 707 743 226,561,937 215,298,382 160,070,283,812 SEC-2 757,529 704 745 215,448,718 203,639,953 151,694,336,504 SEC-3 622,610 707 743 204,177,508 194,333,890 144,372,240,969 SEC-4 555,549 709 741 198,815,718 190,267,766 140,974,687,562 SEC-5 555,549 706 744 199,004,920 188,991,661 140,555,084,180 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-1 906,271 708 742 229,346,340 218,704,320 162,326,736,074 SEC-2 777,551 709 740 217,046,661 207,801,319 153,828,298,534 SEC-3 642,632 716 734 205,250,742 200,258,369 146,974,772,379 SEC-4 575,571 725 725 200,571,755 200,514,864 145,393,896,405 SEC-5 575,571 727 723 202,913,312 203,983,809 147,499,185,357 Composite Section Properties for final stage (service stage) Area Section mm Extreme fibre Bending Modulus Inertia Top y3' Bottom y3 Top W3' Bottom W3 Ix Iy mm mm mm3 mm3 mm4 mm4 SEC-1 1,313,355 657 993 527,799,882 349,564,487 346,976,886,001 SEC-2 1,184,635 631 1,018 523,037,949 324,053,964 329,944,321,913 SEC-3 1,049,716 600 1,050 524,191,054 299,221,794 314,303,438,731 SEC-4 982,655 583 1,067 529,864,796 289,642,063 308,999,693,990 SEC-5 982,655 584 1,066 533,754,873 292,680,636 311,896,727,716 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 02 Calculation I-Beam_I25.7m.xls【Internal force】 SHEET NO : / 3.1 Internal forces Due to S.W of Girder (DL1) A B 12850 3750 4050 200 200 200 3850 120 110 690 250200 1000 250 1450 200 80 600 8350 4150 350 12500 A A - A 00 80 00 100 690 1450 250 200 1213 1450 B B -B 00 110120 80 800 600 37 120 80 100 20 00 0 600 L1= 1600 L2= 886248.89 Fsec2= Fsec1= W = Σ(FsecixLix0.0000025x9.8066)/ΣLi = 00 8300 754429.39 15.700 N/mm W= L3= Fsec3= 15800 555548.89 15.700 N/mm Ltt=25.00 m Bending Moment and Shear forces due to S.W of Girder (DL1) Component Unit Sec - Sec - Sec - Distance from section to left bearing mm 1,563 3,125 Distance from section to right bearing mm 25,000 23,438 21,875 Moment M N.mm 287,467,534 536,606,064 Shear V N 196,245 171,714 147,183 Due to S.W of Deck Slab and S.W of longitudinal gider (DL2) Bb Tw Tb 3.2 Sec - Sec - 6,250 12,500 18,750 12,500 919,896,110 1,226,528,146 98,122 Bb= 2350 mm Tb= 200 mm Fb=Bb*Tb = 470000 mm2 Wb= Fbx0.0000025x9.8066= 11.523 N/mm W= Bw= 1750 mm Tw= 80 mm Fw=Bw*Tw = 140000 mm2 Ww= Fwx0.0000025x9.8066= 3.432 N/mm Wdr= (2.65*0.2*2*0+2.52*0.2*2)x25/23.3 1.008 N/mm 15.963 N/mm Ltt= 25.00 m W = Wb+Ww+Wdr = 15.963 N / mm Bending Moment and Shear forces due to S.W of deck slab (DL2) Component Unit Sec - Sec - Sec - Distance from section to left bearing mm 1,563 3,125 Distance from section to right bearing mm 25,000 23,438 21,875 Moment M N.mm 292,292,450 545,612,573 Shear V N 199,538 174,596 149,654 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Sec - Sec - 6,250 12,500 18,750 12,500 935,335,840 1,247,114,453 99,769 02 Calculation I-Beam_I25.7m.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= 361000 mm2 Fpc= mm2 SF=(2*Flc+Fpc)= 722000 mm2 Nd= Nos W =(SFx0.0000025x9.8066)/Nd= 3.540 N/mm W= 3.540 N/mm Ltt= 25.00 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 1,563 3,125 6,250 Space from section to right bearing mm 25,000 23,438 21,875 18,750 Moment M N.mm 64,822,679 121,002,335 207,432,574 Shear V N 44,252 38,721 33,189 22,126 3.4 Sec - 12,500 12,500 276,576,766 Due to S.W of surface (DW) W= 2.481 Ltt=25.00 Tlp= Bdeck= Nd W = (Bdesk xTlp * 0.0000023*9.8066)/Nd = Component Section Location Space from section to left bearing Space from section to right bearing Moment M Shear V Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 50 11000 2.481 N/mm m mm mm Nos N / mm Bending Moment and Shear forces due to S.W of Surface (DW) Unit Sec - Sec - Sec - 0L 0.0625L 0.125L mm 1,563 3,125 mm 25,000 23,438 21,875 N.mm 45,429,745 84,802,190 N 31,013 27,137 23,260 Sec - 0.25L 6,250 18,750 145,375,184 15,507 Sec - 0.50L 12,500 12,500 193,833,578 02 Calculation I-Beam_I25.7m.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 = 25000.00 575571 818.00 1.5.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 mm2 mm mm4 Nos 2350.00 mm 200.00 mm 810.00 mm 0.00 Deg 1.06 0.87 1.25 6.15E+11 mm4 1.00 0.6896 g = 0.7305 g = g = 0.2149 0.1870 VEHICULAR LIVE LOADING DATA Unit Standard load Distance from axle to front axle 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 4300 4300 1200 Calculation value of influence line 4.3 Xi P1 P2 MY1 4.3 P1 Ltt P4 P3 MY2 1.2 Xi 4.3 MY3 MY4 4.3 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 25,000 12,500 0 0 0 1.00 0.83 0.66 1.00 0.95 Sec - 0.02L 1,563 23,438 18,310,547 10,986 -49 1465 1196 902 1427 0.94 0.77 0.59 0.94 0.89 Sec - 0.25L 3,125 21,875 34,179,688 9,570 -195 2734 2197 2209 2659 0.88 0.70 0.53 0.88 0.83 VY5 Ltt Sec - 0.50L 6,250 18,750 58,593,750 7,031 -781 1463 4688 3613 4238 4538 0.75 0.58 0.41 0.75 0.70 Sec - 0.50L 12,500 12,500 78,125,000 3,125 -3,125 4100 6250 4100 5950 5950 0.50 0.33 0.16 0.50 0.45 02 Calculation I-Beam_I25.7m.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 - 1,563 3125 6,250 X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) -4,300 -2,738 -1,175 1,950 63,984,375 0 1,563 265,502,930 3,125 495,605,469 6,250 849,609,375 4,300 5,863 216,791,992 7,425 398,183,594 10,550 654,765,625 -4,300 4,300 0 -0.6 0.6 0 482,294,922 -2,738 1,563 5,863 265,502,930 52,329,102 1,562 1,563 124,072,266 196,259,766 0 1,200 495,605,469 96,113,281 3,124 3,126 303,789,063 365,664,063 317,832,031 1,568,359,375 1,950 6,250 10,550 591,718,750 265,078,125 849,609,375 158,046,875 2,055,312,500 8,200 12,500 16,800 1,272,734,375 6,249 6,251 582,656,250 623,906,250 743,125,000 1,132,812,500 179,375,000 2,055,312,500 12,499 12,501 818,125,000 818,125,000 320,332,031 669,453,125 1,206,562,500 170,288,086 317,871,094 544,921,875 726,562,500 476,716,343 885,126,017 1,543,766,382 2,032,178,682 Sec - X(mm) V(N) 8,600 4,300 893,789,063 -1,175 3,125 7,425 X(mm) 8,200 12,500 16,800 Sec - 12500 M(N.mm) 179,375,000 1,132,812,500 743,125,000 16,772 105,923 122,696 80,356 80,356 116,250 51,353 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 - 1,563 3125 6250 X(mm) V(N) X(mm) V(N) X(mm) 10,163 5,863 1,563 1,563 2,763 25,966 138,747 169,922 334,634 128,906 122,306 251,213 102,173 93,876 11,725 7,425 3,125 3,125 4,325 23,231 127,419 158,594 309,244 120,313 113,713 234,025 89,004 85,589 14,850 10,550 6,250 6,250 7,450 1,636,250,000 Sec - 12500 V(N) X(mm) V(N) 17,763 104,763 135,938 258,463 103,125 96,525 199,650 65,391 69,601 21,100 16,800 12,500 6,825 59,450 90,625 156,900 68,750 62,150 130,900 29,063 39,966 12,500 13,700 02 Calculation I-Beam_I25.7m.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 3454.5 n yc Specified compressive strength of Concrete f'c Specified compressive strength of Concrete at time of stress transfer f'ci = 0.9f'c Elastic modulus of Prestressing Steel Ep Elastic modulus of Concrete Ec Stress in Prestressing steel at jacking fpj = 0.72fpu 5.0 2500 40 36 1.97E+05 33990 1339 The number of identical Density of concrete Loss due to Friction and Anchor set T1 T2 T3 T4 T5 Average Friction and anchor set: Unit Sec - Sec - 1562.5 250 230 N/mm2 250 230 N/mm2 250 230 N/mm2 250 230 N/mm2 250 230 N/mm2 249.86 230.04 N/mm2 Loss due to Elastic shortening MPa MPa MPa MPa mm2 Kg/m3 MPa MPa MPa MPa MPa Sec - 3125 220 220 220 220 220 219.59 Sec - 6250 200 200 200 200 200 199.84 Sec - 12500 156 156 156 156 156 156.08 ∆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) = n is the number of identical tendon 32250 MPa 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 17.8 MPa fo due to self - weight of girder 0.00 MPa fo = Mo*e / Ix = Mo Moment due to self-weight of girder fp due to prestressing steel : fp = N/ A + N*e*e/Ix 17.79 MPa N = 0.7*fpu*Aps1 = 4497759 e : Distance from CGS to center of gravity of girder -572 mm Unit Sum of concrete stress at CGS fcgp Loss due to elastic shortening ∆fpES N/mm2 N/mm2 Sec - 17.8 43.5 Sec - 17.8 43.5 Sec - 17.8 43.5 Sec - 17.8 43.5 Sec - 17.8 43.5 Sec - 80 25.0 Sec - 80 25.0 Sec - 80 25.0 Sec - 80 25.0 Sec - 17.8 -6.66 166.9 Sec - 17.8 -6.66 166.9 Loss due to Shrinkage ∆fpSR = (93-0.85*H) The average annual ambient relative humidity H Loss due to Shrinkage ∆fpSR Unit % N/mm2 Sec - 80 25.0 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 -6.66 MPa Msw : Moment due to self - weight of deck slab , surface, railing and parapet Msw = 1,717,524,797 N.mm Sum of concrete stress at CGS fcgp 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 - 17.8 -6.66 166.9 Sec - 17.8 -6.66 166.9 Sec - 17.8 -6.66 166.9 02 Calculation I-Beam_I25.7m.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 = 0.72*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 24.7 24.7 N/mm2 3.6.2 Sec - 14 25.0 24.7 Sec - 14 25.0 24.7 Sec - 14 25.0 24.7 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 Sec - 3454.5 268 1395 1127 439 Sec - 5 3454.5 225 1395 1170 572 0.08 0.07 3.79E+06 3.82E+06 -316679 -274329 0.05 3.89E+06 -206193 4.04E+06 N.mm 0.00E+00 -6.66E+08 -1.07E+09 FINAL STAGE AT SERVICE Prestress σi = Jacking stress σj - (total losses of prestress) 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 = 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 -1.71E+09 -2.31E+09 Sec - 485 1339 854 781 Sec - 441 1339 898 915 0.05 2.95E+06 -156348 -2.30E+09 3.10E+06 -2.84E+09 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 d1 mm2 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 0.08 3.72E+06 -300576 Sec - 3454.5 298 1395 1097 176 Sec - 3454.5 288 1395 1107 279 M Total of Losses Jacking stress at bottom fibre σj1 Stress at bottom fibre σi1 Distance from CGS at bottom fibre to neutral axles d1 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 : Sec - 3454.5 318 1395 1077 56 CGS : Central gravity of strand Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Sec - 535 1339 804 306 0.08 2.78E+06 -224539 0.00E+00 Sec - 515 1339 824 454 Sec - 505 1339 835 596 0.08 0.07 2.85E+06 2.88E+06 -238016 -206829 -1.29E+09 -1.72E+09 02 Calculation I-Beam_I25.7m.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 - 196,245 3,719,456 -300,576 0 199,538 Section - 171,714 287,467,534 3,787,916 -316,679 -666,166,502 174,596 292,292,450 Section - 147,183 536,606,064 3,824,016 -274,329 -1,068,146,202 149,654 545,612,573 Section - 98,122 919,896,110 3,892,251 -206,193 -1,709,098,460 99,769 935,335,840 Section - 0 1,226,528,146 4,043,399 -2,313,198,546 0 1,247,114,453 Section - 174,596 292,292,450 38,721 64,822,679 27,137 45,429,745 93,876 476,716,343 2,847,005 -238,016 -1,291,905,757 Section - 149,654 545,612,573 33,189 121,002,335 23,260 84,802,190 85,589 885,126,017 2,883,106 -206,829 -1,717,762,640 Section - 99,769 935,335,840 22,126 207,432,574 15,507 145,375,184 69,601 1,543,766,382 2,951,340 -156,348 -2,304,503,700 Section - 0 1,247,114,453 0 276,576,766 0 193,833,578 39,966 2,032,178,682 3,102,488 -2,837,707,680 3.7.2 Summary of sectional forces for final stage(service stage) N 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 Self - Weight of deck (DL2) 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 - 199,538 0 44,252 0 31,013 0 51,353 2,778,545 -224,539 02 Calculation I-Beam_I25.7m.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 40 36 21.6 1.38 f'c f'ci = 0.9*f'c [ f1 ] = 0.6*f'ci 0.5 [ f2 ] = 0.25*(f'ci )