D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m I STRUCTURAL PARAMETER: Design standard Type of beam Number of beam Width of deck Width of sidewalk Width of median Length of span Spacing from beam top to bearing centerline Design length Height of deck slab Height of beam section Spacing of beams Deck overlay Diameter of wastewater pipe : : : B : BPL : L : : Ls hb h S II STRENGTH AND ULTIMATE STRESS OF MATERIAL 2.1 Steel: 2.1.1 Prestress reinforcement Type of stress Modulus of elasticity Required tensile strength of prestressing steel Liquid limit of prestreesing steel Before the force transferred to concrete After stress loss : : : : : : Ep fpu fpy 22TCN272-05 Super T 11 26.30 m 2.00 m 1.3 m 38.30 m 0.35 m 37.60 m 200 mm 1,750 mm 2,370 mm 70 mm 630 mm = 0.9 fpu = 0.75 f pu = 0.80 f py Area of reinforcement, class of 15.2mm Tension strength desinged for tendon Ppj Stress of reinforcement during kicking fpj 2.1.2 High-strength steel bar Under standard 22TCN 272-05 Modulus of elasticity Ep Required tensile strength of steel bar fpu Liquid limit of steel bar fpy = 0.8 fpu 2.1.3 Plain reiforcement Under standard TCVN 1651:2008 Modulus of elasticity Es Liquid limit strength of reinforcement CB400-V fsy Liquid limit strength of reinforcement CB300-T fsyr 2.2 Concrete Density of concrete γc ######### Thermal expansion coefficient of concrete Mean humidity H 2.2.1 Main beam Theoretical compressive strength of concrete at 28 age days f'c Concrete compressive strength when tranfering force f'ci = 0.85 f' c Ec = 0.043 yc1.5 f'c0.5 Modulus of elasticity Shear bearing capacity of plain concrete Ultimate stress of concrete Ultimate compressive stress when force tranfer applied fr Ultimate tension stress when force tranfer applied Ultimate compressive stress when losing stress * Prestressing + long-term load * Live load +1/2(prestressing+long-term load) * Prestressing + Long-term load + Live load Tension stress after losing stress 2.2.2 Bridge deck Theoretical compressive strength of concrete at 28 age days Modulus of elasticity Ultimate compressive stress when losing stress * Prestressing + long-term load = = Dr Songkiat Dated 4/21/2010 ### mm Pretension stress 197,000 (MPa) 1,860 (MPa) 1,674 (MPa) 1,395 (MPa) 1,339 (MPa) (A.5.4.2) (T.5.4.4.1-1) (T.5.4.4.1-1) (T.5.9.3-1) (T.5.9.3-1) 140 mm2 195 KN 1395 MPa = = = 207,000 (MPa) 1,035 (MPa) 828 (MPa) (A.5.4.4) (T.5.4.4.1-1) (T.5.4.4.1-1) = = = 200,000 (MPa) 400 (Mpa) 300 (Mpa) (A.5.4.3.2) = = = 2,400 (Kg/m³) 10.8E-6 / C 85 % (Bảng 3.5.1) (A.5.4.2.2) = = 50 (MPa) 42.5 (MPa) (A.5.4.2.1) = 35,750 (MPa) (A.5.4.2.1) = 4.45 (MPa) (A.5.4.2.6) = 0.6 f'ci = 25.5 (MPa) (A.5.9.4.1.1) =0.58f'ci0.5 = 3.78 (MPa) (T5.9.4.1.2) = 0.45 f' c = 0.4 f'c = 0.6 f'c = = = 22.5 (MPa) 20 (Mpa) 30 (Mpa) (T5.9.4.2.1-1) (T5.9.4.2.1-1) (T5.9.4.2.1-1) = 0.5 f'c0.5 = 3.54 (Mpa) (T5.9.4.2.2-1) f'cs = 35 (MPa) (A.5.4.2.1) Ecs = 0.043 yc1.5 f'cs0 = 29,910 (MPa) (A.5.4.2.1) = 15.8 (MPa) (T5.9.4.2.1-1) = 2.96 (Mpa) (T5.9.4.2.2-1) = Page: : = = = = = Phucdh Checked by =0.63f'c0.5 = 0.45f'cs Tension stress after losing stress => be = Calculated by 0.5f'cs0.5 Initial Data D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 2.3 Material conversion factor Prestressing reinforcement/Concrete of main beam Rpc = Ep / Ec Reinforcement/Concrete of main beam Rsc = Es / Ec Concrete of bridge deck/Concrete of main beam Rdc = Ecs / Ec Load and impact During construction, the following loads shall be considered and calculated - Self weight of beam - Tensile force of prestressing strand - Effect of creep shrinkage during construction During the using, there are additional loads as follows - Effect of creep shrinkage during the using - Weigth of dead load , part (bridge deck, hand rail, wheel guard) - Live load of vehicle 3.1 Design live load effects on one main beam 3.1.1 Dead load of seft beam - Dead load of seft beam, DC1= 18.27 - Lead load of divided wall, DC2= 0.32 - Concrete of bridge deck, DC3= 11.16 - Remaining formwork, DC4= 1.00 Total: 30.75 3.1.2 Weigth of dead load, part - Hand rail, sidewalk, DC5= 2.50 - Deck overlay, DW= 3.77 Total: 6.27 3.2 Live load 3.2.1 Live load of vehicle Carriage-way width Bx = 21.00 Number of lanes as designed nx = Coefficient of lane m= 0.65 Designed live load of vehicle HL-93 consists one combination of Design truck and load of lane or two-axled truck and load of lane 3.2.2 Designed truck has total of weight 325 kN = = = 5.51 5.59 0.84 kN/m kN/m kN/m kN/m kN/m kN/m kN/m kN/m (Calculation for exteior beam) m lane 4.3 m 4.3 to m P3 P2 35 kN 145 kN 145 kN 3.2.3 Designed two-axled truck Two-axled truck consists a pair of axles 110 kN, apart 1.2m Horizontal spacing of wheels is 1.8m, total weigth of vehicle is : 220 KN Impact coefficient follows to Clause 3.6.2 - Standard 22TCN272-05 1.20 m P1 110 kN 110 kN 3.2.4 Designed load of lane qL Stressing force of designed load of lane does not include impact coefficient 3.2.5 Live load of pedestrian (PL) Width of road for pedestrian Bpl = Number of lanes for pedestrian npl = Load for pedestrian Uniform load of pedestrian according to longitudinal of bridge PL = qpl = 9.3 kN/m 2.00 m 3.0 kN/m2 6.0 kN/m/1side III DISTRIBUTION COEFFICIENT Calculate the horizontal distribution coefficient due to live load Look up the table 4.6.2.2.1-1, we have the formula for computation of horizontal distribution coefficient as follows: The values used for computation : + Nb : Number of beam = 11 beam Page: Initial Data D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls +S : Spacing of beams +L : Span of beam + ts : Thickness of concrete slab of bridge deck +n : Ratio of elasticity modulus +d : Height of main beam 1.1 Distribution coefficient of moment * Internal beam • One design lane loaded = = = = = 2370 38300 200 0.837 1750 = 0.32 = 0.55 = 0.39 = = 0.00 mm 0.97 = 0.53 gV = (S/3050)0.6(d/L)0.1 • Two or more design lanes loaded = 0.63 gV = (S/2250)0.8(d/L)0.1 = 0.77 gM = (S/910)0,35(Sd/L2)0,25 • Two or more design lanes loaded gM = (S/1900)0,6(Sd/L2)0,125 mm mm mm mm * Exterior beam • One design lane loaded gMSE • Two or more design lanes loaded de = e = 0,97 + d e/8700 gMSE = 1,2gM = egM 1.2 Distribution coefficient of shear force * Internal beam • One design lane loaded * Exterior beam • One design lane loaded, lever rule P/2 P/2 R1 R1 = P/2*1070/2370 = 0.23 P gVSE = 1.2R1 =1.2x0.23 = 0.27 P • Two or more design lanes loaded e = 0,8 + d e/3050 gVSE Effect of skewed bridge (4.6.2.2.2d) = egV = 0.80 = 0.61 • Skewed bridge θ = 0o Reduction of distribution coefficient of load for moment of longitudinal beam on skewed support min(1.05-0.25tgθ ; 1) = 1.00 Adjustment of distribution coefficient of load for shear force of the longitudinal beam on skewed support + ((Ld)0.5/6S)tan(θ) Computation result of distribution coefficient of load Position of beam Internal Internal Exterior Exterior = Number of lane ≥2 MAX ≥2 MAX 1.00 gM 0.32 0.55 0.55 0.39 0.53 0.53 gV 0.63 0.77 0.77 0.27 0.61 0.61 IV PERIOD OF COMPUTATION Structure to be analysed through phases as follows: Phase - Computation with load: + Dead live of self section of beam (DC) + Dead load of divided wall (DC) + Acting of Prestressing (PS) Page: Initial Data D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls Phase - Computation with load: + Dead load of self beam (DC) 18.27 + Dead load of divided wall (DC) 0.32 + Dead load of self deck (DC) 11.16 + Dead load of remaining formwork 1.00 + Hand rail, sidewalk (DC) 2.50 + Dead load of deck overlays (DW) 3.77 + Wastewater treatment pipe (P) 3.33 + Live load of vehicle (combined compact stress) LL+ IM; human V LOAD COMBINATION Adjustment coefficient of load Adjustment coefficient of load : Relative coefficients Strength limit state Service limit state η= ηDηRηΙ Flexibility ηD 1.00 1.00 Strength limit states and load combination coefficient: Load combination at strength limit state I η{1.25DC+1.5DW+1.2P+1.75PL + 1.75(LL+IM)} Load combination at service limit state η{DC+DW+P+PL+(LL+IM)} Page: kN/m/1beam kN/m/1beam kN/m/1beam kN/m/1beam kN/m/1beam kN/m/1beam kN/m/1beam (1.3.2) Redundancy ηR 1.00 1.00 Importance ηI 1.05 1.00 η 1.05 1.00 (3.4) Initial Data D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m Calculated by Phucdh Checked by Dr Songkiat Dated 4/21/2010 MORPHOLOGIC FEATURE OF SECTION I.INTRODUCTION: Character of reinforcement concrete section shall be calculated in 41 positions of length of beam (0.025Ls for section) Character of section shall be calculated with two main states First state : Beam combinate strand before concreting bridge deck Second state : Beam combinate strand and bridge deck at the time of using II CHARACTER OF BEAM COMPUTATION SECTION Height of beam : 1,750 (mm) Height of beginning section of beam : 800 (mm) Height of bridge deck : 200 (mm) Width conversion of deck slab : 1,983 (mm) Length of beginning section of beam : 850 (mm) : 1,425 (mm) Length of plain section : Length of hollow section 33,750 (mm) Section Stage I (at the completion time of tensile) f sup Aconc Iconc e conc Astrand Istrand estrand A*e (mm) 940 1,880 2,820 3,760 4,700 5,640 6,580 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 16,920 17,860 18,800 Section f sup (mm) 940 1,880 2,820 3,760 4,700 5,640 6,580 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 (m2) 0.943 1.671 1.671 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 (m4) 0.056 0.456 0.456 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 (m) 1.399 0.993 0.993 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 Aconc Iconc econc (m2) 0.943 1.671 1.671 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 0.692 (m4) 0.056 0.456 0.456 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 0.265 (m) 1.399 0.993 0.993 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 0.888 (m2) 0.002 0.015 0.015 0.018 0.025 0.028 0.028 0.033 0.033 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 (m4) 0.000 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 (m) 1.675 0.306 0.306 0.277 0.237 0.226 0.226 0.211 0.211 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 (m3) 1.322 1.663 1.663 0.619 0.620 0.621 0.621 0.621 0.621 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 AcombI (m2) 0.945 1.686 1.686 0.710 0.717 0.720 0.720 0.725 0.725 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 Stage I (at the time of concreting the bridge deck) Astrand Istrand estrand A*e AcombI (m2) 0.002 0.014 0.014 0.017 0.023 0.026 0.026 0.031 0.031 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 Page: (m4) 0.000 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 (m) 1.675 0.306 0.306 0.277 0.237 0.226 0.226 0.211 0.211 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 (m3) 1.322 1.663 1.663 0.619 0.620 0.620 0.620 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 0.621 (m2) 0.945 1.685 1.685 0.709 0.715 0.718 0.718 0.723 0.723 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 IcombI (m4) 0.057 0.466 0.466 0.276 0.279 0.281 0.281 0.284 0.284 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 IcombI (m4) 0.056 0.466 0.466 0.275 0.278 0.280 0.280 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 ecombI (m) 1.400 0.987 0.987 0.872 0.865 0.862 0.862 0.857 0.857 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 ecombI (m) 1.400 0.987 0.987 0.873 0.867 0.864 0.864 0.859 0.859 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 Section D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 16,920 17,860 18,800 Section f sup (mm) 940 1,880 2,820 3,760 4,700 5,640 6,580 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 16,920 17,860 18,800 0.692 0.692 0.692 AcombI (m2) 0.945 1.685 1.685 0.709 0.715 0.718 0.718 0.723 0.723 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.265 0.265 0.265 IcombI (m4) 0.056 0.466 0.466 0.275 0.278 0.280 0.280 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.888 0.888 0.888 ecombI (m) 1.400 0.987 0.987 0.873 0.867 0.864 0.864 0.859 0.859 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.032 0.032 0.032 0.004 0.004 0.004 0.210 0.210 0.210 0.621 0.621 0.621 Aslab Stage II (At service) Islab eslab A*e (m2) 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 0.397 (m4) 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 (m3) 2.056 2.397 2.397 1.353 1.353 1.354 1.354 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 1.355 Page: (m) 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 1.850 0.724 0.724 0.724 AcombI (m2) 1.341 2.081 2.081 1.106 1.112 1.115 1.115 1.119 1.119 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 0.283 0.283 0.283 IcombI (m4) 0.114 0.706 0.706 0.519 0.526 0.530 0.530 0.535 0.535 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.857 0.857 0.857 ecombI (m) 1.533 1.151 1.151 1.224 1.217 1.215 1.215 1.210 1.210 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 Section D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE Calculated by Phucdh Checked by Dr Songkiat STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m Dated 4/21/2010 POSITION OF TENDONS I DIMENSION OF MAIN BEAM Calculated length : 37.60 (mm) Height of beam : 1,750 (mm) Height of section of beam edge 800 (mm) Length of section at the beam edge 850 (mm) At the time of completion of tensile Elasticity modulus of concrete when 32,959 Mpa Force transfer applied 197,000 Mpa Elasticity modulus of tendon Diameter of wire : 15.2 (mm) Conversion factor : 6.0 At the time of concreting the bridge deck Elasticity modulus of concrete when 35,750 Mpa concreting the bridge deck Elasticity modulus of tendon 197,000 Mpa Diameter of wire : 15.2 (mm) Conversion factor : Period of service Elasticity modulus of concrete when force transfer applied Elasticity modulus of tendon Diameter of wire : Conversion factor 5.5 140 (mm2) 837 (mm2) 1,589 (mm4) 56,757 (mm4) 140 (mm2) 771 (mm2) 1,589 (mm4) 48,243 (mm4) 140 (mm2) 771 (mm2) 1,589 (mm4) 48,243 (mm4) 35,750 Mpa 197,000 Mpa 15.2 (mm) : 5.5 II POSITION OF STRAND From CL -510 -300 -250 -200 -150 -100 -50 50 100 150 200 250 300 510 Total of tendons Position of tendon 10 11 12 13 14 15 Row A 75 Debonded length (mm) Row B Row C Row D 125 175 225 Row E 1675 0 2000 3000 6000 6000 3000 2000 0 0 3000 4000 6000 3000 3000 6000 4000 3000 0 3000 4000 6000 8000 2000 8000 6000 4000 3000 2000 11 13 12 42 strand III CHARACTER OF TENDON SECTION: AT THE COMPLETION TIME OF FORCE TRANFER Section 0.025Ls 0.050Ls 0.075Ls 0.100Ls 0.125Ls 0.150Ls 0.175Ls Position 940 1,880 2,820 3,760 4,700 5,640 6,580 Row A 5 9 11 Row B 5 11 11 13 Row C 4 8 10 Page: Row D Row E 2 4 4 Total 2 2 2 2 18 18 22 30 34 34 40 Aconversion 1,674 15,062 15,062 18,409 25,104 28,451 28,451 33,471 Distance to bottom of beam 1,675 306 306 277 237 226 226 211 Iconversion 113,514 3,566,311,687 3,566,311,687 3,651,633,104 3,774,283,293 3,798,785,323 3,798,785,323 3,851,434,228 Cable D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 0.200Ls 0.225Ls 0.250Ls 0.275Ls 0.300Ls 0.325Ls 0.350Ls 0.375Ls 0.400Ls 0.425Ls 0.450Ls 0.475Ls 0.500Ls 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 16,920 17,860 18,800 11 11 11 11 11 11 11 11 11 11 11 11 11 13 13 13 13 13 13 13 13 13 13 13 13 13 10 12 12 12 12 12 12 12 12 12 12 12 12 4 4 4 4 4 4 2 2 2 2 2 2 40 42 42 42 42 42 42 42 42 42 42 42 42 33,471 35,145 35,145 35,145 35,145 35,145 35,145 35,145 35,145 35,145 35,145 35,145 35,145 211 210 210 210 210 210 210 210 210 210 210 210 210 3,851,434,228 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 3,853,642,198 AT THE TIME OF CONCRETING THE BRIDGE DECK Section 0.025Ls 0.050Ls 0.075Ls 0.100Ls 0.125Ls 0.150Ls 0.175Ls 0.200Ls 0.225Ls 0.250Ls 0.275Ls 0.300Ls 0.325Ls 0.350Ls 0.375Ls 0.400Ls 0.425Ls 0.450Ls 0.475Ls 0.500Ls Position 940 1,880 2,820 3,760 4,700 5,640 6,580 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 16,920 17,860 18,800 Row A 5 9 11 11 11 11 11 11 11 11 11 11 11 11 11 11 Row B 5 11 11 13 13 13 13 13 13 13 13 13 13 13 13 13 13 Row C Row D 4 8 10 10 12 12 12 12 12 12 12 12 12 12 12 12 Row E 2 4 4 4 4 4 4 4 4 4 Total 2 2 2 2 2 2 2 2 2 2 2 18 18 22 30 34 34 40 40 42 42 42 42 42 42 42 42 42 42 42 42 Aconversion 1,543 13,887 13,887 16,973 23,144 26,230 26,230 30,859 30,859 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 Distance to bottom of beam 1,675 306 306 277 237 226 226 211 211 210 210 210 210 210 210 210 210 210 210 210 210 Iconversion 96,487 3,287,903,404 3,287,903,404 3,366,549,528 3,479,594,744 3,502,168,164 3,502,168,164 3,550,683,552 3,550,683,552 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 PERIOD OF USING Section 0.025Ls 0.050Ls 0.075Ls 0.100Ls 0.125Ls 0.150Ls 0.175Ls 0.200Ls 0.225Ls 0.250Ls 0.275Ls 0.300Ls 0.325Ls 0.350Ls 0.375Ls 0.400Ls 0.425Ls 0.450Ls 0.475Ls 0.500Ls Position 940 1,880 2,820 3,760 4,700 5,640 6,580 7,520 8,460 9,400 10,340 11,280 12,220 13,160 14,100 15,040 15,980 16,920 17,860 18,800 Row A 5 9 11 11 11 11 11 11 11 11 11 11 11 11 11 11 Row B 5 11 11 13 13 13 13 13 13 13 13 13 13 13 13 13 13 Row C 4 8 10 10 12 12 12 12 12 12 12 12 12 12 12 12 Page: Row D Row E 2 4 4 4 4 4 4 4 4 4 Total 2 2 2 2 2 2 2 2 2 2 2 18 18 22 30 34 34 40 40 42 42 42 42 42 42 42 42 42 42 42 42 Aconversion 1,543 13,887 13,887 16,973 23,144 26,230 26,230 30,859 30,859 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 32,402 Distance to bottom of beam 1,675 306 306 277 237 226 226 211 211 210 210 210 210 210 210 210 210 210 210 210 210 Iconversion 96,487 3,287,903,404 3,287,903,404 3,366,549,528 3,479,594,744 3,502,168,164 3,502,168,164 3,550,683,552 3,550,683,552 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 3,552,711,032 Cable D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m Calculated by Checked by Dated Phucdh Dr Songkiat 4/21/2010 COMPUTATION OF INTERNAL FORCE I DESIGNED INTERNAL FORCE DUE TO DEAD LOAD ĐAH Moment ĐAH Shear Table value of influence line for moment Section x y Area (m) (m) (m) (m2) 0.00 0.000 0.000 0.00 0.94 0.940 0.917 17.23 1.88 1.880 1.786 33.58 2.82 2.820 2.609 49.04 3.76 3.760 3.384 63.62 4.70 4.700 4.113 77.32 5.64 5.640 4.794 90.13 6.58 6.580 5.429 102.06 7.52 7.520 6.016 113.10 8.46 8.460 6.557 123.26 9.40 9.400 7.050 132.54 10.34 10.340 7.497 140.93 11.28 11.280 7.896 148.44 12.22 12.220 8.249 155.07 13.16 13.160 8.554 160.82 14.10 14.100 8.813 165.68 15.04 15.040 9.024 169.65 15.98 15.980 9.189 172.74 16.92 16.920 9.306 174.95 17.86 17.860 9.377 176.28 18.80 18.800 9.400 176.72 Section (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 Table value of influence line for shear x y1 y2 Area (+) Area (+) (m) (m) (m) (m2) (m2) 0.000 1.000 0.000 18.800 0.000 0.940 0.975 0.025 17.872 0.012 1.880 0.950 0.050 16.967 0.047 2.820 0.925 0.075 16.086 0.106 3.760 0.900 0.100 15.228 0.188 4.700 0.875 0.125 14.394 0.294 5.640 0.850 0.150 13.583 0.423 6.580 0.825 0.175 12.796 0.576 7.520 0.800 0.200 12.032 0.752 8.460 0.775 0.225 11.292 0.952 9.400 0.750 0.250 10.575 1.175 10.340 0.725 0.275 9.882 1.422 11.280 0.700 0.300 9.212 1.692 12.220 0.675 0.325 8.566 1.986 13.160 0.650 0.350 7.943 2.303 14.100 0.625 0.375 7.344 2.644 15.040 0.600 0.400 6.768 3.008 15.980 0.575 0.425 6.216 3.396 16.920 0.550 0.450 5.687 3.807 17.860 0.525 0.475 5.182 4.242 18.800 0.500 0.500 4.700 4.700 Page: Area (m2) 18.800 17.860 16.920 15.980 15.040 14.100 13.160 12.220 11.280 10.340 9.400 8.460 7.520 6.580 5.640 4.700 3.760 2.820 1.880 0.940 0.000 Loading D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls MOMENT DUE TO DEAD LOAD Phase I Section Load of main beam (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 (KNm) 0.00 314.79 613.45 895.95 1,162.32 1,412.54 1,646.62 1,864.55 2,066.34 2,251.99 2,421.50 2,574.86 2,712.08 2,833.15 2,938.08 3,026.87 3,099.52 3,156.02 3,196.38 3,220.59 3,228.66 Phase II Divided Remainin wall g forwork Deck overlay (KNm) 0.00 5.52 10.75 15.70 20.37 24.75 28.85 32.67 36.21 39.46 42.43 45.12 47.52 49.65 51.48 53.04 54.31 55.30 56.01 56.44 56.58 (KNm) 0.00 64.88 126.44 184.67 239.57 291.14 339.39 384.31 425.90 464.17 499.10 530.71 559.00 583.95 605.58 623.88 638.85 650.50 658.82 663.81 665.47 (KNm) 0.00 17.24 33.60 49.07 63.66 77.36 90.18 102.12 113.17 123.34 132.62 141.02 148.54 155.17 160.91 165.78 169.76 172.85 175.06 176.39 176.83 Deck slab Hand rail, sidewalk (KNm) 0.00 192.29 374.71 547.28 709.98 862.82 1,005.81 1,138.93 1,262.19 1,375.59 1,479.13 1,572.81 1,656.62 1,730.58 1,794.67 1,848.91 1,893.28 1,927.80 1,952.45 1,967.24 1,972.17 (KNm) 0.00 43.08 83.94 122.60 159.05 193.29 225.32 255.14 282.75 308.16 331.35 352.34 371.11 387.68 402.04 414.19 424.13 431.86 437.38 440.70 441.80 Wastewater treatment pipe (KNm) 0.00 57.39 111.84 163.34 211.90 257.52 300.19 339.92 376.71 410.55 441.46 469.41 494.43 516.50 535.63 551.82 565.06 575.36 582.72 587.14 588.61 SHEAR FORCE DUE TO DEAD LOAD Phase I Section Load of main beam (mm) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 (KN) 343.47 326.30 309.13 291.95 274.78 257.61 240.43 223.26 206.08 188.91 171.74 154.56 137.39 120.22 103.04 85.87 68.69 51.52 34.35 17.17 0.00 Phase II Divided Remainin wall g forwork (KN) 6.02 5.72 5.42 5.12 4.82 4.51 4.21 3.91 3.61 3.31 3.01 2.71 2.41 2.11 1.81 1.50 1.20 0.90 0.60 0.30 0.00 (KN) 18.81 17.87 16.93 15.99 15.05 14.11 13.17 12.23 11.29 10.35 9.41 8.47 7.52 6.58 5.64 4.70 3.76 2.82 1.88 0.94 0.00 Deck overlay (KN) 70.79 67.26 63.72 60.18 56.64 53.10 49.56 46.02 42.48 38.94 35.40 31.86 28.32 24.78 21.24 17.70 14.16 10.62 7.08 3.54 0.00 Page: 10 Deck slab Hand rail, sidewalk (KN) 209.81 199.32 188.82 178.33 167.84 157.35 146.86 136.37 125.88 115.39 104.90 94.41 83.92 73.43 62.94 52.45 41.96 31.47 20.98 10.49 0.00 (KN) 47.00 44.65 42.30 39.95 37.60 35.25 32.90 30.55 28.20 25.85 23.50 21.15 18.80 16.45 14.10 11.75 9.40 7.05 4.70 2.35 0.00 Wastewater treatment pipe (KNm) 62.62 59.49 56.36 53.23 50.09 46.96 43.83 40.70 37.57 34.44 31.31 28.18 25.05 21.92 18.79 15.65 12.52 9.39 6.26 3.13 0.00 Loading D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 6,640 6,640 7,812 7,812 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 92.63 89.41 107.07 104.28 108.12 105.78 103.67 101.78 100.11 98.66 97.43 96.43 95.65 95.10 94.76 94.65 162.71 152.40 184.70 175.82 180.67 173.24 166.51 160.50 155.19 150.59 146.69 143.51 141.03 139.26 138.20 137.84 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 29.45 16.52 16.70 15.72 15.87 15.66 15.79 15.91 16.01 16.10 16.18 16.25 16.31 16.35 16.38 16.40 16.41 18.75 19.76 15.70 16.57 15.82 16.54 17.20 17.79 18.31 18.76 19.14 19.45 19.69 19.87 19.97 20.00 109.15 106.11 122.79 120.15 123.78 121.57 119.57 117.79 116.21 114.84 113.69 112.74 112.00 111.48 111.16 111.06 320.07 307.73 352.64 342.00 349.72 340.80 332.74 325.52 319.15 313.64 308.97 305.15 302.18 300.05 298.78 298.36 1,523.52 1,464.78 1,974.79 1,915.19 2,056.34 2,003.92 1,956.49 1,914.06 1,876.63 1,844.18 1,816.73 1,794.27 1,776.80 1,764.32 1,756.83 1,754.34 5,116.68 5,175.42 5,837.21 5,896.81 6,146.26 6,198.68 6,246.11 6,288.54 6,325.97 6,358.42 6,385.87 6,408.33 6,425.80 6,438.28 6,445.77 6,448.26 Prestress force before and after all losses 9,000.00 Prestress force (KN) 8,000.00 7,000.00 6,000.00 5,000.00 4,000.00 3,000.00 2,000.00 1,000.00 0.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 Distance from support (m) P after all losses Page: 18 P prestress P all losses Stress loss D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m CHECKING THE STRESS IN BEAM I STRESS AT THE TIME OF FORCE TRANSFER We shall check the stress of top fiber and bottom fiber of beam Stress at top fiber of beam when force transfer applied is to be calculated as follows: ft1 = P working/Agirder - Pworking*estrand1*Yt1/Igirder + Mstg1*Yt1/Igirder Stress at bottom fiber of beam when force transfer applied is to be calculated as follows: fb1 = Pworking/Agirder + Pworking*estrand1*Yb1/Igirder - Mstg1*Yb1/Igirder Ultimate tensile stress when force transfer applied = - 0.58f'ci0.5 Ultimate compressive stress when force transfer applied = 0.6f'ci SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 Ptension Pworking (KN) 391 3,515 3,515 4,297 5,859 6,640 6,640 7,812 7,812 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 8,203 (KN) 383 3,388 3,394 4,063 5,441 6,121 6,135 7,124 7,139 7,475 7,488 7,500 7,510 7,519 7,527 7,534 7,540 7,544 7,547 7,549 7,550 Agirder Igirder (m2) 0.945 1.686 1.686 0.710 0.717 0.720 0.720 0.725 0.725 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 (m4) 0.057 0.466 0.466 0.276 0.279 0.281 0.281 0.284 0.284 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 (m) -0.275 0.681 0.681 0.595 0.628 0.635 0.635 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 (-) (+) = = estrand Mstg1 (KNm) 0.00 314.79 613.45 895.95 1,162.32 1,412.54 1,646.62 1,864.55 2,066.34 2,251.99 2,421.50 2,574.86 2,712.08 2,833.15 2,938.08 3,026.87 3,099.52 3,156.02 3,196.38 3,220.59 3,228.66 Calculated by Phucdh Checked by Dr Songkiat Dated 4/21/2010 Tensile stress Compressive stress -3.78 (MPa) +25.50 (MPa) Yt1 Yb1 (m) 0.350 0.763 0.763 0.878 0.885 0.888 0.888 0.893 0.893 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 (m) 0.450 0.987 0.987 0.872 0.865 0.862 0.862 0.857 0.857 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 ft1 fb1 (Mpa) 1.06 -1.25 -0.77 0.88 0.44 0.68 1.41 1.22 1.85 2.19 2.72 3.19 3.61 3.99 4.31 4.59 4.81 4.99 5.11 5.19 5.21 (Mpa) -0.43 6.22 5.60 10.53 14.57 16.08 15.41 18.07 17.51 18.01 17.54 17.12 16.74 16.41 16.12 15.88 15.68 15.52 15.41 15.34 15.32 STRESS AT TRANSFER 30.00 27.00 24.00 STRESS (Mpa) 21.00 18.00 15.00 12.00 9.00 6.00 3.00 0.00 -3.000.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 -6.00 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited II STRESS WHEN CONCRETING BRIDGE DECK (deck without load applied) Stress at top fiber of beam when concreting bridge deck is to be calculated as follows: ft2 = ft1 + ΔPlosses1/Agirder - ΔPlosses1*estrand1*Yt1/Igirder + Mstg2*Yt1/Igirder Stress at bottom fiber of beam when concreting bridge deck is to be calculated as follows: fb2 = f b1 + ΔPlosses1/A girder + ΔPlosses1*estrand1*Yb1/Igirder - Mstg2*Yb1/Igirder 0.5 Ultimate tensile stress when force transfer applied = - 0.5f'ci Page: 19 = -3.54 (MPa) Stress D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls Ultimate compressive stress when force transfer applied = 0.45f'ci SECTION ΔPlosses1 (m) (KN) 0.00 -8 0.94 -128 1.88 -121 2.82 -234 3.76 -418 4.70 -520 5.64 -505 6.58 -688 7.52 -673 8.46 -728 9.40 -715 10.34 -703 11.28 -693 12.22 -683 13.16 -675 14.10 -668 15.04 -663 15.98 -659 16.92 -655 17.86 -654 18.80 -653 Agirder (m2) 0.945 1.685 1.685 0.709 0.715 0.718 0.718 0.723 0.723 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 Igirder (m4) 0.056 0.466 0.466 0.275 0.278 0.280 0.280 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283 estrand1 (m) -0.275 0.681 0.681 0.595 0.628 0.635 0.635 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 0.645 Mstg2 (KNm) 0.00 209.53 408.31 596.35 773.64 940.19 1,095.99 1,241.05 1,375.36 1,498.93 1,611.75 1,713.83 1,805.16 1,885.75 1,955.59 2,014.69 2,063.04 2,100.65 2,127.51 2,143.63 2,149.00 = Yt1 (m) 0.350 0.763 0.763 0.878 0.885 0.888 0.888 0.893 0.893 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 +22.50 (MPa) Yb1 (m) 0.450 0.987 0.987 0.872 0.865 0.862 0.862 0.857 0.857 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 ft2 (Mpa) 1.04 -0.84 -0.03 2.90 3.15 3.98 5.20 5.60 6.64 7.41 8.28 9.07 9.78 10.40 10.94 11.40 11.77 12.06 12.27 12.39 12.43 fb2 (Mpa) -0.42 5.52 4.49 7.86 10.77 11.45 10.35 12.01 11.09 11.06 10.30 9.60 8.99 8.44 7.97 7.57 7.24 6.99 6.81 6.70 6.66 STRESS AT TOPPING 30.00 27.00 24.00 STRESS (Mpa) 21.00 18.00 15.00 12.00 9.00 6.00 3.00 0.00 -3.000.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 -6.00 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited III STRESS IN THE PERIOF OF SERVICE III.1 Stress of beam due to live load +1/2 (Prestressing+Permanent load): Stress at top fiber of beam in the period of operation is to be calculated by: ft3 = P losses/Acomb - Plosses*estrand2*Yt2/Icomb + Mstg3*Yt2/Icomb Stress at bottom fiber of beam in the period of operation is to be calculated by: fb3 = P losses/Acomb + Plosses*estrand2*Yb2/Icomb - Mstg3*Yb2/I comb 0.5 Ultimate tensile stress when force transfer applied = - 0.5f'ci Ultimate compressive stress when force transfer applied = 0.4f'c SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 Plosses (KN) 361 3,086 3,113 3,582 4,616 5,117 Acomb (m ) 1.341 2.081 2.081 1.106 1.112 1.115 Icomb (m ) 0.114 0.706 0.706 0.519 0.526 0.530 estrand2 Mstg3 (m) (KNm) -0.142 25.6 0.846 -615.2 0.846 27.6 0.946 267.1 0.981 280.1 0.988 561.3 Page: 20 = = Yt2 Yb2 (m) 0.417 0.799 0.799 0.726 0.733 0.735 (m) 0.583 1.151 1.151 1.224 1.217 1.215 -3.54 (MPa) +20.00 (MPa) ft3 (Mpa) 0.55 -2.17 -1.45 -1.13 -1.76 -1.65 fb3 (Mpa) -0.12 6.74 5.74 10.60 13.97 14.89 Stress D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 5,175 5,837 5,897 6,146 6,199 6,246 6,289 6,326 6,358 6,386 6,408 6,426 6,438 6,446 6,448 1.115 1.119 1.119 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 0.530 0.535 0.535 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.988 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 1,041.5 1,156.4 1,563.5 1,838.7 2,177.1 2,481.7 2,752.7 2,990.0 3,193.6 3,363.5 3,499.8 3,602.3 3,671.2 3,706.3 3,707.8 0.735 0.740 0.740 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 1.215 1.210 1.210 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 -1.01 -1.25 -0.71 -0.46 -0.01 0.38 0.74 1.05 1.31 1.53 1.71 1.84 1.93 1.98 1.98 13.97 15.78 15.04 15.16 14.57 14.03 13.55 13.14 12.78 12.48 12.25 12.07 11.96 11.90 11.91 STRESS AT SERVICE 30.00 27.00 24.00 21.00 STRESS (Mpa) 18.00 15.00 12.00 9.00 6.00 3.00 0.00 -3.000.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 -6.00 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited III.2 Stress of beam due to live load + Prestressing + Permanent load : Stress at top fiber of beam in the period of operation is to be calculated by: ft4 = P losses/Acomb - Plosses*estrand2*Yt2/Icomb + Mstg4*Yt2/Icomb Stress at bottom fiber of beam in the period of operation is to be calculated by: fb4 = P losses/Acomb + Plosses*estrand2*Yb2/Icomb - Mstg4*Yb2/I comb Ultimate tensile stress when force transfer applied = - 0.5f'ci0.5 Ultimate compressive stress when force transfer applied = 0.6f'c SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 Plosses (KN) 361 3,086 3,113 3,582 4,616 5,117 5,175 5,837 5,897 6,146 6,199 6,246 6,289 6,326 6,358 6,386 6,408 6,426 Acomb (m ) 1.341 2.081 2.081 1.106 1.112 1.115 1.115 1.119 1.119 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 1.121 Icomb (m ) 0.114 0.706 0.706 0.519 0.526 0.530 0.530 0.535 0.535 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 estrand2 Mstg3 (m) (KNm) -0.142 51.2 0.846 -1,601.6 0.846 -667.4 0.946 -520.0 0.981 -805.8 0.988 -535.5 0.988 152.8 0.999 130.3 0.999 712.1 0.999 1,049.9 0.999 1,533.7 0.999 1,970.1 0.999 2,358.9 0.999 2,700.1 0.999 2,993.8 0.999 3,240.0 0.999 3,438.6 0.999 3,589.6 Page: 21 = = Yt2 Yb2 (m) 0.417 0.799 0.799 0.726 0.733 0.735 0.735 0.740 0.740 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 0.741 (m) 0.583 1.151 1.151 1.224 1.217 1.215 1.215 1.210 1.210 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 1.209 -3.54 (MPa) +30.00 (MPa) ft3 (Mpa) 0.64 -3.28 -2.24 -2.23 -3.27 -3.17 -2.24 -2.66 -1.89 -1.54 -0.90 -0.32 0.19 0.65 1.04 1.36 1.63 1.83 fb3 (Mpa) -0.25 8.35 6.88 12.46 16.49 17.40 16.01 18.10 16.97 16.94 16.01 15.18 14.44 13.79 13.23 12.76 12.39 12.10 Stress D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 16.92 17.86 18.80 6,438 6,446 6,448 1.121 1.121 1.121 0.537 0.537 0.537 0.999 0.999 0.999 3,693.1 3,749.1 3,757.5 0.741 0.741 0.741 1.209 1.209 1.209 1.96 2.04 2.05 11.91 11.81 11.79 STRESS AT SERVICE 35.00 30.00 STRESS (Mpa) 25.00 20.00 15.00 10.00 5.00 0.00 0.00 -5.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Page: 22 Compresive stress limited Tensile stress limited Stress D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m Calculated by Phucdh Checked by Dr Songkiat Dated 4/21/2010 CHECKING THE STATE OF STRENGTH LIMIT IN BEAM I CHECKING THE REINFORCEMENT LIMITS I.1 Maximum reiforcement limit Percentage of reinforcement shall be limited so that: Where: (A.5.7.3.3.1-1) c ≤ 0,42 de + c : Height of compression region A ps f pu − 0,85 β f' c (b − b w )h f f pu 0,85 β f' c b w + kA ps dp c= (A.5.7.3.1-1) + de : Distance from extreme compression fiber to the center of tension reinforcement de = A ps f ps d p + A s f y d s A ps f ps + A s f y + β : Stressing cubic coefficient f ' −28 β1 = 0,85 − c 0,05 ≥ 0,65 + b : Width of compressive flange + bw : Width of web + hf : Height of compressive flange + fps : average stress in prestressing tendon f ps = f p u (1 − k c ) dp + dp (ds): Distance from extreme compression fiber to the center of tendon (plain tensile iron) + k : Coefficient depend on nature of reinforcement k = 2.(1,04 SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 − f py f pu bw (mm) 890 700 700 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 β1 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 ) k 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 Position neutral axis Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever c (mm) 80 80 98 134 152 152 178 178 187 187 187 187 187 187 187 187 187 187 187 187 de (mm) 275 1,644 1,644 1,673 1,713 1,724 1,724 1,739 1,739 1,740 1,740 1,740 1,740 1,740 1,740 1,740 1,740 1,740 1,740 1,740 1,740 c/de Conclusion 0.03 0.05 0.05 0.06 0.08 0.09 0.09 0.10 0.10 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK 1.2 Minimum reinforcement limit (5.7.3.3.2) Volume of prestressing tendon and plain reiforcement shall be sufficient to develop bending resistance Mr, take less-than value of : M r ≥ min(1,2M cr ;1,33M tt ) * 1,2 crack resistance M cr to be defined on the basis of elastic stress distribution and tensile strength when bending of concrete f r M = 0,63 cr = f r f' c I comb Zt (5.4.2.6) (5.7.3.6.2) Page: 23 Strength D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls * 1,33 time of required design moment under combination of appropriate intensity of load, in the table 3.4.1-1 SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 fr Icomb (Mpa) 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 4.45 (m4) 0.114 0.706 0.706 0.519 0.526 0.530 0.530 0.535 0.535 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 0.537 1.2Mcr (KNm) 1,467 4,726 4,726 3,819 3,841 3,852 3,852 3,868 3,868 3,872 3,872 3,872 3,872 3,872 3,872 3,872 3,872 3,872 3,872 3,872 3,872 1.33Mtt (KNm) 0.0 2,043.3 3,979.9 5,809.9 7,533.1 9,149.5 10,659.3 12,062.4 13,358.7 14,548.3 15,631.3 16,607.5 17,477.0 18,239.8 18,895.8 19,445.2 19,887.9 20,223.8 20,453.0 20,575.5 20,591.4 Mr Conclusion (KNm) 140 OK 7,474 OK 7,474 OK 9,234 OK 12,738 OK 14,430 OK 14,430 OK 16,965 OK 16,965 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK II CHECK MOMENT RESISTANCE The factored moment resistance Mr , shall be taken as: Mr = ϕ Mn ≥ Mu (KN) Where: ϕ= 1.00 : Resistance factored as specified in Article 5.5.4.2 M n = A ps f ps (dp − + Mu + Mr + Mn + dp + fps + a = c.β SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 a a h ) + 0,85.fc' (b − b w ).β h f ( − f ) 2 (A.5.7.3.2.1-1) (A.5.7.3.2.2-1) : Flexural moment in beam due to applied load : Factored flexural moment of beam : Nominal flexural resistance moment of beam : Distance from extreme compression fiber to the center of tendon : Avarage stress in tendon ≤ fpy : Thickness of equivalent stress block a (mm) 6.18 55.62 55.62 67.98 92.70 105.06 105.06 123.60 123.60 129.78 129.78 129.78 129.78 129.78 129.78 129.78 129.78 129.78 129.78 129.78 129.78 fps (Mpa) 1843 1835 1835 1829 1819 1814 1814 1807 1807 1804 1804 1804 1804 1804 1804 1804 1804 1804 1804 1804 1804 Mn (KNm) 140 7,474 7,474 9,234 12,738 14,430 14,430 16,965 16,965 17,773 17,773 17,773 17,773 17,773 17,773 17,773 17,773 17,773 17,773 17,773 17,773 Mu (KNm) 0.0 1,536.3 2,992.4 4,368.3 5,663.9 6,879.3 8,014.5 9,069.4 10,044.1 10,938.6 11,752.8 12,486.8 13,140.6 13,714.1 14,207.4 14,620.5 14,953.3 15,205.9 15,378.2 15,470.3 15,482.2 Mr Conclusion (KNm) 140 OK 7,474 OK 7,474 OK 9,234 OK 12,738 OK 14,430 OK 14,430 OK 16,965 OK 16,965 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK 17,773 OK III CHECK SHEAR RESISTANCE III.1 Nominal shear resistance Nominal shear resistance V n shall take less-than value of : (A.5.8.3.3) Vn = Vc + Vs + Vp Vn = 0,25f'cbvdv + Vp Page: 24 Strength D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls Where: Vc = 0,083β f c' b vd v Vs = Av f y d v (cot gθ + cot gα)sin α s + bv : Width of minimum web of beam (mm) dv = max(0,9d e ; 0,72h) + dv : Effective shear height (mm), + s : Distance of hoop reinforcement (mm) + β : Capability coefficient of crossed crack concrete + θ : Inclination angle of crossed compressive stress (Độ) + α : Inclination angle of cross reinforcement on longitudinal center line (degree) + Av : Area of shear reinforcement in distance of s (include area of plain reiforcement + prestressing reiforcement) (mm 2) A vmin = 0,083 f' c b vs fy + Vp : Component of effective prestress towards active shearing force, is positive (+) if in opposing direction of shearing force 0.0 KN + Vp = Σfps.Aps.sinαi = + αi : Inclination angle of strand compared with horizontal direction Proposed arrangement of hoop reinforcement ia as follows: fy Av SECTION S d (Mpa) (m) (mm) (mm) (mm2) Avmin 0.00 0.94 1.88 2.82 20.00 20.00 20.00 20.00 100 100 100 100 400 400 400 400 628 628 628 628 (mm2) 131 103 103 35 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 20.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 16.00 100 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 628 402 402 402 402 402 402 402 402 402 402 402 402 402 402 402 402 35 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 Conclusion OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK ` III.2 Determination of β and θ β and θ taken from the table 5.8.3.4.2-1 depend on the ratio v/f' c and improvise in reinforcement of flexure side Shear stress in concrete v : Vu − ϕV p v= Improvise in tension reiforcement εx: εx ϕbv d v Mu + N u + 5V u cot g θ − A ps f po dv ≤ 002 = E s A s + E p A ps If value of εx is minus so we take absolute value and reduce by multiply with coefficient F ε Fε = Where: E ps A ps E c A c + E ps A ps + f'c : Compressive strength of concrete f'c = 50 MPa + Ec : Elasticity of concrete Ec = 35750 MPa Ep = 197000 MPa + Es : Elasticity modulus of tendon + ϕ : Shear resistance coefficient ϕ= 0.9 + fpo : Stress in tendon when stress in concrete around it is zero fpo = fpe + fpc.Ep/Ec + fpe : Effective stress in tendon after deduct the loss + fpc : Compressive stress at section's center fpc = F/A Page: 25 Strength D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls + Nps = Σfps.Aps.cosαi : Axial force effects on beam due to prestress N ps Determination of parameter β and θ fpo v v/f'c Fε (Mpa) (N) θ (Độ) β 5.32 6.99 6.90 43.00 43.00 43.00 1.72 1.72 1.72 0.015 6.92 43.00 1.72 0.020 0.023 0.023 0.027 0.027 0.028 0.028 0.028 0.028 0.028 0.028 0.028 0.028 0.028 0.028 0.028 0.028 6.92 7.19 7.12 7.08 7.02 6.97 6.91 6.86 6.81 6.76 6.71 6.67 6.63 6.59 6.55 6.51 6.48 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 43.00 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.72 (KN) 360.86 3,086.24 3,112.62 dv (mm) 576 1480 1480 fpc (Mpa) 0.27 1.48 1.50 1,290.27 1,232.87 1,243.41 3.635 1.718 1.637 0.073 0.034 0.033 0.001 0.007 0.007 2.82 3,582.03 1505 3.24 1,180.85 4.462 0.089 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 4,615.53 5,116.68 5,175.42 5,837.21 5,896.81 6,146.26 6,198.68 6,246.11 6,288.54 6,325.97 6,358.42 6,385.87 6,408.33 6,425.80 6,438.28 6,445.77 6,448.26 1542 1551 1551 1565 1565 1566 1566 1566 1566 1566 1566 1566 1566 1566 1566 1566 1566 4.15 4.59 4.64 5.21 5.27 5.48 5.53 5.57 5.61 5.64 5.67 5.70 5.72 5.73 5.74 5.75 5.75 1,121.81 1,100.23 1,112.86 1,071.09 1,082.03 1,075.50 1,084.67 1,092.97 1,100.39 1,106.94 1,112.62 1,117.42 1,121.35 1,124.41 1,126.60 1,127.91 1,128.34 4.129 3.880 3.655 3.399 3.176 2.950 2.727 2.504 2.281 2.058 1.836 1.613 1.390 1.167 0.944 0.721 0.513 0.083 0.078 0.073 0.068 0.064 0.059 0.055 0.050 0.046 0.041 0.037 0.032 0.028 0.023 0.019 0.014 0.010 Vc+Vs 0.25f'cbvdv ϕVn (KN) 1,862 4,529 4,529 3,978 4,075 1,943 1,943 1,960 1,960 1,962 1,962 1,962 1,962 1,962 1,962 1,962 1,962 SECTION (m) 0.00 0.94 1.88 SECTION (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 Nu α Av Vc Vs (Degree) 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 (mm2) 628 628 628 628 628 402 402 402 402 402 402 402 402 402 402 402 402 (KN) 517.49 1,045.81 1,045.81 364.73 373.58 375.81 375.81 379.13 379.13 379.50 379.50 379.50 379.50 379.50 379.50 379.50 379.50 (KN) 1,551.62 3,986.81 3,986.81 4,055.38 4,153.82 1,783.20 1,783.20 1,798.95 1,798.95 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 Page: 26 (KN) 2,069.12 5,032.62 5,032.62 4,420.11 4,527.41 2,159.01 2,159.01 2,178.07 2,178.07 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 (KN) 6,408 12,950 12,950 4,516 4,626 4,654 4,654 4,695 4,695 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 1000εx Vu Vu ≤ ϕVn (KN) 1,677 1,602 1,526 1,451 1,375 1,300 1,224 1,149 1,074 998 923 847 772 696 621 546 470 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK Strength D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls 15.98 16.92 17.86 18.80 90 90 90 90 402 402 402 402 379.50 379.50 379.50 379.50 1,800.73 1,800.73 1,800.73 1,800.73 2,180.24 2,180.24 2,180.24 2,180.24 4,699 4,699 4,699 4,699 1,962 1,962 1,962 1,962 IV CHECK SHEAR RESISTANCE AT INTERFACE PLANE IV.1 We will consider open section which's nearest support: x= = 1,677.08 (KN) At Strength-I: Calculation shear Vu The nominal shear resistance of the interface plane V n , shall be taken as: (5.8.4.1) Vn = cAcv + μ[Avffy + Pc ] The interface shear resistance, V n, will not exceed : ≤ 0.2 f'cAcv or Vn ≤ 5.5Acv Vn Where: Acv = ⇒ ⇒ ⇒ Avf = fy = c= μ= Pc = f'c = Vn = 0.2 f'cAcv = 5.5Acv = Vn = Vr =ϕVn = 1.34 (m ) 6,434 400 0.52 0.60 0.00 35 2,241.54 9,387.84 7,376.16 2,241.54 2,017.38 (mm2) (MPa) (MPa) (KN) (MPa) (KN) (KN) (KN) (kN) (kN) ⇒ ⇒ ⇒ 1,583 400 0.52 0.60 3,113 35 2,822.46 7,738.85 6,080.52 2,822.46 2,540.22 (mm2) (MPa) (MPa) (KN) (MPa) (KN) (KN) (KN) (kN) (kN) OK OK OK OK 0.00 m Area of concrete in shear transfer plane Area of shear reinforcement crossing the shear plane yield strength of reinforcement Cohesion factor specified in 5.8.4.2 Friction factor specified in 5.8.4.2 Permanent net compressive force normal to the shear plane; if force is tensile; P c=0 Specified 28 day copressive strength of the weaker concrete > Vu = 1,677.08 (KN) IV.2 We will consider open section which's nearest support x= At Strength-I: Calculation shear Vu = 1,450.79 (KN) The nominal shear resistance of the interface plane V n , shall be taken as: Vn = cAcv + μ[Avffy + Pc ] (5.8.4.1) The interface shear resistance, V n, will not exceed : Vn ≤ 0.2 f'cAcv or Vn ≤ 5.5Acv Where: 1.11 (m ) Acv = Area of concrete in shear transfer plane Avf = fy = c= μ= Pc = f'c = Vn = 0.2 f'cAcv = 5.5Acv = Vn = Vr =ϕVn = 395 319 244 174 => OK 2.82 m Area of shear reinforcement crossing the shear plane yield strength of reinforcement Cohesion factor specified in 5.8.4.2 Friction factor specified in 5.8.4.2 Permanent net compressive force normal to the shear plane; if force is tensile; P c=0 Specified 28 day copressive strength of the weaker concrete > Vu = 1,450.79 (KN) => OK (5.10.10) V CHECK PRETENSION ANCHORAGE ZONES We will consider solid section which's nearest support x= 940 mm = 3,388 KN At Strength-I: Calculation axial force Nu The bursting resistance of pretension anchorage zone P r , shall be taken as: Pn = fs*As Where: fs = 140 (MPa) Stress in steel not exceeding 140 Mpa As = h= ϕ= ⇒ ⇒ Pn = Pr = 2,450 (mm ) 1,950 (mm) 0.70 343.06 (KN) 240.14 (KN) Total area of vertical reinforcement located within the distance h/5 from the ending Overall depth of member Resistance factor as specified in Article 5.5.4.2 > 0.04Nu = Page: 27 135.51 (kN) => OK Strength D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL COMPUTATION OF SUPER-T BEAM Calculated by Phucdh Checked by Dr Songkiat Ngày 4/21/2010 I HALVING JOINT DESIGN 350 Arrange the reinforcement according to strut-and-tie model Section size on top of pier abutment Height of main beam 1,750 (mm) Height of section of other beam 800 (mm) Length of section of other beam 850 (mm) 800 350 (mm) Distance from bearing center to the b (A.5.6.3) Section A 600 T2 C1 T1 100 950 100 Vu 643 136 850 143 Strut-and-tie model for halving joint design Checking the internal force produced in halving joint: Maximum counter force calculated for strength combination 1,677.08 (KN) Vu = α= 43 (degree) Inclination angle compared to the vertical diretion of the bar C1 Compressive force in bar C1 2,459.07 (KN) C1 = Force in bracing T1 T1 = 1,798.45 (kN) I.1 Checking the cross bracing T Nominate resistance of tension bracing bar shall be taken as: 2573.593 KN Pn=fyAst+Apsfpe= Where: n= (bar) : Number of tension high-strength steel bar D= 32 (mm) : Diameter of tension high-strength steel bar in the beam Ast= 6,433.98 (mm ) : Total of tension high-strength reinforcement 400 (Mpa) : Liquid limit of high-strength steel bar fy= Aps= 0.00 (mm ) : Total area of tension prestressing steel ⇒ Pr = ϕPn = 2316.23 KN > T1 = 1798.45 KN => OK I.2 Checking the compressive bar C1 Nominate resistance of compressive bar shall be taken as: 4630.169 KN Pn= fcuAcs = Where: 284 (mm) : Dimension of compressive bar la sinα = Acs= 108,945 (mm ) : Area of effective section of compressive bar 42.50 Mpa: ultimate compressive stress+F40 fcu=min(f'c/(0.8+170ε1),0.85f'c)= ε1=(εs+0.002)cotg α= 0.000828 εs= -0.000003 : Deformation of concrete towards tension bracing ⇒ Pr = ϕPn = 4167.15 KN > C1 = 2459.07 KN => OK II CHECKING BRACKET AT HALVING SECTION OF GIRDER Calculation shear Calculation axial force Vu Nu Nu = 1677.08 (KN) = 360.86 (KN) Punching crack d1 Horizontal bar d2 Nuc Grillage bar Section centroid Vu Page: 28 HalvingDesign D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls II.1 Design for flexure and horizontal The area of primary tension reinforcement, As ,shall satisfy the requirements : As ≥ 0.667Avf required + An (A.5.13.2.4) Area of tie within a distance equal to 2/3 height of halving section from primary reinforcement ≥ 0.5 (A s - An) Ah Where Avf required = [(1.1Vu + cAcv)/μ - Pc ] /fy Avf required = 10592 (mm ) Avf grillage n D Avf hor = 6434 = 10 = 25 = 4909 (mm ) Avftotal = (mm) (mm2) 11343 (mm ) = Nuc/φfy = Nu*d1/d2 = 0.275 = 0.425 = 234 Area of grillage-bar reinforcement crossing the shear plane Number of horizontal bar Diameter of horizontal bars Area of horizontal-bar reinforcement crossing the shear plane Total area of reinforcement crossing the shear plane (mm ) (KN) (m) (m) (KN) ⇒ An Nuc d1 d2 Nuc ⇒ An = 649 ⇒ As n1 D1 n2 D2 = = = = = 7714 10.0 20 10.0 16 (mm) < As = 11343 (mm ) => OK Number of ties bar from 2/3 height of halving section Diameter of ties bar Number of ties bar from 2/3 height of halving section Diameter of ties bar Ah hor = 5152 (mm ) area of horizontal-bar reinforcement within 2/3 height of section ⇒ Ah = 3533 II.2 Design for punching shear (mm ) (mm ) (mm ) (mm) < Ah = 5152 (mm ) => OK The nominal punching shear resistance Vn , shall be taken as: Vn = 0.328 f'c0.5 (W+L+de)de (5.13.2.5.4) where ⇒ ⇒ f'c W L de Vn Vr = = = = = = 50 500 450 800 3247 2922 (Mpa) (mm) (mm) (mm) (KN) (KN) Specified compressive strength at 28 days Width of elastic bearing (450x500x85)mm Length of elastic bearing (450x500x85)mm Height of section > Vu Page: 29 = 1677.1 (KN) => OK HalvingDesign D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER-T BEAM, L=38.3m Calculated by Phucdh Checked by Dr Songkiat Dated 4/21/2010 DEFLECTION AND CAMBER OF BEAM I INTRODUCTION: Deflection of beam shall be calculated in main states: Phase I : Deflection when force transfer applied Phase II : Deflection when force transfer applied until concreting the bridge deck Operation phase : Deflection of service phase II DEFLECTION WHEN FORCE TRANSFER APPLIED II.1 Deflection due to sefl weight of main beam (phase I) δ DC = 5.DCI L4 384.Eci II Where: + DCI : Load due to beam self weight in phase I + Li : Factored span length + Eci : Elasticity modulus of concrete in phase I, Eci = 32,959 + II : Moment of inertia of beam in phase I II.2 Camber of beam due to prestress Camber due to prestress is calculated according to the following formula: δP = M p Li E ci I I = PP e P Li E ci I I (MPa) Where: + Mp : Moment created by prestress on beam center + Li : Factored span length + Eci : Elasticity modulus of concrete in phase I + II : Moment of inertia of beam in phase I 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 δDC (mm) 0.00 0.00 0.00 0.03 0.08 0.20 0.42 0.78 1.32 2.11 3.22 4.72 6.68 9.20 12.38 16.31 21.12 26.92 33.83 42.00 51.56 δP (mm) Σδ (mm) 0.00 -0.07 -0.28 -1.11 -2.75 -4.86 -7.02 -11.17 -14.62 -19.32 -23.89 -28.96 -34.51 -40.55 -47.08 -54.09 -61.59 -69.57 -78.03 -86.96 -96.36 0.00 -0.07 -0.28 -1.08 -2.67 -4.66 -6.60 -10.39 -13.29 -17.21 -20.67 -24.24 -27.83 -31.35 -34.70 -37.78 -40.47 -42.66 -44.20 -44.96 -44.80 Deformation Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Deflection of girder at transfer 60.00 Deflection(mm) Section (m) 45.00 30.00 15.00 0.00 -15.000.00 5.00 10.00 15.00 20.00 -30.00 -45.00 -60.00 Length of design span (m) III DEFLECTION WHEN FORCE TRANSFER APPLIED UNTIL CONCRETING THE BRIDGE DECK III.1 Deflection of main beam due to dead load (phase II) δ DCII = 5.DC II L4 384.E ci I II Trong : + DCII : Load due to beam self weight + bridge deck phase II + Li : Factored span length Page: 30 Deflection D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls + Eci : Elasticity modulus of concrete in phase II, Eci = 32,959 + III : Moment of inertia of beam in phase II III.2 Camber of beam due to prestress Camber due to prestress is calculated according to the following formula: δP = M p Li E ci I I = PP e P Li E ci I I (MPa) Where: + Mp : Moment created by prestress on beam center + Li : Factored span length + Eci : Elasticity modulus of concrete in phase II + III : Moment of inertia of beam in phase II δDC (mm) 0.000 0.000 0.003 0.027 0.084 0.204 0.423 0.776 1.324 2.114 3.223 4.718 6.682 9.204 12.380 16.314 21.119 26.915 33.829 41.997 51.561 δBMC (mm) δP (mm) 0.000 0.000 0.002 0.016 0.051 0.123 0.255 0.468 0.798 1.276 1.944 2.847 4.032 5.553 7.470 9.844 12.743 16.240 20.412 25.340 31.111 Σδ (mm) 0.000 -0.066 -0.266 -1.060 -2.633 -4.653 -6.716 -10.688 -13.989 -18.494 -22.872 -27.719 -33.034 -38.817 -45.067 -51.781 -58.959 -66.598 -74.694 -83.244 -92.245 0.000 -0.066 -0.261 -1.017 -2.499 -4.326 -6.038 -9.444 -11.867 -15.104 -17.705 -20.154 -22.320 -24.060 -25.217 -25.624 -25.097 -23.442 -20.453 -15.907 -9.573 Deformation Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Deflection of girder at topping 40.000 Deflection(mm) Section (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 30.000 20.000 10.000 0.000 -10.0000.00 5.00 10.00 15.00 20.00 -20.000 -30.000 -40.000 Length of design span (m) IV DEFLECTION OF OPERATION PHASE IV.1 Deflection of main beam due to dead load (service phase) δ DCKT = 5.DC KT L4 384.E c I KT Where: + DCKT : Load due to total of dead load + Li : Factored span length + Ec : Elasticity modulus of concrete in service phase, Ec = + IKT : Moment of inertia of beam in service phase IV.2 Camber of beam due to prestress Camber due to prestress is calculated according to the following formula: δP = M p Li E c I KT 35,750 (MPa) = PP e P Li E c I KT Where: + Mp : Moment created by prestress on beam center + Li : Factored span length Page: 31 Deflection D:\Congtrinh 2010\Ha tang uu tien TP Da Nang\Comp C\NTP bridge\Calculations\Super-T beam (L=38.3m)EN.xls + Ec : Elasticity modulus of concrete in service phase, + IKT : Moment of inertia of beam in service phase IV.3 Deflection due to live load According to 3.6.1.3.2, live load of deflection taken from higher value of : + Deflection due to vehicle load + Deflection due to 25% vehicle load + lane load Deflection due to lane load: δP = M W Li E c I KT δP = M LL Li E c I KT Deflection due to vehicle load: Where: th + Pi : Axle load number i + ci : Distance from position of axle load apply to the bearing Section (m) 0.00 0.94 1.88 2.82 3.76 4.70 5.64 6.58 7.52 8.46 9.40 10.34 11.28 12.22 13.16 14.10 15.04 15.98 16.92 17.86 18.80 δDCKT (mm) 0.00 0.00 0.00 0.03 0.08 0.20 0.41 0.76 1.29 2.06 3.14 4.59 6.50 8.96 12.05 15.88 20.55 26.19 32.92 40.87 50.18 δP (mm) δLL (mm) 0.00 -0.05 -0.19 -0.76 -1.79 -3.09 -4.51 -6.92 -9.14 -12.02 -14.96 -18.24 -21.86 -25.81 -30.08 -34.68 -39.60 -44.83 -50.35 -56.17 -62.26 δW (mm) 0.00 0.01 0.07 0.31 0.70 1.31 2.19 3.34 4.82 6.62 8.76 11.24 14.06 17.18 20.59 24.27 28.17 32.24 36.44 40.70 44.96 δ25%LL+W (mm) 0.00 0.00 0.02 0.10 0.22 0.42 0.70 1.07 1.55 2.14 2.84 3.65 4.57 5.61 6.75 7.98 9.29 10.68 12.13 13.62 15.13 0.00 0.01 0.04 0.17 0.40 0.75 1.25 1.91 2.76 3.79 5.03 6.46 8.09 9.90 11.89 14.04 16.34 18.74 21.24 23.79 26.37 Σδ (mm) 0.000 -0.039 -0.121 -0.430 -1.008 -1.587 -1.903 -2.829 -3.024 -3.343 -3.065 -2.408 -1.301 0.329 2.559 5.462 9.119 13.607 19.007 25.401 32.873 Deformation [Δ] (mm) Conclusion Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Deflection Deflection Deflection Deflection Deflection Deflection Deflection Deflection 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 38.300 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK Deflection of girder at service 40.000 Deflection(mm) 30.000 20.000 10.000 0.000 0.00 -10.000 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00 -20.000 -30.000 -40.000 Length of design span (m) V TOTAL DEFLECTION AT THE SECTION OF MIDDLE OF BEAM Deflection due to transfer of prestressing load Ztransfer = -44.80 (mm) Deflection after concreting the bridge deck Ztopping = -9.57 (mm) Deflection of service phase Zservice = 32.87 (mm) Page: 32 Deflection ... Phase II State of strength limit I State of strength limit I State of using limit Exterior Intermediate Exterior Intermediate Exterior Intermediate VMax VMax VMax beam beam beam beam beam beam (KN)... uu tien TP Da NangComp CNTP bridgeCalculations Super- T beam (L=38. 3m)EN. xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION OF SUPER- T BEAM, ... D:Congtrinh 2010Ha tang uu tien TP Da NangComp CNTP bridgeCalculations Super- T beam (L=38. 3m)EN. xls DANANG PRIORITY INFRASTRUCTURE INVESTMENT PROJECT NGUYỄN TRI PHƯƠNG BRIDGE STRUCTURAL CALCULATION