Ban tinh dam super t khue dong

Sở giao thông vận tảI đà nẵng Da nang department of transport ****************************** dự án ĐầU TƯ CƠ Sở Hạ TầNG ƯU TIÊN Đà NẵNG HợP ĐồNG: A23+A24+B37 Danang priority infrastructure investment project Package :A23 + A24 + B27 tiểu hợp phần c12: cầu khuê đông Subcomponent c12: khue dong bridge Bảng tính Dầm super-T Super-T girder calculation (Shop drawing design stage) (Version 1) - Ha noi: 10 -2011 - Sở giao thông vận tảI đà nẵng Da nang department of transport ****************************** dự án ĐầU TƯ CƠ Sở Hạ TầNG ƯU TIÊN Đà NẵNG HợP ĐồNG: A23+A24+B37 Danang priority infrastructure investment project Package :A23 + A24 + B27 tiểu hợp phần c12: cầu khuê đông Subcomponent c12: khue dong bridge Bảng tính dầm super-T Super-T girder calculation (Shop drawing design stage) (Version 1) NHà thầu Contractor T vấn giám sát Consultant Chủ đầu t Employer - Ha noi: 10 -2011 - SUPER-T GIRDER SPAN 37.5M Bridge joint stock company no.12 Project Structure Calculation of super-t beam Calculate by (Shop drawing design stage) Bui Van Duan Checked by Duong Van Chien Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=37.5m I KCH THC HèNH HC - STRUCTURAL PARAMETER: Tiờu chun thit k - Design standard: Loi dm - Type of beam: S dm (tớnh cho na cu) - Number of beam: B rng mt cu - Width of deck B rng l b hnh - Width of sidewalk B rng di phõn cỏch - Width of median Chiu di dm - Length of beam Spacing from end beam to bearing centerline: Chiu di nhp tớnh toỏn - Calculation span length Chiu cao bn mt cu - Height of deck slab Chiu cao dm - Height of beam section Khong cỏch gia cỏc dm - Spacing of beams Lp ph mt cu - Deck overlay 22TCN272-05 Super T 13.15 m 2.00 m 0.65 m 37.50 m 0.35 m 36.80 m 200 mm 1,750 mm 2,440 mm 70 mm B : BPL : L : Ls hb h S : : : : : Date mm II CNG V NG SUT GII HN CA VT LIU - STRENGTH AND ULTIMATE STRESS OF MATERIAL 2.1 Thộp - Steel: 2.1.1 Ct thộp ng sut trc - Prestress reinforcement Type of stress : Pretension stress Modulus of elasticity Ep = 197,000 (MPa) (5.4.2) = 1,860 (MPa) (5.4.4.1-1) Required tensile strength of prestressing steel fpu Liquid limit of prestreesing steel fpy = 0.9 fpu = 1,674 (MPa) (5.4.4.1-1) Prior to seating - short - term fs = 0.9 fpy = 1,507 (MPa) (5.9.3-1) = 1,302 (MPa) (5.9.3-1) At anchorages and couplers immediately after anchor set = 0.7 fpu At end of seating loss zone immediately after anchor set = 0.74 fpu = 1,376 (MPa) (5.9.3-1) = 0.8 fpy = 1,339 (MPa) (5.9.3-1) At service limit state after losses fpe (Pre-tensioning) Before the force transferred to concrete = 0.75 fpu = 1,395 (MPa) (5.9.3-1) = 1,339 (MPa) (5.9.3-1) After stress loss = 0.80 fpy Area of reinforcement, class of 15.2mm 140 mm Tension strength desinged for tendon Stress of reinforcement during kicking 2.1.2 Thanh cng cao - High-strength steel bar Modulus of elasticity Required tensile strength of steel bar Liquid limit of steel bar 2.1.3 Ct thộp thng - Plain reiforcement Modulus of elasticity Liquid limit strength of reinforcement CB400-V Tensile stress of reinforcement Liquid limit strength of reinforcement CB300-T Tensile stress of reinforcement 2.2 Bờ tụng - Concrete Density of concrete Thermal expansion coefficient of concrete H s t l gia bờ tụng v ct thộp Mean humidity Ppj fpj Ep fpu fpy = 0.8 fpu Es fsy fsa fsyr fsar = 0.6 fsy c ######### p H = 0.6 fsyr = 195 KN = 1395 MPa (Standard 22TCN 272-05) = 207,000 (MPa) = 1,035 (MPa) = 828 (MPa) (Standard TCVN 1651:2008) = 200,000 (MPa) = 400 (Mpa) = 240 (MPa) = 300 (Mpa) = 180 (MPa) = = = = 2,400 (Kg/m) 10.8E-6 / C 0.2 85 % (5.4.4) (5.4.4.1-1) (5.4.4.1-1) (5.4.3.2) (7.3.4-1) (7.3.4-1) (Bng 3.5.1) (5.4.2.2) (5.4.2.5) InputData-1/5 2.2.1 Dm ch - Main beam Theoretical compressive strength of concrete at 28 a Concrete compressive strength when tranfering forc Modulus of elasticity f'c f'ci = 0.85 f'c Ec = 0.043 yc1.5 f'c0.5 = = 50 (MPa) 42.5 (MPa) (5.4.2.1) = 35,750 (MPa) (5.4.2.1) Shear bearing capacity of plain concrete fr Ultimate stress of concrete Ultimate compressive stress when force tranfer applied =0.63f'c = 4.45 (MPa) (5.4.2.6) = 0.6 f'ci = 25.5 (MPa) (5.9.4.1.1) 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 =0.58f'ci0.5 = 3.78 (MPa) (5.9.4.1.2) = 0.45 f'c = 0.4 f'c = 0.6 f'c = = = 22.5 (MPa) 20 (Mpa) 30 (Mpa) (5.9.4.2.1-1) (5.9.4.2.1-1) (5.9.4.2.1-1) = 0.5 f'c0.5 = 3.54 (Mpa) (5.9.4.2.2-1) Tension stress after losing stress 2.2.2 Mt cu - Bridge deck Theoretical compressive strength of concrete at 28 a 0.5 f'cs Modulus of elasticity Ecs = 0.043 yc1.5 f'cs0.5 Ultimate compressive stress when losing stress * Prestressing + long-term load = 0.45f'cs * Hot ti+1/2(ng sut trc+ti trng lõu di) = 0.4 f'cs = 35 (MPa) (5.4.2.1) = 29,910 (MPa) (5.4.2.1) = = 15.8 (MPa) 14 (Mpa) (5.9.4.2.1-1) (5.9.4.2.1-1) 2.96 (Mpa) (5.9.4.2.2-1) Tension stress after losing stress = 0.5f'cs0.5 = 2.3 Material conversion factor Prestressing reinforcement/Concrete of main beam Rpc = Ep / Ec = Reinforcement/Concrete of main beam Rsc = Es / Ec = = Ecs / Ec = Concrete of bridge deck/Concrete of main beam Rdc Ti trng - 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= 18.31 kN/m - Lead load of divided wall, DC2= 0.33 kN/m - Concrete of bridge deck, DC3= 12.38 kN/m - Remaining formwork, DC4= 1.00 kN/m Total: 32.02 kN/m 3.1.2 Weigth of dead load, part - Hand rail, sidewalk, DC5= 2.50 kN/m - Deck overlay, DW= 4.14 kN/m Total: 6.64 kN/m 3.2 Live load 3.2.1 Live load of vehicle Carriage-way width Bx = 10.50 m Number of lanes as designed nx = lane Coefficient of lane m= 0.85 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 5.51 5.59 0.84 (Calculation for exteior beam) InputData-2/5 325 kN 3.2.2 Designed truck has total of weight 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 ln 3.0 kN/m 6.0 kN/m/1side III H S PHN B - 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 : : Number of beam = beam + Nb +S : Spacing of beams = 2440 mm +L : Span of beam = 37500 mm + ts : Thickness of concrete slab of bridge deck = 200 mm +n : Ratio of elasticity modulus = 0.837 +d : Height of main beam = 1750 mm 1.1 Distribution coefficient of moment * Internal beam One design lane loaded gM = (S/910)0,35(Sd/L2)0,25 Two or more design lanes loaded 0,6 0,125 gM = (S/1900) (Sd/L ) = 0.33 = 0.56 = 0.40 = = 0.00 mm 0.97 = 0.55 * Exterior beam One design lane loaded gMSE = 1,2gM Two or more design lanes loaded de = e = 0,97 + de/8700 gMSE = egM InputData-3/5 1.2 Distribution coefficient of shear force * Internal beam One design lane loaded gV = (S/3050)0.6(d/L)0.1 Two or more design lanes loaded 0.8 0.1 gV = (S/2250) (d/L) = 0.64 = 0.79 * Exterior beam One design lane loaded, lever rule P/2 P/2 R1 R1 = P/2*1880/2440 gVSE = 1.2R11.2x0.39 = Two or more design lanes loaded e = 0,8 + de/3050 gVSE Effect of skewed bridge (4.6.2.2.2d) = egV = 0.39 P = 0.46 P = 0.80 = 0.63 Skewed bridge = 0o Reduction of distribution coefficient of load for moment of longitudinal beam on skewed support min(1.05-0.25tg ; 1) = 1.00 Adjustment of distribution coefficient of load for shear force of the longitudinal beam on skewed support 0.5 + ((Ld) /6S)tan() = 1.00 Computation result of distribution coefficient of load Position of beam Number of lane gM gV Internal 0.33 0.64 Internal 0.56 0.79 MAX 0.56 0.79 Exterior 0.40 0.46 Exterior 0.55 0.63 MAX 0.55 0.63 IV GIAI ON TNH TON - PERIOD OF COMPUTATION Structure to be analysed through phases as follows: Giai on - Phase - Computation with load: + Dead live of self section of beam (DC) + Dead load of divided wall (DC) + Acting of Prestressing (PS) Giai on - Phase - Computation with load: + Dead load of self beam (DC) 18.31 kN/m/1beam + Dead load of divided wall (DC) 0.33 kN/m/1beam + Dead load of self deck (DC) 12.38 kN/m/1beam + Dead load of remaining formwork 1.00 kN/m/1beam + Hand rail, sidewalk (DC) 2.50 kN/m/1beam + Dead load of deck overlays (DW) 4.14 kN/m/1beam + Wastewater treatment pipe (P) 0.00 kN/m/1beam + Live load of vehicle (combined compact stress) LL+ IM; human InputData-4/5 V T HP TI TRNG - LOAD COMBINATION H s iu chnh ti trng - Adjustment coefficient of load Adjustment coefficient of load : = DR Relative coefficients Flexibility D Strength limit state Service limit state 1.00 1.00 (1.3.2) Redundancy R 1.00 1.00 Importance I 1.05 1.00 Trng thỏi gii hn v t hp ti trng - Strength limit states and load combination coefficient: Load combination at strength limit state I {1.25DC+1.5DW+1.75PL + 1.75(LL+IM)} Load combination at service limit state {DC+DW+PL+(LL+IM)} 1.05 1.00 (3.4) InputData-5/5 Bridge joint stock company no.12 Calculation of super-t beam Calculate by (Shop drawing design stage) Bui Van Duan Checked by Duong Van Chien Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=37.5m Project Structure Date C TRNG MT CT - 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 C TRNG CC MT CT TNH TON - CHARACTER OF BEAM COMPUTATION SECTION Height of beam 1,750 (mm) Height of beginning section of beam (mm) Height of bridge deck (mm) Width conversion of deck slab 2,041 (mm) Length of beginning section of beam 850 (mm) Length of plain section 1,425 (mm) Length of hollow section 32,950 (mm) Section f sup (mm) 920 1,840 2,760 3,680 4,600 5,520 6,440 7,360 8,280 9,200 10,120 11,040 11,960 12,880 13,800 14,720 15,640 16,560 17,480 18,400 Aconc (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 Iconc (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 e conc (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 Stage I (at the completion time of tensile) Astrand Istrand estrand A*e (m2) (m4) (m3) (m) 0.002 0.018 0.018 0.023 0.027 0.030 0.030 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 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 1.675 0.277 0.277 0.252 0.233 0.224 0.224 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 1.322 1.664 1.664 0.620 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 0.622 0.622 AcombI (m2) 0.945 1.689 1.689 0.715 0.719 0.722 0.722 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 0.727 IcombI (m4) 0.057 0.469 0.469 0.278 0.280 0.282 0.282 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 0.285 ecombI (m) 1.400 0.985 0.985 0.867 0.863 0.860 0.860 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 Super-T 37,5m-Section-1/3 Section f sup (mm) 920 1,840 2,760 3,680 4,600 5,520 6,440 7,360 8,280 9,200 10,120 11,040 11,960 12,880 13,800 14,720 15,640 16,560 17,480 18,400 Section f sup (mm) 920 1,840 2,760 3,680 4,600 5,520 6,440 7,360 8,280 9,200 10,120 11,040 11,960 12,880 13,800 14,720 15,640 16,560 17,480 18,400 Aconc (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 AcombI (m ) 0.945 1.688 1.688 0.714 0.717 0.720 0.720 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 Iconc (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 IcombI (m4) 0.056 0.468 0.468 0.277 0.279 0.281 0.281 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 econc (m) Stage I (at the time of concreting the bridge deck) Astrand Istrand estrand A*e AcombI (m2) (m4) (m3) (m2) (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 ecombI (m) 1.400 0.986 0.986 0.869 0.865 0.862 0.862 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.002 0.017 0.017 0.022 0.025 0.028 0.028 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 Aslab (m2) 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 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 0.004 0.004 0.004 1.675 0.277 0.277 0.252 0.233 0.224 0.224 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 0.210 Stage II (At service) Islab eslab (m4) (m) 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 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 1.322 1.664 1.664 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 0.621 0.621 0.621 0.621 0.621 A*e (m3) 2.078 2.419 2.419 1.375 1.375 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 1.376 0.945 1.688 1.688 0.714 0.717 0.720 0.720 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 AcombI (m2) 1.353 2.096 2.096 1.122 1.125 1.128 1.128 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 IcombI (m4) 0.056 0.468 0.468 0.277 0.279 0.281 0.281 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 IcombI (m4) 0.116 0.715 0.715 0.529 0.533 0.536 0.536 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 ecombI (m) 1.400 0.986 0.986 0.869 0.865 0.862 0.862 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 0.857 ecombI (m) 1.536 1.154 1.154 1.226 1.223 1.220 1.220 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 Super-T 37,5m-Section-2/3 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 + Plosses1/Agirder - Plosses1*estrand1*Yt1/Igirder + Mstg2*Yt1/Igirder Stress at bottom fiber of beam when concreting bridge deck is to be calculated as follows: fb2 = fb1 + Plosses1/A girder + Plosses1*estrand1*Yb1/Igirder - Mstg2*Yb1/Igirder Ultimate tensile stress when force transfer applied = - 0.5f'ci0.5 Ultimate compressive stress when force transfer applied = 0.45f'ci SECTION (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 Plosses1 (KN) -8 -183 -175 -375 -475 -582 -567 -759 -744 -730 -717 -705 -695 -686 -678 -671 -665 -661 -658 -656 -656 Agirder (m2) 0.945 1.688 1.688 0.714 0.717 0.720 0.720 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 0.724 Igirder (m4) 0.056 0.468 0.468 0.277 0.279 0.281 0.281 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 0.708 0.708 0.615 0.631 0.636 0.636 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) 0.00 228.18 444.65 649.42 842.49 1,023.86 1,193.53 1,351.50 1,497.77 1,632.33 1,755.19 1,866.36 1,965.82 2,053.58 2,129.64 2,193.99 2,246.65 2,287.60 2,316.86 2,334.41 2,340.26 Yt1 (m) 0.350 0.765 0.765 0.883 0.887 0.890 0.890 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 Yb1 (m) 0.450 0.985 0.985 0.867 0.863 0.860 0.860 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 0.855 -3.54 (MPa) +22.50 (MPa) ft2 (Mpa) 1.04 -1.33 -0.50 2.27 3.12 4.00 5.25 5.70 6.77 7.76 8.66 9.47 10.20 10.84 11.40 11.87 12.25 12.55 12.76 12.89 12.94 fb2 (Mpa) -0.42 7.04 5.99 10.84 11.52 12.10 10.98 12.52 11.58 10.71 9.93 9.21 8.57 8.01 7.52 7.11 6.77 6.51 6.32 6.20 6.17 16 18 STRESS AT TOPPING 30 27 24 STRESS (Mpa) 21 18 15 12 -3 10 12 14 20 -6 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited Super-T 38,25m-StressChk-2/4 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 = Plosses/Acomb + Mstg3*Yt2/Icomb Stress at bottom fiber of beam in the period of operation is to be calculated by: fb3 = Plosses/Acomb - Mstg3*Yb2/I comb Ultimate tensile stress when force transfer applied = - 0.5f'ci0.5 Ultimate compressive stress when force transfer applied = 0.4f'c SECTION (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 Plosses Acomb Icomb (KN) 361 3,696 3,729 4,340 4,846 5,333 5,396 6,034 6,097 6,155 6,208 6,256 6,299 6,337 6,370 6,398 6,421 6,438 6,451 6,459 6,461 (m2) 1.353 2.096 2.096 1.122 1.125 1.128 1.128 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 (m ) 0.116 0.715 0.715 0.529 0.533 0.536 0.536 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 estrand2 = = Mstg3 (m) -0.139 0.877 0.877 0.974 0.990 0.996 0.996 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 (KNm) 25.1 -916.8 -265.1 -114.7 193.2 491.3 978.8 1,113.9 1,527.2 1,906.2 2,250.9 2,561.2 2,837.3 3,079.0 3,286.4 3,459.4 3,598.2 3,702.6 3,772.7 3,808.5 3,821.7 -3.54 (MPa) +20.00 (MPa) Yt2 Yb2 (m) 0.414 0.796 0.796 0.724 0.727 0.730 0.730 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 (m) 0.586 1.154 1.154 1.226 1.223 1.220 1.220 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 ft3 fb3 (Mpa) 0.36 0.74 1.48 3.71 4.57 5.40 6.12 6.84 7.45 8.02 8.53 9.00 9.41 9.77 10.08 10.34 10.55 10.71 10.81 10.87 10.89 (Mpa) 0.14 3.24 2.21 4.13 3.86 3.61 2.56 2.83 1.96 1.16 0.43 -0.22 -0.80 -1.31 -1.75 -2.11 -2.40 -2.62 -2.77 -2.84 -2.87 STRESS AT SERVICE 24 21 18 STRESS (Mpa) 15 12 -3 10 12 14 16 18 20 -6 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited Super-T 38,25m-StressChk-3/4 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 = Plosses/Acomb+ Mstg4*Yt2/Icomb Stress at bottom fiber of beam in the period of operation is to be calculated by: fb4 = Plosses/Acomb - 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 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 Plosses Acomb Icomb (KN) 361 3,696 3,729 4,340 4,846 5,333 5,396 6,034 6,097 6,155 6,208 6,256 6,299 6,337 6,370 6,398 6,421 6,438 6,451 6,459 6,461 (m2) 1.353 2.096 2.096 1.122 1.125 1.128 1.128 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 1.133 (m ) 0.116 0.715 0.715 0.529 0.533 0.536 0.536 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 estrand2 (m) -0.139 0.877 0.877 0.974 0.990 0.996 0.996 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 1.006 = = Mstg3 (KNm) 50.3 -2,207.6 -1,258.3 -1,291.3 -989.5 -687.5 13.4 29.6 622.1 1,166.0 1,661.3 2,107.8 2,505.8 2,855.0 3,155.6 3,407.6 3,610.8 3,765.4 3,871.4 3,928.7 3,949.1 -3.54 (MPa) +30.00 (MPa) Yt2 Yb2 (m) 0.414 0.796 0.796 0.724 0.727 0.730 0.730 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 0.735 (m) 0.586 1.154 1.154 1.226 1.223 1.220 1.220 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 1.215 (Mpa) 0.45 -0.70 0.38 2.10 2.96 3.79 4.80 5.37 6.23 7.02 7.73 8.38 8.96 9.47 9.90 10.27 10.56 10.79 10.95 11.03 11.06 ft3 14 16 fb3 (Mpa) 0.01 5.33 3.81 6.86 6.58 6.29 4.75 5.26 3.99 2.82 1.76 0.80 -0.06 -0.81 -1.45 -1.99 -2.43 -2.76 -2.99 -3.11 -3.15 STRESS AT SERVICE 35 30 STRESS (Mpa) 25 20 15 10 0 10 12 18 20 -5 DISTANCE FROM SUPPORT (m) Top fibre Bottom fibre Compresive stress limited Tensile stress limited Super-T 38,25m-StressChk-4/4 Bridge joint stock company no.12 Calculation of super-t beam Calculate by (Shop drawing design stage) Bui Van Duan Checked by Duong Van Chien Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=38.25m Project Structure Date KIM TRA TRNG THI GII HN - CHECKING THE STATE OF STRENGTH LIMIT IN BEAM I KIM TRA GII HN V CT THẫP - CHECKING THE REINFORCEMENT LIMITS I.1 Hm lng ct thộp ti a - Maximum reiforcement limit Percentage of reinforcement shall be limited so that: (A.5.7.3.3.1-1) c 0,42 (5.7.3.3.1-1) de Where: + c : Height of compression region c= A ps f pu 0,85 f c (b b w )h f f pu 0,85 f c b w + kA ps dp (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 (5.7.3.1-2) A ps f ps + A s f y + : Stressing cubic coefficient = 0,85 f ' c 28 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 pu (1 k c ) dp (5.7.3.1.1-1) + 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 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 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 bw (mm) 890 700 700 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 f py f pu ) (5.7.3.1.1-2) 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 Position neutral axis Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever Cantilever c (mm) 95 95 121 139 156 156 182 182 182 182 182 182 182 182 182 182 182 de (mm) 275 1,673 1,673 1,698 1,717 1,726 1,726 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 0.06 0.06 0.07 0.08 0.09 0.09 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK Super-T 38,25m-LimitStateChk-1/6 16.83 17.77 18.70 0.69 0.69 0.69 240 240 240 0.280 0.280 0.280 Cantilever Cantilever Cantilever 182 182 182 1,740 1,740 1,740 0.10 0.10 0.10 OK OK OK 1.2 Hm lng ct thộp ti thiu - 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 : Mr min(1.2Mcr, 1.33Mtt) * 1,2 crack resistance Mcr to be defined on the basis of elastic stress distribution and tensile strength when bending of concrete M cr = f r fr = 0.63 I comb Zt (5.7.3.6.2) f c (5.4.2.6) * 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 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 fr (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 Icomb (m ) 1.2Mcr (KNm) 0.116 0.715 0.715 0.529 0.533 0.536 0.536 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 0.542 1,492 4,800 4,800 3,903 3,916 3,926 3,926 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 3,942 1.33Mtt (KNm) 0.0 2,087.9 4,066.7 5,936.5 7,697.2 9,348.9 10,891.6 12,325.2 13,649.8 14,865.4 15,971.9 16,969.4 17,857.9 18,637.3 19,307.7 19,869.0 20,321.3 20,664.6 20,898.8 21,024.0 21,068.9 Mr (KNm) Conclusion 140 9,244 9,244 11,834 13,594 15,281 15,281 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK II KIM TRA KHNG UN - CHECK MOMENT RESISTANCE The factored moment resistance Mr , shall be taken as: Mr = Mn Mu (KN) Where: = 1.00 : Resistance factored as specified in Article 5.5.4.2 a Mn = Aps*fps * d p + 0.85*f'c*(b-bw)*1*hf* + Mu + Mr + Mn + dp + fps + a = c.1 SECTION (5.7.3.2.1-1) h a f 2 (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 fps Mn Mu Mr Conclusion Super-T 38,25m-LimitStateChk-2/6 (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 (mm) 6.00 66.03 66.03 84.04 96.04 108.05 108.05 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 126.06 (KNm) 140 9,244 9,244 11,834 13,594 15,281 15,281 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 (Mpa) 1844 1830 1830 1823 1818 1813 1813 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 1806 (KNm) 0.0 1,569.8 3,057.7 4,463.5 5,787.4 7,029.3 8,189.2 9,267.1 10,263.0 11,177.0 12,009.0 12,759.0 13,427.0 14,013.0 14,517.0 14,939.1 15,279.2 15,537.3 15,713.4 15,807.5 15,841.2 III KIM TRA KHNG CT - CHECK SHEAR RESISTANCE III.1 Nominal shear resistance Nominal shear resistance Vn shall take less-than value of : Vn = Vc + Vs + Vp Vn = 0,25f'cbvdv + Vp Where: Vc = 0,083 f cb v dv Vs = (KNm) 140 9,244 9,244 11,834 13,594 15,281 15,281 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 17,809 Conclusion OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK (A.5.8.3.3) A v f y d v (cotg + cotg )sin s + bv : Width of minimum web of beam (mm) dv = max(0,9de ; 0,72h) + dv : Effective shear height (mm), + s : Distance of hoop reinforcement (mm) + : Capability coefficient of crossed crack concrete + : Inclination angle of crossed compressive stress () + : 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) A vmin = 0.83 f c' b vs fy + Vp : Component of effective prestress towards active shearing force, is positive (+) if in opposing direction of shearing force + Vp = fps.Aps.sini = 0.0 KN + i : Inclination angle of strand compared with horizontal direction Proposed arrangement of hoop reinforcement ia as follows: fy d SECTION S Av (Mpa) (m) (mm) (mm) (mm2) 0.00 20.00 75 400 628 0.94 20.00 75 400 628 1.87 20.00 75 400 628 2.81 20.00 100 400 628 3.74 20.00 100 400 628 4.68 16.00 150 400 402 Avmin Conclusion 77.030445 98 OK 77 OK 77 OK 35 OK 35 OK 53 OK Super-T 38,25m-LimitStateChk-3/6 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 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 16.00 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400 402 402 402 402 402 402 402 402 402 402 402 402 402 402 402 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK III.2 Determination of and and 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 Vp (5.8.3.4.2-1) v = Improvise in tension reiforcement x: b v d v Mu + ,5 N u + 0,5 V u cot A ps f po d x = v 0, 002 E s A s + E p A ps (5.8.3.4.2-2) If value of x is minus so we take absolute value and reduce by multiply with coefficient F F = Where: SECTION (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 E s A s + E p A ps E c A c + E s A s + E p A ps + f'c : Compressive strength of concrete f'c = 50 MPa Ec = 35750 MPa + Ec : Elasticity of concrete + Es : Elasticity modulus of tendon Ep = 197000 MPa + : Shear resistance coefficient = 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 + Nps = fps.Aps.cosi : Axial force effects on beam due to prestress Nps 0.0011392 Determination of parameter and Nu fpc fpo v v/f'c 0.0080315 dv (Mpa) (Mpa) (N) 0.0188907 (KN) (mm) 360.86 576 0.27 1,290.25 3.734 0.075 0.001 3,695.90 1505 1.76 1,209.68 1.735 0.035 0.008 3,729.29 1505 1.78 1,220.61 1.653 0.033 0.008 4,340.32 1528 3.87 1,128.54 4.514 0.090 0.019 4,845.81 1545 4.31 1,105.39 4.232 0.085 0.021 5,332.71 1554 4.73 1,084.13 3.978 0.080 0.024 5,395.62 1554 4.78 1,096.92 3.747 0.075 0.024 6,033.85 1566 5.33 1,055.52 3.488 0.070 0.028 6,097.06 1566 5.38 1,066.58 3.258 0.065 0.028 6,155.22 1566 5.43 1,076.75 3.029 0.061 0.028 6,208.31 1566 5.48 1,086.04 2.800 0.056 0.028 6,256.34 1566 5.52 1,094.44 2.571 0.051 0.028 6,299.32 1566 5.56 1,101.96 2.342 0.047 0.028 6,337.24 1566 5.59 1,108.59 2.112 0.042 0.028 (5.8.3.4.2-3) 0.008031539 1000ex () 5.64 42.00 7.02 43.00 6.94 43.00 7.10 40.00 7.03 40.80 7.26 41.40 7.18 42.00 7.13 42.20 7.06 42.40 7.00 42.60 6.94 42.80 6.88 43.00 6.83 43.00 6.78 43.00 1.65 1.72 1.72 1.53 1.57 1.61 1.65 1.66 1.68 1.69 1.70 1.72 1.72 1.72 Super-T 38,25m-LimitStateChk-4/6 13.09 14.03 14.96 15.90 16.83 17.77 18.70 SECTION (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 6,370.10 6,397.90 6,420.65 6,438.35 6,450.99 6,458.57 6,461.10 (Degree) 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 1566 1566 1566 1566 1566 1566 1566 5.62 5.65 5.67 5.68 5.70 5.70 5.70 1,114.34 1,119.20 1,123.18 1,126.28 1,128.49 1,129.82 1,130.26 Av (mm2) 628 628 628 628 628 402 402 402 402 402 402 402 402 402 402 402 402 402 402 402 402 Vc Vs (KN) 496.43 1,063.79 1,063.79 329.38 341.77 352.36 361.11 366.26 370.68 372.88 375.09 379.50 379.50 379.50 379.50 379.50 379.50 379.50 379.50 379.50 379.50 (KN) 2,142.61 5,407.17 5,407.17 4,575.53 4,497.59 1,889.28 1,849.86 1,851.91 1,838.97 1,826.13 1,813.38 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1,800.73 1.883 1.654 1.425 1.196 0.967 0.737 0.524 0.038 0.033 0.028 0.024 0.019 0.015 0.010 Vc+Vs 0.25f'cbvdv Vn Vu Vu Vn (KN) 6,408 13,173 13,173 4,585 4,636 4,661 4,661 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 4,699 (KN) 2,375 5,824 5,824 4,127 4,173 2,017 1,990 1,996 1,989 1,979 1,970 1,962 1,962 1,962 1,962 1,962 1,962 1,962 1,962 1,962 1,962 (KN) 1,723 1,645 1,568 1,490 1,413 1,335 1,258 1,180 1,102 1,025 947 870 792 715 637 560 482 405 327 250 177 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK (KN) 2,639.04 6,470.96 6,470.96 4,904.91 4,839.36 2,241.63 2,210.97 2,218.18 2,209.65 2,199.01 2,188.47 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 2,180.24 IV CHECK SHEAR RESISTANCE AT INTERFACE PLANE IV.1 The open section nearest support: = 1,704.48 (KN) At Strength-I: Calculation shear Vu The horizontal shear per unit length Vh , shall be taken as: (KN/m) Vh = Vu/de de = 1.673 (m) Vh = 1,018.98 (KN/m) x= 0.028 0.028 0.028 0.028 0.028 0.028 0.028 6.74 6.69 6.65 6.61 6.57 6.53 6.50 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 0.00 m The distance between the centroid of steel in tension side of the beam to the centre of the compression block in the deck The nominal shear resistance of the interface plane Vn , shall be taken as: Vn = cAcv + à[Avffy + Pc ] (5.8.4.1) The interface shear resistance, Vn, will not exceed : Vn 0.2 f'cAcv or Vn 5.5Acv Where: Acv = 1.35 (m ) Area of concrete in shear transfer plane Avf = fy = c= à= Pc = 6,434 400 0.52 0.60 0.00 (mm2) (MPa) (MPa) (KN) 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; Pc=0 Super-T 38,25m-LimitStateChk-5/6 f'c = Vn = 0.2 f'cAcv = 5.5Acv = Vn = Vr =Vn = 35 2,247.63 9,469.83 7,440.58 2,247.63 2,022.87 (MPa) (KN) (KN) (KN) (kN) (kN) Specified 28 day copressive strength of the weaker concrete > Vu = 1,722.79 (KN) IV.2 The open section nearest support x= At Strength-I: Calculation shear Vu = 1,490.17 (KN) The nominal shear resistance of the interface plane Vn , shall be taken as: Vn = cAcv + à[Avffy + Pc ] (5.8.4.1) The interface shear resistance, Vn, will not exceed : 0.2 f'cAcv or Vn Vn 5.5Acv Where: 1.12 (m ) Area of concrete in shear transfer plane Acv = 1,583 (mm ) 14 (thanh) 12 (mm) Avf hor = = 1583 (mm ) fy = 400 (MPa) c= 0.52 (MPa) à= 0.60 Pc = 3,729 (KN) 35 (MPa) f'c = Vn = 3,200.96 (KN) 0.2 f'cAcv = 7,853.24 (KN) 5.5Acv = 6,170.40 (KN) Vn = 3,200.96 (kN) 2,880.87 (kN) Vr =Vn = Avf = n= D= => OK 2.81 m Area of shear reinforcement crossing the shear plane number of horizontal bar diameter of horizontal bars area of horizontal-bar 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; Pc=0 Specified 28 day copressive strength of the weaker concrete > Vu = 1,490.17 (KN) => OK V CHECK PRETENSION ANCHORAGE ZONES (5.10.10) The solid section nearest support x= 935 mm At Strength-I: Calculation axial force Nu = 4,114 KN The bursting resistance of pretension anchorage zone Pr , shall be taken as: Pn = fs*As Where: 140 (MPa) Stress in steel not exceeding 140 Mpa fs = S= 75 (mm) Spacing of stirrups (mm) n= Number of reinforcement within distance S D= 20 (mm) Diameter of reinforcing bars As = 3,267 (mm ) Total area of vertical reinforcement located within the distance h/5 from the ending h= 1,950 (mm) Overall depth of member = Pn = Pr = 0.70 457.42 (KN) 320.19 (KN) Resistance factor as specified in Article 5.5.4.2 > 0.04Nu = 164.55 (kN) => OK Super-T 38,25m-LimitStateChk-6/6 Bridge joint stock company no.12 Project Structure Calculation of super-t beam Calculate by (Shop drawing design stage) Bui Van Duan Checked by Duong Van Chien Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=38.25m Date I HALVING JOINT DESIGN 350 950 350 Section A T C1 T1 100 Vu 600 100 800 Arrange the reinforcement according to strut-and-tie model (A.5.6.3) 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) Distance from bearing center to the beam anchorage 350 (mm) 800 100 950 136 850 850 Strut-and-tie model for halving joint design Checking the internal force produced in halving joint: Maximum counter force calculated for strength combination Vu = 1,704.48 (KN) = 43 (degree) Inclination angle compared to the vertical diretion of the bar C1 Compressive force in bar C1 C1 = 2,499.24 (KN) Force in bracing T1 T1 = 1,827.83 (kN) I.1 Checking the cross bracing T1 Nominate resistance of tension bracing bar shall be taken as: 2573.5927 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 = Pn = 2316.23 KN > T1 = 1827.83 KN => OK I.2 Checking the compressive bar C1 Nominate resistance of compressive bar shall be taken as: Pn= fcuAcs = 4630.1687 KN Where: la sin = 284 (mm) : Dimension of compressive bar Acs= 108,945 (mm ) : Area of effective section of compressive bar 42.50 Mpa: ultimate compressive stress+F40 fcu=min(f'c/(0.8+1701),0.85f'c)= 1=(s+0.002)cotg2= s= Pr = Pn = 0.000831 0.000004 : Deformation of concrete towards tension bracing 4167.15 KN > C1 = 2499.24 KN => OK Super-T 38,25m-HalvingJoint -1/2 II CHECKING BRACKET AT HALVING SECTION OF GIRDER Calculation shear Calculation axial force Vu Nu = = 1704.48 360.86 (KN) (KN) Nu Punching crack d1 Horizontal bar d2 Nuc Grillage bar Section centroid Vu II.1 Design for flexure and horizontal The area of primary tension reinforcement, As ,shall satisfy the requirements : 0.667Avf required + An (A.5.13.2.4) As Area of tie within a distance equal to 2/3 height of halving section from primary reinforcement Ah 0.5 (As - An) Where Avf required = [(1.1Vu + cAcv)/à - Pc ] /fy Avf required = 10743 (mm ) (mm2) Avf grillage = 6434 n D = = 10 25 Avf hor = 4909 Avftotal = 11343 (mm ) (mm) (mm2) An As n1 D1 n2 D2 = = = = = = Ah hor = Ah = 3583 (mm ) = Nuc/fy = Nu*d1/d2 = 0.275 = 0.425 = 234 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) 649 (mm ) 7815 (mm ) 14.0 20 (mm) 14.0 16 (mm) 7213 (mm ) An Nuc d1 d2 Nuc Area of grillage-bar reinforcement crossing the shear plane (mm2) => OK < As Number of ties bar from 2/3 height of halving section Diameter of ties bar Number of ties bar from 7213.0967 2/3 height of halving section Diameter of ties bar area of horizontal-bar reinforcement within 2/3 height of section (mm2) => OK < Ah II.2 Design for punching shear The nominal punching shear resistance Vn , shall be taken as: Vn = 0.328 f'c0.5 (W+L+de)de f'c bv W L de Vn Vr = = = = = = = (5.13.2.5.4) where 50 890 500 450 800 3247 2922 (Mpa) (mm) (mm) (mm) (mm) (KN) (KN) Specified compressive strength at 28 days Minimum width of section Width of elastic bearing 1722.7925 (450x500x85)mm Length of elastic bearing (450x500x85)mm Height of section > Vu = 1704.5 (KN) => OK Super-T 38,25m-HalvingJoint -2/2 company no.12 Calculate by (Shop drawing design stage) Bui Van Duan Checked by Duong Van Chien Da Nang priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super-T beam L=38.25m Project Bridge joint stock Calculation of super-t beam Structure Date 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) DCI = Where: 5.DC I Li 384.Eci I I + DCI : Load due to beam self weight in phase I + Li : Factored span length 32,959 + Eci : Elasticity modulus of concrete in phase I, Eci = + 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: P = (MPa) M P L2i PP eP L2i = 8Eci I I Eci I I 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 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 DC (mm) 0.00 0.00 0.00 0.03 0.08 0.20 0.41 0.76 1.29 2.07 3.16 4.62 6.54 9.01 12.12 15.97 20.68 26.35 P (mm) 0.00 -0.09 -0.35 -1.41 -2.89 -5.07 -7.31 -11.52 -15.07 -19.11 -23.63 -28.64 -34.13 -40.11 -46.57 -53.50 -60.92 -68.81 (mm) 0.00 -0.09 -0.34 -1.38 -2.81 -4.87 -6.90 -10.76 -13.78 -17.04 -20.48 -24.02 -27.59 -31.10 -34.44 -37.53 -40.24 -42.46 Deformation Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Deflection of girder at transfer 60 45 Deflection(mm) Section (m) 30 15 -15 10 15 20 -30 -45 -60 Length of design span (m) Super-T 38,25m-Def&Camb-1/4 16.83 17.77 18.70 33.12 41.12 50.48 -77.18 -86.01 -95.31 -44.06 -44.89 -44.83 Camber Camber Camber III DEFLECTION WHEN FORCE TRANSFER APPLIED UNTIL CONCRETING THE BRIDGE DECK III.1 Deflection of main beam due to dead load (phase II) DCII = 5.DC II Li 384.Eci I II Trong ú : + DCII : Load due to beam self weight + bridge deck phase II + Li : Factored span length + 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: P = Where: (MPa) M P L2i P e L2 = P P i Eci I II Eci I II + 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 DC (mm) 0.000 0.000 0.003 0.026 0.082 0.199 0.413 0.758 1.292 2.070 3.155 4.619 6.542 9.011 12.120 15.972 20.677 26.351 33.120 41.117 50.481 BMC (mm) 0.000 0.000 0.002 0.017 0.055 0.133 0.276 0.507 0.865 1.386 2.112 3.092 4.380 6.033 8.114 10.693 13.843 17.641 22.173 27.526 33.795 P (mm) (mm) 0.000 -0.083 -0.331 -1.349 -2.768 -4.847 -6.996 -11.023 -14.427 -18.294 -22.624 -27.417 -32.674 -38.394 -44.575 -51.216 -58.315 -65.869 -73.876 -82.333 -91.235 0.000 -0.082 -0.326 -1.305 -2.631 -4.515 -6.307 -9.758 -12.270 -14.838 -17.357 -19.706 -21.752 -23.350 -24.340 -24.550 -23.795 -21.876 -18.583 -13.689 -6.959 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 30 Deflection(mm) Section (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 15.90 16.83 17.77 18.70 20 10 -10 10 15 20 -20 -30 -40 Length of design span (m) Super-T 38,25m-Def&Camb-2/4 IV DEFLECTION OF OPERATION PHASE IV.1 Deflection of main beam due to dead load (service phase) DCKT = 5.DC KT Li 384.Ec 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: P = 35,750 (MPa) M P L2i P e L2 = P P i Ec I KT 8Ec I KT Where: + Mp : Moment created by prestress on beam center + Li : Factored span length + 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: P = M W L2i Ec I KT P = M LL L2i Ec I KT Deflection due to vehicle load: Where: + Pi : Axle load number ith + ci : Distance from position of axle load apply to the bearing Section (m) 0.00 0.94 1.87 2.81 3.74 4.68 5.61 6.55 7.48 8.42 9.35 10.29 11.22 12.16 13.09 14.03 14.96 DCKT (mm) 0.00 0.00 0.00 0.03 0.08 0.20 0.42 0.76 1.30 2.08 3.17 4.65 6.58 9.07 12.19 16.07 20.80 P (mm) 0.00 -0.06 -0.23 -0.92 -1.85 -3.18 -4.63 -7.05 -9.30 -11.88 -14.79 -18.04 -21.61 -25.52 -29.75 -34.30 -39.17 LL (mm) 0.00 0.01 0.07 0.30 0.67 1.27 2.13 3.24 4.68 6.44 8.53 10.94 13.68 16.72 20.04 23.62 27.41 W (mm) 0.00 0.00 0.02 0.09 0.21 0.41 0.68 1.04 1.50 2.07 2.75 3.54 4.44 5.44 6.54 7.74 9.02 25%LL+W (mm) 0.00 0.00 0.04 0.17 0.38 0.72 1.21 1.85 2.67 3.68 4.88 6.28 7.86 9.62 11.56 13.64 15.87 (mm) 0.000 -0.049 -0.164 -0.602 -1.092 -1.708 -2.088 -3.043 -3.318 -3.357 -3.090 -2.447 -1.353 0.267 2.488 5.389 9.050 Deformation [ ] (mm) Conclusion Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Camber Deflection Deflection Deflection Deflection 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 38.250 OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK Super-T 38,25m-Def&Camb-3/4 15.90 16.83 17.77 18.70 26.51 33.32 41.37 50.79 -44.34 -49.80 -55.56 -61.58 31.38 35.46 39.61 43.94 10.37 11.77 13.21 14.68 18.21 20.63 23.11 25.66 13.553 18.981 25.419 33.150 Deflection Deflection Deflection Deflection 38.250 38.250 38.250 38.250 OK OK OK OK Deflection of girder at service 40 Deflection(mm) 30 20 10 0 10 12 14 16 18 20 -10 -20 -30 -40 Length of design span (m) V TOTAL DEFLECTION AT THE SECTION OF MIDDLE OF BEAM Deflection due to transfer of prestressing load Ztransfer = -44.83 (mm) Deflection after concreting the bridge deck Ztopping = -6.96 (mm) Deflection of service phase Zservice = 33.15 (mm) Super-T 38,25m-Def&Camb-4/4 ... priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super- T beam L=37.5m Project Structure Date KIM TRA TRNG THI GII HN - CHECKING THE STATE OF STRENGTH LIMIT IN BEAM... priority Infrastructure Investment Project Sub_component C12 - Khue Dong bridge Super- T beam L=37.5m Project Structure Date C TRNG MT CT - MORPHOLOGIC FEATURE OF SECTION I.INTRODUCTION: Character... 17.48 18.40 Phase I State of strength limit I Exterior Intermediate MMax beam beam Phase II State of strength limit I State of using limit Exterior Intermediate Exterior Intermediate MMax MMax beam