Bảng tính mố chữ U cao tốc Hải Phòng

Ha noi - Hai Phong Expressway Project ABUTMENT CALCULATION Package: Bridge name: Abutment Name: EX-10 Lach Tray Bridge A1, A2 MATERIALS 1.1 Material Unit Weights • Unit Weight of Concrete • Unit Weight of Soil • Unit Weight of Saturated Soil 1.2 Concrete = = = 10 71 13 129 γc γs γsw → → → f'c = 35 Ec = 31799 β1 = 0.80 fr =0.63√f'c = 3.73 Reinf Standart: fy = 420 Es = 200000 Reinforcing bar Area 19 22 25 284 387 510 Compressive Strength of concrete at 28 days Modulus of Elasticity Stress Block Factor Modulus of Rupture 1.3 Reinforcement Yield strength Modulus of elasticity Diameter (mm2) 2500 kg/m3 1800 kg/m3 1100 kg/m4 16 199 = = = 24.5 kN/m3 17.7 kN/m3 11.0 kN/m4 MPa MPa MPa MPa MPa 29 645 32 819 36 1006 LOADS FROM SUPERSTRUCTURE ng = girders Number of Girders 2.1 Dead load = 16.50 m Width of Bridge W Reaction due to dead load of super-T girder Span Members - Main Girder - Deck Slab - Diaphargms - Precast plank - Curbs - Railing and other - Surface wearing DC DW Total 2.2 Live load Vehicular live loading name Number of lanes Mutiple Presence Factors of Live Load = = Volume Gravity Reaction (m3) (kN/m3) (kN) 220.00 24.5 2697.8 126.39 24.5 1549.9 15.00 24.5 183.9 11.40 24.5 139.8 28.73 24.5 352.2 10.0 48.10 22.6 542.7 4923.6 552.7 HL-93 0.650 Design Truck Live load Forces 0.004448 0.3048 V1 = 4.3m 35kN P1 P2 P3 V2 = 4.3m - 9.0m 145kN 145kN P4 P5 Wl Design Truck 35 kN V1 145 kN V2 145 kN Design Tandem 110 kN V3 110 kN Design Lane Load 9.3 kN/m Wheel Spacing 4.3 m 4.3 m 1.2 m Design Tandem 1.200m Abutment-A1A2(OK).xls - SuperLoad Date: 9/26/2011 Page: of Ha noi - Hai Phong Expressway Project Design Tandem Dynamic Load Allowance Component Deck Joint - All Limit States All Other Components Fatigue and Fracture Limit State All Other Limit States 1.200m 110kN 110kN Design Lane load IM 75% 15% 25% LIVE LOAD APPLYING ON SUPERSTRUCTURE 9.3 kN/m Design Truck P1 P2 P3 Ls Total span length Calculation span leng Pedestrian load Width of sidewalk Number of sidewalk Pedestrian load Lst Ls Wsw nsw Wp = 38.300 m = 37.600 m = = = = R P4 Design Tandem P5 0.0 kN/m2 0.000 m 0.000 0.0 kN/m R Design Lane Load WL R Reaction Notes: Design Truck P2 P3 333.9 377.0 P1 70.2 Design Tandem P4 P5 Total 365.0 286.0 651.0 Total 781.1 Lane Load Pedestrian Load 454.6 Live Load 1430.9 Reaction due to live load HL- 93 = max (Rtruck, Rtandem) + Rlane Combine live load HL-93 and pedestrian for disadvantage BR = 211.3 KN 2.3 Braking force 2.4 Temprature Load o Uniform temperature change +/-20.0 ΔT = C = 1.08E-5 /oC Coefficient of thermal expansion = 0.0081 m Movement Δu = 1000 KPa Shear Modulus of Elastomer G A = 0.158 m2 Area of bearing b hrt = 0.078 m Height of bearing H = G.A.Δu/hrt = 131.2 KN Horizontal Force due to ΔT 2.5 Creep and Shrinkage Load =20.2 oC Convert to Uniform temperature change ΔT = = 0.0082 m Movement Δu H = G.A.Δu/hrt = 132.6 KN Horizontal Force due to ΔT 2.4 Wind Load V = S.VB The design wind velocity, V, shall be determined from: VB: where: Basic second gust wind velocity with 100 years return period appropriate to the Wind Zone in which the bridge is located, as specified in table VB Wind zone according to TCVN 2737-1995 (m/s) I II III IV S: Abutment-A1A2(OK).xls - SuperLoad 38 Wind zone: IV VB = 59.0 m/s 45 53 59 Correction factor for up wind terrain and deck height S = 67.3 m/s V Date: 9/26/2011 = 1.140 Page: of Ha noi - Hai Phong Expressway Project 2.5.1 Wind load on structures Transverse wind load on structure Overall width of the bridge between outer faces of parapets b Depth of superstructure, including solid parapets d Ratio b/d C = f(b/d) Dag coefficient d At Area of the structures for calculation of transverse wind load Transverse wind load PD = max(0.0006V 2.Cd.At,1.8At) = FWSL = 0.25PD = Longitudinal wind load 2.5.2 Wind load on vehicles (WL) Transverse wind load on vehicle Longitudinal wind load on vehicles Vertical wind load Area Vertical wind load 2.6 Earthquke effects (EQ) Acceleration coefficient Seismic Performance Zones Soil profile type Site Coefficients Response Modification Factor For Stem wall For Foundation Elastic seismic response coefficient Longitudinal Force due to Earthquake Abutment-A1A2(OK).xls - SuperLoad = 15.700 m = 3.060 m = 5.131 = 1.4 = 58.599 m2 = 222.7 KN = 111.3 KN = = 28.7 KN 28.7 KN Av = 315.975 m2 Pv = 0.00045V Av = 643.2 KN A S R R Csm EQ Date: 9/26/2011 = 0.1168 IV = = 1.5 = 1.0 = 0.292 = 3198.1 KN Page: of Ha noi - Hai Phong Expressway Project STRUCTURE ANALYSIS w n b3 t Bearing Type: b4 c Move G/L g j d7 d4 m d1 d6 0.5m d2 h b1 d2 a d5 b2 d3 G/L e f b d s1 s2 C.G s3 x1 s4 Pile Row PILE DATA si No of Row Piles i (m) 1.500 4 4.500 Total Piles - Np x x1 x2 Ip 3.750 2.250 2.250 40.50 m m m m2 s1 x2 x 3.1 Other input Data • Internal Friction Angle of Soil • Friction Angle between Abutment and Backfill • Friction Coefficient of Movable Bearing Shoes • Acceleration Coefficient = • Skew angle (square bridge α = 90o) Item Stem Height Footing Width Stem Width Footing Depth Footing Slope Bearing Seat Length Ballast Wall Height Ballast Wall Thickness Wingwall Length Soil Cover at Toe Girder Reaction Curb height Bearing Seat Width Shield Wall thickness Abutment-A1A2(OK).xls - Analysis φs δ frs A 90.0 º ABUTMENT DIMENSIONS (IN METRES) Symbol Value Item h 7.500 Horizontal Dimension b 7.500 Horizontal Dimension a 1.500 Horizontal Dimension d 2.500 Horizontal Dimension f - Horizontal Dimension n 1.000 Vertical Dimension j 2.200 Vertical Dimension t 0.500 Vertical Dimension w 6.000 Vertical Dimension e 0.500 Vertical Dimension g 0.600 Vertical Dimension c 1.200 Vertical Dimension bb 0.600 Abutment Length te 0.200 Wingwall Thickness Footing length Date: 9/26/2011 α = 30.0 º = 20.0 º = 0.5 = 0.1168 = 1.571 rad Symbol b1 b2 b3 b4 m d1 d2 d3 d4 d5 d6 d7 L u Lf Value 2.500 3.500 3.500 2.000 0.400 2.950 4.550 1.500 2.000 0.100 1.500 16.500 0.800 16.500 Page: of 13 Ha noi - Hai Phong Expressway Project 3.2 Internal Forces at Bottom Footing Live Load Surcharge Loading Data: Ht = 10.000 m KA kh kv θ δs KAE = = = = = = Vertical Reaction 0.297 0.175 0.070 0.19 rad 0.35 rad 0.442 E I J H EQ, BR D G X PH2 Ht B F K +M PV2 δ P2 PH1 P1 0.5H PV1 δ +H Ht/3 +V A A1 C Sign Convention (KA, KEA)γsHt Live Load Surcharge ABUTMENT LOADS Description VERTICAL LOADS Section A Section A1 Section B Section C Section D Section E Section F Section G Section H Section I Section J Bearing Seat Concrete Block Shield Wall Curb Railing Total (DC) Section A Section A1 Section B Section C Section D Section F Section G Section H Section J Total (WA) Section F Section G Section H Section K Abutment-A1A2(OK).xls - Analysis Area Length (m2) (m) Force X1 (kN) (m) Selfweight 6.25 16.500 2529.1 1.250 3.75 16.500 1517.5 3.250 7.95 16.500 3217.1 3.250 8.75 16.500 3540.8 5.750 1.10 16.500 445.1 3.750 15.93 1.600 624.9 5.750 10.33 1.600 405.2 5.750 0.14 14.900 49.3 4.133 5.00 1.600 196.2 8.367 0.04 4.800 4.7 3.100 0.61 3.360 50.2 3.100 1.50 0.400 14.7 3.000 0.75 6.000 110.4 6.500 6.0 6.500 12525.2 Buoyancy effect on Abutment Soil weight 15.93 14.900 4189.9 5.750 10.33 14.900 2716.6 5.750 1.25 16.500 364.2 1.250 Date: 9/26/2011 Arm Arm Moment MLong Moment MTrans (m) (m) (kN•m) (kN•m) 2.500 0.500 0.500 -2.000 -2.000 -2.000 -0.383 -4.617 0.650 0.650 0.750 -2.750 -2.750 - 6322.9 758.7 1608.5 -7081.6 -1249.8 -810.3 -18.9 -905.8 3.1 32.6 11.0 -303.5 -16.5 -1649.5 - - - - - -2.000 -2.000 2.500 - -8379.9 -5433.1 910.5 - Page: of 13 Ha noi - Hai Phong Expressway Project Total (EV) Section F Section G Section H Section K Total (WA) PV1 PV2 PV1-EQ ESv = = = heq = 610 mm LOADS LONGITUDINAL DC DW Live Load WL Earth Pressure (EH) Horizontal pressure due to Surcharge Braking force Longitudinal wind load on Structure Longitudinal wind load on Vehicle Temprature Load Earth Pressure due to EQ PH1-EQ EQ from Superstructure Section A Section A1 Section B Section C Section D Section E Section F Section G Section H Section I Section J Bearing Seat Concrete Block Shield Wall Curb Railing Total Abutment-A1A2(OK).xls - Analysis 6.25 3.75 7.95 8.75 1.10 15.93 10.33 0.14 5.00 0.04 0.61 1.50 0.75 - 7270.7 Buoyancy effect on Soil 16.500 1481.4 7.500 16.500 180.7 7.500 16.500 2204.7 7.500 14.900 561.7 5.750 Load from SuperStructure 4923.6 3.100 552.7 3.100 1430.9 3.100 643.2 3.100 16.500 4070.0 14.900 448.4 105.6 55.7 14.4 65.6 16.500 6057.4 1599.1 EQ from Abutment 16.500 738.5 16.500 443.1 16.500 939.4 16.500 1033.9 16.500 130.0 1.600 182.5 1.600 1.600 118.3 14.900 14.4 1.600 57.3 4.800 1.4 3.360 14.7 0.400 4.3 6.000 32.2 1.8 3711.7 Date: 9/26/2011 -12902.5 - - - -3.750 -3.750 -3.750 -2.000 - -5555.1 -677.7 -8267.6 -1123.5 0.650 0.650 0.650 0.650 3.333 5.000 7.850 7.850 7.850 7.850 3.333 7.850 - 3200.3 359.3 930.1 418.1 13566.7 2242.0 829.2 437.0 112.7 514.9 20191.2 12552.7 - 1.250 1.250 5.150 1.250 8.900 4.775 7.050 8.525 9.250 9.060 7.850 0.870 8.550 10.600 11.400 - 923.1 553.9 4837.8 1292.4 1156.8 871.3 1008.5 133.2 519.0 10.8 12.7 36.7 341.6 20.0 11718.0 - Page: of 13 Ha noi - Hai Phong Expressway Project HORIZONTAL LOADS Horizoltal Wind Load on Structure Horizontal Wind Load on Vehicle EQ form Superstructure Notes: Section A Section A1 Section B Section C Section D Section E Section F Section G Section H Section I Section J Bearing Seat Concrete Block Shield Wall Curb Railing Total 6.25 3.75 7.95 8.75 1.10 15.93 10.33 0.14 5.00 0.04 0.61 1.50 0.75 - 222.7 28.7 479.7 EQ from Abutment 16.500 221.6 16.500 132.9 16.500 281.8 16.500 310.2 16.500 39.0 1.600 54.7 1.600 1.600 35.5 14.900 4.3 1.600 17.2 4.800 0.4 3.360 4.4 0.400 1.3 6.000 9.7 0.5 1113.5 - - 7.850 7.800 7.800 - 1748.0 224.1 3741.8 - - 1.250 1.250 5.150 1.250 8.900 4.775 7.050 8.525 9.250 9.060 7.850 0.870 8.550 10.600 11.400 - 276.9 166.2 1451.3 387.7 347.0 261.4 302.6 40.0 155.7 3.2 3.8 11.0 102.5 6.0 3515.4 Distance 'X' is measured horizontally from Toe of Abutment to C.G of Section Moment 'Arm' is measured from Pile C.G Horizontally and from Underside of Footing Vertically Description SUMMARY LOADING AT FOOTING CENTER Longitudinal Vertical Symbol V Hx My Seflweight of Abutment DC of Superstructure DW of Superstructure Soil cover at toe Earth Pressure Vertical pressure due to LL surcharge Horizontal pressure due to LL surcharge Live Load from Superstructure Braking Force Longitudinal Wind Load on Superstructure Longitudinal Wind Load on Vehicle Horizontal Wind Load on Superstructure Horizontal Wind Load on Vehicle Vertical Wind Load Temperature Load Earth pressure due to EQ EQ from Abutment EQ from Superstructure Buoyancy effect on Abutment Buoyancy effect on Soil Abutment-A1A2(OK).xls - Analysis DC DC DW EV EH ESV ESL LL BR WSL WLL WST WLT WSV TU EH-EQ EQ EQ WA WA (kN) 12525 4924 553 7271 1481 562 181 1431 643 2205 - Date: 9/26/2011 (kN) 4070 448 106 56 14 66 6057 3712 1599 - (kN•m) -1650 3200 359 -12902 8012 -1123 1564 930 829 437 113 418 515 11924 11718 12553 - Transverce Hy (kN) - Mx (kN•m) - 223 29 1113 480 - 1748 224 3515 3742 - Page: of 13 Ha noi - Hai Phong Expressway Project Description Symbol Seflweight of Abutment DC of Superstructure DW of Superstructure Soil cover at toe Earth Pressure Vertical pressure due to LL surcharge Horizontal pressure due to LL surcharge Live Load from Superstructure Braking Force Longitudinal Wind Load on Superstructure Longitudinal Wind Load on Vehicle Horizontal Wind Load on Superstructure Horizontal Wind Load on Vehicle Vertical Wind Load Temperature Load Earth pressure due to EQ EQ from Abutment EQ from Superstructure Buoyancy effect on Abutment Buoyancy effect on Soil STR-IA 1.25 1.25 1.50 1.35 1.50 1.75 1.50 1.75 1.75 0.50 1.00 1.00 DC DC DW EV EH ESV ESL LL BR WSL WLL WST WLT WSV TU EH-EQ EQ EQ WA WA LOAD FACTOR Service STR-IIIA STR-IIIB SER-I 1.25 0.90 1.00 1.25 0.90 1.00 1.50 0.65 1.00 1.35 0.90 1.00 1.50 0.90 1.00 1.35 1.35 1.00 1.50 0.75 1.00 1.35 1.00 1.00 1.35 1.00 1.00 0.40 0.40 0.30 1.00 1.00 1.00 0.50 0.50 0.50 1.00 1.00 1.00 1.00 1.00 1.00 Strength STR-IB 0.90 0.90 0.65 0.90 0.90 1.75 0.75 1.75 1.75 0.50 1.00 1.00 LOAD COMBINATIONS Longitudinal Load combinations N Hx My (kN) (kN) (kN.m) Description Symbol Strength IA STR-IA 38436 6995 793 Strength IB STR-IB 27563 4217 -229 Strength IIIA STR-IIIA 37639 6990 826 Strength IIIB STR-IIIB 26265 4174 -812 Service I SER-I 28927 4688 -279 Extreme IA EXT-IA 35747 11645 22353 Extreme IB EXT-IB 25898 11645 27311 Front side Extreme EXT-IA 1.25 1.25 1.50 1.35 0.50 0.50 0.50 0.50 1.00 1.00 1.00 1.00 1.00 EXT-IB 0.90 0.90 0.65 0.90 0.50 0.50 0.50 0.50 1.00 1.00 1.00 1.00 1.00 Transverce Hy Mx (kN) (kN.m) 0 0 1593 1593 0 0 7257 7257 Back fill side ΣV +M +H ΣM ΣH +V P1, M1 Quy −íc No Com STR-IA STR-IB STR-IIIA STR-IIIB SER-I EXT-IA EXT-IB P1 (kN) -23660 -16335 -23264 -15557 -17298 -28971 -24920 P3, M3 P2, M2 P4, M4 Internal Force at Head Pile P2 P3 P4 M1 (kN) (kN) - - (kN) -14775 -11228 -14375 -10708 -11629 -6775 -978 (kN.m) -9599 -5860 -9587 -5861 -6517 -13794 -13279 M2 M3 M4 (kN.m) - (kN.m) - (kN.m) -9599 -5860 -9587 -5861 -6517 -13794 -13279 Note: the above pile internal forces are taken from a 3D pile analysis software Abutment-A1A2(OK).xls - Analysis Date: 9/26/2011 Page: of 13 Ha noi - Hai Phong Expressway Project 3.3 Section analysis Live Load surcharge Vertical Reaction EQ, BR A PH2 Ht X P2 C PV2 δ PH1 D B P1 0.5H PV1 δ Ht/3 P1, M1 P2, M2 P3, M3 P4, M4 Live Load surcharge Internal Force at Section A-A Area Length Force Description (m) (kN) (m ) Selfweight of Abutment Section I 0.14 14.900 49.3 Section E 1.10 16.500 445.1 Curb 0.75 1.000 18.4 Total (DC) 494.5 Earth Pressure (EH) 16.500 197.0 Horizontal Pressure due to Surcharge 16.500 109.2 Earth Pressure due to EQ 16.500 293.2 EQ from Abutment Section I 0.14 14.900 14.4 Section E 1.10 16.500 130.0 Curb 0.75 1.000 5.4 Total 144.4 Notes: (KA, KEA)γsHt X1 (m) Arm (m) 4.133 3.750 3.750 -0.383 - - 0.880 1.100 0.880 - 0.750 1.100 2.800 Moment (kN•m) -18.9 -18.9 173.4 120.2 258.0 10.8 143.0 15.0 153.8 Distance 'X' is measured horizontally from Toe of Abutment to C.G of Section Moment 'Arm' is measured from Pile C.G Horizontally and from Underside of Footing Vertically Summary Load Combinatons at Section a-a Longitudinal Load Combinations N Hx My (kN) (kN) (kN) Description Symbol Service SER 494 306 275 Strength IA STR-IA 618 487 447 Extreme IA EXT-IA 618 492 448 Abutment-A1A2(OK).xls - Analysis Date: 9/26/2011 Page: of 13 Ha noi - Hai Phong Expressway Project Internal Force at Section B-b Description Area Length LONGITUDINAL LOADS VERTICAL LOADS (m2) Section B Section D Section E Section I Bearing Seat Concrete Block Shield Wall Curb Total (DC) Section B Section D Total (WA) DC of Superstructure DW of Superstructure Live Load Reaction due to Vertical Wind Load Earth Pressure (EH) Horizontal pressure due to Surcharge Braking force Longitudinal wind load on Structure Longitudinal wind load on Vehicle Temprature Load Earth Pressure due to EQ EQ from Superstructure Section B Section D Section E Section F Section G Section H Section I Section J Bearing Seat Concrete Block Shield Wall Curb Railing Total Abutment-A1A2(OK).xls - Analysis Force X1 (m) (kN) (m) Selfweight of Abutment 7.95 16.500 3217.1 3.250 1.10 16.500 445.1 3.750 0.14 14.900 49.3 4.133 0.04 4.800 4.7 3.100 0.61 3.360 50.2 3.100 1.50 0.400 14.7 3.000 2.50 1.000 61.3 3.750 3842.4 Buoyancy effect on Abutment 4923.6 3.100 552.7 3.100 1430.9 3.100 643.2 3.100 16.500 2289.4 16.500 372.4 105.6 55.7 14.4 65.6 16.500 3407.3 1599.1 EQ from Abutment 7.95 16.500 939.4 1.10 16.500 130.0 15.93 1.600 182.5 10.33 1.600 118.3 0.14 14.900 14.4 5.00 1.600 57.3 0.04 4.800 1.4 0.61 3.360 14.7 1.50 0.400 4.3 0.75 6.000 32.2 1.8 1496.1 Date: 9/26/2011 Arm Arm Moment MLong Moment MTrans (m) (m) (kN•m) (kN•m) -0.500 -0.883 0.150 0.150 0.250 - - -222.6 -43.6 0.7 7.5 3.7 -254.2 - - - 0.150 0.150 0.150 0.150 3.000 3.750 5.350 5.350 5.350 5.350 3.000 5.350 - 738.5 82.9 214.6 96.5 6868.2 1396.5 565.1 297.8 76.8 350.9 10221.8 8555.0 - 2.650 6.400 2.275 6.025 6.750 6.560 5.350 -1.630 6.050 8.100 8.900 - 2489.4 831.9 415.1 712.8 97.2 375.8 7.4 -23.9 26.0 261.0 15.6 5208.2 - Page: of 13 Ha noi - Hai Phong Expressway Project STRENGTH – Element Shear X: STRENGTH – Element Shear Y: Abutment-A1A2(OK).xls - Analysis Date: 9/26/2011 Page: 13 of 13 Ha noi - Hai Phong Expressway Project SECTION A-A CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 500 16500 70 362 68 430 487 487 618 275 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = 132 Ds = 16 As = 26268 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = 66 D's = 16 A's = 13134 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = Transverse Reinf nv = 68 Dv = 16 Av = 13532 sv = 500 0.90 0.90 28 mm 22 mm > 4158 kN•m 0.065 < 1.2Mcr 1.33Mu = = 647 kN•m < 2d's 487 kN•m O.K 0.42 O.K 4158 kN•m O.K 2562 kNm 647 kNm < Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.023 m + 2m = j = (1-k/3) = 0.194 0.935 k = −m + fs = Abutment-A1A2(OK).xls - A-A Ms A s jd s = dc 6.290 26 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 84 21000 30000 248 252 mm mm N/mm Mpa Mpa OK Page: of Ha noi - Hai Phong Expressway Project SECTION A-A CHECK Shear Resistance dv Effective Shear Depth = 419 mm bv Effective Shear Width = 16500 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 487 < = 4937 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 24.3 78 KN/m2 = 0.00013 = = = = = = = = = 0.128 0.002 3.2 24.3 10972 10519 21492 60459 21492 > 19342 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.08 Mpa < sv < Abutment-A1A2(OK).xls - A-A No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 487 kN 9645 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 335 mm O.K Page: of Ha noi - Hai Phong Expressway Project SECTION B-B CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 1500 16500 75 1355 70 1425 4210 14667 14291 9953 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = 132 Ds = 25 As = 67320 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = 66 D's = 19 A's = 18744 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = 0.051 1.2Mcr 1.33Mu 0.90 0.90 72 mm 58 mm > 35529 kN•m = = 19507 kN•m Transverse Reinf nv = 68 Dv = 16 Av = 13532 sv = 500 < 2d's 14667 kN•m O.K < 0.42 23062 kNm 19507 kNm < 35529 kN•m O.K O.K Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.018 m + 2m = j = (1-k/3) = 0.173 0.942 k = −m + fs = Abutment-A1A2(OK).xls - B-B Ms A s jd s = dc 6.290 110 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 89 22125 30000 240 252 mm mm N/mm Mpa Mpa OK Page: of Ha noi - Hai Phong Expressway Project SECTION B-B CHECK Shear Resistance dv Effective Shear Depth = 1396 mm bv Effective Shear Width = 16500 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 4210 < = 12710 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 31.9 203 KN/m2 = 0.00061 = = = = = = = = = 0.611 0.006 2.5 31.9 28244 25477 53721 201576 53721 > 48349 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.20 Mpa < sv < Abutment-A1A2(OK).xls - B-B No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 4210 kN 9645 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 600 mm O.K Page: of Ha noi - Hai Phong Expressway Project SECTION C-C CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 2500 16500 120 2260 120 2380 20499 29307 20653 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = 132 Ds = 25 As = 67320 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = 132 D's = 22 A's = 51084 d = 125 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = 0.030 1.2Mcr 1.33Mu 0.90 0.90 72 mm 58 mm > 59831 kN•m = = 38979 kN•m Transverse Reinf nv = 68 Dv = 16 Av = 13532 sv = 500 < 2d's 29307 kN•m O.K < 0.42 64060 kNm 38979 kNm < 59831 kN•m O.K O.K Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.011 m + 2m = j = (1-k/3) = 0.136 0.955 k = −m + fs = Abutment-A1A2(OK).xls - C-C Ms A s jd s = dc 6.290 135 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 129 32125 30000 187 252 mm mm N/mm Mpa Mpa OK Page: of Ha noi - Hai Phong Expressway Project SECTION C-C CHECK Shear Resistance dv Effective Shear Depth = 2351 mm bv Effective Shear Width = 16500 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 20499 < = 21404 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 31.9 587 KN/m2 = 0.00061 = = = = = = = = = 0.611 0.017 2.5 31.9 47565 42905 90470 339455 90470 > 81423 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.59 Mpa < sv < Abutment-A1A2(OK).xls - C-C No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 20499 kN 9645 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 600 mm O.K Page: of Ha noi - Hai Phong Expressway Project SECTION D-D CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 2500 16500 166 2234 100 2334 1697 9526 6219 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = 132 Ds = 22 As = 51084 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = 132 D's = 25 A's = 67320 d = 125 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = 0.90 0.90 55 mm 44 mm > 44647 kN•m 0.023 1.2Mcr 1.33Mu Transverse Reinf nv = 68 Dv = 16 Av = 13532 sv = 500 = = 12670 kN•m < 2d's 9526 kN•m O.K < 0.42 64060 kNm 12670 kNm < 44647 kN•m O.K O.K Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.008 m + 2m = j = (1-k/3) = 0.121 0.960 k = −m + fs = Abutment-A1A2(OK).xls - D-D Ms A s jd s = dc 6.290 54 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 77 19250 30000 263 252 mm mm N/mm Mpa Mpa not.OK Page: of Ha noi - Hai Phong Expressway Project SECTION D-D CHECK Shear Resistance dv Effective Shear Depth = 2312 mm bv Effective Shear Width = 16500 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 1697 < = 27279 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 24.3 49 KN/m2 = 0.00013 = = = = = = = = = 0.127 0.001 3.2 24.3 60620 58124 118744 333816 118744 > 106870 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.05 Mpa < sv < Abutment-A1A2(OK).xls - D-D No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 1697 kN 9645 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 600 mm O.K Page: of Ha noi - Hai Phong Expressway Project SECTION E-E CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 800 1000 71 659 70 729 120 180 115 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = Ds = 22 As = 3096 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = D's = 19 A's = 1136 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = Transverse Reinf nv = Dv = 16 Av = 796 sv = 500 0.90 0.90 55 mm 44 mm > 828 kN•m 0.075 < 1.2Mcr 1.33Mu = = 239 kN•m < 2d's 180 kN•m O.K 0.42 O.K 398 kNm 239 kNm 828 kN•m < O.K Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.027 m + 2m = j = (1-k/3) = 0.206 0.931 k = −m + fs = Abutment-A1A2(OK).xls - E-E Ms A s jd s = dc 6.290 55 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 87 21750 30000 243 252 mm mm N/mm Mpa Mpa OK Page: of Ha noi - Hai Phong Expressway Project SECTION E-E CHECK Shear Resistance dv Effective Shear Depth = 707 mm bv Effective Shear Width = 1000 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 120 < = 470 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 26.1 189 KN/m2 = 0.00022 = = = = = = = = = 0.223 0.005 3.0 26.1 1044 965 2009 6188 2009 > 1808 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.19 Mpa < sv < Abutment-A1A2(OK).xls - E-E No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 120 kN 585 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 566 mm O.K Page: of Ha noi - Hai Phong Expressway Project SECTION F-F CHECK Vu Mu Nu Ms Factored Shear Factored Moment Factored Axial Force Service Moment = = = = = = = 800 1000 70 659 71 730 260 225 150 KN KNm KN KNm n's, D's SECTION DIMENSIONS h b d1 d2 d3 d's de = ds = = = = a mm mm mm mm mm mm mm A's•fy d's nv,Dv 0.85•f'c•a•b h ds d3 As•fy d2 d1 ns, Ds b REINFORCEMENT Tension Reinforcement ns = Ds = 22 As = 3096 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = D's = 19 A's = 1136 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = Transverse Reinf nv = Dv = 16 Av = 796 sv = 500 0.90 0.90 55 mm 44 mm > 829 kN•m 0.075 < 1.2Mcr 1.33Mu = = 299 kN•m < 2d's 225 kN•m O.K 0.42 O.K 398 kNm 299 kNm 829 kN•m < O.K Control of cracking by distribution of reinforcement Components shall be so proportioned that the tensile stress in the mild steel reinforcement at the service limit state Z does not exceed fsa, determined as: f = ≤ f y sa ( d c A )1 / n = Es/Ec m= nA s bd s = = 0.027 m + 2m = j = (1-k/3) = 0.206 0.931 k = −m + fs = Abutment-A1A2(OK).xls - F-F Ms A s jd s = dc 6.290 71 Mpa A Z fsa 0.6fy Check: Date: 9/26/2011 = = = = = 87 21750 30000 243 252 mm mm N/mm Mpa Mpa OK Page: of Ha noi - Hai Phong Expressway Project SECTION F-F CHECK Shear Resistance dv Effective Shear Depth = 708 mm bv Effective Shear Width = 1000 mm Vu > 0.5 ϕVc Regions requiring transverse reinforcement: Vu = 260 < = 442 KN The norminal shear resistance, Vn, shall be determined as the lesser of: (Vn1 = Vc + Vs, Vn2 = 0.25f'cbvdv) for which: Vc = 083 β f ' c b v d v Vs = A v f y d v (cot g θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 5N u + Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Norminal Shear Resistance Factored Shear Resistance Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 27.9 408 KN/m2 = 0.00033 = = = = = = = = = 0.333 0.012 2.8 27.9 982 895 1877 6196 1877 > 1689 kN b s A v = 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.41 Mpa < sv < Abutment-A1A2(OK).xls - F-F No need = (Supposition) ≤ 0.001 [ β = F(v/f'c, 1000*εx)] kN kN kN kN kN 260 kN 585 mm2 0.125f'c smax OK = = O.K O.K 4.38 Mpa 567 mm O.K Page: of Ha noi - Hai Phong Expressway Project CREEP AND SHRINKAGE General input Length of girder Number of Strands Jacking Force Elastic Shortening Average ambient relative humidity Specified compressive strength of concrete of girder at 28 days Compressive strength of concrete of girder at time of initial prestress Modulus of elasticity L ntr Pj ΔL = H f'c f'ci Ec Eci ε Coefficient of thermal expansion for normal concrete Creep coefficient The creep coefficient may be estimated as: = = = = = = 38.3 42 195 14.1 85 50 42.5 38007 35041 1.08E-5 m strands KN mm % Mpa Mpa Mpa Mpa (t − t i ) H ⎞ − 0.118 ⎛ ψ (t, t i ) = k c k f ⎜ 58 − ⎟t i 0.6 120 10 + (t − t i ) ⎠ ⎝ Where: kf = 62/(42+f'c) t ti kc : Factor for the effect of concrete strength : Maturity of concrete (day) ti : Age of concrete when load is initially applied (day) = days : Factor for the effect of the volume-to-surface ratio of the component specified Figure 5.4.2.3.2-1 of AASHTO LRFD 2004 or taken as: t ⎤ ⎡ − 0213 ( A / P ) 0142 ( A / P ) ⎢ ⎤ + t ⎥ ⎡ 80 + 77 e k c = ⎢ 26 e ⎥⎢ ⎥ t 587 ⎦ ⎢ ⎥⎣ ⎥⎦ 45 + t ⎣⎢ Item Area of Section, A (m2) Perimeter of Section, P (m) Volume to Surface ratio, A/P (mm) kc kf Creep coefficient, ψ(t,ti) Maturity of concrete (day) 10 150 10950 0.635 0.635 0.993 10.248 10.248 12.434 62 62 80 0.665 0.806 0.818 0.674 0.674 0.674 0.292 0.969 1.424 Strain due to shrinkage t ⎛ ⎞ −3 The strain due to shrinkage, esh, at time, t, mat be taken as: ε sh = − k s k h ⎜ ⎟0 51 × 10 ⎝ 35 + t ⎠ Where: t : Drying time (day) kh : Humidity Factor kh = (140-H ) / 70 for H < 80% kh kh = 3(100-H )/ 70 for H ≥ 80% = 0.643 ks : Size factor specified Figure 5.4.2.3.3-2 of AASHTO LRFD 2004 or taken as: t ⎡ ⎤ ⎢ 26 e 0142 ( A / P ) + t ⎥ ⎡ 1064 − 70 ( A / P ) ⎤ ks = ⎢ ⎥⎢ ⎥ t 923 ⎦ ⎢ ⎥⎣ ⎢⎣ ⎥ 45 + t ⎦ Item Area of Section, A (m2) Perimeter of Section, P (m) Volume to Surface ratio, A/P (mm) kh ks Strain due to shrinkage, εsh Abutment-A1A2(OK).xls - CR&SH Date: 9/26/2011 Maturity of concrete (day) 10 150 10950 0.635 0.635 0.993 10.248 10.248 12.434 62 62 80 0.643 0.643 0.643 0.684 0.829 0.830 -0.00005 -0.00022 -0.00027 Page: of Ha noi - Hai Phong Expressway Project Movement due to Creep Maturity of concrete (day) 10 150 10950 4.1 13.7 20.1 Item Shortening (mm) Movement due to Shrinkage Maturity of concrete (day) 10 150 10000 1.9 8.4 10.4 Item Shortening (mm) Movement due to Creep and Shrinkage ΔL = 8.4 mm Convert to Uniform Temperature Change ΔT = -20 0C Abutment-A1A2(OK).xls - CR&SH Date: 9/26/2011 Page: of [...]... Abutment DC of Superstructure DW of Superstructure Earth Pressure Horizontal pressure due to LL surcharge Live Load from Superstructure Braking Force Longitudinal Wind Load on Superstructure Longitudinal Wind Load on Vehicle Horizontal Wind Load on Superstructure Horizontal Wind Load on Vehicle Vertical Wind Load Temperature Load Earth pressure due to EQ EQ from Abutment EQ from Superstructure Buoyancy... 'X' is measured horizontally from Toe of Abutment to C.G of Section 2 Moment 'Arm' is measured from Pile C.G Horizontally and from Underside of Footing Vertically Description SUMMARY LOADING AT SECTION B-B Longitudinal Vertical Symbol V Hx My Selfweight of Abutment DC of Superstructure DW of Superstructure Earth Pressure Horizontal pressure due to LL surcharge Live Load from Superstructure Braking... Superstructure Braking Force Longitudinal Wind Load on Superstructure Longitudinal Wind Load on Vehicle Horizontal Wind Load on Superstructure Horizontal Wind Load on Vehicle Vertical Wind Load Temperature Load Earth pressure due to EQ EQ from Abutment EQ from Superstructure Buoyancy effect on Abutment Abutment-A1A2(OK).xls - Analysis DC DC DW EH ESH LL BR WSL WLL WST WLT WSV TU EH-EQ EQ EQ WA (kN) 3842 4924... 11638 12822 M -29478 -20836 -29478 -20836 -22960 Wing Wall Calculation Wing Wall is modeled and Calculated by ACES5.5 program: d4 = 1.5000 m = tgφ h1 = 3.5000 m Earth Pressure due to LL Surcharge = h2 = 4.0000 m b2 = 3.5000 m b3 = 3.5000 m b4 = 2.0000 m E b3 5.250 3.202 KN/m LL Surcharge b4 d4 h1 Ht h2 0.5H F 0.4Ht b2 KAγsHt LL Surcharge Abutment-A1A2(OK).xls - Analysis Date: 9/26/2011 Page: 10 of 13... 16 A's = 13134 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking moment 1.33 times the factored moment Min (1.2*Mcr or 1.33*Mu) = Minimum Reinf ϕ ϕv = = c a = = Transverse Reinf nv = 68... Page: 1 of 2 Ha noi - Hai Phong Expressway Project Movement due to Creep Maturity of concrete (day) 10 150 10950 4.1 13.7 20.1 Item Shortening (mm) Movement due to Shrinkage Maturity of concrete (day) 10 150 10000 1.9 8.4 10.4 Item Shortening (mm) Movement due to Creep and Shrinkage ΔL = 8.4 mm Convert to Uniform Temperature Change ΔT = -20 0C Abutment-A1A2(OK).xls - CR&SH Date: 9/26/2011 Page: 2 of 2... θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 0 5N u + 0 5 Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ... Vr = 1000*εx vu/f'c β θ Vc Vs Vn1 Vn2 Vn = = = Date: 9/26/2011 90 0 24.3 0 78 KN/m2 = 0.00013 = = = = = = = = = 0.128 0.002 3.2 24.3 10972 10519 21492 60459 21492 > 19342 kN b s A v min = 0 083 f ' c v Minimum transverse reinforcement fy Maximum spacing of transverse reinforcement If vu < 0.125f'c, then: s ≤ 0.8dv ≤ 600mm If vu ≥ 0.125f'c, then: s ≤ 0.4dv ≤ 300mm vu = 0.08 Mpa < sv < Abutment-A1A2(OK).xls... Reinforcement ns = 132 Ds = 25 As = 67320 Number (bars) Diameter (mm) Area (mm2) Spacing (mm) s = 125 Compresion Reinf n's = 66 D's = 19 A's = 18744 d = 250 Resistance factor for Flexure: Resistance factor for Shear: Flexural Resistance Distance from extreme compression fiber to the neutral axis: Depth of the equivalent stress block: Mr Factored Flexural Resistance = c / de Maximum Reinf = 1.2 times the cracking... θ + cot g α ) sin α s Determination of β and θ: Angle of inclination of transverse Reinf to longitudinal axis α Angle of inclination of diagonal compressive stresses θ vu = Vu/(ϕbvdv) Shear stress on the concrete Strain in the reinforcement on the flexural tension side of the member Mu + 0 5N u + 0 5 Vu cot g θ dv εx = 2E s A s Ratio Factor β taken from Table 5.8.3.4.2-1 (AASHTO LRFD 2004) Factor θ ... of Abutment DC of Superstructure DW of Superstructure Earth Pressure Horizontal pressure due to LL surcharge Live Load from Superstructure Braking Force Longitudinal Wind Load on Superstructure... Abutment DC of Superstructure DW of Superstructure Soil cover at toe Earth Pressure Vertical pressure due to LL surcharge Horizontal pressure due to LL surcharge Live Load from Superstructure... B-B Longitudinal Vertical Symbol V Hx My Selfweight of Abutment DC of Superstructure DW of Superstructure Earth Pressure Horizontal pressure due to LL surcharge Live Load from Superstructure Braking