BANG TINH TUONG CHAN

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bảng tính toán tường chắn theo 22TCN 27205bảng tính toán tường chắn theo 22TCN 27205bảng tính toán tường chắn theo 22TCN 27205bảng tính toán tường chắn theo 22TCN 27205bảng tính toán tường chắn theo 22TCN 27205 SOCIALIST REPUBLIC OF VIETNAM MINISTRY OF TRANSPORT PROJECT MANAGEMENT UNIT 85 NHAT TAN BRIDGE CONSTRUCTION PROJECT DỰ ÁN XÂY DỰNG CẦU NHẬT TÂN PACKAGE 2/ GÓI THẦU SỐ PHU THUONG INTERCHANGE CALCULATION REPORT FOR DESIGN MODIFICATION OF RETAINING WALLS (REDESIGN ACCORDING TO NEWLY INVESTIGATED SOIL CONDITIONS) BLOCK C1-1 TO C1-2 ON BRANCH 1E SPREAD FOOTING Hanoi November 28th 2013 Hanoi, SOCIALIST REPUBLIC OF VIETNAM MINISTRY OF TRANSPORT PROJECT MANAGEMENT UNIT 85 NHAT TAN BRIDGE CONSTRUCTION PROJECT DỰ ÁN XÂY DỰNG CẦU NHẬT TÂN PACKAGE 2/ GÓI THẦU SỐ PHU THUONG INTERCHANGE CALCULATION REPORT FOR DESIGN MODIFICATION OF RETAINING WALLS (REDESIGN ACCORDING TO NEWLY INVESTIGATED SOIL CONDITIONS) BLOCK C1-1 TO C1-2 ON BRANCH 1E SPREAD FOOTING Prepared by: Nguyen Van Duong Checked by: Tran The Hiep Reviewed by: Pham Dang Hung Approved by: Tran Manh Toan Hanoi, November 28th 2013 CALCULATION REPORT FOR RETAINING WALL - BLOCK C1-1, C1-2 GENERAL INFORMATIONS: - Project: Nhat Tan Bridge Construction Project Project - Construction Package: PK2 - Work Item: Retaining Wall of Phu Thuong Interchange - Block: C1-1, C1-2 DATA FOR CALCULATION: Design Specifications and References: 2.1 1) 22TCN 272-05: Vietnamese bridge design specifications 2) AASHTO LRFD 1998: American highway bridge design specifications 2.2 Geometry Data of Retaining Wall: T.R B B B.R A A - The vertical and transversal dimension data: h1 = 0.760 m b1 = 0.100 m h2 = 4.540 m b2 = 0.300 m h3 = 1.000 m b3 = 0.400 m h4 = 3.600 m b4 = 4.100 m h5 = 0.700 m b5 = 0.400 m h6 = 4.600 m b6 = 4.500 m h= 5.300 m b7 = 0.700 m TR = 8.120 m b8 = 4.100 m BR = 2.820 m b= 4.800 m - The longitudinal dimension (the length for this block): L= 20 m - The natural ground level at this block: G.L = 3.92 m Page 2.3 Material: a Concrete: - Compressive strength of concrete at 28 days f'c = 25 MPa - Unit weight of concrete γc = 24.5 kN/m3 - Modulus of Concrete Ec 26875.0 MPa - Yield Strength fy' 390 MPa - Modulus of Reinforcement Es 200000 MPa b Reinforcement: c Filling soil behind the retaining wall: - Unit weight of filling soil - Angle of internal friction γs = 1800 kg/m3 γs = 17.7 kN/m3 ϕ= 30 degree LOADS AND ACTIONS: The following loads shall be considered for calculating the retaining wall: - Self weight of retaining wall - Static earth pressure and earth pressure due to earthquake - Pedestrian load - Live load surcharge - Earthquake load 3.1 Dead Load of Retaining Wall (DC): Section N (kN) H (kN) M (kN.m) A-A 2712.6 0.0 2306.5 B-B 1066.2 0.0 120.7 3.2 Vertical Earth Pressure behind the Wall (EV): Section N (kN) H (kN) M (kN.m) A-A 7056.1 0.0 -1596.6 B-B 395.5 0.0 -76.3 3.3 Horizontal Earth Pressure (EH): (Article 3.11.5 - 22TCN 272-05) 3.3.1 Horizontal Active Earth Pressure (EHa): - Earth pressure shall be assumed to be linearly proportional to the depth of earth and taken as: EH = Pa*L = (γs*H *k)/2*L (kN) θ β γ' σa = ka γ' H , φ' Pa = γ' H 2k H a/2 δ δ P 0.4 Page Where: H= Height of filling soil HA = Depth off earth pressure acting on section A-A = HB = Depth of earth pressure acting on section B-B = L 5.300 (m) 4.600 (m) Length of this retaining wall block = 20.000 (m) γs = Unit weight of filling soil k= Coefficient of lateral earth pressure For this case, k is equal to the coefficient of active pressure ka = Sin (θ + ϕ ′ ) TSin 2θ Sin (θ − δ ) ⎡ Sin.(ϕ′ + δ )Sin.(ϕ′ − β ) ⎤ T = ⎢1+ ⎥ Sin.(θ − δ )Sin.(θ + β ) ⎦⎥ ⎣⎢ In which δ= Friction angle between fill and wall = 15.0 (degree) β= Angle of fill to the horizontal = 0.0 (degree) θ= Angle of backfill of wall to the vertical = 85.0 (degree) ϕ' = Effective angle of internal friction = 30.0 (degree) We have: T= ka = 2.607 0.338 Active Horizontal Earth Pressure (EHa) Section P (KN) e (m) N (KN) H (KN) M (KNm) A-A 1674.8 2.120 572.0 1574.1 4401.0 B-B 1261.6 1.840 430.9 1185.8 2099.9 3.3.2 Horizontal Passive Earth Pressure (EHp): This is calculated for horizontal passive earth pressure at the front of the retaining wall For cohesive soil, passive pressure may be estimated by: -9 0.5 pp = kp*γs*g*Z*10 + 2*c*(Kp) Where: γs = Density of soil (kg/m ) γs = 1800 kg/m3 g= Gravitational constant (m/s2) g= 9.81 m/s2 Z= Depth below surface of soil (mm) ZA-A = 600 mm ZB-B = mm c= Unit cohension (MPa) c= 0.080 Mpa kp = Coefficient of passive pressure in Figure 1, in 22TCN272-05 kp = pp = Passive earth pressure (MPa) ppA-A = 0.171 MPa ppB-B = 0.161 MPa 1.0 Passive Horizontal Earth Pressure (EHp) Section P (KN) e (m) N (KN) H (KN) M (KNm) A-A 1028.9 0.200 -266.3 -993.8 -837.9 B-B 0.0 0.0 0.0 0.0 0.0 Page 3.4 Live Load (LS): (Article 3.11.6.2 - 22TCN 272-05) a Pedestrian Load (PL): This is considered for pedestrian load on the retaing wall - Pedestrian load shall be taken from Article 3.6.1.3 - 22TCN272-05: qpl = - Vertical force due to Pedestrian load to Section B-B: Npl.B-B = 42.0 kN - Vertical force due to Pedestrian load to Section A-A: Npl.A-A = 288.0 kN 0.338 / kN/m2 b Live load surcharge (LS): The live load surchage (LS) shall be calculated by the following formula: LS = Δp*H*L = k*γs*heq*H*L where: k= Coefficient of lateral earth pressure k= γs = Unit weight of filling soil γs = 17.7 kN/m3 H= Height of the wall heq = Equivalent height of soil for the live load heq = 0.86 m Live Load Surcharge (LS) Section LS (KN) e (m) N (KN) H (KN) M (KNm) A-A 545.2 2.650 186.2 512.4 1711.7 B-B 473.2 2.300 161.6 444.7 998.7 3.5 Earth Pressure due to Earthquake (E q ( AE)): ((Appendix pp A11.1 - Section 11 - AASHTO LRFD 1998)) 3.5.1 Active Earth Pressure due to Earthquake (EAE): Active earth pressure due to earthquake shall be calculated by the below formula: Where: E AE = g.γ.H2 (1 − k v ).K AE.10−9 p y be taken as: - Values for the coefficient of active pressure KEA may ⎡ cos2 (ϕ − θ − β) sin(ϕ + δ)sin(ϕ − θ − i) ⎤ + KAE = x ⎢ ⎥ cosθ.cos2 β.cos(δ + θ + β) ⎣ cos(δ + θ + β) cos(i − β) ⎦ −2 = 0.378 In which: g= Acceleration of gravity (m/s2) 9.81 m/s2 γ= Density of soil (kg/m3) 1800 kg/m3 H= Height of soil face (mm) ϕ= Angle of Internal friction of soil (DEG) θ= arctg (kh/(1-kv)) (DEG) δ= Angle of friction between soil and wall (DEG) A= Acceleration coefficient 0.12 kh = Horizontal acceleration coefficient 0.06 kv = Vertical acceleration coefficient 0.03 mm 30.0 deg 3.5 deg 15.00 deg i= Backfill slope angle 0.0 deg β= Slope of wall to the vertical (DEG) 5.0 deg Page Section Active earth pressure due to earthquake (EAE) EAE (KN) e (m) A-A 1820.1 1.767 621.6 1710.7 4203.3 B-B 1371.1 1.533 468.3 1288.7 1905.7 N (KN) H (KN) M (KNm) 3.5.2 Passive Earth Pressure due to Earthquake (EAE): p q Active earth pressure due to earthquake shall be calculated byy the below formula: E PE = g.γ.H (1 − k v ).K PE 10−9 Where: - Values for the coefficient of active pressure KEA may be taken as: ⎡ cos2 (ϕ − θ + β) sin(ϕ + δ) sin(ϕ − θ + i) ⎤ KAE = x⎢1− ⎥ cos(δ + θ − β) cos(i − β) ⎦ cosθ.cos β.cos(δ + θ − β) ⎣ −2 = 0.341 In which: g= Acceleration of gravity (m/s2) 9.81 m/s2 γ= Density of soil (kg/m3) 1800 kg/m3 H= Height of soil face (mm) ϕ= Angle of Internal friction of soil (DEG) 30.0 deg θ= arctg (kh/(1-kv)) (DEG) 3.54 deg δ= Angle of friction between soil and wall (DEG) A= Acceleration coefficient 0.12 kh = Horizontal acceleration coefficient 0.06 kv = Vertical acceleration coefficient 0.03 mm 15.00 deg i= Backfill slope angle 0.0 deg β= Slope of wall to the vertical (DEG) 0.0 deg Section Passive earth pressure due to earthquake (EPE) EAE (KN) e (m) A-A 21.0 0.200 -5.4 -20.3 B-B 0.0 0.000 0.0 0.0 N (KN) H (KN) M (KNm) -17.1 0.0 Page 3.6 Earthquake Force: (Article 3.10 - 22TCN 272-05) The earthquake force shall be calculated as formula below: EQ Q= C sm * W R where: W= Weight of retaining wall (kN) R= Response Modification factor (Table 3.10.7.1-1_22TCN272-05) R= Csm = The elastic seismic response coefficient Cms = 1.5 0.1179 In general, the Csm shall be taken as: C sm = * A * S ≤ * A Tm2 / Exception, for soil profiles III and IV, and for modes other than the fundamental mode that have periods less than 0.3s, Csm shall be taken as: Csm = A*(0.8 + 4.0*Tm) (this formula is applied for this retaining wall) if the period of vibration for any mode exceeds 4.0 s, the value of Csm for that mode shall be taken as: C sm = 3* A *S Tm4 / in which: A= Acceleration coefficient (Taken from technical general notes) A= 0.1200 S= Site coefficient (Soil profile type III) S= 1.5 Tm = Period of vibration, shall be taken as: Tm = Tm = * Π * 0.0457 second f g in which: g= Gravitational accelaration g= f= Horizontal displacement at the top p p of the retaining g wall 9.81 m/s2 For retaining wall on spread foundation, Tm shall be calculated: T = 2π f = 2π g ( 23Q ) H 3 gEI Q= Retaining wall weight Q= H= Height from top of retaining wall to top of footing H= 1066.2 kN 4.60 m In order to calculate the earthquake force, the retaining wall shall be divided into parts as figure below: Page Earthquake effects acting on the Retaining wall No Section B-B Part of the Retaining wall Q (kN) HEQ (kN) e (m) MEQ (kN.m) Part 149.0 17.6 4.220 74.1 Part 35.3 4.2 3.720 15.5 Part 529.2 62.4 1.800 112.3 Part 352.8 41.6 1.200 49.9 1066.2 125.7 251.8 83.8 167.9 Total Total (Consider the Response modification factor) No Section A-A Part Q (kN) HEQ (kN) e (m) MEQ (kN.m) Part 149.0 17.6 4.920 86.4 Part 35.3 4.2 4.420 18.4 Part 529.2 62.4 2.500 156.0 Part 352.8 41.6 1.900 79.0 Part 1646.4 194.1 0.350 67.9 2712.6 319.9 407.8 213.2 271.9 Total Total (Consider the Response modification factor) LOAD COMBINATIONS: 4.1 Summary of Load: No Section A-A Load Section B-B N (kN) H (kN) M (kNm) N (kN) H (kN) M (kNm) Dead load of retaining wall (DC) 2712.6 0.0 2306.5 1066.2 0.0 120.7 Vertical earth pressure (EV) 7056 7056.1 00 0.0 -1596.6 1596 395 395.5 00 0.0 -76.3 76 3 Active horizontal earth pressure (EHa) 572.0 1574.1 4401.0 430.9 1185.8 2099.9 Passive horizontal earth pressure (EHp) -266.3 -993.8 -837.9 0.0 0.0 0.0 Pedestrian load (PL) 288.0 0.0 0.0 42.0 0.0 0.0 Live load surcharge (LS) 186.2 512.4 1711.7 161.6 444.7 998.7 Active earth pressure at seismic (EAE) 621.6 1710.7 4203.3 468.3 1288.7 1905.7 Passive earth pressure at seismic (EPE) -5.4 -20.3 -17.1 0.0 0.0 0.0 Earthquake Forces (EQ) 0.0 213.2 271.9 0.0 83.8 167.9 Page 4.2 Load Combinations: These load combinations as below shall be considered for the retaining wall calculation: - Combination I (Service limit state): 1.0*DC + 1.0*EV + 1.0*EHa + 1.0*EHp + 1.0*PL + 1.0*LS - Combination II (Strength I limit state): 1.25*DC + 1.35*EV + 1.5*EHa + 0.9*EHp + 1.75*PL + 1.75*LS - Combination III (Extremem Event limit state): 1.25*DC + 1.35*EV + +0.5*PL + 0.5*LS + 1.5*EAE + 0.9*EPE + 1.0*EQ where: DC = Dead load of the retaining wall EV = Vertical earth pressure EHa = Active horizontal earth pressure EHp = Passive horizontal earth pressure PL = Pedestrian load on top of retaining wall LS = Live load surcharge EAE = Active earth pressure at seismic EPE = Passive earth pressure at seismic EQ = Earthquake force 4.3 Load Combination at Service Limit State: No Load Section A-A Factor Section B-B N (kN) H (kN) M (kNm) (kN ) N (kN) H (kN) M (kNm) (kN ) Dead load of retaining wall (DC) 1.00 2712.6 0.0 2306.5 1066.2 0.0 120.7 Vertical earth pressure (EV) 1.00 7056.1 0.0 -1596.6 395.5 0.0 -76.3 Active horizontal earth pressure (EHa) 1.00 572.0 1574.1 4401.0 430.9 1185.8 2099.9 Passive horizontal earth pressure (EHp) 1.00 -266.3 -993.8 -837.9 0.0 0.0 0.0 Pedestrian load (PL) 1.00 288.0 0.0 0.0 42.0 0.0 0.0 Live load surcharge (LS) 1.00 186.2 512.4 1711.7 161.6 444.7 998.7 Active earth pressure at seismic (EAE) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Passive earth pressure at seismic (EAE) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Earthquake Forces (EQ) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 10548.7 1092.7 5984.7 2096.3 1630.5 3143.1 Summary Page 4.4 Load Combination at Strength I Limit State: No Load Section A-A Factor Section B-B N (kN) H (kN) M (kNm) N (kN) H (kN) M (kNm) Dead load of retaining wall (DC) 1.25 3390.8 0.0 2883.2 1332.8 0.0 150.9 Vertical earth pressure (EV) 1.35 9525.8 0.0 -2155.5 534.0 0.0 -103.0 Active horizontal earth pressure ((EHa) 1.50 858.0 2361.2 6601.5 646.3 1778.6 3149.9 Passive horizontal earth pressure (EHp) 0.90 -239.7 -894.4 -754.1 0.0 0.0 0.0 Pedestrian load (PL) 1.75 504.0 0.0 0.0 73.5 0.0 0.0 Live load surcharge (LS) 1.75 325.9 896.7 2995.5 282.8 778.3 1747.7 Active earth pressure at seismic (EAE) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Passive earth pressure at seismic (EAE) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Earthquake Forces (EQ) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 14364.8 2363.5 9570.6 2869.4 2557.0 4945.5 Summary 4.5 Load Combination at Extreme Limit State: No Load Section A-A Factor Section B-B N (kN) H (kN) M (kNm) N (kN) H (kN) M (kNm) Dead load of retaining wall (DC) 1.25 3390.8 0.0 2883.2 1332.8 0.0 150.9 Vertical earth pressure (EV) 1.35 9525.8 0.0 -2155.5 534.0 0.0 -103.0 Active horizontal earth pressure (EHa) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Passive horizontal earth pressure (EHp) 0.00 0.0 0.0 0.0 0.0 0.0 0.0 Pedestrian load (PL) 0.50 144.0 0.0 0.0 21.0 0.0 0.0 Live load surcharge (LS) 0.50 93.1 256.2 855.9 80.8 222.4 499.3 Active earth pressure at seismic (EAE) 1.50 932.4 2566.1 6305.0 702.4 1933.0 2858.6 Passive earth pressure at seismic (EAE) 0.90 -4.9 -18.3 -15.4 0.0 0.0 0.0 Earthquake Forces (EQ) 1.00 0.0 213.2 271.9 0.0 83.8 167.9 14081.2 3017.2 8145.0 2671.0 2239.2 3573.7 Summary Page 4.6 Summary of Load combinations: No Section A-A Limit state Section B-B N (kN) H (kN) M (kNm) N (kN) H (kN) M (kNm) Service limit state 10548.7 1092.7 5984.7 2096.3 1630.5 3143.1 Strength I limit state 14364.8 2363.5 9570.6 2869.4 2557.0 4945.5 Extreme Event limit state 14081.2 3017.2 8145.0 2671.0 2239.2 3573.7 Page 10 CHECK THE CAPACITY OF FOUNDATION 5.1 Data for Calculation - Load combination to the bottom of the foundation: Dimension of footing N Mx My Qx Qy L= 20 m kN kN.m kN.m kN kN B= 4.8 m Strength I limit state 14364.8 9570.6 - - 2363.5 Extreme Event limit state 14081.2 8145.0 - - 3017.2 Limit states For load encentric to the centroid of footing , a reduce effective area B'xL', within the confines of the the physical footing shall be use in geotechnical design for settlement or bearing resistance The design bearing pressure on the effctive area shall be assume to be uniform The reduce effective area shall be concentric with the load The reduced dimensions may be taken as: B' = B - 2*eB (Article 10.6.3.1.5 - 22TCN272-05) L' = L - 2*eL Where: eB Eccentricity parallel to dimension B (mm) eB = MX / N eL Eccentricity parallel to dimension L (mm) eL = MY / N ECCENTRICITY AND EFFECTIVE DIMENSIONS OF FOOTING P Mx My eL=My/P eB=Mx/P L' B' (kN) (kN.m) (kN.m) (m) (m) (m) (m) Limit states Strength I limit state 14364.8 9570.6 - 0.00 0.67 20.00 3.47 Extreme Event limit state 14081.2 8145.0 - 0.00 0.58 20.00 3.64 - Boring log for calculation: BH02, dated 5/11/2013 by VINACONEX The bottom level of footing is: 2.82 The soil layer "Clay, medium stiff" is considered as the soil under the footing This soil layer has the following average properties: + Thickness of this layer: h= 8.0m + SPT value: N= 23 + Natural unit weight: γw = 1970 kg/m3 = + Unconfined compression test: qu = 1.66 kG/cm2 = 0.163 Mpa + Cohension: c= 0.82 kG/cm2 0.080 Mpa + Internal friction angle: ϕ= 3.5 degree 19.3 kN/m3 Page 11 5.2 Bearing Resistance of Soils under Footings: - The factored resistance, qR, at strength limit state shall be taken as: qR = ϕ*qult (Article 10.6.3.1 - 22TCN272-05) where: ϕ= Resistance factor specified in Article 10.5.5 qult = Nominal bearing resistance (Mpa) ϕ= 0.6 for strength limt state, and = 1.0 for Extreme event limt state - The nominal bearing resistance of a layer of clay may be taken as: qult = Su*Ncm + g*γ*Df*Nqm*10-9 where: Su = Undrained shear strength (MPa) g= Gravitational acceleration (m/s2) g= 9.81 m/s2 γ= Density of clay (kg/m3) γ= 1970 kg/m3 Df = Embedment depth taken to the bottom of the footing Df = Ncm, Nqqm = Modified bearing capacity factors that are functions of footing shape, embedment depth, soil compressibility, and load inclination Su = qu/2 Su = 0.081 MPa 1.1 m + For Df/B ≤ 2.5, B/L ≤ 1.0 and H/V ≤ 0.4: Ncm = Nc * [ + 0.2*(Df/B) ] * [ + 0.2*(B/L) ] * [ - 1.3*(H/V) ] (2) + For Df/B > 2.5 and H/V ≤ 0.4: Ncm = Nc * [ + 0.2*(Df/B) ] * [ - 1.3*(H/V) ] (3) Nc = 5.0 for use in Equation on relatively level soil 7.5 for use in Equation on relatively level soil Nqm = 1.0 for saturated clay and relative level ground surfaces - The factored resistance force [P] at strength limit state shall be calculated: [P] = qR*(B'*L') - Checking for Bearing resistance: P ≤ [P] where: P= The factored vertical load at the bottom of footing Limit states B' L' Ncm qR = ϕ.qult qult [P] P (kN) (kN) Check (m) (m) Strength I limit state 3.47 20.00 4.32 373.4 224 15537 14365 OK Extreme Event limit state 3.64 20.00 3.96 344.1 344 25069 14081 OK kN/m (kN/m ) Page 12 5.3 Checking for Overturning: (Article 10.6.3.1.5 and 10.6.3.2.5 - 22TCN272-05) - For foundations on soil, the location of the resultant of the reaction forces shall be within the middle one-half of the base - For foundations on rock, the location of the resultant of the reaction forces shall be within the middle three-fourths of the base Force P M e = M/P Checking ResultantF P Mx My eB=Mz/P EB' /2 (kN) (kN.m) (kN.m) (m) = B'/4 Strength I limit state 14364.8 9570.6 - 0.67 1.20 OK E = 1/2*L (On soil E = 3/4*L (On rock) Extreme Event limit state 14081.2 8145 - 0.58 1.20 OK Width dimension L (or B) Limit states Check Page 13 5.4 Checking for Sliding (Article 10.6.3.3 - 22TCN272-05) - The factored resistance against failure by sliding, in N, may be taken as: QR = ϕQn = ϕT QT + ϕep Qep Where: ϕT = ϕT = Resistance factor for shear resistance between soil and foundation QT = Nominal shear resistance between soil and foundation ϕep = Resistance factor for passive resistance Qep = Nominal passive resistance of soil available throughout the design life of the structure 0.8 for strength limit state, and 1.0 for Extreme event limt state QR = ϕQn = ϕT QT - For safety, the factored resistance shall be taken only the part of shear resistance between soil and foundation: - For footing on soil: + If the soil is cohensionless: QT = V * tan(δ) for which: tanδ = tanϕf for concrete cast against soil = 0.8 * tanϕf for precast concrete footing ϕf = Internal friction angle of soil N= Total vertical force + If the soil is clay: The sliding resistance may be taken as the cohension of the clay QT = Su * (B'*L') - Checking for sliding: Q ≤ QR Where: P= The factored horizontal load at the bottom of footing N Qy B' L' QT QR Q kN kN (m) (m) (kN) (kN) (kN) Strength I limit state 14364.8 2363.5 3.47 20.00 5646.7 4517 2363 OK Extreme Event limit state 14081.2 3017.2 3.64 20.00 5932.7 5933 3017 OK Limit states Check Page 14 CHECK THE RETAINING WALL (SECTION B-B:) T.R B B B.R A A Summary table of loads acting on section B-B Limit state Shear force (kN) Moment (kN.m) Strength I limit state (Comb II) 2557.0 4945.5 Extreme Event limit state (Comb III) 2239.2 3573.7 S i lilimit it state t t (C b I) Service (Comb 1630 1630.5 3143 3143.1 b a' h a 0.85*f'c*a* a fy•A Page 15 Data Value Unit • Factored moment Mu 4945.5 kN.m • Factored shear force Vu 2557.0 kN h 700 mm • Height of section • Width of section b 20000 mm Ac 1.40E+07 mm2 Ig 5.7E+11 mm4 Thickness concrete cover dc 100 mm Distance to extreme compression fiber ds 600 mm Diameter ∅ 20 mm Spacing of bars @ 150 mm n 132 As 41448 mm2 Thickness concrete cover d'c 100 mm Distance to extream compression fiber d's 100 mm • Total area of section • Moment of inertia • Reinforcement in tension: Number Total area • Reinforcement in compression: Diameter ∅' 12 mm Spacing of bars @ 150 mm Number n' 132 A's 14916 • Resistance factor Φ 0.90 • Effective height of section de 600 • Stress block factor β1 0.85 • Depth of equivalent stress block (a = c•β1) a 38.03 mm • Distance from neutral axis to extreme compression filber c 44.75 mm Mn 9391.4 kN.m Mr = Φ•Mn 8452.3 kN.m Total area mm2 Flexural resistance • Nominal resistance • Factored flexural moment Mr > Mu • Check the flexural resistance capacity mm O.K Check the minimum content of reinforcement (Article 5.7.3.3.2 - 22TCN272-05) • Ratio of tension reinforcement to gross area • Limit value ρ = As/(b•d) 0.296% 0.03•f'c/fy 0.192% ρ > 0.03•f'c/fy O.K fr = 0.63•f'c0.5 3.15 Mpa Mcr = fr•Ig/yt 5145.00 kN.m • Limit value 1.2•Mcr 6174.00 kN.m • Limit value 1.33*Mu 6577.56 kN.m • Check the minimum reinforcement Check on cracking moment (Article 5.7.3.3.2 - 22TCN272-05): • Modulus of rupture of concrete • Cracking moment • Check the cracking moment Φ•Mn > Min(1.2•Mcr,1.33•Mu) O.K Check the maximum content of reinforcement (Artcile 5.7.3.3 - 22TCN272-05) • Maximum content of reinforcement • Check the maximum content of reinforcement c/de 0.07 c/de < 0.42 O.K Page 16 Shear resistance • Factored shear force Vu 2557.0 • Shear resistance factor Φ 0.90 • Height of section in shear dv 540 mm • Effective width of web in shear bv 20000 mm • Angle of inclination of diagonal compressive stresses θ 45 degree • Angle of inclination of transverse reinforcement to longitudinal axis α 90 degree β • Factor indicated possibiliy of concrete in being inclining cracked to transmit tension • Value 0.1•f'c•bv•dv kN 27000 kN • Spacing of stirrups s 150 mm • Diameter of stirrup ∅ D 13 mm • Number of stirrup reinforcement in the range of spacing s n • Total area of stirrups Av - mm2 • Nominal resistance of concrete Vc 8964.0 kN • Resistance of stirrups in shear Vs - kN 0.25•f'c•bv•dv 67500.0 kN • Nominal resistance of components Vn 8964.0 kN • Factored resistance Vr 8067.6 kN • Value Vr > Vu • Check O.K Check on cracking • Load combination used for checking Service limit state • Bending moment Mu n = Es/Ec • Ratio of elastic modulus • Reinforcement content ρ = As/(b•de) • Value • Value • Stress of reinforcement in tension 3143.1 kN.m 7.44 0.0035 % 0.7 0.20 j = - k/3 0.93 fs = Ms/(AS•j•de) 135.5 Mpa k = -ρ•n + [(ρ•n) + 2•ρ•n] • Information of cracking width Z 17500 N/mm • Value dc 50 mm • Result of concrete area which covers reinforcement overs number of steel bars A 15151.5 mm2 fsa = Z/(dc•A)1/3 192.0 Mpa 0.6•fy 234.0 Mpa • Tensile stress in reinforcement at service limit state • Value • Check fs < fsa O.K • Check fsa < 0.6•fy O.K Page 17 CHECK THE RETAINING FOOTING (SECTION C-C:) T.R C B B B.R A A C Summary table of loads acting on section B-B Limit state Shear force (kN) Moment (kN.m) Strength I limit state (Comb II) 2557.0 4945.5 Extreme Event limit state (Comb III) 2239.2 3573.7 S i lilimit it state t t (C b I) Service (Comb 1630 1630.5 3143 3143.1 b a' h a 0.85*f'c*a* a fy•A Page 18 Data Value Unit • Factored moment Mu 4945.5 kN.m • Factored shear force Vu 2557.0 kN h 700 mm • Height of section • Width of section b 20000 mm Ac 1.40E+07 mm2 Ig 5.7E+11 mm4 Thickness concrete cover dc 100 mm Distance to extreme compression fiber ds 600 mm Diameter ∅ 20 mm Spacing of bars @ 150 mm n 132 As 41448 mm2 Thickness concrete cover d'c 100 mm Distance to extream compression fiber d's 100 mm • Total area of section • Moment of inertia • Reinforcement in tension: Number Total area • Reinforcement in compression: Diameter ∅' 12 mm Spacing of bars @ 150 mm Number n' 132 A's 14916 • Resistance factor Φ 0.90 • Effective height of section de 600 • Stress block factor β1 0.85 • Depth of equivalent stress block (a = c•β1) a 38.03 mm • Distance from neutral axis to extreme compression filber c 44.75 mm Mn 9391.4 kN.m Mr = Φ•Mn 8452.3 kN.m Total area mm2 Flexural resistance • Nominal resistance • Factored flexural moment Mr > Mu • Check the flexural resistance capacity mm O.K Check the minimum content of reinforcement (Article 5.7.3.3.2 - 22TCN272-05) • Ratio of tension reinforcement to gross area • Limit value ρ = As/(b•d) 0.296% 0.03•f'c/fy 0.192% ρ > 0.03•f'c/fy O.K fr = 0.63•f'c0.5 3.15 Mpa Mcr = fr•Ig/yt 5145.00 kN.m • Limit value 1.2•Mcr 6174.00 kN.m • Limit value 1.33*Mu 6577.56 kN.m • Check the minimum reinforcement Check on cracking moment (Article 5.7.3.3.2 - 22TCN272-05): • Modulus of rupture of concrete • Cracking moment • Check the cracking moment Φ•Mn > Min(1.2•Mcr,1.33•Mu) O.K Check the maximum content of reinforcement (Artcile 5.7.3.3 - 22TCN272-05) • Maximum content of reinforcement • Check the maximum content of reinforcement c/de 0.07 c/de < 0.42 O.K Page 19 Shear resistance • Factored shear force Vu 2557.0 • Shear resistance factor Φ 0.90 • Height of section in shear dv 540 mm • Effective width of web in shear bv 20000 mm • Angle of inclination of diagonal compressive stresses θ 45 degree • Angle of inclination of transverse reinforcement to longitudinal axis α 90 degree β • Factor indicated possibiliy of concrete in being inclining cracked to transmit tension • Value 0.1•f'c•bv•dv kN 27000 kN • Spacing of stirrups s 150 mm • Diameter of stirrup ∅ D 13 mm • Number of stirrup reinforcement in the range of spacing s n • Total area of stirrups Av - mm2 • Nominal resistance of concrete Vc 8964.0 kN • Resistance of stirrups in shear Vs - kN 0.25•f'c•bv•dv 67500.0 kN • Nominal resistance of components Vn 8964.0 kN • Factored resistance Vr 8067.6 kN • Value Vr > Vu • Check O.K Check on cracking • Load combination used for checking Service limit state • Bending moment Mu n = Es/Ec • Ratio of elastic modulus • Reinforcement content ρ = As/(b•de) • Value • Value • Stress of reinforcement in tension 3143.1 kN.m 7.44 0.0035 % 0.7 0.20 j = - k/3 0.93 fs = Ms/(AS•j•de) 135.5 Mpa k = -ρ•n + [(ρ•n) + 2•ρ•n] • Information of cracking width Z 17500 N/mm • Value dc 50 mm • Result of concrete area which covers reinforcement overs number of steel bars A 15151.5 mm2 fsa = Z/(dc•A)1/3 192.0 Mpa 0.6•fy 234.0 Mpa • Tensile stress in reinforcement at service limit state • Value • Check fs < fsa O.K • Check fsa < 0.6•fy O.K Page 20 Page 21 ... THẦU SỐ PHU THUONG INTERCHANGE CALCULATION REPORT FOR DESIGN MODIFICATION OF RETAINING WALLS (REDESIGN ACCORDING TO NEWLY INVESTIGATED SOIL CONDITIONS) BLOCK C1-1 TO C1-2 ON BRANCH 1E SPREAD FOOTING... Hiep Reviewed by: Pham Dang Hung Approved by: Tran Manh Toan Hanoi, November 28th 2013 CALCULATION REPORT FOR RETAINING WALL - BLOCK C1-1, C1-2 GENERAL INFORMATIONS: - Project: Nhat Tan Bridge... Thuong Interchange - Block: C1-1, C1-2 DATA FOR CALCULATION: Design Specifications and References: 2.1 1) 22TCN 272-05: Vietnamese bridge design specifications 2) AASHTO LRFD 1998: American highway
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