CẦU THÉP TIẾNG ANH ĐHXD

NATIONAL UNIVERSITY OF CIVIL ENGINEERING BRIDGE & TUNNEL PROJECT DESIGN STEEL BRIDGE GROUP: STUDENTS: 06 Đào Công Chiến Nguyễn Thị Hoan Nguyễn Thị Nhung LECTURER: 404759 297259 303959 Dr Khúc Đăng Tùng Hà Nội, 10/05/2018 59CDE 59CDE 59CDE PROJECT DESIGN STEEL BRIDGE CONTENTS APPENDIX APPENDIX PROJECT DESIGN STEEL BRIDGE 1.1 CHAPTER DESIGN STEEL BRIDGE INPUT DESIGN DATA 1.1.1 - Design standard and load effects Bridge Design Standard 22TCN 272-05 Design Live Load HL93 Table1-1.Dimension of Components Effective Length Ltt 30.2 m Length of bridge L 30.8 m Total width B 11.82 m Bcx 10.82 m S 2400 mm 1110 mm Roadway width Dimension between girders Overhang Strength of concrete f'c 40 MPa Strength of steel fy 400 MPa Specific weight of steel Ws 7850 Kg/m3 Specific weight of concrete Wc 2400 Kg/m3 Specific weight of wearing surface Ww 2250 Kg/m3 Yield limit of steel M270 235 MPa Yield limit of steel M270M 235 MPa 1.1.2 Materials 1.1.2.1 Steel of structure beam - I girder use grade 250 with standard ASTM A709 or equivalent - SpecificGravity of Steel γs=78.5KN/m3 - Modulus of elasticity of Steel Ep = 200000 Mpa - The minimum drag intensity of steel fpu = 400 Mpa - Yield limit of steel fpy = 235 Mpa PROJECT DESIGN STEEL BRIDGE 1.1.2.2 Steel of anchorbolts - Anchor bolts use steel grade 1020 of standard ASTM A108 - The minimum drag intensity of steel fsu = 400 Mpa - Yield limit of steel fsy = 235 MPa 1.1.2.3 Steelreinforcement - Modulus of elasticity of steel Es = 200000 MPa - Yield limit of corrugated bar fy = 400 MPa - Yield limit of plain round bar Fy = 240 MPa 1.1.2.4 Concrete - SpecificGravity of reinforcedconcrete γc= 24.0 KN/m3 - Poisson’s ratio p = 0.2 - Deck slap bridge and barrier pour in place o Modulus of elasticity of concrete Ec = 27690 MPa o Modulus of elasticity of concrete f’c = 30 MPa 1.1.2.5 Wearing surface - Specific Gravity of wearing surface γws= 22.5 KN/m3 PROJECT DESIGN STEEL BRIDGE 1.2 DESIGN CROSS - SECTION 1.2.1 Cross- section 11820 500 10820 1110 500 4*2400 1110 11820 Figure1-1: General Section of Steel Bridge Cross section of girder 18 30 30 450 Figure1- End- Span Section 2000 100 30100 200 350 1640 100 1670 100 200 2400 2000 1.2.2 PROJECT DESIGN STEEL BRIDGE 18 40 450 Figure1- 3.Mid-Span Section 2000 100 30100 200 350 1630 100 1700 2000 100 200 2400 PROJECT DESIGN STEEL BRIDGE Table1- 2.Composite Girder Dimensions Midspan Section Endspan Section Height of composite girder D 2000 2000 Height of steel girder Ds 1700 1700 Height of concrete hbt 200 200 Width of concrete hb 200 200 Height of concrete haunch hv 100 100 Width of concrete haunch bv 100 100 bft 350 350 tft 30 30 bft 450 450 tft 40 30 hs 1630 1640 ts 18 18 Top flange Bottom flange Web PROJECT DESIGN STEEL BRIDGE 2.1 CHAPTER DETERMINE INTERNAL FORCES DETERMINE PROPERTIES OF SECTION 1630 18 40 1700 30 350 450 Figure2- Cross section of girder 2.1.1 • Non-composite section 1- Middle section The area of section : A =btf ´ ttf +t w ´ hw +bbf ´ tbf A =350 ´ 30 +18´ 1630 +450 ´ 40 ( A =57,840 mm • ) The distance fromneutral axis to bottomgirder : (2-1) PROJECT DESIGN STEEL BRIDGE tbf h t tf b tf ´ t tf ´ (H - ) +hw ´ t w ´ ( H - t tf - w ) +b bf ´ t bf ´ 2 yb = A æ æ 350 ö 1630 ö 40 350 ´ 30 ´ ç ÷ ÷ ç1700 ÷+1630 ´ 18´ ç ç1700 - 30 ÷+450 ´ 40´ ø ø è è yb = 57840 yb =745.82 ( mm) (2-2) - Moment of inertia of section girder: • Top flange ỉ btf ´ ttf3 ttf ÷ I1 = +A1 ỗ H y b ỗ ữ 12 ố ø ỉ 350 ´ 30 30 ÷ I1 = +( 350 30) ỗ ỗ1700 - 745.82 ÷ 12 2ø è I1 =9.26´ 109 mm ( • ( (2-3) ) Web ỉ t ´ h3 h I = w w +A2 ´ ç H - ttf - w - yb ÷ ç ÷ 12 è ø ỉ 18´ 1630 1630 I2 = +29,340 ỗ - 745.82 ữ ç1700 - 30 ÷ 12 è ø I =6.85´ 109 mm ( • ( (2-4) ) Bottomflange ỉ tbf b ´ t3 ÷ I = bf bf +A3 ỗ ỗ yb - ÷ 12 è ø ỉ 450´ 403 40 ữ I3 = +18, 000 ỗ ỗ745.82 ữ 12 2ứ è I =9.49´ 109 mm4 ( - ) Section modulus with respect to bottom fiber of steel girder: (2-5) PROJECT DESIGN STEEL BRIDGE åI Sb = yb ( (2-6) 9.26 ´ 109 +6.85´ 109 +9.49´ 109 Sb = 745.82 Sb =34,315, 720 mm3 ( - ) Section modulus with respect to top fiber of steel girder: St = åI H - yb ( (2-7) 9.26 ´ 109 +6.85´ 109 +9.49´ 109 St = 1700 - 745.82 St =26,822,318 mm3 ( ) Table 2-3 Properties of non-composite section Elements Top flange Web Bot flange Cross-section Area Parameter Width Depth A y 350 30 10500 1685 18 1630 29340 855 450 40 18000 20 57840 yb yt 745.82 mm Sb 954.18 mm St 2- End Section 10 3.43E+0 2.68E+0 A*y 1.77E+0 2.51E+0 3.60E+0 4.31E+0 mm3 mm3 Inertia moment Ix 9.26E+0 6.85E+0 9.49E+0 2.56E+1 PROJECT DESIGN STEEL BRIDGE ( Sr =1065´ 3.504 ´ 108 • ) - 0.19 =25.34 ( cycles) (4-1 60) The allowable shear force Zr for a specific life of N loading cycles of the stud p Z r = d S r = 836 N - 0.19 d (4-1 61) ) (4-1 62) ( ( ) Z r = 836 ´ 3.504 ´ 108 ´ 182 =6445.91( N ) d = the nominal diameter of the stud (mm) N = loading cycles The horizontal shear per unit of length due to fatigue load vh • V Q vh = sr I (4-1 63) Where: Vsr = the shear force rangedue to the fatigue truck (N) Q = the first moment of the transformed deck area about the neutral axis of the short-term composite section n (mm3) I = the moment of inertia of the short-term composite section n (mm4) The shear force per unit length that can be resisted by n connectors at a cross section with a distance p • nZ vh = r p • (4-1 64) From (4-5) and (4-6): The center-to-center pitch of shear connectors in fatigue limit state: nZ I p= r Vsr Q • (4-1 65) Calculate for section 103: o The horizontal shear per unit of length due to fatigue load vh The first moment of the transformed deck area about the neutral axis of the short-term composite section n (mm3) 53 PROJECT DESIGN STEEL BRIDGE ( Q =1.02´ 108 mm3 (4-1 66) ) 99.09 ´ 1.02 ´ 108 vh = =152.09 ( N / mm) ´ 1010 (4-1 67) o Choice : n = (studs) The center-to-center pitch of shear connectors in fatigue limit state: 5´ 6445.91 p= =210.79 ( mm) 152.09 (4-168) Choice: p = 210 (mm)=>OK o With the same section Section 100 101 102 103 104 105 Vh 260.65 228.84 197.04 152.90 123.47 94.05 ns 5 5 5 Cin 75 75 75 75 75 75 Cex 25 25 25 25 25 25 P 123.65 140.84 163.57 210.79 261.03 342.70 Choice P 120 140 160 210 260 340 mm mm mm mm mm mm æ1510 3020 3020 3020 3020 1510 ữ N s =3 ỗ + + + + + ỗ ữ ố 120 140 160 210 260 340 ø (4-169) N s =418 ( studs) 4.1.3 Caculate the number of anchors according to the strength limit state • • Two failure modes: o The studs sheared of the steel beam and remainded embedded in the concrete slab o The concrete failed and the connectors were pulled out of the slab together with a wedge of concrete Nominal shear resistance Qn for a single shear stud connector: Qn =0.5 Asc f c ' Ec £ Asc Fu (4-170) Where: o Asc = the cross-sectional area of a shear stud connector (mm2) 54 PROJECT DESIGN STEEL BRIDGE p´ 182 Asc = =254.34 mm ( ) (4-171) o f’c = 30(Mpa) = the specified 28-day concrete-compressive strength (Mpa) o Ec = concrete modulus of elasticity in A.5.4.2.4 (Mpa) Ec =0.043´ 24001.5 ´ 30 =27691.47 ( Mpa) (4-172) o Fu = 235(Mpa) = specified minimum tensile strength of a shear stud connector • Qn =0.5´ 254.34´ 30 ´ 27691.47 =115909.3 ( N ) (4-173) Qn =91582.65 >Asc Fu =254.34 ´ 235 =59769.9 ( N ) (4-174) Choice: Qn = 59769.9 (N) The factored resistance of one shear connector: Qr =f sc Asc Fu (4-175) Where: ϕsc = 0.85 = resistance factor of shear connector Q r =0.85´ 59769.9 =50804.42 ( N) • (4-176) Determine number of shear stud connectors o If sufficient shear connectors are provided, the maximum possible flexural strength of a composite section can be developed o The shear connectors placed between a poit of zero moment and a point of maximum positive moment must resist thecompression force in the slab t the location of maximum moment: ns Qr =Vh (4-177) o Required number of shear connectors in length Ls: V ns = h Qr (4-178) Where: Vh = nominal horizontal shear force at the interface that must be resisted 55 PROJECT DESIGN STEEL BRIDGE Qr = factored resistance ofa single shear connector in Eqs (6.10.7.4.4a-1) o The nominal horizontal shear force Vh:  Have PNA in slab  Have PNA in steel o Vh is taken as the lesser of either: Vh1 =Fyw Dtw +Fyt bt tt +Fyc b f t f Vh1 =235´ ( 1640 ´ 18 +450 ´ 30 +350 ´ 30) (4-179) Vh1 =12577.2 ´ 10 ( N ) Or: Vh =0.85 f c ' bt s Vh =0.85 ´ 30 ´ 2310 ´ 200 (4-180) Vh =11781´ 10 ( N ) Because: Vh1< Vh2 =>Choice: Vh = Vh1 = 12577.2x103(N) Vh 12577.2 ´ 103 ns = = =248 ( studs / half - girder ) Qr 50804.42 (4-181) So: N s =248 ( studs) (4-182) From (4-11) and (4-23): Choice: Ns = 418 (studs) 4.2 DESIGN GIRDER CONNECTIONS • The axial force per unit length of beam: V SB T= I • Where: V = shear force SB = first moment at beam flange I = moment of interia of section With composite girder 56 (4-183) PROJECT DESIGN STEEL BRIDGE top 101 T V D1S bs V D S b V AD S b = + 3n + n Is I td I td 196.35´ 1.25´ 2.59´ 107 26.65´ 1.25´ 6.73´ 107 T = + 2.32 ´ 1010 4.34 ´ 1010 54.09 ´ 1.5´ 6.73´ 107 396.68´ 1.75´ 9.98´ 1010 + + 4.34 ´ 1010 5.98´ 1010 top T101 =1409.538 ( kN / m) top 101 (4-184) Table 4- 27: Calcutate axial force Sectio n 100 101 102 T-top 1677.1 1409.5 1141.9 793.89 553.86 363.15 T-bot 986.20 818.01 649.81 503.52 326.98 174.08 • 103 104 105 Unit kN/m m kN/m m Shear stress along the beam ( acting on two welds of web) Dh =0.7 ´ 12 =8.4 ( mm) The effective height of weld: T 1677.13 top f100 = = =99.83( Mpa) 2Dh ´ 8.4 (4-185) Table 4- 28: Shear stress along beam fH • Sectio n top bot 100 101 102 103 104 105 Unit 99.83 58.70 83.90 48.69 67.97 38.68 47.26 29.97 32.97 19.46 21.62 10.36 Mpa Mpa Shear force along the beam: fV =( +IM ) P l 2Dh (4-186) Due to shear force is very small compared to shear stress along the beam => ignore • Stress combination: top f100 = fV2 +f H2 » • f H2 =99.83 ( Mpa) Condition: 57 (4-187) PROJECT DESIGN STEEL BRIDGE f £ Rr =0.6f e Fexx (4-188) where: φexx = 0.8 Fexx = 485 Mpa = shear strength of welds (Mpa) Choose welding rod E43.0, with tensible strength of 485 (Mpa) Rr =0.6f e Fexx =0.6 ´ 0.8´ 485 =232.8 ( Mpa) (4-189) Table 4- 29: Checking shear stress Section fH to p bo t Rr 4.3 4.3.1 100 101 102 103 104 105 Uni t 99.83 83.90 67.97 47.26 32.97 21.62 Mpa 58.70 48.69 38.68 29.97 19.46 10.36 Mpa 232.8 OK 232.8 OK 232.8 OK 232.8 OK 232.8 OK 232.8 OK Mpa DESIGN STIFFENRERS Intermediate transverse stiffeners 1- Slenderness • The width bt of each projecting stiffeners element D E 50 + £ bt £ 0.48t p 30 Fys (4-190) Where : D = 1700 mm =The depth of the steel section tp= Choice = 16 mm = Thickness of the projecting stiffener element Fys = 235 Mpa = Specified minimum yeild strength of the stiffener bf = 350 mm = Full with of the widest compression flange And : 16t p ³ bt ³ 0.25b f (4-191) 16´ 16 =256 ³ bt ³ 0.25´ 350 =87.5 (4-192) Choice : bt = 150 mm 1700 50 + =106.67 £ 150 £ 0.48´ 16 ´ 30 =>OK 58 200000 =224.05 235 (4-193) PROJECT DESIGN STEEL BRIDGE 2- Stiffness • The requirement for the moment of inertia of any tranverse stffneners : I t ³ tw3 J (4-194) ổD p ử2 ữ J =2.5 ỗ ỗ d ÷ - 2.0 ³ 0.5 o è ø (4-195) Where : It = Moment of inertia of the tranverse stiffener taken about the edge in contact with the web for single stiffeners and about the mid-thickness of the web for stiffener pairs (mm4) 1 I t = t pbt3 = ´ 16 ´ 1503 =18´ 106 mm 3 ( ) (4-196) tw= 18 mm = The thickness of web (mm) = The smaller of the adjacent web panel widths(mm) Choice: = 4000 mm Dp = 1640 mm = The web depth for webs without longitudinal stiffeners or maximum subpanel depth for webs with longitudinal stiffeners (mm) ổ1640 ử2 ỗ ữ - 2.0 =- 1.58 J =2.5 ỗ ữ ố4000 ứ =>J < 0.5 => Choice: J=0.5 ( d ot w3 J =4000 ´ 183 ´ 0.5 =648000 mm (4-197) ) I t ³ d ot w3 J ị OK (4-198) (4-199) 3-Strength The area As of transverse intermediate stiffeners required to carry the tensionfield action of the web : é ùỉFyw V ÷ As ³ ê0.15 BDt w ( - C ) u - 18t w2 ỳỗ ỗ ữ ú Vr ë ûè Fys ø (4-200) Where : tw = 18 mm = The thickness of the web D = 1700 mm = The steel girder depth Vr = 4023.58 kN =Factored shear resistance Vu = 1115.43 kN = Shear due to factored loads at strength limit state As = 16150 = 2400 mm2 = Stiffener area (mm2) Fys = 235 Mpa = Specifird minimum yeild strength of the stiffener 59 PROJECT DESIGN STEEL BRIDGE C = Ratio between bucking stress and yeild strength specified at 6.10.7.3.3a D 1700 = =90.56 tw 18 (4-201) Ek 200000 ´ 5.83 = =70.44 Fyw 235 Because D Ek 0 Þ OK (4-203) Þ b ´ t p =150´ 16 ( mm) Þ OK 4.3.2 Bearing stiffeners 1- Rolled beam shapes • Bearing stiffeners are required on webs of rolled beams if: Vu >0.75j bVn (4-204) Where: φb = = the resistance factor of bearing Vn = 4023.58 kN = the nominal shear resistance determined in Section 8.8 1115.43 OK Axial resistance R £ Pr =f c Pn Where: Φc = 0.9 = the resistance factor for compression Pn = the norminal compressive resistance = 2000 mm A = 4As+tw(18tw+2000) = 51432 mm2 = the effective area I = 8.57107 mm4 I r = A = 40.83 mm 61 (4-210) PROJECT DESIGN STEEL BRIDGE kL/r = 31.23 λ = 1.27 10-7< 2.25 => OK Pn =0.66l Fy As =12086.52 ( kN ) (4-211) Pr =f c Pn =0.9´ 12086.52 =10877.87 ( kN ) (4-212) Þ b ´ t p =150´ 16 ( mm) Þ OK 4.4 4.4.1 DESIGN GIRDER SPLICES Caculate the web splices 1- Calculate internal force Devide girder to states: 6.04+6.04+6.04+6.04+6.04=30.2 m • Moment & Shear: M w =M Iw I (4-213) Vw » V • (4-214) Internal force transmitted to a bolt is: o Shear : V Rv = w k (4-215) o Moment RM max =M w ymax å yi2 (4-216) Where: k = number of bolt y =the distance from centroid axis of cross-section to center of bolt Checking condition: Rmax = (R V ) +RM2 max £ Rr (4-217) With : Rr = Resistance of the bolt-head worked with two friction plates 62 PROJECT DESIGN STEEL BRIDGE • Structure is composite girder: M w =M D1 Iw I 3n In +M D w3n +M AD wn I I I (4-218) Vw » V =V D1 +V D +V AD • (4-219) Calculate maximum moment and shear for limit state o Strength Limit State  Moment 6.68´ 109 M =1185.94 ´ 1.25´ 2.32 ´ 1010 7.85´ 109 +( 128.77 ´ 1.25 +261.38´ 1.5) 4.34 ´ 1010 1.56 ´ 1010 +1631.28´ 1.75´ 5.98´ 1010 M W =1268.72 ( kN ) w 102  (4-220) Shear w V102 » V =1.25´ 147.26 +1.25´ 15.99 +1.5´ 32.46 +1.75 ´ 284.49 (4-221) w V102 » V =750.61( kN ) • Choice Number of rows in total splices n Maximum distance from centroid of bolt to splice edge Cex 45 Number of bolts in a row N 21 Distance between rows in a row Cin 73.5 mm mm o Determine the sliding resistance: Using high-strength bolts, diameter d = 20 mm (M253, have friction force) 63 PROJECT DESIGN STEEL BRIDGE Ab = 314 mm2 Fub = 780 Mpa The number of friction plating : Ns = Sliding resistance of a bolt: o Determine the force acting on a bolt: The force transmitting to a bolt due to shear force: V w 750.61 Rw = 102 = =8.94 ( kN ) N n 21´ (4-222) The maximum force transmitting to a bolt due to bending moment: w Rw =M 102 ymax 735 =1915.69 ´ 1000 ´ =112.09 ( kN ) nå yi 8´ 2079866 (4-223) The total force transmitting to a bolt: R = RV2 +RM2 = ( 8.94) +( 112.09) =112.44 ( kN ) (4-224) Rr =0.38´ Fub ´ Ab ´ N s =0.38´ 780 ´ 314 ´ / 1000 =148.91( kN ) (4-225) 2 Rr >R Þ OK Section Vw Mw Rv Rw Rmax Rr 100 1115.43 0.00 13.28 0.00 13.28 148.91 OK Table 4- 30: Checking force transmitting to bolts 101 102 103 104 105 933.02 750.61 568.20 385.79 235.35 718.10 1268.72 1390.10 1570.61 1637.44 11.11 8.94 6.76 4.59 2.80 63.44 112.09 122.81 138.76 144.66 64.41 112.44 123.00 138.83 144.69 148.91 148.91 148.91 148.91 148.91 OK OK OK OK OK Unit kN kN kN kN kN kN Fns = 2156010 = 31200(mm2)>Fs =163018 =29340 (mm2)=> OK 4.4.2 Caculate flange splices • • Choice diameter of bolts: d = 20 mm Force of beam flange: N =Fr Af Where: N = material resistance at beam flange 64 (4-226) PROJECT DESIGN STEEL BRIDGE Fr= stress at beam flange Af = 350x30= 10500 mm2 =the caculated area of beam flange Af = 450x40= 18000 mm2 =the caculated area of beam flange o Top flange N =111.085´ 10500 =1166392 ( N ) n= N 1166.392 = =7.8 Þ n =8 Rr 148.91 (cái) (4-227) (4-228) Choice: rows, bolts each row: Area: 320160 mm o Bottom flange N =131.33´ 18000 / 1000 =2363.88 ( kN ) (4-229) N 2363.88 = =15.87 Þ n =16 Rr 148.81 (cái) (4-230) n= Choice: rows, bolts each row: Area: 320320 mm 65 PROJECT DESIGN STEEL BRIDGE DOCUMENTS [1] LêĐìnhTâm, Cầuthép, NhàxuấtbảnGiaothơngvậntải, 2004 [2] LêĐìnhTâm, NguyễnTiếnOanh, NguyễnTrâm, Xâydựngcầuthép, Nhàxuấtbảnxâydựng, 1996 [3] Wai Fan Chen and Lien Duan, Bridge Engineering Handbook, CRC press, NewYork, 2000 [4] BộGiaothôngvậntải, Tiêu chuẩn thiết kếcầu 22TCN 272-05, 2005 [5] RichardM.Baker, Jay A.Pucket, Design of highway bridge, MC Graw Hill, 1997 66 PROJECT DESIGN STEEL BRIDGE 67