BANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM T CẦU ĐƯỜNG TIẾNG ANH
05 Calculation Super T Girder L=38.2m_Skew 20.xls【I.General】 SHEET NO : / 1 GENERAL 1.1 Design standard Specification for Bridge Design: 22TCN-272-05 1.2 Material strength and stress limits 1.2.1 Prestressing Steel: Type of low relaxation strand complies with : ASTM A416, Grade 270 Diameter of tendon = 15.2 mm Area of tendon = 140 mm2 Tensile Strength fpu = 1860 MPa Yield Strength fpy = 1674 MPa Modulus of elasticity of strand Ep = 197000 Modulus Ratio np = Ep/Ec = 6.00 1395 MPa Jacking Force = 195.30 kN Stress in the prestressing steel at jacking = 1.2.2 Reinforcing Steel: Reinf Standart ASTM or TCVN 1651-2008 Yield strength fs = 400 MPa Modulus of elasticity Es = 200000 MPa 1.2.3 Concrete: 1.2.3.1 Main Girder: Specified compressive strength at 28 days f'c = 50 MPa Compressive strength at time of initial prestress f'ci = 42.50 MPa Modulus of elasticity Ec = 38007 MPa (5.4.2.4-1) Modulus of elastic of concrete at release time Eci = 35041 MPa (5.4.2.4-1) Tensile strength of concrete at 28 days fr = 4.45 MPa Specified compressive strength at 28 days f'c = 35 MPa Modulus of elasticity Ed = 1.2.3.2 Deck Slab: 1.3 Design loads and load combination 1.3.1 Dead Loads: + Unit weight of Concrete = 2500 Kg/m3 + Unit weight of reinforcement Concrete = 7850 Kg/m3 + Unit weight of asphant concrete = 2300 Kg/m3 1.3.2 Live Loads: + Live Loads HL93 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 31799 Mpa => nd = Ed/Ec = 0.84 05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】 SHEET NO : / GEOMETRIC PROPERTIES ELEVATION A B SECTION A-A C B b1 b2 h8 CL OF BEARING h2 h5 h1 hd hd b3 10 11 b9 b9 h1-hd b1 L2 bd L3 A B b4 C SECTION B-B SECTION C-C B B b3 h9 11 10 b9 b11 h3 h1 H b3 b12 h5 10 b9 h1 11 b9 b2 h2 h5 h2 H b1 h8 b2 h8 b1 b3 b4 b7 b7 b8 b8 h6 L1 h4 h7 b1 bd b4 b3 b1 b4 b10 b4 b6 b5 b4 b3 b5 2.1 Dimension profiles Distance from bearing to end of girder Distance from bearing to girder notch Length of full section (not inlcude notch) Items Distance to bearing Section in/out of length of link slab Height of girder Height of composite section Height of other components Slab thickness Thickness of precast concrete plate Effective width of concrete slab Width of other components Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Notation h1; hd H h2 h3 h4 h5 h6 h7 h8 h9 B b1 b2 b3 b4 b5 b6 b7 L1 L2 L3 = 550 mm = 450 mm = 1200 mm Sec Sec Sec Sec Sec Sec 18550 14750 10950 6450 3850 1650 no no no no no yes 1750.0 1750 1750 1750 1750 1750 1945.0 1945 1945 1945 1945 1750 75.0 75 75 75 75 75 1425.0 1425 1425 1425 1425 250.0 250 250 250 250 75.0 75 75 75 75 75 350.0 350 350 350 350 50.0 50 50 50 50 195.0 195 195 195 195 195 35.0 35 35 35 35 2350.0 2350 2350 2350 2350 2350 650.0 650 650 650 650 650 1050.0 1050 1050 1050 1050 1050 650.0 650 650 650 650 650 175.0 175 175 175 175 175.0 135.0 135 135 135 135 430.0 430 430 430 430 82.5 82.5 82.5 82.5 82.5 Sec 450 yes 800 800 75 75 195 2350 650 1050 650 65 05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】 SHEET NO : / b8 b9 b10 b11 b12 bd Width of girder bottom 215.0 100.0 25.7 7.5 810.0 700.0 215 100 25.7 7.5 810 700 215 100 25.7 7.5 810 700 215 100 25.7 7.5 810 700 215 100 25.7 7.5 810 700 100 100 700 920 Sec Sec Sec Sec Sec Sec 650 650 650 650 650 650 75 75 75 75 75 75 48750 48750 48750 48750 48750 48750 7.5 7.5 7.5 7.5 7.5 75 75 75 75 75 562.5 562.5 562.5 562.5 562.5 100 100 100 100 100 100 75.0 75 75 75 75 75 7500 7500 7500 7500 7500 7500 135 135 135 135 135 1750 1750 1750 1750 1750 472500 472500 472500 472500 472500 82.5 82.5 82.5 82.5 82.5 175.0 350 350 350 350 350 1675 28875 28875 28875 28875 28875 293125 215 215 215 215 215 50 50 50 50 50 10750 10750 10750 10750 10750 430 430 430 430 430 700 250 250 250 250 250 1675 107500 107500 107500 107500 107500 1172500 25.7 25.7 25.7 25.7 25.7 250 250 250 250 250 6425 6425 6425 6425 6425 650 650 650 650 650 650 75 75 75 75 75 75 48750 48750 48750 48750 48750 48750 1050 75 78750 Sec 650 75 48750 2.2 Section properties in each stage 2.2.1 Stage I&II: Non-composite section 2.2.1.1 Section area: Element Shape QuantityNotation K1 chữ nhật b rectangle h A1 K2 tam giác b triangle h A2 K3 tam giác b triangle h A3 K4 chữ nhật b rectangle h A4 K5 tam giác b triangle h A5 K6 tam giác b triangle h A6 K7 chữ nhật b rectangle h A7 K8 tam giác b triangle h A8 K10 chữ nhật b rectangle h A10 K11 chữ nhật b rectangle h A11 K12 A12 Tendon Unit (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm) (mm) (mm2) (mm2) A I&II Total section area 30800 30800 30800 28000 762413 762413 762413 759613 23100 18900 100 75 7500 65 725 47125 920 725 667000 650 75 48750 1050 75 78750 - 754713 1668275 897875 Sec Sec Sec Sec Sec Sec 1713 1713 1713 1713 1713 1713 Sec 763 2.2.1.2 Static moment of area Items Distance from centroid of Notation z1 Unit (mm) component to bottom fiber z2 (mm) 1700 1700 1700 1700 1700 of girder z3 (mm) 1650 1650 1650 1650 1650 z4 (mm) 875 875 875 875 875 z5 (mm) 367 367 367 367 367 z6 (mm) 267 267 267 267 267 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 1650 700 1117 483 05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】 SHEET NO : / z7 (mm) z8 (mm) z10 (mm) z11 (mm) Tendon Static moment of inertia of component about bottom z12 (mm) s1 (mm3) fiber of girder s2 s3 s4 s5 s6 125 125 838 363 1713 763 1713 763 166.6667 166.667 166.667 166.667 166.667 1713 191 1713 191 1713 191 1713 195 1713 236 236 - 83484375 8.3E+07 8.3E+07 8.3E+07 8.3E+07 8.3E+07 3.7E+07 956250 956250 956250 956250 956250 - - 12375000 1.2E+07 1.2E+07 1.2E+07 1.2E+07 1.2E+07 5250000 4.13E+08 4.1E+08 4.1E+08 4.1E+08 4.1E+08 10587500 1.1E+07 1.1E+07 1.1E+07 1.1E+07 3.3E+08 2.3E+07 (mm ) (mm ) (mm ) (mm3) SI&II 125 (mm ) (mm ) s12 125 s8 s11 Tendon (mm ) s7 s10 Total for stage I&II 125 (mm ) 2866667 2866667 2866667 2866667 2866667 1070833 1070833 1070833 1070833 1070833 (mm ) - - - 83484375 8.3E+07 8.3E+07 8.3E+07 8.3E+07 8.3E+07 3.7E+07 1798125 (mm ) (mm ) - - 13437500 1.3E+07 1.3E+07 1.3E+07 1.3E+07 9.8E+08 2.4E+08 3 - 5897500 5897500 5897500 5456500 5456500 4464409 800625 - 6.28E+08 6.3E+08 6.3E+08 6.3E+08 6.3E+08 1.5E+09 3.4E+08 2.2.1.3 Centroid Distance from neutral axis to top fiber of girder Distance from neutral axis to bottom fiber of girder yt1 (mm) -927 -927 -927 -924 -919 -854 -416 yd1 (mm) 823 823 823 826 831 896 384 Distance from center e1 (mm) -889 -889 -889 -887 -882 -816 -378 of component to neutral axis e2 (mm) -877 -877 -877 -874 -869 896 384 e3 (mm) -827 -827 -827 -824 -819 -754 -316 e4 (mm) -52 -52 -52 -49 -44 896 384 e5 (mm) 457 457 457 459 464 -221 -99 e6 (mm) 557 557 557 559 564 896 384 e7 (mm) 698 698 698 701 706 59 22 e8 (mm) 657 657 657 659 664 896 384 e10 (mm) -889 -889 -889 -887 -882 -816 -378 e11 (mm) -816 -378 e12 (mm) 660 384 22851563 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2E+07 Tendon 2.2.1.4 Moment of inertia a About centroid of components I1 (mm4) I2 I3 I4 I5 I6 (mm ) 175781 631 175781 595 175781 1.97E+08 (mm ) - 2E+08 2E+08 2E+08 - 2E+08 4.6E+10 1493056 1493056 1493056 1493056 1493056 5.6E+08 5.6E+08 5.6E+08 5.6E+08 5.6E+08 2.7E+11 (mm ) - 2343750 2343750 2343750 2343750 2343750 2343750 2343750 1.21E+11 1.2E+11 1.2E+11 1.2E+11 1.2E+11 (mm4) Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 175781 632 (mm ) (mm ) I12 175781.3 632 I8 I11 15.2 mm Sum (a) (mm ) I7 I10 D= 632 22309028 2.2E+07 2.2E+07 2.2E+07 2.2E+07 - 1E+09 3E+10 - 22851563 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2.3E+07 2E+07 4E+07 4E+07 (mm ) (mm ) (mm ) 691748.4 691748 691748 628862 518811 518811 0E+00 1.21E+11 1.2E+11 1.2E+11 1.2E+11 1.2E+11 3.2E+11 3.1E+10 05 Calculation Super T Girder L=38.2m_Skew 20.xls【II.Section】 SHEET NO : / b Moment of inertia of components about centroid of section I1 (mm4) 3.86E+10 3.9E+10 3.9E+10 3.8E+10 3.8E+10 3.2E+10 7E+09 I2 (mm4) 4.32E+08 4.3E+08 4.3E+08 4.3E+08 4.2E+08 I3 (mm ) 5.13E+09 5.1E+09 5.1E+09 5.1E+09 5E+09 4.3E+09 7.5E+08 I4 (mm4) 1.27E+09 1.3E+09 1.3E+09 1.2E+09 9.2E+08 I5 I6 6.02E+09 6E+09 6E+09 6.1E+09 6.2E+09 1.4E+10 4.6E+08 3.33E+09 3.3E+09 3.3E+09 3.4E+09 3.4E+09 (mm ) I7 (mm ) 5.24E+10 5.2E+10 5.2E+10 5.3E+10 5.4E+10 I8 (mm4) 2.77E+09 2.8E+09 2.8E+09 2.8E+09 2.8E+09 I10 I11 Sum (b) Moment of inertia stage I&II (mm4) (mm ) - - 4E+09 3.1E+08 - 3.86E+10 3.9E+10 3.9E+10 3.8E+10 3.8E+10 3.2E+10 7E+09 5.2E+10 1.1E+10 1.23E+10 1.2E+10 1.2E+10 1.1E+10 8.2E+09 8.2E+09 1.61E+11 1.6E+11 1.6E+11 1.6E+11 1.6E+11 1.5E+11 2.7E+10 2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10 (mm ) I12 (mm ) II&II (mm4) 2.2.2 Stage III: Composite section K9 chữ nhật rectangle b h A9 (mm2) ΣA III (mm2) Distance from K9 to bottom fiber of girder z9 (mm) Static moment of K9 about bottom fiber of girder s9 Total static moment of area SIII Total section area (mm) (mm) 2350 195 458250 2350 195 458250 2350 195 458250 2350 195 458250 2350 195 458250 - 1220663 1220663 1220663 1217863 1212963 1668275 1847.5 1847.5 1847.5 1847.5 897875 1847.5 1750 800 (mm3) 8.47E+08 8.5E+08 8.5E+08 8.5E+08 8.5E+08 - - (mm3) 1.47E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 3.4E+08 Distance from neutral axis to top fiber of girder yt2 (mm) -542 -542 -542 -540 -535 -854 -416 Distance from neutral axis to bottom fiber of girder yd2 (mm) 1208 1208 1208 1210 1215 896 384 Distance from neutral axis to top fiber of slab yb2 (mm) -737 -737 -737 -735 -730 -854 -416 Distance from neutral axis to center of tendons ec2 (mm) 1016 1016 1016 1015 979 660 384 Moment of inertia stage I&II Distance from neutral axis of stage I to stage II Moment of inertia about centroid of section at stage II Moment of inertia of K9 Distance from center of K9 to neutral axis of composite section Moment of inertia about centroid of composite section Moment of inertia of composite section II&II (mm4) e (mm) (mm4) I9 (mm ) (mm) IIII Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 2.82E+11 2.8E+11 2.8E+11 2.8E+11 2.8E+11 4.7E+11 5.7E+10 -385 -385 -385 -385 -384 - - - - 1.13E+11 1.1E+11 1.1E+11 1.1E+11 1.1E+11 1.45E+09 1.5E+09 1.5E+09 1.5E+09 1.5E+09 -640 -640 -640 -637 -632 -756 -318 (mm4) 1.88E+11 1.9E+11 1.9E+11 1.9E+11 1.8E+11 - - (mm4) 5.84E+11 5.8E+11 5.8E+11 5.8E+11 5.7E+11 4.7E+11 5.7E+10 05 Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】 SHEET NO : / TENDON ARRANGEMENT 3.1 Input date Using straight tendons with diameter 140.0 mm 15.2 mm A_ten To reduce tensile stress at bearing locations, unbonded tendons are created by using PE tube Effective length of tendons Type of tendons Effective length (m) Remark 36.20 Full length tendons 34.20 Tendons with 1.0m unbonded 30.20 Tendons with 3.0m unbonded 26.20 Tendons with 5.0m unbonded 22.20 Tendons with 7.0m unbonded Tendon h(mm) Number of strands bottom Tendon h(mm) Number of strands top Row E Row A 75 2 Row B 130 2 Row C 185 2 Row D 240 1690 2 h(mm): distance from center of tendons to bottom fiber of girder 510 60 ROW E HÀNG E ROW D - HÀNG D ROW C - HÀNG C ROW B - HÀNG B ROW A - HÀNG A 55 55 75 55 250 1750 510 60 SECTION 50 11 13 10 12 12x50=600 700 50 TABLE OF NUMBER, LOCATION AND DEBONDING LENGTHS OF STRANDS STRAND (Ndeg) ROW E 1000 + + + ROW D ROW C ROW B ROW A + 3000 + + 5000 + 3000 + 5000 + 3000 + 7000 + 7000 + 5000 5000 + 7000 + 5000 TOTAL NUMBER OF STRANDS : 44 (A - E) Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung + 7000 + 10 11 12 5000 + 3000 5000 + 3000 + + 3000 + + 13 1000 + + + 05 Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】 SHEET NO : / 3.2 Sum of tendons at sections Section Type of tendons Aps (mm2) Area of tendons 5 √ √ √ √ √ 3500 280 840 980 560 √ √ √ √ √ 3500 280 840 980 560 √ √ √ √ √ 3500 280 840 980 560 √ √ √ √ X 3500 280 840 980 √ √ √ X X 3500 280 840 0 √ √ X X X 3500 280 0 X X X X X 0 0 Section Distance from center of tendons to bottom fiber of girder Distance from center of ΣA all tendons ps(mm ) to bottom fiber of girder n 145 1690 130 161 158 191 mm 6160 44 145 1690 130 161 158 191 mm 6160 44 145 1690 130 161 158 191 mm 6160 44 145 1690 130 161 195 mm 5600 40 145 1690 130 0 236 mm 4620 33 145 1690 0 260 mm 3780 27 0 0 0 mm 0 3.3 Force transfering length & developing length of tendons = 60dp = Force transfering length (mm) 912 (5.11.4.1-272-05) Developing length of normal tendon (mm) ld = [0.15fps-0.097fpe]dp = 2535 (5.11.4.2-272-05) Developing length of covered tendon (mm) ld = 2[0.15fps-0.097fpe]dp = 5071 (5.11.4.3-272-05) Group 1: 25 tendons with bond length taken from girder edge mm Group 2: tendons with bond length taken from girder edge 1000 mm Group 3: tendons with bond length taken from girder edge 3000 mm Group 4: tendons with bond length taken from girder edge 5000 mm Group 5: tendons with bond length taken from girder edge 7000 mm Prestress of tendons at tension stage - prestress loss due to shrinkage = 1304 MPa Prestress in tendons after all loss = 1104 MPa Prestress of tendons for bending resistant = 1826 MPa Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 05 Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】 SHEET NO : / 3.4 Internal forces due to prestressed tendons at sections PRESTRESSING FORCE FOR TENDONS Group number Distance from section to girder notch (mm) 14300 10500 Compression forces at tension stage Group 1: 4563.31 Group 2: 365.06 Group 3: 1095.19 Group 4: 1277.73 Group 5: 730.13 18100 4563.31 365.06 1095.19 1277.73 730.13 4563.31 4563.31 4563.31 4563.31 365.06 365.06 365.06 80.06 1095.19 1095.19 480.35 0.00 1277.73 1277.73 0.00 0.00 730.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Summary (kN) 8031.42 8031.42 7301.29 5408.72 4643.37 0.00 3865.63 3865.63 3865.63 3865.63 0.00 8031.42 6000 3400 1200 Compression forces after all prestress loss Group 1: 3865.63 3865.63 Group 2: 309.25 309.25 309.25 309.25 309.25 67.82 0.00 Group 3: 927.75 927.75 927.75 927.75 406.91 0.00 0.00 Group 4: 1082.38 1082.38 1082.38 1082.38 0.00 0.00 0.00 Group 5: 618.50 618.50 0.00 0.00 0.00 6803.51 6803.51 6803.51 6185.01 4581.79 3933.45 0.00 6391.66 6391.66 6344.55 4152.58 0.00 Summary (kN) 618.50 0.00 Compression forces to determine resistant Group 1: 6391.66 6391.66 Group 2: 511.33 511.33 472.17 368.55 67.82 0.00 Group 3: 1534.00 1534.00 1534.00 1177.40 406.91 0.00 0.00 Group 4: 1789.66 1789.66 1722.35 1094.65 0.00 0.00 0.00 Group 5: 1022.67 1022.67 0.00 0.00 0.00 11249.32 11249.32 10984.12 9135.88 7120.01 4220.40 0.00 Summary (kN) 511.33 824.78 0.00 Tendon Group to bottom fiber of girder (mm) 145.40 145.40 Tendon Group to bottom fiber of girder (mm) 1690.00 1690.00 Tendon Group to bottom fiber of girder (mm) 130.00 130.00 130.00 130.00 130.00 0.00 0.00 Tendon Group to bottom fiber of girder (mm) 161.43 161.43 161.43 161.43 0.00 0.00 0.00 Tendon Group to bottom fiber of girder (mm) 157.50 157.50 157.50 0.00 0.00 0.00 0.00 677.77 680.23 685.59 750.67 0.00 -866.83 -864.37 -859.01 -793.93 0.00 693.17 695.63 700.99 896.07 0.00 661.74 664.20 830.99 896.07 0.00 665.67 825.63 830.99 896.07 0.00 -4867.15 -4399.04 -3151.67 -3362.00 0.00 -4123.02 -3726.48 -2669.82 -2847.99 0.00 Prestressing moment at tension stage (kN-m) Tendon Group to neutral axis (mm) 677.77 677.77 Tendon Group to neutral axis (mm) -866.83 -866.83 Tendon Group to neutral axis (mm) 693.17 693.17 Tendon Group to neutral axis (mm) 661.74 661.74 Tendon Group to neutral axis(mm) 665.67 665.67 Sum of moment (kN-m) -4867.15 -4867.15 145.40 145.40 145.40 145.40 0.00 1690.00 1690.00 1690.00 1690.00 0.00 Prestressing moment after all stress losses (kN-m) Sum of moment (kN-m) -4123.02 -4123.02 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Lực nén - Compression force (kN) 05 Calculation Super T Girder L=38.2m_Skew 20.xls【III.Tendon】 SHEET NO : / Lực nén trước sau mát ứng suất Compression forces before and after all prestress loss 9000.00 8000.00 7000.00 6000.00 5000.00 4000.00 3000.00 2000.00 1000.00 0.00 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 Khoảng cách đến đầu dầm (mm) Distance from girder edge (mm) P cang cap - P at tension stage P sau mat mat us - P after all prestress loss Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 05 Calculation Super T Girder L=38.2m_Skew 20.xls【IV.Distribution】 SHEET NO : / LIVE LOAD DISTRIBUTION FACTOR 4.1 Superstructure profiles Span length L= 38200 mm Distance from bearing to girder edge 550 mm Le = Effective span length 37100 mm Width of all lanes 11000 mm Width of pedestrian path (1 side) mm Width of parapet (1 side) 500 mm Total width of deck W= ts = Concrete slab thickness 11700 mm 195 mm Number of loaded lanes lanes (Section 3.6.1.1.1 - 22TCN-272-05) Multiple presence factor (lane factor) m= 0.85 Section 3.6.1.1.2 - 22TCN-272-05) Width of lane 3500 mm Number of girders Nb = Distance between girders 2350 mm Width of cantilever slab S= wo = Width of loaded lane within cantilever slab de = 800 mm Depth of girder d= 1750 mm Width between top flanges of girder b= 1050 mm girders 1150 mm Design for exterior/interior girder ( E/I ) 4.2 Effective width of girder flange Interior girder 1/4 Le = 12ts + b/2 S => bei E According to Section 4.6.2.6 in 22TCN-272-05) 9275 mm Exterior girder bei/2 + 1/8 Le = = 2865 mm bei/2 + 6ts + b/4 = = = 2350 mm bei/2 + wo = 2325 mm 2350 mm => bee = 2325 mm 5813 mm 2607.5 mm According to Section 4.6.2.2.2 - 22TCN-272-05) 4.3 Live load distribution factor Applied section according to Table 4.6.2.2.1.1 is typical section c Moment distribution for interior girders Scope of application 1800< S OK 6000 3=> OK For >2 loaded lanes: gm,I = (S/1900)0.6 (Sd/L2)0.125 = 0.545 gm,I = = 0.545 For >2 loaded lanes gm,E = (0.97 + de/8700)gm,I = 0.579 Table 4.6.2.2.2c-1-22TCN-272-05) gm,E = = 0.579 For >2 loaded lanes: gs,I = (S/2250)0.8(d/L)0.1 = 0.761 gs,I = = 0.761 For >2 loaded lanes: gs,E = (0.8 + de/3050)gs,I = 0.808 Table 4.6.2.2.3b-1-22TCN-272-05) gs,E = = 0.808 Moment distribution for exterior girders < de < 910 => Scope of application OK Shear distribution for interior girder Shear distribution for exterior girder Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 05 Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】 SHEET NO : / Load combination for Strength-I Limit State No Loads Coeff Stage 1 Girder selfweight Max bending moment (kN-m) M1 1.25 M2 M3 M4 M5 M6 MA-A 4021.30 3852.55 3346.30 2310.30 1496.00 683.56 192.74 4021.30 3852.55 3346.30 2310.30 1496.00 683.56 192.74 2002.74 1382.71 895.35 409.11 115.35 78.50 50.83 23.23 6.55 2116.44 1461.20 946.18 432.34 121.90 Total Stage Concrete slab 1.25 2406.73 2305.73 Precast concrete plate 1.25 136.63 130.90 2543.36 2436.63 Total 113.70 Stage Wearing surface 1.50 553.18 529.97 460.33 317.81 205.79 94.03 26.51 D.L of parapet & Technical Box 1.25 828.00 793.25 689.01 475.70 308.03 140.75 39.69 Live load HL93 1.75 4746.83 4586.76 4009.78 2801.98 1824.26 836.86 0.00 Pedestrian 1.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Shrinkage of concrete 0.5 24.88 24.88 24.88 24.87 24.83 37.69 21.54 10 Creep of concrete 0.5 -18.15 -15.57 -7.85 3.87 5.96 11.48 -6.88 6134.74 5919.29 5176.15 3624.22 2368.87 1120.81 80.86 12699.41 12208.47 10638.89 7395.73 4811.05 2236.71 395.50 Total Sum of all stages 1+2+3 No Loads Coeff Stage 1 Girder selfweight Max shear forces (kN) Q1 1.25 Q2 Q3 Q4 Q5 Q6 QA-A 0.00 88.82 177.63 282.81 343.58 395.00 423.05 0.00 88.82 177.63 282.81 343.58 395.00 423.05 Total Stage Concrete slab 1.25 0.00 53.16 106.31 169.26 205.63 236.40 253.19 Precast concrete plate 1.25 0.00 3.02 6.04 9.61 11.67 13.42 14.37 0.00 56.17 112.35 178.87 217.30 249.83 267.56 Total Stage Wearing surface 1.50 0.00 12.22 24.44 38.90 47.26 54.34 58.20 D.L of parapet & Technical Box 1.25 0.00 18.29 36.58 58.23 70.74 81.33 87.11 Live load HL93 1.75 341.09 445.72 556.54 695.79 780.21 853.91 894.99 Pedestrian 1.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total 341.09 476.22 617.55 792.93 898.22 989.58 1040.29 Sum of all stages 1+2+3 341.09 621.21 907.53 1254.61 1459.10 1634.40 1730.90 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 05 Calculation Super T Girder L=38.2m_Skew 20.xls【VII.Foerces】 SHEET NO : / Load combination for Fatigue Limit State No Loads Coeff Stage 1 Girder selfweight Max bending moment (kN-m) M1 0.00 M2 M3 M4 M5 M6 MA-A 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total Stage Concrete slab 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Precast concrete plate 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total Stage Wearing surface 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 D.L of parapet & Technical Box 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Live load HL93 0.75 2034.36 1965.75 1718.48 1200.85 781.83 358.65 0.00 Pedestrian 0.75 0.00 0.00 0.00 0.00 0.00 0.00 Total 2034.36 1965.75 1718.48 1200.85 781.83 358.65 0.00 Sum of all stages 1+2+3 2034.36 1965.75 1718.48 1200.85 781.83 358.65 0.00 No Loads Coeff Stage 1 Girder selfweight 0.00 Max shear forces (kN) Q1 0.00 Q2 Q3 Q4 Q5 Q6 QA-A 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total Stage Concrete slab 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Precast concrete plate 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total Stage Wearing surface 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 D.L of parapet & Technical Box 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Live load HL93 0.75 146.18 191.02 238.52 298.20 334.38 365.96 383.57 Pedestrian 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total 146.18 191.02 238.52 298.20 334.38 365.96 383.57 Sum of all stages 1+2+3 146.18 191.02 238.52 298.20 334.38 365.96 383.57 Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung 05 Calculation Super T Girder L=38.2m_Skew 20.xls【VIII.Resistance】 SHEET NO : / RESISTANCE CHECK 8.1 Bending moment resistance fps = fpu*(1 - k*c/dp) Average stress in prestressing tendons k = 2*(1.04 - fpy/fpu) Where: (Section 5.7.3.1.1-1-22TCN-272-05) = 0.28 (Section 5.7.3.1.1-2-22TCN-272-05) Aps*fpu + As*fy - A's*f'y - 0.85*β1*f'c*(b-bw)*hf Distance from C.L to compression part c = 0.85*b1*f'c*bw + k*Aps*fpu/dp (Section 5.7.3.1.1-3 - 22TCN-272-05 - Assume equivalent section as T-section) Aps = Area of prestressing tendons fpu = Ultimate tensile strength of prestressing tendon mm2 1860 MPa Yield strength of prestressing tendon fpy = Area of tensile reinforcing bar As = 1674 MPa mm2 Area of compressive reinforcing bar A's = mm2 Yield strength of tensile reinforcing bar fy = 400 MPa Yield strength of compressive reinforcing bar f'y = 400 MPa Strength of 28-day concrete Width of compresion flange Thickness of compression flange f'c b hf = = = 50 MPa 2325 mm 195 mm Width of girder web bw = mm Distance from extreme compression fiber to center of all tendons dp β1 Coeff of reduction of stress block = mm = 0.69 Mr = ϕ*Mn Bending moment resistance (Section 5.7.3.2.1-1 - 22TCN-272-05) Where: ϕ= Resistant factor for bending and tension of prestressed concrete Mn = Aps*fps*(dp - a/2) + As*fỵ*(ds - a/2) - A's*f'y*(d's - a/2) (Section 5.7.3.2.2-1 - 22TCN-272-05) a = c*β1 = mm Depth of equivalent stress block Distance from extreme compression fiber to center of compressiond'reinforcing = bars s ds bars Distance from extreme compression fiber to center of tensile reinforcing = Items Unit Aps = mm2 dp = mm b'w = bw = Equivalent section type (rectangle or T) c = fps = a = As = ds = d's = Mn = Bending resitance Bending moment at Strength-I Bending resistance check Checked by LEE, Jong Dae Approved by CHO, Wan Hyoung Mr mm mm Section Sec Sec Sec Sec Sec Sec Sec 6160 6160 6160 5600 4620 3780 1754 1754 1754 1750 1709 1514 800 mm 270 270 270 270 270 700 920 mm mm Mpa mm mm2 2325 Rec 114 1826 79 2325 Rec 114 1826 79 2325 Rec 114 1826 79 2325 Rec 104 1829 72 2325 Rec 86 1834 59 2325 Rec 70 1836 49 2325 Rec 26 1843 18 6434 mm 0 0 0 750 mm 0 0 0 kNm 19282 19282 19282 17559 14226 10336 1907 kNm 19282 19282 19282 17559 14226 10336 1907 kNm 12699 12208 10639 7396 4811 2237 395 OK OK OK OK OK OK OK 05 Calculation Super T Girder L=38.2m_Skew 20.xls【VIII.Resistance】 SHEET NO : / 8.2 Shear resistance check Vr = ϕ*Vn Shear resistance (Section 5.8.2.1-2 - 22TCN-272-05) Where: ϕ= Resistance factor for shear and torsion of normal concrete 0.9 Vn = min(Vn1 = Vc + Vs + Vp ; Vn2 = 0.25*f'c*bv*dv + Vp) Nominal shear resistance (Section 5.8.3.3-2 - 22TCN-272-05) 0.5 Vc = 0.083*β*(f'c) *bv*dv (Section 5.8.3.3-3 - 22TCN-272-05) Vs = [ Av*fy*dv*(cotgθ + cotga)*sinα ]/s (Section 5.8.3.3-4 - 22TCN-272-05) Effective girder web thickness bv = mm Effective shear depth dv = mm Stirrup spacing s= 100 mm Angle between transverse reinforcement and longitudinal axis α= 90 o Area of transverse reinforcement within distance s Av = 402 mm Area of transverse reinforcement near bearing within distance s Av = 1257 mm Area of incline reinforcement near bearing Ax = 4580 mm Vp = Component of effective prestressing force on direction of applied shear force Diagonally cracked ability factor β= Angle of inclination of diagonal compressive stresses θ= Shear stresses in concrete for (β & θ) kN o Table 5.8.3.4.2-1 v = (Vu - ϕ*Vp)/(ϕ*bv*dv) (Section 5.8.3.4.2-1 - 22TCN-272-05) Vu = Factored shear resistance Strain in rebars in tensile fiber due to bending kN εx = (Mu/dv + 0.5*Nu + 0.5*Vu*Cotgθ - Aps*fpo) < 0.002 Es*As + Ep*Aps (Section 5.8.3.4.2-2 - 22TCN-272-05) If value of Then εx