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COLD BENDING RESEARCH NEEDS Courtesy S. Kozel UNIVERSITY OF BALAMAND RESEARCH COUNCIL JUNE 23rd, 2004 1 OUTLINE • MOTIVATION • PROPOSED METHOD • PREVIOUS WORK • CURRENT WORK • FUTURE WORK 2 Cut Curving Flange Flange Flange Scrap 3 Fit-Up Pressure Applied During Fit-up Pressure Applied During Fit-up Web Flange Flange Fitting Jig 4 Problems ? - Costly because of excessive waste - Too much scrap for sharp curvatures - Used for mild curvatures (R 300m) - Fit-up operation too complicated 5 Heat Curving HEATED AREA Continuous Intermittent V-Heating 6 7 8 Problems ? - Trial and error process relying on uneven expansion/contraction. - Takes time to heat and much longer to cool down. - Results not known till AFTER cooling. - If it is not right, process must be repeated. - Ties up shop, slow and costly. 9 3-ROLLERS BENDING PINCHING ROLLER Courtesy AISC 10 Bridges: Current Status ? • Not allowed by AASHTO, concerns: - Cracking, Fracture - Flange Upsets - Dimples - Web Crippling • No criteria is available • Depends on skill and knowledge of fabricators 11 12 MIAMI METROMOVER PROJECT 13 1: Hydraulic jack (bot. flange) TAMPA 2: Hydraulic jack (top flange) 3: Longitudinal arms 4: Steel plate 5: Clamps TAMPA STEEL STEEL 14 PROPOSED CONCEPT L 1 2 3 3 2 4 5 6 7 5 max = 4 δmax 6 L2 8R x δ δmax R R x 2 2 15 FULL-SALE FULL-SCALE DEMODEMO 16 Top Flange Bending S 17 Bot Flange Bending 1: Jack 2: Head 3: Plate 4: Angle 5: Support 6: String Line 7: Stiffener 5 7 1 4 3 2 6 18 FORMULATION PARAMETERS: - Load Frame Spacing S - Bending Loads Ptf, Pbf S - Deflection within span S - Segment Length Li - Number of Segments n - Offsets Li Ptf 19 LOAD FRAME SPACING (S) Based on lateral bracing limit: E S 1.76rt Fy S = 14.4c for Grade 250 steel S = 12.2c for Grade 345 steel For unsymmetrical sections use ctf Flange Width 2c Load P Comp. side Flange S = Lp 20 BENDING LOADS (Ptf, Pbf) From simple beam plastic load analysis: P 4Fy t f c Top Flange: Ptf based on ttf, ctf Bot. Flange: Pbf based on tbf, cbf 2 S Constant P PS Mp 4 Fytfc Fytfc S c c Mp = Fytfc2 21 DEFLECTION Δ 2 ctf cbf 216Ec Ptf Pbf 13Fy S tf bf Load P set = cte = tf bf bf ??? Plastic Hinge tf S Set P = Pbf, P Pbf Load in cycles (not in this scope) m=tf/bf 22 SEGMENT LENGTH Li tf 4RΔ Li S [m-1] Constant 2 2Li/S 2Li S [m] l 8R 2Li S [m+1] 2Li Radius R 23 NUMBER OF SEGMENTS n Length L nLi a 1 2 3 4 n n+1 5 a Line of symmetry Round-down to the nearest even integer L-S n Li adjust (L - S) Li n 24 OFFSETS ii, ij Load: 2 Load: 3 1 2 3 4 6 5 22 7 i(i 1) δ ii 4δ max 3 n i 1 n 23 33 24 34 Load: 4 44 Load: 5 (i - 1) j n j 1 ij δ ii 8δ max 2 n n ji 1 25 35 Load: 6 45 55 max 26 36 46 56 66 25 FABRICATION AIDS (LOADS) Ptf =0.462.5152 = 260kN,Pbf =0.465252 = 1440kN (kN/cm3) P/tfc2 1.0 0.8 G 400 G 345 0.6 0.46kN/cm3 0.4 0.2 100 G 250 200 300 215cm 400 S (cm) 500 600 700 26 FABRICATION AIDS (Deformations) tf = 3.5/15 = 0.23cm,bf = 3.5/25 = 0.14cm 60 G 400 c (cm2) 50 3.5cm2 G 345 40 G 250 Δ tf 0.23 1.65 Δ bf 0.14 round-up to 2 30 20 10 0 100 S (cm) 200 300 S = 215cm 400 S (m) 500 600 700 27 /(S2/c)105 FABRICATION AIDS (Multiple Load) 10 9 G 400 Bot. Flange load 8 G 345 G 250 7 Δ tf (round up) 2 Δ bf = (tf – bf)=0.09cm 6 [/(S2/c)]105 = 4.9. 4.9 5 4 3 2 1 90 100 110 120 130 140 97 Px=975(25)2/215=1400kN (m) R/cS(cm/cm) 150 Px/tfc2/S 160 (kN/cm2) 28 FABRICATION AIDS (Segments) 1.50 1.25 Li/S cm/cm) R 12000 800 ctf 15 G 400 G 345 1.00 G 250 Li=0.25215=53.75cm 0.75 n=(1200–215)/53.75= 18.3 0.50 Round-down to n=18. 0.25 Li=(1200–215)/18= 55 cm 0.00 250 750 800 1250 1750 2250 S (m) R/c (cm/cm) 2750 3250 29 SUMMARY - Development of a standardized cold curving procedure. - Relationships (loads vs. deformations), Fabrication Aids are now available. - Limits are set on maximum strains (plastic) Note: Residual stresses may be released by heat treatment 30 PUBLICATIONS • Sen,R., Gergess,A. & Issa,C. “Finite Element Modeling of HeatCurved I-Girders” ASCE Journal of Bridge Eng, Vol. 8, No. 3, May/June 2003,pp.153-161. • Gergess A. & Sen R. (2003). “Simplified Heat-Curving Analysis”. Journal of Transportation Research Board, No. 1861, Construction, pp. 101 - 114 • Gergess, A. & Sen, R. “Inelastic Response of Simply Supported I-Girders Subjected to Weak Axis Bending,” Proceedings of the International Conference on Structural Engineering, Mechanics and Computation, Cape Town, South Africa, Edited by A.Zingoni, Vol. I, pp 243-250, 2001. • Gergess, A. and Sen R. “Fabrication Aids for Cold Straightening Structural Steel Girders”. AISC, Engineering Journal (in press), 2004. • Gergess, A. and Sen R. “Cold Curving Un-symmetric Unstiffened Steel Girders, Journal of Constructional Steel 31 Research, London, UK (in press), 2004. Current Work • Theoretical Investigation: 3D Finite Element Modeling 32 Current Work Loading Fy STRESS max 10 y Strain Hardening Un-Loading y residual 8.5 y STRAIN 33 Current Work - Effects of Cold Bending on Steel mainly fracture characteristics: - Perform Visual Inspection using NDT Techniques 34 AASHTO Requirements ASTM A709 ASTM A709 Grade 345 HPS 485W Plate Thickness up to 5 cm (2 in.) up to 10 cm (4 in.) Yield Strength 345 Mpa (50 ksi) 485 Mpa (70 ksi) min. 404 MPa 620 – 758 MPa (min. 58 ksi) (90 – 110 ksi) 21% 19% Toughness: CVN 35 m-N @ -12C 47 m-N @ -23C Fracture Critical (25 ft-lbf @ 10F) (35 ft-lbf @ -10F) Property Tensile Strength Min. Elongation 5 cm (2 in.) Zone 3 6.35 cm (TO 2.5 in.) 6.35 cm (TO 4in.) 35 ASSESSMENTS 36 37 Acknowledgments • Samuel & Julia Flom Fellowship: USF • Dr. Rajan Sen • Ronald Medlock, Texas DOT “Performance and Effect of Hole Punching and Cold Bending on Steel Bridges”. Research project conducted by University of Texas at Austin and Texas A&M University, 2003. • TRB/AASHTO/NSBA 38 39