Cold Bending Steel Beams: a State-of The-Art Engineering Solution that Meets Industry Challenges By: Antoine N. Gergess, PhD, PE, F.ASCE Professor, University of Balamand, Lebanon www.balamand.edu.lb World Congress and Exhibition on Steel Structure, Dubai November 15-17, 2015
Horizontal Curves
Heat Curving Continuous heat V heat (R > 300m)
Drawbacks Procedure is complex Numerical computations have to account for material and geometric non-linearity Temperature distribution along the flange width are not exactly uniform Analysis has to account for the girder behavior during heating and during cooling (natural cooling). During heating, heated zone elongates to form a larger outer radius During cooling, the heated portion shortens to form a reverse curvature
Material Properties 1.0 0.8 Yield Stress Modulus of Elasticity Ratio 0.6 E/E 0.4 F y /F y 0.2 0 135 270 405 540 675 Temperature, C
Cut-Curving Flange Flange Flange Scrap Pressure Applied During Fit-up Web Flange Flange Fitting Jig
Draw-Backs Too costly because of excessive waste Too much scrap for sharp curvatures Used for mild curvatures (R 300m) Fit-up operation too complicated
3-ROLLERS BENDING Mainly used in buildings Fit-up difficult for larger size bridge girders Perfect curve
OTHER IDEAS? 118
COLD BENDING
Analysis = a /L; = x 2 /a P F y t f b 2 f 3 χl 2 f P 3.75t F (limit state of flange local buckling) flange y E L p 0.255bf (lateral bracing limit) F y
Stress-strain curve
res (m) Idealization 0.125 0.1 0.075 0.05 0.025 0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 Distance x (m) a' = 0.333L a' = 0.25L Circular a' = 0.1L a
Residual Stresses Flexural stiffness is reduced by the presence of cold bending residual stresses. ROLLED BEAMS WELDED SHAPES
Influence of Residual Stress on Average Stress-Strain Curve
Tampa Steel Concept Apply smaller loads at uniform intervals to achieve desired curvature
Idealization of Curve L 1 2 3 4 5 6 7 2 3 max = 4 5 6 δ max 2 L 8R x δ δ max R R 2 x 2
S S Load P L i
OFFSETS ii, ij Load: 2 Load: 3 1 2 3 4 5 6 22 7 Load: 4 23 33 Load: 5 24 34 44 Load: 6 25 35 45 55 max 26 36 46 56 66
Test Girder
Loading Details
Test Girder after Curving
STRESS Idealized Stress-Strain Curve 2.27 y F y 1.89 y max 10 y R = 255 m R = 115 m r 0.39 y r 0.77 y y residual 8.5 y 1.5 y STRAIN
FORMULATION PARAMETERS: Load Frame Spacing S Bending Loads P tf, P bf Deflection within span S S Segment Length L i Number of Segments n Offsets P tf L i
Flange Width 2c LOAD FRAME SPACING (S) Based on lateral bracing limit: S = 14.4c for Grade 250 steel S = 12.2c for Grade 345 steel For unsymmetrical sections use c tf S 1.76r t E F y Load P Comp. side Flange S = L p
BENDING LOADS (P tf, P bf ) From simple beam plastic load analysis: P 4F y t S f c 2 Top Flange: P tf based on t tf, c tf Bot. Flange: P bf based on t bf, c bf Constant M PS 4 p P F y t f c c F y t f c c S M p = F y t f c 2
DEFLECTION Δ 13F y S 216Ec 2 c tf c bf P tf P bf Load P tf bf set = cte = tf bf bf??? tf Plastic Hinge Set P = P bf, P P bf S Load in cycles (on-going research) m= tf / bf
SEGMENT LENGTH L i 4RΔ L i S Constant tf [m-1] [m] 2L i S [m+1] 2 Li S 2 L i /S l 2 8R 2L i Radius R
NUMBER OF SEGMENTS Length L a nl i 1 2 3 4 5 n n+1 a Line of symmetry Round-down to the nearest even integer n L - Li S adjust Li (L- n S)
Challenges? Cracking, Fracture Flange Upsets Dimples Web Crippling
Challenges? - Effects on Steel mainly fracture characteristics - Does it lead to a permanent reduction in the ductility and fracture resistance of steel? - Effects if steel is loaded beyond plastic limits - ANSWERS? Specific need for full-scale testing.
How could it be assessed - 1? Perform visual inspection using NDT techniques Instrument to measure loads, offsets, strains and web movement
How could it be assessed - 2? Perform in-depth material testing of the bent zone, e.g. Charpy V-notch test Fracture sensitivity Tensile strength Brinell hardness
How could it be assessed 3? Check for compliance with AASHTO Requirements Property ASTM A709 Grade 345 ASTM A709 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) Tensile Strength Min. Elongation 5 cm (2 in.) Toughness: CVN Fracture Critical Zone 3 min. 404 MPa (min. 58 ksi) 620 758 MPa (90 110 ksi) 21% 19% 35 m-n @ -12C 47 m-n @ -23C (25 ft-lbf @ 10F) (35 ft-lbf @ -10F) 6.35 cm (to 2.5 in.) 6.35 cm (to 4in.)
HPS 485W Results of FHWA Tensile Tests on HPS 485W Specimens. Wright W, Candra H, Albrecht P. Fracture Toughness of A709 Grade HPD -485W Steel. Draft FHWA Report, Washington, D.C, 2005.
How could it be assessed 4? 3D Finite Element Modeling
Specifications Develop criteria and specifications for consideration by AASHTO Limits on strain Limits on applied load Limits on minimum radius Guidelines for localized damage repair Guidelines for inspection Fabrication aids
Acknowledgment Dr. Rajan Sen, PhD, PE, F.ASCE, Samuel and Julia Flom Professor, University of South Florida, Tampa Tampa Steel Erecting Company, Tampa, Florida
Thank You! www.balamand.edu.lb