Cold Bending Steel Beams: a State-of The-Art Engineering Solution that Meets Industry Challenges

Transcription

1 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 World Congress and Exhibition on Steel Structure, Dubai November 15-17, 2015

2 Horizontal Curves

3 Heat Curving Continuous heat V heat (R > 300m)

4 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

5 Material Properties Yield Stress Modulus of Elasticity Ratio 0.6 E/E 0.4 F y /F y Temperature, C

6 Cut-Curving Flange Flange Flange Scrap Pressure Applied During Fit-up Web Flange Flange Fitting Jig

7 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

8 3-ROLLERS BENDING Mainly used in buildings Fit-up difficult for larger size bridge girders Perfect curve

9 OTHER IDEAS? 118

10 COLD BENDING

11 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

12 Stress-strain curve

13 res (m) Idealization Distance x (m) a' = 0.333L a' = 0.25L Circular a' = 0.1L a

14

15 Residual Stresses Flexural stiffness is reduced by the presence of cold bending residual stresses. ROLLED BEAMS WELDED SHAPES

16 Influence of Residual Stress on Average Stress-Strain Curve

17 Tampa Steel Concept Apply smaller loads at uniform intervals to achieve desired curvature

18 Idealization of Curve L max = δ max 2 L 8R x δ δ max R R 2 x 2

19 S S Load P L i

20 OFFSETS ii, ij Load: 2 Load: Load: Load: Load: max

21 Test Girder

22 Loading Details

23 Test Girder after Curving

24 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

25 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

26 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

27 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

28 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

29 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

30 NUMBER OF SEGMENTS Length L a nl i n n+1 a Line of symmetry Round-down to the nearest even integer n L - Li S adjust Li (L- n S)

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32 Challenges? Cracking, Fracture Flange Upsets Dimples Web Crippling

33 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.

34 How could it be assessed - 1? Perform visual inspection using NDT techniques Instrument to measure loads, offsets, strains and web movement

35 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

36 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) MPa ( ksi) 21% 19% C C (25 10F) (35 -10F) 6.35 cm (to 2.5 in.) 6.35 cm (to 4in.)

37 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.

38 How could it be assessed 4? 3D Finite Element Modeling

39 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

40 Acknowledgment Dr. Rajan Sen, PhD, PE, F.ASCE, Samuel and Julia Flom Professor, University of South Florida, Tampa Tampa Steel Erecting Company, Tampa, Florida

41 Thank You!