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THE COLD WORK OF FORMING EFFECT IN STEEL STRUCTURAL MEMBERS

THE COLD WORK OF FORMING EFFECT IN STEEL STRUCTURAL MEMBERS. Tian Gao and Dr. Cris Moen The Charles E. Via Jr. Department of Civil & Environmental Engineering Virginia Tech SDSS’Rio 2010 Stability and Ductility of Steel Structures Thursday, September 9, 2010.

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THE COLD WORK OF FORMING EFFECT IN STEEL STRUCTURAL MEMBERS

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  1. THE COLD WORK OF FORMING EFFECT IN STEEL STRUCTURAL MEMBERS TianGao and Dr. Cris Moen The Charles E. Via Jr. Department of Civil & Environmental EngineeringVirginia TechSDSS’Rio 2010 Stability and Ductility of Steel Structures • Thursday, September 9, 2010

  2. Cold bending results in large plastic strains. rz t/2 Top Y(2) t/2 Bottom X(1) true strain in Mises strain space -t/2 Z(3) -t/2 Residual plastic strain

  3. Cold bending produces residual stresses. t/2 σy=0 Y(2) σx X(1) σz=0.5σx Top σz Bottom Z(3) σx σx σz=0.5σx σz σz σx σx σy=0 -t/2 t/2 t/2 t/2 Top Bottom -t/2 Plastic bending -t/2 Quach, W.M., Teng, J.G., and Chung, K.F. (2006 ). "Finite element predictions of residual stresses in press-braked thin-walled steel sections." Engineering Structures, 28, 1609-1619. -t/2 Residual stresses Elastic spring back Key, P., and Hancock, G.J. (1993). "A Theoretical Investigation of the Column Behaviour of Cold-Formed Square Hollow Sections." Thin-Walled Structures, 16, 31-64.

  4. The treatment of cold work of forming effects in finite element models vary widely. • There are several common assumptions that crop up: • Ignore cold work of forming effects • (often matches experiments the best) • Increase yield stress at cold-bent corners, ignore RS • (consistent with current design practice) • Add longitudinal RS but ignore transverse RS • (inconsistent with 3D von Mises yield criteria)

  5. We have simplified methods for approximating cold bending residual stress and plastic strain distributions. Moen, C.D., Igusa, T., and Schafer, B.W. (2008). "Prediction of Residual Stresses and Strains in Cold-Formed Steel Members." Thin-Walled Structures, 46(11), 1274-1289.

  6. We have well validated steel plasticity laws. Isotropic hardening Kinematic hardening single load application repetitive loadings back stress Bauschinger effect

  7. Let’s get to the bottom of this cold work of forming stuff. • Column finite element modeling study: • isolate corner • load in compression (disp. control) • Riks solution algorithm • boundary conditions prevent buckling 2 3 1 t=2.58 mm rz =5t=12.9mm End nodes move together in displacement control Sides restrained in 1 and 2 End restrained in 3

  8. This study explores different cold work of forming treatments. • (1)- Ignore cold work of forming effects • (2) - Increase yield stress (Isotropic hardening) (Isotropic hardening) • (3) - Input plastic strains and RS as initial state • (4) - Input plastic strains, RS, and back stresses as initial state (Isotropic hardening) (Combined isotropic - kinematic hardening)

  9. Some load-displacement results… Increased yield stress results in higher capacity • Case 2- increase yield stress (isotropic) • Case 1- do nothing (isotropic) • P • P/Py • D • L • D/L

  10. Cases 3 and 4 get more interesting because residual stresses and initial plastic strains are input directly into ABAQUS. Residual stresses are input into ABAQUS at section points through the shell thickness Plastic strains tell ABAQUS how much the yield stress should be increased. +0.5 σyield -0.05 σyield t/2 20/99 T-1 Top (Compression) +σyield +0.5 σyield T-2 49/99 σ3 -σyield σ1 B-2 51/99 -0.5 σyield Bottom (Tension) B-1 80/99 -t/2 -0.5 σyield +0.05 σyield Residual stress in 1-direction (transverse) Residual stress in 3-direction (longitudinal) Effective plastic strain (Mises)

  11. Continue the comparison… • Case 2- increase yield stress (isotropic) • Case 3- input RS and PS (isotropic) • Case 1 – Do nothing (isotropic) • P • P/Py The presence of residual stresses softens the load-deformation response. • D • L • D/L

  12. Through thickness stress variations for Case 3... Size of yield surface varies through the thickness. σ1 σ3 Yield lag Through-thickness strain-strain response is influenced by residual stresses and yield surface size. B-2 B-1 T-1 T-2 Isotropic hardening

  13. Through thickness stress variations for Case 4... Yield lag The benefit of strain hardening is diluted by the shifted yield surface. (Yield surface expansion not shown for clarity.)

  14. Which one best represents real life? • Case 2- increase yield stress (isotropic) • Case 3- input RS and PS (isotropic) • Case 1 – Do nothing (isotropic) • P • Case 4- input RS and PS (iso-kinematic) • P/Py • D • L • D/L

  15. Conclusions and future work • Conclusions: • The cold-work of forming effect is not just an increase in yield stress • Residual stresses and initial plastic strains coexist and influence load deformation-response • The initial stress-strain state from cold-bending can be input into finite element programs • A combined iso-kinematic plasticity law is applicable to cold-formed structural members when the initial stress-strain state is explicitly defined • Future work: • Use recently updated CFS column database to isolate the cold-work of forming effect on capacity • Does current cold-work of forming treatment in design codes need revisiting?

  16. Thank you!

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