Strain Distribution in Locally Slender Structural Steel Crosssections Seif, M. , Schafer, B. W. Civil Engineering at JOHNS HOPKINS UNIVERSITY
Acknowledgments • AISC Faculty Fellowship Program • Professor Ben Schafer • The thin-walled structures research group at JHU
Overview • • • Motivation Cross-section stability Design methods FE parametric study Strain Distributions Ongoing work
Motivation AISC definition of locally slender
AISC Q-factor AISI Effective Width AISI Direct Strength App. 1
Column curve
Overview • • • Motivation Cross-section stability Design methods FE parametric study Strain Distributions Ongoing work
ABAQUS elements S 4 10 elements
Residual stresses Galambos and Ketter (1959)
Material modeling Barth, White, Righman, & Yang (2005)
Geometric imperfections
Geometric imperfections
Geometric imperfections
LOCAL slenderness W 14 FI: W 14 x 233 with variable Flange thickness, varies c Independently from all other dimensions W 14 FR: W 14 x 233 with variable Flange thickness, but the web thickness set so that the Ratio of the flange-toweb thickness remains the same as the original W 14 x 233 W 36 FR: W 36 x 330 with variable Web thickness, but the flange thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W 36 x 330 W 36 WI: W 36 x 330 section with variable Web thickness, that varies Independently from all other dimensions
LOCAL slenderness
Results Columns
Results App. 1 Columns
Overview • • • Motivation Cross-section stability Design methods FE parametric study Strain Distributions Ongoing work
Results Thicker W 36 WI Pn, kips x Original W 36 x 233 x W 36 x 330 x Thinner Displacement, in.
Deformed shape Thinner web Original W 36 x 330 Thicker Web
Membrane longitudinal stress ~ Zero = Yield Thinner web Original W 36 x 330 Thicker web
~ 10 ey ~ Zero Membrane plastic strain Thinner web Original W 36 x 330 Thicker web
3 D 2 D
x 3 D S 4 - Element
2 D Stress/Strain distributions Thinner flange Thicker flange
Effective Area NO !!!! 2 D
Equilibrium Clear height
W 14 FI: Strain Energy Distribution Thinner Original W 14 x 233 Thicker
W 14 FI: Postulated Effective Width Distribution Thinner Original W 14 x 233 Thicker
W 14 FR: Strain Energy Distribution Thinner Original W 14 x 233 Thicker
W 14 FR: Postulated Effective Width Distribution Thinner Original W 14 x 233 Thicker
W 36 FR: Strain Energy Distribution Thinner Original W 36 x 330 Thicker
W 36 FR: Postulated Effective Width Distribution Thinner Original W 36 x 330 Thicker
W 36 WI: Strain Energy Distribution Thinner Original W 36 x 330 Thicker
W 36 WI: Postulated Effective Width Distribution Thinner Original W 36 x 330 Thicker
Ongoing work • Strain Distributions • Effective Areas • DSM for Structural Steel
Work continues…. . more at: www. ce. jhu. edu/bschafer/aisc
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