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**Strain Distribution in Locally Slender Structural Steel Cross-sections**

Seif, M., Schafer, B.W. Civil Engineering at JOHNS HOPKINS UNIVERSITY

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**Acknowledgments AISC Faculty Fellowship Program Professor Ben Schafer**

The thin-walled structures research group at JHU

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**Overview Motivation Cross-section stability Design methods**

FE parametric study Strain Distributions Ongoing work

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**AISC definition of locally slender**

Motivation AISC definition of locally slender

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AISC Q-factor AISI Effective Width AISI Direct Strength App. 1

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Column curve

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**Overview Motivation Cross-section stability Design methods**

FE parametric study Strain Distributions Ongoing work

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ABAQUS elements S4 10 elements

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Residual stresses Galambos and Ketter (1959)

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Material modeling Barth, White, Righman, & Yang (2005)

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**Geometric imperfections**

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**Geometric imperfections**

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**Geometric imperfections**

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LOCAL slenderness c W14FI: W14x233 with variable Flange thickness, varies Independently from all other dimensions W14FR: W14x233 with variable Flange thickness, but the web thickness set so that the Ratio of the flange-to-web thickness remains the same as the original W14x233 W36FR: W36x330 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 W36x330 W36WI: W36x330 section with variable Web thickness, that varies Independently from all other dimensions

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LOCAL slenderness

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Results Columns

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Results App. 1 Columns

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**Overview Motivation Cross-section stability Design methods**

FE parametric study Strain Distributions Ongoing work

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**Results x W36x330 Thicker Original Thinner W36WI Pn, kips W36x233**

thicker (recall tw is varied here) specimens develop significant strain hardening (in compression!) while the thinner specimens exhibit less displacement before collapse Take them through the whole plot Thinner Displacement, in.

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Deformed shape Thicker Web Thinner web Original W36x330

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**Membrane longitudinal stress**

~ Zero = Yield Shown is the membrane or mid-plane longitudinal stress essentially at peak load/collapse. Areas in blue indicate regions where the applied load is being carried. In all the section the flange is carrying the load, and basically uniformly. Recall from an AISC standpoint these are all compact flanges The web carries a variable amount of load; though even in the thick section some local buckling reduction is experienced, not consistent with AISC which says this is a compact web Overall the notion of an eff. Width for the web seems generally supported by the stress contours Further reductions in the web and flange are certainly dis-similarl Original W36x330 Thicker web Thinner web

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**Membrane plastic strain**

~ 10ey ~ Zero Plastic strain provides a look at collapse again membrane plastic strain In thin section yielded flanges, but elastically buckling web In the original section you have yielding in both flange and web, but recall stress was still dominant in the flange Thicker section shows less yield in the web compared with the original.. RED indicates that the section can chew up a lot of energy Original W36x330 Thicker web Thinner web

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3D 2D

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x x 3D S4 - Element

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**2D Stress/Strain distributions**

Thinner flange Thicker flange

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Effective Area NO !!!! 2D

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Equilibrium Clear height

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**W14 FI: Strain Energy Distribution**

Original W14x233 Thicker Thinner

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**W14 FI: Postulated Effective Width Distribution**

Original W14x233 Thicker Thinner

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**W14 FR: Strain Energy Distribution**

Original W14x233 Thicker Thinner

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**W14 FR: Postulated Effective Width Distribution**

Original W14x233 Thicker Thinner

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**W36 FR: Strain Energy Distribution**

Original W36x330 Thicker Thinner

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**W36 FR: Postulated Effective Width Distribution**

Original W36x330 Thicker Thinner

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**W36 WI: Strain Energy Distribution**

Original W36x330 Thicker Thinner

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**W36 WI: Postulated Effective Width Distribution**

Original W36x330 Thicker Thinner

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**Ongoing work Strain Distributions Effective Areas**

DSM for Structural Steel

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Work continues….. more at:

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