Elastic Buckling of Thin-Walled Structural Components with Stiffened Holes Cris Moen, Virginia Tech Cheng Yu, University of North Texas 51st AIAA/ASME/ASCE/AHS/ASC.

Elastic Buckling of Thin-Walled Structural Components with Stiffened Holes

Cris Moen, Virginia Tech Cheng Yu, University of North Texas

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials ConferenceMonday, April 12, 2010

Outline

• Where are stiffened holes used in structures?• Intro to thin-walled component design• Elastic buckling including stiffened holes:

– Global buckling– Distortional buckling– Local buckling

• Conclusions

Applications

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Minimize weight, provide pass through access

Outline

• Where are stiffened holes used in structures?• Intro to thin-walled component design• Elastic buckling including stiffened holes:

– Global buckling– Distortional buckling– Local buckling

• Conclusions

Elastic buckling curve

Buckling modes (and loads) are revealed…

Pcrl

PcrdPcre

Schafer, B. W., and Ádàny, S. "Buckling analysis of cold-formed steel members using CUFSM: conventional and constrained finite strip methods," Eighteenth International Specialty Conference on Cold-Formed Steel Structures. Orlando, FL, 2006.

Thin-walled buckling modes

Mode shapes and buckled half-wavelengths are consistent with elastic buckling curve

Moen, C. D., and Schafer, B. W. "Experiments on cold-formed steel columns with holes," Thin-Walled Structures Vol. 46, 2008, pp. 1164-11

Design curvesUse elastic buckling loads with design curves to predict capacity.

For thin-walled members, we have design curves for local and global instability limit states.

Design curvesMembers with holes – calculate elastic buckling properties including holes and use similar design curves

Moen, C. D., and Schafer, B. W. "Direct Strength Design of Cold-Formed Steel Columns with Holes," 2010 Annual Technical Session and Meeting, Structural Stability Research Council. Orlando, FL, 2010.

Elastic buckling curve

Shell finite element eigen-buckling analysis is slightly painful but needed for members with holes.

Motivation

Simplified methods were recently developed for predicting the elastic buckling properties of thin-walled structural components with unstiffened holes.

Moen, C. D., and Schafer, B. W. "Elastic buckling of cold-formed steel columns and beams with holes," Engineering Structures Vol. 31, No. 12, 2009, pp. 2812-2824.

Are these methods viable for stiffened holes?

Outline

• Where are stiffened holes used in structures?• Intro to thin-walled component design• Elastic buckling including stiffened holes:

– Global buckling– Distortional buckling– Local buckling

• Conclusions

Global buckling

Approximate the critical elastic buckling loads for columns and beams with holes using a weighted average hand calculation.

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dxdx

xvdxEIU

L

0

2

2

2 )()(

2

1

dxdx

xdvPW

L

0

2)(

2

1

v

Flexural buckling

Rayleigh-Ritz Energy Solution:

L

IITLILI

L

EP netgnetnetggcre 2

2

L

LILI

L

EP netnetggcre 2

2

L

L

L

cLT jhole

n

j

j ,

1

sin2

cos2

Weighted average of moment of inertia!

Holes at the midlength of a column reduce Pcre the most

Flexural buckling

Evenly spaced holes

Arbitrary hole spacing

The solution is a “weighted average” equation for Euler buckling.

Global buckling

Hole spacing is 500 mm.Column length is 2500 mm.Hole diameter is varied from 0.1 to 0.7 of H.

Q=0.12hholeYu, C. "Behavior and design of cold-formed steel joists with edge stiffened perforations," 2007 Annual Stability Conference, April 18, 2007 - April 21, 2007. Structural Stability Research Council, New Orleans, LA, United States, 2007, pp. 239-258.

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Flexural buckling

0.10 0.30 0.50 0.70 m s

Pcre,ABAQUS*/Pcre,no hole (stiffened) 0.94 0.89 0.88 0.82 --- ---

Pcre,ABAQUS*/Pcre, weighted av erage (stiffened) 0.94 0.90 0.92 0.91 0.92** 0.02

Pcre,ABAQUS*/Pcre,no hole (unstiffened)*** 0.93 0.91 0.88 0.79

ABAQUS-to-predicted statistics

Column weak axis flexural buckling

h hole /HBuckling Mode Comparison

* ABAQUS results are systematically 6% lower than the Euler buckling solution. The difference is caused by the assumption of a rigid cross-section in the classical stability equations.

0r

yPPP

r

xPPP

PPPPPP

2o

2o

2cre

crecrex2o

2o

2cre

crecrey

crecrecrecrexcrecrey

J St. Venant torsionCw Warping torsion

YES! Need to investigate…

Timoshenko and Gere (1961), Chajes (1974)

Torsional bucklingThe “weighted average” approximation can be extended to the classical cubic column buckling equation…

Cw does not follow the weighted average approximation!

and the equation for lateral torsional buckling of beams with holes.

2

2

LECGJEIM wycre

A comment on warping torsionHoles prevent warping torsion resistance from developing along the length of a member. Buckling modes dominated by torsion are especially sensitive to the presence of holes.

Outline

• Where are stiffened holes used in structures?• Intro to thin-walled component design• Elastic buckling including stiffened holes:

– Global buckling– Distortional buckling– Local buckling

• Conclusions

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Distortional buckling

The web provides rotational restraint to the flange. How does a stiffened hole affect this restraint?

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Distortional buckling

Study the hole influence within one distortional buckling half-wave.

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Distortional buckling

Edge stiffener increased web bending stiffness

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Distortional bucklingHole spacing is 560 mm.Column length is 2794 mm.Q=0.12hhole

Outline

• Where are stiffened holes used in structures?• Intro to thin-walled component design• Elastic buckling including stiffened holes:

– Global buckling– Distortional buckling– Local buckling

• Conclusions

For evenly spaced holes:

Local buckling

When an unstiffened hole is added, deformation concentrates at the hole.

Elastic buckling stress is reduced by the presence of a hole.

For evenly spaced holes:

Local bucklingDepending upon the hole size and plate geometry, buckling may occur away from a hole.

Moen, C. D., and Schafer, B. W. "Elastic buckling of thin plates with holes in compression or bending," Thin-Walled Structures Vol. 47, No. 12, 2009, pp. 1597-1607.

Elastic buckling stress is unaffected by the hole.

For evenly spaced holes:

Local buckling

Prediction method – assume buckling occurs at a hole or away from (between) holes.

Pcrl=min(Pcrlnh, Pcrlh)

Buckling loads be calculated with a finite strip analysis at the gross section and the net cross section.

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Local buckling

An important benefit of stiffened holes!

For evenly spaced holes:

Local buckling

Wavelength stiffening occurs when holes are spaced closely together.

For evenly spaced holes:

Holes at the midlength of a column reduce Pcre the most

Conclusions

•Simplified elastic buckling prediction methods outlined in Moen and Schafer (2009) are viable for stiffened holes (more validation work is needed for other cross-sections and hole sizes, shapes, spacings,…)

•Edge stiffeners did not improve global buckling loads because I, J, and Cw all decreased due to the presence of holes

•Distortional buckling loads were minimally affected by the presence of stiffened holes, although new hole modes with half waves forming between holes were observed

•Edge stiffeners prevented local buckling at holes, and closely

spaced holes boosted the critical elastic buckling load.

Thank you for your attention!

This presentation can be downloaded at www.moen.cee.vt.edu

Engineering tools

Thin-walled component design

• Thin-walled components are susceptible to failure caused by cross-section and/or global instabilities.

• Elastic buckling properties are useful for predicting structural capacity.

• How do holes influence elastic buckling?• Can edge stiffeners improve performance

and how can we quantify this improvement?