Tutorial 3: Exploring how cross-section changes influence cross-section stability

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Tutorial 3Exploring how cross-section changes
influence cross-section stability

• an extension to Tutorial 1

prepared by Ben Schafer, Johns Hopkins
University, version 1.0
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Acknowledgments

• Preparation of this tutorial was funded in part
  through the AISC faculty fellowship program.
• Views and opinions expressed herein are those of
  the author, not AISC.

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Target audience

• This tutorial is targeted at the under-graduate
  level.
• It is also assumed that Tutorial 1 has been
  completed and thus some familiarity with the use
  of CUFSM is assumed.

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Learning objectives

• Study the impact of flange width, web thickness,
  and flange-to-web fillet size on a W-section
• Learn how to change the cross-section in CUFSM
• Learn how to compare analysis results to study
  the impact of changing the cross-section

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Summary of Tutorial 1

• A W36x150 beam was analyzed using the finite
  strip method available in CUFSM for pure
  compression and major axis bending.
• For pure compression local buckling and flexural
  buckling were identified as the critical buckling
  modes.
• For major axis bending local buckling and
  lateral-torsional buckling were identifies as the
  critical buckling modes.

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W36x150 column review of Tutorial 1
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web and flange local buckling is shown
remember, applied load is a uniform compressive
stress of 1.0 ksi
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Pcr,local 47.12 x 42.6 2007
k or fcr,local 47.12 x 1.0 ksi
47.12 ksi
Pref 42.6 k or fref 1.0 ksi load factor for
local buckling 47.12
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this is weak axis flexural buckling...
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note that for flexural buckling the
cross- section elements do not distort/bend,
the full cross-section translates/rotates
rigidly in-plane.
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Pref 42.6 k or fref 1.0 ksi load factor for
global flexural buckling 7.6 at 40 ft. length
Pcr 7.6 x 42.6 k 324 k or fcr 7.6 x
1.0 ksi 7.6 ksi
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Tutorial 1 Column summary

• A W36x150 under pure compression (a column) has
  two important cross-section stability elastic
  buckling modes
• (1) Local buckling which occurs at a stress of 47
  ksi and may repeat along the length of a member
  every 27 in. (its half-wavelength)
• (2) Global flexural buckling, which for a 40 ft.
  long member occurs at a stress of 7.6 ksi (other
  member lengths may be selected from the curve
  provided from the analysis results)

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Modifying the cross-section

• Once we start changing the depth, width,
  thickness, etc. the section is no longer a
  W36x150 but by playing with these variables we
  can learn quite a lot about how geometry
  influences cross-section stability.
• Lets
• see what happens when the web thickness is set
  equal to the flange thickness
• see what happens when the flange width is reduced
  by 2 inches.

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Modifying the cross-section

• Once we start changing the depth, width,
  thickness, etc. the section is no longer a
  W36x150 but by playing with these variables we
  can learn quite a lot about how geometry
  influences cross-section stability.
• Lets
• see what happens when the web thickness is set
  equal to the flange thickness
• see what happens when the flange width is reduced
  by 2 inches.

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load up the default W36x150
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change the web thickness to 0.9 in
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the model should look like this now.
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default post-processor results, change the
half-wavelength to the local buckling minimum
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local buckling at a stress of 84.6 ksi lets
save this file and load up the original file, so
we can compare.
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now we can readily see that the local
buckling stress increases from 47 ksi to 85 ksi.
load the actual W36x150
(Advanced note if one was using plate theory the
prediction would be that the buckling stress
should increase by (new thickness/old
thickness)2 but the increase is slightly less
here because the web and flange interact
something that finite strip modeling includes.)
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At longer length the section with the
thicker web buckles at slightly lower stress,
this reflects the increased area, with little
increas in moment of inertia that results
with this modification.
W36x150 _at_ 40 fcr 7.6 ksi Pcr 324 k W36x150
w/ twtf fcr6.2 ksi Pcr328 k
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Modifying the cross-section

• Once we start changing the depth, width,
  thickness, etc. the section is no longer a
  W36x150 but by playing with these variables we
  can learn quite a lot about how geometry
  influences cross-section stability.
• Lets
• see what happens when the web thickness is set
  equal to the flange thickness
• see what happens when the flange width is reduced
  by 2 inches.

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Modifying the cross-section...
The W36x150 we have been studying in local
buckling is largely dominated by the web. Do the
fillets at the ends of the web help things at all?
Lets make an approximate model to look into this
effect.
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Load up the W36x150 model and go to the input
page.
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Lets divide up these elements so that we can
increase the thickness of the web, near the
flange to approx- imate the role of the fillet.
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now divide element 5 at 0.2 of its length..
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the model should look this this now, lets change
the thickness of elements 5 and elements 10 to
2tw2x0.61.2in.
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save this result, so that we can load up earlier
results and compare them. After hitting save
above I named my file W36x150 with approx
fillet this now shows up to the left and in the
plot below.
next, lets load the original centerline model
W36x150...
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After loading W36x150 now I have two files
of results and I can see both buckling curves
and may select either bucking mode shape. Lets
change the axis limits below to focus more on
local buckling..
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of course global flexural buckling out in this
range changes very little since the moment of
inertia changes only a small amount when the
fillet is modeled
the reference stress is 1.0 ksi, the fillet
increases local buckling from 47 ksi to 54 ksi, a
real change in this case.
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Other modifications...

• Change the web depth and explore the change in
  the buckling properties
• Add a longitudinal stiffener at mid-depth of the
  web and explore
• Modify the material properties to see what
  happens if your W-section is made of plastic or
  aluminium, etc.
• Add a spring (to model a brace) at different
  points in the cross-section