Tutorial 3:Exploring how cross-section changes

influence cross-section stability

an extension to Tutorial 1

prepared by Ben Schafer, Johns Hopkins University, version 1.0

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.

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.

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

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.

W36x150 column – review of Tutorial 1

web and flange local buckling is shown

remember, appliedload is a uniform compressive stressof 1.0 ksi

Pref = 42.6 korfref = 1.0 ksi

load factor for localbuckling = 47.12

Pcr,local = 47.12 x 42.6 = 2007 k

or

fcr,local = 47.12 x 1.0 ksi = 47.12 ksi

this is weak axis flexuralbuckling...

note that for flexuralbuckling the cross-section elements donot distort/bend, thefull cross-sectiontranslates/rotates rigidly in-plane.

Pref = 42.6 korfref = 1.0 ksi

load factor for globalflexural buckling = 7.6at 40 ft. length

Pcr = 7.6 x 42.6 k = 324 k

or

fcr = 7.6 x 1.0 ksi = 7.6 ksi

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. (it’s 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)

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.

• Let’s– 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.

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.

• Let’s– 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.

load up the defaultW36x150

change the web thickness to 0.9 in

the model should look like this now.

default post-processor results, change the half-wavelength to thelocal buckling minimum

local buckling at astress of 84.6 ksi

let’s save this fileand load up the originalfile, so we can compare.

load the actualW36x150

now we can readily seethat the local bucklingstress increases from47 ksi to 85 ksi.

(Advanced note: if one was usingplate theory the prediction wouldbe that the buckling stress should increase by (new thickness/old thickness)2

but the increase is slightly less here becausethe web and flange interact – somethingthat finite strip modeling includes.)

At longer length the section with the thickerweb buckles at slightlylower stress, this reflectsthe increased area, withlittle increas in momentof inertia that results withthis modification.

W36x150 @ 40’fcr= 7.6 ksiPcr= 324 k“W36x150” w/ tw=tffcr=6.2 ksiPcr=328 k

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.

• Let’s– 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.

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?

Let’s make an approximate model to look into this effect.

Load up the W36x150 modeland go to theinput page.

Let’s divide upthese elementsso that we can increase the thickness of theweb, near the flange to approx-imate the role ofthe fillet.

now divide element 5 at0.2 of its length..

the model shouldlook this this now,let’s change thethickness ofelements 5 andelements 10 to 2tw=2x0.6=1.2in.

save this result, so that wecan load up earlier resultsand compare them. After hitting save above I namedmy file “W36x150 withapprox fillet” this now showsup to the left and in the plotbelow.

next, let’s load theoriginal centerline model W36x150...

After loading “W36x150”now I have two files ofresults and I can seeboth buckling curves andmay select either buckingmode shape.

Let’s change the axis limitsbelow to focus more on local buckling..

the reference stress is 1.0 ksi, thefillet increases local buckling from47 ksi to 54 ksi, a real change in this case.

of course global flexuralbuckling out in this rangechanges very little sincethe moment of inertiachanges only a smallamount when the filletis modeled

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