Maximum width to thickness before a stiffened element of a section elastically buckles?

[mlevett3]

I'm getting a contradiction in this book:

https://books.google.com/books/abou...urce=kp_read_button&hl=en#v=onepage&q&f=false

When designing a section, say an I-beam, you'd determine the critical buckling stress from the buckling equation from Von Karman plate theory right?

Then the max width to thickness ratio to buckle in the elastic region would be found from the same equation, subbing in the stress for the yield stress, would boil down to (width/thickness)_critical=1.9*sqrt(E/sigma_yield)

However, after some empirical relations he shows for effective width, and setting effective width=1 (the condition it is at before critical width to thickness is reached) then solving for the width to thickness ratio, it boils down to (width/thickness)_critical=0.95*sqrt(E/sigma_yield) (eq. 3.34), or (width/thickness)_critical=1.28*sqrt(E/sigma_yield) if you worked through the math using the effective width formula from eq.3.44.

Can anybody clear up this confusion about what is the best way to compute maximum width to thickness ratio to buckle in the elastic region?

 

[rb1957]

this is the effective width of thin sheet in compression. The rule of thumb is 30t (similar to your 1.9*... expression, but i think it is 1.7*... based on tests).

don't quite get your 2nd paragraph ...

another day in paradise, or is paradise one day closer ?

 

[mlevett3]

Some sources, such as the AISI manual (

http://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=1059&context=ccfss-aisi-spec)

use one of the many empirical formulas for effective width out there and set the effective width over the nominal width to 1 (because if it buckles in the elastic region, it's fully effective, therefore the ratio of effective width to nominal width is 1). Then they back out the maximum allowed nominal width to thickness ratio based on the yield stress. You can see they go from effective width Eq. B2.1-l to having a maximum nominal width to thickness ratio Eq. B4-1.


Depending on the source I've seen the constant go from 0.95 to 1.9.

Having a rule of thumb isn't ideal since it's dependent upon yield stress and yield stress in steels has such a large range nowadays.

 

[rb1957]

rule of thumb is from my industry, where E/fcy is surprisingly constant (10E6/40E3, 30E6/120E3 = 250) ... ok some Al, some Steels have higher fcy, but 30t is the rule.

I'd probably take exception to "fully effective if it buckles elastically". Different industries have different rules ...

I note that 0.95 is 1/2 of 1.9 ... hummm

another day in paradise, or is paradise one day closer ?

 

[mlevett3]

Just a coincidence on that half. They start from an empirical relationship for effective width, too.

 

[rb1957]

don't believe in coincidence ... smile.

another day in paradise, or is paradise one day closer ?