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Support Lug Gusset Allowable Stress

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Aconnell

Aerospace
Sep 1, 2004
39
Hello on page 167 of the Pressure Vessel Design Handbook by Bednar in the example for designing support lugs he references a formula to calculate the allowable compressive stress for the gusset.

"Sa=18,000/(1+1/18,000*(L/r)^2)=9,885 psi"

I cannot find reference to this formula in any structural analysis texts and unless I am missing something the units do not work out. Does anyone know where this formula comes from and why the units don't seem to work?

Regards,

Alex
 
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You will probably find that the limit is based on buckling criteria.

Regards,

athomas236
 
The given formula is from very old editions of the AISC (American Institute of Steel Design) Steel Design Manual for allowable compressive stress of columns. The numerical factor of 18,000 psi is basically 0.6*Fy, where Fy was the 30 ksi yield stress of common structural steels of that era (late 1940's/1950's).

See the description in Timoshenko's treatise "Theory of Elastic Stability", Section 4.3 (page 195 in my copy).
 
The basic formula goes back to the 19th century and was eventually refined by Rankine, so it is known as Rankine's formula.

An important point is that in this formula there are two constants related to the material (cast iron, steel, etc): "a" and "b". Constant "a" is the numerical constant in the numerator and constant "b" is a dimensionless numerical constant in the denominator.

It is somewhat confusing or misleading in the formula as given in Bednar that the numerical values of the constants are the same. This leads one to think that the 18,000 is "psi" allowable stress in both places (or at least I did at one time until I studied this). The 18,000 in the denominator (factor "b") is a dimensionless value based on the material characteristics. Thus the only dimensional value comes from factor "a" which is the allowable tensile stress.

The same formula is given in "Process Equipment Design" by Brownell and Young, although with different values for constants "a" and "b". They were working with a later edition of AISC.

One could use the more modern formulas for allowable compressive stress as given in the AISC, etc. But this would likely be analysis overkill for this component.

See Timoshenko's "History of Strength of Materials" (section 46) for a review of column design formulas as developed over time.
 
Thank you very much for your responses. Trying to figure this out was driving me a little nuts.

Regards,

Alex
 
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