Support Lug Gusset Allowable Stress
Support Lug Gusset Allowable Stress
(OP)
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
"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





RE: Support Lug Gusset Allowable Stress
Regards,
athomas236
RE: Support Lug Gusset Allowable Stress
See the description in Timoshenko's treatise "Theory of Elastic Stability", Section 4.3 (page 195 in my copy).
RE: Support Lug Gusset Allowable Stress
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.
RE: Support Lug Gusset Allowable Stress
Regards,
Alex