Eq. 4.16 of STS-1a 2003

[gdubyuh]

I'm using ASME Specification STS-1a-2003 to create a MathCad sheet for steel stack design. In section 4.4.5 of the specification, the reader is presented with equations for required minimums for moment of inertia, area and section modulus of the composite section comprised of a portion of the shell and the circumferential stiffener.

In equation 4.16, my minimum section modulus seems excessive...on the magnitude of 1000 times excessive.

The equation is written as follows:

S = [(qz)(D)^2(ls)(FS)]/[1830*Fy]

where S = composite section modulus, in^3
qz = wind pressure, 42 psf
D = stack diameter, 72.875 in
ls = vertical distance between stiffeners, 120 in
FS = Facotr of Safety, unitless
Fy = Yield strength of stiffener, 36,000 psi

The equation looks like it is in the form of
Section Modulus = Bending Moment / Allowable Stress
where (qz)*(D)(ls)*(1/144) gives you the force qz over the projected area (D)(ls) with 1/144 used to convert qz from psf to psi.

Then to get the moment arm, that would have to be D/2 to use your other D term. You now have 288 in the denominator (144*2).

Finally, assuming the allowable stress is 60% of yield, your constant in the denominator would now be
144)(2)(0.60)= 173. The equation actualy has a constant of 1830 in the denominator.

I'm wondering if all the unit defined in section 4.10 are correct. Is D actually in inches, not feet, etc. Am I trying to interpret this equation correctly? If not, can someone clarify it for me? I see there is a 2006 edition of STS-1, but I have not found any information online to suggest this equation has changed.

 

[jte]

The equation has not changed in the 2006 edition.

I suspect you need to revisit your approach to defining the moment acting on the stiffener: You seem to be looking at the ring as a simply supported beam with a load in the middle. If you evaluate as a beam of length = (diameter of stack) fixed at both ends with a uniform loading, you should get the same formula as in the standard but with a 1728 in the denominator. Not 1830, but close. I would not be trying to factor in 60% against the Fy at this point – that should be handled by the FS.

If you were to go beyond straight beams to curved beams (look in Roark’s Formulas for Stress and Strain) you might find some correction which brings the 1728 more in line with the 1830.

jt

 

[gdubyuh]

I agree with that jt. I have since realized that I had my Fy term redefined in units of ksi further down in my MathCad sheet, rather than psi (thus my magnitude of error)...the pitfall of the copy and paste procedure. Thanks for the insight regarding the moment calculation method.