Clarification required for ASME SEC VIII DIV 2 - reg.,

[VIJAYANSA]

Hi,
In ASME SEC VIII DIV 2, Design Rules for Supports and Attachments, There are two formulas for calculating angle ρ,
ie) ρ = tan ρ[0.5+(∏-ß)cotß].
ρ = -158.58+7.8668θ-8.8037(10)^-2θ²+4.3011(10)^-4θ³-8.0644(10)^-7θ⁴

Can anyone pls. suggest me which one can I use to calculate ρ for Stress coefficients (K₉,K₁₀) for horizontal vessels on saddle supports?

Thanks,

VIJAYAN S A

 

[prex]

This is clarified in the code: the first formula is the theoretical one, but it is not easy to solve (except by iteration), the second one is an interpolating function that you can calculate directly. The two should give the same result (hopefully).

prex
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[VIJAYANSA]

Thanks Prex,

In above formulae, the first one needs the value of ρ(highlighted in red color),
ie) ρ = tan ρ[0.5+(∏-ß)cotß].

I am confused with the similar notation like ρ, where can I get the value of ρ(highlighted in red color).

If you say, use the second formulae, then it wont matching with the table value given in code itself. Please, see my below calculation.

Let θ=120 degree
= 2.09439 radian
ß=∏-(θ/2)
=∏-(2.09439/2)
=2.094395 radian
By using second formula (interpolating function),
ρ = -142.48 radian
When I substitute the above ρ value in first forumula (theoretical one),
I will get, ρ=-0.5902 rad
=-33.82 degree

But the table value is for θ=120 degree; ρ = 93.667 degree.

Please, Clarify....

 

[VIJAYANSA]

Is there anybody to answer the above question???

VIJAYAN S A

 

[EnergyMix]

umm, that's why the first formula requires iteration. you go back in and substitute your new value for ρ into the formula and recalculate it. You'll get another value ... and you plug it back in. Eventually your ρ's should converge close to a value that should match what you got by interpolating the second formula. You also need to check to make sure you haven't made any math errors.

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[pksingla11]

Try to use Goak Seek function in excel to reach at conclusion