Reaction on equipment

Dear all!! As far as I know B31.1 (so CAESAR) uses cold modulus of elasticity when calculating pipe stress in all cases (suatained, exapansion, occasional). But what happens when calculating reactions on supports? B31.1 in section 119.10.1 states that reactions in hot condition may be reduced by the ratio between hot and cold modulus of elasticity. When CAESAR provides reactions in opearating condition, how does it manages modulus of elasticity? Does it use the hot or cold one?

Thanks for any help

CAESAR II uses the cold modulus here also. If you want to take advantage of section 119.10.1, you will need to "post process" the CAESAR II results.

I suppose that what I have to do is applying the ratio between hot and cold modulus to the reactions obtained from thermal expansion only because reactions due to sustained loads are not dependant on elasticity modulus, are they?

This way I could have the operating reaction in a more realistic way. Am I right?
Thanks again

You would apply the ratio to the operating reactions.

But, sustained reactions (due to weight of pipe) is affected by modulus of elasticity? I thought that only thermal expansion reactions are influenced by it...

The modulus of elasticity effects everything, because it is a component of the stiffness matrix. So when [K]{x}={f} is solved for the displacements ({x}), the displacement values are directly affected by the modulus values (in [K]).



Using {x}, the elemental forces and moments are determined, by multiplying with the local element stiffness matrix ([k]), which includes the modulus value. Restraint loads are then determined from these values.



Now the codes state that "flexibility analysis" shall be performed using the cold modulus of elasticity. So all the "k" values above use Ec. Section 119.10.1 permits subsequent reduction in restraint loads for the cold (equation 10) and hot (equation 9) conditions. In CAESAR II, this would correspond to the SUS and OPE cases respectively. You would not apply the modulus ratio to the EXP (expansion) case, as this case yields a restraint load "range" rather than a restraint "load".

Carletes' point about applying the ratio to the thermal (and displacement) component of the operating load but not the weight, pressure and spring loads is interesting. Note I didn't call it the expansion component as I didn't want to confuse this with the expansion case range calculation described in the previous post above. If we assume the entire system sees the same change in the elastic modulus, and if the system is totally linear (regarding support conditions), then I would agree that both the hot and cold modulii would develop the same sustained load distribution. If, however, the system has different temperatures or materials and, therefore, different ratios of hot to cold modulus, or, if there are complicating nonlinear supports, then all loads are in question. The B31.3 complement to the referenced paragraph 119.10.1 of B31.1 above (B31.3 - 319.5.1) limits this calculation only to simple, two anchor systems.

Keep in mind that the code was developed long before comprehensive analytical tools were available. These paragraphs provide accepted shortcuts used to reduce those formidable hand calculations.

So why not just run the analysis in CAESAR II where you use the proper modulii? Not for stress, but for load. Those numbers would not be subject to the stipulations above and would be more "correct" in any case.

Also, keep in mind that B31.3 does not insist on avoiding the operating modulus for stress. Para. 319.2.2(b)(4) states that "When differences in the elastic modulus within a piping system will significantly affect the stress distribution, the resulting displacement stresses shall be computed based on the actual elastic moduli ... and then multiplied by the [ambient-to-operating] ratio ..."