Hi all,
I've got one question about the influence of the piping temperature on the natural frequencies of a piping system.
If i remember well, stiffness matrix of a piping element would be something like E.Iz/L3 [ ... ] so it is influenced by the temperature since the Young modulus varies with the temp.
I am currently studying a piping system which operates either at 100°C or at 400°C, what induces a slight difference on Young modulus (4%).
So i want to know if it is possible in CAESAR to take it into account, or if you think it is negligible...
I first thought that when you specified a load case for the restraint linearization, CAESAR uses it to choose the appropriate Young modulus as well, but it seems it's not true.
Does CAESAR use the cold Young modulus as default in modal analysis?
Thanks in advance for your help...

Hi Thomas

Yes it is possible to change elastic modulus manually for respective temperature.
While building the load case go to load case option & from the drop menu change EC to EH1 or EH2 as you required.

Yes CAESAR II uses the defined EC value for the stiffness matrix when determining natural frequencies.

Thank you for your replies,
However i now wonder if it's necessary to change default values EC to EH1 & others on every load case in static calculations as well.
Is it a common practice to use hot elastic modulus?
In a quick reasoning, I guess using hot modulus will lower reaction forces and expansion stresses because the system will be "less stiff" during thermal cases, doesn't it?
This could be useful when results are close to allowable values !
From another point of view, using EC in thermal cases will be conservative...
So what to do? What do you think about it?

Hi Thomas
Yes you are right. Using EC as default case we get conservative calculation. It is the safety margin we have within our calculated value. We may use EH since it is the practical one at that particular temperature. Some time I use EH instead to pass nozzle load. Nozzle load reduce slightly sometime that is very useful just to meet allowable load on paper.

The natural frequencies need to meet |[K] - w^2[M]| = 0, for isometric material if the modulus reduces 4% from 100 C to 400 C, the [K] will reduce 4% too, the natural frequencies will reduce 1 - ( 1 - 4% ) ^ 0.5 = 2%. That means if you have one mode with a frequency at 10 Hz at 100 C, the natural frquency at 400 C for that mode will be 9.98 Hz.

The dynamic analysis is different from static one, high temperature causes the system more flewxible, which may reduce the nozzle loads due to the temperature. But, it also reduces natural frequencies which makes system easier to get exicted by dynamic loads.

Regards,

Shawn Zhong
COADE, Inc.

All expansion stress range calculations must use the reference modulus of elasticity, what we call the cold modulus.

Markl did his fatigue work by applying strain bending. Load (and stress) due to his strain was calculated using modulus at ambient temperature. To reduce load by using hot modulus would effectively reduce the fatigue-based strain. That would be incorrect.

Many Codes allow hot modulus for reactions.

I wonder how much the thermal strain affects frequency.
Strain certainly changes the pitch of guitar strings.
So the question might be posed as - if I push a two anchor system closer together (simulating thermal strain without changing temperature & modulus), how much would the natural frequency change? Can it be significant?

This is a purely academic question...

Hi Dave
Generally nozzle load rather than stress range is the governing parameter for piping close to equipment nozzle . So if I check stress range based on EC & then take advantage of EH to pass nozzle load , do you think that I can go ahead with the calculation as a technically correct one. I am using B31.3.

Dave was there a response to this question?

Normally Response Analyse is a conservativ dynamic calculation method, because not incluse all effects like small gaps, friction, pipe masstoleranz, stiffness restraint etc.
Stiffness change from E-modul or from longer pipe (cold/hot) are very small. Forget it .

German KTA say :
Thermal load case calculated with Eh, the stress multiplied with Ec/Eh.

Yes, use Ea for stress but Eh for load - if you wish.

Hi Dave,

You said that "many codes allow hot modulus for reaction". Could you please tell me which codes allow the use of hot modulus to get the supports and nozzles reactions?

I need some reference to put in my work since I´m using hot modulus for reaction and cold modulus for stresses (as required by B31.3 code). This is just to let my customer more confident.

Thank you in advanced.

Regards.
Roberto

Is really B31.3 allow hot modulus for reactions?