According to Appendix –P para 302.3.5 “The operating stress is the calculated stress at any operating condition,including pressure,weight and other sustained loads, and displacement…….The operating stress range is the range of stress between two operating conditions,including the ranges between operating conditions and a sustained case with piping at ambient temperature”

In this context I have one query.

If there are two operating cases W+P1+T1+D1 and W+P2+T2+D2 then the operating strains as calculated in this two states will be with respect to installed condition. So the corresponding stress calculations will be that of OPERATING STRESS RANGE . Can some one tell me how the OPERATING STRESS will be calculated at these individual states(including the displacement strains).

I would like to add a bit more which may explain what I feel.

What I am looking for is operating stress range & operating stress as defined in AppendixP and this has all components i.e pressure , weight, displacement and not just pure thermal .
Sustained deflection in installed condition is x1 and thermal =0.
In operating case sustained deflection is x2 and thermal is y2 . So total strain is x2+y2.
operating stress range ={(x2+y2)-x1 }*E
Operating stress =(x2+y2)*E

Is this ok .Comments appreciated
_

Appendix P with its "operating" stresses in any state (hot postion, ambient position, upset position, whatever) and operating stress ranges avoids the troubles of nonlinear conditions as they affect the sustained stress. As you know, the allowable limit for expansion stress includes the sustained stress. One may not know "which" sustained stress to use as the Code has an interpretation stating that sustained stresses shall be calculated for all support configurations. So Appendix P examines total stress states and ranges as an ALTERNATIVE to the expansion stress ranges and eliminates the need for sustained stress in the allowable limit.

I am uncertain of your question so let me respond this way...

Since we are talking about handling nonlinear conditions we must be sure to calculate states using the total load set and not the sum of the responses to the individual load components. (Summing the results from a weight analysis and athermal analysis is not the same as the results from a weight+thermal analysis.) CAESAR II does this quite nicely.

Dipanjan,

For elastic systems, Stress=E Times Strain.

Strain= Actual strain-Initial strain.

Initial strain=Thermal strain.

In case of stress range check what we are basically doing is the strain corresponding to a strain range from max to min. temp. or max/min. to installation temp. . We can get this by a load case T also, but to include the effect of non linearity ( non linearity in the simplest of mathematical terms means a case where stiffness is a function of displacement and the principle of superposition is invalid)we go for L1-L2 type of load cases. To include the effect of the mean stress ( Goodman or Soderberg effect) we subtract the mean stress ( in terms of sigma SL from the allowable range ) to get the allowable for this case.

Now an operating case stress=E times ( actual strain- initial strain) and the strain due to non thermal loading also takes part.

This is the difference between operating stress and stress range.

Regards

Hey Y'all,

It is interesting to note that if you were to look at para. 1-705.2 (Satisfaction of Primary Plus Secondary Stress Intensitiy Range) of the olde B31.7 (1969) document you would find the same approach.

The range of stresses is defined as the difference in stresses resulting from the consideration of two sets of loading conditions (i.e., P+W+T)and......

"the unloaded set (Po=0, Mi=0, delta T =0, Ta=Tb+70 deg.F) shall be considered a loading condition"

Now, if only B31.3 would include the "Forward" of B31.7-1969, which is titled "Design Philosophy" as a non-mandatory appendix. Those four pages are worth their weight in gold to new piping analysts who are looking at Appendex "P" for the first time. Maybe COADE would reproduce those pages on a web site for all of us to read over??????? Hmmmmm...just a thought.

Regards, John.

Dipanjan,
In my opinion if your ambient conditon is 21degc then operating stress is just equal to W+P1+D1+T1 (which includes non linear effects too.

regards,

Manko