Could anyone please tell the formulae used by Caesar to calculate------

a) Axial stress
b) Bending Stress
c) Code Stress
d) Hoop stress

I am using B 31.1. Another query is that if axial stress calculated by Caesar is simply the longitudinal stress due to internal pressure as per code, then its value should remain same if pressure and thickness are constant. But it has been observed that its value keep on changing in the stress report under sustained case.
Regards
Paritosh Garg

a) Longitudinal Pressure Stress + F/A

b) iM/Z, but varies by code. May have 0.75i as the multiplier, and M could be two or three moments combined.

c) Refer to the Quick Reference Guide.

d) Depends on the configuration setting (ID, OD, or Lame's) if not explicitly defined by the active piping code.

Axial stress will change from pipe to pipe if the pipe has a vertical component.

a)Quick reference guide says Caesar II default is Slp= P(Di^2)/((Do^2)-(Di^2)). Which force is F?

b) I am using 31.1 and as per code there has to be 0.75i multiplier and moment should be resultant of Mx, My and Mz. However, as per the stress report in sustained condition,and it has been observed that factor of 0.75 is not being considered and also only combination of two moments is being considered to calculate M, leaving the torsion moment. In nutshell, its using B31.3 method of calculation for bending stress, though I have defined it for B31.1

c) I have seen the formulae given in quick reference guide. As per that sum of axial stress and bending stress should give code stress, which is not found to be the case in reports for B31.1. However, B31.3 gives the desired result by adding the two.

Regards,
Paritosh Garg pari2dce@vsnl.net

First, be aware that the stresses reported to the left of the "SIF" columns are not directly used in the determination of the "code stress". The "code stress" value is computed directly from the element's forces and moments, by applying the code equation(s).

The other stresses in the report (axial, bending, torsional, hoop, and 3D/VonMises) are computed after the code stress value, using standard strength of materials equations. Typically, you can not sum these stresses to yield the reported value of the code stress.

Why does the software work this way? For historical reasons. When CAESAR II was first introduced back in 1984, this is the way all the mainframe programs of that era worked. We had to mimic this behavior. We do have plans to change this (hopefully for the next version - time permitting) so that these component stresses are actually what was used to determine the "code stress".

As to your current questions:

a) "F" is the structural force, as in "stress = F/A". Maybe "F/A" is included in the code stress - this depends on the code and the setting of this directive in the configuration.

The equation Slp= P(Di^2)/((Do^2)-(Di^2)) is the "more exact" form of the Slp = PD/4t equation found in the code. If you want to force the use of PD/4t, there is a configuration directive to do so.

b) You're right. For the "Sb" term in B31.1, the equation is .75iMa/Z, where Ma is the SRSS of all three moment values. This is not the "bending stress" reported in the stress report. The bending stress in the stress report does not include the ".75" or the torsional moment. The code stress value is computed as detailed in the Quick Reference Guide.

c) As mentioned above, as a general rule, you can't add the stress components (to the left of the SIF columns) to obtain the code stress value. If you do, and you do obtain the code stress, it is a coincidence.

Thanks Richard, for all the clarification so far, but I have a few queries even now, hope they get completely clarified in your next reply.

Okay, lets take the case of B31.1 specifically--

a)If we put all sustained loads = 0 and pipe density, no insulation, fluid density=0, which I suppose should make all weight = 0. Now, axial stress should be only Longitudinal Pressure Stress and should match with Slp. But again axial stress keeps on varying.


b) Ok, so bending stress is calculated in the same way irrespective of the code because moment calculation method is same for all i.e M is combination of two moments M1 and M2 where M1, M2 could be along x,y,z depending on the arrangement but not along the pipe element as that is considered in torsional moment. I hope you mean this only.

c) So we cant add up axial stress and bending stress to give code stress , however, i observed the coincidence to happen at every node with B31.3 settings. And now I know its not a coincidence in case of B31.3 because it asks to add F/A in Sustained stresses, so the (Slp + F/A) part of code equation becomes the axial stress and the bending stress is simply the third term Sb which is a combination of in-plane and out-plane moments based on in-plane SIFs and out-plane SiFs.
Coming back to B31.1 , if I have taken sample reading from sustained case global force elements with----


MX(Nm)
MY
MZ


Now with Caesar default settings with code B31.1. and SIF mulplier set to 0.75.

will the code stress be calculated by the following formula----

S= Slp + 1000*0.75*i*M/Z

1000 because of metric units.
M= sqrt(Mx^2 + My^2 + Mz^2)
Slp= P(Di^2)/((Do^2)-(Di^2))

Am I right in my understanding now?

Regards
Paritosh Garg

a) Check the "local force report" for the elements in question. If you have "fx" values, then you will have an "F/A" stress. (Did you zero your rigid weights also?)

b) Yes.

c) Yes, the code stress will be computed as S= Slp + 0.75*i*M/Z. Note, that all computations in CAESAR II are performed in English units. The values you see are passed through a units filter so that you see the values in your units.

a)Yes, I forgot to zero rigid weights, after doing that ,they were giving the value purely based on internal pressure.

Regards
Paritosh Garg