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# Failure Theories for B31.1, B31.3, B31.4 and B31.8

## Failure Theories for B31.1, B31.3, B31.4 and B31.8

(OP)
Hello,

I understand that without a well defined "Failure Theory", a piping stress in a piping component is a useless number. I know that there are several Failure Theories employed to assess the stress failure in piping systems(Maximum Stress Theory, Maximum Shear Stress Theory, Maximum Strain Theory and Maximum Distortion Energy Theory).

I am a bit unclear about which of these "Failure Theories" is used by each of the Piping Codes B31.1,B31.3, B31.4 and B31.8? Which of Failure Theories is applicable to which of these four Piping Design Codes?

I have read in CASTI Guidebook to ASME B31.3 (by Glyn Woods & Roy Baguley)on page 13 that:"The two failure theories that form the design basis of B31.3 code are the Maximum Principal Stress Theory and The Maximum Shear Stress Failure theory."

On page 14 from the same textbook mentioned above, it is mentioned that B31.3 bases the stress limit for stresses caused by weight & pressure on Maximum Principal Stress Failure theory while Expansion Stresses caused by temperature change are calculated by an equation based on the Maximum Shear Stress Theory of Failure.

Are there any other references that would explain what Failure Theory is used and in what situations is used by each of the B31.1, B31.3 B31.4 and B31.8 codes?

I would appreciate any suggestions and comments on this subject matter.

Best Regards,
Bogdan Chivulescu[/b]

### RE: Failure Theories for B31.1, B31.3, B31.4 and B31.8

Here are my 2 cents. The books written by Becht (B31.1 and B31.3) provide excellent reference. Refer to page 23 (chapter 4) of the B31.1 Power Piping book for more details;

#### Quote:

The equations in the Code provide the minimum thickness required to limit the membrane and, in some
cases, bending stresses in the piping component to the appropriate allowable stress. The pressure design
rules in the Code are based on maximum normal stress or maximum principal stress versus maximum shear
stress or von Mises stress intensity. When the rules were developed in the 1940s, it was understood that stress
intensity provided a better assessment of yielding, but it was felt that the maximum principal stress theory
could generally provide a better measure of pressure capacity in situations where local yielding could simply
lead to stress redistribution (Rossheim and Markl, 1960).

Another excellent book is Peng & Peng on Pipe Stress Engineering. This book Ive found to be the best book when it comes to details on pipe stress analysis, and I always have it at hand as a reference guide.

### RE: Failure Theories for B31.1, B31.3, B31.4 and B31.8

Well to start with I'm uncertain what you mean by "a piping stress in a piping component". I'm familiar with hoop stress, axial stress ( tensile or compressive), shear stress, torsional stress, combined stress / von mises and other stress combinations as listed in the codes but not "piping" stress. So please define what this piping stress is.

B31.1 and 31.3 are similar codes and the stress values they use in their equations are based on a minimum of 1/3 UTS or 2/3 yield stress, which ever is lower. Hence high yield strength materials where the UTS is close (85-90% say) to yield stress suffer because they get downrated to 1/3 of UTS.

How the code makers came up with this is often shrouded in some mystery, but B31/1 and 31.3 are basically above ground piping codes where a variety of stresses, hoop, shear, bending, point loads from supports and heavy bits of kit ( valves etc) are prevelant.

B31.4 and 31.8 on the other hand are buried pipeline codes, where the pipe material needs to be used much more cost effectively as it becomes a high proportion of material costs. Here the pipes are continuously supported, subject to far more continuous and spread out loads and where the predominant stress is hoop and tensile. These codes only deal in Yield Stress of the material and the safety factors associated with that. For thermal expansion and bending stresses arising from it, use of controlled displacement can sometimes be used to relieve stress by accepted some yielding and plastic deformation, which may not be possible if e.g. that bending is caused by the weight of some tank or valve (B31.3)

Hence this may not answer your theory type question, but I hope gives you a bit of background and real life issues involved.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

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