Hello All,

I have confusion point for EXP load combinations on B31.3 code.
Generally we use load combination as below on piping analysis.
L1) [OPE] W+T1+P1
L2) [OPE] W+T2+P1
L3) [SUS] W+P1
L4) [EXP] L1-L3
L5) [EXP] L2-L3
L6) [EXP] L4-L5 ( for Cold pipe line )

My questions are for L4~L6.

First, L4 and L5 case are used on piping stress check. But, I want to know why dead load (W) is not included in these EXP case. I think that only thermal case without dead load will not occur on site. I think this EXP case is not realistic. Is it specified on B31.3 code why we should use this load case?

Second, I think that L6 case also is not realistic. If stress ratio of L4 is 90%, and stress ratio of L5 is 50%, L6 load case will be failure with 140%. (I assume that L4 is hot temperature, and L5 is cold temperature.)
Is it specified on B31.3 code why we should use this load case?

Could someone please resolve my confusion?
Thank you,

To answer your first question:
Because you're trying to answer the question "what are my stresses due to thermal expansion?" My allowable stress for this is 100%S.The allowable stress for dead weight effects is much lower, hence the sustained case.

Before I answer your second question:
It is not just "hot case" "minus" "cold case." To meet code requirements, this applies to other cases, such as "Pump 1 operating" vs "Pump 2 operating" vs "Pumps 1 and 2 operating." There are examples in the code that describe this.

To answer your second question, here's an example:
I have an anchor, an element, and a support. Node 10-20, anchor and a +Y. I installed it at standard conditions. 70°F if in US, 20°F if somewhere else.
(For sake of example, you can imagine node 10 is a pump, and node 20 is the first support.)
I activate the pipe. Because it gets hot, it grows. It exerts a force on my pump nozzle and it exerts a force on the support due to friction.

With me so far?

Now it rains. Or my pump gets to vibrating. Now that friction "goes away" due to slip. That support, due to its internal moments and forces moves on its own to its original position, but my pump is still hot, as is my pipe.

Now, in the dead of winter, I turn it all off and let it cool down to minimum ambient (which for me might be 15°F). When the pipe goes from hot to "normal" ambient conditions (70°F), you'll have as much force acting on that support as you initially did when you turned it on, but in the opposite direction. But, we're not done. It's going all the way down to 15°F.

I hope that clears it up.

I question your LC6. I think you want that to be L1-L2.

The B31.3 code provides two, distinct, evaluations - one for system collapse and a separate check against fatigue failure. There is no evaluation of state of stress for the combined loads (i.e., operating stress). Our SUS & OCC stress types are limited by yield and our EXP stress ranges are limited by an adjusted fatigue limit.

I will only answer your first question on Expansion stress range.

The self limiting stresses in piping systems are essentially cyclic and the initial hot stresses, if they are of sufficient magnitude, will decrease with time because of the plastic strains and will reappear as a stress of reversed direction when the pipe cools.
This phenomenon forms the basic difference self limiting stresses and the sustained stresses from weight and pressure.
Plastic strains can decrease the magnitude of thermal stresses by a change in the shape of the pipe centreline. This change in shape has no effect on sustained weight and pressure stresses. For this reason sustained stresses are limited to the design stress at the highest operating temperature.
This phenomenon is called self springing of the pipe and is similar to the effect of cold springing the pipe. The degree of self springing will depend on the magnitude of the initial hot stresses and the temperature, so that while the hot stresses will gradually decrease with time, the sum of the hot and cold stresses will stay the same. This sum we call the "EXPANSION STRESS RANGE"
Because it is the sum of hot and cold stresses no reduction can be taken for any coldspring applied during erection. The concept of a constant expansion stress range leads us on to the selection of an allowable expansion stress range. Since self springing occurs at the higher temperature then the maximum stresses must
occur in the cold condition. From this we must calculate our stresses to the cold modulus of elasticity.

For materials below the creep range the allowable stresses are 62.5% of the yield stress, so that a conservative estimate of where the bending stress at which plastic flow starts at an elevated temperature is l.6Sh and by the same reasoning l.6Sc will be the stress at which flow would take place at the minimum temperature. Hence the sum of these stresses represents the maximum stress range to which a system could be subjected to without flow occurring in either the hot or cold condition.
therefore Smax = 1.6(Sc+Sh)
But ANSI B31.3, the code to which most of us work, limits the stress range to 78% of the yield stress, which gives a total stress range of
Sa= 1.25(Sc+Sh)

From this total stress range 0.5Sh is deducted for the pressure stress and 0.5Sh is deducted for the deadweight stresses, giving us an allowable stress range of Sa= l.25Sc + 0.25Sh
There are reductions for excessive cyclic conditions and credits allowed for unused sustained allowable which you can use by enabling liberal stresses setting.

Hope it make sense to my fellow readers. If you get the logic above, you would automatically get answer to your second question.

Thanks Stress_Admirer for that very detailed explanation of the Expansion Stress concept of Elastic shakedown.

It's good that most of the general piping systems doesn't experience significant pressure cycling so it can be considered a static load.

Cheers!!!

I found the link below about elastic shakedown although the operating stress is already not applicable to the latest ASME B31.3 Code.

https://www.youtube.com/watch?v=-uMBO9P9RfI

Any other opinion is greatly appreciated.

Cheers!!