Most of the piping systems I deal with are in relatively low seismic zones so horizontal acceleration alone is considered. In some projects with much higher seismic values, the horizontal and vertical components will be combined.

The Caesar II user guide shows multiple methods of doing this, without providing much guidance on why you'd choose one method over another, other than saying "sometimes you want to do this".

Below is a condensed version of the load cases.

Method 1:
L1 = Operating
L2 = Operating + U1 (horizontal) + 0.67U2 (vertical)
L3 = Sustained
L4 = L2 - L1 (algebraic)
L5 = L3 + L4 (abs or scalar)

Method 2:
L1 = Operating
L2 = Operating + U1 (horizontal)
L3 = Operating + U2 (vertical)
L4 = Sustained
L5 = L2 - L1 (algebraic)
L6 = L3 - L1 (algebraic)
L7 = L5 + L6 (SRSS)
L8 = L4 + L7 (abs or scalar)


What drives the decision to use either method? From a quick test the stresses appear almost identical while restraint loads are different due to the different combination of loads in the operating cases.

Not a direct answer, but please see
http://forums.coade.com/ubbthreads/ubbthreads.php?ubb=showflat&Number=70542
and we can continue the discussion about 0.67 factor.

Is there really no literature/background on pros/cons on Method 1 vs Method 2?

The only thing I can think of, since the stresses come out about the same, is that Method 1 without the 0.67 factor gives you more conservative restraint loads since forces are applied in two directions.

To understand your test results and your question, is there a relation between U1 and U2 definitions? Is this relationship a general one or is specific to your test?

I think the best approach is to follow what B31Ea recommend:

The seismic loading shall be specified for each three orthogonal directions (typically plant east-west, north-south and vertical). The seismic design should be based on either a three-dimensional excitation, east-west plus north-south plus vertical, combined by square-root sum of the squares (SRSS), or a two-directional design approach based on the envelope of the SRSS of the east-west plus vertical and north-south plus vertical seismic loading.

That means Method 2 should consider three spatial earthquake components or should be completed when consider two-directional earthquake components.

SRSS is often replaced by the 100-40-40 rule with the response spectrum analysis method to determine the maximum seismic responses from structural responses resulting from the three spatial earthquake component. See an article you can easy find "ON THE CORRECT APPLICATION OF THE 100-40-40 RULE FOR COMBINING RESPONSES DUE TO THREE DIRECTIONS OF EARTHQUAKE LOADING ". In my understanding Method 1 is not applying such rule.

Both of those methods are found in the User Guide. As far as I know, U1 is a lateral seismic vector and U2 is a vertical seismic vector.

Both of these are looking a static model and not using response spectrum dynamic analysis, but that is interesting and I'll look into those documents.

Dear "anubis512",

Considering the main question is how the horizontal and vertical components will be combined, the answer may be as the User Guide says in Combinations description: SRSS method is typically used to combine seismic directional components. In addition B31Ea is more precise when recommend how the SRSS must be applied.

How to make the step from "response spectrum" to "static" is just other discussion. You may start constructing the spectra (horizontal and vertical) as per applicable seismic code or other reference (FEMAP is a good reference for vertical spectrum, just google for fema_p-1050-1.pdf and can find a lot in C23.1 Design Vertical Response Spectrum) and see roughly what are the accelerations corresponding with your first modal response. Or you can just take the "peak" of all spectra with the idea that is the worst that can be coincident. After that you need to imagine (or not!) that there is a mechanism of reducing the level of seismic effects due to ductility. Here is another pain hidden in the coefficient "Rp": it means that my piping developed plasticity (contrary to the Code intent of limiting occasional stress!) or rather the supports "helped" me developing such plastic response? And I need to consider Rp just coincident with "ductility level of earthquake" or I can consider it in any level of seismic I want?

Without an answer, let's suppose you succeeded having two accelerations as
"equivalent" static: horizontal and vertical. You may go ahead as B31Ea says about SRSS, why not?

Now, to the next level of discussion: are the vertical and horizontal seismic components related somehow? Well, starting with Newmark's works in 70's, vertical acceleration is set how FEMAP says: "Historically, the amplitude of vertical ground motion has been inferred to be two-thirds (2/3) the amplitude of the horizontal ground motion. 2/3 = 0.67 and here is the point where this coefficient appears.
I don't know why engineers were so terrified by SRSS and turn to 100-40-40 or 100-30-30 rules, but let's check for a set of just two horizontal and vertical which are proportional with 1 and 2/3: SRSS(1,2/3)=sqrt (1+4/9)=1.20, 1+30%*2/3=1.20, 1+40%*2/3=1.26. Not bad, but really necessary?

Returning now to "User guide". With U2 set as vertical, I cannot see the logic to include there 0.67U2 instead to take SRSS! Is 0.67 coming from discussion about vertical?- I hope no.

I hope the above is enough to convince you to go ahead with method 2, because in method 2 the intend is clear: to combine seismic directional components!

To clarify, I'm not as confused about the 0.67 factor on U2 as I am with the varying load case strategies (one combining horizontal and vertical in a single load case and another using SRSS).

But I agree that SRSS method seems to be the more "proper" method, despite the extra numerous load cases to do the SRSS math.

I was mainly curious that, since the stress works out almost the same for both methods, why you may use one versus the other from a pipe displacement/restraint load point of view, since that is the only thing that's significantly different.