Greetings to all,
Most building codes these days include a term of the form (1 + n * z/h) in their equations for equivalent static loading on mechanical components, where "h" is the average roof height, "z" is the height in the structure at the point of attachment of the component, and "n" is usually 2. The purpose of the term is to amplify the equivalent static seismic load according to the height of the component above grade.
I'm hoping someone can provide guidance in how to appropriately apply this term to piping systems. Specifically, if a piping system is supported from the building structure at an elevation near the roof of a building, then it makes sense to use z/h=1. But if the piping system is on top of a pipe rack (inside or outside the building) that is only 20' or 30' high, what z/h should be used? Taking this further, if the piping were on top of a structural frame that is only a few feet above grade, what then would be the appropriate z/h? In short, what did the structural guys have in mind?

Bruce,

Since the seismic loads are related to the mass, I would normally consider the mass centreline elevation of the piping as z. Having z/h=1 may seem conservative, however some exceptional cases it may be necessary.

You can select some support locations on the piping at different elevations, derive series of static load coefficient and make judgement by considering the masses on the pipe. This can get worse in case the piping rises from one structure to another at different levels. The structures will have probably completely different response for the same directional seismic event.

It is going to be your judgement. Some cases the structure might be flexible and the response of the structure may attract piping masses at the upper levels. Some complicated cases I would add the structures into the analysis. If the structures are a lot stronger than pipe will start responding separately between the support locations while the supports are following the structure response. Modelling them together may solve many pipings very economically.

Hope it helps.

Ibrahim Demir

Some commentary about the ASCE eqn.

Fp= (ap 0.4Sds/Rp) x Wx I X ( 1+2z/h) ( Equation 13.3-1 of ASCE 7-05)

In this eqn. the base shear is expressed by a factor 0.4Sds where Sds is the peak spectral acceleration. 0.4Sds gives the ZPA or zero period acceleration ( this is due to the fact that more most earthquakes, the ratio of Peak Spectral acceleration to ZPA is in then range 2.4). Now the response acceleration will be equal to Zero Period Acceleration , only for very rigid systems. The response will get amplified as the system becomes more flexible and will be equal to the peak spectral acceleration. To achieve this effect the term 0.4Sds is multiplied by a factor ap which is a function of the stiffness of the structure and the term z/h compensates for the account of the location of the pipe on the structure and the height of the structure. This is based on the fact that higher modes contribute more to the top shear than the base shear, so inclusion of this term is basically to compensate for the effect of higher modal response .Ideally this should be a function of Time Period which ASCE 7-05 does not consider. If we have a pipe located at 2M on a 2M structure and a pipe located at 100 M on a 100 M structure, other parameters kept constant, they will have identical base shear applied. This is based on the consideration that the two structures have same fundamental period and mode shape which is a conservative assumption. However if a pipe is located at 2M on a 10 M structure and at 2 M on a 100 M structure, other parameters kept constant, the pipe in the first case will be subjected to higher base shear This is again based on the concept that the two structures have same natural period and mode shape( but mode shape coefficients can be different) ]
For vertical component, the eqn. is: V= 0.2 Sds W.

The ap, Rp , values can change between OBE,/SSE , between one category of piping to the other . ( This is based on the fact that in SSE the system is expected to undergo plastic or elasto-plastic deformation and hence the dissipation of energy will be higher in SSE . Also for more critical systems it is likely to use lower factors for Rp for added conservatism. Rp is a function of stiffness, damping and normalized yield strength (ratio of Yield Strength to the strength of a linearly elastic system for peak deformation).
The factor Rp ( typical values for piping systems is between 3 and 4 for details refer ASCE Chapter 13 where values are shown for B31.3 pipes) measures the energy absorbing capability of a structure and represents the reduction in seismic forces by allowing energy dissipation once the structure begins to respond in inelastic range.

The relationship between the A/g factor of dynamics and the base shear factor for static analysis is a much more complex issue the details of which can be found in Dynamics of Structures by Anil K Chopra. A factor to note that not considering R to be a factor of Time Period can result in underestimation of the shear force. This is valid for ASCE-7-05 requirements also).

Regards