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


Edited by anindya stress (10/02/08 05:58 AM)
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anindya