Dynamic Seismic Analysis

DOE-STD-1020-2002

(1) the input is represented by a response spectrum or time history; (2) important SSC

frequencies are estimated or the peak of the input spectrum is used; and (3) resulting inertial

forces are properly distributed and a load path evaluation is performed. Equivalent static force

methods with forces based on the applicable response spectra may be used for equipment and

distribution system design and evaluation.

In dynamic seismic analysis, the dynamic characteristics of the structure are represented

by a mathematical model. Input earthquake motion can be represented as a response spectrum or

an acceleration time history. This DOE standard endorses ASCE 4 (Ref. C-16) for acceptable

methods of dynamic analysis.

The mathematical model describes the stiffness and mass characteristics of the structure

as well as the support conditions. This model is described by designating nodal points that

correspond to the structure geometry. Mass in the vicinity of each nodal point is typically

lumped at the nodal point location in a manner that accounts for all of the mass of the structure

and its contents. The nodal points are connected by elements that have properties corresponding

to the stiffness of the structure between nodal point locations. Nodal points are free to move

(called "degrees of freedom") or are constrained from movement at support locations. Equations

of motion equal to the total number of degrees of freedom can be developed from the

mathematical model. Response to any dynamic forcing function such as earthquake ground

motion can be evaluated by direct integration of these equations. However, dynamic analyses

are more commonly performed by considering the modal properties of the structure.

For each degree of freedom of the structure, there are natural modes of vibration, each of

which responds at a particular natural period in a particular pattern of deformation (mode shape).

There are many methods available for computing natural periods and associated mode shapes of

vibration. Utilizing these modal properties, the equations of motion can be written as a number

of single degree-of-freedom equations by which modal responses to dynamic forcing functions

such as earthquake motion can be evaluated independently. Total response can then be

determined by superposition of modal responses. The advantage of this approach is that much

less computational effort is required for modal superposition analyses than direct integration

analyses because fewer equations of motion require solution. Many of the vibration modes do

not result in significant response and thus can be ignored. The significance of modes may be

evaluated from modal properties before response analyses are performed.

The direct integration or modal superposition methods utilize the time-history of input

motion to calculate responses using a time-step by time-step numerical procedure. When the

input earthquake excitation is given in terms of response spectra, the maximum structural

response may be most readily estimated by the response spectrum evaluation approach. The

complete response history is seldom needed for design of structures; maximum response values

usually suffice. Because the response in each vibration mode can be modeled by single

degree-of-freedom equations, and response spectra provide the response of single

degree-of-freedom systems to the input excitation, maximum modal response can be directly

computed. Procedures are then available to estimate the total response from the modal maxima

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