Comparison of Spectrum and Time History Techniques in Seismic Design of Platforms
Authors: Nair Damodaran , Valdiviesco Jorge B. , Johnson Charles M. 
Published: December 2007

Summary
The seismic response of an offshore platform in 500 ft (152 m) of water has been investigated using time history and response spectrum techniques. The principal objectives were to assess the uncertainties principal objectives were to assess the uncertainties associated with the SRSS (square root of the sum of the squares) method of modal and directional combination rules used in the spectrum method. This was accomplished by subjecting the platform to selected sets of ground motion records and their corresponding spectra. A number of key response parameters were monitored and compared. parameters were monitored and compared.The SRSS method of combining modal responses underestimated individual peak values of member forces in almost all types of platform members. This was true both under uni- and multidirectional input motions. However, when the response spectrum results were applied to member-design criteria in which the individual peak values of bending and axial forces are assumed to occur simultaneously, the accuracy was satisfactory in most cases. Modifications of the SRSS method which will improve the accuracy of forces predicted in jacket legs, vertical diagonal braces, and piles will enhance the usefulness of response spectrum method as a reliable design tool.

Introduction
The principal methods of analysis recommended for the earthquake-resistant design of offshore platforms are time history and response spectrum techniques. In the time history method, the structure is subjected to timewise variations of ground motions, and the response of the structure is determined by integrating the equations of motion in a step-by-step manner. Having established the structural model and the input motions, the time history analysis per se is considered exact and yields accurate data. However, analysis is quite involved, voluminous data are generated, and interpretation of the results is tedious.
On the other hand, the response spectrum concept is relatively simple and the computations are not as involved as the time history method. Starting with a time history, the response spectrum itself can be obtained by analyzing the response of a series of simple oscillators having different natural periods and subjected to ground motion histories. Spectra obtained from ground motion records are quite jagged. In practice, a smooth design spectrum often is used, and it permits one to account for uncertainties associated with future ground motions.
The simplifications associated with the response spectrum method introduce uncertainties in the computed results. An appreciation of the magnitude of these errors for typical platforms is needed for the proper use of response spectrum technique. This proper use of response spectrum technique. This paper presents preliminary results of an ongoing paper presents preliminary results of an ongoing investigation to compare the design data computed from response spectrum and time history analysis.
Problem Statement Problem Statement In the response spectrum method, the response of the platform subjected to a specified spectrum is platform subjected to a specified spectrum is computed for each significant mode of vibration. The total response can be obtained only by combining the maximum modal responses using approximate procedures. The SRSS method is probably the most widely used technique of modal combination in design practice. In this procedure, the combined maximum response is taken to be the square root of the sum of the squares of the response obtained in each mode of vibration. The API RP 2A recommends that this method be used in the design of platforms. The theoretical basis for the SRSS method is presented in Ref. 2 for a class of whitenoise transient inputs assuming that the distribution of the response is Gaussian.
JPT
P. 437