Effects of currents on the stochastic response to earthquakes of multiple degree of freedom models of guyed offshore towers S. Brynjolfsson and J. W. Leonard Ocean Engineering Program, Oregon State University, Corvallis OR 97330, USA (Received August 1987; revised December 1987) The dynamic response of multiple degree of freedom (MDOF) guyed offshore towers to stochastic earthquake loads and a steady uniform current is investigated. The nonlinear cable stiffness and the fluid- structure interaction were linearized by using the stochastic linearization method. To investigate the importance of higher modes on the stochastic forces and moments of the guyed tower, numerical results for several load cases are presented and discussed. The displacement statistics from the MDOF linear analysis were compared with the statistics of an equivalent single degree of freedom (SDOF) time simulation that incorporated the nonlinearities of the structure. The increased damping of the structure with increasing current was found to significantly reduce the stochastic forces and moments of the structure. Keywords: offshore tower, multiple degree of freedom, earthquakes, currents The primary aim of this paper is to investigate the response of MDOF guyed towers to earthquake loads in the presence of a steady ocean current. Guyed offshore towers are generally softer than conventional fixed plat- forms. Their natural periods are greater than 20 s for the first mode and 0.4 to 5 s for the lower flexural modes. The dominant excitation periods of earthquakes are between 0.2 and 0.8 s. So guyed towers will have more flexural frequencies in the excitation range of an earth- quake than fixed platforms. It is therefore important to know the effect of higher modes on the forces and moments of a guyed tower. In recent years, the guyed tower has become feasible for offshore oil production in water depths ranging from 200 to 400 m. A sketch of a guyed tower ~ is shown in Figure 1. The tower is long and slender and depends upon a group of guy lines for lateral stability. Each guy line consists of a lead line, a clump weight and a trailing line. The presence of the clump weights limits the maximum tensions in the cables. Tower specifications are given in Table 1. Some guyed towers may be located in seismically active regions. Earthquakes are therefore an important design consideration for guyed towers. Owing to the random nature of the wave and earthquake loads, probabilistic methods are more appropriate than deterministic methods for the analysis of guyed towers. Monte Carlo simulations are popular due to their simplicity in imple- mentation, but extensive computer time is required, huge amounts of data are generated and interpretation of the results is tedious 1-3. On the other hand, analyses in the frequency domain are not as involved as in the time domain, and are therefore preferable. However, they are only applicable to linear systems. The governing equation of an offshore guyed tower has two main sources of nonlinearities: fluid-structure interaction and the restoring force of the cable system. Therefore, it has both nonlinear stiffness and damping. The equations of motion can be linearized to allow solution to the frequency domain using spectral tech- niques. MWL i ,/-- Figure 1 Compliant guyed tower I 0141-0296/88/03194-10/$03.00 194 Eng. Struct. 1988, Vol. 10, July ,~t~ 1988 Butterworth& Co (Publishers) Ltd