In a previous study, we investigated the effect of interaction between interconnected electrical substation equipment subjected to ground motions. Each equipment item was modeled as a system with distributed mass and stiffness properties and, through the use of a displacement shape function, was characterized by a single degree of freedom. Two kinds of connecting elements were considered: One was a linear spring-dashpot-mass element, representing a rigid bus conductor, and another was an extensible cable, representing a flexible conductor, in which the flexural rigidity and inertia effects were neglected. It was shown that the interaction effect resulting from the interconnection could have a significant influence on the equipment responses. Amplification factors as high as 6 to 8 in the response of the higher frequency equipment item, relative to its stand-alone response, were estimated. In the cable-connected system, the response of the lower frequency equipment item may also be amplified but to a lesser extent.
The present study extends the results of the previous investigation in two important directions. First, it extends the investigation of the rigid bus conductor by accounting for the nonlinear behavior of the flexible strap connector (FSC), which is usually installed at one end of the bus conductor to allow for thermal expansion. Second, it extends the investigation of the flexible (cable) conductor by accounting for its flexural rigidity, inertia and damping characteristics. Both problems are highly nonlinear and advanced finite element models are used to perform the analyses.
To idealize the FSC, an elasto-plastic, large deformation finite element model is used with more than 500 elements. The material properties are determined from the results of monotonic uniaxial tests of the material coupons performed at the University of California at San Diego (UCSD). More accurate characterization of the material properties is possible if cyclic test data of the material coupons are ava ilable. The finite element model of the FSC is used to compute force-elongation hysteresis loops under a prescribed cyclic loading. These predictions show reasonable agreement with the experimental results obtained at UCSD. Closer agreement can be achieved by using a refined finite element model that accounts for contact and friction between the bars and straps of the FSC. With such refinement, the finite element model can be used to predict the behavior of other FSC configurations, thus avoiding costly tests.
For dynamic analysis of the combined system, we develop a mathematical model of the hysteretic behavior of the FSC. Forth is purpose, we use a modified version of the well-known Bouc-Wen model. Using this model, time history analysis of a combined system, consisting of two equipment items connected by a rigid bus with a FSC, is carried out for two recorded ground motions. The effect of interaction on each equipment item is measured by computing the ratio of its response in the connected system to its stand-alone response. Separate analyses are performed to show the influences of the flexibility and energy dissipation of the FSC on the interaction effect. The results show that the flexibility and energy dissipation characteristics of the FSC significantly reduce the adverse effect of interaction on the higher frequency equipment item. These results appear to be in agreement with test results obtained at UCSD. The analytical approach developed can be used with confidence in the future to investigate the effect of interaction on equipment items connected by conductors that have grossly nonlinear behavior.
For the flexible (cable) conductor, a finite element model using frame elements and a Lagrangian formulation is used that accounts for large displacements. First, comparisons are made with previous experimental results for cables subjected to out-of-phase support motions. Good qualitative agreement with experimental results are obtained, which show very large amplification of the cable force due to the flexural rigidity and inertia effects. Parametric studies showing the influences of the flexural rigidity and damping of the cable are carried out. Next, the finite element model is used to carry out time history
analyses of a combined system, consisting of two equipment items and a connecting cable, for five different recorded ground motions. Separate analyses are performed to show the influences of the cable flexural rigidity, inertia and damping. The effect of interaction on each equipment item is measured in terms of the ratio of the equipment response in the connected system to its stand-alone response. These response ratios are plotted as functions of an interaction parameter introduced in our previous study. The results show that, for certain ground motions and equipment/cable configurations, the cable flexural rigidity and inertia may further amplify the adverse effect of interaction. Based on these results, a recommendation for the minimum cable length to avoid the adverse interaction effect is developed.
Conductor cables used in the power industry are usually made of braided aluminum strands of wire. Under dynamic excitation, the strands may slip against each other under friction forces. The present study accounts for this effect in an approximate manner by using an equivalent moment of inertia and a judgmentally assigned damping value. For a more accurate prediction of the cable response, it is necessary to develop a refined model that explicitly accounts for the slippage and friction between the cable strands. Until verified by such refined analyses, the results and recommendations presented in this study should be regarded as preliminary in nature.
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