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Large industrial facilities and power plants often require a huge number fo information and control cables between the differnet structures. These I&C-cables can be routed in reinforced concrete cable ducts or in isolated buried cable runs. KTA 2206 is the German lightning protection standard for nuclear power plants. During the last several years considerable effort has been made to revise this standard. Despite the well established principles and design guidelines for the construction of the lightning protection system, this standard puts special emphasis on the coupling of transient overvoltages to I&C-cables.
For the application of the concept of Lightning Protection Zones (LPZ), the knowledge of the magnetic fields and induced voltages inside a structure is necessary. Laboratory experiments have been conducted at a downscaled model of a building (scale factor 1:6) to determine these electromagnetic quantities in case of a direct strike to the structure. The model (3 m x 2 m x 2 m) represented a small industrial building using the reinforcement of the concrete as electromagnetic shield. The magnetic fields and magnetic field derivatives were measured at several location inside the scaled model. Further, the voltages induced on three typical cable routes inside the model was determined. The influence of the lightning current waveshape, point-of-strike, bonding of the cable routes, and bridging of an expansion joint in the middle of the building on these quantities was studied.
In IEC 61312-2 equations for the assessment of the magnetic fields inside structures due to a direct lightning strike are given. These equations are based on computer simulations for shields consisting of a single-layer steel grid of a given mesh width. Real constructions, however, contain at least two layers of reinforcement steel grids. The objective of this study was to experimentally determine the additional shielding effectiveness of a second reinforcement layer compared to a single-layer grid. To this end, simulated structures were set up in the high current laboratory. The structures consisted of cubic cages of 2 m side length with one or with two reinforcement grids, respectively. The structures were exposed to direct lightning currents representing the variety of anticipated lightning current waveforms. The magnetic fields and their derivatives at several positions inside the structure as well as the voltage between “floor” and “roof” in the center were determined for different current injection points. From these data the improvement of the shielding caused by a second reinforcement layer is derived.
This work is an attempt to answer the question: How to use convex programming in shakedown analysis of structures made of materials with temperature-dependent properties. Based on recently established shakedown theorems and formulations, a dual relationship between upper and lower bounds of the shakedown limit load is found, an algorithmfor shakedown analysis is proposed. While the original problem is neither convex nor concave, the algorithm presented here has the advantage of employing convex programming tools.
IEC Technical Committee 81 is currently creating the new IEC 62305 series of standards on Lightning Protection. Working Group 9 is responsible for Part 2 of this series, which deals with the assessment and management of risk its CDV (Committee Draft for Voting) stage and has been circulated to National Committees for comment. The paper details the development of the Simplified IEC Risk Assessment Calculator software tool as described in Informative Annex J of IEC62305-2 Ed.1/CDV 2. This tool is intended as a simplified implementation of the more rigorous treatment of risk management found in the written document. It is designed to be relatively intuitive for users who wish to obtain an initial assessment of risk sensitivity, but should not be considered a substitute to a full understanding of the methods provided in the standard when dealing with more complicated structures or those where greater risks to personal or system operation are involved.
Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of safety factors or of the load carrying capacity under constant and varying loads. Simple versions of limit and shakedown analysis are the basis of all design codes for pressure vessels and pipings. Using Finite Element Methods more realistic modeling can be used for a more rational design. The methods can be extended to yield optimum plastic design. In this paper we present a first implementation in FE of limit and shakedown analyses for perfectly plastic material. Limit and shakedown analyses are done of a pipe–junction and a interaction diagram is calculated. The results are in good correspondence with the analytic solution we give in the appendix.
Safety and reliability of structures may be assessed indirectly by stress distributions. Limit and shakedown theorems are simplified but exact methods of plasticity that provide safety factors directly in the loading space. These theorems may be used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. In a FEM formulation the limit state function is obtained from a nonlinear optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error. Moreover, the direct way leads to highly effective and precise reliability analyses. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis.
Structural design analyses are conducted with the aim of verifying the exclusion of ratcheting. To this end it is important to make a clear distinction between the shakedown range and the ratcheting range. In cyclic plasticity more sophisticated hardening models have been suggested in order to model the strain evolution observed in ratcheting experiments. The hardening models used in shakedown analysis are comparatively simple. It is shown that shakedown analysis can make quite stable predictions of admissible load ranges despite the simplicity of the underlying hardening models. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis. Both give identical or similar shakedown ranges. Structural shakedown analyses show that the loading may have a more pronounced effect than the hardening model.
Limit loads can be calculated with the finite element method (FEM) for any component, defect geometry, and loading. FEM suggests that published long crack limit formulae for axial defects under-estimate the burst pressure for internal surface defects in thick pipes while limit loads are not conservative for deep cracks and for pressure loaded crack-faces. Very deep cracks have a residual strength, which is modelled by a global collapse load. These observations are combined to derive new analytical local and global collapse loads. The global collapse loads are close to FEM limit analyses for all crack dimensions.
Improved collapse loads of thick-walled, crack containing pipes and vessels are suggested. Very deep cracks have a residual strength which is better modelled by a global limit load. In all burst tests, the ductility of pressure vessel steels was sufficiently high whereby the burst pressure could be predicted by limit analysis with no need to apply fracture mechanics. The relative prognosis error increases however, for long and deep defects due to uncertainties of geometry and strength data.