Response of piping system on friction support to bi-directional excitation

Installation of friction devices between a piping system and its supporting medium is an effective way of energy dissipation in the piping systems. In this paper, seismic effectiveness of friction type support for a piping system subjected to two horizontal components of earthquake motion is investigated. The interaction between the mobilized restoring forces of the friction support is duly considered. The non-linear behavior of the restoring forces of the support is modeled as an elastic-perfectly plastic system with a very high value of initial stiffness. Such an idealization avoids keeping track of transitional rules (as required in conventional modeling of friction systems) under arbitrary dynamic loading. The frictional forces mobilized at the friction support are assumed to be dependent on the sliding velocity and instantaneous normal force acting on the support. A detailed systematic procedure for analysis of piping systems supported on friction support considering the effects of bi-directional interaction of the frictional forces is presented. The proposed procedure is validated by comparing the analytical seismic responses of a spatial piping system supported on a friction support with the corresponding experimental results. The responses of the piping system and the frictional forces of the support are observed to be in close agreement with the experimental results validating the proposed analysis procedure. It was also observed that the friction supports are very effective in reducing the seismic response of piping systems. In order to investigate the effects of bi-directional interaction of the frictional forces, the seismic responses of the piping system are compared by considering and ignoring the interaction under few narrow-band and broad-band (real earthquake) ground motions. The bi-directional interaction of the frictional forces has significant effects on the response of piping system and should be included in the analysis of piping systems supported on friction supports. Further, it was also observed that the velocity dependence of the friction coefficient does not have noticeable effects on the peak responses of the piping system.     

Residual load method for modal analysis of piping systems subjected to seismic excitation

Due to the fact that piping systems normally possess a large number of unknowns, the computation of eigenvectors and frequencies is limited. It does not seem to be reasonable to calculate all modes because of the wellknown phenomenon that the accuracy of the higher modes is deteriorating the more the higher the frequency of these eigenforms. When the modal-analysis method is used, this means, that the complete response of piping systems remains unknown.In this paper two methods which pretend to take the neglected higher modes into account are discussed. These are the residual-load-method and the modal-acceleration-method. Error investigations on both methods reveal that the residual-load-method might be given preference.Two examples are presented in which piping systems are dealt with the residual-load-method. It seems surprising, that even for branched systems it is sufficient to compute a few eigenvectors and then apply the residual load.     

New techniques for nondestructive testing of piping systems in nuclear power plants

Pipelines of power plants, nuclear facilities and chemical industries are often affected by corrosion effects. In order to reduce the inspection effort for nondestructive testing of these systems a new inspection technique was developed.The inspection of the pipes is done by means of shearography, a laser optical measuring technique, from outside the pipe. A measuring head is attached to the piece of the pipe to be inspected. During pressure build-up in the pipe the expansion of the pipe is registered with a special video camera. All defects in the wall of the pipe e.g. resulting from corrosion lead to local deformations of the wall and are on-line shown on a video monitor.Therefore shearography offers fast and reliable pipeline inspection for corrosion control.     

Automated analysis of multiple-support excitation piping problems

An automated solution algorithm is presented for the treatment of multiple-support excitation piping problems. The method is an extension of the well-known response spectrum analysis method which is routinely used for seismic analysis of structural systems. The new algorithm was incorporated in Kraftwerk Union's proprietary computer code KWUROHR for static and dynamic analysis of piping systems.In this paper the numerical results from the use of envelope and multiple-support acceleration input spectra are presented for two typical piping systems in nuclear power plants. From the comparison of these results it becomes obvious that the multiple-support excitation method should be recommended as standard analysis procedure for systems attached to support points which are subjected to different acceleration spectra. The additional computer cost is negligible.     

Inelastic analysis methods for piping systems

The analysis of pipework systems which operate in an environment where local inelastic strains are evident is one of the most demanding problems facing the stress analyst in the nuclear field. The spatial complexity of even the most modest system makes a detailed analysis using finite element techniques beyond the scope of current computer technology. For this reason the emphasis has been on simplified methods. It is the aim of this paper to provide a reasonbly complete, state-of-the-art review of inelastic pipework analysis methods and to attempt to highlight areas where reliable information is lacking and further work is needed.     

Outline of dynamic analysis for piping systems

The paper deals, in a coherent mathematical manner, with a number of theoretical and practical problems involved in the solution of dynamic structural problems by the modal superposition method. In particular, problems related to piping system structures subject to single or multi-level support movement loading are treated.     

Seismic response analysis of structural system subjected to multiple support excitation

In the seismic analysis of a multiply supported structural system subjected to nonuniform excitations at each support point, the single response spectrum, the time history, and the multiple response spectrum are the three commonly employed methods. In the present paper the three methods are developed, evaluated, and the limitations and advantages of each method assessed. A numerical example has been carried out for a typical piping system. Considerably smaller responses have been predicted by the time history method than that by the single response spectrum method. This is mainly due to the fact that the phase and amplitude relations between the support excitations are faithfully retained in the time history method. The multiple response spectrum prediction has been observed to compare favorably with the time history method prediction. Based on the present evaluation, the multiple response spectrum method is the most efficient method for seismic response analysis of structural systems subjected to multiple support excitation.     

Comparative methods for analysis of piping systems subjected to seismic motion

The dynamic analysis of a three-dimensional piping system of a nuclear power plant is conveniently performed through a finite element method. When the modal analysis is used, only the first few modes of vibration are computed for practical purposes. In this paper is proposed a method of residues which evaluates the neglected modes and combines them with the first calculated modes to estimate the total seismic response of the piping. This methods emphasizes the importance of the selected modes. When the approach is made through a time history input function, this latter is usually characterized by a combination of several recorded accelerograms, e.g. El Centro, San Francisco and Taft. The response of a particular piping has been evaluated by means of these two methods: the use of the modal approach will be strongly recommended due to its inherent advantage of economy and also computation time and reliability.     

Loads of piping systems due to malfunctions of snubbers

The aim of the numerical investigations reported here was to extend our analyses in order to obtain a broader basis for evaluations of the behavior of piping systems which are subjected to anticipated malfunctions of snubbers. The investigated piping systems were assumed to be supported by mechanical snubbers and hydraulic snubbers, as well. For assessment purposes stress and force/moment criteria were applied. The effects of malfunctions were studied for several configurations of snubbers, assuming clamping of these devices under normal operational conditions in some cases and postulating failure due to limited dynamic motions due to earthquake excitation in others. The analyses were performed with hot-running and cold systems as well. In case of the investigated hot-running piping systems it was found that clamping of snubbers can result in substantial load increases, especially in elbows. Failure to lock rapidly varying displacements in these systems was found to be less severe. In the latter case higher stress levels were observed only at some isolated positions. The analysis of the cold system revealed that the postulation of non-responding snubbers raised the stress level considerably in the piping system due to shifts of eigenfrequencies towards the region of higher values of the underlying floor response spectrum. In this case restraining of earthquake induced deformation by less vulnerable systems than snubbers would be preferable. The investigation has shown that appropriate variations of the position, the effective direction, and the number of snubbers can lead to considerable stress reductions in a piping system.     

核电站反应堆冷却剂系统主管道安装焊接

以秦山核电二期工程为例,论述了核电站反应堆冷却剂系统主管道安装焊接技术及质量控制要点,并对反应堆冷却剂系统主管道的安装顺序、安装技术要求、焊接质量检验方法以及焊接变形的控制等方面给予了详细的阐述,对核电站反应堆冷却剂系统主管道安装焊接及质量控制具有借鉴作用。     

An implicit three-dimensional finite-element formulation for long-duration structural analysis of piping systems

This paper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping systems. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads.The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects.The implicit-time integration scheme described herein has been incorporated into the three-dimensional piping code SHAPS. Two sample problems are presented to illustrate the analysis. The first problem deals with a dynamic analysis of a pipe-elbow loop. The second problem studies the piping response to seismic excitation. The results are discussed in detail.     

Assessment of coupling effects of coolers and piping systems

In the dynamic analysis of large systems there is a great incentive to perform the calculations separately for smaller, decoupled subsystems. This simplification has to be justified, as best by using appropriate decoupling criteria. In practice, however, this procedure is difficult to accomplish thoroughly due to the unsatisfactory state-of-the-art at present, as shown in this paper on the basis of two investigations.In these investigations (see A and B below) linear elastic FEM-calculations have been carried out for both the large joint (coupled) systems and the decoupled subsystems. The resulting coupled and uncoupled loads at significant nodal points are evaluated.In investigation A which deals with coolers and connected piping systems it is shown that an uncoupled analysis of the subsystems and a superposition of the influence of the piping systems to the coolers will yield adequate loads at the supports and the nozzles.The investigation B for piping systems with different diameter ratios of the main system to the subsystem leads to the following results: Uncoupled analysis for the main system without considerations of any effects of connected subsystems results in a satisfactory accuracy only for diameter ratios higher than 3:1, the comparison of the coupled and uncoupled analysis for a diameter ratio of 2:1 shows a necessary correction factor for the uncoupled analysis of about 7.     

Earthquake and aircraft impact simulation testing of piping systems

Safety-related piping systems in nuclear power plants and their supports are usually designed and analysed as linear elastic structures within elastic limits of material behavior. This applies for earthquake loads (SSE) and in Germany also for the external event of aircraft impact (AI). This load case with its extremely low probability and short duration is comparable in frequency content with internal shock loads.In order to define the conservativities of realistic systems designed in that way, at high SSE and AI load levels a large series of tests with different configurations were performed.AI runs were made up to a level of more than 300% of the design level. SSE loads met a system pressurized with 45 bar up to 6 times the analytically determined dynamic capacity. In spite of high displacement (90 mm = 3.6″), response accelerations (10 g) and strains (1.3%) and of maximum loss of dowel torque of about 50%, all load levels were withstood by all configurations without leakage or loss of pressure, without loss of integrity of fixed point structures and without failure of fixtures of steel to concrete.Postcalculations with linear elastic methods yielded analytic stresses up to 10.2 times the allowable stress with an artificially weakened configuration.Safety margins found in that way are due to nonlinear behavior of systems and materials.     

Case studies of risk-informed inservice inspection of nuclear piping systems

In the present paper, a probabilistic failure analysis is used to find failure probabilities of piping segments, and a probabilistic risk assessment model is employed to obtain risks to a nuclear power plant should these failures occur. The multiplication of the piping failure probability and the consequence for that particular failure results in the risk contribution of the pipe. The degrees of risk for different piping segments can then be ranked, and their results can be used as the basis for planning a risk-informed inservice inspection program. Numerical studies are offered with special emphases on: (1) the status and experience with RI-ISI applications in Taiwan; (2) the comparison of risk-rankings performed with three different methods developed in the US; (3) aspects of the probabilistic fracture mechanics calculation including the flaw size distributions and stress corrosion cracking model. The results indicate the proposed method can indeed be adopted for planning a cost effective inservice inspection program.     

Analysis and test correlation of flexible and stiff piping systems

An in situ pipe test program was conducted to provide a basis for evaluating piping analysis methodologies and design philosophies. In this program, a 20.3-cm boiler feedwater line with two fundamentally different support systems was tested and analyzed. One system employed hanger supports and was very flexible. The second system employed strut and snubber supports and was relatively stiff. Snapback and forced vibration tests were performed on the piping systems. The test results were used to determine piping damping values and to correlate with analyses. These analyses were used to evaluate current piping analysis methodologies and their analytical models. Also, parametric studies were performed with the analytical models to evaluate the effect of different support systems on the pipe behavior for thermal and seismic loads. In addition, the seismic analysis results were compared to quantify the differences between direct time integration and response spectra analysis methods.     

Response spectrum analysis of piping systems with elastic-plastic gap supports

A new seismic support device and its application in piping systems is described. The device, E-BAR (patented), can be cost effectively used for snubber replacement programs, mitigation of hydraulic transients, pipe whip and as a thermal stop. The device has pre-set gaps to allow free thermal movement. During a seismic or other dynamic load event, if the pipe movement exceeds the gap dimension, the device acts as an elastic or elastic-plastic restraint. The device also has a unique design feature for not exceeding the restraint force beyond a specified limit design value. To analyze piping systems with gap supports having elastic-plastic characteristics, modal analysis procedures for both response spectrum and time history methods are developed. The comparison of responses obtained from the procedures with nonlinear time history analysis and test results available in the literature shows excellent correlation. A pilot program conducted for snubber replacement with E-BARs demonstrates that the limit force feature of E-BAR makes them very attractive for snubber replacement. This is because a particular E-BAR with a specified limit design force can be selected, such that, the E-BAR replacing the snubber does not require any modifications be made to the existing support steel and hardware.     

Combined analysis and evaluation of piping systems using the computer

The organization and theoretical aspects of a computer program designed primarily for the analysis and evaluation of power piping with particular emphasis on nuclear class I and II piping are described. The program includes a one-dimensional (radial coordinate in a cylindrical system) thermal analysis which computes the required entries in eqs (10), (11) and (13) of section NB 3600. Six types of loadings may be considered simultaneously: deadweight, sustained design mechanical loads, thermal expansion, thermal anchor movement, earthquake-response spectra or time history, and other anchor movement. For dynamic analysis the generalized Rayleigh-Ritz method using unit loads to generate the trial vectors is utilized. This method provides a consistent reduction of both the stiffness matrix and the mass matrix. The Ritz method is not without its problems, however, in the selection of the so-called ‘master nodes’. While getting enough master nodes is generally not a problem (easier than lumping masses) it is easy to over-specify and therefore introduce ill conditioning. To overcome this shortcoming a method is described for checking the trial vectors for their degree of parallelism in kinetic energy space, and for automatically removing those degrees of freedom which may lead to difficulties. Sample solutions with the program are presented.     

Influence of gap size on the dynamic behaviour of piping systems

This paper addresses the effects of dynamic events induced by support motion on piping systems with snubbers having variable gap sizes. The investigation consists of 3 parts: (i) Mathematical examination of a linear I DOF mass-spring-snubber system with gap size zero or infinity. (ii) Numerical analysis of a piecewise linear I DOF mass-spring-snubber system with varying gap sizes, by means of a simple computer code. (iii) Numerical analysis of a realistic three-dimensional piping system with 3 snubbers, each having 4 different gap sizes, with the aid of a non-linear F.E. code.     

Consideration of uncertainties in seismic analysis of coupled building piping systems

In this paper, we present an analytical study for incorporating the effect of uncertainties in modal properties of uncoupled primary and secondary systems in the seismic analysis of non-classically damped coupled systems such as building piping by response spectrum method. Monte Carlo simulation is used to illustrate that the secondary system design response when defined at a non-exceedence probability of 0.84 over the individual responses obtained from multiple response spectrum analyses by considering uncertainties in modal parameters is excessively higher than the design response specified at the same non-exceedence probability over the responses obtained from multiple time history analyses. This is so because the earthquake input in a response spectrum method is characterized by a design spectrum which by itself is specified at a non-exceedence probability of 0.84 over the multiple time histories with normalized peak ground acceleration. Accurate evaluation of design response at a non-exceedence probability of 0.84 in the response spectrum method requires that the individual modal responses be defined at appropriate probability levels that may be different than the conventionally used non-exceedence probability value of 0.84. The required probability values are evaluated by using first order reliability method. It is shown that the modal responses, when defined at a non-exceedence probability of 0.84, would give relatively accurate values of design response only if the individual modes are perfectly correlated or a single mode contributes to the particular response quantity of interest. For all other cases, the design response would be excessively high. The accurate probability values needed to specify each modal response evaluated using the first order reliability method cannot be incorporated directly in a response spectrum analysis due to computational inefficiency. Two simplified methods, based on total probability theorem, are developed in this paper to overcome this limitation. It is shown that these methods give design response values that are very close to the true values obtained from multiple time history analyses.