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The yielding metallic devices have been used to improve the performance of building structures at design level intensities. They dissipate large levels of vibration energy through yielding of disposable steel plate elements but they may also enhance acceleration response related damage of mechanical and electrical components. This paper addresses the optimal design of these devices that minimizes the expected life-cycle object cost considering the story drift and acceleration related damages over the entire spectrum of seismic intensities that can occur on a building site. Genetic algorithm is used to calculate the optimal design parameters of the devices. The uncertainties associated with the frequency of occurrence of earthquakes of different intensities and random characteristics of the structural response are included in the life-cycle failure cost and the object cost calculations. It shown that these devices can be used effectively to reduce the overall life-cycle object cost and can be considered as good protective investment for structural designs in seismic regions.

In civil structures such as bridges the changes in vibration characteristics such as modal frequencies are often used to detect damage for structural health monitoring. These vibration characteristics, however, change not only due to structural damage but also due to changes in the environmental conditions such as temperature variations. For structural health monitoring using modal frequencies, it is much desirable to be able to estimate the structural frequencies as a function of structural temperatures which can be conveniently measured. In this paper, we develop an approach to establish this modal frequency and bridge body temperature relationship. The subspace system identification-based approach, combined with input data filtering to capture trends introduced by seasonal changes in the temperature, is used to develop an approach to obtain this bridge body temperature–frequency relationship. Utilizing the simulated data for two types of bridge structures, the approach is exhaustively tested for its reproduction and generalization performances over different thermal regimes that are encountered in practice.

Vibration based structural health monitoring methods often use the changes in the modal parameters to identify damage. However, the modal parameters are not only influenced by damage but also by environmental factors including thermal and humidity conditions. The environmental effects can be large enough to mask the changes caused by damage, especially in the bridge structures that are always exposed to environmental elements. In this paper, a simulation study is conducted to examine the variations in the modal frequencies of concrete box girder and T-beam bridge structures caused by the ambient temperature, solar irradiance and wind speed, utilizing the environmental data recorded at a site in North Carolina, USA. The study includes the effects of temperature dependent material modulus, thermal gradients and prestressing effects on the modal frequencies. Like the environmental temperature variations, the bridge temperatures and model frequencies variations have strong yearly (seasonal) and diurnal trends. The study provides temperature–frequency data at hourly intervals for each bridge structure for future studies and the companion paper where, recognizing the observed seasonal and diurnal trends, the models are proposed to estimate frequencies across seasons from the measured temperature values of a bridge structure.

A methodology for calculating the life-cycle cost of building structures under seismic loading was presented in the companion appear Shin and Singh, 2014. In this paper, this methodology is applied to obtain the minimum failure cost-based optimal designs of fluid viscous dampers for model structures in three different seismic regions in the USA. Genetic algorithm is utilized to obtain the optimal number and location of dampers to be installed on the buildings. The failure costs are optimally reduced at all seismic intensities that are expected to occur on the site to achieve the minimum life-cycle and object costs. The numerical results show the impact of optimal designs on structural performance in terms of reduced fragilities covering different performance objectives over the spectrum of expected seismic intensities. The results also demonstrate that although the structural system may go in inelastic range at the higher intensities of motion, the response spectrum method can still be effectively used for the failure cost-based optimal design of linear damper.

This and the companion papers are focused on the optimal utilization of viscous dampers for performance improvement of building structures by minimizing the failure/life-cycle costs. The cost minimization is a natural choice as the primary motivation for introducing the multi-objective performance based design concept in the earthquake engineering community was to reduce the observed unacceptable levels of damage costs in buildings for moderate intensity but more frequent earthquakes. This paper describes an approach to calculate the failure and life-cycle costs associated with different levels of damage and their consequences considering the random occurrences of seismic events and uncertainties in the calculated response. The inter-story drift is used as an effective response variable to define fragilities and failure costs, although it is realized that damage of some components may be better expressed in terms of the acceleration response. Since a life-cycle cost-based optimization methodology could be computationally demanding especially for yielding structures, the use a response spectrum method of analysis is considered for the response and failure cost calculations. Comparison of the numerical results, for three example buildings in Los Angeles, Seattle and Boston, obtained by the approximate response spectrum method and accurate time-stepping method utilizing an ensemble of base motions indicates that the response spectrum methods can provide a good estimate of the failure cost for a quick performance-based evaluation of different design alternatives. The companion paper utilizes this failure cost and performance evaluation approach to determine optimal designs of damping systems.

SUMMARY It is often of interest to detect the time of occurrence of sudden change in structural parameters, particularly the changes in structural stiffness for health monitoring purposes as a change in stiffness also implies some damage in one or more structural elements. Although well known, it is formally shown here that a sudden change in stiffness induces a sudden change in the acceleration response. Several methods have been used in the literature to detect such sudden changes. The wavelet transform, in particular the discrete wavelets transform, is one of the popular approaches. In this approach, the sudden changes have been shown to manifest themselves as spikes in the plots of the details of the discrete wavelet transform of the acceleration response. In this paper, we provide an analytical rationale to explain what constitutes these spikes and their relationship to the discontinuity being detected. In particular, it is shown that a spike corresponds to the scaled step-response of a high-pass filter and that a step discontinuity can be detected using a high-pass filter with properly chosen cut-off frequency where the discontinuity manifests as a clear spike in the filtered output. How the measurement error and sampling frequency affect the detection is discussed. An example of a multi-degree-of-freedom system subjected to the base excitation, with sudden changes in its structural elements, is presented to illustrate the approach. Copyright © 2011 John Wiley & Sons, Ltd.

This paper presents two simplified methods for calculating the seismic force coefficients for flexible nonstructural components in building structures. The methods utilize the dynamic characteristics, expressed in terms of the fundamental periods and damping ratios, of the component and the supporting structure to calculate the force coefficient. The cases with the building period and component period known or unknown are considered. The formulas with less information tend to provide more conservative estimates of the force to cover the worst case situations. The new formulas now include the effect of possible resonance with higher modes. The validity of the proposed formulas is verified by a comprehensive numerical study of several buildings of different fundamental periods.

The paper examines the seismic design force formulas that are currently prescribed in the 2003 NEHRP Provision for the design of nonstructural components in buildings, and presents new formulas to improve the these recommendations. The current code provisions are building independent and overly conservative, especially for the design of nonstructural components in tall buildings. This conservatism can be reduced by utilizing the information about the fundamental period of the building. New force formulas that depend on the building period are proposed. The proposed formulas are intended to avoid more involved analyses. They are validated by a comprehensive numerical study of several buildings of different periods analyzed for an ensemble of recorded earthquake acceleration time histories.

The counterweight in an elevator, being the heaviest component, can often overstress the guide rails during a strong earthquake. To reduce the in-plane counterweight response, the use of a part of the counterweight mass as a tuned mass damper in the passive and active modes is examined. The passive TMDs can reduce the stresses in the rails, but their performance can be significantly improved when they are used in the active mode. An actuator with saturation capacity less than 10% of the weight of the counterweight could reduce the critical stress response to as low a level as, or even lower than, the maximum response induced by the out-of-plane motion of the counterweight. Copyright © 2005 John Wiley & Sons, Ltd.

Elevators in buildings serve a very important function and are among the critical components of an essential facility. They have several mechanical and electrical components that are known to be susceptible to damage during earthquake occurrences. The counterweights, being the heaviest, are among their most vulnerable components. The ASME code has made several provisions to improve the performance of the counterweights in seismic events. To evaluate their performance under code-mandated provisions, it is necessary that a comprehensive and realistic analytical model is used. This paper uses a detailed model of a counterweight of a traction elevator to study its in-plane and out-of-plane dynamic behavior. The model incorporates the multiple support inputs and flexibilities of the counterweight guidance system along with their non-linearities caused by the clearance limitations. The study examines the effect of changing clearances, variability of input motions, and the use of tie brackets on the system response, and evaluates the impact of some of the code provisions on the dynamic behavior of the system.

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical models have been used to characterize their dynamic force deformation characteristics. The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the analysis of linear systems, for solving the equations of motion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved by numerical or analytical procedures. Both numerical and analytical procedures are formulated. These procedures are then used to calculate the dynamic response of a multi-degree of freedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.

The rail-counterweight systems in building elevators are known to be susceptible to earthquake-induced ground motions. Besides avoiding costly repairs and economic disruptions, it is of special interest to maintain the functionality of the elevators in critical facilities such as hospitals during, and especially after, a strong earthquake event. This paper presents an approach to develop a realistic analytical model of these vulnerable systems to study their seismic response behaviour. The model includes the flexibilities of the guidance and supporting components of the counterweights in a systematic manner. Currently only the linear response behaviour is considered; however, the sources of non-linearities in the flexible components are clearly identified. The model considers the effect of the differential support motions from the building. Both the out-of-plane and in-plane responses of the rail-counterweight are studied and included in the stress calculations. Several sets of numerical results considering simultaneous action of the two orthogonal components of historic earthquakes are obtained to study the seismic response characteristics of the rail-counterweight system.

This paper discusses a neural-network controller used to reduce the seismic response of building structures. The training process is carried out through a novel gradient-search technique that minimizes a desired cost function defined in terms of a set of structural response quantities. The proposed training approach does not require an additional neural network for the identification of the structural system. The training method is quite flexible with regard to the choice of the cost function to be minimized. A series of earthquake, base-acceleration time histories are considered to train the network. The effectiveness of the controller is demonstrated through several sets of numerical results obtained for a multistory building equipped with an active tuned mass damper.

A method to generate an efficient control law for a neural-network controller is presented to reduce the dynamic response of buildings exposed to earthquake-induced ground excitations. The proposed training scheme for the neural-network controller does not rely on the emulation of the structure to be controlled. The approach used for this work is based on a force-matching procedure, and it directly utilizes the dynamic data characterizing the structure response to generate an efficient training signal. The proposed controller has a feedback structure, utilizing a limited set of response quantities. A shear building actuated at its top by a tuned-mass damper is utilized to demonstrate the effectiveness of the controller. For training purposes, an ensemble of synthetically generated ground-motion time histories, with appropriate site spectrum characteristics, have been used. The performance of the trained controller is then evaluated for two different historic ground-acceleration records that do not belong to the training set of time histories. The numerical simulations show the control effectiveness of the proposed scheme with modest control requirements.

The paper presents a control scheme based on the sliding-mode-control approach. The analytical formulation focuses on the development of (1) a convenient, systematic and general scheme to achieve the so-called regular form of the equations of motion required to uncouple the control actions from the sliding motion description, (2) a systematic treatment of control redundancy where the number of sliding constraints imposed are less than the number of independent control actions, and (3) a method to improve sliding surface design by incorporating auxiliary dynamic systems. Both full-state-feedback and output-feedback cases are considered. In the output-feedback formulation, a generalized procedure is developed so that arbitrary combinations of unavailable system states (unmeasured displacements or velocities, for example) need not participate in the design of the sliding surface or the controller. A controller design utilizing only bounding information on the intensity of ground motion and the unmeasured states is proposed. The analytical formulation developed herein is applied to a 10-storey building structure to obtain the numerical results. The advantages of introducing auxiliary systems in the design of the sliding surface and the corresponding controller are noted. The results for both full-state-feedback and output-feedback cases are presented and compared to demonstrate applicability of the proposed control scheme. © 1998 John Wiley & Sons, Ltd.

Considerable effort has been devoted to develop passive and active methods for reducing structural response under seismic excitations. Passive control approaches have already found application in practice. Active control methods, on the other hand, are being vigorously examined for application to civil structures. This paper investigates the application of active and semi-active control schemes to structures subjected to seismic excitations, and it focuses on the use of the sliding-mode control approach for the development of the control algorithms. The possibility of control redundancy with respect to the number of sliding constraints is taken into account in the controller design. Several sets of numerical results are obtained for a realistic 10-storey shear building, subjected to earthquake-induced ground motions and controlled by active or semi-active control schemes. It is observed that both active and semi-active control schemes can be used to reduce the dynamic response. Active control performs very effectively in reducing the structural response, but the required control force values can be quite large to limit its practical application in the case of large and massive buildings. Active regulation of linear viscous dampers was found unnecessary for this type of structural system, as it did not induce any significantly more reduction in the response than the dampers acting passively. On the other hand, it is shown that active regulation of stiffness can be used with advantage to reduce the response. © 1997 by John Wiley & Sons, Ltd.

Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit 'pinching' of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model-an extension of the Bouc-Wen differential hysteresis model-is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies.

A method is presented to incorporate the flexibility of connections in the seismic analysis of framed structures. The flexible connections are represented by rotational springs with linear moment rotation relationships. Although additional deformation coordinates representing the rotational deformations of the connections exist, the formulation developed here avoids this increase in the degrees of freedom. The changes in the element matrices introduced by the eccentricity and flexibility of mass and stiffness on the connections are explicitly defined in closed form. Numerical results showing the effects of flexibility and eccentricity on the dynamic characteristics as well as on the seismic response of a building frame are presented.

The paper presents the analysis of a thin walled beam with a longitudinal crack of random location and size. The research objective is to understand the response characteristics of such a damaged beam with the ultimate objective of examining the growth of a crack under random loading. This initial study is expected to guide the future analysis of an aircraft wing with uncertain damage characteristics first on the overall aircraft performance. An analytical method is presented to obtain the response of a simple thinwalled beam of a closed cross section with a longitudinal crack of finite size. For random location and size of the crack, the methodology for the first order reliability analysis with analytically calculated response is described. The numerical results of the reliability analysis of the beam for the reliability defined as the non-exceedance of a limit state are presented.

The paper describes the response spectrum methods which are being used currently in the industry for the calculation of seismic design response of piping systems supported at several points of primary structures. In actual practice, the seismic input motions at the piping supports are correlated to varying degrees. To include the effect of this correlation between different support motions in the calculation of piping response, several methodologies with different simplifying assumptions have been proposed. This paper evaluates the effect of these assumptions on the accuracy of the calculated piping response. For this evaluation the results obtained by some of the currently used approximate approaches have been compared with the results obtained by an analytically rational and a more accurate approach. The comparison shows large differences in the two sets of results. For the example problem, the response values calculated by the approximate approaches are rather on the overly conservative side. This conservatism is, however, neither uniform nor assured. The use of these approximate approaches is, therefore, not recommended.

Often changes in the frequencies extracted from the vibration response are used for the detection of damage. However, these structural characteristics are also affected by the outside thermal envonment; this effect could be large enough to mask the changes caused by the damage. So it is important to understand and predict the effect of the environmental variations on these characteristics to separate them from those caused by the damage. In this paper, we examine the trends in the frequencies variations of a reinforced concrete box girder bridge structure subjected to a nine-year long record of measured temperature, radiation, and wind speed. It is observed that the major trends in the frequency variations are parallel to the major trends in thermal environment. The paper then presents and validates an identification approach to estimate the system frequencies directly from a few measured temperature values without a detailed finite element analysis.

A response spectrum method which combines the analytical advantage of the mode acceleration formulation and the practical advantage of the mode displacement formulation is developed for seismic response calculation of non-classically damped structures. It reduces the error associated with the truncation of the high frequency modes without explicitly using them in the analysis. The method is especially effective for calculating the response of stiff structural systems and also for calculating the response quantities which are strongly affected by high frequency modes. Even with flexible structures, it is shown to provide more accurate response results than the results obtained with the mode displacement approach.

Coulomb damping can be utilized effectively to reduce the dynamic response of structures subjected to seismic ground motions. To activate this damping, some parts of a vibrating structure are allowed to slide at rough interfaces. The dynamic response of structures provided with sliding interfaces at the base, between a floor slab and frame and in the cross bracings of a frame has been examined recently. In this paper, a simple slab sliding system provided with a spring to introduce a recovery mechanism and to reduce the sliding displacement requirement for low frequency structures has been examined. The equations of motion for this system are developed. An approach is presented to solve these coupled equations for earthquake induced ground motions. Structures with varying frequency and friction characterisics are considered and the numerical results are presented in response spectrum form. It is observed that, in low frequency structures, provision of a rather weak spring can reduce the sliding displacement requirements without significantly increasing the forces in the supporting frame and the acceleration input to supported secondary systems.

In general, military vehicles are heavier, wider, and have much different axle/tire configurations than 'civilian' type trucks for which conventional load distribution factors have been developed. Thus, use of conventional load distribution factors to rate bridges for military deployments often results in inaccurate ratings and thus unnecessarily limits mobility options for the military or threatens the safety of military personnel. This report provides an overview of an extensive study conducted to develop lateral load distribution factors specifically for military vehicles. The study considered six different types of military vehicles, three of which were wheeled vehicles and the other three were tracked vehicles. Formulas were developed for three different types of bridges: steel girder bridges, prestressed concrete bridges, and concrete T-beam bridges. The study resulted in a total of 52 new formulas for different categories of military vehicles, different types of bridges, bending moment and shear force values, interior and exterior girders, and for single- and multiple-lane loading cases. The distribution factors calculated with the formulas were compared with those calculated by direct analyses of the bridges to evaluate the accuracy of the proposed formulas.

In this paper we discuss the new concept of Intelligent Evacuation System (IES). This new technology will make a major change in evacuation strategies. Control, communication and computing technologies will be combined into IES system that can increase crowd safety and management without changing the physical structure of the facility. This paper outlines the key features of small and large area IES and shows how core crowd decisions are improved. We also propose a basic IES control system architecture and discuss the information technology issues related to its implementation.

Currently, the overly conservative thermal design forces are obtained on the basis of simplified assumptions made about the temperature gradient across the containment wall. Using the method presented in this paper, a more rational and better estimate of the design forces can be obtained. Herein, the outside temperature is considered to consist of a constant mean on which yearly and daily harmonic changes plus a randomly varying part are superimposed. The random part is modeled as a stationary random process. To obtain the stresses due to random and harmonic temperatures, the complex frequency response function approach has been used. Numerical results obtained for a typical containment show that the higher frequency temperature variations, though of large magnitude, induce relatively small forces in a containment. Therefore, in a containment design, a rational separation of more effective, slowly varying temperatures, such as seasonal cycle from less effective but more frequently occuring daily and hourly changes, is desirable to obtain rational design forces.

In a tendon surveillance program of containment structures, a small sample of tendons is periodically tested to measure adequacy of the existing prestressing force. The sample size required for such testing depends upon the method of sampling adopted and, of course, on the confidence desired in the testing program. For measurable quality characteristics, such as prestressing forces in containment tendons, the method of “sampling by variable” is most appropriate. Using this method of sampling, a test plan for in-service tendon surveillance of containment structures is proposed. The mathematical background and procedural details of the plan are given. The plan is proposed for typical containments provided with about 900 tendons. Also, it is demonstrated here that, for containments provided with about 400 tendons, the required sample size is still the same, and therefore, the proposed scheme is appropriate. The proposed plan is considered to be efficient and simple enough to be adopted in practice.

A mode synthesis method is developed for obtaining the modal properties of a combined single‐degree‐of‐freedom (SDF) equipment and structure system in terms of the modal properties of the individual systems. The eigenvalues of the combined system are obtained as the roots of a simple non‐linear characteristic equation. A simple Newton‐Raphson solution technique can be used to solve this equation. Also, the closed form expressions are provided to calculate the eigenvectors. These combined eigenproperties can be utilized to calculate the structure or equipment response, such as floor response spectra, which will incorporate the effect of the dynamic interaction between the two systems. As no assumption is made about the size of the equipment in the development presented here, this approach can be used equally effectively with light as well as heavy equipment.

A mode synthesis-based direct approach is presented to calculate seismic response of equipment supported on structures. The approach incorporates the effect of the dynamic interaction between the equipment and the supporting structure. The modal properties of the combined structure–equipment system are obtained by synthesizing the modal properties of the individual structures. The seismic input defined in terms of smoothed ground response spectra can be directly utilized in this approach. Both heavy and light equipment can be considered by the approach equally effectively. Numerical examples demonstrating the effectiveness of the proposed approach are presented.

A method is presented to obtain the exact complex-valued eigenproperties of a classically damped structure and equipment system. The non-classically damped character of the combined system as well as the effect of dynamic interaction between primary structure and equipment are properly included in the calculation of these eigenproperties. It is necessary only to know the classical modal properties of the structure and, of course, the equipment characteristics. The eigenvalues are obtained as the solution of a non-linear equation which can be easily solved by the Newton–Raphson algorithm. Once the eigenvalues are known, the corresponding eigenvectors are obtained from simple closed-form expressions. The method can be used equally effectively with light as well as heavy equipment. Numerical results demonstrating the effectiveness of the method are presented. A procedure which utilizes the complex-valued eigenproperties is developed for calculating the floor response spectra directly from the ground spectra. Numerical results of floor response spectra obtained from this procedure are presented. The floor spectra calculated by this approach include the structure–equipment interaction effect.

The effectiveness of introducing Coulomb damping in structures to reduce seismic response is evaluated. Response characteristics of simple one-degree-of-freedom structures with sliding interfaces between the top slab and supporting frame and between the base and foundation are studied and compared. It is shown that, analytically, the top slab sliding system is a special case of the base sliding system. The slab sliding system is seen to offer certain advantages over the base sliding system inasmuch as it provides a more effective reduction in the lateral forces in the supporting frame as well as a better isolation of supported secondary systems, as depicted by a significantly reduced level of floor spectrum response. The analytical ease of predicting the response of the slab sliding system is also demonstrated. The required unobstructed sliding displacements seem to be reasonable except, may be, for flexible systems. The similarities and differences between the hysteretic and slab sliding systems are also highlighted by comparison of their response results.

The truncation of the high frequency modes, so commonly used in dynamic structural analysis, sometimes can cause significant errors in the calculated response; this is caused by the so‐called missing mass effect. Such mode truncations can also affect the accuracy of floor spectra generated for stiff structural systems, and also for floors close to the base in even not so stiff structural systems, especially if the mode displacement methods are employed in the analysis. However, this problem due to mode truncation can be alleviated and virtually removed by employing the mode acceleration formulation in the analysis. Here, a direct response spectrum approach for generation of floor response spectra has been developed on the basis of the mode acceleration formulation and random vibration principles. As seismic input, this approach requires the relative acceleration spectra in lieu of the pseudo‐acceleration spectra—so commonly used with the mode displacement approaches. Because the relative spectrum values b...

A method is developed to obtain floor spectra curves that include the effect of nonstationarity of seismic motions. Such spectra are usually required for design or qualification of light secondary systems such as piping and equipment. The response of a simple structure-equipment system is examined for excitations modeled by Gaussian shot-noise and filtered shot-noise. The Markov vector approach is used to obtain the time-dependent second moments of the response in closed form. The nonstationarity due to time-varying intensity of the excitation and also due to the zero-starting condition is considered. The effects of various seismic intensity modulation functions and structural parameters on the response are evaluated. Useful results of practical importance are obtained in terms of response ratios of nonstationary-to-stationary responses, and their application in the generation of floor spectra curves for a structure is illustrated.

A response spectrum procedure is developed for seismic analysis of multiply supported secondary systems. The formulation is based on the random vibration analysis of structural systems subjected to correlated inputs applied at several supports. For a proper response spectrum analysis of a multiple support system, the support inputs are required to be defined in terms of the auto and cross pseudo-acceleration and relative velocity floor response spectra. Also information about the floor displacements and velocities as well as their correlations is required. The response of the secondary system is expressed as a combination of the dynamic and pseudo-static response components. The dynamic component is associated with the inertial effects of the support accelerations, whereas the pseudo-static component is due to the displacement of the supports relative to each other. Herein, the correlation between these two parts of the response is included through a term called the cross response component. Each of these components of the response can be calculated by a response spectrum method. The application of the proposed method is demonstrated by numerical examples.

The paper describes a method for the calculation of structural response of nonclassically damped structures subjected to six correlated earthquake components. The rotational components of the inputs are related to the translational components. A methodology to obtain the maximum response of a nonclassically damped structure, which can possibly occur in an orientation of the structure with respect to the impinging seismic waves, is developed. The approach is suitable for its adoptation with seismic inputs defined in terms of response spectra or spectral density functions. The numerical results demonstrating the application of the approach are presented. It is observed that the effect of the rotational components on the calculated response can be significant.

The square root of the sum of the squares (SRSS) procedure and its modified forms are often used to obtain seismic design response. The design inputs for such procedures are usually defined in terms of pseudo velocity or acceleration response spectra. Erroneous results have been obtained with these existing SRSS procedures, especially in the calculation of responses where high frequency effects dominate. Here an alternative SRSS procedure is developed using the so-called mode acceleration approach of structural dynamics. The design input in this procedure is defined in terms of relative acceleration and relative velocity spectra. The relative spectra can be related to pseudo spectra. For a given number of modes to be included in the analysis the new SRSS rule proposed here will reduce the error due to the so-called ‘missing mass’ effect and predict a more accurate response value than the rules which use pseudo spectra as input, for systems either with or without dominant high frequency mode effects.

A simple method is presented for generation of floor response spectra directly from a given ground response spectrum. A common practice to generate floor spectra is to carry out time-history analysis for a ground spectrum-consistent accelerogram. Unless an ensemble of such accelerograms is used the response results cannot be relied upon, but the use of an ensemble of accelerograms is cumbersome and costly. A method which can directly use a prescribed spectrum is preferred. The proposed method is based on transfer characteristics of the structure for random excitation, and makes use of the structural frequencies, mode shapes and participation factors, and the prescribed spectrum to generate floor spectra. In the paper, the use of the proposed method is demonstrated by generating floor spectra of a building. The proposed method is simple and especially convenient for use on digital computers.

The wind pressure distribution and dynamic behavior of hyperbolic cooling towers are significantly different from those of simple slender structures. Therefore, the gust response factors developed for design of these simple structures may not be applicable to cooling towers. A method which considers the dynamic interaction of the wind and tower is presented to obtain the gust factors for cooling tower design. Wind pressure distribution measurements made on model towers in wind tunnels are used. Simplifying assumptions are made concerning the correlation characteristics of wind pressure on a tower surface. Effect of change in wind and tower parameters on gust factors is examined.

Most soil systems behave nonlinearly under dynamic loads. For design and safety evaluation of such nonlinearly behaving soil systems, a direct approach is presented in which seismic design inputs defined in the form of response spectra can be directly used. The proposed approach is essentially an equivalent linear approach in which an iterative analysis scheme is used. Though equivalent strain dependent soil properties are used, a linear analysis is performed in each iteration. The choice of shear modulus and damping values in each iteration is based on a stochastic linearization procedure. As smoothed design spectra are to be used as seismic inputs, the normal mode approach is employed in the analysis. Thus response quantities like stress and strains are obtained by the (modified) square-root-of-the-sum-of-the-squares procedure. The applicability of the approach for nonlinear dynamic analysis is verified by a numerical simulation study in which the numerical results obtained for an ensemble of time histories by a step-by-step nonlinear approach are compared with the results obtained by the proposed approach for an equivalent seismic input defined by response spectra. A favorable comparison is obtained in the calculated maximum stress and peak stress characteristics. The approach can be used to obtain a conservative estimate of factor of safety against cumulative damage type of failures.

In the current practice of seismic design of secondary systems, the interaction between the supporting structure and the secondary systems is often ignored, and the interaction between any two secondary systems through their supporting structure is rarely considered. This paper examines the latter type of interaction between simple pieces of equipment. This is done by evaluating the effect on the floor response spectra, representing the response of an oscillator with varying frequency due to an additional of a second oscillator. To include the interaction effect, the modal properties of a composite system consisting of the primary structure and two oscillators are obtained and used in calculating the floor spectra. The frequencies are calculated by solving a characteristic equation, the expression of which is defined in terms of the parameters of the oscillators and the eigenproperties of the supporting structure. A method is presented to solve this characteristic equation by a simple Newton-Raphson scheme. The mode shape for a calculated frequency is defined by a closed-form expression. A parametric study is conducted to ascertain the interaction effect. This interaction between the two pieces of equipment can be significant if the second piece of equipment is tuned to a dominant mode of the supporting structure. The effect also depends upon the mass of the second piece of equipment as well as its location with respect to the first piece of equipment.

When measurements of stress-strain in a prestressed concrete structure are made, extraneous strains due to creep and shrinkage of concrete and relaxation of steel are also recorded. In the presence of these extraneous strains, the significance of making the measurements for surveillance of grouted tendon containment structures is critically examined from a statistical standpoint. The discriminating power of stress-strain measurement schemes to unmistakably detect the occurrence of abnormal losses in prestress due to various causes, including corrosion, is expressed in terms of power functions. The measurements of stress or strain by meters cannot be relied upon for detection of abnormal situations which may arise due to excessive corrosion of tendon steel. Elaborate instrumentation for the purpose of surveillance seems unnecessary.

A method is presented to obtain seismic design response of linearly behaving structures with nonproportional damping characteristics. For such systems, time history analyses are usually performed to obtain accurate seismic response. To obtain design response, such procedures can become expensive and cumbersome as an ensemble of time histories may have to be considered as seismic input. Other procedures have been developed to ascertain appropriate values of modal dampings so that modal analysis approach and thus commonly adopted square-root-of-the-sum-of-the-sqaures (SRSS) procedures can be used. The approach presented here considers nonproportional damping effects exactly in analytical sense. It uses state-vector formulation and is based on random virbration priciples. The approach is similar to conventional SRSS approach and thus ground response spectrum can be directly used to obtain designd respose.

Mode truncation is often used in seismic structural analyses of the classically as well as the nonclassically damped structures. In some cases, however, it can introduce significant error in calculated response due to the, so-called, missing mass effect. This error can be minimized by employing the mode acceleration technique, originally proposed by William in 1949. Herein, this technique is applied to develop a response spectrum approach for generation of interaction-free floor response spectra for nonclassically damped structures. This approach requires that the seismic input be defined in terms of the relative acceleration and relative velocity ground response spectra. Because of the special characteristics of these inputs, this approach can calculate floor response spectra as accurately with only a first few modes as those calculated with the complete set of modes. The applicability of the approach for generation of floor spectra directly from the ground response spectra is established by a numerical simulation study.

For proper seismic analysis of secondary systems with multiple supports, the prescription of the seismic input in terms of the conventional pseudo-acceleration floor response spectra is quite inadequate. It is necessary that the relative velocity floor response spectra as well as the cross floor response spectra, characterizing the correlation between the motions of various floors where the secondary system is attached, be also prescribed as the inputs. In addition to these, it is also necessary to define the floor displacements, velocities and their correlations. In this paper, the methods which can use the ground response spectra directly to obtain these inputs are developed. These methods are based on the random vibration analysis of the supporting primary structure, but still do not require the base input in stochastic form; conventional ground response spectra can be directly used. Numerical results demonstrating the application of the approaches are given.

Hydrodynamic loads such as those due to safety relief valve discharges and a postulated accidental loss of coolant are some of the major loads on boiling water reactor (RWR) containments. Structural analysis of containments for these highly transient loads can be more efficiently carried out if the response transfer function approach is used. The formulation of such an approach is developed for axisymmetric containment structures. The load parameters, e.g. the maximum intensity, arrival time and predominant frequency may be randomly defined. To obtain the design response, repeated analyses for various sets of parameter values may be required. In such cases the transfer function approach as presented here is computationally very efficient. The formulation to obtain the mean and standard deviation of response for uniformly distributed load arrival time is also provided and the numerical results for a typical BWR containment are given.

Acceleration floor spectra curves are commonly used as seismic design inputs for light equipment and other secondary systems. Earlier the writer had presented a method for generation of floor spectra directly from prescribed ground spectra. Further complementary developments in this method are made. These are: (1)The development of the method for generation of floor spectra at structural frequencies (an important resonance case); and (2)evaluation of nonstationarity of earthquake motions on floor spectra curves. Also, some approximations made in earlier work are further evaluated. As a result of these developments and evaluations, a comprehensive procedure based on stochastic principles is presented in the paper for definition of seismic design inputs for secondary systems. This procedure avoids the use of often used and recently criticized spectrum-consistent time history as seismic input for generation of floor spectra curves.