Force Analogy Method Research Articles

Energy density spectra in actively controlled inelastic structures—application

An accurate method of predicting peak structural responses and energy forms in actively controlled structures using generated response spectra and energy density spectra developed in the first part of this research is proposed for both elastic and inelastic structures. The accuracy of the predicted responses is compared with that obtained using inelastic time history analysis. Conventional analysis of controlled structures generally uses structural models that are simplified to a significant extent such that the results usually do not represent the actual behaviour of real moment resisting frames. In this research, inelastic structural control analysis based on force analogy method is extended to analyse real moment-resisting frames with plastic hinges offsets from the member ends. By using static condensation, additional degrees of freedom in real moment resisting frames are condensed out, and thereby the procedure of force analogy method in analysing inelastic structural response remains unchanged. Numerical simulation is performed using the modified 1940 El Centro earthquake time history and response spectra for both elastic and inelastic structural models to study the controlled responses using both optimal linear control and ad hoc control algorithms. Results show that the proposed method of predicting the maximum structural responses gives very accurate results for both elastic and inelastic structural systems. Copyright © 2005 John Wiley & Sons, Ltd.

New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P -delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional increme...

Predictive instantaneous optimal control of inelastic structures based on ground velocity

One of the challenges confronting structural engineers in structural control is to find more efficient control algorithms to ensure better and more reliable control results to protect structures against the damaging effects of destructive environmental forces. In this paper, a simple control algorithm, namely the Predictive Instantaneous Optimal Control (PIOC) algorithm, is proposed by introducing a new state space form. Different from the classical ground acceleration-based control algorithms, this new control algorithm uses earthquake ground velocity as the input. Since the earthquake ground velocity is not at high frequency as compared with the ground acceleration, it can be predicted at certain time steps beforehand in real-time domain with higher accuracy. This ensures the synchronous execution of the proposed PIOC algorithm with real-time application of the control force. To capture the damaging effects during earthquake ground motions, the force analogy method is used to characterize structures responding in the inelastic domain. Numerical studies are performed to compare the structural response with and without control using both single degree of freedom and multi-degree of freedom structural models. Results show that the PIOC algorithm is effective in reducing the structural response under earthquake excitation. Copyright © 2006 John Wiley & Sons, Ltd.

A numerical study based on sequential procedure for optimally placing active controllers

A sequential procedure based on the concept of degree of controllability is developed for optimally placing active controllers in structures. The optimal locations are selected to be located where the largest structural response occurs. This sequential procedure uses time history analysis to determine these optimal locations, and the effect of each additional controller on the next optimal location is considered in every step of the analysis procedure. Force analogy method (FAM) is used to take into consideration any possible structural inelasticity during earthquakes. Different from conventional methods of inelastic analysis using changing stiffness, FAM varies the structural displacement field, and therefore greatly simplifies the computation. Since only initial stiffness is used in the inelastic analysis, it can be easily incorporated into the optimal linear control algorithm using the state space method. Numerical simulation of a six-storey frame is performed to demonstrate the simplicity of optimal placement procedure while considering structural inelasticity. Results show that optimal locations determined by the proposed sequential procedure have advantages over other locations in terms of control efficiency, where placement of the controllers in these locations reduces the desired overall structural and energy response most effectively. Copyright © 2005 John Wiley & Sons, Ltd.

INELASTIC SEISMIC RESPONSE ANALYSIS BASED ON ENERGY DENSITY SPECTRA

Energy balance is used to characterise the seismic energy in inelastic structures where energy input to the structure is decomposed into strain energy, kinetic energy, damping energy, and plastic energy. The exact quantification of plastic energy is derived based on force analogy method for moment-resisting frames. A method of generating energy density spectra is then proposed based on yield displacement of a single degree of freedom system. The effects of different structural vibration characteristics are then studied on energy density spectra. These effects include variations of yield displacement level, earth-quake scaling factor, and damping ratio, which proves to be useful in improving the basic understanding of energy characteristics in structural dynamic response. Finally, the use of energy density spectra is demonstrated on a multi-degree of freedom structure to show the practical applications of these spectra.

Predictive inelastic state control of modern structures during earthquakes

The predictive inelastic state control (PISC) algorithm is proposed by incorporating an elastic-based predictive state control algorithm with inelastic structural analysis. Force analogy method based on initial stiffness is used in the analysis to simplify the numerical computation. This proposed inelastic control algorithm compensates for the time delay that occurs in practical application of structural control by predicting the inelastic structural response over a period equal to the time delay, and substituting the predicted structural response in the expression of an ideal control force without considering time delays. A one-storey moment-resisting frame with different inelastic characteristics is analyzed using this algorithm. Numerically simulated results show that the proposed control algorithm is feasible for various types of inelastic structures. While the control efficiency deteriorates with increase in time delay magnitude, PISC shows good performance within a certain range of time delays. More importantly, it is found that a control system with smaller time delay magnitude does not guarantee better performance than that with larger time delay magnitude. Finally, numerical simulation on a six-storey moment-resisting frame is performed to demonstrate that PISC gives good control results in a practical inelastic structure. Copyright © 2004 John Wiley & Sons, Ltd.

Energy‐based design of structures using modified force analogy method

AbstractSummaryEnergy due to earthquake excitations is used to evaluate the performance of a structure. This energy is derived analytically based on the force analogy method, which uses only initial stiffness with changing displacement to accurately capture the inelastic material behaviour. However, numerical calculation using the classical force analogy method considers mass matrices that are invertible, and therefore it is not appropriate for use in analysing real structures where rotational mass moment of inertia is generally ignored. In this research, derivation of the force analogy method is modified to analyse real moment‐resisting frames using static condensation. Using this modified force analogy method in the condensed form significantly reduces the size of the structural problem because a large number of rotational degrees of freedom can be condensed. Numerical simulation is then performed to analyse the dynamic response of a six‐storey moment‐resisting frame and the concept of performance‐based design is used to improve the structural performance in terms of energy dissipation ‘demand’ at each plastic hinge. Results show that the amount of total plastic energy dissipation remains about the same for structures with similar frequency contents. This is significant because it shows that understanding the flow of energy in the structure is important in improving structural performance under earthquake excitations. Copyright © 2003 John Wiley & Sons, Ltd.

Earthquake Response and Energy Evaluation of Inelastic Structures

A computational method is derived to characterize the energy in inelastic structures and the transfer among various energy forms over the duration of an earthquake. This computational method is based on the force analogy method, which uses a change in displacement field to represent the inelastic behavior of structure instead of the traditional method of changing stiffness. The evaluation of plastic energy due to inelastic deformation in the structure becomes very simple using the force analogy method, where the accumulation of plastic energy due to plastic rotations is exactly equal to the elastic moment multiplied by the change in plastic rotations. In addition, this plastic energy formula can be used for any material with predefined stress–strain relationship, and therefore the transfer of energy among various forms can be calculated at any specific time. Once the energy equation is derived, numerical analyses are performed on a single degree of freedom system to study the characteristics of energy transfer. This is then extended to study the transfer of energy among various forms in a multidegree of freedom system. These two studies show that the analytically derived equation for plastic energy is accurate in studying the structural energy response due to earthquake excitations.

Probabilistic structural damage assessment and control based on energy approach

AbstractThis paper proposes a probabilistic method for assessing the seismic damage to structures based on both plastic rotation and plastic energy. Four basic features of this method are: (1) the incorporation of the state space method and force analogy method in inelastic dynamic analysis; (2) the exact quantification of the overall plastic energy and individual plastic energy dissipated at each plastic hinge; (3) the definition of damage model with both the monotonic and cyclic damage extremes; and (4) the probabilistic expression of the structural damage indices. An example of a ten‐storey moment‐resisting steel frame is presented to demonstrate the practical application of the proposed procedure. Optimal linear control is applied to improve the structural performance. Responses and energies at selected plastic hinges arising from 28 earthquake ground motions are compared, and statistical characteristic values of these variables are computed. Finally, comparisons are made between the drift ratio and failure probability of the proposed local damage index. Results show that active control can reduce plastic rotation and plastic energy, therefore reducing the damage. In addition, this study shows that using the drift ratio alone is inadequate to predict damage on certain occasions, and the proposed damage index is a more rational measure. Copyright © 2001 John Wiley & Sons, Ltd.

Energy‐based damage assessment on structures during earthquakes

AbstractSeveral seismic damage indices have been developed using the energy concept in attempt to compensate for the inadequacy of ductility criteria. However, these indices are either based on implicitly defined energy as a cumulative effect on ductility or are unable to consider energy in a quantitative manner. In this paper, a method of assessing the structural performance during earthquakes based on both explicitly computed plastic rotation and plastic energy at every hinge of a moment‐resisting frame is proposed. This method uses the force analogy method to evaluate the structural response and energy in the inelastic domain. Inelastic deformation is expected to occur during major earthquakes, and active control based on an instantaneous optimal control algorithm is used to improve the structural performance. Comparisons are made between uncontrolled response and instantaneous optimal control response based on a single‐degree‐of‐freedom system to demonstrate the computation of plastic energy. Damage analysis of a six‐storey moment‐resisting steel frame is then presented to evaluate the performance and applicability of the proposed damage measure. Results show that the proposed damage assessment criteria are feasible and that active control can reduce plastic rotation and plastic energy, thereby reducing damage to a certain acceptable limit. Copyright © 2001 John Wiley & Sons, Ltd.

Inelastic earthquake control of weld failure Part I: Limit state approach

Active structural control of inelastic response is proposed for the first time on existing buildings. The optimal linear control theory and the force analogy method are combined in state space form to calculate the response of the structure. Application of this combined method is performed to reduce the risk of weld failure in steel buildings. A six-story moment resisting building damaged during the 1994 Northridge earthquake is used to study the sensitivity of the response and the magnitude of the structural control force to the earthquake ground motion. The limit state approach is used to design the structural control system by limiting the maximum plastic rotations in the building to an acceptable level. In the process, structural control is shown to be very effective in reducing the plastic rotations during excitations, and therefore reducing the risk of weld failure. In addition, structural control is effective in reducing the responses, which include displacement, velocity, acceleration and drift of the structure. Copyright © 1999 John Wiley & Sons, Ltd.

Inelastic Dynamic Response of Structures Using Force Analogy Method

A new algorithm based on the force analogy method for studying the inelastic structural behaviors subjected to dynamic loadings is proposed. Inelastic analysis is performed based on varying the structural displacement field, which differs from the conventional method of changing stiffness. Each inelastic deformation of the structure is denoted as a degree of freedom, and therefore all inelastic behaviors are represented by a single equation. The algorithm is very time efficient because only initial stiffness is used, and it achieves high numerical accuracy when incorporating the use of a state space numerical integration method in dynamic analysis. Moreover, this algorithm is dynamically stable in analyzing structures with not only strain-hardening properties, but also elastic-plastic properties and strain-softening properties. Comparison between the proposed algorithm and an existing inelastic dynamic analysis software program is performed to demonstrate the accuracy and efficiency of this algorithm. Finally, application of the proposed algorithm to the dynamic response of a six-story hospital building is presented to show the complete inelastic analysis procedure in analyzing realistic structures.

Active control of inelastic structural response during earthquakes

The controlled response of structures in the inelastic domain is presented using the state space theory of optimal linear control. Using the force analogy method, structural inelastic behavior can be expressed in state space form. One-step time delay compensation is incorporated in the derivation. Numerical simulation is perfomed on a one-story frame using active tendon control system. © 1997 John Wiley & Sons, Ltd.