• Structural Engineering and Mechanics
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• v.9 no.3
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• pp.241-256
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• 2000

The major sources of energy dissipation in steel frames with partially restrained (PR) connections are evaluated. Available experimental results are used to verify the mathematical model used in this study. The verified model is then used to quantify the energy dissipation in PR connections due to hysteretic behavior, due to viscous damping and at plastic hinges if they are formed. Observations are made for two load conditions: a sinusoidal load applied at the top of the frame, and a sinusoidal ground acceleration applied at the base of the frame representing a seismic loading condition. This analytical study confirms the general behavior, observed during experimental investigations, that PR connections reduce the overall stiffness of frames, but add a major source of energy dissipation. As the connections become stiffer, the contribution of PR connections in dissipating energy becomes less significant. A connection with a T ratio (representing its stiffness) of at least 0.9 should not be considered as fully restrained as is commonly assumed, since the energy dissipation characteristics are different. The flexibility of PR connections alters the fundamental frequency of the frame. Depending on the situation, it may bring the frame closer to or further from the resonance condition. If the frame approaches the resonance condition, the effect of damping is expected to be very important. However, if the frame moves away from the resonance condition, the energy dissipation at the PR connections is expected to be significant with an increase in the deformation of the frame, particularly for low damping values. For low damping values, the dissipation of energy at plastic hinges is comparable to that due to viscous damping, and increases as the frame approaches failure. For the range of parameters considered in this study, the energy dissipations at the PR connections and at the plastic hinges are of the same order of magnitude. The study quantitatively confirms the general observations made in experimental investigations for steel frames with PR connections; however, proper consideration of the stiffness of PR connections and other dynamic properties is essential in predicting the dynamic behavior.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.537-549
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• 2001

The effect of partially restrained(PR) connections and the uncertainties in them on the reliability of steel frames subjected to seismic loading is addressed. A stochastic finite element method(SFEM) is proposed combining the concepts of the response surface method(RSM), the finite element method(FEM), the first-order reliability method (FORM), and the iterative linear interpolation scheme. The behavior of PR connections is captured using moment-relative rotation curves, and is represented by the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The seismic loading is applied in the time domain for realistic representation. The reliability of steel frames in the presence of PR connections is calculated considering all major sources of nonlinearity. The algorithm is clarified with the help of an example.

• Steel and Composite Structures
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• v.5 no.4
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• pp.271-287
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• 2005

The seismic behavior of two steel moment-resisting frames, which satisfy all the current seismic design requirements, are evaluated and compared in the presence of pre-Northridge connections denoted as BWWF and an improved post-Northridge connections denoted as BWWF-AD. Pre-Northridge connections are modeled first as fully restrained (FR) type. Then they are considered to be partially restrained (PR) to model their behavior more realistically. The improved post-Northridge connections are modeled as PR type, as proposed by the authors. A sophisticated nonlinear time-domain finite element program developed by the authors is used for the response evaluation of the frames in terms of the overall rotation of the connections and the maximum drift. The frames are excited by ten recorded earthquake time histories. These time histories are then scaled up to produce some relevant response characteristics. The behaviors of the frames are studied comprehensively with the help of 120 analyses. Following important observations are made. The frames produced essentially similar rotation and drift for the connections modeled as FR type and PR type represented by BWWF-AD indicating that the presence of slots in the web of beams in BWWF-AD is not detrimental to the overall response behavior. When the lateral displacements of the frames are significantly large, the responses are improved if BWWF-AD type connections are used in the frames. This study analytically confirms many desirable features of BWWF-AD connections. PR frames have longer periods of vibration in comparison to FR frames and may attract lower inertia forces. However, calculated periods of the frames of this study using FEMA 350 empirical equation is longer than those calculated using dynamic characteristics of the frames. This may result in even lower design forces and may adversely influence the design.

• Steel and Composite Structures
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• v.1 no.4
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• pp.459-480
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• 2001

The damage suffered by steel structures during the Northridge (1994) and Kobe (1995) earthquakes indicates that the fully restrained (FR) connections in steel frames did not behave as expected. Consequently, researchers began studying other possibilities, including making the connections more flexible, to reduce the risk of damage from seismic loading. Recent experimental and analytical investigations pointed out that the seismic response of steel frames with partially restrained (PR) connections might be superior to that of similar frames with FR connections since the energy dissipation at PR connections could be significant. This beneficial effect has not yet been fully quantified analytically. Thus, the dissipation of energy at PR connections needs to be considered in analytical evaluations, in addition to the dissipation of energy due to viscous damping and at plastic hinges (if they form). An algorithm is developed and verified by the authors to estimate the nonlinear time-domain dynamic response of steel frames with PR connections. The verified algorithm is then used to quantify the major sources of energy dissipation and their effect on the overall structural response in terms of the maximum base shear and the maximum top displacement. The results indicate that the dissipation of energy at PR connections is comparable to that dissipated by viscous damping and at plastic hinges. In general, the maximum total base shear significantly increases with an increase in the connection stiffness. On the other hand, the maximum top lateral displacement $U_{max}$ does not always increase as the connection stiffness decreases. Energy dissipation is considerably influenced by the stiffness of a connection, defined in terms of the T ratio, i.e., the ratio of the moment the connection would have to carry according to beam line theory (Disque 1964) and the fixed end moment of the girder. A connection with a T ratio of at least 0.9 is considered to be fully restrained. The energy dissipation behavior may be quite different for a frame with FR connections with a T ratio of 1.0 compared to when the T ratio is 0.9. Thus, for nonlinear seismic analysis, a T ratio of at least 0.9 should not be considered to be an FR connection. The study quantitatively confirms the general observations made in experimental results for frames with PR connections. Proper consideration of the PR connection stiffness and other dynamic properties are essential to predict dynamic behavior, no matter how difficult the analysis procedure becomes. Any simplified approach may need to be calibrated using this type of detailed analytical study.

• Steel and Composite Structures
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• v.9 no.6
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• pp.499-518
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• 2009

The present paper investigates the stochastic seismic responses of steel structure systems with Partially Restrained (PR) connections by using Perturbation based Stochastic Finite Element (PSFEM) method. A stiffness matrix formulation of steel systems with PR connections and PSFEM and MCS formulations of structural systems are given. Based on the formulations, a computer program in FORTRAN language has been developed, and stochastic seismic analyses of steel frame and bridge systems have been performed for different types of connections. The connection parameters, material and geometrical properties are assumed to be random variables in the analyses. The Kocaeli earthquake occurred in 1999 is considered as a ground motion. The connection parameters, material and geometrical properties are considered to be random variables. The efficiency and accuracy of the proposed SFEM algorithm are validated by comparison with results of Monte Carlo simulation (MCS) method.

• Steel and Composite Structures
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• v.8 no.4
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• pp.265-280
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• 2008

An investigation on the combined effect of foundation type, foundation flexibility, axial load and PR (semi-rigid) connections on the natural frequencies of steel frames is presented. These effects were investigated using a suitable modified FE program for cases where the foundation flexibility, foundation connectivity, and semi-rigid connections could be treated as equivalent linear springs. The effect of axial load on the natural frequency of a structure was found to be significant for slender structures subjected to high axial loads. In general, if columns of medium slenderness are designed without consideration of axial load effects, the frequency of the structure will be overestimated. Studies on the 3-story Los Angeles PR SAC frame indicate that the assumption of rigid connections at beam-column and column-base interfaces, as well as the assumption of a rigid foundation, can lead to significant errors if simplified design procedures are used. These errors in an equivalent static analysis are expected to lead to even more serious problems when considering the effect of higher modes under a non-linear dynamic analysis.

• Journal of the Korean Society for Advanced Composite Structures
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• v.2 no.4
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• pp.1-10
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• 2011

This study investigates the performance of composite (steel-concrete) frame structures through numerical experiments on individual connections. The innovative aspects of this research are in the use of connections between steel beams and concrete-filled tube (CFT)columns that utilize a combination of low-carbon steel and shape memory alloy (SMA) components. In these new connections, the intent is to utilize the recentering provided by super-elastic shape memory alloy tension bars to reduce building damage and residual drift after a major earthquake. The low-carbon steel components provide excellent energy dissipation. The analysis and design of these structures is complicated because the connections cannot be modeled as being simply pins or full fixity ones they are partial restraint (PR). A refined finite element (FE) model with sophisticated three dimensional (3D) solid elements was developed to conduct numerical experiments on PR-CFT joints to obtain the global behavior of the connection. Based on behavioral information obtained from these FE tests, simplified connection models were formulated by using joint elements with spring components. The behavior of entire frames under cyclic loads was conducted and compared with the monotonic behavior obtained from the 3D FE simulations. Good agreement was found between the simple and sophisticated models, verifying the robustness of the approach.

• Structural Engineering and Mechanics
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• v.23 no.4
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• pp.387-407
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• 2006

A Genetic Algorithm (hereinafter GA) based optimum design algorithm and program for plane steel frames with partially restrained connections is presented. The algorithm was incorporated with the refined plastic hinge analysis method, in which geometric nonlinearity was considered by using the stability functions of beam-column members and material nonlinearity was considered by using the gradual stiffness degradation model that included the effects of residual stress, moment redistribution by the occurrence of plastic hinges, partially restrained connections, and the geometric imperfection of members. In the genetic algorithm, a tournament selection method and micro-GAs were employed. The fitness function for the genetic algorithm was expressed as an unconstrained function composed of objective and penalty functions. The objective and penalty functions were expressed, respectively, as the weight of steel frames and the constraint functions which account for the requirements of load-carrying capacity, serviceability, ductility, and construction workability. To verify the appropriateness of the present method, the optimum design results of two plane steel frames with fully and partially restrained connections were compared.

• Steel and Composite Structures
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• v.8 no.1
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• pp.35-52
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• 2008

The paper investigates the seismic performance of a Partially-Restrained (PR) steel-concrete composite frame using the probabilistic approach. The analysed frame was tested at the ELSA laboratory of the Joint Research Centre of Ispra (Italy), while the representative beam-to-column composite connections were tested at the Universities of Pisa, Milan and Trento (Italy). The component modelling of both interior and exterior composite joints is described first, including the experimental-numerical validation. The Latin Hypercube method has been used to draw the probabilistic distribution curves of joints, and then the whole PR composite frame has been analysed. Pushover and incremental dynamic analyses have been carried out using the non-linear FE code SAP2000 version 9.1. The fragility and performance curves of the PR composite frame have been determined for four damage limit states.

• Journal of the Korean Society for Advanced Composite Structures
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• v.5 no.1
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• pp.28-36
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• 2014

This study describes the development of innovative connections between steel beams and concrete-filled tube columns that utilize a combination of low-carbon steel and super-elastic shape memory alloy components. The intent is to combine the recentering behavior provided by the shape memory alloys to reduce building damage and residual drift after a major earthquake with the excellent energy dissipation of the low-carbon steel. The analysis and design of structures requires that simple yet accurate models for the connection behavior be developed. The development of a simplified 2D spring connection model for cyclic loads from advanced 3D FE monotonic studies is described. The implementation of those models into non-linear frame analyses indicates hat the recentering systems will provide substantial benefits for smaller earthquakes and superior performance to all-welded moment frames for large earthquakes.