Partially Restrained Connections Research Articles

Stochastic Finite Element Analysis of Composite Structures with Partially Restrained Connections under Earthquake Loads

The stochastic analysis of composite structures with partially restrained (PR) connections under seismic loads present some interesting and challenging issues to practicing engineers. This paper proposes an efficient, robust, and accurate method for stochastic finite element analysis of concrete–steel composite structures allowing for PR connections. These are followed by suitable numerical example which indicates that employment of such a stochastic finite element analysis. The Kocaeli earthquake in 1999 is considered as a ground motion. The connections parameters and material properties are random variables. It is essential to properly consider the PR connections in the stochastic dynamic analysis and design of the steel-concrete composite structures since design forces change significantly. The assumption that the connections are rigid, which is routinely used in the application, is not proper. The effect of the variability connection stiffness on the composite structures responses is sufficiently important for consideration in structural safety.

Experimental and numerical study on the hysteretic behavior of composite partially restrained steel frame-reinforced concrete infill walls with vertical slits

The work presented in this study aimed to investigate the hysteretic behavior of composite partially restrained (PR) steel frame-reinforced concrete infill walls (PSRCW) with vertical slits, which consisted of a PR steel frame, a slit-reinforced concrete (RC) infill wall, and shear connectors. An experimental program at one-third scale of a one-bay by three-story PSRCW with vertical slits was tested under horizontal cyclic loading. The seismic behavior was examined in terms of the lateral load-carrying capacity, ductility, deformability, lateral stiffness, and energy dissipation. The results showed that this kind of structure exhibited superior ductility and deformability, as well as excellent energy-dissipation capacity. The slit RC infill walls exhibited flexure-dominated behavior and significantly increased the lateral load-carrying capacity. In contrast, the slit RC infill walls decreased the rotation demand on the PR connections from earthquake, which avoided the fracture failure of the beam-to-column connection. Additionally, the test results were verified, and relative parametric analyses of PSRCW with vertical slits were conducted by using a simplified macro fiber model to illustrate the factors that influence the structural hysteretic behavior.

Evaluation of proposed PR steel frame connection with torsional plate and its optimal placement

Characteristics of connections in steel moment-resisting frames are of utmost importance in determining the seismic performance of these structural systems. The results of several previous experimental studies have indicated that Partially-restrained (PR) connections possess excellent properties, which makes this connection a reliable substitution for Fully-restrained (FR) connections. These properties include needing less base shear, being more economic and in many cases, being able to absorb more energy. In this study, the behavior of two proposed PR connections with torsional plate is studied through finite element simulations. The results of the numerical studies regarding initial stiffness and maximum strength capacity of the proposed connections are calibrated against the results of solid mechanics formulations. Over 50 parametric studies are performed to determine the importance of various design variables of the proposed PR connections. A relation based on spring model is proposed to estimate the maximum strength capacity of the proposed connection. Seismic performance of the proposed connection is studied in a typical portal frame with various connection characteristics using nonlinear time-history analysis. The results explicitly show that using PR connections can considerably reduce the moment-rotation demands in the columns and as a result, higher performance levels can be achieved according to ASCE41.

Direct displacement-based seismic design of semi-rigid steel frames

Semi-rigid steel frames are often considered a cost-effective alternative to conventional fully rigid steel frames, because they use the economical partially restrained (PR) connections instead of the costly moment connections while performing satisfactorily under seismic loads. So far, semi-rigid steel frames have typically been designed using the traditional force-based method that is meant for the design of fully rigid steel frames. With this method, the sizing of various structural components is firstly carried out per code strength requirements and then revised iteratively to satisfy the stiffness requirements on both individual structural components and the overall frame. As a result, a designer often encounters considerable difficulty in achieving a structural solution that meets the target displacement and attains a desired yield mechanism. To address this issue, we propose a facile displacement-based method for the seismic design of semi-rigid steel frame structures by directly and explicitly relating the target displacement and deformation to the appropriate sizing of various structural components in terms of their strength, stiffness, and ductility. The new method is based on a simplified analytical semi-rigid frame model assuming that the structural plastic deformation is mainly concentrated within the PR connections while beams and columns largely remain elastic. A step-by-step procedure for implementing the new method is described and illustrated with example semi-rigid steel frame designs. The usefulness of the new method is demonstrated by comparing the target displacement and deformation values specified as a design objective with the actual values predicted by a nonlinear static pushover analysis.

Seismic response of 3D steel buildings considering the effect of PR connections and gravity frames.

The nonlinear seismic responses of 3D steel buildings with perimeter moment resisting frames (PMRF) and interior gravity frames (IGF) are studied explicitly considering the contribution of the IGF. The effect on the structural response of the stiffness of the beam-to-column connections of the IGF, which is usually neglected, is also studied. It is commonly believed that the flexibility of shear connections is negligible and that 2D models can be used to properly represent 3D real structures. The results of the study indicate, however, that the moments developed on columns of IGF can be considerable and that modeling buildings as plane frames may result in very conservative designs. The contribution of IGF to the lateral structural resistance may be significant. The contribution increases when their connections are assumed to be partially restrained (PR). The incremented participation of IGF when the stiffness of their connections is considered helps to counteract the no conservative effect that results in practice when lateral seismic loads are not considered in IGF while designing steel buildings with PMRF. Thus, if the structural system under consideration is used, the three-dimensional model should be used in seismic analysis and the IGF and the stiffness of their connections should be considered as part of the lateral resistance system.

Finite Element Model for the Behavior of Partially Restrained High Strength Web Angle Connections

This study investigates the behavior of Partially Restrained (PR) connections with high strength steel through the use of Finite Element (FE) modeling. The connection model is such that double web angles are represented by radiused corner section shell elements. The full interaction between the angle and the beam and/or column is simulated by the contact element.The analysis of the moment- rotation relationship and behavior characteristics of the connection with high strength steel are compared and discussed. It is established that the contact elements and strength enhancements of the corner regions employed in this model are important parameters for accurate predictions of Double Web Angle (DWA) connection behavior with cold-formed high strength steel. The proposed connection FE model is capable making highly accurate predictions about the ultimate load capacity and the plastic strain pattern. The model presented provides excellent results for significantly increasing the connection capacity as a result of employing a higher strength steel section. A power model expression was proposed to predict the ultimate moment and initial stiffness of the high strength DWA connection. A reasonable prediction was obtained for high strength PR connection.

Fragility analyses of mid-rise T-stub PR frames in the Mid-America earthquake region

Mid-America region is defined as the region of the central and southeastern United States compromising those states that have expected large but infrequent seismicity. Although earthquakes in this region are less frequent than in western U.S., they affect much larger areas than those of similar magnitude in western U.S. due to the deep and loose subsurface conditions. However, as little research has been carried out for partially restrained (PR) steel moment frame structures in this region, it is necessary to evaluate their seismic performance. To achieve this, seismic performance of three proto-type 6-story steel moment frames with T-stub PR connections was evaluated in accordance with FEMA 273/356 limit state criteria using fragility analyses. Three PR frames were designed using the appropriate design codes representing mid-1950s, late 1980s, and current practice. Two different types (“Conventional” and “New”) of fragility curves are developed and compared. In addition, the fragility curves at Los Angeles site representing western U.S. were generated and compared with those at the Mid-America region. Two different fragility analysis results show the same trends. Three proto-type 6 story PR frames in the Mid-America earthquake region performed well and may not collapse. It can be concluded that the seismic performance of the mid-rise PR frames in the Mid-America region will be satisfactory even under large but infrequent ground motions.

Predicted Behaviour of Partially Restrained Connection with Cold Formed High Strength Steel by 3D Finite Element Modelling

Thispaper investigates the behavior prediction of partially restrained (PR) connection with high strength steel bythree-dimensional nonlinear finite-element (FE) analyses. The connectionmodel is such that angle cleats are represented by radiuses corner section shell elements. The full interaction between angle and beam and/or column is simulated by contact element. The analysis results of the moment- rotation relationship and behaviour characteristic of the connection with high strength steel are compared and discussed. It is found that contact element and strength enhancement of the corner regions employed to the model are very important parameters for accurate prediction of PR connection behaviour with cold-formed high strength steel. The moment capacity prediction of top and seat angle connections based on EC3 has been shown to be reasonable compared with FE modeling. Theproposed connection FE model is capable of predicting the ultimate load capacity and the plastic strain pattern with good accuracy. The model presented gives excellent results for increasing the connection capacity significantly due to employed higher strength steel section.

Design, analysis and application of innovative composite PR connections between steelbeams and CFT columns

In this research, three structural design concepts are integrated: the use of compositeconcrete-filled tube (CFT) columns, the use of partially restrained (PR) connections andthe introduction of innovative materials (shape memory alloys) in the connection design.These concepts are used to enhance the robustness and performance of composite-specialmoment frames. These innovative connections intend to exploit the recentering propertiesof super-elastic SMA tension bars, the energy dissipation capacity of low-carbon steel barsand the toughness of CFT columns. PR-CFT connection prototypes were designed basedon a hierarchy of strength models for each connection component. Simplified user jointelements based on the mechanical modeling approach were formulated in an effort tosimulate the realistic behavior of bolted connections. The application of new connections tolow-rise PR composite frames is illustrated by designing four buildings in both 2D and 3Dfor the western US region. The performance of these composite frames was comparedwith those with conventional welded frames in terms of strength, ductility andrecentering behavior. In all three areas, frames with the PR composite connectionsshowed superior performance. This is due primarily to the capability of this systemto redistribute inter-story drift more evenly through the height of the frame.

Performance of the PR connections under combined Axial-tension and moment loading

The inherent moment capacity of bolted top-seat angle connections with double web angles (TSDW), categorized as partially restrained (PR) connections according to AISC-LRFD specifications, can be considered in analyses of semi-rigid connections especially when an accurate analysis of such fames is desired. However, in some cases, developed internal forces in the frame elements may affect the connection behavior, considerably. Axial tension force is one of such internal forces that may be imposed on frame connections in some cases such as construction imperfections, seismic loading or under large deflections of the catenary action during the progressive collapse of the semi-rigid frames. This study aims at the effects of the axial tension force on the performance of the bolted TSDW angle connections using nonlinear finite element method (FEM). The obtained results show that the axial tension force reduces the connection moment capacity and stiffness, considerably. Based on the obtained moment-rotation curves, affected by this particular loading type, equations are proposed to estimate the reduction rate of the connection stiffness and moment capacity.

Stochastic finite element analysis of structural systems with partially restrained connections subjected to seismic loads

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.

Mathematical modelling of a "post-Northridge" steel connection

A robust mathematical model to capture the behaviour of an attractive post-Northridge type, Partially Restrained (PR) steel connection is proposed. The proposed procedure captures the loading behaviour for this type of connection reasonably well. It is suggested that the unloading and reloading parts of M ? θ curves required for seismic analysis can be theoretically generated by using the Masing Rule. This study confirms some of the important desirable features of the connection. Although it is a PR connection, its initial stiffness is similar to that of bolted, a single web angle with top and seat connection, generally considered to be a Fully Restrained (FR) connection. Thus, a steel frame with the connection studied is not expected to show weakness in satisfying serviceability requirements. Furthermore, the beam develops full plastic moment and the ductility of the connection and its seismic energy dissipation characteristics are expected to be significantly improved.

Cyclic behavior of steel frame structures with composite reinforced concrete infill walls and partially-restrained connections

This paper presents an experimental study of the cyclic behavior of a composite structural system consisting of partially-restrained (PR) steel frames with reinforced concrete infill walls. The composite interaction is achieved through the use of the headed stud connectors along the steel frame–infill interfaces so that the two main components of the system share in the resistance of lateral shear and overturning moment. Having the relatively light steel frame constructed using PR connections maximizes the economy of the system, while still ensuring system integrity in the post-peak range of deformation. The one-bay, two-story test specimen was built at one-third scale. The study shows that this system has the potential to offer strength appropriate for resisting the forces from earthquakes and stiffness adequate for controlling drift for low- to moderate-rise buildings located in earthquake-prone regions. Redundancy is also exhibited in this system through alternate load paths occurring at different levels of loading, including shear stud–infill interaction, steel frame–infill strut interaction, and deformation of the steel frame. Improvement is needed for reducing the post-peak strength degradation observed in the present study.

Behavior and Modeling of a Bolt Bearing on a Single Plate

One of the fundamental components of the moment-rotation behavior of a steel or composite partially restrained (PR) connection is the load-deformation behavior associated with high-strength bolts bearing on steel plates. For many PR connections, the writers believe that this bearing behavior can be approximated by the behavior of a single bolt lap plate connection. One of the primary components of the lap plate connection behavior is the local load-deformation behavior associated with a single bolt bearing on a single plate. This paper presents an experimental and analytical study of the single bolt single plate behavior. The results of the paper include specific methods for predicting the initial stiffness, strength, and overall load-deformation behavior of the single bolt single plate connection.

Seismic reliability of non-linear frames with PR connections using systematic RSM

An effective, efficient, and robust reliability analysis algorithm is proposed for non-linear structures, where seismic loading can be applied in the time domain. The method is developed specifically for steel frame structures considering all major sources of non-linearity, including geometry, material, and partially restrained (PR) connections. The non-linearity due to PR connections is modeled by moment-relative rotation curves using 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 proposed algorithm intelligently integrates the response surface method, the finite element method, the first-order reliability method, and an iterative linear interpolation scheme. The uncertainties in all the random variables including the four parameters of Richard model are considered. Two unique features of the proposed algorithm are that (1) actual earthquake time histories can be used to excite structures in the presence of major sources of non-linearity and uncertainty and (2) it is possible to estimate the risk corresponding to both the serviceability and strength limit states. The algorithm is verified using the Monte Carlo simulation technique. The verified algorithm is first used to study the reliability of a frame structure in the presence of PR connections with different degrees of flexibility. Then the algorithm is used to estimate the reliability of a frame structure excited by 13 actual recorded earthquake time histories, 12 of them recorded during the Northridge earthquake of 1994. As expected, the reliabilities of the frame are found to be quite different, when excited by several time histories of the Northridge earthquake.

Refined 3D finite element modeling of partially-restrained connections including slip

This study presents an approach for refined parametric three-dimensional (3D) analysis of partially-restrained (PR) bolted steel beam-column connections. The models include the effects of slip by utilizing a general contact scheme. Non-linear 3D continuum elements are used for all parts of the connection and the contact conditions between all the components are explicitly recognized. A method for applying pretension in the bolts is introduced and verified. The effect of several geometrical and material parameters on the overall moment–rotation response of two connection configurations subject to static loading is studied. Models with parameters drawn from a previous experimental study of top and bottom seat angle connections are generated in order to compare the analyses with test results, with good prediction shown by the 3D refined models. The proposed 3D modeling approach is general and can be applied for accurate modeling of a wide range of other types of PR connections. A pronounced effect of slip and friction, between the connection components is shown with connections having thicker (stiffer) seat angles. This study demonstrates the effects of clamping through the bolts and contact between the components on the overall non-linear moment–rotation response. Equivalent moment–rotation responses of pull-test simulations are compared to FE model responses of full connections without web angles. The moment–rotation from the pull test is shown to be equivalent to that of the full FE model for small rotations. As the rotation increases a softer response is shown by the pull tests.

Seismic response and energy dissipation in partially restrained and fully restrained steel frames: An analytical study

The damage suffered by steel structures during the Northridge (1994) and Kobe (1995) earthquakesrnindicates that the fully restrained (FR) connections in steel frames did not behave as expected. Consequently,rnresearchers began studying other possibilities, including making the connections more flexible, to reduce thernrisk of damage from seismic loading. Recent experimental and analytical investigations pointed out that thernseismic response of steel frames with partially restrained (PR) connections might be superior to that of similarrnframes with FR connections since the energy dissipation at PR connections could be significant. Thisrnbeneficial effect has not yet been fully quantified analytically. Thus, the dissipation of energy at PRrnconnections needs to be considered in analytical evaluations, in addition to the dissipation of energy due tornviscous damping and at plastic hinges (if they form). An algorithm is developed and verified by the authors tornestimate the nonlinear time-domain dynamic response of steel frames with PR connections. The verifiedrnalgorithm is then used to quantify the major sources of energy dissipation and their effect on the overallrnstructural response in terms of the maximum base shear and the maximum top displacement. The resultsrnindicate that the dissipation of energy at PR connections is comparable to that dissipated by viscous dampingrnand at plastic hinges. In general, the maximum total base shear significantly increases with an increase in thernconnection stiffness. On the other hand, the maximum top lateral displacement Umax does not always increasernas the connection stiffness decreases. Energy dissipation is considerably influenced by the stiffness of arnconnection, defined in terms of the T ratio, i.e., the ratio of the moment the connection would have to carryrnaccording to beam line theory (Disque 1964) and the fixed end moment of the girder. A connection with a Trnratio of at least 0.9 is considered to be fully restrained. The energy dissipation behavior may be quite differentrnfor a frame with FR connections with a T ratio of 1.0 compared to when the T ratio is 0.9. Thus, for nonlinearrnseismic analysis, a T ratio of at least 0.9 should not be considered to be an FR connection. The studyrnquantitatively confirms the general observations made in experimental results for frames with PR connections.rnProper consideration of the PR connection stiffness and other dynamic properties are essential to predictrndynamic behavior, no matter how difficult the analysis procedure becomes. Any simplified approach mayrnneed to be calibrated using this type of detailed analytical study.

Seismic risk analysis of frames with uncertain support and PR connection conditions

A hybrid reliability evaluation procedure is proposed to estimate the risk of steel frames considering the rigidity of connections and supports as accurately as possible. Nonlinearities due to geometry, material, partially restrained (PR) connections, and flexible supports are considered in the proposed algorithm. The four-parameter Richard model is used to represent the flexibility of connections and supports. All major sources of uncertainty in the loading and resistance-related parameters and the parameters in the Richard model are incorporated in the algorithm. The unique feature of the algorithm is that the earth-quake loading can be applied in the time domain, providing an alternative to the random vibration approach. The proposed algorithm intelligently integrates the concepts of the finite element method, the response surface method, the first order reliability method, and the iterative linear interpolation scheme. The algorithm is verified using Monte Carlo simulation. With the help of an example, it is shown that the proposed algorithm can be used to estimate risk for both the serviceability and strength limit states. The presence of PR connections and/or flexible supports alters the dynamic properties (stiffness and damping) of the structure and adds a new and major source of energy dissipation. The serviceability limit state may become the controlling limit state, particularly for seismic loading. Thus, the common practice of considering all connections and supports to be rigid and designing the frame for the strength limit state may not be appropriate. The flexibility of connections and supports and the uncertainty in modeling them have a considerable influence on the overall behavior of frames, particularly under seismic loading. An efficient, robust, and accurate method is proposed to evaluate the reliability of such frames.

Probabilistic study of the behavior of steel frames with partially restrained connections

The reliability of steel frames with type PR (partially restrained) connections is dependent on the variability in the moment–rotation characteristics of the connections. In this paper, the contribution of this source of variability to the uncertainty in frame deformation is examined using stochastic finite element analysis to compare the effect of initial connection stiffness to that of bending stiffnesses of the beams and columns. The PR connections have top and seat angles connecting the beam and column flanges, and double web angles connecting the beam web to the column flange. A stochastic finite element analysis is used to develop system fragilities, which depict the probability of exceeding three limit states related to the maximum horizontal displacement, maximum interstory drift ratio and elastic bending moment capacity as a function of lateral force. The effect of the variability in initial connection stiffness on frame response is sufficiently important to require careful consideration in performance-based design.

Energy Dissipation at PR Frames under Seismic Loading

The major sources of energy dissipation, lateral deformation, and base shear in steel frames with partially restrained (PR) connections subjected to seismic loading are analytically studied. The analytical study confirms, in general, the behavior observed during experimental investigation: PR connections reduce the overall stiffness of frames, but add a major source of energy dissipation. It is observed, in general, that the maximum total base shear may significantly increase as the connection stiffness increases. The maximum top lateral displacement does not always increase with a decrease in the connection stiffness. The response under earthquake loading largely depends on the dynamic characteristics of both the structure and the earthquake excitation. Proper consideration of the stiffness of the PR connections and other dynamic properties is essential to predict the dynamic behavior, no matter how difficult the analysis procedure becomes.