Semi-rigid Frames Research Articles

One-dimensional convolutional neural network-based damage detection in structural joints

Structural health monitoring research traditionally focuses on detecting damage in members excluding the possibility of weakened joint conditions. Efficient model-based joint damage detection algorithms demand computationally expensive model that may affect the promptness of detection. Deep learning techniques have recently come up as efficient alternative to this cause. These techniques help in predicting occurrence and location of damage in structures based on some automatically identified features embedded in the measured structural response. This article proposes an output-only approach for joint damage detection in which a 1D-convolutional neural network (CNN) has been introduced to locate weakened joints in semi-rigid frames. CNN architecture merges feature extraction and classification simultaneously within a single learning block to automatically extract abstract features from typically 2D/3D signals. Proposed approach further modifies the usual CNN architecture to enable it to handle 1D response signals. Numerical validation is performed on a 2D-steel frame under different damage locations and severities followed by experimental validation on a steel frame structure. The method is observed to be very precise and prompt in detecting single as well as multiple damage scenarios. False alarm sensitivity of the proposed algorithm is also tested and found to be well within acceptable limits.

Experimental study of hysteretic behavior of semi-rigid frame with a corrugated plate

Corrugated steel plate shear wall (CSPSW) is one of the new structural systems used to resist earthquakes and that has better a hysteretic behavior than a flat plate shear wall. In this paper, three full-scale, single-story, single-bay specimens, consisting of one semi-rigid frame without infill panels and two semi-rigid frames with unstiffened and stiffened doubly trapezoidal corrugated plates, were subjected to cyclic loading. The hysteretic behavior and energy dissipation capacity of the three specimens were compared. The experimental results revealed that the corrugated plate greatly enhanced the stiffness and lateral load-carrying capacity of the semi-rigid frames. Therefore, the frames with the corrugated plates had higher energy dissipation capacity than the frame without infill panels. Moreover, the strength, stiffness and energy dissipation capacity of the stiffened corrugated specimen were greater than those of the unstiffened corrugated specimen, although the ductility of the stiffened corrugated specimen was lower. A method of calculating the lateral capacity of CSPSWs was proposed based on the superposition principle. This method could accurately predict the lateral capacity of the corrugated specimens.

Response of semi-rigid steel frames to sequential earthquakes

In a seismic event, large number of aftershocks are generally triggered due to the complex interaction within and between tectonic plates. Even though aftershocks are typically smaller in magnitude than mainshocks, their ground-motion intensity, measured by peak ground acceleration, is not always smaller. Moreover, mainshocks can result in permanent damage to structural components. As a result, the vulnerability of structures to extensive damage and complete collapse due to aftershocks could increase. Despite their importance in evaluating the true risk of system failure and collapse, the inclusion of aftershocks in code provisions and guidelines for seismic risk assessment and performance-based engineering is lacking. In this study, three semi-rigid frames, with connection capacities of 50%, 60%, and 70% of the plastic moment of the beam, were designed and their performance under mainshock-aftershock sequences assessed. The objective of this study, pertaining to the seismic performance of the frames, is twofold. First, is to develop fragility functions for the subject frames under sequential mainshock-aftershock events. Second, is to evaluate the extent of spread of inelasticity and period elongation in the investigated frames as a result of the sequential events. A new method for selection and scaling of mainshock-aftershock sequences is proposed and non-linear time history analysis of the frames is conducted. The results show that the inclusion of the aftershocks increases the probability of reaching or exceeding a particular damage limit state in the frames, primarily due to the considerable period elongation resulting from the induced permanent damages.

Fuzzy finite element analysis for free vibration response of functionally graded semi-rigid frame structures

This study contributes a practical approach for the fuzzy free vibration quantification of functionally graded semi-rigid frame structures. A new Timoshenko beam element is formulated to include the connection rigidity for the analysis purpose. The finite element formulation is general to present different semi-rigid conditions, whereas hinged and rigid connections are special cases. Furthermore, an efficient response-surface-based fuzzy analysis is established based on the α–cut strategy and first-order Taylor's approximation to predict the fuzzy natural frequencies of the structures. Highlighted point is that various input uncertainties, such as the material characteristics, the member dimensions, and the connection rigidities, can be incorporated in the analysis by the presented fuzzy methodology. Computational efficiency and correctness of the proposed method are shown, and the effect of the uncertainties, especially of the connection rigidities, on the natural frequency of semi-rigid FGM structures is explored via solving some numerical examples.

Fuzzy static finite element analysis for functionally graded structures with semi-rigid connections

In this study, the fuzzy static behavior of functionally graded material (FGM) semi-rigid frame structures is freshly addressed. For the analysis purpose, a new FGM beam element with flexible connections is established. Moreover, a computationally efficient procedure is developed to predict the fuzzy static structural behaviors. An FGM beam and an FGM planar frame involving fuzzy uncertainties in material properties, loads, and connection rigidities, are examined as numerical demonstrations. Fuzzy displacement responses are investigated. It is demonstrated that relatively accurate membership functions of the fuzzy displacements can be obtained by the proposed fuzzy procedure. The method proposed in this study is superior to the traditional vertex method and the global optimization approach in terms of computational efficiency. Furthermore, it is revealing that the presence of uncertainties in connection rigidities can enlarge the fuzziness of the displacement outputs significantly.

Behavior of semi-rigid steel frames under near- and far-field earthquakes

The realistic modeling of the beam-column semi-rigid connection in steel frames attracted the attention of many researchers in the past for the seismic analysis of semi-rigid frames. Comparatively less studies have been made to investigate the behavior of steel frames with semi-rigid connections under different types of earthquake. Herein, the seismic behavior of semi-rigid steel frames is investigated under both far and near-field earthquakes. The semi-rigid connection is modeled by the multilinear plastic link element consisting of rotational springs. The kinematic hysteresis model is used to define the dynamic behavior of the rotational spring, describing the nonlinearity of the semi-rigid connection as defined in SAP2000. The nonlinear time history analysis (NTHA) is performed to obtain response time histories of the frame under scaled earthquakes at three PGA levels denoting the low, medium and high-level earthquakes. The other important parameters varied are the stiffness and strength parameters of the connections, defining the degree of semi-rigidity. For studying the behavior of the semi-rigid frame, a large number of seismic demand parameters are considered. The benchmark for comparison is taken as those of the corresponding rigid frame. Two different frames, namely, a five-story frame and a ten-story frame are considered as the numerical examples. It is shown that semi-rigid frames prove to be effective and beneficial in resisting the seismic forces for near-field earthquakes (PGA = 0.2g), especially in reducing the base shear to a considerable extent for the moderate level of earthquake. Further, the semi-rigid frame with a relatively weaker beam and less connection stiffness may withstand a moderately strong earthquake without having much damage in the beams.

Evaluation of responses of semi-rigid frames at target displacements predicted by the nonlinear static analysis

Responses of semi-rigid frames having different degrees of semi-rigidity obtained by the nonlinear static analysis (NSA) are evaluated at specific target displacements by comparing them with those obtained by the nonlinear time-history analysis (NTHA) for scaled earthquakes. The peak ground accelerations (PGA) of the earthquakes are scaled such that the obtained peak top story displacements match with the target displacements. Three different types of earthquakes are considered, namely, far-field and near-field earthquakes with directivity and fling-step effects. In order to make the study a comprehensive one, three degrees of semi-rigidity (one fully rigid and the other two semi-rigid), and two frames having different heights are considered. An ensemble of five-time histories of ground motion is included in each type of earthquake. A large number of responses are considered in the study. They include the peak top-story displacement, maximum inter-story drift ratio, peak base shear, total number of plastic hinges, and square root of sum of the squares (SRSS) of the maximum plastic hinge rotations. Results of the study indicate that the nonlinear static analysis provides a fairly good estimate of the peak values of top-story displacements, inter-story drift ratio (for shorter frame), peak base shear and number of plastic hinges; however, the SRSS of maximum plastic hinge rotations in semi-rigid frames are considerably more in the nonlinear static analysis as compared to the nonlinear time history analysis.

IMPACT OF INTRODUCING SEMI-RIGID MOMENT FRAMES ON SEISMIC RESPONSE OF BRACED FRAMES

Maximum seismic inelastic drift demand in a steel building with braced frames as primary seismic-force-resisting (SFR) system tends to concentrate in few stories without considering inherent participation of designed gravity-force-resisting (GFR) system in actual structural stiffness and strength. The influence of GFR system on stiffness and strength can be taken into account by considering the composite action in beam-to-column shear connections that exist in modern steel building construction to form actual semi-rigid moment-resisting frames. Therefore, modeling semi-rigid moment frames as an equivalent to the GFR system in braced frame buildings could be utilized as a representative to the strength provided by gravity frames. This paper presents a seismic evaluation of a six-story chevron braced frame, with and without semi-rigid moment frame. Four different cases are investigated under a set of ground motions and results are discussed in terms of story drift distribution along the height. The results pointed out that the current findings lay a foundation to conduct further investigation on the seismic performance of braced frames as designed SFR system together with GFR system.

Cold-formed steel ledger-framed construction floor-to-wall connection behavior and strength

The objective of this paper is to investigate the moment-rotation behavior of floor-to-wall connections used in ledger-framed cold-formed steel building construction with full-scale experiments. Recently completed research employing full-scale shake table tests on a two-story ledger-framed cold-formed steel framed building utilizing oriented strand board (OSB) sheathed shear walls and floors exhibited beneficial lateral system response that exceeded predictions. One hypothesis is that the stiffness of the floor-to-wall connections, and the repetitive nature of this connection, provided beneficial semi-rigid frame response that augmented the designed shear walls. Monotonic and cyclic full-scale connections were tested and reported here to examine the connection strength and stiffness, so that this hypothesis may be explored further in the future. The test matrix is designed to evaluate the presence of OSB floor sheathing, applied moment/shear ratio of the joist, joist-to-ledger clip angle location (inside or outside of the joist section), presence of top and bottom screws connecting the joist and ledger flanges, and location of the joist relative to the studs. The results indicate how the connection details and loading conditions drive the moment-rotation response; in addition, several limit states not checked in current design were also observed. Current design for this connection assumes a pure shear condition governed by screw shear capacity. However, ledger-to-stud screw pull-out, ledger flange buckling, and stud web crippling limit states are all observed in the testing. Design methods to support strength predictions consistent with the observed limit states are developed and assessed. The testing provides needed characterization of cold-formed steel floor-to-wall performance and is augmented by improved design methods for this detail.

Experimental study of the lateral performance of a steel stud wall with a semi-rigid connected frame

Recently, a new type of lightweight steel structural system has been developed: a steel stud wall with a semi-rigid connected frame. The lateral resistance of this system was investigated in this study. Eight tests were conducted on seven steel stud walls with steel frames and one with a semi-rigid frame. The specimens were subjected to cyclic loading. The failure process, bearing capacity, stiffness, and energy dissipation capacity of each specimen were compared and analyzed. Test results showed that the steel stud structure significantly improved the lateral bearing capacity and stiffness of the semi-rigid steel frames, resulting in good hysteretic behavior and energy dissipation capacity. Reducing the spacing or increasing the section of vertical steel tubes can improve bearing capacity and stiffness, but only slightly influences the structure’s energy dissipation capacity. An excessive number of welded joints will increase welding residual stress and residual deformation, decreasing the lateral resistance of the structure due to the thinness of the square steel tube. The oriented strand board contributes considerably to the bearing capacity and stiffness of the structure, and is thus an important load-bearing component of the steel stud wall. The energy dissipation performance and ductility of the structure are mainly provided by the square steel tube and semi-rigid steel frame. In addition, the “pinch” phenomenon of the hysteretic curve is mainly caused by the cover board.

Seismic tests and numerical investigation of blind-bolted moment CFST frames infilled with thin-walled SPSWs

This paper aims to investigate the seismic response of blind-bolted moment concrete-filled steel tubular (CFST) frames infilled with thin-walled steel plate shear walls (SPSWs). Tests of two-storey blind-bolted circular or square CFST frames with thin-walled SPSWs subjected to horizontal low-cyclic loading were performed. Macroscopic finite element (FE) models of the specimens were primarily established by fibre beam-column elements, zero-length springs, and truss elements. The numerical simulation results were verified by the experimental data. A parametric analysis was conducted to analyse the influence of the axial load level, material strength, and height-thickness ratio of the steel plate etc. on the hysteresis behaviour and energy dissipation of blind-bolted moment CFST frames with thin-walled SPSWs. In addition, the mechanics of the semi-rigid frame with SPSWs were compared with the pinned and rigid frames with SPSWs using mechanical analysis model and FE model. The experimental and analytical results show that the blind-bolted moment CFST frames with SPSWs connected to the beams only exhibit preferable hysteretic response, ductility and energy dissipation. The peak strength, initial stiffness and energy dissipation of blind-bolted moment CFST frames infilled with thin-walled SPSWs can be significantly affected by the axial load level as well as the steel plates' yield strength, height-thickness ratio, aspect ratio, and connection type.

Analytical Model for Initial Rotational Stiffness of Steel Beam to Concrete-Filled Steel Tube Column Connections with Bidirectional Bolts

AbstractThe initial rotational stiffness of connections is important for the design of semirigid frames. However, most current studies on steel beam to concrete-filled steel tube column connections...

Lateral performance of a semi-rigid timber frame structure: theoretical analysis and experimental study

Semi-rigidness of the joint connections is one of the main characteristics of timber structures. The pin-joint assumption for the semi-rigid joint connections might be not conservative in the timber structural design. In this paper, structural analysis was conducted on a semi-rigid timber portal frame; the formulas were derived in terms of the internal force and the lateral stiffness, and the influence of the semi-rigid connections was discussed. Moreover, experimental tests were performed on three full-scale timber portal frames and five bolted timber connections to study the lateral performance of the frames and the moment resistance of the connections. For consistency, the connections from the portal frames and the connections for bending tests were of the same configuration. Finally, a calculation flowchart of the lateral performance on a semi-rigid frame was presented to verify the derived formulas and to show a framework of the lateral structural design process.

A shear-deformable beam model for stability analysis of orthotropic composite semi-rigid frames

In this paper, a shear deformable beam model for nonlinear stability analysis of frames made of composite materials is presented. Each wall of the cross-section is assumed to be orthotropic in such a way that normal stress does not cause shear strains to occur. The incremental equilibrium equations for a straight thin-walled beam element are derived within the framework of updated Lagrangian formulation and the nonlinear displacement field of cross-sections, which accounts for the restrained warping and the large rotations effects. Timoshenko’s theory for non-uniform bending and modified Vlasov’s theory for non-uniform torsion are applied to include the shear deformation effects. The coupled bending-torsion shear deformation effects occurring at the asymmetric cross-section are also included in the model. To account for the semi-rigid connection behaviour, the hybrid finite element is introduced through the special transformation procedure. Several benchmark examples are demonstrated for verification purposes. The obtained results indicate that the proposed model can be classified as shear locking-free one.

Dynamic response characteristics of steel portal frames having semi-rigid joints under sinusoidal wave excitation

To demonstrate the characteristics of the nonlinear response of steel frames, an elastic dynamic response analysis of the semi-rigid frame is performed under the harmonic wave. The semi-rigid contact is represented by the alternating spring which is given stiffness by a three-parameter energy model which approaches the hysterical curve by hardening model. The properties of spectra and hysteric curves are presented. This study shows that (1) the greater the acceleration input capacitance the smaller the instant connection capability and the smaller is the response. (2) However, by allowing an extreme increase in capacitance input acceleration, response spectra can be increased as the contact stiffness results near zero.

ANALYSIS OF SPACE FRAMES WITH GENERALIZED SEMI-RIGID CONNECTIONS

A mechanical model and analytic method are proposed, in which, the axial, the shearing and the bending semi-rigid characteristics of space frames are taken into account. An independent zero-length connection element comprising six translational and rotational springs is used to simulate the beam-to-column connection. The model, namely six-spring mechanical model, has an advantage that the element number of structure does not increase. The matrix displacement method is used to analyze mechanism of the model, including element analysis and structural analysis. The stiffness matrix of the element is derived. Some reaction forces at the end of the element are obtained when it is subjected to two kinds of different loads respectively. The obtained stiffness matrix gets the characteristics of symmetry and singularity and that makes the size of total stiffness matrix for semi-rigid frame the same as that for frame with rigid joints.

Investigation of Seismic Behaviour of Steel Pallet Rack Frames

One of the most significant uses of cold-formed members is for steel storage racking structures, such as pallet, drive in, and drive through racking systems. In the current competitive industry, pallets and storage racks may support heavy loads that have the potential to injure workers and damage equipment if the pallets and racks fail and loads fall. Hence, storage racks must remain structurally sound. Additionally, when subjected to earthquake loading, they can exhibit very large transverse displacement. In spite of their complexity, racks are able to carry heavy loads, though they are designed as lightly as possible, and industries often rely on 3-dimensional Finite Element Analysis to achieve this objective. This study, presents a Finite Element model of a conventional rack structure modeled using the commercial software SAP2000. In order to investigate the seismic behaviour of rack frames under real earthquake ground motions, the Time History Analysis was performed with rigid, semi-rigid and pinned connections. The study provided a strong case for the possible benefits of semi-rigid steel frames and motivated the need for detailed, accurate, and reliable analytical models of the connection. Neglecting semi-rigidity cause stiffening of frames resulting in shorter fundamental period and larger lateral displacement which in turn results in a significant error in the evaluation of dynamic loads.

Seismic performance of mid-rise steel frames with semi-rigid connections having different moment capacity

Seismic performance of hybrid steel frames defined as mixture of rigid and semi-rigid connections is investigated in this paper. Three frames with 10, 15 and 20 stories are designed with fully rigid connections and then with 4 patterns for semirigid connection placement, some of beam to column rigid connections would turn to semi-rigid. Each semi-rigid connection is considered with 4 different moment capacities and all rigid and semi-rigid frames consisting of 51 models are subjected to 5 selected earthquake records for nonlinear analysis. Maximum story drifts, roof acceleration and base shear are extracted for those 5 earthquake records and average values are obtained for each case. Based on numerical results for the proposed hybrid frames, story drifts remain in allowable range and the reductions in the maximum roof acceleration of 22, 29 and 25% and maximum base shear of 33, 31 and 54% occur in those 10, 15 and 20-story frames, respectively.

Temperature analysis of extended end plate joints to square CFST columns in fire

Purpose This paper aims to obtain fire resistance of semi-rigid joints for concrete-filled steel tubular (CFST) composite frames and temperature filed distribution of composite joints in fire. Design/methodology/approach The temperature filed model of semi-rigid joints to CFST columns with slabs was made by using ABAQUS finite element (FE) software, in considering temperature heating-up stage of fire modelling. The effects of composite slab, fire type and construction location were discussed, and the model was verified by the test results. The temperature distribution of composite joint under three-side or four-side fire condition was studied by the sequentially coupled thermal analysis method. The temperature versus time curves and temperature distribution of various construction and location were analyzed. Findings The paper provides FE analysis and numerical simulation on temperature field of semi-rigid joints for CFST composite frames in fire. The effects of composite slab, fire type and construction location were discussed, and the model was verified by the test results. It suggests that the temperature distribution of composite joint in three- or four-side fire condition showed a different development trend. Research limitations/implications Because of the chosen FE analysis approach, the research results may lack generalizability. Therefore, researchers are encouraged to test the proposed propositions further. Practical implications The research results will become the scientific foundation of mechanical behavior and design method of semi-rigid CFST composite frames in fire. Originality/value This paper fulfils an identified need to study the temperature field distribution of the semi-rigid joints to CFST columns and investigate the mechanical behavior of the semi-rigid CFST joints in fire.

Computational modelling of the moment-rotation relationship for deconstructable flush end plate beam-to-column composite joints

This paper presents a three-dimensional finite element modelling of an innovative flush end plate semi-rigid beam-to-column composite joint comprising deconstructable post-installed friction-grip bolted shear connectors. The moment versus rotation relationship for these prototype joints subjected to a hogging bending moment with the influence of partial shear connection is investigated using ABAQUS software. This relationship is an indicator of the ductility of a composite joint and is a necessity for a semi-rigid frame analysis. A detailed finite element model of the connection region including the precast concrete slab, steel beam, flush end-plate, bolted shear connectors and the steel column is developed in the paper. Material and geometrical non-linearities as well as the non-linearity of the interfaces are incorporated in the model. The accuracy and reliability of the numerical formulation are verified against experimental data reported elsewhere. In addition, a composite joint with partial shear connection is constructed and tested in this study, and the numerical predictions are compared with the test results. An extensive parametric study is then conducted, using several parameters that include the degree of shear connection, reinforcement ratio, thickness of the precast concrete slab, spacing of bolted shear connectors, size of the bolts in the connection zone, thickness of the flush end plate, steel grade for the beam, column and end plate and the column flange thickness. Finally, moment versus rotation models for deconstructable flush end plate beam-to-column composite joint are proposed, and it is demonstrated that the design models developed can also be used for composite joints with high strength steel components.