Plastic Beam Research Articles

Damage detection in composite and plastic thin-wall beams by operational modal analysis: An experimental assessment

The detection and localization of different damage features in thin-wall beam composite and plastic beams using Operational Modal Analysis (OMA) has been demonstrated experimentally. The detection of small damage features using modal analysis techniques is an emerging field, with few experimental OMA-based assessments having been reported so far. The proposed method is based on OMA combined with Stochastic Subspace Identification (SSI) and the enhancement of damage features by Continuous Wavelet Transforms (CWT). A composite thin-wall beam (CTWB) structure in two measurement configurations and a PVC tube in a free-free configuration have been tested. Damage features detected include extra masses attached to the beam, with a range from 9.5 % to 14.0 % of the beam mass, and small cracks perpendicular to the beam axis with lengths of about 4 % of the perimeter of the cross section. Calibration curves relating the strength of the damage signal with the weight of the attached masses have been constructed. Two simultaneous cracks or two masses could be detected as well. The quantification and localization of damage feature along the beam was possible through the use of Gaussian fit surface applied to damage maps obtained with the CWT technique. The width of the Gaussian fit curve was of the order of the distance between accelerometers, but the accuracy, estimated to be around 3 % of the beam length, was found to have sub-grid resolution. The proposed method was shown to work reliably with a relatively coarse measurement grid, potentially allowing for cost-effective Structural Health Monitoring (SHM) approaches.

Numerical modeling of beam plastic hinges in steel moment resisting frames including local buckling and stiffness/strength degradation

Plastic hinge formation in beams is the main energy dissipation mechanism in moment resisting frames, but its deformation capacity is limited by the strength deterioration after reaching the maximum moment. Such degradation is highly influenced by the onset of local buckling in the plastic hinge region once a significant portion of the cross-section has reached the yield stress. Numerical models developed to study this effect have shown good accuracy against experimental data, but with high computational costs and the need to calibrate several model parameters. This work proposes a numerical model of a beam plastic hinge that uses only one parameter to reproduce the hysteretic behavior under cyclic loading, degrading simultaneously stiffness and resistance with lower computational cost. The proposed model relies on the discretization of the beam cross-section using uniaxial bars with a prescribed geometric imperfection with buckling degrading strength capability spanning along an assumed plastic hinge length. The Euler-Bernoulli hypothesis is imposed at the ends of the plastic hinge region and elastic beam elements are used to model the beam outside this domain. The model is validated against experimental data from three cyclic loading connection tests reported in the literature. Results show that the model can accurately represent the response of the beam plastic hinge with a low computational cost by adjusting one single model parameter as well as the definition of the nominal information of the beam geometry and material properties, expected plastic hinge length, and standard fabrication tolerances.

Seismic performance of a novel concrete-filled steel tube column to continuous reinforced concrete beam joint with multiple openings in the core region

This study developed a novel concrete-filled steel tube column to continuous reinforced concrete beam joint with multiple openings in the core region, aiming to eliminate field welding and improve construction efficiency. To evaluate the seismic performance of the joint, six full-scale specimens were tested under cyclic loading, which and a series of numerical simulations were implemented upon refined models. The effects of reinforcement ratio, steel tube thickness, and concrete strength on the failure mode and the mechanical performance degradation of the joint were quantitively evaluated. The results indicated that depending on the beam-column flexural capacity ratio, three typical failure modes, i.e., compression bending failure at the column end, shear failure at the joint core region, and flexural failure at the beam plastic hinge region, were observed. Among them, the flexural failure-dominated joint possessed the best energy dissipation capacity and a high ductility coefficient greater than 3.72. Moreover, increasing the thickness of steel tube within the core region can effectively compensate for the reduction of seismic performance caused by multiple openings, and a preliminary value of at least 2.5 times the thickness of column steel tube is recommended. This novel joint configuration exemplifies a balance between structural integrity, construction efficiency, and mechanical performance, rendering it a feasible alternative for frame structure in seismic-prone regions.

Variability of strength and stiffness assessment for non-profile beam structures

Introduction. Traditional ways to increase the structural strength and stiffness of beams are now almost exhausted, and optimization of production and operation technologies is mostly based on the use of new materials and increasing their reliability as bearing elements of a complex geometric profile. Bearing elements of building structures operate under high loads and, even despite their predominantly static nature, experience a complex volumetric stress and strain state, which can scarcely ever be confirmed empirically and statistically.Aim. To propose an approach to assessing the strength and stiffness of beam structures operating under conditions of transverse bending of a complex geometric profile.Materials and methods. Classical energy methods, including Castigliano, Maxwell–Mohr and Vereshchagin methods (moment area method), have been used to assess the strength and stiffness of non-profile beam structures, initial parameters, differential equations of the deflection curve.Results. The similarity parameters (fitting criteria) of Mises–Hencky and Zhurkov reflect the behavior of a brittle or plastic beam material reasonably well. These characteristics are proposed to be combined in the Arrhenius–Zhurkov durability functions.Conclusions. The dependencies given in the calculations can be recommended for improving the flexural static and fatigue strength, as well as the stiffness of the bearing elements of building structures.

Selective online model updating in hybrid simulation of a full‐scale steel moment frame

AbstractThis study presents the implementation of an online model updating algorithm within a full‐scale hybrid simulation (HS) of a six story, four bay steel moment frame. The experimental substructure consists of a cruciform subassembly generating critical data on the nonlinear behavior of the first story column and two beams with reduced beam sections (RBSs) on each side. The updating algorithm focuses on the modeling parameters of plastic hinge elements representing the RBSs in the numerical model. A smooth plasticity model is utilized for beam plastic hinges with updating parameters identified from on‐line experimental data through a modified version of the unscented Kalman filter. The HS shows that the numerical beam hinges based on simple hysteretic model with updated parameters are able to capture the characteristic behavior observed in experiments. Due to fracture of beam flanges is observed in the experiments, a selective updating concept is proposed to allow for updating multiple numerical components accounting for asymmetric behavior and variability in the response. The selective updating method is validated through virtual HSs that are better able to identify and isolate the effects of fracture and other behavioral characteristics. The combination of results from physical and virtual tests highlights the benefits of model updating on the local and overall system‐level response.

Cyclic behavior of high-strength steel beam-to-column welded flange-bolted web connections

Four Q690 high-strength steel beam-to-column moment connections, which use welded joints between beam and column flanges as well as a bolted beam web to the column flange, were tested under cyclic loading. The effects of beam-to-column welding details and panel zone strength were studied. Two pairs of welded flange details were incorporated, including the Chinese code-specified complete-joint-penetration (CJP) welded connections with backing plates where the bottom backing plate is reinforced by a fillet weld, and enhanced CJP welded connections with backing plates removed, weld roots backgouged, and further reinforced by fillet welds. Three panel zone thicknesses were designed to characterize strong, intermediate and weak panel zones, respectively. The test results show that backing plates should be removed in these moment connections to prevent brittle weld fracture, but still rendering only limited plastic hinge rotations in the order of 0.01–0.02 rad in the beam end before ductile fracture of the beam flange. The panel zone, however, survived even after a plastic shear rotation of 0.03 rad, demonstrating much higher plastic deformation capacity than the beam plastic hinge. This suggests that ductility can be exploited in 690 MPa high-strength steel panel zones, but not reliably in 690 MPa steel beams.

A closed-form structural stress-strain relation and implications on plastic design limits in codes and standards

The deformation of elastic-perfectly plastic beam or plate under combined through-thickness membrane and bending stresses (i.e., structural stress) is analyzed in this paper. Closed-form solutions of “plane-remains-plane” strain (i.e., structural strain) distribution as a function of applied stress and yield strength is derived. The relationship between structural stress and structural strain is also revealed for gaining insights on not only the plastic collapse conditions, but also through-thickness deformation behaviors leading to limit state. Based on the closed-form strain solutions, four deformation modes are identified: (1) elastic, (2) one-side yielding, (3) two-side yielding, and (4) plastic collapse. A membrane-bending stress interaction diagram is constructed to depict four zones that are associated with the four deformation modes in the normalized membrane and bending stress space. Closed-form solutions of residual stress, residual strain, and structural stress range-strain range relation after a loading-unloading cycle are also derived. Based on the parabolic plastic collapse stress limit curve, parabolic design stress limit curves with coherent safety margins for any combinations of membrane and bending stresses are constructed. The new insights gained in this study offer a more consistent definition of design stress limit than those used in the current codes and standards, e.g., ASME BP&V Code.

Damage analysis of a pseudoclassic reinforced concrete frame structure under the action of the Ms 6.8 Luding earthquake in China

Reinforced concrete (RC) moment-resistant frame structures are very commonly used worldwide. However, previous earthquakes have revealed the occurrence of strong beam–weak column (SBWC) failure, causing heavy human casualties and economic losses. This study analyzed the SBWC failure mechanism in RC frame structures with the pseudoclassic construction named "Que Ti" near the top of a slope topography, based on the author's recent investigation of the Ms 6.8 Luding earthquake in China. Eight refined finite element models (FEMs) were developed to simulate and analyze the influence of slope topography, pseudoclassic construction, and some structural characteristics on structural damage during an earthquake. Furthermore, discussions on using column-to-beam flexural strength ratios (CBFSRs) to mitigate SBWC failure are presented. The results demonstrated the proposed FEMs effectively simulated the performance of the pseudoclassic structure, especially the SBWC failure mode, as validated by their consistency with the observed structural damage during the earthquake. Moreover, it revealed that structures closer to the slope top experienced amplified ground motions during earthquakes, resulting in more severe damage. In addition, the Que Ti and infill walls increased the vulnerability to column damage and maximum requirement for the column shear force. Finally, to achieve the design objective of a strong column–weak beam (SCWB), the CBFSR should be at least increased to 1.8 for this pseudoclassic RC frame. This ensures a probability of the SBWC failure mode of less than 17% (meet less than 20% of recommendations) and proportion of the beam plastic energy dissipation exceeding 80% of the total plastic energy dissipation. The findings of this study are significant for enhancing seismic design and preventing earthquake disasters for the pseudoclassic structure.

Cyclic behavior of UHPC corner beam-column joints under bi-directional bending

Design codes contain special provisions for anchorage lengths of flexural reinforcement and amount of transverse reinforcement in beam-column joints, to safeguard against joint failure and possible structural collapse. However, those stipulations could lead to congested joints with construction problems such as segregation. This study leverages experimental testing of eight corner beam-column joints under constant axial and cyclic bi-directional bending loads. In addition to being one of few on corner joints under a complex and practical loading, the study’s main aim is to evaluate the effectiveness of ultra-high-performance concrete (UHPC) as a joint fill in lieu of normal strength concrete (NSC). Brittle failure, either by pure shear or shear combined with yielding of beam reinforcement occurred in all NSC joints and varied in shape and intensity depending on the column depth-to-beam longitudinal bar diameter (hc ⁄db) ratio and spacing of transverse beam/column reinforcement. Ductile failure characterized by the yielding of beam reinforcement and plastic hinge at the beam-joint interface occurred in all UHPC joints and was independent of the two aforementioned variables. The application of UHPC in the joint region resulted in increasing the joint ultimate strength by 27.6–54.8%, energy dissipation by 24–163%, and stiffness by 20 to 50%, compared to NSC joints. Such results were obtained when no transverse reinforcement is used in the joint, and only half transverse reinforcement is used in the beam/column members, and with hc ⁄db relaxed to 38% of the code recommended ratio, highlighting the advantages of UHPC joints. Predictions of ACI-ASCE 352R code were found to be overly unconservative and in need of future improvement.

A 3D distributed plasticity beam–column element for metal structures considering tangential stresses and warping with minimal DOFs

The fiber model evaluates the normal stress at a number of points over the section for a given strain increment following the plane section assumption and, by integration, axial force and bending moments. The interaction with tangential stresses is usually neglected at the point level due to the inaccurate tangential strains of the kinematics. This work proposes a generalization of the fiber model able to capture automatically the interaction among all stress components. A preliminary cross-section analysis based on the Saint Venant problem provides an accurate 3D strain as a function of the section generalized strains. This field, accurate also in the inelastic case, is exploited to impose at each section point a 3D von Mises elasto-plastic law, obtaining by integration all the resultants and moments with a full interaction. Non-uniform warping is also easily included. The section model is implemented in a mixed 3D beam–column finite element with equilibrated stress field, accurate with a minimal mesh. Numerical tests show the excellent prediction of the proposal compared to analytical and solid FEM solutions also for structures not flexure-dominated. Its efficiency, on the same order as a standard fiber model, makes the approach suitable also for large buildings.

Cyclic Behavior of the Column-Tree Moment Connection with Weakened Plates: A Numerical Approach

The use of column-tree connections is common in controlled shop environments due to their cost-effectiveness in achieving ductile welds. Field bolts are also easy to install and inspect. However, there is currently no prequalification available for these connections, their performance is not fully understood, and the cost of aftermath repairs is still a major concern for owners. In this research, analytical and numerical studies were performed to assess the cyclic behavior considering the effects of the bolted splice location, bolt slippage, and splice plate thickness. Fourteen numerical models using the finite element method in ANSYS software were analyzed to evaluate the nonlinear behavior of moment connection configurations in terms of the strength, stiffness, ductility, energy dissipation, and overall cyclic response. The results showed that appropriately proportioned bolted splice connections can meet the requirements for prequalified moment connections. The models complied with the criteria established in AISC 358 and achieved flexural resistance that was higher than 80% of the beam plastic moment at 4% of the interstory drift ratio. The weakened plates concentrated the inelastic action, which allowed us to prevent the brittle behavior and damage to the column, welding, and other components of the moment connection. Complex geometries or specially fabricated parts were not required, providing a cost-effective way to control seismic-related damage. Also, required repairs are based on the replacement of standard parts, reducing operational detentions in facilities. Finally, the moment connection studied is classified as partially restrained (PR) according to the requirements established in AISC 360.

Experimental investigation of steel frames made of hybrid steel welded I‐sections

AbstractAn experimental investigation into the structural behaviour of steel frames made up of hybrid steel welded I‐section members is presented in this paper. The tested hybrid steel welded I‐section profile had quenched and tempered S690 steel flanges and an S355 steel web. The experimental programme comprised four two‐dimensional, single storey, single bay frames subjected to different combinations of horizontal and vertical loading, thus enabling different beam, sway as well as combined beam and sway plastic collapse mechanisms to be examined. The frames were fully laterally restrained using a bespoke lateral bracing system to ensure that no out‐of‐plane instability phenomena were experienced during testing. The experimental setup, loading schemes, instrumentation and key experimental results are reported. The experimental results are fundamental to developing an understanding of the behaviour of hybrid steel welded I‐sections at the structural system level. Further research is underway to underpin the development of suitable design rules for steel frames made of such hybrid steel welded I‐section members.

A SDoF Response Model for Elastic–Plastic Beams under Impact at Any Point on the Span

This study aims to investigate the elastic–plastic response of a clamped-clamped beam struck by a rigid heavy mass with a low velocity at any point on the span. The impact system is simplified as a single-degree-of-freedom (SDoF) mass-spring model to formulate the beam’s equations of motion during loading and unloading. With the consideration of material elasticity and large deflection, elastic–plastic analytical solutions are derived to predict the global deformation behavior of the beam. Validation and comparison are conducted against numerical simulations performed using ABAQUS, and satisfactory agreement is achieved for the predictions of the structural dynamic behavior. Meanwhile, a parametric study is presented to assess the influence of the impact location on the characteristic response parameters, which suggests that the structural stiffness increases as the impact location approaches the beam’s support. The findings drawn from analytical and numerical studies can be useful in the anti-impact design of engineering structures.

Static behavior of TOBs bolted endplate connection to strengthened HSST with fixed thread length

Five thread-anchored one-side bolts connected endplate connections to Hollow Square Steel Tube (TOBEC-HSSTs) with various strengthening measures were tested to investigate the structural performance under monotonic loads. The thread anchored length was 1.2 times the bolt diameter for all specimens. The connection behaviour were influenced by the endplate thicknesses and the strengthening measures (i.e. the internal polygonal tube, the internal polygonal tube with infilled concrete, and the cross-H section stiffener with infilled concrete). The failure patterns, moment-rotation curves, and strain response of joints were obtained through tests. It was found that (1) 1.2 times the bolt diameter was taken as the safe thread assembled length, which can avoid the premature failure of hole threads not before the fracture of other components under monotonic loads. (2) The presence of the infilled concrete can improve the rigidity and strength of the connection by 84% and 23%, respectively, compared to the reference joint without the infilled concrete, and the thickness of the column wall can be reduced when the concrete was infilled into hollow steel tube. (3) For the connections with thin endplates, the cross-H section stiffener exhibited 8.8% and 3.5% higher preliminary stiffness and yield bending moment than the inner polygonal tube, but the cross-H section stiffener had 14.3% lower rotation capacity. (4) Thickening endplates can change the failure modes of the connections to beam plastic hinge formation, enhance the preliminary stiffness and yield bending moment of joints by 2.4% ∼11%, but decrease the rotation capacity of joints by 54% compared to thin endplates. Based on experimental results, the calculation methods of the bending moment bearing capacity for TOBEC-HSSTs considering the strengthening effect of internal stiffeners and infilled concrete under different failure patterns were proposed with errors no greater than 15%.

Cyclic behavior of a novel bolted beam-to-box column connection with reduced beam section

The present research investigates the seismic performance of innovative subassemblages in built-up box columns with reduced beam sections (RBS) technique through the finite element (FE) analysis method. The configuration of the subassemblages additionally benefits from having an extended endplate connection, which allows the subassemblages to be erected quickly and at a lower cost. So far, there has been very little detailed research on RBS moment connections in box columns with extended bolted endplates due to the closed shape of box columns and difficulty of accessing the column inside for developing a reliable load path. To solve these complexities, a novel configuration called “Reduced Bolted Extended Endplate accompanied by Stub Beam (Reduced BEEP-SB)” is introduced. The new load transfer mechanism of the subassemblages is described. Furthermore, 35 various exterior beam-to-column subassemblages are modelled in ABAQUS/STANDARD FE analysis software and tested under the connection qualification cyclic loading conditions. The results indicate that the proposed subassemblages can push away plastic hinge formation at an appropriate distance from the column endplate interface. Also, the flexural capacity of subassemblages is approximately 10–20% higher than the beam plastic moment capacity. Moreover, the results in terms of moment-rotation curves and strain in critical sections show that the models without continuity plates could satisfy the connection qualification criteria. It is noteworthy that the accuracy of the introduced models was validated via two experimental models.

Development and seismic performance evaluation of New high strength reinforced concrete column and steel beam (New-RCS) joint

Reinforced Concrete column and Steel beam (RCS) structural systems have recently become popular in Taiwan for office buildings. High seismic demand makes the size of conventional concrete columns enormous and the reinforcement over-crowded, which can be solved using high-strength materials. However, due to the lacuna of research regarding the usage of high-strength materials, existing design guidelines for the RCS systems have restricted the maximum grade of steel reinforcement to 410 MPa. Also, using high-strength materials in RCS joints necessitates innovative joint detailing and design to develop sufficient joint bearing and shear strength. Thus, a new high-strength reinforced concrete column and steel beam (New-RCS) joint was developed in this study, incorporating the use of Grade 690 MPa steel as reinforcement along with Grade 84 MPa concrete. A combination of wide flange bearing plate and flange doubler plate joint detailing was developed to improve the bearing and shear capacity of the joint. Also, a design methodology based on moment–curvature analysis was proposed to include the contribution of locked longitudinal reinforcement to bearing resistance. Subsequently, two large-scale interior beam-column subassemblies were subjected to quasi-static cyclic loading to verify the seismic behaviour of the proposed joint. One specimen was designed explicitly considering the material hardening and overstrength of steel beams. While the other was designed following the Taiwanese practice, which does not explicitly consider material hardening and overstrength but implicitly does it through strength reduction factors. Both the specimens exhibited a drift capacity of 4% with a stable and ductile hysteretic response and eventually failed through beam plastic hinging.

Power spectral density moment of having defective 3D printed plastic beams under moving load based on deep learning

Power spectral density moment of having defective 3D printed plastic beams under moving load based on deep learning

Advancement Study in Jumbo Beam-Column Connection Using Tubular Flange Cut and Web Cut Reduced Beam Section

Abstract: There is an increasing demand for jumbo shapes in the construction of high-rise buildings. Super jumbos are very heavy rolled wide flange sections with up to 140 mm flange thickness and weigh up to 1377 kg/m. However, there is a lack of knowledge of the behavior of these types of construction, especially under seismic loading. In this paper, a tubular reduced section (RBS) is designed. A tubular reduced beam section (RBS) is made by replacing a part beam with a steel tube at a suitable location of the beam plastic hinge.

State-of-art summary of the strength hierarchy assessment and its applications

Strength hierarchy assessment is a method developed to be able to identify the governing failure mechanisms at reinforced concrete (RC) beam-column joints. The main failures that can be identified in this method are: i) beam plastic hinge; ii) column plastic hinge/shear failure; iii) beam-column joint shear failure. Through the identification of the governing failure mode in a joint, the validity of the capacity design principles can be checked for the considered RC beam-column joint. The obtained observations can then be used in finding the most optimal repair/strengthening application. This method has been going through updates and developments in the last decade and new applications have emerged. In this article, a state-of-the-art summary of the procedure is reported with its most recent updates as well as its practical engineering applications.

Response of Seismically Damaged Steel Reduced Beam Section Joints under Fire

The behaviour of seismically damaged steel joints with reduced beam section (RBS) at elevated temperatures has not been widely investigated yet. Therefore, the study summarized in this article aimed to (i) analyse the response of RBS joints at high temperatures and (ii) investigate the influence of plastic damage, due to cyclic loading, on the fire performance of the joints. A set of RBS joints with rib stiffeners on the both lower and upper beam flanges was designed according to European standards and the following parameters were considered: (i) location of the joint (i.e., internal or external joint) and (ii) reduction in the beam flexural resistance (i.e., 65% or 80% of the beam plastic moment). The mechanical response of these joints was simulated by means of finite element models (FEM). The accuracy and effectiveness of the adopted modelling assumptions to mimic the seismic response of the joints were validated against experimental results available from the existing literature. The numerical results highlight that under cyclic loading, all investigated joints exhibit ductile behaviour, allowing the concentration of the plastic deformation within the reduced segment of the beam. The designed reduction in the beam flexural resistance influences the joint fire performance, being impaired in the cases with lower flexural resistance. In contrast, the imposed cyclic pre-damage does not appreciably affect the fire resistance of the investigated joints.