Moment-rotation Curves Research Articles

Experimental and numerical investigations on flexural behavior of apex joints in aluminum alloy portal frames

Aluminum alloy portal frames (AAPFs) find extensive applications in lightweight and temporary structures owing to their light weight, excellent corrosion resistance, and ease of installation and disassembly. Existing design equations for cold-formed steel portal frame (CFSPF) apex joints are not applicable to AAPF apex joints due to significant differences in structural configuration. Therefore, dedicated research is needed to develop design guidelines for AAPF apex joints. Consequently, this paper conducts experimental and numerical investigations on flexural behavior of AAPF apex joints. Initially, bending tests are conducted on three AAPF apex joints, revealing failure modes including clamping plate buckling and beam failure. The flexural behavior of apex joints throughout the entire process is analyzed based on moment-rotation curves and moment-strain curves. Subsequently, finite element (FE) models are established and validated by comparing the FE results with the experimental results. Following this validation, parameter analysis is conducted considering the influence of beam cross-sectional dimensions, clamping plate dimensions, bolt dimensions, and layout. Finally, based on theoretical and numerical investigation, the calculation equation for the flexural capacity of AAPF joints is derived, offering valuable reference for engineering design.

Deformation ability of modular gymnasium steel inner sleeve all-bolt cross connection joint based on 3D-DIC method

Immense roof loads present a significant hurdle for the functionality of continuously supported modular connection joints in movable modular gymnasium structures. Consequently, we introduced leveraging inner sleeves and bolts to interconnect the modular units of the upper and lower columns, aiming to bolster the strength of inter-unit connections. Despite its noteworthy benefits, the deformation behavior and force distribution characteristics of this novel design remain underexplored. Hence, our study employs three-dimensional digital image correlation (3D-DIC) measurement to precisely capture the full-field displacement and strain distributions within the core area of this joint. Four distinct joint specimens were designed, and conducted comprehensive static tests, encompassing variables such as the inclusion or exclusion of inner sleeves, reinforcing ribs, and diverse loading directions. 3D-DIC detected subtle deformations and local buckling phenomena, undetectable by the naked eye, and revealed their occurrence patterns. Furthermore, the detections underscore the critical role of weld quality between beams and columns in ensuring the overall safety of the joints. The joint exhibited earlier yielding in beam bending compared to column bending. To delve deeper into this joint, we generated moment-rotation curves leveraging DIC results, deducing that this joint exhibits rigid-joint characteristics. The specimens primarily showed damage modes such as beam-root fractures or member buckling, while the core area remained intact. This observation reinforces the classification of the joint as a full-strength entity. These insights enrich our comprehension of this novel joint and serve as invaluable references and aids for designers.

Analytical models for predicting the moment‒rotation relationships of steel hub joints with bolted steel side plates in single-layer wood reticulated domes

A very popular and efficient pattern of joints adopted for wood reticulated domes is steel hub joints featuring end-bearing and bolt-connected wood members (EBBC joints). This type of joint shows clear semi-rigidity, which affects the rigidity and overall stability of the structures. This study developed analytical models for predicting the moment‒rotation curves of EBBC joints, considering the effect of axial compression. Specifically, two models termed the WR and WEP models, were developed assuming rigid and elastic-plastic constitutive behaviour, respectively, of the wood in the compression zone of the joint. A tri-linear model for the lateral force-slip relationship of bolt connections was derived. A formula for calculating the deformation modulus and predicting the shear failure of wood members under local compression was proposed and verified. The moment–rotation relationship of the joint was established with equilibrium and compatibility conditions. The accuracy of the analytical models was verified by comparison with a series of experimental results as well as the parametric study results obtained using a refined finite element model. It was revealed that both the WR and the WEP models can predict the moment–rotation relationships accurately for joints without axial compression, whereas for the case of non-negligible axial compression loads, the WEP model offers more accurate predictions. The analytical WEP model proposed in the current paper provides a versatile tool for general design practice to predict moment–rotation curves for traditional or novel EBBC joints.

Calculation Method of New Assembled Corrugated Steel Initial Support Structure of Highway Tunnel

The assembled corrugated steel initial support structure is a new prefabricated structure in highway tunnel engineering, achieving a balance between economy and safety. This study proposes a simplified calculation method and elucidates the mechanical mechanisms of assembled corrugated steel initial support structures. Firstly, the stiffness characteristics of corrugated steel plates were studied based on full-scale tests. A general equivalent stiffness coefficient table was established. Numerical simulations of corrugated steel flange joints were conducted to explore their bending mechanical properties. A two-stage rotational stiffness model for corrugated steel flange joints was proposed. Finally, a plane strain-spring simplified calculation method for the assembled corrugated steel initial support structure was developed, and the monitoring data from the Qipanshan Tunnel validated the correctness and reliability of the proposed method. The results demonstrate that (1) the plane strain-spring simplified model consists of the planar strain equivalent calculation method for corrugated steel plates and the two-line stiffness equivalent spring of the corrugated steel flange joint. The simplified model was validated as effective by monitoring data. (2) Corrugated steel plates exhibit two stages under loading, namely gap elimination and elastic stages. The elastic stage stiffness of corrugated steel plates decreases with increasing ratio of depth to pitch (RDP), positively correlating with plate thickness when the RDP exceeds 0.333 and otherwise negatively correlated. (3) Corrugated steel lining flange joints exhibit distinct elastic and plastic stages in their linear moment–rotation curves under loading.

Spatial rotational behaviour of intact and damaged column foot joints: numerical modelling

Columns in traditional Chinese timber structures barely rest on stone bases, and the column foot joints are capable of resisting moment around any direction. This study numerically investigated the spatial rotational behaviour of intact and damaged columns based on experiments. Unidirectional cyclic loading tests were carried out on two intact and three damaged column foot joint specimens. A fibre element-based numerical model for the column foot joints was developed and validated by use of the unidirectional loading test results. Numerical analyses were performed based on the fibre element-based model to obtain the rotational behaviour of the intact and damaged column foot joints under spatial loading. The analyses indicated that the moment–rotation curve of an intact column foot joint under spatial loading was on an umbrella-shaped surface. The damage at the column foot not only unidirectionally decreased the moment-resisting capacity of a column foot joint but also resulted in a rotational performance degradation valley on the moment–rotation surface of the joint. The rotational behaviour of both the intact and damaged column foot joints under spatial loading was highly non-linear. This developed fibre element-based model can be further utilised to analyse the structural performance of traditional timber structures under three-dimensional excitations.

Damaged mortise–tenon joint strengthened using an assembled spring–steel hoop based on a design of similar rotational stiffness

The excessive enhancement of rotational stiffness leads to an uneven distribution of rotational stiffness across the entire timber frame. This uneven distribution concentrates the load effect on the strengthened mortise–tenon joints (MJs), causing localized failure in advance. To address this issue, a reversible and non-destructive strengthening method for the damaged MJs is devised, involving the utilization of an assembled spring-steel hoop. The rotational stiffness of a strengthened MJ is derived from the springs that link the steel hoop of the beam and column, resembling the rotational stiffness of an intact MJ. A comparison of the measured moment-rotation curves of various types of MJ reveals that the rotational stiffness similarity necessitates the strengthened MJ's yield moment and ultimate moment, along with the associated rotation angles, to closely resemble those of the intact MJ. Secondly, a design methodology is developed for the assembled spring-steel hoop, which involves determining the parameters of the connecting spring. The comparative analysis of the hysteretic test results on multiple strengthened and intact MJs indicates that the strengthened MJs exhibit rotational stiffness deviations of less than 12.2 % during the elasticity stage and 6.6 % during the plasticity stage, in comparison to the intact MJs. A spring exhibits a lower ultimate extension compared to timber, leading to a maximum discrepancy of 37.5 % in the ductility coefficients between the strengthened MJs and intact MJs. The strengthened and intact MJs display similar patterns of stiffness reduction and energy dissipation progression.

Deformation ability of steel inner sleeve T-joint in modular gymnasia based on 3D-DIC method

Substantial loads the roofs bear exert stringent performance standards on connecting joints in movable modular gymnasiums. Previously, we introduced a novel joint design, utilizing internal sleeves and bolts to integrate the upper and lower columns of modular units. To explore the actual deformation behavior and force distribution of this joint, this study employed a three-dimensional digital image correlation (3D-DIC) measurement method to visualize its full-field displacement and strain distribution. The reliability of the 3D-DIC results was confirmed through comparison with traditional measurement methods. Building upon this solid foundation, this study proceeds to assess the static performance of this innovative joint in two distinct directions, successfully revealing micro-deformation and local buckling phenomena undetectable to the naked eye. Notably, the quality of the welds connecting the beams and columns plays a pivotal role in ensuring the overall structural integrity of the joint. Under lateral loading conditions, the destructive behavior of the joints is primarily governed by material strength. Moment-rotation curves were plotted to delve further into the mechanical characteristics of the joint, revealing that the inner-sleeve T-joint exhibits the attributes of a rigid joint. Moreover, the primary damage modes observed in the specimens were fractures at the beam root or buckling of the column, with the joint area remaining intact. Consequently, this joint qualifies as a full-strength connection. These findings will deepen knowledge and understanding of this novel joint for designers.

Seismic probabilistic assessment of steel and reinforced concrete structures including earthquake-induced pounding

Recent earthquakes demonstrate that prioritizing the retrofitting of buildings should be of the utmost importance for enhancing the seismic resilience and structural integrity of urban structures. To have a realistic results of the pounding effects in modeling process of retrofitting buildings, the present research provides seismic Probability Factors (PFs), which can be used for estimating collision effects without engaging in intricate and time-intensive analysis. To include the low-, to mid-rise buildings, the 3-Story, 5-Story, and 9-Story adjacent steel and Reinforced Concrete (RC) moment-resisting frames were modeled in OpenSees software capable to take into account the structure in a state of collapse during the analysis, which can provide the real condition of buildings under seismic excitations. Results of analysis confirmed that the impact force can considerably affect the moment–rotation curve of beams and columns, in which, it can affect the structural response of structures during earthquakes. Therefore, seismic PFs proposed to examine the possibility of changes in the performance levels and fragility assessments. Moreover, proposed PFs can be used as coefficient factors to facilitate the retrofitting process of buildings and improve the environmental effects.

Influence of Shallow Foundations on the Response of Steel Wind Towers

The objective of this study, concerning the soil–structure interaction of shallow reinforced concrete foundations of wind towers with circular cross-sections, was determination in a closed form of the monotonic moment–rotation curve of the soil–foundation complex. This study was based on elastic and plastic analyses of shallow rigid foundations assuming a Winkler soil type including the flexibility of the foundation in the elastic range and the nature of the soil (cohesive and non-cohesive types) through corrective factors of the constant of the Winkler model. The flexibility of the foundations influences the moment–rotation response through the initial rotational stiffness with a coefficient between 1 and 0.7 for a width-to-span ratio between 5 and 2. The nature of the soil is considered through corrective factors of 0.75 and 1.3 of the Winkler constant for cohesive and non-cohesive soil, respectively. Analyses carried out stressed that a possible design valued to be adopted in a steel wind tower with shallow foundations is a diameter of the steel tube 1/15 of the height of the tower, a diameter of foundation 0.75 of the length, and a depth of foundation 1/10 of the diameter and thickness of steel tower ratio diameter equal to 1/10. In this range it was observed that the effects of the soil-to-foundation interaction in the elastic range influences the critical length in the stability of the steel wind tower, with values between 2.5 and 2 (column fixed at the base) in a range of Winkler constant between 0.1 and 1 daN/cm3. Finally, an experimental validation of the proposed model was carried out with the data available from the literature.

Experimental investigation on cold-formed steel hollow sections with moderate heat treatment under combined compression and cyclic lateral loads

This paper presents an experimental investigation on cold-formed steel rectangular and square hollow sections (RHSs and SHSs) with subsequent heat-treatment under combined compression and cyclic lateral loads. A total of 25 specimens designed with different parameters, including slenderness ratios (b/t and d/t) and axial load ratio (n) ranging from 0 to 0.5 were tested. Material tests were carried out to confirm the material ductility requirements stated in Eurocode being reached. Failure modes, moment-rotation curves, secant stiffness, energy dissipation and plastic hinge length presented were analysed. In addition, deformation capacity was evaluated in terms of maximum and ultimate rotations. The comparison results between plastic rotation limits proposed by design codes and the test results indicate that AISC 341-16 is more suitable for the design of cold formed hollow sections with moderate heat treatment under this investigation, though the recommended reduction factor of axial load might be conservative.

Experimental and numerical investigation of the bending behavior in nontraditional steel beam-to-beam tip connections

This study aimed to conduct combined experimental testing and numerical studies on the static performance of tip beam-to-beam flush endplate moment connections. The research parameters considered were bolt layout, diameters, and end plate thickness. Three specimens consisting of two IPE 300 beams connected to a beam of section HEA 300 using two end plates were designed and assembled with different bolt configurations. The grade of the steel elements was S235, while that of the bolts was 8.8. A monotonic load was applied to the specimen during testing, revealing failure modes such as fractures in bolts, end plate bending, and necking loosening of bolts. The study presented and discussed the moment rotation relationship, rotation capacity, and initial stiffness for the three specimens. A finite element (FE) model was constructed based on the moment-rotation curves of the tested connections, and the numerical and experimental results showed good agreement. An extensive parametric study was conducted to investigate the effect of different end plate thicknesses and bolts of various diameters and configurations on the connection's behavior. The study revealed that increasing the bolts' row number in tension rather than increasing the number of bolts in a row significantly affects the ultimate capacity and ductility of the connection. A thick end plate increases the connection's rotation capacity but decreases its ductility. The study also introduced a simple approach based on virtual work to predict the connections' bending stiffness using load and deflection results.

A novel analytical formulation for the stiffness of the component column web panel in shear with additional plates in bolted steel joints.

Given that the stiffness of joints has an important influence on the global behavior of steel structures, considerable efforts have been made to develop methods to characterize their behavior. In the component method, that is adopted by Eurocode 3, one of the most relevant components is the column web panel in shear; however, this component has never been the subject of research when additional plates are welded between the column flanges to attach the secondary beams to the minor axis of the column. This paper proposes a stiffness formulation for the component column web panel in shear with additional plates, taking into account the stiffening contribution of these additional plates. To archive this, four experimental tests of beam-to-column joints were carried out, a finite element model was calibrated with the experimental data by comparing moment-rotation and moment-deformation curves, a parametric study of sixty different configurations was performed with the calibrated finite element models to obtain the stiffness of the component column web panel in shear and the initial stiffness of the joint. Then, the proposed stiffness formulation for the component was validated with the results of the parametric study, obtaining a very good agreement. Finally, a compilation of the stiffness formulation of all the components of the joint type extended end plate with additional plates was made and validated, when comparing this analytical stiffness with the initial stiffness of the joints of the parametric study, satisfactory concordance was found.

Comparative investigation on beam-to-beam connection with different types of connecting plates

The spliced glued laminated timber (glulam) beams have extensive applications in large-span timber structures since the length of the long solid wood beams is limited by transportation and construction. This paper investigated the flexural performance of glulam beam-to-beam connections with connecting plates and self-trapping screws. The influence of connecting plate types (steel plate, bamboo scrimber, and plybamboo plate) on the flexural performance of the spliced beams was studied. A total of 12 beams were designed, including the intact beam group (3 specimens) and the spliced beam group (9 specimens). The failure modes, ultimate bearing capacity, stiffness, moment-rotation curves, and carbon emissions of spliced beams with different connecting plates were studied. The test results showed that the failure mode of the spliced beams mainly included bending failure of glulam and fracture of the connecting plates. The average bearing capacity of the spliced beams with bamboo scrimber plates and those with steel plates could reach the intact beams. The average stiffness of the spliced beams with bamboo scrimber plates was higher than that of the splice beams with steel plates, reaching 97.6% of the intact beams. The average bearing capacity and stiffness of the splice beams with plybamboo plate reached 80.9% and 92.7% of the intact beams, respectively. A theoretical model of the spliced beams with bamboo scrimber plates was proposed and verified by tests data. Comparisons of the analytical and the test results reveal that the model can predict the moment capacity of the spliced beams with bamboo scrimber plates corresponding specific failure mode in this test.

Effect of Footing Shape on the Rocking Behavior of Shallow Foundations

Sources such as wind or severe seismic activity often exert extreme lateral loading onto the shallow foundations supporting high-rise structures such as bridge piers, buildings, shear walls, and wind turbine towers. Such loading conditions may cause the foundation to exhibit nonlinear responses such as uplift and bearing capacity mobilization of the supporting soil (i.e., rocking behavior). Previous numerical and experimental studies suggest that while such inelastic behaviors may engender residual deformations in the soil–foundation system, they offer potential benefits to the overall integrity of structures through dissipating energy and reducing inertia forces transmitted to the superstructure, thereby limiting seismic demand on structural elements. This study investigates the effect of footing shape on the rocking performance of shallow foundations in different subgrade densities and initial vertical factor of safety (FSv). To this end, a series of reduced-scale slow cyclic tests under 1 g condition were conducted using a single degree of freedom (SDOF) structure model. The performance of different footing shapes was studied in terms of moment capacity, recentering ratio, rocking stiffness, damping ratio, and settlement. For three foundations with different length-to-width ratios, the results indicate that increasing the safety factor and length-to-width ratio leads to thinner, S-shaped moment–rotation curves, mainly owing to the enhanced recentering capability and the P-δ effect. Moreover, across all foundation types, the repetition of a limited loading cycles with consistent rotation amplitude does not cause stiffness degradation or moment capacity reduction.

Experimental testing of spliced glulam joints for large-span timber structures

In recent years, wood has become an increasingly popular building material for its environmental friendliness. Large-span timber structures are in high demand, of which the spliced joints play an important role for the main structural members. In this research, six specimens with two connection configurations, i.e., the slotted-in-steel-plate connection (SC) and the cover-plate connection (CC), were designed and subjected to cyclic loading tests. Besides the traditional data acquisition system, contact-free displacement measurement was also applied. The feasibility was verified since the moment-rotation curves obtained through the two methods showed strong consistency. Through the analysis of the mechanical properties of the joints, different methods for the determination of the yielding point of the specimens were compared and discussed. The test results show that the ultimate strength and stiffness of the CC connection were 59.04% and 187.7% higher than that of the SC connection, whereas the ductility of the former was 77.02% lower than that of the latter. Factors influencing on their mechanical properties were further analyzed. It is noted that while the ultimate strength is dominated by the steel plates, the stiffness and ductility depend more on the glulam elements and fasteners. Recommendations were also proposed as a design basis for the two types of connections.

Rotational Stiffness Investigation and Parametric Analysis of a Novel Assembled Joint in Lattice Shells

Although there are currently many types of lattice shell joints with different characteristics, assessing the flexural capacity of lattice shell joints is always a great challenge. In this paper, a fan-shaped assembled joint and a welded joint for comparison were subjected to bending tests to investigate the flexural behavior and rotational stiffness of the assembled joint. The strain distribution, load–displacement curve, moment–rotation curve, and damage modes of key parts were analyzed to determine the vulnerable parts of the joints. Our test results show that, with an initial rotational stiffness of about one third of that of the welded joint, the assembled joint specimen exhibits the obvious characteristics of a semi-rigid joint. The finite element analysis results were in good agreement with the experimental results. The results of our parametric analysis show that the rotational stiffness and ultimate moment of the assembled joint increase with increases in the spacing of the bolts and the number of bolts. The performance of the high-strength bolts had a significant influence on the flexural stiffness of the assembled joints. The spacing of the bolts and the number of bolts for the assembled joint are suggested to be greater than the height of the member section and more than three, respectively. The proposed theoretical formula can approximately simulate the initial rotational stiffness of the joint. More in-depth investigations are required in the future for assessing the mechanical behavior of FSA joints subjected to combined bending–compression loads.

Boundary-oriented optimization of semi-rigid connections in steel frames using BNSGA

In recent decades, scholars have focused their research on optimizing semi-rigid frame structures. However, in most studies, semi-rigid connections are commonly treated as design variables without undergoing optimization during their construction phase. Considering that connection design encompasses multiple parameters, incorporating these design parameters as structural optimization variables could exponentially expand the search domain. To address the abovementioned issues, this study introduces a pre-optimization method for semi-rigid connections based on the boundary-oriented non-dominated sorting genetic algorithm (BNSGA). By adopting the Eurocode 3 (EC3) component method to calculate the moment-rotation curve of connections and utilizing cost as the objective function, the distribution of connection boundary surfaces in the initial stiffness-bearing capacity-lowest cost objective space is determined using the BNSGA. Through the maximum direct distance strategy (MDDS), typical connection points are selected from the fitting points on the boundary surface based on construction parameters and performance metrics. The effectiveness of this approach in generating a connection database is further validated by analyzing two structural optimization examples.

Investigation on the mechanical behavior of prestressed glulam bolted joints under combined moment and axial force

Among the different methods of strengthening glulam bolted joints, the reinforcement method that utilizes steel straps offers the advantages of low cost, convenient installation and satisfactory reinforcing effect. This research presents the results of a series of tests on glulam bolted joints with prestressed steel straps under combined bending moment and axial force, including a theoretical derivation of moment-rotation curves. The findings indicated that the existence of steel straps led to a delay in glulam splitting with a pronounced increase in bearing capacity compared with ordinary glulam bolted joints, i.e. by 46.85 %, 63.17 %, and 53.65 %, respectively. A three-line moment-rotation model was established to predict its mechanical behavior. This research provides valuable insights for the reinforcement of glulam connections under combined load and serves as a reference for future research in this field.

Experimental programme on austenitic stainless steel RHS members subjected to monotonic and cyclic bending

Stainless steel is a corrosion resistant iron alloy with great potential in structural engineering due to its excellent mechanical features, durability and aesthetic properties. Since most of the existing research has concerned the behaviour of the material, the response of individual structural members, or the performance of simple structural systems under monotonic loading, one of the challenges that remains is the evaluation of the cyclic performance of members to promote its use in seismic design and exploit the excellent ductility and strain hardening properties of this material. For this reason, an experimental programme on austenitic stainless steel Rectangular Hollow Section (RHS) specimens was carried out at the Department of Civil Engineering of the Università degli Studi di Salerno in collaboration with the Universitat Politècnica de Catalunya. A total of eight RHS specimens were tested around the minor axis under both monotonic (three specimens) and cyclic (five specimens) loading, in an experimental set-up that followed a cantilever scheme. The main purpose of this study was to acquire information on the cyclic performance of austenitic steel structural members, focusing on the comparison between monotonic and cyclic behaviours. The outcomes of the tests included the load–displacement and the moment–rotation curves, the energy dissipation capacity, and the evaluation of the key rotation capacities of the members. The reported data are essential to enhance the still scarce research on the seismic behaviour of stainless steel structures.

Experimental investigation of the rotational characteristics of a novel hybrid laminated glass beam-column connection prototype

This article presents an experimental investigation of the rotational characteristics of a novel hybrid laminated glass beam-column connection prototype. The testing of small-scale prototype specimens is conducted to assess the effect of the main structural parameters such as glass pane thickness, interlayer and reinforcement properties on the rotational characteristics. To explore the possibility of using different lamination technologies for the realization of the joints, two different bonding technologies are considered separately: (a) autoclave and (b) UV-curing lamination. The specimens are subjected to a pair of self-equilibrated compressive forces up to failure in a custom-made setup. Digital image correlation (DIC) measurements together with strain gauges are used for tracking the kinematics of the main components. It was found that the prototype is able to develop a significant post-fracture and rotational capacity in a properly balanced combination of structural and material parameters. The results are presented in terms of moment-rotation (M - θ) curves, strains evolution in the steel and evolution of the crack patterns. Experimental observations suggest that depending on the choice of structural parameters three failure modes are possible: (a) crushing failure of the joint core, (b) plastic failure of the adjoining sections and (c) failure due to debonding of one of the bars in tension. It is concluded that one can achieve a desirable post-fracture and ultimate behaviour by properly balancing the structural and material parameters. Additionally, pull-out opening and tensile stresses in steel are measured at the interrupted section, revealing a transition in sectional behaviour from fully interrupted to a hybrid section over a certain transition length.