Initial Rotational Stiffness Research Articles

Study on Seismic Behavior and Influencing Factors of Composite Connection in Moment-resisting Steel Frame

To study the seismic behavior and influencing factors of prefabricated steel frame composite joints, cyclic loading tests of two groups of scaled specimens were carried out, and the refined numerical model was established and its validity was verified. The failure mode, hysteretic behavior and moment-rotation curve of composite joints and pure steel joints were compared, and the influence of composite slab on the mechanical properties of joints was summarized. At the same time, the parameters of the key components were selected as variables to study the changing law of the stress properties of the joints. The results indicate that the main failure modes of the overhanging end plate connection are end plate yield, bolt breakage and stiffener buckling, and the composite joints will also have local crushing of composite slab. The factors that significantly affect the bearing capacity and initial rotational stiffness of joints include the thickness of end plate, the setting of end plate stiffener, the extension of end plate, the strength of steel, the thickness of slab and the diameter of steel bars. In addition, the shape of end plate stiffeners has obvious influence on the stress distribution of joints. Finally, the calculation model of the overhanging end plate connection composite joint's initial rotational stiffness was proposed, and the stiffness superposition method was used to consider the bending stiffness of the end plate. At the same time, its reliability and high accuracy were verified, which was of great significance to engineering application.

Mechanical properties of corrugated steel lap joint under combined compression and bending

The lap joint of a prefabricated corrugated steel structure is one of the most critical components to be considered during design. Full-scale mechanical tests under combined compression and bending (N–M) were conducted to investigate the effect of axial forces and bending moments on the mechanical behavior of lap joints. Numerical methods were used to examine the effects of different axial forces on the bending behavior of the joint. Analysis revealed that buckling of the corrugated steel plate lapped on the upper layer, located near the innermost row of bolt holes, was the failure mode of the lap joint. The yield of the bolt holes on the compression (crest) and tension (valley) sides was accelerated and postponed by the axial force, respectively. Additionally, three phases with linear, nonlinear, and linear characteristics were identified from the bending moment-rotational angle (M–θ) curves. The initial rotational stiffness of the joint was the highest and decreased gradually with increasing axial force. The residual rotational stiffness of the joint was minimal and was only minimally affected by the axial force. A greater axial force on the joint lowered the bending capacity. Compared with N = 0, when N = 1200 kN, the corresponding bending moment decreased by approximately 17.1% and 9.6% for θ = 0.02 and 0.1, respectively. An empirical formula for calculating the joint rotational stiffness (Kθ) was proposed based on the N–M–Kθ relationship. These findings provide a reference for the joint design of prefabricated corrugated steel structures.

Experimental study on flexural capacity and fire resistance of high strength Q690 steel flush end-plate connections

High-strength steel is widely used in building structures, but fire-induced damage and collapse of high-strength steel structures cause huge economic losses. As a primary part of the structure, the reliability of beam–column joints is essential for the structure’s fire safety. This paper presents an experimental study on high-strength Q690 steel flush end-plate connections (Q690-FEC) at ambient and elevated temperatures. Ultimate bending capacity tests were conducted at ambient temperature to investigate its structural performance, where initial rotational stiffness, bending capacity, and ultimate rotation were obtained. Numerical models were developed to reproduce the tests, and parametric analyses were performed to investigate the influence of load ratio, end-plate thickness, and bolt diameter. Transient fire-resistance tests were performed on specimens with different end-plate thicknesses, where specimen temperature, furnace temperature, and joint rotation were measured. The test results indicate that increasing end-plate thickness has little influence on the critical temperature and fire resistance. Finally, a rotation-temperature relationship model was proposed to predict the fire behavior of Q690-FEC and validated against the experimental data.

Mechanical model for seismic nonlinear behavior of rubber bearings with end-rotation in highway bridges

Rubber bearings in seismic isolated structures are mainly modeled by combination of shear and axial springs. However, the placed isolators under large girders or tall piers are faced with considerable end-rotation which affects their seismic performance. To date, some studies have tried to simulate this effect in bearings with linear elastic behavior. Nevertheless, these models are not proper for high damping elastomeric bearings (HRBs) or lead rubber bearings (LRBs) with nonlinear behavior.In this regard, the present study introduces an improved two-dimensional mechanical model to simulate the interaction between nonlinear shear deformation and end-rotation. The model is verified by previous experimental studies. Later, a sensitivity analysis is conducted by various axial and shear loads with end-rotation to investigate the coupling behavior in HRBs or LRBs. The results indicate that increasing the axial load and shear deformation have a reverse effect on rotational stiffness. Furthermore, end rotation does not have a remarkable effect on critical displacement, however, has a significant impact on the shear force. Moreover, Compressive and shear forces can alter the initial rotational stiffness of the elastomeric bearings.

Innovative inner sleeve composite bolted connections for modular steel constructions: Experimental and numerical studies

The application scenarios of modular steel constructions (MSCs) are becoming more and more extensive due to their exceptional advantages: minimum on-site work, and higher construction speed and quality. Inter-module connections are the critical components, which can significantly affect the integrity and seismic behavior of MSCs. This study proposed an innovative inner sleeve composite bolted connection which combines blind bolts, high-strength bolts and inner sleeve to improve the constructability and seismic behavior. Experimental tests on four full-scale cruciform connections composed of hollow structural steel (HSS) columns and H-section steel beams with different configurations were carried out under cyclic load. The failure modes, moment-rotation relations, initial rotational stiffness, ductility and energy dissipation were analyzed. GB 50011–2010 was used to evaluate the seismic performance and verify the applicability for the seismic design of the proposed connection, in which the lower limit of elastic inter-story drift ratio [θe] is 0.004 rad (or 1/250) and that of elasto-plastic inter-story drift ratio [θp] is 0.02 rad (or 1/50). The yield inter-story drift ratio, [θy] = 4.00–6.75[θe], and the ultimate inter-story drift ratio, [θu] = 1.00–2.00[θp] for the test specimens under cycle load, demonstrating the satisfactory deformation capacity and ductility. Furthermore, EC3 Part 1–8 was adopted to evaluate the stiffness characteristic of the proposed connection, indicating that the proposed connection can be classified as a “semi-rigid” and partial strength connection. Finally, refined numerical models calibrated against the experimental results were established and parametric evaluation was conducted based on the numerical models. The results demonstrate that the effect of the thickness of the inner sleeve and column in the panel zone and the diameter of the blind bolt and vertical high-strength bolt is insignificant. The presented research will provide useful references for further application and popularization of MSCs.

Experimental study on high-strength Q460 steel extended end-plate connections at elevated temperatures

This paper presents an experimental study on high-strength Q460 steel extended end-plate connections at ambient and elevated temperatures. Ambient temperature tests were conducted on connections with 8 and 12 mm end-plates to investigate the ambient temperature structural response, including the initial rotational stiffness, plastic flexural resistance and ultimate rotation. The results show that high-strength steel connection with 12 mm end-plates significantly improves mechanical properties compared to that with 8 mm end-plate with an increase of 22% at least while not influencing the failure modes. Then, the experimental results were compared with the theoretical predictions of Eurocode 3. There are reasonable agreements between these two methods on plastic resistance, while the calculation by Eurocode 3 on initial rotational stiffness exhibits much higher results. In addition, the temperature distribution of the connection specimens and furnace air, rotation-temperature characteristics, and failure modes of the connections in transient tests were obtained to study the influence of different end-plate thicknesses. The 12 mm end-plate effectively improves the connection's rotation capacity at elevated temperatures with an increase of 29% compared to 8 mm end-plate while influencing the critical temperature and fire endurance lightly. Besides, the fire performance results were compared and discussed between mild steel and high-strength steel connections. Finally, a rotation-temperature relationship model was proposed to predict the fire behavior of high-strength steel end-plate connections under transient conditions and validated against the experimental data with considerable accuracy.

DETERMINATION OF BASE PLATE STIFFNESS OF STEEL STORAGE RACKS

In recent trends the development of structural steel using cold formed steel section plays a vital role in main frame construction of portal frames. These frames find its use in the construction of economic industrial, agricultural and residential buildings due to its lightweight and robustness. With the major claims in comparison with hot rolled steel profiles, cold formed steel possesses low cost, highly versatile with standard design procedures. Among various structural designs, industrial storage racks are the most prominent structures constructed using cold formed steel. It has been widely incorporated with the rational space utilization in warehouses and factories for goods storage. These rack systems have been classified as static and dynamic types. The adjustable pallet rack was found to be the commonly used static system. It consists of transversal beams and column upright which is grounded with base plate connections. This system provides the stability in down aisle direction. The beams (stringers) have boxed cross-sections while columns (uprights) are open thin walled perforated to accept the tabs of beam end- connectors, which join beams and columns together without bolts or welds. This paper addresses the problem of determining the stiffness and strength of steel storage rack base plate assemblies. Base plate assemblies are usually bolted to an upright and to a concrete floor, and they are used to provide resistance against the flexural buckling of the upright and/or the overall down-aisle buckling of the frame. The semi-rigid stiffness is usually determined by means of a test of two pre-loaded uprights connected to a concrete block in a dual-actuator set-up. Guidance for conducting the test is provided in the European Standard EN 15512. However, several aspects of the test need clarification, notably the test set-up and the transducer arrangement for measuring the rotations of the base plate. Keywords: storage rack, base plate assembly, initial rotational stiffness.

Optimal Design of Failure Mode Control for Semi-rigid Steel Frame Based on Elitist Retained Genetic Algorithm

The post-earthquake reports show that failure mode control design is of great significance to improve the seismic performance of structures. To realize the optimal design of failure mode in semi-rigid steel frame, a failure mode optimisation design method based on an elite retained genetic algorithm was developed in this study. Firstly, a database of 96 extended end-plate connections was established using the ABAQUS finite element software to obtain the initial rotational stiffness and yield moment under failure criteria. Secondly, with section size as the optimisation variable, failure mode as the constraint condition, and total steel consumption as the objective function, elite gene transfer was realized through gene sequence replication, hybridisation and mutation. With a 10-story, 3-span, semi-rigid steel frame as an example is proposed to demonstrate the application of the proposed semi-rigid design method, and pushover and time history analyses were conducted on the optimized results to verify the accuracy of the proposed method. The analysis results showed that the stable and reliable optimal design results were obtained through 1317 generation genetic iterative calculations, and the energy consumption ratio of the semi-rigid connection (including the beam ends) was 95.82% and that of the column was 4.18%; in addition, 76% of the beam ends had plastic hinges to dissipate energy in the pushover analysis. This finding indicates that the optimized frame can achieve the global failure mode during earthquakes, and the design method can effectively improve the seismic performance of the frame.

Structural behaviour and design of stainless steel end-plate beam-to-exterior column minor-axis joints

The structural behaviour of stainless steel end-plate minor-axis joints of I-section columns is investigated through comprehensive experimental and numerical studies. Four stainless steel end-plate beam-to-exterior column minor-axis joints were fabricated and tested subject to both monotonic and cyclic loading, wherein two joints were made of austenitic grade EN 1.4301 and another two joints were in duplex grade EN 1.4462. The obtained failure modes, structural properties and local characteristics were discussed. Meanwhile, advanced finite element (FE) models were generated by means of the ABAQUS software package, and were validated against the obtained experimental results, and the effects of key factors on structural behaviour of minor-axis joints were examined via subsequent parametric studies. The initial rotational stiffness and moment resistance of the tested joints were compared with the predictions from the existing design method, and a new design approach for the column web in bending and punching that can account for the strain hardening of stainless steels and the restraint from transverse stiffeners was proposed. The reliability of the novel design proposal was demonstrated by a statistical analysis of the ratios of test/FE over calculated results.

Fire resistance design of the bolted-welded hybrid composite connection in steel frame

As a key component of the steel frame, the connection is important for the behaviour of the steel frame and for the prevention of progressive collapse under fire. To investigate the fire resistance of the bolted-welded hybrid composite connection in steel frame (BWC-SF), based on a completed test, a refined finite element model of the BWC-SF with a reinforced concrete slab was established. A parametric analysis was carried out to investigate the effects of the beam end load ratio, axial compression ratio of the column, thickness of the beam web and flange, thickness of the column web and flange, thickness of the concrete slab and reinforcing bar diameter. The fire resistance of the connection improved with a decrease in the beam end load ratio and reinforcing bar diameter and with an increase in the thicknesses of the beam flange, beam web and concrete slab. The flexural capacity and stiffness of BWC-SF components, which had great effects on the fire resistance, were analysed. The flexural capacity and initial rotation stiffness calculation method of the BWC-SF at elevated temperatures were established based on the component method and verified according to the test and finite element results.

Assessment of Design Approaches for Stainless‐Steel Joints Through an Equivalent FE Modelling Technique

AbstractConsidering the significant strain‐hardening and ductility characteristics of stainless steel and the influential role of beam to column joints in the overall response of structures, a clear understanding of their moment rotation behaviour appears fundamental. In the present study, a review of the European design code for three typical semi‐continuous beam‐to‐column joints (extended end plate, flush end plate and top‐and‐seat angle connections) is first carried out. Then, using a hybrid modelling strategy with uncoupled elastic‐plastic springs for the bolts and shell elements for the members, more refined 3D finite element (FE) models are developed and validated against available test results. An equivalent stress definition is then proposed for calculating the joint moment resistance. Finally, the initial rotational stiffness, moment resistance, rotation capacity, and failure patterns are used to evaluate critically the accuracy of the predictions of the European design code. As a result, the need for more comprehensive design guidance in accordance with the observed findings is pointed out.

Flexural behavior of clad rack beam-to-column bolted connections at high temperatures

The fire resistance of beam-to-column connections affects the safety of clad racks under fire conditions. However, existing research lacks studies on the behavior of these special connections at high temperatures. This study investigates the fire resistance of clad rack beam-to-column bolted connections (CRBCs). Firstly, single cantilever tests of CRBCs at temperatures of 20 °C, 300 °C, 400 °C, 500 °C, 600 °C, and 700 °C are carried out. The failure modes of the CRBCs at 600 °C and below are identical to that at ambient temperature, while the failure mode at 700 °C is different. The stiffness and strength of the CRBCs decrease with the increasing temperature. Subsequently, an FE model considering the high-temperature metal fracture is established, which can accurately simulate the typical failure mechanisms and satisfactorily predict the full range moment-rotation behavior of CRBCs. Furthermore, parametric analyses are conducted to investigate the influences of related parameters on the failure mechanism, initial rotational stiffness, and flexural capacity of CRBCs. Finally, theoretical models based on the component method are established for calculating the initial rotational stiffness and flexural capacity of CRBCs at high temperatures, respectively. The comparison of the theoretical model, experimental results, and numerical results indicates that the theoretical model can accurately calculate the mechanical properties of CRBCs at high temperatures. The findings of this study can provide a reference for the analysis and design of the fire resistance of clad rack structures.

Intelligent meta-model construction and global stochastic sensitivity analysis based on PSO-CNN

A large-scale simulation model is needed for the stochastic sensitivity analysis of structural uncertainty. The finite element method often exceeds the computing power and cannot meet the analysis requirements and computational efficiency of stochastic sensitivity analysis. With the development of artificial intelligence, the calculation efficiency problem can be solved by a combination of the finite element model and a mathematical model, but the accuracy of the analysis results depends on the accuracy of the mathematical model. However, using artificial neural networks to construct mathematical models also has numerous problems, such as falling into local extrema. Thus, to address the computational efficiency and calculation accuracy problems, the particle swarm optimization (PSO)-convolutional neural network (CNN) meta-model is presented in this paper. This model was used to improve the training and prediction accuracy of a small-sample CNN, where the initial learning rate of the CNN was optimized by PSO. Additionally, the PSO was combined with the Adam optimizer to automatically screen the optimal network structure. The global stochastic sensitivity analysis method based on the Sobol sensitivity method and the Monte Carlo method was used to quantify the degree of influence of the input parameters on the model output parameters and to analyze the influence trend of the parameter changes on the structural response combined with the positive and negative Spearman’s rank correlation coefficients. The accuracy, good adaptability, and extension ability of the PSO-CNN meta-model was verified using the high-dimensional function examples and the structural models. Global stochastic sensitivity analysis was carried out on the joint of an extended end plate. The influence degree of the parameters on the initial rotational stiffness of the joint was determined, and corresponding design suggestions were obtained. These suggestions were consistent with the design specifications and the research results of other scholars, which verified the reliability of this method and could be applied to other types of structural sensitivity analyses.

Analysis of Initial Rotational Stiffness for Different Section of Semi-Rigid Connection

Structural frames are designed for gravity loads. For rigid connections, the entire 100% intensity of the beam section is not used, this is because the end support moment of the beam at the end is always greater than the midspan moment. The end moment value of the beam is reduced by using a semi-rigid connection. In this paper we have analyzed semi rigid connections for different sections. The results of the study indicatethat the formula in the paper appropriately stated the initial rotational stiffness of the top and seat angle connections. The type of semi-rigid connection is usually chosen based on stiffness of connection. In this paper initial connection stiffness (Rki) of an unstiffened top and set angle with double web angle semi-rigid connection of G+3 steel structure is estimated and result obtained are validated using theLiu Wei and Shu Ganping.

Seismic behavior and analytical model for a fully bolted joint between CFDST columns and steel beams

A steel beam to concrete-filled double-skin steel tubular (CFDST) column joint was developed to improve the widespread use of CFDST columns in buildings. The comparative studies of six specimens under pseudo-static cyclic tests were designed and performed to examine the influence of endplate thickness, axial compression ratio, bolt diameter, concrete fill degree, and inner tube shape on the mechanical behavior of the joint. The failure modes were the bending of the endplate, warpage and fracture of bolts, fracture of the weld seam, and buckling of beam flanges. The displacement ductility coefficients exceeded 4.89, indicating that the connection had excellent ductility. Increasing the endplate thickness greatly improved the seismic indices of the joint. Although the higher axial compression ratio increased the bearing capacity and initial stiffness of the joint, the ductility and energy dissipation were unaffected. Improving the bolt diameter did not affect the bearing capacity, ductility, and energy dissipation capacity of the joint; however, it increased the initial stiffness and delayed the strength. The bearing capacity and initial stiffness of the joint were improved by increasing the concrete fill degree and using a square tube instead of the inner circular tube; however, it decreased the ductility and energy dissipation and accelerated the strength degradation of the joint. Finally, a calculation model of the initial rotational stiffness was proposed. The mean and standard deviation of the ratios of the predicted results to the experimental results were 0.95 and 0.14, respectively.

Rotational Performance of Traditional Straight Mortise-Tenon Joints with Gap: Theoretical Model and Numerical Analyses

ABSTRACT Gaps are very common in the mortise-tenon (M-T) joints of traditional timber structures. To investigate the rotational behavior of straight M-T joints with gaps, the mechanical mechanism and contact states between the mortise and tenon for the straight M-T joints with gaps were analyzed. A moment-rotation theoretical model of straight M-T joint with gap, based on the embedded compressive and friction mechanisms of the contact surfaces, was proposed and verified by the cyclic loading tests of four 1/3.2-scaled straight M-T joint specimens with different gaps. To further predict the deformation modes and hysteretic behavior of the joint involving gap, nonlinear numerical analyses were performed using ABAQUS. Results indicated that the predictions of theoretical and numerical model were in good accordance with the experimental results. Then, the parametric analyses were carried out based on the validated finite element model, the effects on the rotational behavior of straight M-T joint of major parameters, such as the friction coefficient of wood, vertical gaps, and horizontal gaps, were analyzed. It is found that the initial rotational stiffness, yielding moment, peak moment, and ductility of the joint with gap increased with an increase in the friction coefficient. The initial rotational stiffness, yielding moment, and peak moment of the joint remarkably decreased with the increase of the vertical and horizontal gap. The ductility of joint significantly reduced with the increasing vertical gap, however, the joint slightly improved with an increase in the horizontal gap.

Optimization of Design Procedure for Column-base Connections according to EN 1993-1-8:2006

The stiffness and the strength of a column-base connection have significant impacts on the behavior of a steel frame. The paper develops an interaction curve between moment and axial force for the column-base connections according to EN 1993-1-8:2006 with the variation of the base plate thickness and the bolt diameter. This is the fundamental base to determine the ultimate strength of a column-base plate that allows the designers to estimate the strength of column-base connections. This research investigates the relationship between the base plate thickness, the bolt diameter, and the moment strength of the column-base plate with a specific axial force to select an optimum solution. Also, the initial rotational stiffness is determined under a specific axial load and varied moments that satisfy the ultimate limit state. The relationship between moment–rotation is subsequently performed with the variation of the base plate thickness or the bolt diameter. The design procedure is proposed based on moment-axial force interaction curves and moment-rotation curves. This allows for optimizing the column-base connection from proper selections of base plate dimensions and bolt diameters.

Tensile behavior of cruciform stubs with staggered bolt patterns

Welding stiffeners to angles improves the initial rotational stiffness and resistance of top-and-seat angle connections, but the unintended side effect is lower ductility. To balance ductility and resistance, a novel large angle connection has just been designed. As a result, there is an urgent need to test the behavior and perform theoretical research. Six cruciform stubs were designed and tested with monotonic load to reveal the plastic development of such connections. The comparison with parallel bolt patterns proved that the staggered bolt pattern could improve the ductility factor from 6.06 to 14.17 without lowering resistance. Furthermore, finite element models were used to investigate the development of bolt force. Finally, a modified method for predicting plastic resistance and a model to calculate initial stiffness are accurately presented.

Effects of gaps on the rotational performance of traditional straight mortise-tenon joints

Gaps are very common in the mortise-tenon (M-T) joints of traditional timber structures, and they significantly reduce the rotational performance of joints. To evaluate the effect of gaps on the rotational behavior of straight M-T joints, we fabricated four 1/3.2-scaled Chinese traditional straight M-T joint specimens using Pinus sylvestris logs, one without a gap and three with different gaps, and subjected them to cyclic loading tests strictly in accordance with the international test standard ISO-16670. The failure modes, strength, initial rotational stiffness, ductility, deformation, and energy dissipation capacity of the joints were investigated. The results indicated that the apparent slippage, the tenon pulled out, and the plastic deformation for the mortise edge were exhibited in the specimens with gaps. The bending moment, initial rotational stiffness, and energy dissipation capacity of the joints with gaps gradually decreased as the damaged degree increased. The ultimate rotation of joints with gaps reached 0.2 rad, indicating a good deformation capacity. Furthermore, the gap can aggravate the degree of stiffness degradation of the M-T joint at the same rotation. Based on the experimental results, the empirical degradation formulas related to key cyclic performance parameters, considering the gap effects, were established. Based on the degradation relationships of the key hysteretic parameters of the joint with gaps, a hysteretic model for a joint with a gap was proposed and validated. Good agreement between the model predictions and experimental results was observed.

Seismic experimental assessment of beam-through beam-column connections for modular prefabricated steel moment frames

This study proposes a beam-through moment-resisting joint for H-section (wide-flange) beams and columns that can be prefabricated and easily assembled onsite for low-rise and mid-rise steel structures. Three groups (six in total) of beam-through beam-column connections are designed and tested under quasi-static loading protocols. The output parameters include joints' deformation, failure mechanism, hysteretic behavior, backbone curves, bearing capacity, ductility, energy dissipation capacity, joint rotational stiffness. The results demonstrate that the combination of through-beam continuity plate stiffeners, panel zone doubler plates, and reduced beam sections provide optimal seismic performance. A simplified analytical method is also proposed to calculate the initial rotational stiffness of the through-beam column joint.