Moment-rotation Response Research Articles

Rotational behavior of bolted glulam beam-to-column connections with knee brace

This paper investigates the rotational behavior of bolted glulam beam-to-column connections reinforced by knee brace. Due to the low rotational stiffness of conventional glulam beam-to-column connections (i.e., bolted connection with slotted-in steel plate), diagonal braces are usually installed to increase the lateral load resisting capacity of the structure. However, the architectural space will be heavily impacted by such installation. Column and beam members combined with knee braces would be a compromise between the enhancement of connection mechanical performance and the flexibility of architectural layout. Sixteen specimens with different knee brace configurations were designed for a series of monotonic and reserved cyclic loading tests. The failure modes, moment-resisting capacity, stiffness degradation, and hysteretic moment-rotation responses of the specimens were tested and evaluated. Results showed that the installation of knee brace led to a more ductile failure mode. For the investigated connections with knee brace, the initial stiffness was 5.98 times that of the corresponding bolted connection without knee brace, and the moment-resisting capacity was 6.80 times that of the corresponding bolted connection without knee brace. Moreover, the influence of different knee brace configurations (e.g., section modulus of the knee brace, installation angle, installation end distance, etc.) on the rotational behavior of the connections were discussed. An optimized knee brace configuration was proposed to improve the rotational behavior of the connections and to decrease the damage accumulation in the glulam beam and column members. Nonlinear numerical models, including a detailed three-dimensional model and a simplified model, were further developed to comprehend the mechanical performance of such connections. The presented experimental and analytical results can be used as reference for the development of design guidelines for the glulam bolted connection with knee brace in practical projects.

Moment-rotation behavior of intervertebral joints in flexion-extension, lateral bending, and axial rotation at all levels of the human spine: A structured review and meta-regression analysis

Spinal intervertebral joints are complex structures allowing motion in multiple directions, and many experimental studies have reported moment-rotation response. However, experimental methods, reporting of results, and levels of the spine tested vary widely, and a comprehensive assessment of moment-rotation response across all levels of the spine is lacking. This review aims to characterize moment-rotation response in a consistent manner for all levels of the human spine. A literature search was conducted in PubMed for moment versus rotation data from mechanical testing of intact human cadaveric intervertebral joint specimens in flexion-extension, lateral bending, and axial rotation. A total of 45 studies were included, providing data from testing of an estimated 1,648 intervertebral joints from 518 human cadavers. We used mixed-effects regression analysis to create 75 regression models of moment-rotation response (25 intervertebral joints × 3 directions). We found that a cubic polynomial model provides a good representation of the moment-rotation behavior of most intervertebral joints, and that compressive loading increases rotational stiffness throughout the spine in all directions. The results allow for the direct evaluation of intervertebral ranges of motion across the whole of the spine for given loading conditions. The random-effects outcomes, representing standard deviations of the model coefficients across the dataset, can aid understanding of normal variations in moment-rotation responses. Overall these results fill a large gap, providing the first realistic and comprehensive representations of moment-rotation behavior at all levels of the spine, with broad implications for surgical planning, medical device design, computational modeling, and understanding of spine biomechanics.

Behaviour of stainless steel beam-to-column bolted connections–Part 1: Simplified FE model

Most of the studies in the area of stainless steel structures concentrated on the structural performance of separate members, while the response of stainless steel connections (especially beam-to-column ones) still has not been well-researched. Some numerical investigations were conducted on these connections, however, in addition to their very limited number, they were all undertaken depending on computationally-demanding three-dimensional (3D) solid models. This paper presents for the first time a simplified finite element model able to simulate the behaviour of stainless steel beam-to-column bolted joints, whilst in the companion paper the suggested model is employed to carry out the first exhaustive parametric study on end-plate connections produced from stainless steel. The proposed model has been constructed using 3D shell elements, taking into account the complex interactions between connection components, as well as the geometric and material nonlinearities (including the considerable strain-hardening of austenitic stainless steel grades). The model was then verified against full-scale tests on stainless steel beam-to-column connections, and very good agreement between the experimental and numerical results (i.e. initial stiffness; ultimate moment capacity; overall moment-rotation response; and failure patterns) was achieved. With regard to computational time, the developed shell model demonstrated apparent superiority, consuming less than 20% of the CPU time of its 3D solid counterpart. Given its efficiency and high accuracy, the suggested model can pave the way for comprehensive systematic studies on beam-to-column connections made of stainless steel.

Finite element modelling of steel-timber composite beam-to-column joints with nominally pinned connections

Non-linear 3D continuum-based finite element (FE) simulations are employed to investigate the structural behaviour of steel-timber composite (STC) beam-to-column connections with shear-tabs and/or double web-angles. In the FE models developed, the material non-linearities of the steel and timber are considered using constitutive laws cast in the framework of classical plasticity and continuum-damage mechanics, respectively. Furthermore, the non-linearities associated with geometry (small strain-large displacement) and non-linear contact (interactions between different components) are considered in the models. A sensitivity analysis is performed to assess the spurious mesh sensitivity associated with softening of the timber, and the 3D FE models of the STC subassemblies are validated against experimental data gathered from previous studies. It is shown that the FE models proposed can predict the structural response and the complex failure modes of STC connections with reasonable accuracy. Finally, a parametric study is carried out and the influence of variables such as the depth of shear tab/web angles or the number and size of the bolts, thickness of the timber slab the and degree of composite efficiency on the failure mode, the peak load carrying capacity and moment-rotation response of the nominally pinned STC beam-to-column connections are evaluated and discussed.

Response of two-pile group subjected to vertical eccentric load

ABSTRACT Deep foundations of several engineering structures like bridge piers under vehicular loads, marine structures (jetties), and high retaining walls are subjected to overturning effect due to the eccentricity of loading. Evaluation of the response of foundations under moment loading is necessary for a proper design for safety and serviceability. The response of two-pile group in terms of load–displacement and moment–rotation is analysed under moment loading with consideration of nonlinear (hyperbolic) ground–foundation interaction and incorporating pile to pile interaction in load transfer. Ultimate load capacity of the two-pile group is then estimated based on these responses. Parametric study quantifies the effect of eccentricity on load–displacement and moment–rotation responses of two-pile group for different L/d and s/d ratios. The rotation of the two-pile group reduces with increase in L/d ratio for any eccentricity and s/d. The predicted moment–rotation response using the proposed nonlinear theory for eccentrically loaded two-pile group compares well with a measured response.

Quasi-static analysis and multi-objective optimization for tape spring hinge

Mechanical attributes of interest are always mutually exclusive in the design process of tape spring hinge. Here we present a complete optimization framework consisting of computational mechanics, optimization design, engineering application, and experimental research to compromise mechanical attributes such that an optimal solution set can be obtained to provide design strategies for engineering practices. Tape spring hinge in folding and unfolding processes with large non-linearity is firstly simulated using quasi-static analysis technique. During the quasi-static process, the ratio of kinetic energy to strain energy is observed to determine mass scaling parameters that measure the precision of analysis. Based on the parameters analyzed, moment-rotation responses of tape spring hinge in quasi-static folding and unfolding processes are investigated and experimentally verified. Yield theory derived from the combination of thin shell theory and Tresca yield criterion is introduced to control the yield of the hinge during folding and deploying processes. In addition, tape spring hinge is released transiently when in spatial conditions; thus the fundamental frequency is calculated and selected herein to be a measurement of stiffness that is maximized to avoid the vibration. Then a multi-objective optimization model is established using the derived yield theory control equation and critical moment as optimization constraints, with the fundamental frequency and strain energy as objectives. The non-dominated sorting genetic algorithm is used to solve the optimization model, and then feasible solution distribution and Pareto frontier are obtained. These results are compared and discussed with two additional single-objective optimizations. Ultimately we achieve the optimal design for tape spring hinge, which is verified well with numerical simulation.

Numerical simulation of bridge piers with spread footings under earthquake excitation

This study simulates the responses of large-scale bridge piers under pseudo-dynamic tests to investigate the performance of four types of numerical models that consider the nonlinear behavior of the pier and the rocking behavior of the footing. In the models, beam-column elements with plastic hinges are used for the pier, two types of foundation models (rotational spring and distributed spring models) are adopted for the footing behavior, and two types of viscous damping models (Rayleigh and dashpot models) are applied for energy dissipation. Results show that the nonlinear pier model combined with the distributed spring-dashpot foundation model can reasonably capture the behavior of the piers in the tests. Although the commonly used rotational spring foundation model adopts a nonlinear moment-rotation property that reflects the effect of footing uplift, it cannot suitably simulate the hysteretic moment-rotation response of the footing in the dynamic analysis once the footing uplifts. In addition, the piers are susceptible to cracking damage under strong seismic loading and the induced plastic response can provide contribution to earthquake energy dissipation.

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

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

Structural behaviour of stainless steel beam-to-tubular column joints

This paper complements previous research conducted by the authors on stainless steel bolted joints and reports the first systematic study on the structural behaviour of stainless steel beam-to-tubular column joints with the use of Hollo-bolts. Six full scale specimens including two flush plate joints, two top and seat cleat connections, and two top, seat and web cleat connections of single-sided beam-to- hollow section column joints have been tested and the results are reported in detail. All specimens were in Grade EN 1.4301 austenitic stainless steel and were designed in such a way that a variety of failure modes could be obtained including plastification of the tubular column face, of the connecting angle cleats or the flush plates. For each specimen the moment-rotation response, the evolution of strains in critical locations of the connections and the separation between the column face and the connected beam was monitored and is reported herein. In parallel with the tests, advanced nonlinear FE models were developed. Following validation against the obtained experimental results, parametric studies were conducted to study the effect of key parameters such as, material grade, column face thickness, end plate/angle cleat thickness and bolt spacing on the stiffness, strength and ductility of the joints. Based on both the experimental and numerical results, it was verified that the connections displayed excellent ductility and attained loads much higher than the ones predicted by design standards for carbon steel joints.

Behaviour of large fabricated stainless steel beam-to-tubular column joints with extended endplates

This paper presents the flexural behaviour of stainless steel beam-to-tubular column joints with extended endplates subjected to static loading. Moment-rotation relationships were investigated numerically by using Abaqus software with geometric and material nonlinearity considered. The prediction of damages among components was achieved through ductile damage models, and the influence of initial geometric imperfections and residual stresses was evaluated in large fabricated stainless steel joints involving hollow columns and concrete-filled columns. Parametric analysis was subsequently conducted to assess critical factors that could affect the flexural performance significantly in terms of the initial stiffness and moment resistance. A comparison between codes of practice and numerical results was thereafter made, and design recommendations were proposed for further applications. Results suggest that the finite element model can predict the structural behaviour reasonably well with the component damage consistent with test outcomes. Initial geometric imperfections and residual stresses are shown to have little effect on the moment-rotation responses. A series of parameters that can influence the joint behaviour remarkably include the strain-hardening exponents, stainless steel strength, diameter of bolts, thickness of endplates, position of bolts, section of beams and columns. AS/NZS 2327 is more reliable to predict the joint performance regarding the initial stiffness and moment capacity compared to EN 1993-1-8.

Behaviour of stainless steel beam-to-column joints-part 2: Numerical modelling and parametric study

This paper reports a detailed numerical (FE) study on planar stainless steel beam-to-column joints. A nonlinear FE model is developed and validated against the first set on full-scale tests on stainless steel beam-to-column joints reported in the companion paper. The FE model is shown to accurately replicate the experimentally determined, initial stiffness, ultimate resistance, overall moment-rotation response and observed failure modes. Parametric studies are conducted to obtain the moment-rotation characteristics of a wide range of beam-to-column joints classified as semi-rigid and/or partial strength. Due to the low ductility of the bolts compared to the high ductility exhibited by all other stainless steel joint components, in all cases the strength and ductility of the simulated joints is limited by the failure of the connecting bolts. The design rules for stainless steel connections, which are based on the specifications of EN 1993-1-8 for carbon steel joints, are reviewed and are found to be overly conservative in terms of strength and inaccurate in terms of stiffness thus necessitating the development of novel design guidance in line with the observed structural response. These conclusions are in agreement with the ones reported in the companion paper.

A study of hybrid self-centring connections equipped with shape memory alloy washers and bolts

This paper presents an innovative type of hybrid self-centring extended end-plate connections incorporating high strength bolts and two basic SMA elements, namely, SMA Belleville washers and SMA bolts. The fundamental mechanical characteristics of the individual SMA elements were first understood via cyclic tests, and subsequently a comprehensive test programme on of four proof-of-concept connections with varying bolt dimensions and washer arrangements was conducted. The connection specimens exhibited flag-shape hysteretic responses with good self-centring ability and cyclic loading repeatability. Satisfactory ductility accompanied by moderate energy dissipation capacity was also shown, and it was found that the SMA washers contributed evidently to the strength, stiffness, and energy dissipation of the connections. A numerical investigation was subsequently performed to enable a more in-depth understanding of the connection behaviour, and it was further shown that increasing the preload levels of either the SMA washers or the SMA bolts could effectively increase the connection stiffness. A design model was finally proposed which enables an idealised bi-linear description of the moment-rotation responses of the hybrid self-centring connections. The design stiffness and strength obtained from the proposed models were found to agree reasonably well with the test results and numerical predictions.

Behaviour and design of demountable beam-to-column composite bolted joints with extended end-plates

This paper presents a novel structural form of demountable beam-to-column composite bolted joints that can be dismantled at the end of its service life. An experimental programme was conducted to investigate the static and hysteretic behaviour of the demountable composite joints. The initial stiffness, moment capacity and failure modes of the demountable beam-to-column joints were evaluated through experimental results. The demountability of the joints was verified by dismantling the specimens during testing. Finite element models were developed, which incorporated the nonlinear contact interaction, ductile damage and plastic damage. The accuracy of the numerical models was validated with the relevant experimental outcomes. A parametric analysis was thereafter conducted to evaluate the effect of the end-plate thickness, width-to-thickness ratio of the column, bolt diameter and number of bolts on the moment-rotation response. A comparison between the test results and Eurocode was conducted to assess the applicability of the existing design guidance. It is found that the specimens designed with bent reinforcing bars exhibit satisfactory performance, and possess a higher level of hogging moment resistance compared to those with straight reinforcing bars. The designed joints are able to be dismantled readily and all steel components remain elastic when they are loaded up to 40% of the ultimate capacity which is equivalent to the typical service load. The end-plate thickness, width-to-thickness ratio of the column and bolt diameter impose the significant effect on the performance of the bolted joints. Two bolt-rows in tension can improve the moment-rotation response for the joints with extended end-plates. The current design standards are not capable of predicting the behaviour of the demountable beam-to-column joints accurately.

Cyclic Behavior of Bolted Extended End-Plate Moment Connections with Different Sizes of End Plate and Bolt Stiffened by a Rib Plate

This paper presents a numerical study on the behavior of prequalified Bolted Extended End Plate (BEEP) moment connections when are affected by cyclic loading. Specimens were six four-bolt extended end-plate connections consist of H-shaped columns and I-shaped beams with different geometry as well as different end-plate size and bolt diameter; three of them were stiffened by a triangular rib plate welded to the top and bottom of the beam flanges, and others remained unstiffened. They were modeled in ABAQUS software and their cyclic behavior was evaluated using finite element analysis. Responses of specimens were examined by presenting their equivalent plastic strain, stress distribution, and moment-rotation hysteretic curves. Results revealed that with the increase of beam height and inertia moment in equal story drift rotations, the reduction of connection strength occurred earlier due to the occurrence of local buckling in the beam web and flange after subjecting to cyclic loading. By comparing moment-rotation hysteretic responses of specimens, it was found out that in unstiffened BEEP connections with thinner end-plate, the use of single vertical rib stiffener can slightly improve their cyclic behavior, but in connections with thicker end plate, it showed no considerable effect. It was concluded that the BEEP connections whose dimensions are not based on the tenth code of the Iranian national building regulations, cannot satisfy the criteria of AISC seismic provisions for both special and intermediate steel moment frames, although they experienced no local beam web and flange buckling.

Contribution of Beam-Column Connections with Bolted Angles in the Reserve Capacity and Full-Scale Cyclic Testing

Partially restrained beam-column connections can be used in the gravity load system of building structures to develop moment frame action to enhance collapse prevention for low-ductility steel lateral systems. The benefit from such reserve lateral strength and stiffness is illustrated for a low-rise building with steel braced frames designed in accordance with Canadian provisions for seismic force resisting systems of the Conventional Construction category. Preliminary results from a comprehensive cyclic test program recently completed on beam-to-column joints with bolted double web angle acting with top and seat angles are presented. The test program included 23 full-scale beam-to-column sub-assemblages subjected to combined gravity shear forces and cyclic rotational demands. Experimental observations on the deformation patterns and failure modes are presented together with representative hysteretic moment-rotation responses of bolted double web angles without and with top and seat angles.

Cyclic performance of bonded sleeve beam-column connections for FRP tubular sections

This paper presents an investigation on the cyclic performance of bonded sleeve connections for joining tubular FRP beams and columns. Specimens with different endplate thickness and number of bolts are examined under cyclic loading. The hysteretic moment-rotation responses of specimens, including rotational stiffness, ultimate moment and rotation capacity, and local strain responses are experimentally obtained and comparatively investigated. The cyclic performance of specimens is also characterized in terms of their ductility and energy dissipation capacity. Excellent ductility and energy dissipation capacity can be achieved through yielding of the steel endplate prior to the final connection failure. Detailed finite element analysis is also performed to describe the cyclic performance of beam-column specimens with bonded sleeve connections. Numerical and experimental results agree well in terms of hysteretic moment-rotation responses, ductility and energy dissipation capacity. Further parametric study of the endplate thickness provides evidence that reduction in endplate thickness may decrease the moment capacity with satisfactory ductility and energy dissipation capacity through the full development of steel yielding.

Numerical simulation of beam-to-column joints with flange cleats

Although the effect of semi-rigid steel beam-to-column connections on the behaviour of steel frames and their substantial economic benefits are recognized nowadays, many structural analyses still consider connections as either fixed or pinned. For that reasons, there is need to be able the generate moment-rotation responses of semi-rigid connections that can be used for analysis and design proposes. Characteristic of the joints can be found using FEM models. The objective of the analysis was to find moment-rotation curves for beam-to-column joints with flange cleats and compare them to curves obtained from experimental studies. Numerical elastic-plastic 3D finite models was performed in order to establish a numerical analysis method for evaluating deformation of connections. For all joints there were obtained the FE results lightly underestimates results achieved from experiments. Some differences in the initial value of stiffness and resistances indicate the need for further work on improving FEM models. The inclusion of dimensional deviations of the IPE nad HEB sections, variability in the values of the prestressing forces of the bolts and the not centric positions of the bolts in the holes in the FEM model may contribute to increasing the degree of compliance of the results from experimental and numerical analyzes.

Seismic behaviour of gravity load designed flush end-plate joints

Flush end-plate (FEP) beam-to-column joints are commonly used for gravity load resisting parts in steel multistorey buildings. However, in seismic resisting structures FEP joints should also provide rotation capacity consistent with the global structural displacements. The current version of EN1993-1-8 recommends a criterion aiming at controlling the thickness of the end-plate in order to avoid brittle failure of the connection, which has been developed for monotonic loading conditions assuming elastic-perfectly plastic behaviour of the connection's components in line with the theory of the component method. Hence, contrary to the design philosophy of the hierarchy of resistances implemented in EN1998-1, the over strength and the hardening of the plastic components are not directly accounted for. In light of these considerations, this paper describes and discusses the results obtained from parametric finite element simulations aiming at investigating the moment-rotation response of FEP joints under cyclic actions. The influence of bolt diameter, thickness of end-plate, number of bolt rows and shape of beam profile on the joint response is discussed and design requirements are proposed to enhance the ductility of the joints.

Inelastic moment-rotation response of 690 MPa grade steel I-section girders

Recent specifications have adopted moment-rotation relationships for I-section girders with yield strengths up to 485 MPa to realize adequate and reliable ductility and the development of strength significantly greater than the yield moment. In this study, experiments were performed in order to verify the inelastic moment strength and examine an equation that appropriately expresses the inelastic moment-rotation response of high-strength steel I-section girders in the negative moment region. Three test girder specimens were fabricated and tested to their ultimate bending strengths up to failure. The test results were compared with the maximum strengths predicted for I-girders by finite element analysis and the nominal moment-plastic rotation curve in the specifications. A sufficiently redundant shakedown behavior was revealed by the comparison, which experimentally confirmed the adequacy of the current design equation for the moment-plastic rotation curve to 690 MPa grade steel I-girders. Based on the experimental results, conclusions were drawn regarding the inelastic moment-rotation behavior.

Experimental Investigation on Flexural Response of Hybrid Steel Plate Girder

Flexural tests were conducted on five full scale I-shaped steel beams, three hybrid and two homogeneous, with two aims: 1) validate the inelastic flexural behavior of hybrid girder that is manufactured using lower grade steel 2) simplify finite element (FE) analysis procedure, for further parametric studies, by neglecting residual stresses when symmetrical welding sequence is adopted. Effect of material properties and member slenderness on flexural strength, ductility, and failure mode shapes is discussed. It is also found that failure mode shape and expansion of plastic field are mainly influenced by slenderness of member. Load-deflection and moment rotation response in tests are closely matching with non-linear finite element study. Close match is also observed in failure mode shapes and plastic field expansion. Considerable reduction is observed in residual stresses in symmetrically welded sections as compared to sections welded without proper sequence. This validates non-linear FE analysis procedure by neglecting residual stresses. Test results are compared with prediction equations for flexural strength, rotation capacity available in literature. Test results are also compared with provisions in EN 1993-1-1 and IS 800. Moment gradient (3-P) and uniform moment (4-P) loading have been considered to ensure that results are equally applicable in both cases.