Moment-rotation Response Research Articles

The development of a moment-rotation model for progressive collapse analysis under the influence of tensile catenary action

This paper presents a new empirical-based model for nonlinear modelling of a steel beam using the concentrated hinge approach for the progressive collapse assessment. The new empirical-based model defines the moment-rotation response of a steel beam considering the development of tensile catenary action. In the ASCE41–17, the nonlinear behaviour defining the backbone curve was derived purely based on the flexural behaviour of the structural member under cyclic loading without integrating the effect of high tensile catenary action build-up. Therefore, the backbone curve can further be improved. A comprehensive parametric study was first carried out to investigate the effect of the tensile catenary action on the flexural resistance of the beam under various structural parameters using ABAQUS software. Four variables were examined, which includes the span length, section size, material strength and ductility. A new empirical moment-rotation model was then derived based on the data obtained from the parametric study. A detailed comparison was made between the generated output results of the moment-rotation response predicted by the ASCE41–17 backbone curve and the new empirical moment-rotation model proposed in this paper. The moment-rotation response results generated by the ASCE41–17 model illustrates that the model tends to overestimate the ultimate chord rotation (θu) of the beam member as the beam slenderness ratio (L/D) approaches 20. Meanwhile, the new empirical model consistently predicts the flexural behaviour of the beam up to ultimate moment resistance.

Blast Performance Evaluation of Steel Moment-Resisting Frame Equipped with Smart Bolted Connection

This paper deterministically evaluates the blast performance of steel moment-resisting frame (MRF) smart structures equipped with nickel titanium shape-memory alloy (NiTi SMA) bolted connections. The recentering capacity of the NiTi SMA bolts is exploited to limit the structural damage and reduce the residual drift after a near-field explosion event. A simplified blast over-pressure calculation approach is used to draw the blast overpressure profile. Numerically, the NiTi SMA–based connection is designed conforming to current European standards and is modeled with a solid finite element. The effect of high-strain-rate actions is considered. The response of the NiTi SMA–based connection is obtained by the nonlinear transient analysis and compared with the steel bolted connection. The NiTi SMA–based connection provided excellent recentering capacity. Later, the moment-rotation response of the NiTi SMA–based connection is utilized in the MRF structure. A simplified self-centering connection is proposed to produce smart behavior in the MRF structures. The results reveal that using NiTi SMA connections keep interstory drift relatively low and substantially provide reasonable structural lateral resistance under near-field blast loading.

Serviceability analysis of piled foundations supporting tall structures

Pile foundations supporting tall structures, such as wind turbines, chimneys, silos, elevated water tanks or bridge piers, are subjected during their life span to remarkably eccentric loads. These may lead to significant rotations which, however, cannot exceed the limiting values corresponding to the safe operation of the structure. A physically motivated mathematical framework aimed at the prediction of the serviceability performance of such kind of structures is herein presented and discussed. Piles are idealized as uniaxial nonlinear elements characterized by two yielding loads, one in compression and one in uplift, while pile-to-pile interaction effects are modeled by means of superposition, through an approximate solution. The axial load–moment capacity of the pile group is preliminary determined from a recent closed form, exact solution based on upper and lower bound theorems, allowing the analysis to be performed under load control. The model is capable of accounting for the dependence of the moment–rotation response from the dead load of the structure and the ‘coupling effect’ between generalized loads and displacements. The prediction performance of the proposed calculation method is validated against both numerical and experimental benchmarks. Finally, a parametric study allowed to assess the importance of pile-to-pile interaction on the foundation response under eccentric loads.

Experimental study of fire effects on out-of-plane bending strength/flexibility of steel tubular T-joints

Steel tubular structures are popular in ocean and offshore structures, buildings, bridges, space frames, mining equipment, recreation structures and transportation vehicles. A tubular joint has a critical role in maintaining the integrity of a steel tubular structure under operational and extreme loading conditions. This paper reports the first experimental investigation on the out-of-plane bending (OPB) strength and stiffness of steel tubular T-joints under fire conditions. The tubular specimens were tested to failure under OPB at ambient temperature and under ISO-834 standard fire. The moment rotation response, critical temperature, fire endurance time, structural strength and flexibility of the T-joint specimens were explored. The failure mode of the specimens was noticed to change from “development of a plastic hinge in the brace” at ambient temperature to “the chord face plastification” under fire conditions. Temperature adjustments were made to available parametric equations, basically proposed for the OPB capacity and stiffness of steel tubular joints at ambient temperature. The temperature-modified OPB capacity equations somewhat under-predicted the test results for OPB strength under fire conditions. The temperature-modified OPB stiffness equations showed satisfactory correlation with the test results under fire conditions.

Experimental investigation of steel-concrete composite beam to reinforced-concrete column joints with single plate shear connection

This paper focused on the behavior of steel–concrete composite beam (SCCB) to reinforced-concrete (RC) column exterior joint with single plate shear (SPS) connection under monotonic loading. Four SCCB to RC column exterior joints were constructed, and the test parameters were the longitudinal reinforcement ratio and high-strength bolt diameter. The failure modes, moment-rotation responses, strain distribution along composite beam depth, strain distribution of anchor bar and the influence of parameters were investigated. Compared with open literature, the influence of RC slab was also discussed. Finally, a calculation model accounting for the influence of RC slab was proposed to evaluate the yield moment and ultimate moment capacity of the joint under hogging moment. The test results showed that the longitudinal reinforcement ratio (ρsl), high-strength bolt diameter (db) and the RC slab effect had a great influence on static behavior of the SCCB to RC column joints with SPS connection. When ρsl was increased from 0.57% to 0.98%, the ultimate moment was increased by 40.3%. When db was increased from 16 mm to 20 mm, the ultimate moment was increased by 10.9%. Compared with the joints without RC slab, the ultimate moment of joints with RC slab was increased by 118% to 254%. Moreover, the proposed model provided a good prediction and laid a foundation for the design of SCCB to RC column joints with SPS connection.

Numerical study on the compression-bending response of grouted connections in offshore structures

Grouted connections (GCs) are widely used to link the substructures and towers for offshore wind turbines and transfer various loads from the turbine and tower to the substructure. Extremely complex stresses are developed in these composite connections formed with steel pipes and grout fillings. This paper presents a numerical study, using ABAQUS, on the mechanical response of GCs under axial compression coupled with bending. The effect of axial load ratio on the moment-rotation responses, contact stress between steel pipes and grout, as well as compositions of flexural capacity. Further study is conducted on the stress distribution in the grouted connection under axial compression coupled with bending, and the stress distribution was derived with python script. Analysis shows that, axial load ratio plays a non-negligible role and the distribution of contact stress differs from that recommended by current design guide. These should be considered with caution in industrial design. In addition, this paper also proposes a method to derive the contact stress from numerical model constructed with Abaqus. The results show that contact pressure and shear keys provide the main components for the flexural capacity and the sum of Mp and Mshear-keys accounts for about 75% of the total capacity. And the values of the non-uniform coefficient of shear keys ηsk are all larger than 0.75 which shows that the force distribution between shear keys is extremely uneven. The outputs of this paper provide a further understanding of the GCs subject axial compression coupled with bending.

Intersegmental Kinematics of the Upper Cervical Spine: Normal Range of Motion and Its Alteration After Alar Ligament Transection.

Biomechanical study using cadaveric cervical spines. To evaluate joint mobility and stiffness at the craniovertebral junction. Data on the intersegmental kinematics of the craniovertebral joints are available in the literature with a widespread range of values. The effect that alar ligament injuries have on intersegmental kinematics remains unclear and requires further biomechanical investigation. Ten occipito-atlanto-axial (C0-C1-C2) human specimens were articulated to flexion, extension, bilateral lateral bending, and bilateral axial rotation. The moment-rotation response was continuously tracked through the entire range of motion before and after unilateral alar ligament transection of the right side. The intersegmental (C0-C1/C1-C2) moment-rotation response was continuously quantified in full flexion (7.2 ± 6.6°/12.1 ± 5.8°), extension (11.1 ± 6.4°/3.0 ± 2.8°), lateral bending to the right (3.1 ± 2.2°/1.6 ± 1.2°) and left sides (3.3 ± 1.6°/2.1 ± 1.5°), and axial rotation to the right (1.2 ± 3.5°/32.3 ± 9.3°) and left sides (2.7 ± 2.6°/25.3 ± 8.3°). Unilateral alar ligament transection increased the range of motion of C0-C2 in the three planes of movement; however, intersegmental motion alterations were not always observed. Increases in the range of extension and lateral bending at C0-C1, which had not been reported previously, were observed. Further, the range of rotation on the right and left sides increased, in conjunction with the increased ranges at C0-C1 and C1-C2.Level of Evidence: N/A.

Numerical and FEA investigation of sectional capacity and moment redistribution behavior of steel fiber reinforced concrete (SFRC) beam

Steel fiber reinforced concrete exhibits ductility. This ductility behavior enables redistribution of moment between the negative and positive moment zones in continuous SFRC beams. The sectional capacity of an SFRC continuous beam was determined using the moment-curvature response, the ductility of the member using the moment-rotation response, and the moment redistribution behavior using the moment-rotation response. The theoretical moment-curvature response was calculated from the stress-strain response for 0 % (control), 0.5 %, 0.75 %, and 1.5 % SFRC member which served the basis for the defined moment-rotation behavior and FEA. A five-point bending test was conducted on a two-span beam using a constitutive material model in the FEA software package, Abaqus/CAE. The concrete damage plasticity (CDP) model was used to conduct a displacement-controlled analysis on the fully integrated 3D hexahedral element (C3D8). The numerical study revealed that the flexural behavior, bending capacity, rotation capacity, and ductility of the 0.5 %, 0.75 %, and 1.5 % SFRC beams were significantly enhanced than the 0 % SFRC beam. However, as steel fiber volume increased, the quantity of moment redistribution in the SFRC beam decreased. The amount of moment redistribution obtained was 21.8 % for 0 %, 19 % for 0.5 %, 18.1 % for 0.75 %, and 13.9 % for 1.5 % SFRC.

Partial Strength Beam-to-column Connection of Cold-formed Single Channel Section: Numerical and Experimental Study

A full understanding of complex structural behaviour can be developed perfectly by using the combination of experimental and numerical approach. Although the basic method to determine the moment-rotation responses of the beam-to-column CFS joints has recently established from the full-scale testing, practising the finite element modelling (FEM) nowadays could explore in-depth on the number of variables and potential failure modes. In this paper, three-dimensional (3-D) model to simulate the actual behaviour of the beam-to-column CFS joints has been proposed by using multi-purpose finite element package ABAQUS version 6.14 in order to validate analysis data against the experimental works. The approach of nonlinear material characteristics, contact and sliding between different components and adopting C3D8R solid elements are proposed in this model. A total of three (3) beam-to-column CFS connections consisting of three different types of beam depths were tested in isolation in order to observe the structural behaviour based on its strength and stiffness. Comparisons between experimental and FE analysis results in term of ultimate moment capacity have shown a good correlation with strength ratios ranging from 1.12 to 1.17. Therefore, it is possible to develop a realistic model for future parametric studies such as type and configurations of the connections.

Centrifuge modelling of the behaviour of pile groups under vertical eccentric load

Annular shaped pile groups are a very common foundation layout for onshore wind turbines and other slender structures. In this study, their performance under vertical loads of moderate to high eccentricity, including moment rotation response and bearing capacity, was investigated by centrifuge testing on small scale physical models embedded in kaolin clay. To identify experimentally the capacity of the examined pile groups under different load paths, the model foundations were loaded monotonically until a clear collapse mechanism was achieved. The testing procedure and the proposed interpretation methodology can be easily adapted to load paths or pile layouts other than those considered in the current study. The experimental data can be adopted as a useful benchmark for mathematical models aimed at predicting the response of pile groups to complex load paths. The results of this testing program can also be used to assess the degree of conservatism of current methods adopted by industry for the design of piled foundations subjected to eccentric loads.

Behaviour of Precast Concrete Beam-to-Column Connection with SHS Hidden Corbel Subjected to Monotonic Load

Beam-to-column connection is the most critical part of a precast concrete (PC) structure as it governs the integrity of the entire structure. In this study, a beam-to-column connection with square hollow section (SHS) hidden corbel was developed. A full-scale test was conducted on eleven T-subframe specimens with various configurations to investigate the behaviour of the connection under an incremental static load. The behaviour of the connection was evaluated in terms of the moment-rotation response and the mechanical properties were obtained by using the beam-line method. Due to the extensive usage of steel elements, the PC connect possessed a higher ultimate strength than the reinforced concrete (RC) connection. The moment resistance of the connection was largely contributed to by the hidden corbel embedded in the beam and column. However, the PC connection gave a lower stiffness, which resulted in a larger rotation deformation than the RC connection, and thus lowered its design strength. The PC connection was classified as semi-rigid and partial strength, and only specimen PC-3 was considered feasible for PC structures.

An optimized machine learning based moment-rotation analysisof steel pallet rack connections

The moment-rotation (M-o) response of steel pallet rack (SPR) beam-to-column connections (BCCs) is naturally complex and predicted through repeated experimental investigations motivated by the variety in the geometry of commercially available beam end connectors (BECs). Past literature has shown that even finite element modeling (FEM) was somehow unable to fully capture the structural behavior of SPR BCCs in the plastic region. This study proposes an innovative Support vector machine (SVM)-Discrete Wavelet transform (DWT)-based optimized model for M-O analysis of SPR BCCs. A data set of total thirty-two experiments on SPR BCCs was used to develop the model. The experimental investigations identified the most influential parameters affecting the M-O response of SPR BCCs which are column thickness, beam depth, and depth of the BEC. Those parameters were optimized using Firefly algorithm and selected as input parameters. Reliability assessment of proposed predictive model was performed using root-mean-square error (RMSE), Pearson coefficient (r), and coefficient of determination 'r-square' (R2). The findings of predictive model were juxtaposed with experimental outcomes and FEM results, available in the literature, and a close agreement was achieved. The R2 value of 0.958 and 0.984 were achieved for moment and rotation predictions, respectively. Hence, the proposed SVM-DWT model can be efficiently used to forecast the optimum and reliable M-O response of SPR BCCs and to minimize the need of repetitive testing.

Studies on cyclic behavior of tripod suction bucket foundation system supporting offshore wind turbine using centrifuge model test

AbstractTo be competitive in offshore wind energy production, safe and economical foundation design is essential. In recent years, tripod suction bucket foundations have been considered as an alternative to conventional foundations owing to their unique features suitable for offshore construction environments, economic installation, and high overturning resistance. However, it is difficult to accurately predict the behavior of tripod foundation because the load acting on the tripod is complex in HVM (i.e., horizontal, vertical, and moment loads) and the response varies depending on the size and direction of the load. Moreover, it is harder to analyze because the effects of cyclic loads must be considered in an offshore environment. This study, therefore, has investigated the behavior of the tripod suction bucket foundation under cyclic loadings. To analyze the complex responses of the tripod foundation in detail, the overall behavior of the tripod foundation system was observed based on the compression–pullout behavior of a single bucket. Moment–rotation responses, the cyclic stiffness, and permanent displacements of the tripod foundation are evaluated by analyzing the vertical behavior of the single‐bucket foundations as well as the rotational behavior of the tripod foundation. A number of centrifuge model tests were carried out with different loading conditions (i.e., loading amplitudes and directions). It was confirmed that the cyclic behavior of the tripod bucket foundation is significantly affected by loading amplitudes and directions. Furthermore, this study emphasized the importance of considering load characteristics when designing the tripod foundation.

Snap-through of a pinned-clamped elastica with arbitrarily movable support at the clamped end

This paper studies the snap-through of a pinned-clamped elastica when the support of the clamped end can be moved arbitrarily in plane. The universal snap curve, which describes the critical boundary conditions of the pinned-clamped elasticas, is firstly obtained by determining the saddle-node bifurcation points of the moment-rotation response curves. Based on the universal snap curve, the stability of the pinned-clamped elastica can be determined when the support at the clamped end is moved. The critical boundary can also be directly obtained, where the elastica loses stability and the snap-through occurs between the non-inverted shape and the inverted shape. This study can be useful to reveal the snap-through behavior for some other complex systems where movable supports exist.

Moment-rotation response of cold-formed steel joist-to-ledger connections with variable-finishes in ledger-framed construction

Ledger framing is the dominant framing system in North American cold-formed steel (CFS) construction. In this system, the floor, which is typically sheathed with oriented strand board, is framed into the top of the wall via a rim track (ledger) and clip angle connection. The diaphragm is essentially hung from the walls. Recently completed experimental work involving full-scale shake table tests on a ledger-framed CFS building exhibited the presence of alternate load paths that contributed to the lateral force resisting system. Within the goal of quantifying this contribution to the overall diaphragm response, experimental tests on joist-to-ledger connection have demonstrated to have a complex behavior involving limit states such as ledger flange buckling, stud web crippling, and fastener pull-out. Current design practices do not account for these limit states. To improve design recommendations and understanding of load transfer mechanisms, a robust finite element model for a joist-to-ledger connection in ABAQUS, validated via existing experimental tests, is presented herein. Experimental testing on the pull-out capacity of screw-fastened connections was conducted for implementation into the finite element environment. Results were then implemented directly in ABAQUS as connection behavior. Generally, the modeling approach accurately captures connection capacity and behavior. In addition, influence of other floor sheathing materials, fiber cement board and steel deck, on the moment-rotation stiffness and strength of this connection is explored. In steel deck sheathing, effects of deck thickness and fastener spacing are explored. This work enables predictions for both design and system-scale characterization.

Moment-rotation model for steel-timber composite connections with slab continuity steel rods

Detailed 3D nonlinear finite element (FE) analyses of steel-timber composite (STC) cruciform subassemblies including material, geometrical and contact nonlinearities are carried out. In the STC subassemblies, the steel beams are connected to the column flange by fin plates and/or double web-cleats and the continuity of the cross laminated timber (CLT) slabs across the column is preserved by mechanically anchored rods. The FE models are verified against experimental data and it is shown the adopted constitutive law of materials (i.e. steel and timber) and proposed modelling strategies accurately predict the failure mode, local (load-strain) and global (bending moment-rotation) response of the STC connections. Variables influencing the bending moment-rotation response of the STC connections are identified and considered in a parametric study and a mathematical model for the moment-rotation of the STC joints is developed by non-linear regression of the data obtained from the parametric study. The calibrated mathematical model is employed for blind prediction of the moment-rotation of the STC connections and the accuracy of the model compared to the detailed 3D nonlinear FE models is demonstrated by a few examples. Lastly, nonlinear FE analysis of a multi-storey STC frame with nominally pinned connections is carried out and it is shown that the continuity steel rods (anchored in the CLT slabs) reduce the mid-span deflection of the STC beams by approximately one-third.

Influence of seat angles on the behaviour of cold-formed steel concrete composite joints

This paper presents an experimental study on cold-formed steel (CFS) concrete composite joints, with and without seat angles, to investigate their structural behaviour and determine the influence of seat angle on this kind of connection. These CFS-concrete composite joints were made up of a cold-formed steel (CFS) connection consisting of two lipped CFS C-channels (bolted back-to-back as a beam and column with a trough plate or gusset plate), a composite slab (comprising a reinforced concrete slab with profiled CFS deck, and bolted shear connectors). In the literature review, the CFS-concrete composite beams and composite slabs were found to have been investigated experimentally and analytically in several studies but little attention has been paid to CFS-concrete composite joints. This is the reason for the current investigation on these kinds of composite joints. Six full-scale specimens of composite joints, three bare joints and three seat-angle joints, were evaluated experimentally by isolated joint tests, in which a one-point load was monotonically applied to the beams. The responses of the specimens were recorded by measuring instruments: i.e. five LVDTs, two inclinometers, and five strain gauges. The results obtained were used to provide moment-rotation relationships of the connections, which were necessary for quantifying the key characteristics of the connections. The three linear moment-rotation responses of the tested composite joints showed that adding the seat angles to the CFS-concrete composite joints increases both their moment resistance and rotational stiffness (by 8% and 21%, respectively), and reduces the rotation capacity (by 17%), on average. Furthermore, it was observed that the behaviour of these types of joints tends to transform from partial strength to full strength by adding a seat angle.

Moment–rotation response of post-tensioned self-centring beam–column connection

In order to overcome common problems such as low stiffness, insufficient ductility and enormous residual displacements in beam–column connections, a steel beam–column connection equipped with high-strength strands was developed. These so-called post-tensioned (PT) steel connections consist of high-resistance strands passing parallel to the beam web and through drilled holes in the column flange and the top and bottom beam angles, which act as energy dissipation elements. The displacement and rotation of connections in earthquake events is a problem that can be avoided by a self-centring feature of steel PT connections. In this research, the cyclic response of PT beam–column steel connections with stiffeners connected to the top and bottom beam angles was investigated. Different stiffener geometries and thicknesses were examined and numerical models were simulated using Abaqus software. The results showed that installation of stiffeners on the top and bottom beam angles had a direct effect on the gap opening of the beam–column interface and reduced the relative rotation. Under large applied drifts, primary elements of the connection experienced large deformation and failure. Thus, by equipping angles with stiffeners, all of the induced stresses and damage will be concentrated in the stiffeners. In all the models equipped with stiffeners, the behaviour of beam reached the plastic phase and the minimum value of Mmax/Mpn was almost 1·1. Failure of the angles was also delayed and the primary elements of the connection (beam and column) remained undamaged.

Modelling of hysteresis behaviour of moment-resisting timber joints strengthened with FRP composites

The integrity of moment-resisting timber framed structures can be compromised in a seismic event due to damage of the joint region. Externally bonded carbon fibre-reinforced polymer (CFRP) composites offers an effective retrofit strategy for such joints and the concept has been proven in a limited number of experimental studies to date. There is a, however, a distinct lack of numerical modelling studies of the system. This paper therefore reports the numerical modelling of the hysteresis behaviour of FRP-strengthened moment-resisting timber joints utilising the finite element method. Three types of joints are investigated, namely (1) plain unstrengthened joints, (2) FRP-strengthened joints that do not experience degradation in strength, and (3) FRP-strengthened joints with strength degradation. The joints are subjected to a displacement controlled cyclic load and the moment-rotation responses are extracted from the finite element results. In addition, the dissipated energy of each joint relative to the joint rotation is also provided. The modelling procedure is shown to be effective upon comparison with test results when the joint rotation is within an acceptable range of seismic activity.

Cyclic performance of splice connections for hollow section fibre reinforced polymer members

This study investigates the cyclic performance of splice connections developed for hollow section fibre reinforced polymer (FRP) members. Splice connection specimens, each consisting of a steel bolted flange joint between two hollow section steel-FRP bonded sleeve joints, are prepared in three configurations with difference in bolt arrangement or bond length. Correspondingly, detailed finite element (FE) models are constructed with consideration of yielding of the steels, damage in the adhesive bond, pre-tensioning of the bolts and contact between the bolt-fastened parts. Tested under a cyclic flexural loading, the specimens experience different levels of yielding in the steel flange-plates before ultimate failure in the FRP member or in the steel flange-plate. Excellent ductility and energy dissipation capacity are demonstrated in a specimen where plastic deformation of the steel flange-plates is fully developed. The strain responses are also analysed to identify damage in the adhesive bond and yielding in the flange-plates. The FE modelling agrees well with the experimental results in terms of moment-rotation and load-strain responses, and can also predict the initiation of the ultimate failure in the FRP using the Tsai-Wu failure criterion.