Hinge Model Research Articles

Experimental research on the propagation of plastic hinge length for multi-scale reinforced concrete columns under cyclic loading

The plastic hinge lengths of beams and columns are a critical demand parameter in the nonlinear analysis of structures using the finite element method. The numerical model of a plastic hinge plays an important role in evaluating the response and damage of a structure to earthquakes or other loads causing the formation of plastic hinges. Previous research demonstrates that the plastic hinge length of reinforced concrete (RC) columns is closely related to section size, reinforcement ratio, reinforcement strength, concrete strength, axial compression ratio, and so on. However, because of the limitations of testing facilities, there is a lack of experimental data on columns with large section sizes and high axial compression ratios. In this work, we conducted a series of quasi-static tests for columns with large section sizes (up to 700 mm) and high axial compression ratios (up to 0.6) to explore the propagation of plastic hinge length during the whole loading process. The experimental results show that besides these parameters mentioned in previous work, the plastic hinge of RC columns is also affected by loading amplitude and size effect. Therefore, an approach toward considering the effect of these two parameters is discussed in this work.

Analysis for multi-linear stress-crack opening cohesive relationship: Application to macro-synthetic fiber reinforced concrete

An analytical formulation for flexure behaviour of concrete considering a multi-linear stress-crack separation (σ-w) relationship is developed using the cracked hinge model. An inversion procedure for obtaining the multi-linear cohesive stress response from the flexural load response of a beam is presented. The procedure is applied to obtain the σ-w relationship for macro-synthetic fiber reinforced concrete. An experimental investigation of the crack propagation in flexural response of macro-synthetic fiber reinforced concrete is presented using the digital image correlation technique. The post-cracking response of macro-synthetic fiber reinforced concrete during the initial softening and the subsequent load recovery is experimentally shown to be associated with a hinge-type behaviour and is produced by crack closing stresses contributed by fibers. From the optical measurements the hinge length is identified with a zone of length equal to twice the aggregate size. Using the measured hinge length, the multi-linear σ-w relationship for macro-synthetic fiber reinforced concrete obtained by matching the experimental and the analytical load responses exhibits a stress recovery following initial softening. The cohesive stress subsequently decreases following the recovery at large crack separation. The crack closing stresses contributed by the pullout of fibers produce stress recovery in the σ-w relationship and are primarily active after the formation of the hinge resulting in significant contribution to fracture energy at large crack openings. There is a good correlation in the fracture energy obtained from load response and the σ-w relationship at different values of crack opening displacements.

Seismic behavior of special truss moment frame with double hollow structural sections as chord members

Research work carried out on steel special truss moment frames (STMFs) with double-angle sections as chord members during the 1990s led to the formulation of design code provisions. Further research results using double-channel specimens resulted in a modified equation for the expected vertical shear strength of the central special segments, Vne, and has been incorporated into the current AISC Seismic Provisions for Structural Steel Buildings. Double hollow structural sections (double-HSS) have the advantages of minimizing lateral torsional buckling and maximizing compactness in the flanges as compared to single HSS with the same flexural capacity. In this research, double-HSS members were proposed for the chord and web members of STMFs instead of double-angle, double-channel, or single-HSS. Double-HSS can effectively delay flange local buckling and enhance rotational ductility due to reduced width-to-thickness ratio (b/t) without increasing the wall thickness of the members. A full-scale STMF subassemblage with double-HSS as truss members was tested under large displacement reversals to simulate a severe earthquake ground motion. Testing results indicate that using double-HSS truss members is a viable alternative for STMFs in high seismic regions. Plastic hinge models are also suggested for computer analysis and design of non-yielding members outside of the special segments.

Characterisation of Fracture and HAC Resistance of an Individual Microstructural Constituent with Micro-Cantilever Testing

This paper focuses on the application of miniaturized fracture tests to evaluate the fracture and hydrogen assisted cracking (HAC) resistance of a selected microstructural constituent (acicular ferrite, AF) which only occurs in microscopic material volumes. Site-specific Focused Ion Beam (FIB) micro-machining was used to fabricate sharply notched micro-cantilevers into a region fully constituting of AF. The micro-cantilevers were subsequently tested under uncharged and hydrogen charged conditions with a nanoindenter. The load displacement curves were recorded and analysed with a simplified plastic hinge model for the uncharged specimen, as AF demonstrated an essentially ductile behaviour. The simplified model assisted with FE simulations provided values of the critical plastic crack tip opening displacement (CTOD). A value of the conditional fracture toughness was thereby determined as 12.1 MPa m1/2. With LEFM, a threshold stress intensity factor, Kth, to initiate hydrogen crack propagation in AF was found to range between 1.56 MPa m1/2 and 4.36 MPa m1/2. All these values were significantly below the corresponding values reported for various ferrous alloys in standard macro-tests. This finding indicates that the fracture and HAC resistance at the micro-scale could be very different than at the macro-scale as not all fracture toughening mechanisms may be activated at this scale level.

Incremental-iterative model for time-variant analysis of SFRC subjected to flexural fatigue

Fatigue behaviour of plain (PC) and steel fibre reinforced concrete (SFRC) is of growing interest in concrete engineering since structural reliability often depends on the concrete’s damage state. The current paper deals with its investigation. Starting from a new and universal SN-approach for PC and SFRC based on stress- and material-dependent ductility and a cycle-dependent strain evolution under centric pulsating loads an isotropic and time-dependent material damage parameter is derived. In the framework of the elasto-plastic damage theory, wherein PC and SFRC are idealized homogeneously on macroscopic level, this damage parameter in conjunction with the established envelope concept enables to compute time-dependent stiffness and strength degradations as well as increasing plastic strains. Additionally, an assessment of the total number of cycles to failure of specimens subjected to multi-staged cyclic loading is permitted by a specific damage accumulation procedure. Decisive parameters like fibre type, length, orientation, dosages and bond on the axial static and cyclic material response are covered. To compute numbers of cycles to failure, deflections and stress redistributions of members exposed to flexural fatigue, the findings are integrated into a plastic hinge model. This accounts for localization of damage after cracking in a discontinuity region typical for both, PC and SFRC. Cycle- and crack-width-dependent deflections are obtained for valid states of equilibriums between external loads and internal stress resultants. To assess macroscopic cracking a strain criterion serves. In the numerical simulation, time-increments are performed according to Lemaitre’s jump-in-cycles procedure. For verification test results from literature are recalculated. Theoretical and experimental data are in good accordance on average proving a comparable fatigue behaviour of PC and SFRC in principle. However, fibre’s impact on fatigue life and deformation capacities of concrete is ambivalent, depending on specific material and load characteristics.

Triangle–hinge models for unoriented membranes

Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes. The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N limit. In this paper, after clarifying that all the tetrahedra resulting in the original models are orientable, we define a version of triangle-hinge models that can describe the dynamics of unoriented membranes. By regarding each triangle as representing a propagation of an open membrane of disk topology, we introduce a local worldvolume parity transformation which inverts the orientation of triangle, and define unoriented triangle-hinge models by gauging the transformation. Unlike two-dimensional cases, this local transformation generally relates a manifold to a nonmanifold, but still is a well-defined manipulation among tetrahedral decompositions. We further show that matter fields can be introduced in the same way as in the original oriented models. In particular, the models will describe unoriented membranes in a target spacetime by taking matter fields to be the target space coordinates.

Influence of adjusted models of plastic hinges in nonlinear behaviour of reinforced concrete buildings

Among the procedures available for the seismic analysis of structures, pushover analysis is one of the most frequently used methods by structural engineers. An adequate modelling of the plastic hinges generated during the pushover analysis is crucial in order to obtain accurate results. Thus, the yielding and ultimate states of the cross-section must be defined in order to model the generalised force-deformation relation of plastic hinges. For this purpose, the use of empirical expressions that obtain the aforementioned states from the cross-section properties can prove beneficial.The main objective of this work is to study the influence of different plastic hinge models on the structural nonlinear behaviour of reinforced concrete structures. To that end, several nonlinear analyses have been performed with the software SAP2000®, considering the following plastic hinge models: (i) the model of FEMA-356 included in SAP2000®, and (ii) two additional models developed by some researchers by using empirical expressions calibrated with different experimental data. Simplified structures of two buildings have been used as examples.The results obtained show that plastic hinges modelled with empirical expressions can be used by structural engineers to more precisely model the behaviour of structural elements in ordinary reinforced concrete buildings located in seismic areas, and to compare with the results offered by the models included in seismic building design codes.

Behavior of Q690 high-strength steel columns: Part 2: Parametric study and design recommendations

Prediction of the column strength, associated with buckling and material yielding, is vital in a successful design. In this paper, a completely numerical analysis technique is employed for simulating the compressive behavior of Q690 high-strength steel columns with box- and H-sections, and its accuracy is verified by the experimental results as presented in the part 1 of the companion papers. To this, the curved Pointwise-Equilibrating-Polynomial (PEP) is introduced for representing the column deformations with an explicit simulation on the member initial imperfection. Further, the refined plastic hinge model combined with the use of sectional yield surfaces is employed to reflect inelastic yielding at the critical location. A cross-sectional analysis approach allowing for residual stresses modeling is also incorporated into the numerical method. Sequentially, a parametric study is conducted extensively for the Q690 high-strength steel welded columns. At last, the buckling curves from Chinese (GB 50017-2003), European (Eurocode 3), and American (ANSI/AISC 360-10) codes are examined, and some recommendations for design of Q690 high-strength steel columns are presented.

Numerical Analysis for an Novel Hooke Hinge Based on ANSYS

This paper utilizes SolidWorks to establish accurate Hooke hinge model and imports it into ANSYS using the data switching interface between SolidWorks and ANSYS. The stress-strain behavior of the Hooke hinge is analyzed using finite element method, and the reliability and stability of the structure is evaluated, which provides some theoretical guidance for the design of Hooke hinge.

Matter fields in triangle–hinge models

The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane. In a recent paper [arXiv:1503.08812] a new class of models are introduced that generate three-dimensional random volumes, where the Boltzmann weight of each configuration is given by the product of values assigned to the triangles and the hinges. These triangle-hinge models describe three-dimensional pure gravity and are characterized by semisimple associative algebras. In this paper, we introduce matter degrees of freedom to the models by coloring simplices in a way that they have local interactions. This is achieved simply by extending the associative algebras of the original triangle-hinge models, and the profile of matter field is specified by the set of colors and the form of interactions. The dynamics of a membrane in $D$-dimensional spacetime can then be described by taking the set of colors to be $\mathbb{R}^D$. By taking another set of colors, we can also realize three-dimensional quantum gravity coupled to the Ising model, the $q$-state Potts models or the RSOS models. One can actually assign colors to simplices of any dimensions (tetrahedra, triangles, edges and vertices), and three-dimensional colored tensor models can be realized as triangle-hinge models by coloring tetrahedra, triangles and edges at a time.

Displacement and curvature estimation for the design of reinforced concrete slender walls

SUMMARY Previous earthquakes, such as the 2010 Maule earthquake in Chile, have demonstrated the need to establish suitable predictors of compressive or tensile strains in concrete or steel in reinforced concrete shear walls, which can provide limit states or confinement requirements. Slender walls are commonly controlled by flexural deformations that can be divided into elastic and inelastic components. This study provides calibrated expressions for the elastic and inelastic components of flexural deformations using a fiber model for slender walls. These expressions are obtained for rectangular and T-shaped walls. The elastic component is dependent on the axial load and the boundary steel reinforcement ratio. The impact of wall coupling is investigated, which requires a correction for the elastic component. The investigation of the inelastic component is based on a plastic hinge model, in which the length of the plastic hinge is a function of the lateral inelastic drift of the wall among other parameters. The traditional linear inelastic curvature distribution over the wall height is also modified for cases with steel reinforcement with a long yield plateau or low strain hardening, which results in a larger curvature at the wall base. The distribution is validated with experimental data from the literature. Copyright © 2016 John Wiley & Sons, Ltd.

Evaluation of the out-of-plane behavior of stud-to-track connections in nonstructural partition walls

A series of component-level experiments have been performed aiming to characterize the out-of-plane force-displacement response and damage mechanisms of stud-to-track connections in nonstructural steel-framed partition walls. The performance of connections with various stud-to-track gap dimensions, stud and track thicknesses, and screw-attachment configurations were evaluated and compared. In addition, the accuracy of available design provisions for estimating the ultimate connection capacity was assessed. The experimental data was then used to generate capacity fragility curves in terms of displacement and force. Finally, a series of nonlinear numerical hinge models were developed and calibrated that represent the out-of-plane hysteresis behavior of stud-to-track connections.

Influence of mix composition and strength on the fracture properties of self-compacting concrete

Self-compacting concrete (SCC) has undergone extensive investigations that have led to confidence in its fresh and hardened properties, yet its composition variations raise concerns as to its fracture behaviour. This paper presents the results of an experimental study on fracture behaviour of SCC mixes differing by the coarse aggregate volume, paste to solids ratio (p/s) and water to binder (or cementitious material (w/cm)) ratio. First the size-dependent fracture energy (Gf) has been determined using the RILEM work-of-fracture test on three point bend specimens of a single size, half of which contained a shallow starter notch (notch to depth ratio=0.1), while the other half contained a deep notch (notch to depth ratio=0.6). Then the specific size-independent fracture energy (GF) was calculated using the simplified boundary effect formalism in which the variation in the fracture energy along the unbroken specimen ligament is approximated by a bilinear diagram. Finally, the bilinear approximation of the tension softening diagram corresponding to GF has been obtained using the non-linear hinge model. It is found that GF and the critical crack opening (wc) are dominated by the coarse aggregate volume in the mix and the mix grade. The larger the coarse aggregate volume (or the smaller the paste to solids ratio) the larger are both the mix toughness (GF) and the critical crack opening (wc). However, the higher the mix grade the larger is the mix toughness (GF) but the lower is the critical crack opening (wc).

Capacity Evaluation of Typical Stud-Track Screw Connections in Nonstructural Walls

A series of component-level experiments have been conducted aiming to evaluate the force and displacement capacities of typical stud-track screw connections (STCs) in steel-framed partition walls. The variables considered in these experiments included screw-edge distances, loading protocols (monotonic or cyclic), and stud and track thicknesses. The experimental data was then utilized to develop different capacity fragility curves for STCs in terms of displacements. A series of analytical STC hinge models were also proposed and validated using this data. The hinge models can be adopted in future studies to develop a comprehensive analytical model for a typical partition wall assembly.

Cyclic Shear Behavior of Gypsum Board-to-Steel Stud Screw Connections in Nonstructural Walls

Gypsum steel-stud partition walls are composed of light-gauge, cold-formed steel studs, and gypsum boards attached with self-drilling screws. Previous experimental studies on the seismic performance of these walls have shown widespread failure of gypsum-to-stud connections (GSCs), initiated at very low amplitude excitation. The failure of GSCs resulted in loss of strength and stiffness of the partition walls. A series of component tests has been conducted at University of Nevada, Reno to evaluate the shear force and displacement capacities of GSCs. Fastener spacing (center to center and also center to edge), loading protocol (monotonic or cyclic), and stud thickness were varied between specimens. The test data were then used to develop fragility curves for shear capacities of GSCs in terms of displacements. Additionally, a series of nonlinear GSC hinge models were proposed and validated using component experimental data.

System reliability evaluation of steel frames with semi-rigid connections

This paper presents an accurate and efficient numerical procedure for evaluating the system reliability of steel frames with semi-rigid connections. The ultimate strength and behaviour of the frame were predicted using a refined plastic hinge model due to its computational efficiency, whilst the nonlinear behaviour of semi-rigid connections was captured using a three-parameter power model. The statistical properties for the three parameter power model were obtained based on available experimental results. The sensitivity of reliability to the model error was also studied. Monte Carlo simulation was used to estimate the probability of failure and the reliability index of a system. Two example frames subjected to combined gravity and wind loads were examined and their system reliability indices for both strength and serviceability limit states were evaluated based on the randomness in loadings, material and geometric properties and semi-rigid connections. The results indicate that the frame reliability is strongly affected by semi-rigid connections.

A fully general and adaptive inverse analysis method for cementitious materials

The paper presents an adaptive method for inverse determination of the tensile relationship, direct tensile strength and Young's modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear function. Usually, simple bi- or tri-linear functions are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear functions. The proposed method is fully general in the sense that it relies on least square fitting between test data obtained from various kinds of test setup, three-point bending or wedge splitting test, and simulated data obtained by either FEA or analytical models. In the current paper adaptive inverse analysis is conducted on test data obtained from three-point bending of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased number of variables describing the relationship constitutes the basis for obtaining detailed information of crack propagation in any cementitious material.

Geometric and material property dependencies of the plastic rotation factor in the drop-weight-tear test

We carry out significance testing on experimental and computational data sets to determine which material and geometric parameters affect the plastic rotation factor (which is used to estimate the crack-tip-opening angle based on the plastic hinge model) for pipeline steels. It is shown, using the Xue-Wierzbicki damage mechanics model and a statistical analysis, that the rotation factor mainly depends on the Charpy V-notch energy, and empirical fits for the rotation factor are proposed.

Investigation on the rotational deformation of SEB specimens with various crack length to width ratio

A new CTOD calculation formula was proposed by using a correction factor for the blunted crack tip in the authors’ previous report[Kawabata et al(2016)], and the calculated CTOD by the formula significantly corresponded to the actual CTOD obtained by FE analysis in the wide range of specimen thicknesses. However, the use of the CTOD formula is limited to the frequently used crack depth-to-width ratio, a0/W, between 0.45 and 0.55, and this does not satisfy a strong demand for wider a0/W range. Meanwhile, ISO15653 covers a wider range of a0/W between 0.10 and 0.70, where J-based CTOD calculation formula has been specified in the annex-E of ISO15653. In this context, the plastic hinge model was investigated for a0/W between 0.05 and 0.70 by using FE analysis, and the analytical deformation of SEB specimens revealed that the plastic hinge model was applicable to the specimens even though their a0/W were out of the frequently used a0/W range from 0.45 and 0.55. Their rotational center points were almost steady when changing the applied load and the work hardening coefficient.

様々なき裂深さを持つ構造用鋼の破壊靭性試験におけるCTOD算定式の一考察（Bx2B，3点曲げ試験片）

The authors have already established a new CTOD calculation formula, and have been revised a CTOD testing standard of WES1108 in the Japanese Welding Engineering Society by using this formula. Because the fatigue pre-crack tip should be placed in the specified microstructure such as HAZ for the critical CTOD evaluation of welded joints, the next step is the application of the formula to various crack length-to-width ratio, a0/W, conditions, especially for shallow crack specimens. In the previous work, a rotational deformation was apparently observed, and the plastic rotational factor, rp, was described as a function of wide a0/W range. However, a simple use of rp did not result in a better CTOD estimation for shallow crack specimens.In the present work, another way of calculating CTOD was developed by the numerical investigation of single edge notch bend, SE(B), specimens with various a0/W. Non-linear crack opening profiles were dominant for smaller a0/W specimens than 0.2 due to plastic deformation behind their crack tips, or a straight crack opening profile deviated from a triangle side assumed by the plastic hinge model for a0/W =0.7. In this paper, a correction factor of the plastic component of clip gauge displacement, CVp, was proposed considering non-linear crack opening and crack profile deviation, and it was demonstrated that CVp gave a better CTOD estimation than current CTOD formulae such as BS7448 and ASTM E1820 for the wide range of a0/W.