Plastic Hinge Rotations Research Articles

Alternative mathematical modeling for plastic hinge of reinforced concrete beam

The presentation of the plastic zone for flexural members is basic as it administrates the load carrying and deformation capacities of the member. Therefore, plastic hinge study has been of great attention to structural researchers for decades. The behavior of plastic hinge is very tricky due to the high nonlinearity of materials, and relative movement between the component materials and strain localization. As a result, most researchers investigated the problem experimentally or by using programs which depend on the materials nonlinearity such as ANSYS, ABAQUS or ADINA programs. This paper tries to investigate the problem analytically by proposing a simple approximate equation to compute the plastic hinge rotation. A lot of parameters such as the tension and compression steel ratios, concrete strength, steel yield, section geometry and the load position were considered in the suggested equation. The analytical results of simply supported beams under middle concentrated load with different parameters were presented and compared with the conjectures of the various formulations, software programs (ANSYS and NONLACS2) and experimental results. The simplified suggested equation gave satisfying results. Moreover this paper presented a structural mathematical model based on the suggested equation to predict the deformations behavior of the beams. The plastic rotation and deflections can be predicted by the mathematical model after yielding till the failure moment, not only at the failure moment as in the common formulations. The mathematical model was verified and gave values of deflections matching experimental results.

Optimal FRP Jacket Placement in RC Frame Structures Towards a Resilient Seismic Design

This paper proposes an optimal plan for seismically retrofitting reinforced concrete (RC) frame structures. In this method, the columns are wrapped by fiber-reinforced polymer (FRP) layers along their plastic hinges. This technique enhances their ductility and increases the resiliency of the structure. Two meta-heuristic algorithms (i.e., genetic algorithm and particle swarm optimization) are adopted for this purpose. The number of FRP layers is assumed to be the design variable. The objective of the optimization procedure was to provide a uniform usage of plastic hinge rotation capacity for all the columns, while minimizing the consumption of the FRP materials. Toward this aim, a single objective function containing penalty terms is introduced. The seismic performance of the case study RC frame was assessed by means of nonlinear pushover analyses, and the capacity of the plastic hinge rotation for FRP-confined columns was evaluated at the life safety performance level. The proposed framework was then applied to a non-ductile low-rise RC frame structure. The optimal retrofit scheme for the frame was determined, and the capacity curve, inter-story drift ratios, and fragility functions were computed and compared with alternative retrofit schemes. The proposed algorithm offers a unique technique for the design of more resilient structures.

Development of the Performance-Based Plastic Design Method by Considering the Effects of Aftershocks

ABSTRACT One of the efficient methods for seismic design of structures is Performance-based Plastic Design (PBPD) in which by choosing the desired yield mechanism and the target drift at the beginning of the design, unlike that in conventional design methods, there is no need for a time-consuming process of trial and error to achieve the desired performance. On the other hand, recent earthquakes have shown that aftershocks can increase the damage to a building after the main earthquake and thereby threaten the safety of the inhabitants. However, the seismic hazard of aftershocks is still not explicitly included in the current design codes. In this study, attempts have been made to develop the PBPD method for considering the effects of aftershocks. For this purpose, by performing an incremental dynamic analysis (IDA), the ductility factor μ and the ductility reduction factor Rμ of six PBPD frames (2-, 4-, 6-, 8-, 10-, and 12-story) were calculated under mainshock and mainshock-aftershock sequences. Then, the energy modification factor γ, which is related to the two parameters μ and Rμ, was calculated for both the mainshock and the mainshock-aftershock sequences. An equation is presented in order to calculate the ratio of the energy modification factor of the mainshock-aftershock sequence to the mainshock energy modification factor () according to the design period, and the factor obtained is multiplied by the energy modification factor γ so that the effect of aftershock can be considered for the frame design, and by using this modification, the performance of the frame under the mainshock-aftershock sequence can be improved. The results of the time-history analysis performed on the modified PBPD frames show better performance by the frames designed on the basis of modified PBPD than the frames designed on the basis of the original PBPD method under MS-AS sequences in terms of inter-story drift and rotation of plastic hinges.

Effects of soil–structure interaction on inelastic response of torsionally-coupled structures

In this paper, effect of torsion on the inelastic responses of structures resting on a nonlinear flexible medium is studied. Similar studies have shown that soil–structure interaction can result in augmentation of nonlinear responses of lower stories. The focus here is on the plan-wise distribution of inelastic responses of a torsional structure considering soil–structure interaction (SSI). For this purpose, 4, 8, and 12-story steel structures consisting of special moment frames are considered on a relatively soft soil. A nonlinear set of non-uniform springs is used for modeling of SSI. For each building, different structural responses are calculated under 11 suitably scaled earthquake ground motions at the design basis and maximum considered earthquake hazard levels. The mass eccentricity ratio is varied from zero to 30%. The inelastic responses include the story drift ratios and distribution of plastic hinge rotations and performance levels of each story and frame. The results clearly show that SSI increases the drift ratio of the first story up to 30% regardless of the eccentricity value. On the other hand, SSI amplified the cumulative plastic hinge rotation of the upper stories, especially in the taller buildings. The maximum value of amplification exceeded 3 and it was very sensitive to the extent of eccentricity. The local amplification effect of combination of torsion and SSI was much more severe where it reached values over 8 in the outer frames of the buildings, with SSI having the larger share in amplification.

Plastic hinge behavior and rotation capacity in reinforced ductile concrete flexural members

Ductile concrete materials, such as high-performance fiber-reinforced cementitious composites (HPFRCCs), are being considered as a new material that can be used in plastic hinge regions of buildings and bridges to reduce damage as compared to ordinary reinforced concrete. In flexure, a highly nonlinear plastic strain distribution of the primary tensile reinforcement is observed at dominant crack locations, leading to significant differences in plastic hinge length and behavior as compared to ordinary reinforced concrete flexural members. In this study, two-dimensional finite element models were validated with experimental results using a recently developed bond-slip constitutive model, which aids in simulating multiple damage states, such as yield and collapse level drift states. After validation, the modeling approach was used to study the plastic hinge region behavior of reinforced HPFRCC flexural members with variations in mechanical properties, boundary conditions, and geometric properties. The particular areas of interest were reinforcement yielding location, plastic strain distribution, and curvature localization region. New expressions were proposed to predict the equivalent plastic hinge length, Lp, using variables such as shear-span, tensile strength of HPFRCC, reinforcement ratio, yield strength of the reinforcement, boundary condition, and loading scenario. Proposed equations for plastic hinge length of reinforced HPFRCCs are incorporated into a mechanics-based approach to predict rotational capacity of flexural members. The analytical approach was also shown to estimate yield and nominal flexural strength with reasonable accuracy. The proposed methodology is compared with experimental results and expressions for plastic hinge length found throughout the literature for reinforced concrete and HPFRCC members. The results of the study will help practicing engineers and researchers simulate the performance of reinforced HPFRCC flexural members in a computationally efficient manner.

Seismic Behavior of RC Building with and Without Buckling Restrained Braces

Nonlinear analysis for evaluating seismic performance of building under seismic excitation requires nonlinear properties of any component that are quantified by strength and deformation capacities. The nonlinear behavior of beams and column components are modeled in the form of plastic hinges as described in ASCE41-13 [1] guideline. This document provides the hinge rotation capacity for several ranges of detailing assumption. Buckling restrained braces (BRB) can be modeled as a link element with force-deformation behavior through Wen’s plasticity model. This paper evaluates possible differences of seismic performance of six-story reinforced concrete moment resisting frame with conforming and non-conforming plastic hinge rotation, with and without BRB in placed. The nonlinear static analysis is performed to obtain capacity curve using inverted triangular load pattern as described in ASCE7-10 [2]. The behaviors of investigating frames are discussed and evaluated by means of capacity curves and plastic hinge formation mechanism. Moreover, nonlinear time history analysis is carried out to investigate the effect of BRB properties on the seismic behavior of building model subjected to selected ground motion records. Furthermore, response parameters of building model are presented and compared in the form of base shear, story displacement, and story drift.

Seismic impact between adjacent torsionally coupled buildings

The problem of seismic impact between torsionally coupled multi story moment frame buildings is investigated in this paper. Five pairs of adjacent structures spaced at various separation distances are considered. The buildings are 4–10 stories in height. Although a common plan being symmetric with regard to lateral stiffness is considered, a mass eccentricity variable from zero to 30% of the plan dimension is assumed. By three-dimensional modeling of the nonlinear torsional buildings having common story elevations, the seismic pounding happen anywhere along the adjacent buildings edges. Effect of impact and torsional eccentricity are studied by comparison of nonlinear dynamic responses of buildings at different clear distances under 11 consistent earthquakes. The responses include pounding forces at stories, story drifts, story shears and plastic hinge rotations. It is shown that how pounding incidents increase for larger eccentricities and how pounding occurs even at the clear distances prescribed by seismic design codes. The combined effect of torsional eccentricity and pounding results in amplifying the nonlinear response of structure especially for the peripheral frames.

Flexural performance of steel fibre reinforced concrete beams designed for moment redistribution

This paper presents an experimental study to investigate the flexural and moment redistribution performance of six full-scale two-span continuous reinforced concrete beams with and without steel fibres. The beams were reinforced with conventional bar reinforcement with longitudinal steel reinforcement ratios of between 0.0069 and 0.0138; four of the six beams also contained either 30 kg/m3 or 60 kg/m3 of steel fibres. The specimens were tested under monotonically increasing displacement-controlled loading. The primary variables within different test specimens were the arrangement of longitudinal steel bar and the dosage of steel fibres. The beams were designed for 30% of positive and negative moment redistribution with respect to the linear-elastic condition, the maximum allowed by different codes and standards. Test results showed that the inclusion of steel fibres increases the load carrying capacity of the reinforced concrete beams. Furthermore, the addition of steel fibres increased the number of cracks and decreased the crack spacing. For the steel reinforcement ratios tested, the RC-SFRC beams were found to have good ductility. It was shown that the RC-SFRC beams achieved full moment redistribution demand to form the collapse mechanism, and maintained their load carrying capacity for large plastic-hinge rotations. The guidelines of AS 5100.5-2017 were found to give a good prediction of the load carrying capacity of the tested RC-SFRC beams.

Performance of viscous damping in inelastic seismic analysis of moment‐frame buildings

SummaryThis paper investigates the performance of viscous damping in the inelastic seismic analysis of moment‐frame buildings using a detailed model of a 20‐story steel structure. Damping schemes included are Rayleigh, condensed Rayleigh, Wilson‐Penzien, tangent Rayleigh, elastic velocity Rayleigh, and capped damping. Caughey damping is found not to be computationally viable. Differences among the damping schemes, as quantified by plastic hinge rotations and story drifts, become noticeable once these quantities reach the 3% level. In order of least to greatest hinge rotations and story drifts that occur under lateral response to horizontal ground motion, the damping schemes rank as Rayleigh (most damping action), condensed Rayleigh, Wilson‐Penzien, tangent Rayleigh and capped damping, which are about the same, and elastic velocity Rayleigh (least damping action). Performance of Rayleigh damping under vertical ground motion is discussed, including the effect of soil‐structure interaction. The propensity of Rayleigh damping to generate excessive damping forces and moments during inelastic seismic analysis is explained, and a parameter is introduced that can predict the potential magnitude of the effect. A review of some literature on amplified Rayleigh damping moments is also presented.

Assessment of proposed lateral load patterns in pushover analysis for base-isolated frames

The effectiveness of two proposed lateral load patterns (LLPs) to estimate the seismic demands of base-isolated building frames by the pushover analysis (POA) is assessed by comparing their estimates with the benchmark responses obtained by the nonlinear time history analysis (NTHA). The proposed LLPs include: (i) pattern derived from the square root of the sum of squares (SRSS) of first three mode shapes of BI frame; and (ii) two variants derived by the modification of the uniform force distribution load pattern. The conventional first mode shape LLP is also used in the POA for the purpose of comparison. A mid-rise (5-storey) and a high-rise (10-storey) base isolated (BI) reinforced concrete building frames are considered as illustrative examples for the analysis. An ensemble of five ground motion time-histories, each of far-field and near-field with forward directivity and fling-step effects are employed for NTHA. Target displacement-based comparison is performed by considering three target displacements, which cater to elastic, elastic to plastic and plastic states on the capacity curve of the building frames. The seismic demands namely, peak storey displacement, maximum inter-storey drift, number of plastic hinges, SRSS of plastic hinge rotations, maximum base shear and maximum isolator displacement are considered for comparison. The study reveals that (i) the errors in estimating the seismic demands by different LLPs depend on the state (elastic or elastic–plastic or plastic) of the building frame in which target displacement is considered; and (ii) the proposed LLP (modified uniform distribution) is found to best estimate the NTHA predictions.

Experimental investigation of moment redistribution in ultra-high performance fibre reinforced concrete beams

In the design of statically indeterminate structures the concept of moment redistribution is used to reduce the absolute magnitudes of moments in critical regions, to fully utilise the capacity of non-critical cross sections, and to simplify detailing by enabling a reduction in reinforcement ratios. Due to the complex mechanisms which control the formation and rotation of plastic hinges, moment redistribution capacities are commonly empirically based, and hence not necessarily applicable outside of the bounds of the testing regime from which they were derived. This paper presents the results of an experimental study of the moment redistribution capacity of four two-span continuous beams constructed from ultra-high performance fibre reinforced concrete (UHPFRC) and with various reinforcement ratios, such that the suitability of extending of exiting empirical design approaches to UHPFRC can be investigated. The results of the experimental investigation show that for beams where the hinge formed at the support, the observed moment redistribution was greater than the code predictions. However for the beam where the hinge formed under the load points, observed moment redistribution was significantly less than codes predictions. Hence, the results of this study show current design guidelines do not always provide a conservative prediction of moment redistribution in UHPFRC beams.

More efficient lateral load patterns for seismic design of steel moment-resisting frames

The preliminary design of building structures is normally based on the equivalent lateral forces provided in seismic design guidelines. The height-wise distribution of these loads is predominantly based on elastic vibration modes. However, as structures exceed their elastic limits in severe earthquakes, these design load patterns may not necessarily lead to efficient distribution of strength within the structures. To address this issue, several alternative load patterns have been proposed for the seismic design of non-linear structures. However, due to the simplifications involved in the development of these design load patterns, their adequacy needs to be assessed for different structural systems and earthquake excitations before they can be used in common practice. The aim of this work was to identify the most suitable lateral load patterns for the seismic design of steel moment-resisting frames. To do this, the non-linear seismic behaviour of three-, five-, seven-, ten- and 15-storey frames designed with nine different lateral load patterns were compared under 20 real and synthetic spectrum-compatible earthquakes using performance parameters such as maximum inter-storey drift, maximum plastic hinge rotation and cumulative damage. It was found that, for the same structural weight, structures designed with more efficient load patterns experienced up to 68% less global damage than their code-based counterparts.

A three-dimensional drift pushover method for unsymmetrical plan buildings

The drift pushover analysis method for tall and regular buildings is extended in this paper to the third dimension. The focus of study is on the structures with important torsional response. For this purpose, 10, 15, 20 and 30-story steel moment frame buildings having unsymmetrical plans with 5–30% eccentricity ratios are studied. For evaluation of accuracy, nonlinear dynamic response of the buildings is determined under a consistent suit of earthquake ground motions. The maxima of the story drifts and shears and cumulative plastic hinge rotations of stories are calculated under the ground motions and their averages along with those of the modal pushover procedure are compared with the results of the presented method. The comparative analysis establishes the good accuracy of the three dimensional drift pushover method.

Effect of soil in controlling the seismic response of three-dimensional PBPD high-rise concrete structures

In the last decades, valuable results have been reported regarding conventional passive, active, semi-active, and hybrid structural control systems on two-dimensional and a few three-dimensional shear buildings. In this research, using a three-dimensional finite element model of high-rise concrete structures, designed by performance based plastic design method, it was attempted to construct a relatively close to reality model of concrete structures equipped with Tuned Mass Damper (TMD) by considering the effect of soil-structure interaction (SSI), torsion effect, hysteresis behavior and cracking effect of concrete. In contrast to previous studies which have focused mainly on linearly designed structures, in this study, using performance-based plastic design (PBPD) design approach, nonlinear behavior of the structures was considered from the beginning of the design stage. Inelastic time history analysis on a detailed model of twenty-story concrete structure was performed under a far-field ground motion record set. The seismic responses of the structure by considering SSI effect are studied by eight main objective functions that are related to the performance of the structure, containing: lateral displacement, acceleration, inter-story drift, plastic energy dissipation, shear force, number of plastic hinges, local plastic energy and rotation of plastic hinges. The tuning problem of TMD based on tuned mass spectra is set by considering five of the eight previously described functions. Results reveal that the structural damage distribution range is retracted and inter-story drift distribution in height of the structure is more uniform. It is strongly suggested to consider the effect of SSI in structural design and analysis.

Experimental Study on Strain Penetration Effects in Fixed‐End Rotation of RC Beam‐Column Connections with High‐Strength Reinforcement

The additional fixed‐end rotation resulting from the strain penetration of longitudinal reinforcement in a reinforced concrete beam‐column connection is a crucial factor for the plastic hinge rotation capacity. When it comes to high‐strength reinforcement, the effects of strain penetration on fixed‐end rotation become more obvious because of the increase in yield strength. In this study, 42 beam‐column connections with high‐strength hot rolled ribbed bars were designed and tested under monotonic loading at the beam end. The test results show that the rebar strains gradually decrease from the critical section towards the beam‐column connection, thereby proving the existence of strain penetration in the beam‐column connection. The slippage of the embedment reinforcement at the beam‐column interface and additional fixed‐end rotations were obtained from the test results. In addition, a parametric study involving the yield strength and diameter of reinforcement, concrete tensile strength, and embedment length in the beam‐column connection was performed to investigate the effects of various parameters on the additional fixed‐end rotation. Finally, a new simple and practical calculation model for predicting the additional fixed‐end rotation was proposed. The prediction shows good agreement with the experimental results.

Seismic Damage Detection of Moment Resisting Frame Structures Using Time‐Frequency Features

To detect seismic damage of moment resisting frame (MRF) structures, a data‐driven method using the fractal dimension (FD) of time‐frequency feature (TFF) of structural seismic dynamic responses at measured stories is extended and refined. The TFF is defined as the real part of Gabor wavelet transform of translational interstory displacement, and FD is used to give a quantitative value to describe the calculated TFF. Static condensation method is first used to reduce the degrees‐of‐freedom (DOFs) of MRF and to express the rotational displacements using translational displacements. For linear MRF, the FDs of TFFs at all stories are the same using the definition of TFF and modal superposition principle. For damaged MRF with plastic hinges at the ends of beams and columns, the force analogy method is implemented to establish transformation matrix from plastic hinge rotations to translational interstory inelastic displacements. Due to the sparseness of the transformation matrix, plastic hinges only generate interstory inelastic displacements, which are low‐frequency contents, in the vicinity of plastic hinges. Correspondingly, the FDs of TFFs of interstory displacements with inelastic component are different from the FDs of TFFs of the interstory displacements that do not contain inelastic component. A numerical simulation on a 16‐story MRF was conducted. The simulation included 10 cases such as no damage or linear structure, plastic hinges in single‐story beams, plastic hinges in single‐story columns, plastic hinges in single‐story beams and columns, and plastic hinges in multiple story beams and columns. The robustness to measurement noise was also investigated. The seismic damage detection results demonstrated that the proposed method was capable of locating the stories where the plastic hinges occurred.

Effects of steel-to-member depth ratio and axial load on flexural ductility of concrete-encased steel composite columns

This paper experimentally studies flexural ductility of eight concrete-encased steel composite columns. The composite columns are tested under cyclic loading with various axial load levels. In addition to the axial load level, effects of steel-to-member depth ratios on flexural behavior of encased composite members are investigated in this study. Two types of concrete-encased steel composite specimens are designed to represent two steel-to-member depth ratios. Displacement ductility ratios, drift ratios, and plastic hinge rotations obtained from cyclic load tests are used for evaluating flexural ductility of test specimens. Results from this study show that both the axial load level and steel-to-member depth ratio have a significant impact on flexural performance of concrete-encased steel composite columns.

11.53: Reduced cross‐sections in seismic resistant steel structures

ABSTRACTIn case of flexural dissipative members in eccentrically braced frames, a detail with reduced beam flanges sections at the link ends leads to a better control of the inelastic deformations along the dissipative member, together with a reduction of the plastic hinge rotation demand and with significant lateral stiffness of the braced frame.Configurations resembling the “dog‐bone” near the ends of the upper stories diagonals in concentrically braced frames ensure on one hand, the abidance of the slenderness demand for the braces and on the other hand, small values of the amplification ratio Ωi(N)=NplRd,i/NEd,i. The reduced cross‐section of the diagonal in the “dog‐bone” detail zones ensures an adequate tensile capacity of the braces and small Ωi(N) values. At the same time the buckling behaviour and slenderness of the braces is not significantly affected by the reduced cross‐sections near the member ends and the slenderness demand of the braces will be fulfilled.A favourable global plastic hinge mechanism can be sized by design for concentrically braced frames by providing configurations with reduced cross‐sections for potentially plastic zones located in the frame girders in the neighbourhood of the beam/column connections. So plastic deformations can develop in the braces, at the bottom of first‐story columns and in potentially plastic zones located near the ends of frame girders, and a favourable global plastic failure mechanism can be achieved. The same design concept can be used for sizing a favourable global plastic mechanism for frames with rigid beam/columns connections equipped with buckling restrained braces.Configurations with “dog‐bone” details near the base of bottom‐story columns appear to be safer from the point of view of assuring the general stability of the first‐story column in the situation when plastic deformations occur in the potentially plastic zone at the bottom of the column. Further, a better control of the plastic deformations along the first story columns is ensured.

Development of simple design-oriented procedure for predicting the collision damage of FPSO caisson protection structures

Protection structures for FPSO (Floating Production Storage and Offloading) caissons should be sufficiently strong so as not to contact caisson pipes even when the protection structure is damaged by an impact by attendant vessels. In the present structural design process, non-linear commercial packages are employed for collision analyses. However, non-linear collision analyses using commercial packages are time-consuming and expensive to operate, especially in the initial design stage. In this study, substantiation of the adopted commercial package was first performed using collision test results on single pipes and H-shape pipes. Then, a rigorous parametric study was conducted by changing the design variables. A simple analytical expression was derived assuming that the kinetic energy of the striking vessel was dissipated by the plastic elongation of pipes and rotation of plastic hinges. Using the parametric study results, design equations to predict the maximum deflection and overall bending damage were obtained by which the effects of local denting and dynamic behaviour could be considered. Additionally, an equation to predict the extent of local denting damage was also derived. The developed procedure was numerically substantiated using the predicted extent of damage to an actual protection structure.

A case study on the assessment of response modification coefficient and earthquake-induced collapse potential of a high-rise setback tower

This paper evaluates response modification coefficient (R-factor) and collapse potential of a high-rise tower with setback irregularity under spectral-matched ground motion records. The tower is comprised of two legs with three distinct lateral bearing systems in elevation and curved configuration in plan. Furthermore, it has a setback in elevation, recognised by inclined columns joining two legs of the tower in uppermost stories. These characteristics cause the tower to classify as a complex irregular structure in which using code-based R-factor is highly dubious. In this paper, initially, an analytical model of the tower was subjected to a suite of ground motions to estimate collapse potential and equivalent R-factor in accordance with FEMA P695. Alternatively, structural performance parameters including inter-storey drift ratios, residual drift ratios and plastic hinge rotations were compared to TBI acceptance criteria. To achieve consistent safety margin against collapse, the value of 8 was suitable for R-factor. In spite of satisfactory threshold in accordance with FEMA P695 and TBI guidelines, for a structure with irregular configuration and multiple bearing system, damages can be localised close to zones of change in lateral bearing system that may lead to partial collapse.