Potential Plastic Hinge Regions Research Articles

Seismic Response Analysis of Continuous Beam Bridges with Engineered Cementitious Composite (ECC) in Plastic Hinge Region

This study investigates the seismic performance of potential plastic hinge regions in small and medium-sized bridges using Engineered Cementitious Composite (ECC) concrete. A 4×40m continuous beam bridge is used as an example, with time-history analysis conducted using the OpenSees finite element software, and the type of concrete material in the cross-section of the bridge pier’s plastic hinge region is varied to analyze the structural natural vibration characteristics and seismic responses of the bridge structure under earthquake action. The time-history analysis of seismic motion shows that after replacing the bridge pier’s plastic hinge region with ECC, the stiffness of the bridge pier significantly decreases, and the natural vibration period of the bridge increases. Under the action of longitudinal earthquakes, the energy dissipation capacity and seismic performance of the bridge pier increase with the increase in ECC content in the plastic hinge region at the bottom of the bridge pier. Furthermore, under earthquake action, the concrete at the edge of the cross-section using ordinary concrete throughout cracks under tension, while the tensile stress in the cross-sections using different proportions of ECC concrete remains the same and does not crack under tension, remaining elastic under compression, which also reflects the good seismic performance of ECC concrete.

Seismic behavior of shear walls partially strengthened with UHPC in boundary element

Inspired by studies on shear walls reinforced with high performance cement-based materials, this paper explores the applicability of ultra-high performance concrete (UHPC) for improving the seismic behavior of shear walls. In this study, a novel shear wall partially strengthened with UHPC in the boundary element was developed, in which the UHPC was cast into the potential plastic hinge region of the boundary element. Partial application of UHPC can reduce construction costs and promote its use in building structures. To study the influence of distribution height and width of UHPC and axial load ratio on the seismic performance, six shear walls with a shear span ratio of 2.1 were tested under axial load and cyclic lateral load. The failure modes, lateral load-lateral displacement hysteretic behavior and ductility of the shear walls were also investigated. The experimental results indicated that the partial application of UHPC in boundary elements could effectively improve the performance of shear walls. Moreover, even if the volume ratio of UHPC was only 0.12, the shear wall partially strengthened with UHPC still showed good seismic performance under a high axial load ratio, indicating that this type of shear wall can be applied to the high seismic intensity and high axial load ratio regions.

Seismic performance of composite jacket-confined square high-strength concrete-filled steel tube columns

Adding external confining jackets in the potential plastic hinge regions is a practical approach to improving the deformation capacity of square concrete-filled steel tube (CFST) columns with high-strength concrete (HSC). To investigate the seismic behavior of composite jacket-confined square CFST columns with HSC, three jacket-confined CFST (JCCFST) columns and two CFST counterparts with concrete compressive strength of approximately 125 MPa were tested. The test variables included the jacket configuration and steel tube strength. The test results demonstrated that both the jacket-confined region and the adjacent unconfined region could be damaged when the jacket length was 1.25 times the steel tube width. Finite element analyses were also performed to comprehensively investigate the influence of the parameters on the column behavior. It was found that the ultimate drift ratio, θu, increased approximately in proportion to the effective jacket confinement index, λm, and the confinement index of the CFST section, ξs, and decreased rapidly as the axial load ratio, n, increased. The ratio of the moment capacity of a JCCFST column to that of the corresponding CFST column, Mju/M0u, increased as λm increased. The influence of n and ξs on Mju/M0u was not significant. Formulas for designing the confining jacket were also developed.

Application of engineered cementitious composites in the plastic hinge of reinforced concrete beams for seismic enhancing

AbstractShear failure of the potential plastic hinge region of reinforced concrete (RC) beam usually causes irrational failure mechanism and low seismic response of the whole frame structure. In this study, engineered cementitious composite (ECC) was proposed to apply locally in the potential plastic hinge region of RC beams to improve the failure mode and rotation capacity of the members. One RC beam and five ECC‐RC composite beams were manufactured, and tested by lateral cyclic loading. The test variables were the length of ECC strengthening region, stirrup ratio and longitudinal reinforcement ratio. The test results indicated that the plastic hinge region of the RC beam failed in shear with poor plastic deformation and low energy dissipation. For the ECC strengthened beams, flexural behavior dominated the ECC region and shear failure was migrated up into the concrete region or eliminated. The ECC region of the composite beams exhibited great rotation capacity, thus the hysteretic response, plastic deformability and energy dissipation of the ECC strengthened beams were improved significantly. Meanwhile, applying ECC in the plastic hinge effectively enhances the damage tolerance of the beams. Based on the test results, the substituting length of ECC in the potential plastic hinge of the RC beam is recommended to be no less than the beam height. Besides, the strength of ECC strengthened beam can be calculated and checked by the current design codes.

Cyclic behavior of concrete-filled square tubular columns with stiffened plastic hinge region

The seismic behavior of concrete-filled square steel tube (CFST) columns is greatly influenced by the local-buckling of steel tubes within the plastic hinge region. This paper focuses on a novel stiffener that strengthens the potential plastic hinge regions to enhance the local-buckling resistance of steel tube, hence improving the overall seismic performance of the CFST columns. To verify its effectiveness and investigate the hysteretic behavior of the stiffened CFST (referred to as SCFST) columns, three CFST and three counterpart SCFST columns were fabricated and tested under cyclic lateral load while subjected to constant axial load. Furthermore, flexural capacities calculated using representative design equations in current codes as well as a newly proposed method were compared with the experimental results. Calculation method for the effective strengthening length of SCFST was presented. The test and analytical results showed that: (1) this stiffeners could effectively delay the local buckling of steel tube and change its local buckling modes; (2) the stiffener significantly enhanced the lateral load capacity of SCFST columns with improvement of 14%, 15%, and 38% comparing with the counterpart CFST columns; (3) the thinner the steel tubes, the more significant the effect of the stiffener on the ultimate lateral capacities; (4) the design equations prescribed in current codes tended to underestimate the ultimate flexural strength of SCFST columns with a discrepancy between 22% and 60%; (5) the proposed calculation method taking account of the effect of the stiffener, could more accurately predict the flexural strength of SCFST columns than current design equations with an improved discrepancy ranging between 7% and 32%.

Seismic behavior of carbon fiber reinforced polymer confined concrete filled thin-walled steel tube column-foundation connection

To alleviate the complex construction process of traditional concrete filled steel tube (CFST) column-foundation connections, the anchor rebar column-foundation connection (ARCFC) has been conceived and investigated. To date, the thin-walled steel tube is recommended to be used considering it economic benefits. However, the confinement provided by the thin-walled steel tube is found to be insufficient as bulges of steel tube and concrete are observed. In this paper, carbon fiber reinforced polymer (CFRP) is adopted in the potential plastic hinge region to prevent the local buckling of steel tube. Nine specimens were designed and tested to failure under combined constant axial load and reversed cyclic lateral load. The investigated parameters are the number of CFRP layers and the diameter-to-thickness of steel tube. Experimental results revealed that bulges of steel tube and concrete were observed for ARCFCs with a diameter-to-thickness ratio of steel tube over 120. CFRP could effectively prevent the bulges of steel tube and concrete. All the ARCFCs have excellent energy dissipation capacity and the ductility coefficient is larger than 4.55. A finite element model (FEM) is developed to conduct a parametric study, based on which the sectional strength model is suggested.

Seismic Behavior of RC Bridge Piers Locally Replaced with SFRC-FA Subjected to Torsion Combined with Axial Compression

Under complex seismic forces, the failure characteristics of the plastic hinge region at the bottom of the pier column and the methods improving the ductility have attracted extensive attention. In this study, steel fiber-reinforced concrete with fine aggregate (SFRC-FA) was applied to locally replace the conventional concrete in the potential plastic hinge region at the bottom of the pier column. Five SFRC-FA pier column specimens with different stirrup ratios and different replacement lengths and one conventional reinforced concrete pier column specimen were produced. Using the seismic behavior tests under the combined bending-shear-torsion-axial force, the failure mode, torsional bearing capacity, energy dissipation, and the torsional plastic hinges of the pier columns were investigated. In addition, an equation for calculating the torsional bearing capacity of the new composite pier columns was proposed. The results showed that (1) compared with the reinforced concrete pier column, the plastic hinge was shifted from the bottom of the pier column to the middle of the height of the pier column due to the application of SFRC-FA at the bottom of the pier column, which improved the torsional bearing capacity; (2) the effect of reducing the stirrup ratio of the SFRC-FA replacement region on the torsional bearing capacity, cracking mode, energy dissipation, and ductility was not obvious; (3) the accuracy of the new equation based on the space truss model proposed in this article was verified by comparison with the experiments of this study and other researches.

Development and Application of Spring Hinge Models to Simulate Reinforced Ductile Concrete Structural Components under Cyclic Loading

Ductile concrete materials with randomly oriented fibers have been studied to improve the strength, displacement capacity, and damage tolerance of reinforced concrete structural components in seismic applications. Performance-based earthquake engineering requires numerically efficient models that are capable of estimating the hysteretic behavior, including the strength, stiffness, cyclic degradation behavior, and failure criteria. This paper discusses the development of an experimental database and its use in the calibration of a phenomenological model to simulate the nonlinear behavior of reinforced ductile concrete components under cyclic loading. The modeling parameters are calibrated to predict the initial stiffness, lateral strength, deformation capacity, and cyclic and in-cycle degradation. Backbone parameters were selected using a mechanics-based approach combined with a calibration of hysteretic parameters to match an energy-based damage index. A large-scale experimental database with a variability in material properties, geometry, testing configurations, and fiber types was used for calibration purposes. A forward stepwise regression analysis was conducted to develop an empirical equation for a stiffness reduction factor and a cyclic strength degradation parameter as functions of material behavior and geometry. The modeling strategy is validated by comparing an experimental and simulated cyclic response across a range of metrics. The spring-hinge models are then applied to evaluate the collapse risk of the archetype frame structures using ductile concrete material in the potential plastic hinge region of the beams. The collapse performance is evaluated through an incremental dynamic analysis in which the results of reinforced concrete structures with and without ductile concrete material are compared in terms of the median collapse capacity, fragility curve, mean annual frequency, and sequence of hinge formation in the collapse mechanism. The outcome of this research provides much needed insight into how ductile concrete materials can influence structural system-level seismic performance.

Shear Strength of Reinforced Concrete Columns Retrofitted by Glass Fiber Reinforced Polyurea

Aged structures and structures constructed based on outdated non-seismic design codes should be retrofitted to enhance their strength, ductility, and durability. This study evaluates the structural performance of reinforced concrete (RC) columns enhanced via polyurea or glass fiber reinforced polyurea (GFRPU) strengthening. Four RC column specimens, including a reference specimen (an unstrengthened column), were tested to evaluate the parameters of the strengthening materials and the strengthened area. The tests were carried out under a combined constant axial compressive load and quasi-static cyclic loading. The experimental results show that the composite strengthening provides lateral confinement to the columns and leads to enhanced ductility, shear-resistance capacity, and dissipated energy. The shear strength provided by the composites depends on the degree of lateral confinement achieved by the composite coating. The specimens finally failed through the development of diagonal tension cracks within the potential plastic hinge regions. The specimen treated with GFRPU strengthening showed greater strength and dissipated more energy than the specimen treated with polyurea strengthening. Furthermore, by modifying ATC-40, this study proposed an equation to estimate the shear capacity provided by the composites.

Moment-Curvature Behavior of PP-ECC Bridge Piers under Reversed Cyclic Lateral Loading: An Experimental Study

In the study, the moment–curvature relations of bridge piers constructed with polypropylene-fiber-reinforced engineered cementitious composite (PP-ECC) and reinforced concrete (RC) at the potential plastic hinge regions were performed experimentally. The bridge pier specimens were subjected to a combination of constant axial vertical loading and reversed cyclic lateral loading. The test variables include the reinforcement stirrup ratio, axial compression ratio, and height of the PP-ECC regions. Strain gauges were installed at the plastic hinge regions to determine the curvature. PP-ECC and RC bridge piers presented similar shapes of moment–curvature hysteretic curve. Regardless of the concrete type for the pier, the maximum moment and curvature were located near the bottom of the pier, which was consistent with the observed failure patterns. As greater peak moments and larger areas of hysteretic curves were observed for PP-ECC piers, this indicated that the use of PP-ECC at the potential plastic hinge regions significantly improved the deformation capacity and damage tolerance of bridge piers. Regarding the design variables, it was found that the axial loading ratio has a negative effect on enhancing the rotation capacity and plastic deformability, while the height of the PP-ECC portion and the amount of reinforcement stirrups displayed the opposite trend. Moreover, the contribution of stirrups in PP-ECC piers was more significant than that of RC ones.

Seismic Performance of Bridge Piers Constructed with PP-ECC at Potential Plastic Hinge Regions.

This work presents an experimental investigation on the seismic performance of bridge piers constructed with polypropylene fiber reinforced engineered cementitious composite (PP-ECC) at potential plastic hinge regions. Eight solid square bridge piers are tested under a combination of reversed cyclic lateral loading and constant axial vertical loading. The test variables include the reinforcement stirrup ratio (0 vol.%, 0.46 vol.%, and 0.79 vol.%), axial compression ratio (0.1 and 0.3) and height of the PP-ECC regions (0, 250, and 500 mm). Seismic performance of eight specimens is presented and interpreted, including the failure mode, hysteretic curves, loading–resistance capacity, ductility, stiffness degradation, energy dissipation, and equivalent viscous damping ratio. The material test on the PP-ECC plate specimen suggests that the PP-ECC has obvious strain-hardening behavior and multiple fine-cracking characteristics, with the tensile strength and strain capacity greater than 3.2 MPa and 2.6%, respectively. The PP-ECC material applied at the potential plastic hinge regions notably improves the seismic performance and damage tolerance of bridge piers. The influence of the aforementioned crucial parameters has also been investigated in detail. The axial compression ratio and the height of PP-ECC region have a major influence on the seismic performance of PP-ECC piers. In comparison, the stirrup ratio has a limited effect on the seismic behavior of PP-ECC piers. The experimental findings shed light on the mechanism of the PP-ECC that contributes to the seismic performance of bridge piers and provide some valuable guidance in the seismic design of PP-ECC piers.

Seismic Performance of Bridge Piers Reinforced with Shape Memory Alloys in Plastic Hinge Region

The recent earthquake reconnaissance reports revealed that a large residual displacement had led to the devastation of bridge piers due to serviceability concerns. Shape Memory Alloys (SMA) is the distinctive category of smart materials, which can sustain enormous deformations and reappear to a parent shape after removal of loading or by removal of heat. Replacing the typical steel reinforcement with SMA reinforcement in the potential plastic hinge regions of bridge piers could reduce the residual displacement of a pier. This study is focused on the numerical investigation of circular bridge piers with SMA-based reinforcement in the plastic hinge regions to mitigate the residual displacement. The numerical model of a bridge pier is validated using the experimental results of SMA-reinforced bridge pier. Dynamic time history analyses are performed to compare the performance of SMA-reinforced bridge piers with steel-reinforced bridge piers under the effect of various earthquake ground motions. The results are represented in terms of displacement, base shear, and ductility. Moreover, the influence of several parameters on the performance of bridge piers is investigated, i.e., aspect ratio, axial load ratio, and compositions of SMA. The numerical results have indicated the effectiveness of bridge piers reinforced with SMA by reducing the residual displacement after major earthquake events.

Seismic behavior of 3-D ECC beam-column connections subjected to bidirectional bending and torsion

Special moment resisting frames (SMF) are commonly used in low- and medium-rise buildings located in regions of high seismicity. Although adequate performance of this seismic force resisting system was observed in prior earthquakes in terms of protecting buildings from collapse, the formation of plastic hinges in the beams and columns causes irreparable damage to the beam-column connections. Recently, interest in using fiber-reinforced concrete (FRC) has been growing to enhance energy absorption capacity and damage tolerance of beam-column connections and other components in reinforced concrete (RC) buildings. Prior research has mostly focused on the application of steel FRC (SFRC) in 2-D beam-column connections. However, little is known about the performance of exterior beam-column connections that are usually subjected to more complex loading during an earthquake, involving bi-directional bending and torsion of the column. In addition to the loading, the geometry of the connection requires a more involved test setup (i.e., with an out-of-plane beam and proper boundary conditions). In this research, the use of engineered cementitious composites (ECC) in 3-D exterior beam-column connections is investigated experimentally to improve building seismic performance. ECC is a special class of high-performance fiber-reinforced cementitious composites (HPFRCC) that, compared to conventional concrete, exhibits higher tensile ductility, energy absorption and shear resistance, in addition to improved bond performance with reinforcing steel (rebar). To understand the performance of exterior beam-column connections under complex loading conditions, scaled 3-D specimens were constructed and tested under simulated seismic loads. To improve the performance of the connections, conventional RC was replaced with reinforced ECC (RECC) that extends from the panel zone to the adjoining beams and columns to cover the potential plastic hinge regions. This paper discusses the loading protocols, the test setup for 3-D exterior beam-column connections, and the improvement in the joint behavior with the application of RECC as compared to conventional RC. The results suggest that the efficient use of ECC in the potential plastic hinge regions can improve the capacity and damage tolerance of beam-column connections under realistic seismic loading conditions.

Comparative Analysis of Existing RC Columns Jacketed with CFRP or FRCC.

Reinforced concrete (RC) columns typical of existing structures often exhibit premature failures during seismic events (i.e., longitudinal bars buckling and shear interaction mechanisms) due to the poor quality concrete and the absence of proper seismic details in the potential plastic hinge region. The Fiber Reinforced Polymers (FRP) externally bonded reinforcement is known to be a valid technique to improve the shear capacity or the ductility of existing RC columns. However, few experimental tests have proven its effectiveness in the case of columns affected by shear interaction mechanisms. In this work, the behavior of existing RC columns with border line behavior between flexure and shear have been investigated in the case of poor quality concrete and light FRP strengthening with local jacketing and medium quality concrete and strong FRP strengthening with local jacketing, in order to highlight the effect of concrete strength on the effectiveness of the retrofit intervention. As an alternative to FRP jacketing; the effectiveness of the Fiber Reinforced Cementitious Composite (FRCC) jacketing for the seismic strengthening of columns with highly deteriorated concrete cover or columns already damaged by an earthquake is also evaluated. Six full-scale RC columns have been tested under cyclic loading: one was used as a control specimen; four were strengthened in the potential plastic hinge region with carbon FRP (CFRP); and one was fully jacketed with FRCC. The comparison between poor and medium quality concrete columns showed that the CFRP local jacketing is more effective in the case of poor quality concrete. The FRCC jacketing appears to be a sound repair strategy and a suitable alternative to the FRP jacketing in case of poor quality; however, more experimental research is needed for improving this retrofit technique.

Seismic performance of CFRP-retrofitted large-scale rectangular RC columns under lateral loading in different directions

Considerable studies have been carried out on the seismic performance of fiber-reinforced polymer (FRP) retrofitted reinforced concrete (RC) columns. However, research on the seismic performance of FRP-retrofitted RC columns under lateral loading in different directions remains limited. This paper presents an experimental investigation on both un-retrofitted and carbon FRP (CFRP) retrofitted rectangular RC columns with an emphasis on the effect of the directions of lateral loading on the seismic performance of the columns. A total of ten large-scale cantilever rectangular RC columns were constructed and five of them were retrofitted with CFRP wraps at the potential plastic hinge regions. The overall performance of each specimen is examined in terms of damage evolution, lateral load-displacement hysteretic behavior, lateral strength, ductility capacity, stiffness degradation, and energy dissipation. The direction of lateral loading is found to have significant influence on the seismic performance of both un-retrofitted and CFRP-retrofitted rectangular RC columns. It is also found that the shear strength of the un-retrofitted and FRP-retrofitted rectangular RC columns in nonprincipal directions can be predicted based on the lateral strength in the principal directions by the ellipse equation.

Seismic performance of CFRP-confined circular high-strength concrete columns with high axial compression ratio

This paper presents an experimental investigation on the seismic performance of circular high-strength concrete (HSC) columns confined with carbon fiber-reinforced polymer (CFRP) composites. A total of eleven 1/2 scale columns were constructed of which nine were confined with CFRP wraps at potential plastic hinge regions. All columns were tested under combined high axial compression load and cyclic lateral displacement excursions. The primary variables of the tests were the axial compression load level, concrete strength, and the extent of the CFRP wrapping at the plastic hinge region. In order to evaluate the residual seismic capacity of CFRP-confined columns, three of the confined specimens were initially loaded to induce damage. The load was then removed after which the same columns were loaded to failure. The failure modes, hysteretic responses, energy dissipation and stiffness degradation characteristics, and the equivalent viscous damping ratios of the tested columns were then presented and interpreted. The test results showed that CFRP wraps applied at potential hinge regions resulted in significantly improved ductility and energy dissipation capacities of the columns even when tested under a high axial compression ratio. The plastic deformation capacity of the CFRP-confined columns was observed to decrease with an increase of axial compression ratio though. In addition, pre-damaged CFRP-confined columns may have insufficient residual seismic capacity due to the damage and failure in the unconfined regions under high axial compression load levels. Finally, empirical models of the degradation of effective and unloading stiffness are provided based on the test results.

Seismic retrofitting of full-scale RC interior beam-column-slab subassemblies with CFRP wraps

To investigate the effect of carbon fiber-reinforced polymer (CFRP) retrofitting on the failure modes and seismic performance of reinforced concrete (RC) frames, this paper presents the quasi-static test results of four full-scale interior subassemblies with slab and transverse beams. These beam-column-slab subassemblies consisted of one control specimen and three specimens with different CFRP retrofitting schemes. The seismic performance of subassemblies was discussed by comparing failure modes, hysteretic behavior, displacement ductility, stiffness degradation, energy dissipation capacity, shear deformation of joint region and beam vertical deformations. The test results demonstrated that the control specimen finally exhibited column-hinge failure mode due to the existence of slab and transverse beams. After being retrofitted with CFRP, the failure varied to ductile beam-hinge failure mode and the ductility and energy dissipation capacity were enhanced. For the interior beam-column-slab subassemblies, wrapping CFRP wraps at the potential plastic hinge region of columns is a reasonable method for improving the seismic performance and implementing the strong column-weak beam failure mode.

Vulnerability and improvement of reinforced ECC flexural members under displacement reversals: Experimental investigation and computational analysis

Engineered Cementitious Composite (ECC) is characterized by ductile tensile strain-hardening behavior accompanied by multiple narrow cracks. Its ultimate tensile strain under uniaxial loading is often reported to be more than 3%. This study explores the flexural performance of regular and innovative reinforced ECC members under displacement reversals. Four reinforced cantilever structural beams are prepared and tested under cyclic loading. Among the specimens, two ECC beams are proposed to improve the failure mechanism of regular reinforced ECC beams, which are found to be prone to steel fracture in this study. In one specimen, the flexural rebar is debonded in the potential plastic hinge region. In another specimen, it is flexurally reinforced with Nickel–Titanium shape memory alloy (SMA) rebar with the property of superelasticity. The behaviors of the cantilever beams are evaluated using multiple performance measures, including hysteretic loops, numbers of cracks, beam rotations, and steel strains. In addition to the experimental study, computational models which are capable of simulating the hysteretic behavior of the tested specimens with reasonable accuracy are suggested.

New configuration of transverse reinforcement for improved seismic resistance of rectangular RC columns: Concept and axial compressive behavior

Columns are considered to be critical members of moment-resisting structural systems. In seismically active regions, it is important to improve the ductile deformation capacity and energy dissipation capacity of columns so that the entire structure can endure severe ground motion and dissipate a considerable amount of seismic energy. Against this background, this paper presents the idea of a new transverse reinforcement configuration (TRC) for improved seismic performance of rectangular (including square) reinforced concrete (RC) columns. The novel features of the new TRC compared to conventional TRCs using rectangular hoops and cross ties mainly include the use of additional small circular spirals near the column ends (i.e., potential plastic hinge regions). Such a simple change can significantly enhance the performance of RC columns without complicating their construction. In this paper, the rationale for the new TRC together with its expected advantages is first explained. A series of axial compression tests on RC columns with the new TRC are then presented to demonstrate some of the expected advantages. The test results confirmed that the concrete is very effectively confined by the new TRC, leading to significant enhancements in both the load capacity and ductility of RC columns.

Plastic hinge length of reinforced concrete slender shear walls

This paper proposes a simple model that can reasonably determine the potential plastic hinge region for seismic design of shear walls. To idealise the plastic hinge region, a parametric study is conducted on the curvature distribution over the member length using a non-linear, two-dimensional, finite-element analysis procedure. To solve the plastic hinge length equation derived from the idealised curvature distribution, the equations for yielding and ultimate moment capacities of shear walls are generalised on the basis of Bernoulli's principle, strain compatibility condition and equilibrium condition of forces. The generalised equations promise that the yielding and ultimate moment capacities of shear walls can be straightforwardly evaluated with relatively high accuracy. Ultimately, the plastic hinge length of the shear wall is then simply formulated as a function of longitudinal tensile reinforcement index in the boundary element, vertical shear reinforcement index in the web, and axial force index. The predicted plastic hinge lengths obtained from the current simple model are in better agreement with test results than the previous equations; the mean, standard deviation and coefficient of variation of the ratios between experiments and predictions are 1·019, 0·102 and 0·100, respectively.