Post-yield Stiffness Research Articles

Cyclic behavior of bridge columns with partially unbonded seven-wire steel strands to increase post-yield stiffness

A new method of increasing post-yield stiffness of bridge columns to reduce the residual displacement after large earthquakes is proposed. In the proposed method, partially unbonded unstressed seven-wire steel strands are used as elastic element to increase the post-yield stiffness of the column. Three large-scale column specimens were tested using lateral cyclic loading to investigate the seismic performance of the proposed column. Test results showed that the use of the unstressed partially unbonded steel strands effectively increased the post-yield stiffness ratio of a conventional bridge column from −0.3% to 6.4%, which exceeded the 5% post-yield stiffness ratio that has been shown in the literature to reduce the residual displacement significantly. Test results also showed that the post-yield stiffness could not be maintained when the strands started to bulge in compression. The ultimate drift was slightly reduced from 5.76% to 4.77%. The use of fully bonded strands further increased the post-yield stiffness ratio to 8.8%. However, the ultimate drift ratio was greatly reduced to 2.84%. To predict the behavior of the proposed column under lateral load, a pushover model was developed. The strain of the partially unbonded strand was calculated based on deformation compatibly with the longitudinal deformed steel bar. The effect of anchorage slip was considered. Comparison with the test results showed that the proposed model captured well the envelope response of the proposed column.

Machine learning-based prediction for maximum displacement of seismic isolation systems

This study developed machine learning (ML) models for predicting the peak lateral displacements of seismic isolation systems subjected to earthquakes. Six ML methods were employed for this purpose: linear, ridge, least absolute shrinkage and selection operator (lasso), artificial neural network (ANN), support vector machine, and random forest (RF). The isolated superstructure was assumed to be rigid, and the base isolation system was assumed to be firmly anchored to a bedrock foundation. A total of 234,360 data points were generated using OpenSees to train and test the predictive models. The input variables included three parameters representing the behavior of isolation systems (i.e., the ratio of the initial to post-yield stiffness, normalized characteristic strength, and post-yield period) and the average spectral accelerations at five selected periods (i.e., 1, 2, 3, 4, and 5 s) for the considered ground motions. The RF model exhibited the best performance among the six models. The coefficients of determination (R2) for the RF model were 0.9930 and 0.9498 for the training and testing datasets, respectively. In addition, the ANN model exhibited the second-best performance. The normalized characteristic strength was found to be the most influential variable in the investigation of the individual input variables for the prediction. Finally, a practical analysis of a hypothetical three-story base-isolated moment frame building was performed to demonstrate the effectiveness and limitations of the developed RF model in predicting the maximum displacements of the isolation systems. The prediction results were compared with those from a previous study and with the equivalent linear force procedure in American Society of Civil Engineers (ASCE) 7–16. A graphical user interface was created for the developed RF model for easy access by engineers. This study represents a pioneering step for the application of ML to the estimation of the responses of seismic isolation systems in practical design.

Improved performance-based plastic design method for post-tensioned connection systems

Performance-based plastic design (PBPD) was initially proposed as a method for retrofitting existing structures. The PBPD method gradually became a general approach for designing new structures. This method is a direct method to obtain design base shear and leads to design structures being more economical compared to traditional methods. PT connections were developed after the Northridge earthquake. The self-centering could restore the connection to its original position without damage to the beams and columns. High-strength post-tensioned cables are used to restore the structure to its initial position in PT connections. Also, energy dissipaters (for example, top and bottom angles) are used to increase ductility. In this study, a proposed relationship between the ductility (µ), period (T), and response reduction factor (R) is presented for structures with pinching or flag-shaped behavior, and the effect of the parameters on R has been investigated. Also, a new design approach for structures with PT-steel connections with top-and-bottom angles is presented. The results show that R primarily depends on the post-yield stiffness ratio (α), the yield stress ratio (or energy dissipation) (β), ductility (µ), soil type, etc. Nonlinear time-history analysis indicates that designed models based on the proposed approach satisfy drift limits. The results show that the proposed relationship can be quite suitable for designing PT connections using the PBPD approach.

Seismic Behaviors and Resilience of Concrete-encased Concrete-Filled Steel Tubular Columns with Debonded High-Strength Rebars: Experiment and Assessment

ABSTRACT A total of six cantilever square concrete-encased CFST columns were fabricated for testing under both lateral load and constant compressive load. The debonded high-strength PSB 930 steel rebars were used as the longitudinal rebar to provide resilience for specimen columns. Experimental results indicated that the specimens with debonded PSB longitudinal rebars had smaller residual deformation and smaller yield sectional stiffness compared with the specimen with normal steel rebars because the yielding progress of the longitudinal rebar was delayed. Based on the parametric analytical results, some models are proposed to assess the yield and post-yield sectional stiffness and the residual drift.

Application of seismic resilient energy-dissipative rocking columns with HSS tension braces in steel frames

Steel moment resisting frames are widely used as seismic resisting systems of buildings in earthquake regions. Since their satisfactory performance is achieved by developing plastic deformation in critical regions, it usually leads to inter-storey drift concentration during a strong earthquake and significant residual deformation after a strong earthquake. To mitigate seismic damage concentration and excessive residual deformation, this study proposed a high post-yield stiffness rocking system, namely energy-dissipative rocking columns with high strength steel tension braces (EDR-TB). The study commenced with lateral cyclic loading tests on the proposed EDR-TB column. Subsequently, numerical model of the EDR-TB was built and validated against test results. System-level nonlinear static and time-history analysis were then conducted on the steel frame with various layouts of the EDR-TB columns. Compared with a conventional steel frame, the frame with EDR-TB columns exhibited much reduced maximum and residual drifts. In addition, the frame with EDR-TB columns exhibited more uniform distribution of drifts. The results also reveal that an appropriate arrangement of lateral resisting capacity of the EDR-TB columns over the structural height may achieve an enhanced seismic performance of the whole structures.

Seismic response of RC frames equipped with buckling-restrained braces having different yielding lengths

<abstract> <p>Buckling-restrained braces (BRBs) have proven to be a valuable earthquake resisting system. They demonstrated substantial ability in providing structures with ductility and energy dissipation. However, they are prone to exhibit large residual deformations after earthquake loading because of their low post-yield stiffnesses. In this study, the seismic response of RC frames equipped with BRBs has been investigated. The focus of this research work is on evaluating the effect of the BRB yielding-core length on both the maximum and the residual lateral deformations of the braced RC frames. This is achieved by performing inelastic static pushover and dynamic time-history analyses on three- and nine-story X-braced RC frames having yielding-core length ratios of 25%, 50%, and 75% of the total brace length. The effects of the yielding-core length on both the maximum and the residual lateral deformations of the braced RC frames have been evaluated. Also, the safety of the short-yielding-core BRBs against fracture failures has been checked. An empirical equation has been derived for estimating the critical length of the BRB yielding cores. The results indicated that the high strain hardening capability of reduced length yielding-cores improves the post-yield stiffness and consequently reduces the maximum and residual drifts of the braced RC frames.</p> </abstract>

Shaking table test of concrete columns hybrid reinforced by steel/FRP bars

Post-earthquake residual deformation can be decreased due to the designable post-yield stiffness of concrete column reinforced by steel bars/fiber reinforced polymer (FRP) bars. Shaking table tests of three concrete columns with similar initial stiffnesses were conducted, where the longitudinal reinforcement included ordinary steel bars, steel-FRP composite bars (SFCBs) and hybrid reinforcement (steel bars and FRP bars, C–H). The measurements included acceleration response and strain development. The test results showed that the absolute and relative peak ground acceleration (PGA) responses of different columns were similar to one another. The residual strain in the anchorage region was not consistent (tension or compression) and was affected by the longitudinal reinforcement type and the amplitude of the input PGA. For ordinary reinforced concrete (RC) columns, the plastic strain of steel bars developed rapidly after the input ground motion PGA reached 100 Gal, and the corresponding residual strain also developed dramatically. For the SFCB column, even after the peak strain reached 15,000 με, the residual strain was still below 500 με. For hybrid column C–H, the residual strain of the FRP bar was similar to that of the SFCB column. Even when the input wave PGA reached 560 Gal with concrete cover spalling and steel bar buckling, no damage was observed on the FRP bars. In general, compared to ordinary RC columns, concrete columns with hybrid steel and FRP bar reinforcement can achieve a smaller residual deformation, while SFCB reinforced columns can be constructed in severe environments due to a good anti-corrosion performance, such as in offshore structures.

Comparing Hysteretic Energy and Ductility Uniform Annual Failure Rate Spectra for Traditional and a Spectral Shape-Based Intensity Measure

In this study, with the objective to develop a reliability-based seismic design tool, ductility and dissipated hysteretic energy uniform annual failure rate (UAFR) spectra are obtained and compared using the spectral acceleration at first mode of vibration of the structure Sa(T1) and the well-known spectral shape-based intensity measure INp. Notice that this is the first time in the literature that UAFR spectra are obtained for the advanced spectral shape intensity measure INp. For this aim, 110 simulated ground motions recorded from the soft soil of Mexico City were selected due to their large energy amount demanded to the structures; moreover, four elastoplastic hysteretic behavior models are considered for the dynamic analyses with post-yielding stiffness of 0, 3, 5, and 10%. It is observed that the use of elasto-perfectly plastic models provided similar UAFR spectra in comparison with hysteretic models with different post-yielding stiffness. This conclusion is valid for the two selected intensity measures. In addition, the lateral resistance required to achieve similar structural reliability levels is larger when the INp intensity measure is used, especially for buildings with vibration periods equal or larger than the soil period, in such a way that the traditional use of Sa(T1) could provide structures with less structural reliability levels.

Experimental and numerical study of square HSS BIEs under cyclic loading

Braces with Intentional Eccentricity (BIEs) have recently been introduced as an alternative to traditional Concentrically Loaded Braces (CLBs) whose performance may overcome some of the shortcomings of the latter. It is postulated that the onset of local buckling in BIEs is delayed owing to a more even distribution of the strain demands under compression loading. Further, the significant post-yielding stiffness of the system can provide control over the predicted displacement levels under the action of the design earthquake. In this article, the results of the testing of four full-scale square ASTM A1085 HSS BIE specimens subjected to reversed cyclic loading are presented. The HSS members and eccentricities were selected with the intention of comparing the response of braces complying with and exceeding the CSA S16-14 global and local slenderness limits. The introduction of the eccentricity was achieved by means of side plates linking the HSS to bolted knife and gusset plate assembly connections. The experimental program is expanded and complemented with finite element analyses of additional BIE and CLB models. The experimental and numerical results show that the BIEs’ response displays the purported benefits of the introduction of the eccentricity. However, it was also found that fracture due to the rotational demand under tensile load at the bracing member’s ends can govern the failure mode of BIEs that are more resistant to developing local buckling at mid-length. The implications of the results to the design of Frames with Intentionally Eccentric Braces (FIEBs) are discussed.

Experimental and analytical studies on mechanical performance of innovative energy-dissipating hold-down for CLT structures

Connection is the most important part in cross-laminated timber (CLT) buildings as it guarantees necessary strength, stiffness, ductility, and integrality for the whole CLT structure. This paper proposes an innovative energy-dissipating hold-down connection for CLT structures, which combines the advantages of the soft-steel bracket and high-damping rubber for providing great energy-dissipating capacity and high ductility. A series of tests were performed under quasi-static monotonic and reversed cyclic loading to investigate the failure mechanisms and mechanical properties of the novel hold-down connection. Test results demonstrate that the connections can continue to work as a whole even after the occurrence of preliminary failures of steel ribs rupture and weld fracture. Final failure modes, including debonding between the rubber and steel plates, rupture of the front steel plate and breakage of screws, caused the invalidation of the connection. Meanwhile, load–displacement curves of the connections usually exhibit a bi-linear form, and the connection’s yielding is caused by the yielding of steel ribs. All the tested specimens exhibited stable energy-dissipating capacity in the working stage and were all classified as highly ductile. Furthermore, efforts were made to develop a simplified analytical model for estimating the basic mechanical properties of the novel hold-down connections. Comparison with test results shows that the analytical model can provide reasonable estimations of the initial stiffness, post-yield stiffness, yield force and failure force. The test results and analyses presented herein provide useful technical bases for supporting future studies and practical applications of the novel hold-down connection for CLT buildings.

Recycling of damaged RC frames: Replacing crumbled concrete and installing steel haunches below/above the beam at connections

Experimental and numerical studies are presented evaluating the efficacy of a recycling technique applied to a 1:3 reduced scale damaged RC frame. The crumbled concrete at the beam-column connections was replaced with new high-strength concrete. Epoxy mortar was applied at the interface to secure bonding between the old and new concrete. Additionally, the connections were provisioned with steel haunches, applied below and above the beams. The retrofitted frame was tested under quasi-static cyclic loads. The lateral resistance-displacement hysteretic response of the tested frame was obtained to quantify hysteretic damping, derive the lateral resistance-displacement capacity curve, and develop performance levels. The technique improved the response of the frame; exhibiting an increase in the lateral stiffness, resistance and post-yield stiffness of the frame in comparison to the undamaged original frame. This good behaviour is attributed to the steel haunches installed at connections. A representative numerical model was calibrated in the finite element program SeismoStruct. A set of spectrum compatible ground motions were input to the numerical model for response history analysis. The story drift demands were computed for both the design basis and maximum considered earthquakes. Moreover, the technique was extended to a five-story frame, which was evaluated through nonlinear static pushover and response history analyses. Overstrength factor WR = 4.0 is proposed to facilitate analysis and preliminary design of steel haunches and anchors for retrofitting the low-/mid-rise RC frames.

Cyclic Behavior of Damage-controllable Steel Fiber-reinforced High-strength Concrete Frame-shear Wall Structures

ABSTRACT Quasi-static tests of two 2-story structures reinforced with HRB 600 MPa reinforcement and ultrahigh-strength (UHS) reinforcement were conducted. These two structures showed an evident post-yield stiffness, which can be repaired before a large drift ratio of 2%. The structure with the UHS reinforcement had stable floor stiffness ratio, which can avoid the deformation and energy consumption concentration in the lower floors. The reinforcement diagonal bracing can effectively limit the inclined crack development, and reduce the shear strength degradation of the shear wall under large lateral deformation. According to the structure failure mechanism, an ideal load-deformation response was proposed.

Hysteretic Behavior of Dual-Self-Centering Variable Friction Damper Braces with Low Pretensioned Force

ABSTRACT To satisfy the resilient requirements, a novel dual-self-centering variable friction damper (DSC-VFD) brace with self-centering variable friction damper systems and basalt fiber-reinforced polymer tendons, is proposed. The working mechanism of the DSC-VFD brace was first investigated. Then, four DSC-VFD and SC-VFD braces with different groove angles were designed, and quasi-static experiments were conducted. Finally, finite element models of the DSC-VFD braced frame were created and the seismic responses of the frames were analyzed. The results show that the DSC-VFD brace presents a novel flag shape with large post-yield stiffness and enhanced energy dissipation which can effectively control the structural responses.

Estimation of the Damage-Based Residual Displacement Spectrum for Simple Structures

ABSTRACT A statistical study aimed at estimating residual displacement spectrum (C r) of single-degree-of-freedom (SDOF) systems with a given damage index is developed. The C r are calculated with the Park-Ang damage model, which can be parameterized in terms of the ultimate ductility factor μ u and energy dissipation factor β, for SDOF systems subjected to 228 ground motions. The variation in C r with site conditions, damage model, postyield stiffness ratio and stiffness degradation is investigated. The results showed that μ u and β had moderate and negligible effects on C r, respectively. Reliable estimation of damage-based C r can facilitate the performance-based design of structures.

Behaviour Investigation of SMA-Equipped Bar Hysteretic Dampers Using Machine Learning Techniques

Most isolators have numerous displacements due to their low stiffness and damping properties. Accordingly, the supplementary damping systems have vital roles in damping enhancement and lower the isolation system displacement. Nevertheless, in many cases, even by utilising additional dampers in isolation systems, the occurrence of residual displacement is inevitable. To address this issue, in this study, a new smart type of bar hysteretic dampers equipped with shape memory alloy (SMA) bars with recentring features, as the supplementary damper, is introduced and investigated. In this regard, 630 numerical models of SMA-equipped bar hysteretic dampers (SMA-BHDs) were constructed based on experimental samples with different lengths, numbers, and cross sections of SMA bars. Furthermore, by utilising hysteresis curves and the corresponding ideal bilinear curves, the role of geometrical and mechanical parameters in the cyclic behaviour of SMA-BHDs was examined. Due to the deficiency of existing analytical models, proposed previously for steel bar hysteretic dampers (SBHDs), to estimate the first yield point displacement and post-yield stiffness ratio in SMA-BHDs accurately, new models were developed by the artificial neural network (ANN) and group method of data handling (GMDH) approaches. The results showed that, although the ANN models outperform GMDH ones, both ANN- and GMDH-based models can accurately estimate the linear and nonlinear behaviour of SMA-BHDs in pre- and post-yield parts with low errors and high accuracy and consistency.

Inelastic Displacement Ratios for SDOF Structures Subjected to Earthquake-tsunami Loadings

ABSTRACT This study investigates the inelastic displacement of structures subjected to earthquake-tsunami loadings. The relative intensity is defined as the ratio of the tsunami force per unit mass to the S a of the corresponding ground motion. The effects of the hysteretic model, soil condition, post-yield stiffness, damping, and relative intensity on the inelastic displacement ratios are investigated. The results show that, compared to earthquakes alone, earthquake-tsunami loadings can enlarge the inelastic displacement ratio demands, especially for higher relative intensities. A predictive model is developed by considering several parameters, which may be used in the framework of performance-based seismic design.

Prestressed concrete wall system with friction devices: Seismic performance and direct displacement–based seismic design

It is convenient to use the inelastic displacement ratio spectra and residual displacement ratio spectra to predict the maximum inelastic displacement and residual displacement of building structures based on linear elastic analysis directly. The prestressed concrete wall system with friction devices (PCW-FD system) can be simulated by single-degree-of-freedom (SDOF) model with self-centering behavior. To investigate the seismic performance of PCW-FD system, the SDOF models with fully and non-fully self-centering behavior are analyzed firstly, and it is concluded that the hysteresis parameters (strength reduction coefficient, post-yield stiffness coefficient, energy dissipation coefficient, and period) have significant influence on the seismic responses (such as constant relative strength inelastic displacement ratio, constant relative strength residual displacement ratio, maximum absolute acceleration, the hysteretic energy, and site classifications) during short period, and the trends of the seismic responses are similar at different site classifications. Then a large amount of the result data is summarized, and the constant relative strength inelastic displacement ratio spectra and the constant relative strength residual displacement ratio spectra with enough precision (the correlation coefficients are 0.957 and 0.947, respectively) are established by conducting regression analysis. Finally, the direct displacement–based seismic design method is improved and verified to be suitable for PCW-FD system.

Equivalent viscous damping of steel members for direct displacement based design

Predicting the required equivalent damping ratio is an essential step in predicting the structural element ductility demand through Direct Displacement Based Design methodology. This study presents an equivalent damping ratio model for steel members based on the bilinear hysteresis model with a post-yielding stiffness ratio of 2% and an initial damping ratio of 2%. The hysteresis model and its mechanical properties are derived from shaking table test results conducted in Japan in previous study. The equivalent damping ratio in this study was evaluated at post-yielding stiffness ratios of 2% and 3% as recommended by the experimental study. Where it is concluded that the difference between the selected post yielding stiffness ratios did not influence equivalent damping ratio. Additionally, this study evaluated the effect of near-field earthquake records with forward-directivity and fling-step effects. The results show that the equivalent damping ratio for fling-step records is significantly higher than the equivalent damping ratio obtained using other records. Also, the study evaluated the effect of earthquake duration on the equivalent damping ratio by investigating the duration effect of 25 real records. The duration was measured using different metrics. The result indicated that duration measured by uniform definition is positively correlated to the equivalent damping ratio and longer significant duration imposes higher ductility demand on the structure.

Seismic performance of fibre-reinforced polymer and steel double-reinforced bridge piers

The re-centring ability and durability of important bridges have been the main objectives in recent provisions of seismic design codes. To achieve better recoverability and durability for piers, this article presents a double-reinforced pier configuration, in which the outer layer is reinforced with fibre-reinforced polymer (FRP) rebar and the inner layer is reinforced with steel rebar. An equal flexural capacity design method was used to determine the double-reinforced configurations. The effects of the potentially influential design parameters on the seismic response of piers were studied and compared to those of conventional RC piers. The results show that the proposed design method can satisfy the ultimate capacity and durability demands. The double-reinforced piers had a better performance than conventional piers in terms of the ductility, post-yield stiffness and residual deformation. The maximum deformation and energy dissipation capacity of the double-reinforced piers were comparable to those of the conventional RC piers. The results also demonstrated that the proportion of steel reinforcement had a clear effect on the performance of double-reinforced piers. However, FRP reinforcement with a high modulus of elasticity should be avoided due to the adverse effect on ductility.

Bond performance between SFCBs and grouted sleeves for precast concrete structures

A precast concrete structure reinforced by steel-fiber-reinforced polymer (FRP) composite bars (SFCBs) shows good durability and controllable post-yield stiffness, which makes this kind of structure suitable for marine infrastructure. The connection technology is one of the critical issues of a precast concrete structure with hybrid reinforcement. This paper presents an experimental study on the bond-slip testing (27 pullout specimens) of composite bars connected by a grouted deformed pipe splice (GDPS) connector with different bond lengths. The reinforcement included SFCBs and pure FRP bars. The test results showed that the failure modes could be classified into three categories: rebar pullout before or after the inner steel bar yielded, rupture of the FRP wrapped on the SFCB, and mixed failure of bar pullout with a partial fiber fracture. The average bond strength of the ordinary steel bar was approximately 146.8% that of the SFCB connector with the same anchored length. When the anchored length of the SFCB specimen was 15 d ( d: bar diameter), the specimen could be fully anchored to fracture. An explicit hardening bond-slip model considering the post-yield stiffness of the SFCB was used to predict the bond-slip behavior of the GDPS connector, and the experimental and analytical results agreed well with each other, which demonstrates that the proposed model could provided a reference for the analysis and design of connectors for SFCB-reinforced precast concrete structures.