Initial Stiffness Ratio Research Articles

Assessment of a Force Method for the Resilient Seismic Design of Special Moment-Resisting Steel Frames with Hysteretic Energy Dissipation Devices

In this paper, the authors present the results of nonlinear dynamic analyses of twelve building models designed according to a methodology based upon the force method, capacity design principles and the concept of structural fuses to achieve resilient seismic designs for special moment-resisting steel frames with hysteretic energy dissipation devices mounted on chevron steel bracing. It is demonstrated that the resilient design mechanism previously checked with pushover analyses is also attained for most studied models with nonlinear dynamic analyses using an acceleration record which is compatible with the elastic design spectrum. Also, it is corroborated that the planned second line of inelastic defense is activated if the seismic action surpasses the considered design spectrum. Based upon the obtained results, it is confirmed that it is possible to perform a resilient seismic design for the studied system under the proposed methodology, even for tall and slender buildings. Therefore, the proposed initial stiffness ratio parameters and the global design parameters previously proposed by the authors to use in a code-oriented force method can be used with confidence for the resilient seismic design of this structural system.

Non-Rigid Registration Via Intelligent Adaptive Feedback Control.

Preserving features or local shape characteristics of a mesh using conventional non-rigid registration methods is always difficult, as the preservation and deformation are competing with each other. The challenge is to find a balance between these two terms in the process of the registration, especially in presence of artefacts in the mesh. We present a non-rigid Iterative Closest Points (ICP) algorithm which addresses the challenge as a control problem. An adaptive feedback control scheme with global asymptotic stability is derived to control the stiffness ratio for maximum feature preservation and minimum mesh quality loss during the registration process. A cost function is formulated with the distance term and the stiffness term where the initial stiffness ratio value is defined by an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictor regarding the source mesh and the target mesh topology, and the distance between the correspondences. During the registration process, the stiffness ratio of each vertex is continuously adjusted by the intrinsic information, represented by shape descriptors, of the surrounding surface as well as the steps in the registration process. Besides, the estimated process-dependent stiffness ratios are used as dynamic weights for establishing the correspondences in each step of the registration. Experiments on simple geometric shapes as well as 3D scanning datasets indicated that the proposed approach outperforms current methodologies, especially for the regions where features are not eminent and/or there exist interferences between/among features, due to its ability to embed the inherent properties of the surface in the process of the mesh registration.

Performance-Based Seismic Design for Bridge Bents Retrofitted with BRBs Using the Ductility Demand Spectra of SDOF Oscillators with Bilinear Fuses

ABSTRACT Reinforced concrete bridge bents with double columns in bridge substructures are commonly used, but it has suffered severe damage during strong earthquakes. The seismic retrofit with structural fuses is used to effectively mitigate seismic damage of bridge bents. To obtain the displacement ductility demand for dual systems including the primary structure (PS) and structural fuses (SF), the corresponding ductility demand factor spectra were developed. The interaction between the PS and SF is described by defining two parameters of dual systems: the yield displacement ratio (α) and the initial stiffness ratio (β), and the influence of α, β, and strength reduction factor on the ductility demand factor spectra are also analyzed. For seismic retrofitting in bridge bents, buckling-restrained braces (BRBs) are used as energy dissipation fuses, and the steel core lengath of BRBs with three configurations forms, including diagonal, inverted-V, and toggle systems, are also explored. Then, based on the structural fuses concept and ductility demand factor spectra of dual systems, a performance-based seismic design procedure is proposed for bridge bents retrofitted with BRBs to ensure that the bridge bents maintain the target ductility under design-level earthquakes. Finally, the procedure was utilized to design the bridge bents with BRBs, and the procedure’s feasibility was verified by nonlinear time-history analysis.

Seismic design and performance evaluation of steel braced frames with post-tensioned and disc-spring-based self-centering buckling-restrained braces

In this study, we focus on two types of self-centering buckling-restrained braces (SC-BRBs), which are post-tensioned (PT) SC-BRB and disc-spring-based SC-BRB, and develop a seismic design method for steel braced frames with these braces according to the displacement-based design theory. The whole independent parameters that describe the hysteretic behavior of the SC-BRBs are first determined. Then nonlinear time history analysis (NLTHA) is conducted to explore the effects of these hysteretic parameters on the ductility demands of the nonlinear single-degree-of-freedom (SDOF) system. Based on the analysis results, a ductility demand spectral model is developed, followed by a nonlinear displacement ratio spectral model. Subsequently, the seismic design procedure for SC-BRB frames is proposed based on the two spectral models. Finally, a total of 24 six-story steel frames with the two types of SC-BRBs, two target inter-story drifts, and different parameter combinations are designed at the maximum considered earthquake (MCE) level. The pushover analysis and NLTHA results indicate that a smaller strength ratio β and a larger initial stiffness ratio αs are beneficial for reducing the base shear and obtain an economical design when the designed frames achieve the same target inter-story drift. Considering the initial stiffness of the SC-BRBs is highly sensitive to machining errors, it is recommended that the value of β be taken within 0.25 to reduce the influence of the initial stiffness uncertainty of the braces on seismic design results. Moreover, controlling β within 0.25 also helps to reduce the higher-mode effect and peak floor acceleration responses of the designed structures effectively.

Formulation and implementation of a hypoplastic constitutive model for interface behavior of mechanical joints

The effects of the contact interface must be considered during the design process of the assembly structures connected by mechanical joints. An advanced three-dimensional (3D) constitutive model is needed to describe the complex behavior of the contact interface in a detailed finite element (FE) model. However, the simplified Coulomb friction law, which is a bilinear model without considering the microslip behavior and stiffness degradation, is often applied to the surface-surface contact element for modeling the interface in commercial FE programs. In this paper, a new 3D hypoplastic constitutive model for the nonlinear interface behavior is presented. This model is built on the framework of hypoplasticity developed by Kolymbas and the hypothesis of continuous media. First, the general hypoplastic model is derived based on the kernel formula and several restrictions and simplified according to the characteristics of the contact interface. Then, the coefficients of the model are associated with the widely used physical parameters by combining the model with the initial stiffness ratio, normal contact law and Coulomb law. Benefiting from the hypoplastic theorem, the deduced constitutive model has a simple mathematical formulation in which only five parameters are contained. Simulations of several monotonic and cyclic shear tests show that the model can represent the salient characteristics of the joint interface (e.g. stick/microslip/macroslip behaviors, motion coupling and pressure-dependency). Thus, it can be used to predict the response of the joint interface from arbitrary multi-axial load histories more precisely. The constitutive model is then implemented in a commercial FE program via analysis of a double-beam structure subjected to harmonic excitation. And vibration experiments on several preload levels are performed to validate the effectiveness and the applicability of the proposed model to the real joints. The results calculated from the FE model with the improved reduction techniques are in good agreement with the experimental data.

Strength reduction factor spectra for SDOF systems with structural fuses

Highly ductile replaceable fuses can greatly improve the performance of structures and mitigate seismic damage. A fused structure refers to a dual system that generally includes the primary structural system and the fuses acting in parallel. Few studies have thoroughly investigated the strength reduction factors of dual systems or their nonlinear response behaviors; instead, a restoring force model was adopted to represent the performance of the whole system while ignoring the interactions between the primary structure and fuses. This paper separates the two components and considers their interaction. The behavior of the primary structure and structural fuses is assumed to be similar to elastic-perfect plastic. Two parameters, the yield displacement ratio (α) and the initial stiffness ratio (β), are introduced to describe the relationship between the fuses and the primary structure. Based on a dual system, the dimensionless governing equation of motion is derived. The strength reduction factor spectra with a known displacement ductility factor (μ) are then calculated under two groups of selected ground motions. The influences of α, β, and μ are investigated statistically. The strength reduction factor spectra of the fused structure can be expressed by the four-stage predictive model developed by Newmark and Hall for traditional structures, but the spectral shape and two plateau values are closely related to α, β, and μ. These two plateaus are crucial for the spectral shape of the four-stage model. Finally, a simplified equation is proposed to estimate the strength reduction factors of dual system considering α and β with equivalent μ.

Moment Rotation behavior of Top and Seat Angle Connection with Angle Stiffeners

The design specifications for seven commonly used semi-rigid steel connections have been embodied in Indian Standard Code of Practice for General Construction in Steel (IS800:2007). Bolted connections are proved to be efficient by several researchers for its energy dissipating capability under reversal of loading; among them top and seat angle (TSA) connection has higher capacity. An attempt has been made to investigate the behaviour of stiffened TSA connection by finite element analysis in this research. Previously published experimental specimens of TSA connection (RAMAN 2005) semi-rigid TSA bolted connection and their results have been considered to develop 3D Non-linear Finite Element (FE) model and analyses have been executed using the general purpose FE software. The M-?r behavior of numerical analyses are compared with that of the experimental results and thus, the FE model is validated. Further studies are carried out on TSA with all angles stiffened and TSA with angles subjected to tension alone are stiffened. The FE analysis results showed that TSA connection with only tension angles stiffened behave similar to that of TSA connection with all angles stiffened i.e., the stiffeners provided in compression angles does not contribute to the stiffness and connection capacity. The plastic flexural resistance of stiffened TSA connection has enhanced by 30% to that of TSA connection and the ratio of initial stiffness of stiffened TSA to the unstiffened TSA is found to be 1.25. So, the stiffened TSA connection is proved to be efficient in terms of both capacity and failure. The further studies have been carried out to investigate the influence of stiffener properties on the M-?r mechanism of the connection and the results showed that thickness of stiffener equal to the beam web thickness is more efficient.

Behaviour of rectangular gusset plate with angle cleat connections for cold-formed steel section

Cold-formed steel (CFS) members designed with proper stiffener can significantly increase the loading capacity of the connected member even though they are thin and slender. Design recommendations of connections especially for CFS sections are mostly related to the load-carrying capacities of individual fasteners such as bolts, screws, and rivets. The proposed bolted top-seat flange cleat joint in this paper should be able to categorize as semi-rigid that can further enhance the use of CFS in structural steel. This paper aims to investigate the behaviour of cold-formed steel section with gusset plate integrated with angle cleats. The full-scale isolated joint test was conducted on three specimens where the size of column size is C30024, and the size of beams is C20024, C25024, and C30024. All sections are 2.4mm thick. The connections were stiffened with a rectangular gusset plate of 10mm thick and angle cleat of 6 mm thick, respectively. The result of the test showed that the moment resistance (Mj) of the connection for beam sections C20024, C25024 and C30024 were 45.3 kNm, 48,8 kNm, and 52.5 kNm respectively. The initial stiffness (Sj,ini) of the connections for beam section C20024, C25024 and C30024 were 510 kNm/rad, 650 kNm/rad and 610 kNm/rad respectively. The experimental results showed that the ratio of the moment resistance ranged from 1.00 to 1.16, and the ratio of initial stiffness ranged 1.00 to 1.35 as compared to the numerical analysis adopted from EC3 code.

EVALUACIÓN DEL DISEÑO SÍSMICO RESILIENTE CONFORME AL MÉTODO DE LAS FUERZAS DE MARCOS DÚCTILES DE ACERO CON DISIPADORES DE ENERGÍA HISTERÉTICOS

Se presentan los resultados de análisis dinámicos no lineales realizados a doce modelos de edificios que se diseñaron conforme a una metodología que emplea el método de las fuerzas y principios de diseño por capacidad y de fusible estructural, la cual permite obtener diseños sísmicos resilientes de estructuras con base en marcos contraventeados de acero estructural dúctiles con disipadores de energía histeréticos. Se demuestra que los mecanismos de diseño sísmico resiliente corroborados previamente mediante análisis pushover se cumplen para la enorme mayoría de los modelos ante la acción de un registro de aceleración compatible con el espectro elástico considerado en el diseño de los modelos, y si la excitación dinámica rebasa los parámetros de resistencia o demanda supuestos en el diseño de los modelos, se activa exclusivamente la segunda línea de defensa inelástica planeada para el sistema. Con base en los resultados presentados, se confirma que es muy factible diseñar resilientemente al sistema en estudio, incluyendo a edificios altos y esbeltos. Por lo tanto, se pueden emplear con confianza los parámetros globales de diseño sísmico y balances óptimos de rigideces derivados en estudios previos.

Interpreting strain burst in micropillar compression through instability of loading system

Understanding the mechanism of intermittent plastic flow in single crystal at micron to nano scale is vitally important to the fields where the reliability of system is paramount. Jumps in the stress-strain curves (strain bursts) are usually interpreted from the perspective of internal processes of material such as dislocation avalanches or intermittent activation of dislocation sources. However, the responses obtained by the sensors are also severely affected by the loading system, and this effect is often neglected in understanding the essence of strain burst. Thus, after analyzing the detailed deformation process of the loading system and the pillar during the period of strain burst, the theoretical model with the loading system that is assumed to be linearly elastic and the pillar connected in series is established. Also, the constitutive relations of micro-pillars are obtained by molecular dynamics (MD) in which the plastic flow stresses fluctuate. Based on the model, the critical condition of the instability of loading system is derived. It is shown that strain burst is the response obtained by the sensors during the period of instability of loading system caused by strain softening of the pillar and whether or not strain burst occurs depends on the degree of strain softening of pillar and the ratio of initial stiffness of the pillar to the effective stiffness of the machine. The size of strain burst is also predicted under the assumption that the strain softening stage continues to the point where elastic strain energy released by the loading system is equal to energy absorbed by the pillar and then this softening stage immediately turns into a linear elastic stage. In addition, the mechanism behind large strain burst is also revealed.

Nonlinear displacement ratio for seismic design of self-centering buckling-restrained braced steel frame considering trilinear hysteresis behavior

Self-centering buckling-restrained braced steel frames (SCBRBFs) have drawn increasing attention due to the resilience of this kind of structural system in post-earthquake repair. Constant-strength reduction factor (constant-R) inelastic displacement ratio (CR) can be used for direct inelastic displacement evaluation or design of SCBRBFs. In previous studies, bilinear hysteresis assumption was generally adopted for the self-centering structures, although actual trilinear flag-shaped hysteresis was commonly observed for most of the previously proposed metallic energy-dissipation self-centering systems, such as SCBRBFs. In this study, trilinear hysteresis of the SCBRBF, presented as a combination of the bilinear elastoplastic restoring force of the energy dissipation (ED) system and the bilinear elastic restoring force of the self-centering (SC) system, is considered in the determination of the CR ratio spectra of such system. Comparison between the bilinear SC systems and the trilinear SCBRBFs is discussed to highlight the effect of the trilinear hysteresis on the nonlinear displacement of SCBRBFs. Key parameters affecting the CR ratio are determined, in which the initial stiffness ratio of the ED system to the SC system, αc, is the additional parameter proposed to reflect the trilinear property of SCBRBF. Optimal ranges of these parameters and their effects on the CR spectra are also discussed by nonlinear response history analysis. Nonlinear regression analysis is then performed to obtain the function of CR with respect to the aforementioned parameters for quick and direct displacement evaluation. Nonlinear time history analysis (NTHA) demonstrates that the CR ratios of SCBRBF, determined by the previously derived CR functions from bilinear hysteresis, are often overestimated, while those predicted by the proposed CR functions from trilinear hysteresis show better agreement with the numerical results in extremely-low and medium-to-long period region. Numerical nonlinear displacement ratios of a one-story six-bay and a six-story six-bay SCBRBFs are computed by NTHA to validate the effectiveness of the proposed CR functions.

Comparison of Lateral Behavior of Rock-Socketed Large-Diameter Offshore Monopiles in Sands with Different Relative Densities

Centrifuge tests were performed to investigate the effect of the relative density of the sandy layer on the lateral response of 6-m-diameter offshore monopiles. The end tips of the monopiles are socketed into rock-bearing layers. For the simulation of the rock-socketed monopiles in sands with different relative densities (dense and medium dense sand layers), centrifuge tests at an acceleration of 60 g were conducted using well-instrumented model monopiles under significant lateral loads and bending moments. Based on the centrifuge test results, the p–y relationship and the initial stiffness (initial gradient of a p–y curve) changed with an increasing depth for both dense and medium dense sand layers. As a result, the newly developed p–y curves for rock-socketed large-diameter monopiles in this study were quite different from the existing API (American Petroleum Institute) p–y curves, which were developed based on relatively small-diameter driven piles. It was found that the initial stiffness for the medium dense sand layer was significantly lower than that for the dense sand layer at a shallow depth; however, the ratio of initial stiffness of the medium dense sand layer to that of the dense sand layer decreases significantly as the depth increases and approaches the stiff rock-bearing layer.

Sensitivity Study of Pseudodynamic Algorithm with Structure-Dependent Quadrature Equations

An estimated initial stiffness matrix is generally needed to determine the coefficient matrices of quadrature equations for a structure-dependent pseudodynamic algorithm. It is shown herein that an experimentally determined initial stiffness matrix is, in general, close to the true initial stiffness matrix if an imposed displacement is small enough. This case is often encountered in practice. The case where an estimated initial stiffness is different from a true initial stiffness for employing a structure-dependent pseudodynamic algorithm is also explored. The numerical properties and error propagation properties are evaluated as a function of the initial stiffness ratio, which is the ratio of an estimated initial stiffness over a true initial stiffness. In general, accuracy and error propagation properties are insensitive to the initial stiffness ratio. It seems that the change of bifurcation point between unconditional stability and conditional stability is of worth noting. In order to avoid this stability problem, guidelines are recommended if a structure-dependent pseudodynamic algorithm is used.

Analysis Influence of Pile Embedded Depth and Diameter on Pile Tip Resistance

Pile tip absolute settlement curves and relative settlement curves of several working cases were analyzed. It is found that load-settlement curve characteristic related to the selection standard. The tip resistance initial stiffness of each case was analyzed. Results show that the small diameter pile has higher initial stiffness than large diameter pile, embedded depth has little influence on initial stiffness ratio, but increment of initial stiffness is linear with embedded depth growth.

Relaxation creep rupture of heterogeneous material under constant strain

We focus on a system consisting of an elastic part and a damageable part in series, to study the relaxation creep rupture of a heterogeneous system subjected to a uniaxial constant strain applied instantaneously. The viscoelastic behavior of the damageable part is modeled by a fiber bundle model consisting of Kelvin-Voigt elements and global load sharing is assumed for the redistribution of load following fiber breaking in the damageable part. Analytical and numerical calculations show that the global relaxation creep rupture appears if the elastic energy stored in the elastic part exceeded the fracture energy of the damageable part. The lifetime of the system strongly depends on the values of the applied external strain and the initial stiffness ratio k between the elastic part and the damageable part. We show that a higher stiffness ratio implies a more brittle system. Prior to complete failure, relaxation creep rupture exhibits a sequence of three stages, similar to creep rupture under constant stress, and the nominal force rate presents a power law singularity with a power index -1/2 near the global rupture time.

Cyclic Response of Concrete Beams Reinforced by Plain Bars

There are many reinforced concrete structures throughout the world that have been built in the past decades that lack appropriate seismic details and reinforced by plain bars. To study the behavior of such buildings, seven beams have been tested under cyclic and monotonic load. The specimens include substandard specimens, with deficient seismic details and reinforced by plain bars, specimens designed in accordance with ACI-318-99 but reinforced by plain bars, and standard specimens reinforced by deformed bars. The tests indicate that the substandard specimens sustain relatively large slip of longitudinal bars, separation of specimen relative to foundation and sliding at large deformation phase, low initial stiffness ratio, limited lateral displacement capacity, and loss of nominal yield strength. The specimens reinforced by plain bars in accordance with ACI-318-99 perform almost similar to standard specimens with deformed bars, in terms of elastic stiffness and lateral displacement ductility; but, they sustain larger slip, and smaller yield strength. Failure of all specimens reinforced by plain bars is characterized by flexural cracks without visible shear failure. Residual shear strength of substandard specimens is modeled by dowel action of longitudinal bars to predict a lower limit for lateral strength of the specimens.

Analyzing the Response of Spring-Mass-Capacitor Structure Using Energy Method

The spring-mass-capacitor structure in micro-electro-mechanical systems (MEMS) is a typical macromodel, its response and stability under step voltage is presented in this paper. Energy method is used to analyze the dynamic behavior of mass block where its velocity is zero and accelerometer is zero, respectively. The condition of stability under step voltage is the initial stiffness ratio must less than 0.25, and finally the relation of energy loss and oscillating behavior of block is analyzed. The conclusion is useful to analyze the response of structure and helpful to design a MEMS system composing of spring-mass-capacitor structure.