Displacement-based Approach Research Articles

The comparative role of friction in local out-of-plane mechanisms of masonry buildings. Pushover analysis and experimental investigation

In masonry buildings without a box-type behaviour and subjected to seismic loadings, in-plane and out-of-plane failure mechanisms can take place where frictional resistances might play a predominant role. In this paper a detailed limit analysis of a simple out-of-plane failure mechanism is developed according to static force-based and displacement-based approaches. The main goal is to point out the great importance of the stabilizing role of friction between interlocked walls compared to other extrinsic or intrinsic loading capacities, e.g. the effect of tie-rods and simply supported horizontal diaphragms with frictional resistance. The sensitivity of the load multiplier to these strength parameters is investigated both at the onset of the rocking mechanism and after the hinge formation and a parametric analysis is carried out for the first condition. The results are obtained with reference to different combinations of loading conditions, including the detrimental effect of the static thrust of masonry vaults. Comparative results and pushover curves are developed to evaluate the loading and displacement capacities for each case analyzed and some experimental work is presented to validate the analytical results.

Bending analysis of composite laminated and sandwich structures using sublaminate variable-kinematic Ritz models

This paper presents a novel numerical tool for the bending analysis of thin and thick composite plates, including monolithic and sandwich structures. The formulation is developed within a displacement-based approach, where the Principle of Virtual Displacements (PVD) and the method of Ritz are adopted to derive the governing equations. The approach relies upon the Sublaminate Generalized Unified Formulation (S-GUF) as underlying kinematic theory describing the behavior across the plate thickness. Main idea of the S-GUF is to group the plies into a number of smaller units called sublaminates, each of them characterized by an independent, variable-kinematic theory. Continuity conditions between the sublaminates are enforced in strong form during the assembly procedure of the governing equations. The S-GUF appears particularly useful when theories of different order are needed to approximate the displacement field of different portions of the structure, such as in the case of sandwich panels. A number of test cases from the literature is discussed, and results are validated against exact 3D solutions. The results demonstrate the ability of the approach to obtain accurate results, both in terms of deformed shapes, and intra- and inter-laminar stress distributions. A set of novel results is also presented for future benchmarking purposes.

Direct Displacement-Based Design for Buildings with Hysteretic Dampers, using Best Combinations of Stiffness and Strength Ratios

A direct displacement-based design approach for damage-controlled structures using the best combination of stiffness and strength ratios between the main structure and added hysteretic energy dissipation systems is proposed. Choosing optimal values of the design parameters is an important step toward an efficient structural design; therefore, a parametric study using different combinations of design parameters is performed, from which a simple methodology to calculate a cost-efficiency index based on a cost-benefit analysis is developed. The DDBD methodology is verified and recommendations about adequate combinations of design parameters are given for an 8-story steel building with buckling restrained braces.

Innovative performance-based design of slope stabilizing piles for a railway embankment

The paper presents a simplified displacement-based approach for the design of a slope stabilising system. On the top of the slope, a railway ballasted track induces repeated dynamic loads on the subgrade soil, that, in conjunction with other cyclic environmental loads (seasonal temperature and soil moisture variation) induce a progressive accumulation of soil displacements, despite the safety factors for the slope, if computed by means of traditional limit equilibrium methods, are all larger than one. The design procedure started then from the analysis of preliminary (pre-operam) monitoring data, in order to define the shape and amplitude of the soil displacement field, by interpreting them within a viscoplastic constitutive framework. This allowed to conveniently optimise the slope stabilising system (consisting in FRC piles connected to each other by means of a precast FRC beam and reinforced by pre-stressed ground anchors) with the aim of reducing the soil displacement rates below a prescribed threshold. The focus of the work, rather than presenting advanced constitutive or numerical simulations, is on the design approach, which allows the designer to get a reliable and safe design solution, even in lack of rich and sophisticated site characterisation, as it is often the case in real applications.

Improved free-surface expression for frequency-domain elastic optimal mixed-grid modeling

An accurate and efficient forward modeling is the foundation of full-waveform inversion (FWI). In elastic wave modeling, one of the key problems is how to deal with the free-surface boundary condition appropriately. For the representation of the free-surface boundary condition, conventional displacement-based approaches and staggered-grid approaches are often used in time-domain. In frequency-domain, considering the saving of storage and CPU time, we integrate the idea of physical parameter-modified staggered-grid approach in time-domain with an elastic optimal mixed-grid modeling scheme to design an improved parameter-modified free-surface expression. Accuracy analysis shows that an elastic optimal mixed-grid modeling scheme using the parameter-modified free-surface expression can provide more accurate solutions with only 4 grid points per smallest shear wavelength than conventional displacement-based approaches and is stable for most Poisson ratios. Besides, it also yields smaller condition number of the resulting impedance matrix than conventional displacement-based approaches in laterally varying complex media. These advantages reveal great potential of this free-surface expression in big-data practical application.

A Procedure for the Displacement-Based Seismic Assessment of Infilled RC Frames

The aim of this study was to propose an extension of the displacement-based assessment procedure for infilled reinforced concrete (RC) frames. Two fundamental steps of the displacement-based approach were studied: the determination of the equivalent viscous damping and the definition of the limit-state displacement profile. The proposed criteria were derived by examining the results of two different numerical investigations regarding the nonlinear seismic response of single- and multi-story infilled RC frames. Lastly, the effectiveness of the method was verified through comparisons, in terms of displacement demand, with the results of nonlinear dynamic analyses.

Theory for dielectrics considering the direct and converse flexoelectric effects and its finite element implementation

Flexoelectricity describes the linear energy coupling between the strain gradient and the electric polarization in a solid crystalline material. Based on strain-gradient theory, a new boundary-value model is developed for dielectrics when both the direct and converse flexoelectric effects are considered; here, the electric polarization is considered to be related to both the symmetrical and rotational strain gradients. Then, its finite element implementation is realized by establishing an equivalent-energy weak form of the problem. For this higher-order elastic problem, C1-continuous interpolations of the displacement and electric variables are required in the conventional displacement-based approach. In the present work, we construct an equivalent-energy weak form of the problem by introducing additional nodal degrees of freedom and enforcing the kinematic constraints between displacement and strain in the bulk and surface integration using Lagrange multipliers. The C1-continuous problem then reduces to a C0-continuous form. Using standard C0-continuous shape functions, some mixed-type finite elements are developed herein for dielectrics, in which the unknown variables, i.e., displacement, strain, rotational component and polarization intensity, are interpolated as independent nodal degrees of freedom. These elements are tested and applied to solve certain electromechanical problems, and their good convergence and accuracy are demonstrated via analysis of the mechanical and electrical properties of a dielectric.

Influence of loading path on cyclic mechanical response of small-scale shallow strip footing on loose sand

This paper aims at experimentally exploring the behaviour of a small-scale 1g shallow strip footing on loose dry sand, subjected to vertical and horizontal cyclic loads. An experimental apparatus has been developed and calibrated, and some series of monotonic and cyclic tests with different combinations of load direction and cycle amplitudes have been carried out. Results are presented and discussed in terms of evolution of foundation global stiffness, damping properties, and settlement accumulation along both vertical and horizontal directions with increase in the load cycle’s number. The coupling effect between vertical and horizontal loads is highlighted, underlying its important role even at a low number of cycles, when, in the design practice, the behaviour of the system is often considered to be linear elastic and path independent. The observation also allowed the inference that a variation of the inclination of the cyclic loads may induce significant differences (up to one order of magnitude) in the global stiffness and damping properties. Far from having exhaustively investigated the subject and from the aim of proposing a new empirical quantitative relationship to be directly employed in the design practice, this paper was primarily focused on highlighting some aspects of the mechanical behaviour of the system that are still rather unknown. A further in-depth study allowed the analysis of experimental results within the framework of a meaningful physical interpretation, showing the results to be particularly useful in the perspective of a displacement-based design approach, as required by the current design standards.

A New Displacement-based Approach to Calculate Stress Intensity Factors With the Boundary Element Method

THE ANALYSIS OF CRACKED BRITTLE MECHANICAL COMPONENTS CONSIDERING LINEAR ELASTIC FRACTURE MECHANICS IS USUALLY REDUCED TO THE EVALUATION OF STRESS INTENSITY FACTORS (SIFS). THE SIF CALCULATION CAN BE CARRIED OUT EXPERIMENTALLY, THEORETICALLY OR NUMERICALLY. EACH METHODOLOGY HAS ITS OWN ADVANTAGES BUT THE USE OF NUMERICAL METHODS HAS BECOME VERY POPULAR. SEVERAL SCHEMES FOR NUMERICAL SIF CALCULATIONS HAVE BEEN DEVELOPED, THE J-INTEGRAL METHOD BEING ONE OF THE MOST WIDELY USED BECAUSE OF ITS ENERGY-LIKE FORMULATION. ADDITIONALLY, SOME VARIATIONS OF THE J-INTEGRAL METHOD, SUCH AS DISPLACEMENT-BASED METHODS, ARE ALSO BECOMING POPULAR DUE TO THEIR SIMPLICITY. IN THIS WORK, A SIMPLE DISPLACEMENT-BASED SCHEME IS PROPOSED TO CALCULATE SIFS, AND ITS PERFORMANCE IS COMPARED WITH CONTOUR INTEGRALS. THESE SCHEMES ARE ALL IMPLEMENTED WITH THE BOUNDARY ELEMENT METHOD (BEM) IN ORDER TO EXPLOIT ITS ADVANTAGES IN CRACK GROWTH MODELLING. SOME SIMPLE EXAMPLES ARE SOLVED WITH THE BEM AND THE CALCULATED SIF VALUES ARE COMPARED AGAINST AVAILABLE SOLUTIONS, SHOWING GOOD AGREEMENT BETWEEN THE DIFFERENT SCHEMES.

Flexural Strength and Ductility of FRP-Plated RC Beams: Fundamental Mechanics Incorporating Local and Global IC Debonding

AbstractReinforced concrete (RC) beams and slabs are frequently strengthened or stiffened in flexure by adhesively bonding fiber-reinforced polymer (FRP) plates to their surfaces using a strain-based moment-curvature design technique. This design technique is generally based on the intermediate crack (IC) debonding strain of the FRP reinforcement, that is, on the start of IC debonding; from this analysis it is often deduced that FRP plating is ineffective at the ultimate limit state because FRP debonding occurs before yield of the steel reinforcement. In this paper, it is shown that the strain-based approach is generally a lower bound at the ultimate limit state. Instead, a displacement-based approach is described that shows that FRP plated beams can be designed to achieve a higher strength than that of the RC beam by itself no matter when IC debonding first occurs. The mechanics of the analysis approach developed here treat the FRP debonded plate as a FRP prestressing tendon with a force equal to the IC ...

Modeling Reinforced Concrete Structures Using Smooth Plasticity and Damage Models

AbstractIn this work, a new smooth model for uniaxial concrete behavior that combines plasticity and damage considerations, together with unsymmetrical hysteresis for tension compression and nonlinear unloading, is presented. Softening and stiffness degradation phenomena are handled through a scalar damage-driving variable, which is a function of total strain. Smoothening of the incremental damage behavior is achieved, following similar steps as for Bouc-Wen modeling of classical plasticity, thus exploiting their common mathematical structure. The uniaxial model for concrete, together with the standard steel model exhibiting kinematic hardening, are employed to derive a fiber beam-column element that is used to assemble the numerical model of frame structures. Following the displacement-based approach, the solution of the entire system is established using a standard Newton-Raphson numerical scheme, which incorporates the evolution equations of all fibers elevated at the section, element, and structural l...

Force-based and displacement-based reliability assessment approaches for highway bridges under multiple hazard actions

The strength limit state of American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications is developed based on the failure probabilities of the combination of non-extreme loads. The proposed design limit state equation (DLSE) has been fully calibrated for dead load and live load by using the reliability-based approach. On the other hand, most of DLSEs in other limit states, including the extreme events Ⅰ and Ⅱ, have not been developed and calibrated though taking certain probability-based concepts into account. This paper presents an assessment procedure of highway bridge reliabilities under the limit state of extreme event Ⅰ, i. e., the combination of dead load, live load and earthquake load. A force-based approach and a displacement-based approach are proposed and implemented on a set of nine simplified bridge models. Results show that the displacement-based approach comes up with more convergent and accurate reliabilities for selected models, which can be applied to other hazards.

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an “energy-like measure” in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate “high-frequency” dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacement-based and hybrid approaches against analytical solutions.

Seismic response of precast, posttensioned concrete jointed wall systems designed for low- to midrise buildings using the direct displacement-based approach

Seismic response of precast, posttensioned concrete jointed wall systems designed for low- to midrise buildings using the direct displacement-based approach

System-Level Displacement- and Performance-Based Seismic Design Parameter Quantifications for an Asymmetrical Reinforced Concrete Masonry Building

AbstractThis paper focuses on analyzing the performance of structural walls comprising the seismic force resisting system (SFRS) in a scaled asymmetrical fully grouted reinforced masonry (RM) building tested under quasi-static loading. The in-plane tensile and compressive strains calculated at the wall toes and the curvature profile along the wall height as well as the contributions of the flexural and the shear deformations to the overall wall displacements were quantified. The component-level (when the walls were tested individually) responses were compared with those at the system level (in a building). In addition, key input parameters for displacement-based seismic design approaches, including stiffness degradation and the trend of the building’s effective period increase as well as the variation of hysteretic damping, were quantified. Moreover, the building energy dissipation levels were compared with those generated during the individual wall tests to quantify the contribution of each component to ...

Modelling of recycled aggregate concrete-filled steel tube (RACFST) beam-columns subjected to cyclic loading

A nonlinear finite element analysis (FEA) model is presented for simulating the behaviour of recycled aggregate concrete-filled steel tube (RACFST) beam-columns subjected to constant axial compressive load and cyclically increasing flexural loading. The FEA model was developed based on ABAQUS software package and a displacement-based approach was used. The proposed engineering stress versus engineering strain relationship of core concrete with the effect of recycled coarse aggregate (RCA) replacement ratio was adopted in the FEA model. The predicted results of the FEA model were compared with the experimental results of several RACFST as well as the corresponding concrete-filled steel tube (CFST) beam-columns under cyclic loading reported in the literature. The comparison results indicated that the proposed FEA model was capable of predicting the load versus deformation relationship, lateral bearing capacity and failure pattern of RACFST beam-columns with an acceptable accuracy. A parametric study was further carried out to investigate the effect of typical parameters on the mechanism of RACFST beam-columns subjected to cyclic loading.

A Numerical Failure Analysis of Multi-bolted Joints in FRP Laminates Based on Basalt Fibers

This paper aims to model the progressive damage of multi-bolted joints connecting structural elements made up of FRP (fiber- reinforced polymers) composite laminates and comprising different fiber materials (namely, based on basalt, carbon and glass), as well as different stacking sequences. Differences in failure mode and ultimate-load values are numerically investigated. A numerical home-made finite element model has been conceived, implemented, and validated by means of available experimental data. The numerical model is based on an incremental displacement-based approach and on a plane-stress bi-dimensional for- mulation. The stress analysis has been performed by accounting for micro-structural stress-strain localization mechanisms, and describing the progressive damage process by implementing a failure criterion operating at the constituents’ scale (namely, the Huang's criterion). Proposed results have highlighted that bolted joints based on basalt-FRP laminates and defined by a double- bolted configuration exhibited bearing failure loads comparable to those computed for glass-FRP and carbon-FRP laminates. In the case of single-bolted joints, the use of carbon-FRP laminates allowed to obtain the best mechanical properties, although joints based on basalt-FRP laminates numerically-experienced mechanical response and strength features always comparable with those of glass-FRP.

Seismic Rehabilitation of Existing Reinforced Concrete Buildings with Seismic Isolation: A Case Study

The use of seismic isolation for the seismic rehabilitation of existing buildings is very attractive but often very tricky due to several aspects related to its implementation. In this paper, a case study of seismic rehabilitation of a high-rise residential building with seismic isolation is presented. The building under consideration is located in southern Italy and it is placed next to another building from which it is separated by a gap of 400 mm. In the paper, all the steps of the seismic rehabilitation process are described. First, the target objective of the seismic rehabilitation and the choice of isolation system type and location are discussed. The design of the isolation system, carried out following a direct displacement-based approach, is then examined. Finally, the main phases followed in the installation of the isolation system are described. Some comments on costs and time needed to complete the intervention are also reported.

PERPETUATE guidelines for seismic performance-based assessment of cultural heritage masonry structures

Ancient monumental masonry buildings are complex structures that were not based on an engineered design, underwent many transformations during their life and often present lack of connections among the structural elements. Earthquakes are the main cause of damage for ancient masonry structures and, in order to reduce their vulnerability with compatible and light interventions, it is necessary to have accurate models for the seismic analysis, able to simulate the nonlinear behavior of masonry, and a well defined performance-based assessment procedure, aimed to guarantee the acceptable level of risk for the occupants and for the conservation of the monument itself. The paper outlines the guidelines that were developed within the PERPETUATE European research project. The wide variety of architectural assets is classified and the related proper modeling strategies are identified; moreover, immovable artistic assets are considered in the assessment. A displacement-based approach is adopted, because these structures crack even for low intensity earthquakes and can survive severe ones only if they have a sufficient displacement capacity. Safety and conservation requirements are proposed by considering distinct sets of performance levels, related to use and safety of people, conservation of the building and of the artistic assets that might be present. Some indications on the seismic hazard assessment are provided, considering the distinctive features of some types of ancient structures. Within the fundamental knowledge phase, sensitivity analysis is proposed in order to address and optimize the in-situ investigation and to define proper confidence factors, aimed to consider epistemic and statistical uncertainties. Different modeling approaches and methods of analysis are considered, depending on the characteristics of the structure; both static pushover and incremental dynamic nonlinear analyses are considered. Related verification procedures are defined to evaluate the seismic intensity measure, and the corresponding return period, which is compatible with each performance level that must be fulfilled.

An Analytical Mechanical Model for the Seismic Assessment of Bell Towers

The paper describes the analytical model, recently proposed in the Perpetuate Project, aimed to assess the seismic response of the shaft of bell towers, of which the vulnerability to the seismic action has been dramatically testified also by the recent events (as that which hit L’Emilia region in 2012). As main novelties, the model follows the Displacement Based Approach (DBA) for the seismic verification and catches both the shear and combined bending and compression response of the main body of bell towers. In order to clarify the application and to provide a preliminary validation of the proposed model, the seismic response of the bell tower of the San Carlo Church in Castellazzo Bormida (Al, Italy) has been studied. It includes also a detailed analysis on a 3D FEM model aimed to support the calibration of some parameters which the model is founded on in case of quite irregular bell towers characterized by non symmetric boundary conditions that can significantly affect their dynamic behavior, as the case analyzed.