Single Degree Of Freedom Approach Research Articles

Out-of-plane behaviors of unreinforced and spray polyurea retrofitted one-way masonry infilled walls

Unreinforced masonry infilled wall (MIW) is prone to out-of-plane (OOP) crack, bend, and collapse when subjected to OOP quasi-static and blast loadings. Spray polyurea (SPUA) is an excellent retrofitted material for MIW to improve its blast resistance and reduce fragmentation. Aiming to study the OOP behaviors of one-way unreinforced and SPUA retrofitted MIW under quasi-static and blast loadings, the corresponding OOP resistance functions of MIW under uniform loading are firstly established. The critical collapse deflection of unreinforced MIW is determined as δ = t-a, and the ultimate deflection of SPUA retrofitted MIW depends on the fracture strain of SPUA. Then, the quasi-static OOP uniform loading test on two full-scale one-way MIW was performed, and the OOP loading-deflection curves of MIW were obtained. It indicated that MIW is divided into two parts by the mid-height horizontal crack, and the upper and lower parts are rotated around the top and bottom mortar joints. Furthermore, by comparing with the present and existing quasi-static test data on unreinforced and SPUA retrofitted MIW, as well as the specified resistance functions by regulations (UFC 3-340-02, Eurocode 6, FEMA 306/356) and previous scholars, the applicability of established OOP resistance functions is validated. Finally, the equivalent single degree of freedom (SDOF) calculation approach to predict the dynamic responses of one-way unreinforced and SPUA retrofitted MIW under blast loadings is proposed based on the established resistance functions. The comparisons with five series blast tests demonstrate that the proposed SDOF approach can well predict the OOP deflection of MIW and evaluate whether the wall collapses or not. This work can provide a helpful reference for the blast-resistant evaluation and design of unreinforced and SPUA retrofitted MIW.

Experimental and Numerical Characterization of Violent Sloshing Flows Using a Single Degree of Freedom Approach

In this work, the most fundamental aspects of an aeronautical sloshing problem have been studied using an alternative and simplified model. This model consists of a single degree of freedom version of the original problem which keeps the essence of the fluid structure interaction and also the most relevant physical aspects of the industrial case. Two independent methodologies have been used: first an experimental rig has been designed to measure and visualize different magnitudes of the problem and also a smoothed particle hydrodynamics formulation has been adapted to obtain a local representation of the flow interaction. Two very different fluids in terms of viscosity have been tested, and the differences in terms of the characteristics of the sloshing regimes, free surface fragmentation and relative kinetic energy have been described and compared. Apart from the comparison of the results obtained by both methodologies in terms of tank acceleration, sloshing forces and free surface evolution, a deep study of the sloshing force has been performed. This study focuses on a deeper understanding of the different aspects that constitute the sloshing force, such as its synchronization with the tank movement, the relation to the movement of the liquid’s center of mass and the physical projection of the force on the pressure and viscous parts. Additionally, a reconstruction of the sloshing force as a sum of the pressure signal recorded by a finite number of pressure sensors has been also performed.

Improved SDOF Approach to Incorporate the Effects of Axial Loads on the Dynamic Responses of Steel Columns Subjected to Blast Loads

In this paper, a complicated single‐degree‐of‐freedom (SDOF) approach was developed to determine the global response of steel columns under combined axial and blast‐induced transverse loads. Nonlinear section and member analyses were incorporated into the suggested SDOF method to account for the complex features of the material behavior, the high strain rate effect, and the column geometry. The SDOF technique was validated through comparisons with available finite element and experimental data, and a good consistency was obtained. Then, the validated SDOF approach was utilized to derive the pressure‐impulse curves under various levels of axial loading. The level of the axial load was shown to have a significant influence on the dynamic behavior of a steel column subjected to a blast load.

Suppression of ringing oscillations from high speed rubber compression curves through a detailed modal characterization of servo-hydraulic machines

System ringing is one of the most important factors affecting the quality of data obtained in high speed dynamic material tests using servo-hydraulic machines. This phenomenon is characterized by vibrations originated by the excitation of predominant modes of the machine during tests, producing distinctive waves in material curves that severely distort the required results. In the specialized literature, the quantitative study of these vibrations has mainly been carried out considering the testing machine as a single degree of freedom system, which has led to a general understanding of the variables involved in the process. However, discrepancies between analytical predictions and experimental observations have been detected using the single degree of freedom approach, so the need for further detailed study of machine dynamic characteristics has been reported. The work presented in this paper addresses this requirement by means of a detailed characterization of the dynamic behavior of a MTS 819.10 high rate testing system. Natural frequencies, mode shapes and damping factors have been obtained from an experimental modal analysis performed on the machine and a mathematical model of the process has been developed from these modal parameters. This model has been used to detect the modes that have the greatest influence in system ringing when testing rubber at high strain rates, and to predict quantitatively the amplitudes of vibrations produced in the process. Material curves have been corrected by subtracting the predicted undulations from the original measurements, obtaining smooth curves that adequately reflect the real material behavior at high strain rates and, thus, demonstrating the effectiveness of the proposed procedure. Although the research conducted in this work has been focused on rubber, the procedure can be extended equally to characterize other materials, thus constituting a valuable tool to correct experimental measurements contaminated by ringing.

Numerical strategies for damage assessment of reinforced concrete block walls subjected to blast risk

Computational tools and numerical strategies for the determination of the response of masonry walls under blast overpressure often rely on oversimplifying and conservative assumptions, which, although justifiable for design purposes, are not as warranted when fragility analysis and risk assessment are the objectives. In addition, due to the composite nature of reinforced masonry construction, the evaluation of multivariate fragility functions may likely require significant computational effort, owing to the multiplicity of variables describing the constituent materials and their associated uncertainty. The problem is further compounded by the effects of the high strain rates typically induced by blast loading, which make the understanding of masonry behaviour even more challenging; although efforts are being made in order to account for strain rate effects at the macro-scale, no well established models are available for reinforced masonry walls. Therefore, in order to perform accurate yet expedient fragility analyses that can effectively capture rate dependent phenomena, a dynamic model based on single-degree-of-freedom (SDOF) approach is developed. The SDOF model accounts for the nonlinear stress–strain behaviour obtained from standard prism tests and integrates strain rate dependent formulations provided in the open literature. The model predictions are corroborated using data—including pressure and displacement histories—from field testing of six scaled concrete block walls subjected to the detonation of live explosives. Within the scope of the current study, the proposed model is found to be a reasonable trade-off between computational efficiency and numerical accuracy and is an improvement upon a basic SDOF approach, which is typically based on the fixed dynamic increase factors recommended by modern design standards and technical manuals for blast protection. The results presented in this study are expected to contribute to the ongoing development of a comprehensive framework for the probabilistic risk assessment of structures subjected to explosive loading.

Single-Degree-of-Freedom Approach to Incorporate Axial Load Effects on Pressure Impulse Curves for Steel Columns

AbstractIn this paper, the moment-curvature behavior of a steel column under constant axial loading is implemented into a computationally efficient one-dimensional finite-element approach, utilizing Timoshenko beam theory, to determine the dynamic response of steel columns subjected to blasts. Then, a new single-degree-of-freedom (SDOF) approach is provided for determining pressure impulse curves for steel columns under constant axial loading. This SDOF approach relies on the newly defined concept of the reduced resistance-deflection function to accurately simulate the PΔ effects and the global instability failure mechanism, which are both caused by the axial load. The aforementioned finite-element approach is then used to thoroughly validate the newly proposed SDOF approach for deriving pressure impulse curves. It is shown that, despite the inherent simplicity of the approach, the newly proposed SDOF approach provides accurate and reliable results.

Limitations in Simplified Approach in Assessing Performance of Façade under Blast Pressures

The main function of building facades, which often consists of glazing windows, is to provide protection to the occupants and contents of the building from external hazards. In a blast event, the facade component of a building may become the weakest link of the structure, whereby its breach may lead to blast pressure ingress and hazardous projectiles into a structure. This paper reports part of a study to establish the performance of glass windows under blast pressures. Two modelling techniques were used to simulate the response of a facade panel. They are the Single Degree of Freedom (SDOF) modelling technique and the Finite Element (FE) modelling technique. Although the SDOF approach can be used with a reasonable degree of accuracy, the limitations of its basic assumption lead to loss of details in the idealisation process. This paper presents an attempt to establish performance indices of a facade panel, and to identify the discrepancies between simplified approach and the detailed numerical modelling approach analysis.

Response Prediction of Foam-Insulated Concrete Sandwich Panels Subjected to Blast Loads Using Bilinear Weighted-Resistance SDOF Models

This paper presents the development and validation of a single-degree-of-freedom (SDOF) methodology that can be used for the analysis and design of foam-insulated concrete sandwich panels subjected to blast loads. The experimental program used for validation involved both static and dynamic testing of full-scale wall panels. Static testing demonstrated that the degree of composite action provided depends greatly upon the shear connector used and that the internal shear resistance mechanisms change as the panel undergoes large deflection. Given the extreme complexities involved, a simplified bilinear resistance definition was developed using weighted averages between the composite and non-composite resistances. The weighting values were based upon equating the averaged energy absorption capacity measured during the large deflection static testing with that of the analytical definition. The analytical resistances were then used in SDOF models to examine their applicability through comparison to full-scale blast test responses. The weighted resistance SDOF approach was shown to be a viable option for analyzing foam-insulated sandwich panels subjected to blast loads.

Processing Survey Data with Ordered Alternative Hypotheses

Abstract Testing the hypothesis of equality of means, as in a one-way analysis of variance, against the hypothesis of a particular ordering of the means can be done in two ways. One approach uses the maximum likelihood philosophy while the other uses a single degree of freedom contrast with coefficients chosen to be best in some sense. These two methods are applied to some data from a small scale social survey so as to illustrate their calculations and conclusions. Although the single degree of freedom approach may be accused of arbitrariness in scores, still it is relatively more convenient computationally and permits somewhat more comprehensive conclusions.

Processing Survey Data with Ordered Alternative Hypotheses

Abstract Testing the hypothesis of equality of means, as in a one-way analysis of variance, against the hypothesis of a particular ordering of the means can be done in two ways. One approach uses the maximum likelihood philosophy while the other uses a single degree of freedom contrast with coefficients chosen to be best in some sense. These two methods are applied to some data from a small scale social survey so as to illustrate their calculations and conclusions. Although the single degree of freedom approach may be accused of arbitrariness in scores, still it is relatively more convenient computationally and permits somewhat more comprehensive conclusions.