Search results for: limit analysis

Authors: M. Movahedi Rad

Abstract:

In this study, a general approach to the reliability based limit analysis of laterally loaded piles is presented. In engineering practice, the uncertainties play a very important role. The aim of this study is to evaluate the lateral load capacity of free head and fixed-head long pile when the plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has a significant effect for the load parameter. The solution to reliability-based problems is obtained by a computer program which is governed by the reliability index calculation.

Keywords: reliability, laterally loaded pile, residual strain energy, probability, limit analysis

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Authors: Kishor J. shinde

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We determine the values of k and p such that the Sturm-Liouville differential operator τu=-(d^2 u)/(dx^2) + kx^p u is in limit point case or limit circle case at infinity. In particular it is shown that τ is in the limit point case when (i) for p=2 and ∀k, (ii) for ∀p and k=0, (iii) for all p and k>0, (iv) for 0≤p≤2 and k<0, (v) for p<0 and k<0. τ is in the limit circle case when (i) for p>2 and k<0.

Keywords: limit point case, limit circle case, Sturm-Liouville, infinity

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Authors: Minho Kwon, Jeonghee Lim, Yeongseok Jeong, Jongyoon Moon, Donghoon Shin, Kiyoung Kim

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In the past, the criteria and procedures for the design of concrete structures were mainly based on the stresses allowed for structural components. However, although the frequency of earthquakes has increased and the risk has increased recently, it has been difficult to determine the safety factor for earthquakes in the safety assessment of structures based on allowable stresses. Recently, limit state design method has been introduced for reinforced concrete structures, and limit state-based approach has been recognized as a more effective technique for seismic design. Therefore, in this study, the limit state of the bridge, which is a structure requiring higher stability against earthquakes, was evaluated. The finite element program LS-DYNA and twenty ground motion were used for time history analysis. The fracture caused by tensile and compression of the pier were set to the limit state. In the concrete tensile fracture, the limit state arrival rate was 100% at peak ground acceleration 0.4g. In the concrete compression fracture, the limit state arrival rate was 100% at peak ground acceleration 0.2g.

Keywords: allowable stress, limit state, safety factor, peak ground acceleration

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Authors: Filip Dodigovic, Kreso Ivandic, Damir Stuhec, S. Strelec

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The general difference analysis between the former and new design concepts in geotechnical engineering is carried out. The application of new regulations results in the need for real adaptation of the computation principles of limit states, i.e. by providing a uniform way of analyzing engineering tasks. Generally, it is not possible to unambiguously match the limit state verification procedure with those in the construction engineering. The reasons are the inability to fully consistency of the common probabilistic basis of the analysis, and the fundamental effect of material properties on the value of actions and the influence of actions on resistance. Consequently, it is not possible to apply separate factorization with partial coefficients, as in construction engineering. For the slope stability analysis design procedures problems in the light of the use of limit states in relation to the concept of allowable stresses is detailed in. The quantifications of the safety margins in the slope stability analysis for both approaches is done. When analyzing the stability of the slope, by the strict application of the adopted forms from the new regulations for significant external temporary and/or seismic actions, the equivalent margin of safety is increased. The consequence is the emergence of more conservative solutions.

Keywords: allowable pressure, Eurocode 7, limit states, slope stability

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Authors: Weigao. Wu, Stefano. Utili

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Based on the kinematic approach of limit analysis, a full set of upper bound solutions for the stability of homogeneous rock slopes subjected to tension cracks are obtained. The generalized Hoek-Brown failure criterion is employed to describe the non-linear strength envelope of rocks. In this paper, critical failure mechanisms are determined for cracks of known depth but unspecified location, cracks of known location but unknown depth, and cracks of unspecified location and depth. It is shown that there is a nearly up to 50% drop in terms of the stability factors for the rock slopes intersected by a tension crack compared with intact ones. Tables and charts of solutions in dimensionless forms are presented for ease of use by practitioners.

Keywords: Hoek-Brown failure criterion, limit analysis, rock slope, tension cracks

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Authors: Mohd Ritzman Abdul Karim, Zhaohui Huang

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A current focus in seismic engineering practice is the development of seismic design approach that focuses on the performance-based design. Performance-based design aims to design the structures to achieve specified performance based on the damage limit states. This damage limit is more restrictive limit than life safety and needs to be carefully estimated to avoid damage in piers due to failure in transverse reinforcement. In this paper, a different perspective of damage limit states has been explored by integrating two damage control material limit state, concrete and reinforcement by introduced parameters such as expected yield stress of transverse reinforcement where peak tension strain prior to bar buckling is introduced in a recent study. The different perspective of damage limit states with modified yield displacement and the modified plastic-hinge length is used in order to predict damage-control target displacement for reinforced concreate (RC) bridge pier. Three-dimensional (3D) finite element (FE) model has been developed for estimating damage target displacement to validate proposed damage limit states. The result from 3D FE analysis was validated with experimental study found in the literature. The validated model then was applied to predict the damage target displacement for RC bridge pier and to validate the proposed study. The tensile strain on reinforcement and compression on concrete were used to determine the predicted damage target displacement and compared with the proposed study. The result shows that the proposed damage limit states were efficient in predicting damage-control target displacement consistent with FE simulations.

Keywords: damage-control target displacement, damage limit states, reinforced concrete bridge pier, yield displacement

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

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This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: limit state, shakedown analysis, homogenization, heterogeneous structure

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Authors: Danni Cong, Meiping Wu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokuncai, Hao Qin

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Gravity gradient instrument (GGI) is the core of the gravity gradiometer, so the structural error of the sensor has a great impact on the measurement results. In order not to affect the aimed measurement accuracy, limit error is required in the installation of the accelerometer. In this paper, based on the established measuring principle model, the radial installation limit error is calibrated, which is taken as an example to provide a method to calculate the other limit error of the installation under the premise of ensuring the accuracy of the measurement result. This method provides the idea for deriving the limit error of the geometry structure of the sensor, laying the foundation for the mechanical precision design and physical design.

Keywords: gravity gradient sensor, radial installation limit error, accelerometer, uniaxial rotational modulation

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Authors: Chang He, Hiroshi Tamura, Hiroshi Katsuchi, Jiaqi Wang

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In this study, the aim is to infer the slip limit (static friction limit) of contact interfaces in bolt friction joints by analyzing other bolt friction joints with the same contact surface but in a different shape. By using the Weibull distribution to deal with microelements on the contact surface statistically, the slip limit of a certain type of bolt joint was predicted from other types of bolt joint with the same contact surface. As a result, this research succeeded in predicting the slip limit of bolt joins with different numbers of contact surfaces and with different numbers of bolt rows.

Keywords: bolt joints, slip coefficient, finite element method, Weibull distribution

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Authors: F. Boufera, F. Debbat

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This paper deals with an approach based on limit-cycles method for the problem of obstacle avoidance of mobile robots in unknown environments for any form of obstacles. The purpose of this approach is the improvement of limit-cycles method in order to obtain safe and flexible navigation. The proposed algorithm has been successfully tested in different configuration on simulation.

Keywords: mobile robot, navigation, avoidance of obstacles, limit-cycles method

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Authors: Margarida Plana

Abstract:

The end-users behavior has been identified in the last years as one of the main responsible for the success degree of the energy efficiency improvements. It is essential to create tools to limit their impact on the final consumption. This paper is focused on presenting the results of the analysis developed on the basis of real projects’ data in order to quantify the impact of end-users behavior. The analysis is focused on how the behavior of building’s occupants can vary the achievement of the energy savings targets and how they can be limited. The results obtained show that the management systems are one of the main tools available to control and limit the end-users interaction with the equipment operation. In fact, the results will present the management systems as ‘a must’ on any energy efficiency project.

Keywords: end-users impacts, energy efficiency, energy savings, management systems

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Authors: Reyhan Tekin Sitrava

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Teachers should have robust and comprehensive content knowledge for effective mathematics teaching. It was explained that content knowledge includes knowing the facts, truths, and concepts; explaining the reasons behind these facts, truths and concepts, and making relationship between the concepts and other disciplines. By virtue of its importance, it will be significant to explore teachers and prospective teachers’ content knowledge related to variety of topics in mathematics. From this point of view, the purpose of this study was to investigate prospective mathematics teachers’ content knowledge. Particularly, it was aimed to reveal the prospective teachers’ knowledge regarding the definition of limit and derivate. To achieve the purpose and to get in-depth understanding, a qualitative case study method was used. The data was collected from 34 prospective mathematics teachers through a questionnaire containing 2 questions. The first question required the prospective teachers to define the limit and the second one required to define the derivative. The data was analyzed using content analysis method. Based on the analysis of the data, although half of the prospective teachers (50%) could write the definition of the limit, nine prospective teachers (26.5%) could not define limit. However, eight prospective teachers’ definition was regarded as partially correct. On the other hand, twenty-seven prospective teachers (79.5%) could define derivative, but seven of them (20.5%) defined it partially. According to the findings, most of the prospective teachers have robust content knowledge on limit and derivative. This result is important because definitions have a virtual role in learning and teaching of mathematics. More specifically, definition is starting point to understand the meaning of a concept. From this point of view, prospective teachers should know the definitions of the concepts to be able to teach them correctly to the students. In addition, they should have knowledge about the relationship between limit and derivative so that they can explain these concepts conceptually. Otherwise, students may memorize the rules of calculating the derivative and the limit. In conclusion, the present study showed that most of the prospective mathematics teachers had enough knowledge about the definition of derivative and limit. However, the rest of them should learn their definition conceptually. The examples of correct, partially correct, and incorrect definition of both concepts will be presented and discussed based on participants’ statements. This study has some implications for instructors. Instructors should be careful about whether students learn the definition of these concepts or not. In order to this, the instructors may give prospective teachers opportunities to discuss the definition of these concepts and the relationship between the concepts.

Keywords: content knowledge, derivative, limit, prospective mathematics teachers

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Authors: Agnieszka Dudzik

Abstract:

The problem of correlation between random variables in the structural reliability analysis has been extensively discussed in literature on the subject. The cases taken under consideration were usually related to correlation between random variables from one side of ultimate limit state: correlation between particular loads applied on structure or correlation between resistance of particular members of a structure as a system. It has been proved that positive correlation between these random variables reduces the reliability of structure and increases the probability of failure. In the paper, the problem of correlation between random variables from both side of the limit state equation will be taken under consideration. The simplest case where these random variables are of the normal distributions will be concerned. The case when a degree of that correlation is described by the covariance or the coefficient of correlation will be used. Special attention will be paid on questions: how much that correlation changes the reliability level and can it be ignored. In reliability analysis will be used well-known methods for assessment of the failure probability: based on the Hasofer-Lind reliability index and Monte Carlo method adapted to the problem of correlation. The main purpose of this work will be a presentation how correlation of random variables influence on reliability index of steel bar structures. Structural design parameters will be defined as deterministic values and random variables. The latter will be correlated. The criterion of structural failure will be expressed by limit functions related to the ultimate and serviceability limit state. In the description of random variables will be used only for the normal distribution. Sensitivity of reliability index to the random variables will be defined. If the reliability index sensitivity due to the random variable X will be low when compared with other variables, it can be stated that the impact of this variable on failure probability is small. Therefore, in successive computations, it can be treated as a deterministic parameter. Sensitivity analysis leads to simplify the description of the mathematical model, determine the new limit functions and values of the Hasofer-Lind reliability index. In the examples, the NUMPRESS software will be used in the reliability analysis.

Keywords: correlation of random variables, reliability index, sensitivity of reliability index, steel structure

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Authors: Lakshya Bhat, Anubhav Shrivastava, Shiva Rudraswamy

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There has been a formidable interest in the area of Distributed Generation in recent times. A wide number of loads are addressed by Distributed Generators and have better efficiency too. The major disadvantage in Distributed Generation is voltage control- is highlighted in this paper. The paper addresses voltage control at buses in IEEE 14 Bus system by regulating reactive power. An analysis is carried out by selecting the most optimum location in placing the Distributed Generators through load flow analysis and seeing where the voltage profile rises. MATLAB programming is used for simulation of voltage profile in the respective buses after introduction of DG’s. A tolerance limit of +/-5% of the base value has to be maintained. To maintain the tolerance limit, 3 methods are used. Sensitivity analysis of 3 methods for voltage control is carried out to determine the priority among the methods.

Keywords: distributed generators, distributed system, reactive power, voltage control, sensitivity analysis

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Authors: Lakshya Bhat, Anubhav Shrivastava, Shivarudraswamy

Abstract:

There has been a formidable interest in the area of Distributed Generation in recent times. A wide number of loads are addressed by Distributed Generators and have better efficiency too. The major disadvantage in Distributed Generation is voltage control- is highlighted in this paper. The paper addresses voltage control at buses in IEEE 14 Bus system by regulating reactive power. An analysis is carried out by selecting the most optimum location in placing the Distributed Generators through load flow analysis and seeing where the voltage profile rises. Matlab programming is used for simulation of voltage profile in the respective buses after introduction of DG’s. A tolerance limit of +/-5% of the base value has to be maintained.To maintain the tolerance limit , 3 methods are used. Sensitivity analysis of 3 methods for voltage control is carried out to determine the priority among the methods.

Keywords: distributed generators, distributed system, reactive power, voltage control, sensitivity analysis

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Authors: Taleb Hosni Abderrahmane, Berga Abdelmadjid

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The development of numerical analysis and its application to geomechanics problems have provided geotechnical engineers with extremely powerful tools. One of the most important problems in geotechnical engineering is the slope stability assessment. It is a very difficult task due to several aspects such the nature of the problem, experimental consideration, monitoring, controlling, and assessment. The main objective of this paper is to perform a comparative numerical study between the following methods: The Limit Equilibrium (LEM), Finite Element (FEM), Limit Analysis (LAM) and Distinct Element (DEM). The comparison is conducted in terms of the safety factors and the critical slip surfaces. Through the results, we see the feasibility to analyse slope stability by many methods.

Keywords: comparison, factor of safety, geomechanics, numerical methods, slope analysis, slip surfaces

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Han Bai, Lemei Yu, Tong Zhang, Doudou Xie, Liang Zhao

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The brightness changes at highway tunnel entrance and exit have an effect on the physical and psychological conditions of drivers. It is more conducive for examining driving safety with quantitative analysis of the physical and psychological characteristics of drivers to determine the speed limit sign locations at the tunnel entrance and exit sections. In this study, the physical and psychological effects of tunnels on traffic sign recognition of drivers are analyzed; subsequently, experiments with the assistant of Eyelink-II Type eye movement monitoring system are conducted in the typical tunnels in Ji-Qing freeway and Xi-Zha freeway, to collect the data of eye movement indexes “Fixation Duration” and “Eyeball Rotating Speed”, which typically represent drivers' mental load and visual characteristics. On this basis, the paper establishes a visual recognition model for the speed limit signs at the highway tunnel entrances and exits. In combination with related standards and regulations, it further presents the recommended values for locating speed limit signs under different tunnel conditions. A case application on Panlong tunnel in Ji-Qing freeway is given to generate the helpful improvement suggestions.

Keywords: driver psychological load, eye movement index, speed limit sign location, tunnel entrance and exit

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Authors: Giacomo Ciani

Abstract:

This paper reviews the impact of quantum noise on modern gravitational wave interferometers and explains how squeezed vacuum states are used to push the noise below the standard quantum limit. With the first detection of gravitational waves from a pair of colliding black holes in September 2015 and subsequent detections including that of gravitational waves from a pair of colliding neutron stars, the ground-based interferometric gravitational wave observatories LIGO and VIRGO have opened the era of gravitational-wave and multi-messenger astronomy. Improving the sensitivity of the detectors is of paramount importance to increase the number and quality of the detections, fully exploiting this new information channel about the universe. Although still in the commissioning phase and not at nominal sensitivity, these interferometers are designed to be ultimately limited by a combination of shot noise and quantum radiation pressure noise, which define an envelope known as the standard quantum limit. Despite the name, this limit can be beaten with the use of advanced quantum measurement techniques, with the use of squeezed vacuum states being currently the most mature and promising. Different strategies for implementation of the technology in the large-scale detectors, in both their frequency-independent and frequency-dependent variations, are presented, together with an analysis of the main technological issues and expected sensitivity gain.

Keywords: gravitational waves, interferometers, squeezed vacuum, standard quantum limit

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Authors: Azad A. Mohammed, Dunyazad K. Assi, Alan S. Abdulrahman

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Current ACI 318 Code provides two limits for minimum steel ratio for concrete beams. When concrete compressive strength be larger than 31 MPa the limit of √(fc')/4fy usually governs. In this paper shortcomings related to using this limit was fairly discussed and showed that the limit is based on 90% safety factor and was derived based on modulus of rupture equation suitable for concretes of compressive strength lower than 31 MPa. Accordingly, the limit is nor suitable and critical for concretes of higher compressive strength. An alternative equation was proposed for minimum steel ratio of rectangular beams and was found that the proposed limit is accurate for beams of wide range of concrete compressive strength. Shortcomings of the current ACI 318 Code equation and accuracy of the proposed equation were supported by test data obtained from testing six reinforced concrete beams.

Keywords: concrete beam, compressive strength, minimum steel ratio, modulus of rupture

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Authors: Marcelo Costa Cardoso, Luciano Pessanha Moreira

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In this work, the plastic behaviour of cold-rolled zinc coated dual-phase steel sheets DP600 and DP800 grades is firstly investigated with the help of uniaxial, hydraulic bulge and Forming Limit Curve (FLC) tests. The uniaxial tensile tests were performed in three angular orientations with respect to the rolling direction to evaluate the strain-hardening and plastic anisotropy. True stress-strain curves at large strains were determined from hydraulic bulge testing and fitted to a work-hardening equation. The limit strains are defined at both localized necking and fracture conditions according to Nakajima’s hemispherical punch procedure. Also, an elasto-plastic localization model is proposed in order to predict strain and stress based forming limit curves. The investigated dual-phase sheets showed a good formability in the biaxial stretching and drawing FLC regions. For both DP600 and DP800 sheets, the corresponding numerical predictions overestimated and underestimated the experimental limit strains in the biaxial stretching and drawing FLC regions, respectively. This can be attributed to the restricted failure necking condition adopted in the numerical model, which is not suitable to describe the tensile and shear fracture mechanisms in advanced high strength steels under equibiaxial and biaxial stretching conditions.

Keywords: advanced high strength steels, forming limit curve, numerical modelling, sheet metal forming

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Authors: An-Jui. Li, Kelvin Lim, Chien-Kuo Chiu, Benson Hsiung

Abstract:

This paper details the utilization of artificial intelligence (AI) in the field of slope stability whereby quick and convenient solutions can be obtained using the developed tool. The AI tool used in this study is the artificial neural network (ANN), while the slope stability analysis methods are the finite element limit analysis methods. The developed tool allows for the prompt prediction of the safety factors of fill slopes and their corresponding probability of failure (depending on the degree of variation of the soil parameters), which can give the practicing engineer a reasonable basis in their decision making. In fact, the successful use of the Extreme Learning Machine (ELM) algorithm shows that slope stability analysis is no longer confined to the conventional methods of modeling, which at times may be tedious and repetitive during the preliminary design stage where the focus is more on cost saving options rather than detailed design. Therefore, similar ANN-based tools can be further developed to assist engineers in this aspect.

Keywords: landslide, limit analysis, artificial neural network, soil properties

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Authors: Margarida Plana

Abstract:

End-users behavior has become one of the main aspects to be solved on energy efficiency projects. Especially on the residential sector, the end-users have a direct impact that affects the achievement of energy saving’s targets. This paper is focused on presenting and quantify the impact of end-users behavior on basis of the analysis of real projects’ data. The analysis study which is the role of buiding’s occupants and how their behavior can change the success of energy efficiency projects how to limit their impact. The results obtained show two main conclusions. The first one is easiest to solve: we need to control and limit the end-users interaction with the equipment operation to be able to reach the targets fixed. The second one: as the plugged equipment are increasing exponentially on the residential sector, big efforts of disseminations are needed in order to explain to citizens the impact of their day by day actions through dissemination campaigns.

Keywords: end-users impacts, energy efficiency, energy savings, impact limitations

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Authors: Abdelhak Soudani

Abstract:

Using the limit equilibrium method in geotechnical field is very important for large projects. This work contributes to the understanding and analysis of the building unstable slopes by the technique of soil nailed with the used of software called GEO-SLOPE calculation based on limit equilibrium method. To achieve our objective, we began a review of the literature on landslides, and techniques of slope stability. Then, we presented a real case slope likely to slip through the realization of the EastWest Highway (M5 stretch between Khemis Miliana and Hoceinia). We also process the application of reinforcement technique nailed soil. The analysis is followed by a parametric study, which shows the impact of parameters given or chosen on various outcomes. Another method of reinforcement (use of micro-piles) has been suggested for improving the stability of the slope

Keywords: slope stability, strengthening, slip, soil nail, GEO-SLOPE

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Authors: Marin Senila, Oana Cadar, Thorsten Janisch, Patrick Lacroix-Desmazes

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The study presents the analytical capability and validation of a method based on microwave-assisted acid digestion for quantitative determination of platinum and palladium in catalysts using inductively coupled plasma optical emission spectrometry (ICP-OES). In order to validate the method, the main figures of merit such as limit of detection and limit of quantification, precision and accuracy were considered and the measurement uncertainty was estimated based on the bottom-up approach according to the international guidelines of ISO/IEC 17025. Limit of detections, estimated from blank signal using 3 s criterion, were 3.0 mg/kg for Pt and respectively 3.6 mg/kg for Pd, while limits of quantification were 9.0 mg/kg for Pt and respectively 10.8 mg/kg for Pd. Precisions, evaluated as standard deviations of repeatability (n=5 parallel samples), were less than 10% for both precious metals. Accuracies of the method, verified by recovery estimation certified reference material NIST SRM 2557 - pulverized recycled monolith, were 99.4 % for Pt and 101% for Pd. The obtained limit of quantifications and accuracy were satisfactory for the intended purpose. The paper offers all the steps necessary to validate the determination method for Pt and Pd in catalysts using inductively coupled plasma optical emission spectrometry.

Keywords: catalyst analysis, ICP-OES, method validation, platinum, palladium

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Authors: M. Linek, P. Nita

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In the previous airfield construction industry, pavements made of reinforced concrete have been used very rarely; however, the necessity to use this type of pavements in an emergency situations justifies the need reference to this issue. The paper concerns the problem of airfield pavement dimensioning made of reinforced concrete and the evaluation of selected dimensioning methods of reinforced concrete slabs intended for airfield pavements. Analysis of slabs dimensioning, according to classical method of limit states has been performed and it has been compared to results obtained in case of methods complying with Eurocode 2 guidelines. Basis of an analysis was a concrete slab of class C35/45 with reinforcement, located in tension zone. Steel bars of 16.0 mm have been used as slab reinforcement. According to comparative analysis of obtained results, conclusions were reached regarding application legitimacy of the discussed methods and their design advantages.

Keywords: rainforced concrete, cement concrete, airport pavements, dimensioning

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Authors: Min-Tsai Lai, Taqwa Hariguna

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This paper presents a periodical replacement model for a system, considering the concept of single and cumulative repair cost limits simultaneously. The failures are divided into two types. Minor failure can be corrected by minimal repair and serious failure makes the system breakdown completely. When a minor failure occurs, if the repair cost is less than a single repair cost limit L1 and the accumulated repair cost is less than a cumulative repair cost limit L2, then minimal repair is executed, otherwise, the system is preventively replaced. The system is also replaced at time T or at serious failure. The optimal period T minimizing the long-run expected cost per unit time is verified to be finite and unique under some specific conditions.

Keywords: repair-cost limit, cumulative repair-cost limit, minimal repair, periodical replacement policy

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Authors: Khelifa Tarek, Benmebarek Sadok

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The 2D passive earth pressures acting on rigid retaining walls problem has been widely treated in the literature using different approaches (limit equilibrium, limit analysis, slip line and numerical computation), however, the 3D passive earth pressures problem has received less attention. This paper is concerned with the numerical study of 3D passive earth pressures induced by the translation of a rigid rough retaining wall for associated and non-associated soils. Using the explicit finite difference code FLAC3D, the increase of the passive earth pressures due to the decrease of the wall breadth is investigated. The results given by the present numerical analysis are compared with other investigation. The influence of the angle of dilation on the coefficients is also studied.

Keywords: numerical modeling, FLAC3D, retaining wall, passive earth pressures, angle of dilation

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Authors: N. Abbas, S. Lagomarsino, S. Cattari

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Examining existing experimental results for shallow rigid foundations subjected to vertical centric load (N), accompanied or not with a bending moment (M), two main non-linear mechanisms governing the cyclic ‎response of the soil-foundation system can be distinguished: foundation uplift and soil yielding. A soil-foundation failure limit, is defined as a domain of resistance in the two dimensional (2D) load space (N, M) inside of which lie all the admissible combinations of loads; these latter correspond to a pure elastic, non-linear elastic or plastic behavior of the soil-foundation system, while the points lying on the failure limit correspond to a combination of loads leading to a failure of the soil-foundation system. In this study, the proposed resistance domain is constructed analytically based on mechanics. Original elastic limit, uplift initiation ‎limit and iso-uplift limits are constructed inside this domain. These limits give a prediction ‎of the mechanisms activated for each combination of loads applied to the ‎foundation. A comparison of the proposed failure limit with experimental tests existing in the literature shows interesting results. Also, the developed uplift initiation limit and iso-uplift curves are confronted with others already proposed in the literature and widely used due to the absence of other alternatives, and remarkable differences are noted, showing evident errors in the past proposals and relevant accuracy for those given in the present work.

Keywords: foundation uplift, iso-uplift curves, resistance domain, soil yield

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Authors: Tawanda Mushiri, Charles Mbohwa

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When an external load is applied to one of its ends, a pipe’s bends cross section tends to deform significantly both in and out of its end plane. This shell type behaviour characteristic of pipe bends and mainly due to their curves geometry accounts for their greater flexibility. This added flexibility is also accompanied by stressed and strains that are much higher than those present in a straight pipe. The primary goal of this research is to study the elastic-plastic behaviour of pipe bends under out of plane moment loading. It is also required to study the effects of changing the value of the pipe bend factor and the value of the internal pressure on that behaviour and to determine the value of the limit moments in each case. The results of these analyses are presented in the form of load deflection plots for each load case belonging to each model. From the load deflection curves, the limit moments of each case are obtained. The limit loads are then compared to those computed using some of the analytical and empirical equation available in the literature. The effects of modelling parameters are also studied. The results obtained from small displacement and large displacement analyses are compared and the effects of using a strain hardened material model are also investigated. To better understand the behaviour of pipe elbows under out of plane bending and internal pressure, it was deemed important to know how the cross section deforms and to study the distribution of stresses that cause it to deform in a particular manner. An elbow with pipe bend factor h=0.1 to h=1 is considered and the results of the detailed analysis are thereof examined.

Keywords: elasto-plastic, finite element analysis, pipe bends, simulation

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