Form Of Deflection Research Articles

Behavior of Modified Strut-and-Tie Model (STM) on Concrete Beams

Reinforced concrete components are generally designed to withhold shear and bending based on the assumption at strain varies linearly in a section where the applied force is a combination of shear with bending, torsion, or normal forces. The behavior of shear failure in reinforced concrete beams is very different from that in flexural failure. Shear failure is brittle without warning in the form of significant deflection, resulting in diagonal cracks in the beam then the shear force mechanism will be contributed by an arching action where this action can provide a reserve capacity large enough for the beam to carry the load. Nonlinear analysis using the strut-and-tie method is particularly useful for shear-critical structures where classical beam theory is not valid due to significant shear deformations. Strut-and-Tie Model research which is applied to concrete (25 MPa), also uses the optimal configuration FEM software tool from Strut-and-Tie which leads to the efficiency of Strut-and-Tie. The results of the optimization and modification of the Strut-and-Tie Model on concrete will also be applied to the experimental models tested until they fail so that the optimal conditions for numerical models will be obtained.Based on the analysis result of element model using ANSYS computational assistance program, the ultimate flexural capacity of the beam model will increase depending on the used STM model and inclination angle (Φ), at the STM type 2 high < 1000 mm, inclination angle (Φ) 45° having a decrease in ultimate shear capacity (Vu) of 49,31% against type 1, at the STM model 3 high < 1000 mm, with inclination angle (Φ) 45° having an increase ultimate shear (Vu) of 4,14% against type 1. Stress pattern performed bottle shape in line with diagonal strut. Ductility capacity will be decreased at inclination angle <45° of 27,11%, at inclination angle >45° will be decreased of 55,67%,

Gain scheduled task space control of multi DOF machine tools with non-linear parallel kinematics

Machine tools with multiple degrees of freedom and parallel kinematics offer tremendous opportunities for new kind of processes but at the same time also a lot of control challenges. They are subject to uncertainties in the form of kinematic errors, elasticities and thermal deflections. Their kinematic non-linearity requires the application of model-based control concepts whose full effectiveness can only be unlocked through controls in the task space. In particular, kinematic singularities occur in forming machines such as presses, which make closed-loop control at corresponding operating points considerably more difficult. In this paper, we use the example of a servo-driven press with three ram degrees of freedom to show how parallel kinematic machine tools can be controlled via inverse differential kinematics models in task space and to what extent the controls can benefit from scheduled gain factors. The results are validated both simulatively and experimentally. In the experimental tests, three-dimensional tool paths are traced that can be used to carry out orbital forging processes. Furthermore, the example of a punch hole rolling process demonstrates that the ram pose is controlled more accurately, which also has positive effects on the resulting workpiece geometry. The performance of the developed gain scheduling task space control is compared with that of a robust and non-robust control with static gains.

STABILITY OF RODS WITH INITIAL IMPERFECTIONS IN THE FORM OF ECCENTRICITY OF LOAD APPLICATION UNDER LINEAR AND NON-LINEAR CREEP CONDITIONS

Stability of a compressed rod having initial imperfections in the form of eccentricity of applied load under conditions of linear and nonlinear creep is considered. It is noted that all real elements have some initial imperfections in the form of technological deflections, eccentricities of applied loads, etc., so they begin to bulge from the very beginning of loading. Another important factor in stability theory is the consideration of material creep. In this regard, the loading process is divided into two phases: the instantaneous loading process and the creep phase under constant external load. Moreover, creep can be time-limited or unrestricted. In the paper formulas for determination of critical forces of stability loss of the rod having initial imperfections, under short-term and long-term action of load are obtained. The equation allowing to determine time of the first crack appearance is derived. Derived are equations the roots of which are loads at action of which the first cracks appear at initial moment of time and at arbitrarily long period of load action. Analysis of acting force determining the character of rod deformation is executed. From the constructed stability equation it is possible to determine the critical force corresponding to the critical length of the section with cracks. For similar problems in nonlinear formulation formulas for determining critical force and critical displacement corresponding to maximum load are obtained. For the case of long duration load the equation which establishes relationship between load and displacement is obtained. Equation for determination of critical force under prolonged action of load has been derived. It has been established that critical displacement is the same under short- and continuous action of load. It is shown that at any intermediate moment critical displacement can be achieved under load lying in certain interval. Keywords: stability, rod, initial imperfection, eccentricity, linear creep, non-linear creep, critical force, crack, critical displacement.

Model of a Micromechanical Modal-Localized Accelerometer with a Sensitive Element in the Form of a Beam with an Initial Deflection

The present study is devoted to mathematical modeling of the proposed new architecture of a microelectromechanical modally localized acceleration sensor (MEMS accelerometer/gravimeter) with a sensitive element in the form of a microbeam pinched at both ends with an initial deflection, made in the form of the first asymmetric mode of free vibrations. The article demonstrates that with an asymmetric form of the initial deflection in the region of positive axial forces, there are zones of proximity of the frequency branches corresponding to the second symmetric and the first asymmetric vibration modes. When the required value of the axial tensile force in the microbeam is provided structurally, this effect can be used, in particular, to measure the axial component of the transfer acceleration according to the principle of amplitude modal localization. The possibility of heating the sensitive element with the help of an electric current flowing through the microbeam, provided in the sensor layout, makes it possible to control the operating point of the oscillation mode and, thus, to vary the range of measured accelerations and the degree of sensor sensitivity within a very wide range. The configuration of the oscillation excitation and output signal pickup electrodes proposed in the article makes it possible, with the help of a feedback loop, to stabilize the oscillation amplitude at the required level in the working (third) symmetrical form and, at the same time, to measure the oscillation amplitude associated with the change in the value of the measured component of the portable acceleration according to the asymmetric form. Thus, a mathematical model of an original modal-localized accelerometer (gravimeter) containing a single sensitive microbeam element and involving the effect of energy exchange between its various modes of vibration is proposed and investigated in the article.

Comprehensive Correlations for Small Punch Test Response Post-Processing Toward Preserved Mechanical Strength Estimation

Abstract The small punch test (SPT) approach is a miniature specimen testing technique to estimate the preserved mechanical strength of an in-service component to check its fitness for service. The SPT results are summarized in form of force-specimen deflection, (F − u) and force-punch displacement, (F − v) response. There are many standards published in an attempt to define a universally accepted approach for SPT-aided mechanical characterization. However, it was recognized that such standards were not concerned to practice a consistent approach while SPT response measurement and strength estimation toward outlining proclaimed best-fitting correlations. This paper narrates limitations caused by known inconsistent practices and proposed comprehensive correlations for accurate strength estimation for metallic materials which are exposed to 100–2000 MPa strengths.

Работа связевых стальных каркасов с учетом погрешностей монтажа и изготовления

Introduction. As a building construction material, steel is widely used because of its high mechanical characteristics. Steel load-bearing structures of multi-storey buildings are a system formed by columns, beams, floor slabs and braces. The frame of a multi-storey building has a large number of elements and their connections. Errors in the fabrication, installation and operation of steel frames of multi-storey buildings can lead to a reduction in the load-bearing capacity of structures compared to the design. Deviations from the design position occur because of violations of the technical operatin.rules of the buildings beyond the permissible limits, design errors, imperfect standards and poor quality of work during the fabrication and installation of structures. The current Russian standards do not take into account the impact of fabrication and installation errors on the work of multi-storey frames. The initial geometric defects in the structural system and its individual elements contribute to the difference in performance between the real construction and an idealized one. Materials and methods. The study of the effect of initial imperfections on the stress-strain state of the steel frame is important and relevant. Initial imperfections are taken into account either by applying an equivalent load to the idealized design scheme or by forming a geometrically distorted by imperfections design scheme. The analysis can be linear or geometrically non-linear. Results. The results of the study of braced steel framework performance in the presence of initial imperfections are presented. The effect of initial imperfections in the form of deflection of columns from the vertical is considered. The values of the initial imperfections are determined in accordance with the current RF standards. Conclusions. The results obtained have made it possible to propose a correction factor to the results of the calculation of frames with imperfections to the results of the calculation of an idealized frame.

Finite element modelling of reinforced concrete one-way slabs strengthened using basalt textile reinforced mortars

PurposeThis paper employs a textile reinforcement strain comparison to study the response of Textile Reinforced Mortars (TRM) strengthened reinforced concrete one-way slab members in flexure using the finite element method. Basalt TRM (BTRM) is a relatively new composite in structural strengthening applications. Experimental data on BTRMs are limited in the literature and numerical analyses can help further the understanding of this composite. With this notion, Abaqus finite element software is utilised to create a numerical method to capture the mechanical response of strengthened slab members instead of time-consuming laboratory experiments.Design/methodology/approachA numerical method is developed and validated using existing experimental data set on one-way slabs strengthened using Basalt TRMs from the literature. An explicit solver is utilised to analyse the finite element model created using calibrated Concrete Damage Plasticity (CDP) parameters according to the experimental requirements. The generated model is applied to extract load, deflection and rebar strains sustained by strengthened reinforced concrete slabs as observed from the experimental reference chosen. The applicability of the developed model was studied beyond parametric studies by comparing the generated finite element tensile strain by the textile fibre with available formulae.FindingsCDP calibration done has shown its adaptability. The predicted results in the form of load versus deflection, tensile and compressive damage patterns from the numerical analysis showed good agreement with the experimental data. A parametric study on various concrete strength, textile spacing and TRM bond length obtained shows TRM’s advantages and its favourability for external strengthening applications. A set of five formulae considered to predict the experimental strain showed varied accuracy.Originality/valueThe developed numerical model considers strain sustained by the textile fibre to make results more robust and reliable. The obtained strain from the numerical study showed good agreement with the experiment results.

Analytical and Laboratory Investigation on the Use of RAP and Waste Plastic for Conservative Planning of Road Construction Raw Materials

Abstract The current work emphasizes improving the procedure for analysis and design of flexible pavement by considering a variety of materials to be used in different layers of pavement. Field investigation and laboratory analysis were carried out to classify the subgrade soil based on their strength parameter. It is observed that most of the flexible pavement near Satara is getting deteriorated earlier than its design life. In the present study, the effect of waste materials individually and in combination on the physical properties, rutting, and fatigue behavior of pavement by laboratory and analytical investigation is evaluated. The various important input parameters like traffic characteristics, moduli of paving materials, etc. are used in structural models. The output of structural models in the form of strains, stresses, and deflection are used in distress models while the output of these distress models is examined against fatigue and rutting criteria recommended by the Guidelines for the Design of Flexible Pavements (IRC:37-2012). The computed strains at the critical locations are compared with allowable limits to decide the thicknesses of hypothetical conditions formed under different combinations of varying materials and thicknesses. The design charts proposed by consideration of multiple factors of varying nature are more realistic and optimum design charts, which can be considered to replace existing pavement sections with an eco-friendly and economic approach.

Model test and numerical simulation of foundation pit constructions using the combined artificial ground freezing method

With the increasing demand for water resources protection, realizing undrained excavations in foundation pit engineering has become a crucial technical problem to be urgently solved. In this study, we proposed a new design concept—the combined artificial ground freezing method. This method uses the diaphragm wall as the vertical support and the frozen curtain generated by freezing pipes in a temporary shaft as horizontal support. A model test and numerical simulation were performed to analyze the evolution law of the temperature field and the interaction mechanism between the freezing process and the diaphragm wall. The above research results show that the combined artificial ground freezing method could effectively and inexpensively seal the foundation pit. During the freezing period, the frost heave pressure on the contact surface of the frozen curtain and diaphragm wall was 30– 60 kPa and 25– 35 kPa in numerical simulation, much lower than the diaphragm wall's critical design value. Therefore, frost heave would not damage the diaphragm wall. In the end, the design criterion of the freezing pipes deflection form was proposed. The study provided a reference for designing and constructing foundation pits using the combined artificial ground freezing method.

Quantitative analysis of MEMS piezoresistive squared diaphragm pressure sensor for biomedical applications

Now a days MEMS based for biomedical applications with high performance parameters like sensitivity and linearity are required for low pressure range.The low-pressure range (1–5 kPa) is a significant range that comprises intra-body pressures like intracranial pressure (ICP) and intraocular pressure (IOP).A lot of work on piezoresistive pressure sensor with different shapes diaphragms like squared, circular and rectangular has been carried out.In MEMS Piezoresistive Pressure sensors the most important pressure-sensitive component is the squared diaphragm. The performance of the Micro-sensor is directly determined, under uniform applied pressure with its deformation. In pressure sensor design, the accurate relationship between pressure and deformation plays a very consequence role. In this paper, squared diaphragm of silicon material is modeled and simulate using the analytical equations for a thin plate, along with the theory of small-deflection to providing quick insight regarding important parameter like stress and Deformation for the operating pressure range of 0 kPa–5 kPa. The mechanical behavior of micro-machined silicon diaphragm in terms of stress and deflection generation has been simulated.The piezoresistivity principle is used to assess the sensor's sensitivity. The mechanical change in the thin diaphragm in the form of deflection and stress is calculated and presented. In this Modeling both the analytical and simulated(FEA) results for the performance parameters such as stress, Deflection and the output voltage is computed and compared, it is found that the error between analytical and simulation results is no more than 5.6–6.5%.

Behaviour Analysis of Strengthened-RC Beam with Natural Fiber Reinforced Polymer (NFRP) based on Abaca Fiber by Using Finite Element Method

The use of synthetic Fiber Reinforced Polymer (FRP) as a composite material is an alternative material that has been widely used for strengthening and repairing reinforced concrete structures. However, the high price is one of the obstacles in applying synthetic FRP materials in developing countries such as Indonesia. Utilization of natural fiber as a Natural Fiber Reinforced Polymer (NFRP) composite material is an alternative, especially in shear strengthening of reinforced concrete beams. Because it has good tensile strength and also is environmentally friendly. Technological developments in the field of computing make modelling various aspects easier. One of them is modelling reinforced concrete (RC) beams. ATENA V534 is a software that can be used for finite element-based modelling. Therefore, in this study, the ATENA V534 software was used to evaluate the results of research and testing behaviour of reinforced concrete beams from the previous studies about strengthened beam for shear by using NFRP. Behaviour that is evaluated in the form of load and deflection, the pattern of cracks and failure, and stress and strain of reinforcements. The numerical results obtained in ATENA V534 showed in a good agreement with experimental results.

New Analytical Free Vibration Solutions of Thin Plates Using the Fourier Series Method

This article aims at analytically solving the free vibration problem of rectangular thin plates with one corner free and its opposite two adjacent edges rotationally-restrained, which is difficult to handle by conventional semi-inverse approaches such as the Levy solution and Naiver solution, etc. Based on the classical Fourier series theory, this work presents a first endeavor to treat the two-dimensional half-sinusoidal Fourier series, which is quite similar to the Navier’s form solution, as the solution form of plate deflection. By utilizing the orthogonality of the present trial function and the Stoke’s transformation technique, the present solution procedure converts the complicated plate problem into solving sets of linear algebra equations, which heavily decreases the difficulties. Therefore, the present approach enables one to solve the title problem in a unified, simple and straightforward way, which is very easily implemented by researchers. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through utilizing different types of Fourier series and it can be extended for further dynamic/static analysis of plates under different shear deformation theories. Moreover, without any extra derivation processes, new, precise analytical free vibration solutions for plates under three non-Levy-type boundary conditions are also obtained by choosing different rotating fixed coefficients. Consequently, we present more than 400 comprehensive free vibration results for plates with classical/non-classical boundaries, all the present results are confirmed by FEM/analytical solutions and can be used as benchmark data for further research.

Evaluation of precast beam deflections resulting in cracks in curtain walls

Cracks in brick walls are among the most common examples of failures in residential constructions. This article focuses on the occurrence of cracks in brick curtain walls based on precast beams, made in a non-standard large-panel system. In order to analyse this issue, test loads on natural scale beams were carried out on a specially prepared test stand. Numerical calculations were also performed for a beam in the modified system and for a popular beam-wall in the classic system. The obtained results confirm that the serviceability limit state in the form of deflection was exceeded. The cracking was caused by designing the elements according to archival, less restrictive norms and making them from materials with lower material characteristics in relation to currently used. In addition, the modified beam has a significantly smaller cross-sectional height, while carrying a higher load in relation to the commonly used beam-wall. The resulting defects need to be thoroughly assessed, and then a decision on the acceptability of further use and possible strengthening has to be made, preferably by an approved engineer.

Control of String Vibrations by Displacement of One End with the Other End Fixed, Given the Deflection Form at an Intermediate Moment of Time

We consider a boundary control problem for the equation of string vibration with given initial and final conditions, given the deflection form at an intermediate moment of time. The control is carried out by displacement of one end with the other end fixed. The problem is reduced to the problem of a distributed action control with zero boundary conditions. We propose a constructive approach to constructing a boundary control action by the separation of variables and methods of the theory of control of finite-dimensional systems. The approach is applied to given functions. A computational experiment was carried out with the construction of the corresponding graphs and their comparative analysis. They confirm the obtained results.

The Coal Pillar Width Effect of Principal Stress Deflection and Plastic Zone Form of Surrounding Rock Roadway in Deep Excavation

In order to explore the influence of coal pillar width on the principal stress deflection and plastic zone form of surrounding rock in deep roadway excavation, taking 11030 working face transportation roadway of Zhaogu No. 2 Coal Mine as engineering background, theoretical analysis, numerical simulation, and field detection were used to study the effect of coal pillar width on principal stress deflection and plastic zone form and field detection and verification of plastic zone form of surrounding rock in 11030 transportation roadway. The results show that the maximum principal stress is deflected in the vertical direction, which in roadway surrounding rock excavation. The coal pillar width effect of principal stress deflection on both sides of roadway roof and floor and inside coal pillar are more obvious than that of middle roof and floor, coal pillar edge and coal wall position. The deflection of the principal stress affects the morphological distribution of the plastic zone of the surrounding rock, which led to the width effect of coal pillar in roof, and two sides plastic zone are more obvious than that in floor. The principal stress deflection of roadway surrounding rock is highly consistent with the maximum damage depth of plastic zone, and at the same time, the drilling peep results of surrounding rock are basically consistent with the form characteristics of plastic zone in numerical simulation. On this basis, the surrounding rock reinforcement support scheme of 11030 working face transportation roadway was proposed.

Buckling Behavior of Thick Porous Functionally Graded Material Toroidal Shell Segments Under External Pressure and Elevated Temperature Including Tangential Edge Restraint

AbstractOwing to mathematical and geometrical complexities, there is an evident lack of stability analyses of thick closed shell structures with porosity. Based on an effective analytical approach, for the first time, simultaneous effects of porosities, elasticity of edge constraint, and surrounding elastic media on the buckling resistance capacity of thick functionally graded material (FGM) toroidal shell segments (TSSs) subjected to external pressure, elevated temperature, and combined thermomechanical loads are investigated in this paper. The volume fractions of constituents are varied across the thickness according to power law functions, and effective properties of the FGM are determined using a modified rule of mixture. The porosities exist in the FGM through even and uneven distributions. Governing equations are based on a higher-order shear deformation theory (HSDT) taking into account interactive pressure from surrounding elastic media. These equations are analytically solved and closed-form expressions of buckling loads are derived adopting the two-term form of deflection along with Galerkin method. Parametric studies indicate that the porosities have beneficial and deteriorative influences on the buckling resistance capacity of thermally loaded and pressure-loaded porous FGM TSSs, respectively. Furthermore, tangential constraints of edges lower the buckling resistance capacity of the shells, especially at elevated temperatures.

Vehicle excess fuel consumption due to pavement deflection

The pavement structural rolling resistance (SRR) effect on vehicles' excess fuel consumption (EFC) was investigated. A practical approach was proposed to assess vehicle EFC due to pavement deflection based on the fundamental energy-deformation principles. The proposed model was formulated using a quadratic form of maximum pavement deflection, whose parameters are truck loading and speed and pavement temperature. The proposed model utilizes input used in the current AASHTOWare design methods. This allows the integration of the developed model in pavement design and performance prediction while used in pavement life cycle assessment (LCA). Sensitivity analysis showed the reasonableness of the model over a wide range of loading, temperature, and speed scenarios. The estimated EFC for a heavy truck ranged from 0.03% (half loaded, 0 °C, 115 km/h) and 6.5% (fully loaded, 40 °C, 8 km/h). The truck EFC is highly nonlinear and exponentially grows with decreasing speed and increasing temperature.

Flexural analysis of functionally graded sandwich plate with piezoelectric face sheet based on Lagrangian mechanics

In the present study, the static behaviour of the functionally graded material sandwich plate with the piezoelectric face sheet is analyzed. The sandwich plate comprises of FGM at its core and homogenous piezoelectric forms outer layers. The homogenous face sheets of piezoelectric materials consisting of two different types of materials viz. PZT-4 and PZT-5A. The higher order along with normal shear deformation criterias are considered as a displacement field to analyze the effect of thickness stretching on the deflection and stresses of the sandwich plate. The Lagrangian approach is implemented to derive the governing equations. The equations are solved analytically by the Navier’s method and the responses are being recorded in the form of Transverse deflection, Transverse Shear Stress and Normal Stress with varying external electrical voltages. In this study it is observed that there exists electro-mechanical coupling between FGM core and PZT face sheet. The results for the sandwich plate with FGM core and homogenous face sheets are validated with the previous studies and founds to be in good agreement. It is noted that the deflection and stresses reduces significantly with change in polarity from negative to positive.

Investigation on the influence of point loads on the deflection behaviour of G+5 frame structure

Nowadays, multi-storey structure portal frames are most commonly used worldwide. Multistory frames are used in structural systems in all metropolitan cities, future cities, and important businesses. The present study the effect of various point loads varying from 22 to 32 kN in steps of 2 were applied on the center of horizontal beams of the frame structure. The deflection behaviour in form of deflection, reaction, beading moments under point loading were discussed analytically according to stiffness matrix method and the results are validated with the help of simulation using STAAD Pro software. Results revealed that the analytical method using manual calculations in excel sheet provides approximately similar results as obtained by the costly simulation technique using STAAD Pro software. Therefore, the implementation of this excel sheet can be recommended for standard analysis of portal frame structures based on the outcomes of this study.

Thermal and thermomechanical buckling of CNT-reinforced composite sandwich cylindrical shells including elasticity of tangential edge restraint

This paper presents an analytical approach to investigate the buckling of sandwich cylindrical shells subjected to uniform temperature rise and external lateral pressure. Two sandwich models corresponding to carbon nanotube reinforced composite (CNTRC) face sheets and core layer are considered. The properties of all constitutive materials are assumed to be temperature dependent and effective properties of CNTRC are determined according to an extended rule of mixture. Governing equations are established using first order shear deformation theory and solved employing two-term form of deflection along with Galerkin method for simply supported edge shells. In order to account for practical situations of in-plane boundary condition, the elasticity of tangential constraint of boundary edges is included. Owing to temperature dependence of material properties, critical thermal loads are determined adopting an iteration process. Numerous parametric studies are carried out and interesting remarks are given. The study reveals that sandwich shell model with CNTRC core layer and homogeneous skins has considerably strong capacity of buckling resistance. Numerical results also indicate that tangential edge constraint has significant effects on critical loads, especially at elevated temperature. In addition, in the case of thermal load, an intermediate volume percentage of carbon nanotubes can confer the highest critical temperatures of sandwich shells.