Search results for: buckling

Authors: Abdulkadir Cuneyt Aydin, Mahyar Maali, Mahmut Kılıç, Merve Sağıroğlu

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The moment-rotation curves of semi-rigid connections are the visual expressions of the actual behaviour discovered in beam-to-column connections experiments. This research was to determine the behaviour of the connection using full-scale experiments under statically loaded. The stiffeners which are typically attached to beams web or flanges to control local buckling and to increase shear capacity in a beam web are almost always used in modern designs. They must also provide sufficient moment of inertia to control out of plane deformations. This study was undertaken to analyse the influence of stiffeners in the angles and beams on the behaviour of the beam-to-column joints. In addition, the aim was to provide necessary data to improve the Eurocode 3. The main parameters observed are the evolution of the resistance, the stiffness, the rotation capacity, the ductility of a joint and the Energy Dissipation. Experimental tests show that the plastic flexural resistance and the energy dissipation increased when thickness of stiffener beam, thickness of stiffener angles were increased in the test specimens. And also, while stiffness of joints, the bending moment capacity and the maximum bending moment increased with the increasing thickness of stiffener beam, these values decreased with the increasing thickness of stiffener angles. So, it is observed that the beam stiffener of angles are important in improving resistance moment of beam-to-column semi-rigid joints.

Keywords: bolted angles connection, semi-rigid joints, ductility of a joint, angles and beams stiffeners

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Authors: Arup Saha Chaudhuri

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Structural steel is a very ductile material with high strength carrying capacity, thus it is very useful to make earthquake resistant buildings. It is a homogeneous material also. The member section and the structural system can be made very efficient for economical design. As the steel is recyclable and reused, it is a green material. The embodied energy for the efficiently designed steel structure is less than the RC structure. For sustainable green building steel is the best material nowadays. Moreover, pre-engineered and pre-fabricated faster construction methodologies help the development work to complete within the stipulated time. In this paper, the usefulness of Eccentric Bracing Frame (EBF) in steel structure over Moment Resisting Frame (MRF) and Concentric Bracing Frame (CBF) is shown. Stability of the steel structures against horizontal forces especially in seismic condition is efficiently possible by Eccentric bracing systems with economic connection details. The EBF is pin–ended, but the beam-column joints are designed for pin ended or for full connectivity. The EBF has several desirable features for seismic resistance. In comparison with CBF system, EBF system can be designed for appropriate stiffness and drift control. The link beam is supposed to yield in shear or flexure before initiation of yielding or buckling of the bracing member in tension or compression. The behavior of a 2-D steel frame is observed under seismic loading condition in the present paper. Ductility and brittleness of the frames are compared with respect to time period of vibration and dynamic base shear. It is observed that the EBF system is better than MRF system comparing the time period of vibration and base shear participation.

Keywords: steel building, green and sustainable, earthquake resistant, EBF system

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Authors: Abraham O. Olaniyi, Oluyemi Oke, Atilade Otunla

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The structural performance of bridges decreases progressively throughout their service life due to many contributing factors (fatigue, carbonation, fire incidents etc.). Around the world, numerous bridges have attained their estimated service life and many have approached this limit. The structural integrity assessment of the burnt composite bridge located at CH57+450, Koita village along Abuja-Abaji-Lokoja road, Nigeria, is presented as a case study and shall be forthwith referred to as the 'Koita bridge' in this paper. From the technical evaluation, the residual compressive strength of the concrete piers was found to be below 16.0 N/mm2. This value is very low compared to the expected design value of 30.0 N/mm2. The pier capping beam at pier location 1 has a very low residual compressive strength. The cover to the reinforcement of certain capping beams has an outline of reinforcement which signifies poor concrete cover and the mean compressive strength is also less than 20.0 N/mm2. The steel girder indicated black colouration as a result of the fire incident without any significant structural defect like buckling or warping of the steel section. This paper reviews the structural integrity assessment and repair methodology of the Koita bridge; a composite bridge damaged by fire, highlighting the various challenges of limited obtainable guidance documents about the bridge. The objectives are to increase the understanding of processes and versatile equipment required to test and assess a fire-damaged bridge in order to improve the quality of structural appraisal and rehabilitation; thus, eliminating the prejudice associated with current visual inspection techniques.

Keywords: assessment, bridge, rehabilitation, sustainability

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Authors: Behrang Tavousi Tehrani, Mohammad-Zaman Kabir

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Shape memory alloys (SMA) are often implemented in smart structures as the active components. Their ability to recover large displacements has been used in many applications, including structural stability/response enhancement and active structural acoustic control. SMA wires or fibers can be embedded with composite cylinders to increase their critical buckling load, improve their load-deflection behavior, and reduce the radial deflections under various thermo-mechanical loadings. This paper presents a semi-analytical investigation on the non-linear load-deflection response of SMA-reinforced composite circular cylindrical shells. The cylinder shells are under uniform external pressure load. Based on first-order shear deformation shell theory (FSDT), the equilibrium equations of the structure are derived. One-dimensional simplified Brinson’s model is used for determining the SMA recovery force due to its simplicity and accuracy. Airy stress function and Galerkin technique are used to obtain non-linear load-deflection curves. The results are verified by comparing them with those in the literature. Several parametric studies are conducted in order to investigate the effect of SMA volume fraction, SMA pre-strain value, and SMA activation temperature on the response of the structure. It is shown that suitable usage of SMA wires results in a considerable enhancement in the load-deflection response of the shell due to the generation of the SMA tensile recovery force.

Keywords: airy stress function, cylindrical shell, Galerkin technique, load-deflection curve, recovery stress, shape memory alloy

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Authors: Merve Sagiroglu

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The earthquake-resistant steel structure design is required taking into account the behavior of beam-column connections besides the basic properties of the structure such as material and geometry. Beam-column connections play an important role in the behavior of frame systems. Taking into account the behaviour of connection in analysis and design of steel frames is important due to presenting the actual behavior of frames. So, the behavior of the connections should be well known. The most important force which transmitted by connections in the structural system is the moment. The rotational deformation is customarily expressed as a function of the moment in the connection. So, the moment-rotation curves are the best expression of behaviour of the beam-to-column connections. The designed connections form various moment-rotation curves according to the elements of connection and the shape of placement. The only way to achieve this curve is with real-scale experiments. The experiments of some connections have been carried out partially and are formed in the databank. It has been formed the models using this databank to express the behavior of connection. In this study, theoretical studies have been carried out to model a real behavior of the top and seat angles connections with angles. Two stiffeners in the top and seat angle to increase the stiffness of the connection, and two stiffeners in the beam web to prevent local buckling are used in this beam-to-column connection. Mathematical models have been performed using the database of the beam-to-column connection experiments previously by authors. Using the data of the tests, it has been aimed that analytical expressions have been developed to obtain the moment-rotation curve for the connection details whose test data are not available. The connection has been dimensioned in various shapes and the effect of the dimensions of the connection elements on the behavior has been examined.

Keywords: top and seat angle connection, stiffener, moment-rotation curves, analytical study

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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: R. Al-Dujele, K. A. Cashell

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A tubular flange girder is an I-shaped steel girder with either one of both of the usual flat flange plates replaced with a hollow section. Typically, these hollow sections are either rectangular or circular in shape. Concrete filled tubular flange girders (CFTFGs) are unconventional I-shaped beams that use a hollow structural section as the top flange which is filled with concrete. The resulting section offers very high lateral torsional buckling strength and stiffness compared with conventional steel I-beams of similar depth, width and weight, typically leading to a reduction in lateral bracing requirements. This paper is focussed on investigating the ultimate capacity of concrete filled rectangular tubular flange girders (CFRTFGs). These are complex members and their behaviour is governed by a number of inter-related parameters. The FE model is developed using ABAQUS software, 3-D finite element (FE) model for simply supported CFRTFGs subjected to two point loads applied at the third-span points is built. An initial geometrical imperfection of (L/1000), as well as geometrical and material nonlinearities, are introduced into the model, where L denotes the span of the girder. In this numerical model, the concrete and steel materials are modelled using eight-node solid and four-node shell elements, respectively. In addition to the FE model, simplified analytical expressions for the flexural capacity are also proposed, and the results are compared to those from the FE analyses. The analytical expressions, which are suitable for design, are also shown to be capable of providing an accurate depiction of the bending moment capacity.

Keywords: concrete-filled rectangular tubular flange girders, ultimate capacity, confining effect, finite element analysis

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Authors: K. S. Sivakumaran, Bo Chen

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The floor beams of steel buildings, cold-formed steel floor joists, in particular, often require large web openings, which may affect their shear capacities. A cost effective way to mitigate the detrimental effects of such openings is to weld/fasten reinforcements. A difficulty associated with an experimental investigation to establish suitable reinforcement schemes for openings in shear zone is that moment always coexists with the shear, and thus, it is impossible to create pure shear state in experiments, resulting in moment influenced results. However, finite element analysis can be conveniently used to investigate the pure shear behaviour of webs including webs with reinforced opening. This paper presents that the details associated with the finite element analysis of thick/thin-plates (representing the web of hot-rolled steel beam, and the web of a cold-formed steel member) having a large reinforced openings. The study considered thin simply supported rectangular plates subjected to inplane shear loadings until failure (including post-buckling behaviour). The plate was modelled using geometrically non-linear quadrilateral shell elements, and non-linear stress-strain relationship based on experiments. Total Lagrangian (TL) with large displacement/small strain formulation was used for such analysis. The model also considered the initial geometric imperfections. This study considered three reinforcement schemes, namely, flat, lip, and angle reinforcements. This paper discusses the modelling considerations and presents the results associated with the various reinforcement schemes under consideration. The paper briefly compares the analysis results with the experimental results.

Keywords: cold-formed steel, finite element analysis, opening, reinforcement, shear resistance

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Authors: Katarzyna Rzeszut, Ilona Szewczak

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The review of selected methods of strengthening of steel structures with carbon fiber reinforced polymer (CFRP) tapes and the analysis of influence of composite materials on the steel thin-walled elements are performed in this paper. The study is also focused to the problem of applying fast and effective strengthening methods of the steel structures made of thin-walled profiles. It is worth noting that the issue of strengthening the thin-walled structures is a very complex, due to inability to perform welded joints in this type of elements and the limited ability to applying mechanical fasteners. Moreover, structures made of thin-walled cross-section demonstrate a high sensitivity to imperfections and tendency to interactive buckling, which may substantially contribute to the reduction of critical load capacity. Due to the lack of commonly used and recognized modern methods of strengthening of thin-walled steel structures, authors performed the experimental studies of thin-walled sigma profiles strengthened with CFRP tapes. The paper presents the experimental stand and the preliminary results of laboratory test concerning the analysis of the effectiveness of the strengthening steel beams made of thin-walled sigma profiles with CFRP tapes. The study includes six beams made of the cold-rolled sigma profiles with height of 140 mm, wall thickness of 2.5 mm, and a length of 3 m, subjected to the uniformly distributed load. Four beams have been strengthened with carbon fiber tape Sika CarboDur S, while the other two were tested without strengthening to obtain reference results. Based on the obtained results, the evaluation of the accuracy of applied composite materials for strengthening of thin-walled structures was performed.

Keywords: CFRP tapes, sigma profiles, steel thin-walled structures, strengthening

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Authors: Ersilio Tushaj

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The efficient solution that satisfies the optimal condition is an important issue in the structural engineering design problem. The new codes of structural design consist in design methodology that looks after the exploitation of the total resources of the construction material. In recent years some non-deterministic or meta-heuristic structural optimization algorithms have been developed widely in the research community. These methods search the optimum condition starting from the simulation of a natural phenomenon, such as survival of the fittest, the immune system, swarm intelligence or the cooling process of molten metal through annealing. Among these techniques the most known are: the genetic algorithms, simulated annealing, evolution strategies, particle swarm optimization, tabu search, ant colony optimization, harmony search and big bang crunch optimization. In this study, five of these algorithms are applied for the optimum weight design of a steel truss structure with variable geometry but fixed topology. The design process selects optimum distances and size sections from a set of commercial steel profiles. In the formulation of the design problem are considered deflection limitations, buckling and allowable stress constraints. The approach is repeated starting from different initial populations. The design problem topology is taken from an existing steel structure. The optimization process helps the engineer to achieve good final solutions, avoiding the repetitive evaluation of alternative designs in a time consuming process. The algorithms used for the application, the results of the optimal solutions, the number of iterations and the minimal weight designs, will be reported in the paper. Based on these results, it would be estimated, the amount of the steel that could be saved by applying structural analysis combined with non-deterministic optimization methods.

Keywords: structural optimization, non-deterministic methods, truss structures, steel truss

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Authors: Iyd Eqqab Maree, Habil Jurgen Bast

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Vibration control of machines and structures incorporating viscoelastic materials in suitable arrangement is an important aspect of investigation. The use of viscoelastic layers constrained between elastic layers is known to be effective for damping of flexural vibrations of structures over a wide range of frequencies. The energy dissipated in these arrangements is due to shear deformation in the viscoelastic layers, which occurs due to flexural vibration of the structures. Multilayered cantilever sandwich beam like structures can be used in aircrafts and other applications such as robot arms for effective vibration control. These members may experience parametric instability when subjected to time dependant forces. The theory of dynamic stability of elastic systems deals with the study of vibrations induced by pulsating loads that are parametric with respect to certain forms of deformation. The purpose of the present work is to investigate the dynamic stability of a three layered symmetric sandwich beam (Drone Aircraft wings ) subjected to an end periodic axial force . Equations of motion are derived using finite element method (MATLAB software). It is observed that with increase in core thickness parameter fundamental buckling load increases. The fundamental resonant frequency and second mode frequency parameter also increase with increase in core thickness parameter. Fundamental loss factor and second mode loss factor also increase with increase in core thickness parameter. Increase in core thickness parameter enhances the stability of the beam. With increase in core loss factor also the stability of the beam enhances. There is a very good agreement of the experimental results with the theoretical findings.

Keywords: steel cantilever beam, viscoelastic material core, loss factor, transition region, MATLAB R2011a

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Authors: Smriti, Ajeet Kumar

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We present a variant of the Irving-Kirkwood procedure to obtain the microscopic expressions of the cross-section averaged continuum fields such as internal force and moment in one-dimensional nanostructures in the non-equilibrium setting. In one-dimensional continuum theories for slender bodies, we deal with quantities such as mass, linear momentum, angular momentum, and strain energy densities, all defined per unit length. These quantities are obtained by integrating the corresponding pointwise (per unit volume) quantities over the cross-section of the slender body. However, no well-defined cross-section exists for these nanostructures at finite temperature. We thus define the cross-section of a nanorod to be an infinite plane which is fixed in space even when time progresses and defines the above continuum quantities by integrating the pointwise microscopic quantities over this infinite plane. The method yields explicit expressions of both the potential and kinetic parts of the above quantities. We further specialize in these expressions for helically repeating one-dimensional nanostructures in order to use them in molecular dynamics study of extension, torsion, and bending of such nanostructures. As, the Irving-Kirkwood procedure does not yield expressions of stiffnesses, we resort to a thermodynamic equilibrium approach to obtain the expressions of axial force, twisting moment, bending moment, and the associated stiffnesses by taking the first and second derivatives of the Helmholtz free energy with respect to conjugate strain measures. The equilibrium approach yields expressions independent of kinetic terms. We then establish the equivalence of the expressions obtained using the two approaches. The derived expressions are used to understand the extension, torsion, and bending of single-walled carbon nanotubes at non-zero temperatures.

Keywords: thermoelasticity, molecular dynamics, one dimensional nanostructures, nanotube buckling

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Authors: Aqsa Jamil, Tamura Hiroshi, Katsuchi Hiroshi, Wang Jiaqi

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The yield point represents the upper limit of forces which can be applied to a specimen without causing any permanent deformation. After yielding, the behavior of the specimen suddenly changes, including the possibility of cracking or buckling. So, the accumulation of damage or type of fracture changes depending on this condition. As it is difficult to accurately detect yield points of the several stress concentration points in structural steel specimens, an effort has been made in this research work to develop a convenient technique using thermography (temperature-based detection) during tensile tests for the precise detection of yield point initiation. To verify the applicability of thermography camera, tests were conducted under different loading conditions and measuring the deformation by installing various strain gauges and monitoring the surface temperature with the help of a thermography camera. The yield point of specimens was estimated with the help of temperature dip, which occurs due to the thermoelastic effect during the plastic deformation. The scattering of the data has been checked by performing a repeatability analysis. The effects of temperature imperfection and light source have been checked by carrying out the tests at daytime as well as midnight and by calculating the signal to noise ratio (SNR) of the noised data from the infrared thermography camera, it can be concluded that the camera is independent of testing time and the presence of a visible light source. Furthermore, a fully coupled thermal-stress analysis has been performed by using Abaqus/Standard exact implementation technique to validate the temperature profiles obtained from the thermography camera and to check the feasibility of numerical simulation for the prediction of results extracted with the help of the thermographic technique.

Keywords: signal to noise ratio, thermoelastic effect, thermography, yield point

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Authors: Anthony Khawaja, Jacques Prioux, Ghassan Maalouf, Rawad El Hage

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The regular practice of physical activities characterized by significant mechanical stresses stimulates bone formation and improves bone mineral density (BMD) in the most solicited sites. The purpose of this study was to explore the relationships between maximum power and bone variables in a group of young adult men. Identification of new determinants of BMD, bone mineral content (BMC) and hip geometric indices in young adult men, would allow screening and early management of future cases of osteopenia and osteoporosis. Fifty-three young adult men (18 – 35yr) voluntarily participated in this study. Weight and height were measured, and body mass index was calculated. Body composition, BMC and BMD were determined for each individual by Dual-energy X-ray absorptiometry (DXA; GE Healthcare, Madison, WI) at whole body (WB), lumbar spine (L1-L4), total hip (TH), and femoral neck (FN). FN cross-sectional area (CSA), strength index (SI), buckling ratio (BR), FN section modulus (Z), cross-sectional moment of inertia (CSMI) and L1-L4 TBS were also evaluated by DXA. The vertical jump was evaluated using a field test (sargent test). Two main parameters were retained: vertical jump performance (cm) and power (w). The subjects performed three jumps with 2 minutes of recovery between jumps. The highest vertical jump was selected. Maximum power (P max, in watts) was calculated. Maximum power was positively correlated to WB BMD (r = 0.41; p < 0.01), WB BMC (r = 0.65; p < 0.001), L1-L4 BMC (r = 0.54; p < 0.001), FN BMC (r = 0.35; p < 0.01), TH BMC (r = 0.50; p < 0.001), CSMI (r = 0.50; p < 0.001), CSA (r = 0.33; p < 0.05). Vertical jump was positively correlated to WB BMC (r = 0.31; p < 0.05), L1-L4 BMC (r = 0.40; p < 0.01), CSMI (r = 0.29; p < 0.05). The current study suggests that maximum power is a positive determinant of BMD, BMC and hip geometric indices in young adult men. In addition, it shows also that maximum power is a stronger positive determinant of bone variables than vertical jump in this population. Implementing strategies to increase maximum power in young adult men may be useful for preventing osteoporotic fractures later in life.

Keywords: bone variables, maximum power, osteopenia, osteoporosis, vertical jump, young adult men

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Authors: Maya Saade, Rafic Younes, Pascal Lafon

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This paper explores the transformative impact of smartphones on pedagogy and presents a smartphone application developed specifically for engineering problem-solving and educational purposes. The widespread availability and advanced capabilities of smartphones have revolutionized the way we interact with technology, including in education. The ubiquity of smartphones allows learners to access educational resources anytime and anywhere, promoting personalized and self-directed learning. The first part of this paper discusses the overall influence of smartphones on pedagogy, emphasizing their potential to improve learning experiences through mobile technology. In the context of engineering education, this paper focuses on the development of a dedicated smartphone application that serves as a powerful tool for both engineering problem-solving and education. The application features an intuitive and user-friendly interface, allowing engineering students and professionals to perform complex calculations and analyses on their smartphones. The smartphone application primarily focuses on beam calculations and serves as a comprehensive beam calculator tailored to engineering education. It caters to various engineering disciplines by offering interactive modules that allow students to learn key concepts through hands-on activities and simulations. With a primary emphasis on beam analysis, this application empowers users to perform calculations for statically determinate beams, statically indeterminate beams, and beam buckling phenomena. Furthermore, the app includes a comprehensive library of engineering formulas and reference materials, facilitating a deeper understanding and practical application of the fundamental principles in beam analysis. By offering a wide range of features specifically tailored for beam calculation, this application provides an invaluable tool for engineering students and professionals looking to enhance their understanding and proficiency in this crucial aspect of a structural engineer.

Keywords: mobile devices in education, solving engineering problems, smartphone application, engineering education

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Authors: Vanessa A. Segovia, Sonia E. Ruiz

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The use of energy dissipation systems for seismic applications has increased worldwide, thus it is necessary to develop practical and modern criteria for their optimal design. Here, a direct displacement-based seismic design approach for frame buildings with hysteretic energy dissipation systems (HEDS) is applied. The building is constituted by two individual structural systems consisting of: 1) A main elastic structural frame designed for service loads and 2) A secondary system, corresponding to the HEDS, that controls the effects of lateral loads. The procedure implies to control two design parameters: A) The stiffness ratio (α=K_frame/K_(total system)), and B) The strength ratio (γ= V_damper / V_(total system)). The proposed damage-controlled approach contributes to the design of a more sustainable and resilient building because the structural damage is concentrated on the HEDS. The reduction of the design displacement spectrum is done by means of a damping factor (recently published) for elastic structural systems with HEDS, located in Mexico City. Two limit states are verified: Serviceability and near collapse. Instead of the traditional trial-error approach, a procedure that allows the designer to establish the preliminary sizes of the structural elements of both systems is proposed. The design methodology is applied to an 8-story steel building with buckling restrained braces, located in soft soil of Mexico City. With the aim of choosing the optimal design parameters, a parametric study is developed considering different values of α and γ. The simplified methodology is for preliminary sizing, design, and evaluation of the effectiveness of HEDS, and it constitutes a modern and practical tool that enables the structural designer to select the best design parameters.

Keywords: damage-controlled buildings, direct displacement-based seismic design, optimal hysteretic energy dissipation systems, hysteretic dampers

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Authors: Jikhil Joseph, Satish Kumar S R.

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Cold-formed steel frames are preferable for framed constructions due to its low seismic weights and results into low seismic forces, but on the contrary, significant lateral deflections are expected under seismic/wind loading. The various factors affecting the lateral stiffness of steel frames are the stiffness of connections, beams and columns. So, by increasing the stiffness of beam, column and making the connections rigid will enhance the lateral stiffness. The present study focused on Structural elements made of rectangular hollow sections and fastened with screwed in-plane moment connections for the building frames. The self-drilling screws can be easily drilled on either side of the connection area with the help of gusset plates. The strength of screwed connections can be made 1.2 times the connecting elements. However, achieving high stiffness in connections is also a challenging job. Hence in addition to beam and column stiffness’s the connection stiffness are also going to be a governing parameter in the lateral deflections of the frames. SAP 2000 Non-linear static analysis has been planned to study the seismic behavior of steel frames. The SAP model will be consisting of nonlinear spring model for the connection to account the semi-rigid connections and the nonlinear hinges will be assigned for beam and column sections according to FEMA 273 guidelines. The reliable spring and hinge parameters will be assigned based on an experimental and analytical database. The non-linear static analysis is mainly focused on the identification of various hinge formations and the estimation of lateral deflection and these will contribute as an inputs for the direct displacement-based Seismic design. The research output from this study are the modelling techniques and suitable design guidelines for the performance-based seismic design of cold-formed steel frames.

Keywords: buckling, cold formed steel, nonlinear static analysis, screwed connections

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Authors: T. Walczak, J. K. Grabski, P. Fritzkowski, M. Stopa

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Objectives of the study are i) to perform numerical simulations that permit an analysis of the dynamics of subretinal fluid when an implant has induced scleral intussusception and ii) assess the impact of the physical parameters of the model on the flow rate. Computer simulations were created using finite element method (FEM) based on a model that takes into account the interaction of a viscous fluid (subretinal fluid) with a hyperelastic body (retina). The purpose of the calculation was to investigate the dependence of the flow rate of subretinal fluid through a hole in the retina on different factors such as viscosity of subretinal fluid, material parameters of the retina, and the offset of the implant from the retina’s hole. These simulations were performed for different speeds of eye movement that reflect the behavior of the eye when reading, REM, and saccadic movements. Similar to other works in the field of subretinal fluid flow, it was assumed stationary, single sided, forced fluid flow in the considered area simulating the subretinal space. Additionally, a hyperelastic material model of the retina and parameterized geometry of the considered model was adopted. The calculations also examined the influence the direction of the force of gravity due to the position of the patient’s head on the trend of outflow of fluid. The simulations revealed that fluid outflow from the retina becomes significant with eyeball movement speed of 100°/sec. This speed is greater than in the case of reading but is four times less than saccadic movement. The increase of viscosity of the fluid increased beneficial effect. Further, the simulation results suggest that moderate eye movement speed is optimal and that the conventional prescription of the avoidance of routine eye movement following retinal detachment surgery should be relaxed. Additionally, to verify numerical results, some calculations were repeated with use of meshless method (method of fundamental solutions), which is relatively fast and easy to implement. The paper has been supported by 02/21/DSPB/3477 grant.

Keywords: CFD simulations, FEM analysis, meshless method, retinal detachment

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Authors: Monalisa Pradhan, Ajana Dutta, Irshad Kariyattuparamb Abbas, Boby Joseph, T. N. Guru Row, Diptikanta Swain, Gopal K. Pradhan

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Compounds with the Vanthoffite crystal structure having general formula Na6M(SO₄)₄ (M= Mg, Mn, Ni , Co, Fe, Cu and Zn) display a variety of intriguing physical properties intimately related to their structural arrangements. The compound Na6Mn(SO4)4 shows antiferromagnetic ordering at low temperature where the in-plane Mn-O•••O-Mn interactions facilitates antiferromagnetic ordering via a super-exchange interaction between the Mn atoms through the oxygen atoms . The inter-atomic bond distances and angles can easily be tuned by applying external pressure and can be probed using high resolution X-ray diffraction. Moreover, because the magnetic interaction among the Mn atoms are super-exchange type via Mn-O•••O-Mn path, the variation of the Mn-O•••O-Mn dihedral angle and Mn-O bond distances under high pressure inevitably affects the magnetic properties. Therefore, it is evident that high pressure studies on the magnetically ordered materials would shed light on the interplay between their structural properties and magnetic ordering. This will indeed confirm the role of buckling of the Mn-O polyhedral in understanding the origin of anti-ferromagnetism. In this context, we carried out the pressure dependent X-ray diffraction measurement in a diamond anvil cell (DAC) up to a maximum pressure of 17 GPa to study the phase transition and determine equation of state from the volume compression data. Upon increasing the pressure, we didn’t observe any new diffraction peaks or sudden discontinuity in the pressure dependences of the d values up to the maximum achieved pressure of ~17 GPa. However, it is noticed that beyond 12 GPa the a and b lattice parameters become identical while there is a discontinuity in the β value around the same pressure. This indicates a subtle transition to a pseudo-monoclinic phase. Using the third order Birch-Murnaghan equation of state (EOS) to fit the volume compression data for the entire range, we found the bulk modulus (B0) to be 44 GPa. If we consider the subtle transition at 12 GPa, we tried to fit another equation state for the volume beyond 12 GPa using the second order Birch-Murnaghan EOS. This gives a bulk modulus of ~ 34 GPa for this phase.

Keywords: mineral, structural phase transition, high pressure XRD, spectroscopy

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Authors: F. Mohammadsadeghi

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Relevance of research: Axial compressors are used in both aircraft engine construction and ground-based gas turbine engines. The compressor is considered to be one of the main gas turbine engine units, which define absolute and relative indicators of engine in general. Failure of compressor often leads to drastic consequences. Therefore, safe (stable) operation must be maintained when using axial compressor. Currently, we can observe a tendency of increase of power unit, productivity, circumferential velocity and compression ratio of axial compressors in gas turbine engines of aircraft and ground-based application whereas metal consumption of their structure tends to fall. This causes the increase of dynamic loads as well as danger of damage of high load compressor or engine structure elements in general due to transient processes. In operating practices of aeronautical engineering and ground units with gas turbine drive the operational stability failure of gas turbine engines is one of relatively often failure causes what can lead to emergency situations. Surge occurrence is considered to be an absolute buckling failure. This is one of the most dangerous and often occurring types of instability. However detailed were the researches of this phenomenon the development of measures for surge before-the-fact prevention is still relevant. This is why the research of transient processes for axial compressors is necessary in order to provide efficient, stable and secure operation. The paper addresses the problem of automatic control system improvement by integrating the anti-surge algorithms for axial compressor of aircraft gas turbine engine. Paper considers dynamic exhaustion of gas dynamic stability of compressor stage, results of numerical simulation of airflow flowing through the airfoil at design and stalling modes, experimental researches to form the criteria that identify the compressor state at pre-surge mode detection. Authors formulated basic ways for developing surge preventing systems, i.e. forming the algorithms that allow detecting the surge origination and the systems that implement the proposed algorithms.

Keywords: axial compressor, rotation stall, Surg, unstable operation of gas turbine engine

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Authors: Yeo Kyeong Lee, Ji Yeon Kang, Eun Mi Ryu, Hee Sun Kim, Yeong Soo Shin

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The objective of this paper is an investigation of the effects of the thickness and axial loading during a fire test on the load-bearing capacity of a fire-damaged normal-strength concrete wall. Two factors are attributed to the temperature distributions in the concrete members and are mainly obtained through numerous experiments. Toward this goal, three wall specimens of different thicknesses are heated for 2 h according to the ISO-standard heating curve, and the temperature distributions through the thicknesses are measured using thermocouples. In addition, two wall specimens are heated for 2 h while simultaneously being subjected to a constant axial loading at their top sections. The test results show that the temperature distribution during the fire test depends on wall thickness and axial load during the fire test. After the fire tests, the specimens are cured for one month, followed by the loading testing. The heated specimens are compared with three unheated specimens to investigate the residual load-bearing capacities. The fire-damaged walls show a minor difference of the load-bearing capacity regarding the axial loading, whereas a significant difference became evident regarding the wall thickness. To validate the experiment results, finite element models are generated for which the material properties that are obtained for the experiment are subject to elevated temperatures, and the analytical results show sound agreements with the experiment results. The analytical method based on validated thought experimental results is applied to generate the fire-damaged walls with 2,800 mm high considering the buckling effect: typical story height of residual buildings in Korea. The models for structural analyses generated to deformation shape after thermal analysis. The load-bearing capacity of the fire-damaged walls with pin supports at both ends does not significantly depend on the wall thickness, the reason for it is restraint of pinned ends. The difference of the load-bearing capacity of fire-damaged walls as axial load during the fire is within approximately 5 %.

Keywords: normal-strength concrete wall, wall thickness, axial-load ratio, slenderness ratio, fire test, residual strength, finite element analysis

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Authors: Abulbasit G. Abdulsayid, Zinab F. Abdulla, Asma A. Omer

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On the ground that the orifice plate is relatively inexpensive, requires very little maintenance and only calibrated during the occasion of plant turnaround, the orifice plate has turned to be in a real prevalent use in gas industry. Inaccuracy of measurement in the fiscal metering stations may highly be accounted to be the most vital factor for mischarges in the natural gas industry in Libya. A very trivial error in measurement can add up a fast escalating financial burden to the custodian transactions. The unaccounted gas quantity transferred annually via orifice plates in Libya, could be estimated in an extent of multi-million dollars. As the oil and gas wealth is the solely source of income to Libya, every effort is now being exerted to improve the accuracy of existing orifice metering facilities. Discharge coefficient has become pivotal in current researches undertaken in this regard. Hence, increasing the knowledge of the flow field in a typical orifice meter is indispensable. Recently and in a drastic pace, the CFD has become the most time and cost efficient versatile tool for in-depth analysis of fluid mechanics, heat and mass transfer of various industrial applications. Getting deeper into the physical phenomena lied beneath and predicting all relevant parameters and variables with high spatial and temporal resolution have been the greatest weighing pros counting for CFD. In this paper, flow phenomena for air passing through an orifice meter were numerically analyzed with CFD code based modeling, giving important information about the effect of orifice plate specifications on the discharge coefficient for three different tappings locations, i.e., flange tappings, D and D/2 tappings compared with vena contracta tappings. Discharge coefficients were paralleled with discharge coefficients estimated by ISO 5167. The influences of orifice plate bore thickness, orifice plate thickness, beveled angle, perpendicularity and buckling of the orifice plate, were all duly investigated. A case of an orifice meter whose pipe diameter of 2 in, beta ratio of 0.5 and Reynolds number of 91100, was taken as a model. The results highlighted that the discharge coefficients were highly responsive to the variation of plate specifications and under all cases, the discharge coefficients for D and D/2 tappings were very close to that of vena contracta tappings which were believed as an ideal arrangement. Also, in general sense, it was appreciated that the standard equation in ISO 5167, by which the discharge coefficient was calculated, cannot capture the variation of the plate specifications and thus further thorough considerations would be still needed.

Keywords: CFD, discharge coefficients, orifice meter, orifice plate specifications

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Authors: Jaroslaw Gawryluk, Andrzej Teter

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Simply supported angle columns subjected to uniform shortening are tested. The experimental studies are conducted on a testing machine using additional Aramis and the acoustic emission system. The laminate samples are subjected to axial uniform shortening. The tested columns are loaded with the force values from zero to the maximal load destroying the L-shaped column, which allowed one to observe the column post-buckling behavior until its collapse. Laboratory tests are performed at a constant velocity of the cross-bar equal to 1 mm/min. In order to eliminate stress concentrations between sample and support, flexible pads are used. Analyzed samples are made with carbon-epoxy laminate using the autoclave method. The configurations of laminate layers are: [60,0₂,-60₂,60₃,-60₂,0₃,-60₂,0,60₂]T, where direction 0 is along the length of the profile. Material parameters of laminate are: Young’s modulus along the fiber direction - 170GPa, Young’s modulus along the fiber transverse direction - 7.6GPa, shear modulus in-plane - 3.52GPa, Poisson’s ratio in-plane - 0.36. The dimensions of all columns are: length-300 mm, thickness-0.81mm, width of the flanges-40mm. Next, two numerical models of the column with and without flexible pads are developed using the finite element method in Abaqus software. The L-profile laminate column is modeled using the S8R shell elements. The layup-ply technique is used to define the sequence of the laminate layers. However, the model of grips is made of the R3D4 discrete rigid elements. The flexible pad is consists of the C3D20R type solid elements. In order to estimate the moment of the first laminate layer damage, the following initiation criteria were applied: maximum stress criterion, Tsai-Hill, Tsai-Wu, Azzi-Tsai-Hill, and Hashin criteria. The best compliance of results was observed for the Hashin criterion. It was found that the use of the pad in the numerical model significantly influences the damage mechanism. The model without pads characterized a much more stiffness, as evidenced by a greater bifurcation load and damage initiation load in all analyzed criteria, lower shortening, and less deflection of the column in its center than the model with flexible pads. Acknowledgment: The project/research was financed in the framework of the project Lublin University of Technology-Regional Excellence Initiative, funded by the Polish Ministry of Science and Higher Education (contract no. 030/RID/2018/19).

Keywords: angle column, compression, experiment, FEM

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Authors: Maryam Hasanali, Syed Mohammad Mojtabaei, Iman Hajirasouliha, G. Charles Clifton, James B. P. Lim

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Cold-formed steel (CFS) elements are increasingly being used as main load-bearing components in the modern construction industry, including low- to mid-rise buildings. In typical multi-storey buildings, CFS structural members act as beam-column elements since they are exposed to combined axial compression and bending actions, both in moment-resisting frames and stud wall systems. Current design specifications, including the American Iron and Steel Institute (AISI S100) and the Australian/New Zealand Standard (AS/NZS 4600), neglect the beneficial effects of warping-restrained boundary conditions in the design of beam-column elements. Furthermore, while a non-linear relationship governs the interaction of axial compression and bending, the combined effect of these actions is taken into account through a simplified linear expression combining pure axial and flexural strengths. This paper aims to evaluate the reliability of the well-known Direct Strength Method (DSM) as well as design proposals found in the literature to provide a better understanding of the efficiency of the code-prescribed linear interaction equation in the strength predictions of CFS beam columns and the effects of warping-restrained boundary conditions on their behavior. To this end, the experimentally validated finite element (FE) models of CFS elements under compression and bending were developed in ABAQUS software, which accounts for both non-linear material properties and geometric imperfections. The validated models were then used for a comprehensive parametric study containing 270 FE models, covering a wide range of key design parameters, such as length (i.e., 0.5, 1.5, and 3 m), thickness (i.e., 1, 2, and 4 mm) and cross-sectional dimensions under ten different load eccentricity levels. The results of this parametric study demonstrated that using the DSM led to the most conservative strength predictions for beam-column members by up to 55%, depending on the element’s length and thickness. This can be sourced by the errors associated with (i) the absence of warping-restrained boundary condition effects, (ii) equations for the calculations of buckling loads, and (iii) the linear interaction equation. While the influence of warping restraint is generally less than 6%, the code suggested interaction equation led to an average error of 4% to 22%, based on the element lengths. This paper highlights the need to provide more reliable design solutions for CFS beam-column elements for practical design purposes.

Keywords: beam-columns, cold-formed steel, finite element model, interaction equation, warping-restrained boundary conditions

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Authors: Armin Solemanifar, Arthur Wilkinson, Kinjalkumar Patel

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Carbon fibre (CF) - polymer laminate composites have very low densities (approximately 40% lower than aluminium), high strength and high stiffness but in terms of toughness properties they often require modifications. For example, adding rubbers or thermoplastics toughening agents are common ways of improving the interlaminar fracture toughness of initially brittle thermoset composite matrices. The main aim of this project was to toughen CF-epoxy resin laminate composites using hybrid CF-fabrics incorporating Innegra™ a commercial highly-oriented polypropylene (PP) fibre, in which more than 90% of its crystal orientation is parallel to the fibre axis. In this study, the damage tolerance of hybrid (carbon-Innegra, CI) composites was investigated. Laminate composites were produced by resin-infusion using: pure CF fabric; fabrics with different ratios of commingled CI, and two different types of pure Innegra fabrics (Innegra 1 and Innegra 2). Dynamic mechanical thermal analysis (DMTA) was used to measure the glass transition temperature (Tg) of the composite matrix and values of flexural storage modulus versus temperature. Mechanical testing included drop-weight impact, compression-after-impact (CAI), and interlaminar (short-beam) shear strength (ILSS). Ultrasonic C-Scan imaging was used to determine the impact damage area and scanning electron microscopy (SEM) to observe the fracture mechanisms that occur during failure of the composites. For all composites, 8 layers of fabrics were used with a quasi-isotropic sequence of [-45°, 0°, +45°, 90°]s. DMTA showed the Tg of all composites to be approximately same (123 ±3°C) and that flexural storage modulus (before the onset of Tg) was the highest for the pure CF composite while the lowest were for the Innegra 1 and 2 composites. Short-beam shear strength of the commingled composites was higher than other composites, while for Innegra 1 and 2 composites only inelastic deformation failure was observed during the short-beam test. During impact, the Innegra 1 composite withstood up to 40 J without any perforation while for the CF perforation occurred at 10 J. The rate of reduction in compression strength upon increasing the impact energy was lowest for the Innegra 1 and 2 composites, while CF showed the highest rate. On the other hand, the compressive strength of the CF composite was highest of all the composites at all impacted energy levels. The predominant failure modes for Innegra composites observed in cross-sections of fractured specimens were fibre pull-out, micro-buckling, and fibre plastic deformation; while fibre breakage and matrix delamination were a major failure observed in the commingled composites due to the more brittle behaviour of CF. Thus, Innegra fibres toughened the CF composites but only at the expense of reducing compressive strength.

Keywords: hybrid composite, thermoplastic fibre, compression strength, damage tolerance

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Authors: Ashutosh Verma, Satyendra MIttal

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The loss of strength at the facing-reinforcement interface brought on by the seasonal thermal expansion/contraction of the bridge deck has been responsible for several geosynthetic reinforced soil abutment failures over the years. This results in excessive settlement below the bridge seat, which results in bridge bumps along the approach road and shortens abutment's design life. There are surely a wide variety of facing configurations available to designers when choosing the sort of facade. These layouts can generally be categorised into three groups: continuous, full height rigid (FHR) and modular (panels/block). The current work aims to experimentally explore the behavior of these three facing categories using 1g physical model testing under serviceable cyclic lateral displacements. With configurable facing arrangements to represent these three facing categories, a field instrumented GRS abutment prototype was modelled into a N scaled down 1g physical model (N = 5) to reproduce field behavior. Peak earth pressure coefficient (K) on the facing and vertical settlement of the footing (s/B) for footing offset (x/H) as 0.1, 0.2, 0.3, 0.4 and 0.5 at 100 cycles have been measured for cyclic lateral displacement of top of facing at loading rate of 1mm/min. Three types of cyclic displacements have been carried out to replicate active condition (CA), passive condition (CP), and active-passive condition (CAP) for each footing offset. The results demonstrated that a significant decrease in the earth pressure over the facing occurs when footing offset increases. It is worth noticing that the highest rate of increment in earth pressure and footing settlement were observed for each facing configuration at the nearest footing offset. Interestingly, for the farthest footing offset, similar responses of each facing type were observed, which indicates that the upon reaching a critical offset point presumably beyond the active region in the backfill, the lateral responses become independent of the stresses from the external footing load. Evidently, the footing load complements the stresses developed due to lateral excitation resulting in significant footing settlements for nearer footing offsets. The modular facing proved inefficient in resisting footing settlement due to significant buckling along the depth of facing. Instead of relative displacement along the depth of facing, continuous facing rotates around the base when it fails, especially for nearer footing offset causing significant depressions in the backfill area surrounding the footing. FHR facing, on the other hand, have been successful in confining the stresses in the soil domain itself reducing the footing settlement. It may be suitably concluded that increasing the footing offset may render stability to the GRS abutment with any facing configuration even for higher cycles of excitation.

Keywords: GRS abutments, 1g physical model, footing offset, cyclic lateral displacement

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Authors: Erik Vassøy Olsen, Hirpa G. Lemu

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Inspired by the Formula-1 competition, IMechE (Institute of Mechanical Engineers) and Formula SAE (Society of Mechanical Engineers) organize annual competitions for University and College students worldwide to compete with a single-seat race car they have designed and built. The design of the chassis or the frame is a key component of the competition because the weight and stiffness properties are directly related with the performance of the car and the safety of the driver. In addition, a reduced weight of the chassis has a direct influence on the design of other components in the car. Among others, it improves the power to weight ratio and the aerodynamic performance. As the power output of the engine or the battery installed in the car is limited to 80 kW, increasing the power to weight ratio demands reduction of the weight of the chassis, which represents the major part of the weight of the car. In order to reduce the weight of the car, ION Racing team from the University of Stavanger, Norway, opted for a monocoque design. To ensure fulfilment of the above-mentioned requirements of the chassis, the monocoque design should provide sufficient torsional stiffness and absorb the impact energy in case of a possible collision. The study reported in this article is based on the requirements for Formula Student competition. As part of this study, diverse mechanical tests were conducted to determine the mechanical properties and performances of the monocoque design. Upon a comprehensive theoretical study of the mechanical properties of sandwich composite materials and the requirements of monocoque design in the competition rules, diverse tests were conducted including 3-point bending test, perimeter shear test and test for absorbed energy. The test panels were homemade and prepared with an equivalent size of the side impact zone of the monocoque, i.e. 275 mm x 500 mm so that the obtained results from the tests can be representative. Different layups of the test panels with identical core material and the same number of layers of carbon fibre were tested and compared. Influence of the core material thickness was also studied. Furthermore, analytical calculations and numerical analysis were conducted to check compliance to the stated rules for Structural Equivalency with steel grade SAE/AISI 1010. The test results were also compared with calculated results with respect to bending and torsional stiffness, energy absorption, buckling, etc. The obtained results demonstrate that the material composition and strength of the composite material selected for the monocoque design has equivalent structural properties as a welded frame and thus comply with the competition requirements. The developed analytical calculation algorithms and relations will be useful for future monocoque designs with different lay-ups and compositions.

Keywords: composite material, Formula student, ION racing, monocoque design, structural equivalence

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Authors: Kaviyarasan D., Satish Kumar S. R.

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India being vast in area and population with great scope of international business, roadways and railways network connection within the country is expected to have a big growth. There are numerous rail-cum-road bridges constructed across many major rivers in India and few are getting very old. So there is more possibility of repairing or coming up with such new bridges in India. Analysis and design of such bridges are practiced through conventional procedure and end up with heavy and uneconomical sections. Such heavy class steel bridges when subjected to high seismic shaking has more chance to fail by stability because the members are too much rigid and stocky rather than being flexible to dissipate the energy. This work is the collective study of the researches done in the truss bridge and steel concrete composite truss bridges presenting the method of analysis, tools for numerical and analytical modeling which evaluates its seismic behaviour and collapse mechanisms. To ascertain the inelastic and nonlinear behaviour of the structure, generally at research level static pushover analysis is adopted. Though the static pushover analysis is now extensively used for the framed steel and concrete buildings to study its lateral action behaviour, those findings by pushover analysis done for the buildings cannot directly be used for the bridges as such, because the bridges have completely a different performance requirement, behaviour and typology as compared to that of the buildings. Long span steel bridges are mostly the truss bridges. Truss bridges being formed by many members and connections, the failure of the system does not happen suddenly with single event or failure of one member. Failure usually initiates from one member and progresses gradually to the next member and so on when subjected to further loading. This kind of progressive collapse of the truss bridge structure is dependent on many factors, in which the live load distribution and span to length ratio are most significant. The ultimate collapse is anyhow by the buckling of the compression members only. For regular bridges, single step pushover analysis gives results closer to that of the non-linear dynamic analysis. But for a complicated bridge like heavy class steel bridge or the skewed bridges or complicated dynamic behaviour bridges, nonlinear analysis capturing the progressive yielding and collapse pattern is mandatory. With the knowledge of the postelastic behaviour of the bridge and advancements in the computational facility, the current level of analysis and design of bridges has moved to state of ascertaining the performance levels of the bridges based on the damage caused by seismic shaking. This is because the buildings performance levels deals much with the life safety and collapse prevention levels, whereas the bridges mostly deal with the extent damages and how quick it can be repaired with or without disturbing the traffic after a strong earthquake event. The paper would compile the wide spectrum of modeling to analysis of the steel concrete composite truss bridges in general.

Keywords: bridge engineering, performance based design of steel truss bridge, seismic design of composite bridge, steel-concrete composite bridge

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Authors: Ramprasad Srinivasan

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Engineers create inventions and put their ideas in concrete terms to design new products. Design drivers must be established, which requires, among other things, a complete understanding of the product design, load paths, etc. For Aerospace Vehicles, weight/strength ratio, strength, stiffness and stability are the important design drivers. A complex built-up structure is made up of an assemblage of primitive structural forms of arbitrary shape, which include 1D structures like beams and frames, 2D structures like membranes, plate and shell structures, and 3D solid structures. Justification through simulation involves a check for all the quantities of interest, namely stresses, deformation, frequencies, and buckling loads and is normally achieved through the finite element (FE) method. Over the past few decades, Fiber-reinforced composites are fast replacing the traditional metallic structures in the weight-sensitive aerospace and aircraft industries due to their high specific strength, high specific stiffness, anisotropic properties, design freedom for tailoring etc. Composite panel constructions are used in aircraft to design primary structure components like wings, empennage, ailerons, etc., while thin-walled composite beams (TWCB) are used to model slender structures like stiffened panels, helicopter, and wind turbine rotor blades, etc. The TWCB demonstrates many non-classical effects like torsional and constrained warping, transverse shear, coupling effects, heterogeneity, etc., which makes the analysis of composite structures far more complex. Conventional FE formulations to model 1D structures suffer from many limitations like shear locking, particularly in slender beams, lower convergence rates due to material coupling in composites, inability to satisfy, equilibrium in the domain and natural boundary conditions (NBC) etc. For 2D structures, the limitations of conventional displacement-based FE formulations include the inability to satisfy NBC explicitly and many pathological problems such as shear and membrane locking, spurious modes, stress oscillations, lower convergence due to mesh distortion etc. This mandates frequent re-meshing to even achieve an acceptable mesh (satisfy stringent quality metrics) for analysis leading to significant cycle time. Besides, currently, there is a need for separate formulations (u/p) to model incompressible materials, and a single unified formulation is missing in the literature. Hence coupled field formulation (CFF) is a unified formulation proposed by the author for the solution of complex 1D and 2D structures addressing the gaps in the literature mentioned above. The salient features of CFF and its many advantages over other conventional methods shall be presented in this paper.

Keywords: coupled field formulation, kinematic and material coupling, natural boundary condition, locking free formulation

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Authors: De-Shin Liu, Po-Chun Wen, Zhen-Wei Zhuang, Hsueh-Chih Liu, Pei-Chen Huang

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Wafer probing tests play an important role in semiconductor manufacturing procedures in accordance with the yield and reliability requirement of the wafer after the backend-of-the-line process. Accordingly, the stable physical and electrical contact between the probe and the tested wafer during wafer probing is regarded as an essential issue in identifying the known good die. The probe card can be integrated with multiple probe needles, which are classified as vertical, cantilever and micro-electro-mechanical systems type probe selections. Among all potential probe types, the vertical probe has several advantages as compared with other probe types, including maintainability, high probe density and feasibility for high-speed wafer testing. In the present study, the mechanical response of the wafer probing test with the vertical cobra probe on 720 μm thick silicon (Si) substrate with a 1.4 μm thick aluminum (Al) pad is investigated by the experiment and transient dynamic simulation approach. Because the deformation mechanism of the vertical cobra probe is determined by both bending and buckling mechanisms, the stable correlation between contact forces and overdrive (OD) length must be carefully verified. Moreover, the decent OD length with corresponding contact force contributed to piercing the native oxide layer of the Al pad and preventing the probing test-induced damage on the interconnect system. Accordingly, the scratch depth of the Al pad under various OD lengths is estimated by the atomic force microscope (AFM) and simulation work. In the wafer probing test configuration, the contact phenomenon between the probe needle and the tested object introduced large deformation and twisting of mesh gridding, causing the subsequent numerical divergence issue. For this reason, the arbitrary Lagrangian-Eulerian method is utilized in the present simulation work to conquer the aforementioned issue. The analytic results revealed a slight difference when the OD is considered as 40 μm, and the simulated is almost identical to the measured scratch depths of the Al pad under higher OD lengths up to 70 μm. This phenomenon can be attributed to the unstable contact of the probe at low OD length with the scratch depth below 30% of Al pad thickness, and the contact status will be being stable when the scratch depth over 30% of pad thickness. The splash of the Al pad is observed by the AFM, and the splashed Al debris accumulates on a specific side; this phenomenon is successfully simulated in the transient dynamic simulation. Thus, the preferred testing OD lengths are found as 45 μm to 70 μm, and the corresponding scratch depths on the Al pad are represented as 31.4% and 47.1% of Al pad thickness, respectively. The investigation approach demonstrated in this study contributed to analyzing the mechanical response of wafer probing test configuration under large strain conditions and assessed the geometric designs and material selections of probe needles to meet the requirement of high resolution and high-speed wafer-level probing test for thinned wafer application.

Keywords: wafer probing test, vertical probe, probe mark, mechanical response, FEA simulation

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