Search results for: Equivalent stiffness
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 671

Search results for: Equivalent stiffness

671 Finite Element Modeling of Stockbridge Damper and Vibration Analysis: Equivalent Cable Stiffness

Authors: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

Abstract:

Aeolian vibrations are the major cause for the failure of conductor cables. Using a Stockbridge damper reduces these vibrations and increases the life span of the conductor cable. Designing an efficient Stockbridge damper that suits the conductor cable requires a robust mathematical model with minimum assumptions. However it is not easy to analytically model the complex geometry of the messenger. Therefore an equivalent stiffness must be determined so that it can be used in the analytical model. This paper examines the bending stiffness of the cable and discusses the effect of this stiffness on the natural frequencies. The obtained equivalent stiffness compensates for the assumption of modeling the messenger as a rod. The results from the free vibration analysis of the analytical model with the equivalent stiffness is validated using the full scale finite element model of the Stockbridge damper.

Keywords: Equivalent stiffness, finite element model, free vibration response, Stockbridge damper.

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670 Comparison of Double Unit Tunnel Form Building before and after Repair and Retrofit under in-Plane Cyclic Loading

Authors: S. A. Anuar, N. H. Hamid, M. H. Hashim, S. M. D. Salleh

Abstract:

This paper present the experimental work of double unit tunnel form building (TFB) subjected to in-plane lateral cyclic loading. A one third scale of 3-storey double unit of TFB is tested until its strength degradation. Then, the TFB is repaired and retrofitted using additional shear wall, steel angle and CFRP sheet. The crack patterns, lateral strength, stiffness, ductility and equivalent viscous damping (EVD) were analyzed and compared before and after repair and retrofit. The result indicates that the lateral strength increases by 22% in pushing and 27% in pulling direction. Moreover, the stiffness and ductility obtained before and after retrofit increase tremendously by 87.87% and 39.66%, respectively. Meanwhile, the energy absorption measured by equivalent viscous damping obtained after retrofit increase by 12.34% in pulling direction. It can be concluded that the proposed retrofit method is capable to increase the lateral strength capacity, stiffness and energy absorption of double unit TFB.

Keywords: Crack pattern, stiffness, ductility, equivalent viscous damping.

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669 Stiffness Modeling of 3-PRS Mechanism

Authors: Xiaohui Han, Yuhan Wang, Jing Shi

Abstract:

This paper proposed a stiffness analysis method for a 3-PRS mechanism for welding thick aluminum plate using FSW technology. In the molding process, elastic deformation of lead-screws and links are taken into account. This method is based on the virtual work principle. Through a survey of the commonly used stiffness performance indices, the minimum and maximum eigenvalues of the stiffness matrix are used to evaluate the stiffness of the 3-PRS mechanism. Furthermore, A FEA model has been constructed to verify the method. Finally, we redefined the workspace using the stiffness analysis method.

Keywords: 3-PRS, parallel mechanism, stiffness analysis, workspace.

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668 Foil Bearing Stiffness Estimation with Pseudospectral Scheme

Authors: Balaji Sankar, Sadanand Kulkarni

Abstract:

Compliant foil gas lubricated bearings are used for the support of light loads in the order of few kilograms at high speeds, in the order of 50,000 RPM. The stiffness of the foil bearings depends both on the stiffness of the compliant foil and on the lubricating gas film. The stiffness of the bearings plays a crucial role in the stable operation of the supported rotor over a range of speeds. This paper describes a numerical approach to estimate the stiffness of the bearings using pseudo spectral scheme. Methodology to obtain the stiffness of the foil bearing as a function of weight of the shaft is given and the results are presented.

Keywords: Foil bearing, simulation, numerical, stiffness estimation.

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667 Main Bearing Stiffness Investigation

Authors: B. Bellakhdhar, A. Dogui, J.L. Ligier

Abstract:

Simplified coupled engine block-crankshaft models based on beam theory provide an efficient substitute to engine simulation in the design process. These models require accurate definition of the main bearing stiffness. In this paper, an investigation of this stiffness is presented. The clearance effect is studied using a smooth bearing model. It is manifested for low shaft displacement. The hydrodynamic assessment model shows that the oil film has no stiffness for low loads and it is infinitely rigid for important loads. The deformation stiffness is determined using a suitable finite elements model based on real CADs. As a result, a main bearing behaviour law is proposed. This behaviour law takes into account the clearance, the hydrodynamic sustention and the deformation stiffness. It ensures properly the transition from the configuration low rigidity to the configuration high rigidity.

Keywords: Clearance, deformation stiffness, main bearing behaviour law, oil film stiffness

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666 Layout Design Optimization of Spars under Multiple Load Cases of the High-Aspect-Ratio Wing

Authors: Yu Li, Jingwu He, Yuexi Xiong

Abstract:

The spar layout will affect the wing’s stiffness characteristics, and irrational spar arrangement will reduce the overall bending and twisting resistance capacity of the wing. In this paper, the active structural stiffness design theory is used to match the stiffness-center axis position and load-cases under the corresponding multiple flight conditions, in order to achieve better stiffness properties of the wing. The combination of active stiffness method and principle of stiffness distribution is proved to be reasonable supplying an initial reference for wing designing. The optimized layout of spars is eventually obtained, and the high-aspect-ratio wing will have better stiffness characteristics.

Keywords: Active structural stiffness design theory, high-aspect-ratio wing, flight load cases, layout of spars.

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665 Equivalent Field Calculation to Irregular Symmetric and Asymmetric Photon Fields

Authors: N. Chegeni, M. J. Tahmasebi Birgani

Abstract:

Equivalent fields are frequently used for central axis depth-dose calculations of rectangular and irregular shaped photon beam. Since most of the proposed models to calculate the equivalent square field, are dosimetry-based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square for rectangular fields was constructed and then compared with the well-known tables of BJR and Venselaar with the average relative error percentage of 2.5±2.5 % and 1.5±1.5 % respectively. To evaluate the accuracy of this method, the PDDs were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.

Keywords: Equivalent field, asymmetric field, irregular field, multi leaf collimators.

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664 Comparison of Meshing Stiffness of Altered Tooth Sum Spur Gear Tooth with Different Pressure Angles

Authors: H. K. Sachidananda, K. Raghunandana, B. Shivamurthy

Abstract:

The estimation of gear tooth stiffness is important for finding the load distribution between the gear teeth when two consecutive sets of teeth are in contact. Based on dynamic model a C-program has been developed to compute mesh stiffness. By using this program position dependent mesh stiffness of spur gear tooth for various profile shifts have been computed for a fixed center distance and altering tooth-sum gearing (100 by ± 4%). It is found that the C-program using dynamic model is one of the rapid soft computing technique which helps in design of gears. The mesh tooth stiffness along the path of contact is studied for both 20° and 25° pressure angle gears at various profile shifts. Better tooth stiffness is noticed in case of negative alteration tooth-sum gears compared to standard and positive alteration tooth-sum gears. Also, in case of negative alteration tooth-sum gearing better mesh stiffness is noticed in 20° pressure angle when compared to 25°.

Keywords: Altered tooth-sum gearing, bending fatigue, mesh stiffness, spur gear.

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663 Effect of Drawbar Force on the Dynamic Characteristics of a Spindle-Tool Holder System

Authors: Jui-Pui Hung, Yu-Sheng Lai, Tzuo-Liang Luo, Kung-Da Wu, Yun-Ji Zhan

Abstract:

This study presented the investigation of the influence of the tool holder interface stiffness on the dynamic characteristics of a spindle tool system. The interface stiffness was produced by drawbar force on the tool holder, which tends to affect the spindle dynamics. In order to assess the influence of interface stiffness on the vibration characteristic of spindle unit, we first created a three dimensional finite element model of a high speed spindle system integrated with tool holder. The key point for the creation of FEM model is the modeling of the rolling interface within the angular contact bearings and the tool holder interface. The former can be simulated by a introducing a series of spring elements between inner and outer rings. The contact stiffness was calculated according to Hertz contact theory and the preload applied on the bearings. The interface stiffness of the tool holder was identified through the experimental measurement and finite element modal analysis. Current results show that the dynamic stiffness was greatly influenced by the tool holder system. In addition, variations of modal damping, static stiffness and dynamic stiffness of the spindle tool system were greatly determined by the interface stiffness of the tool holder which was in turn dependent on the draw bar force applied on the tool holder. Overall, this study demonstrates that identification of the interface characteristics of spindle tool holder is of very importance for the refinement of the spindle tooling system to achieve the optimum machining performance.

Keywords: Dynamic stiffness, Drawbar force, Interface stiffness, Spindle-tool holder.

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662 Seismic Retrofitting of RC Buildings with Soft Storey and Floating Columns

Authors: Vinay Agrawal, Suyash Garg, Ravindra Nagar, Vinay Chandwani

Abstract:

Open ground storey with floating columns is a typical feature in the modern multistory constructions in urban India. Such features are very much undesirable in buildings built in seismically active areas. The present study proposes a feasible solution to mitigate the effects caused due to non-uniformity of stiffness and discontinuity in load path and to simultaneously hold the functional use of the open storey particularly under the floating column, through a combination of various lateral strengthening systems. An investigation is performed on an example building with nine different analytical models to bring out the importance of recognising the presence of open ground storey and floating columns. Two separate analyses on various models of the building namely, the equivalent static analysis and the response spectrum analysis as per IS: 1893-2002 were performed. Various measures such as incorporation of Chevron bracings and shear walls, strengthening the columns in the open ground storey, and their different combinations were examined. The analysis shows that, in comparison to two short ones separated by interconnecting beams, the structural walls are most effective when placed at the periphery of the buildings and used as one long structural wall. Further, it can be shown that the force transfer from floating columns becomes less horizontal when the Chevron Bracings are placed just below them, thereby reducing the shear forces in the beams on which the floating column rests.

Keywords: Equivalent static analysis, floating column, open ground storey, response spectrum analysis, shear wall, stiffness irregularity.

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661 Equivalent Circuit Modelling of Active Reflectarray Antenna

Authors: M. Y. Ismail, M. Inam

Abstract:

This paper presents equivalent circuit modeling of active planar reflectors which can be used for the detailed analysis and characterization of reflector performance in terms of lumped components. Equivalent circuit representation has been proposed for PIN diodes and liquid crystal based active planar reflectors designed within X-band frequency range. A very close agreement has been demonstrated between equivalent circuit results, 3D EM simulated results as well as measured scattering parameter results. In the case of measured results, a maximum discrepancy of 1.05dB was observed in the reflection loss performance, which can be attributed to the losses occurred during measurement process.

Keywords: Equivalent circuit modelling, planar reflectors, reflectarray antenna, PIN diode, liquid crystal.

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660 A Variable Stiffness Approach to Vibration Control

Authors: S. A. Alotaibi, M. A. Al-Ajmi

Abstract:

This work introduces a new concept for controlling the mechanical vibrations via variable stiffness coil spring. The concept relies on fitting a screw though the spring to change the number of active spring coils. A prototype has been built and tested with promising results toward an innovation in the field of vibration control.

Keywords: Variable stiffness, coil spring, vibration control.

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659 A Compact Quasi-Zero Stiffness Vibration Isolator Using Flexure-Based Spring Mechanisms Capable of Tunable Stiffness

Authors: Thanh-Phong Dao, Shyh-Chour Huang

Abstract:

This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: Vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism.

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658 Equivalent Transformation for Heterogeneous Traffic Cellular Automata

Authors: Shih-Ching Lo

Abstract:

Understanding driving behavior is a complicated researching topic. To describe accurate speed, flow and density of a multiclass users traffic flow, an adequate model is needed. In this study, we propose the concept of standard passenger car equivalent (SPCE) instead of passenger car equivalent (PCE) to estimate the influence of heavy vehicles and slow cars. Traffic cellular automata model is employed to calibrate and validate the results. According to the simulated results, the SPCE transformations present good accuracy.

Keywords: traffic flow, passenger car equivalent, cellular automata

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657 The Effect of Cracking on Stiffness of Shear Walls under Lateral Loads

Authors: Anas M. Fares

Abstract:

The lateral stiffness of buildings is one of the most important properties which define resistance to displacements under lateral loads. Moreover, it has a great impact on the natural period of the structures. Different stiffness’s values can ultimately affect the behavior of the structure under the seismic load and the lateral forces that will be applied to it. In this study the effect of cracking is studied on 2D shell thin cantilever shear wall by using ETABS. Multi linear elastic analysis is conducted with the ACI stiffness modifiers for each analysis step. The results showed that the cracks affect the value of the drift especially at the top of the high rise buildings and this will change the lateral stiffness and so change the fundamental period of the structures which lead to change in the applied shear force that comes from the earthquake. Finally, this study emphasizes that the finite element method can be considered as a good tool to predict the tensile stresses in the elements.

Keywords: Lateral loads, lateral displacement, reinforced concrete, shear wall, Cracks, ETABS, ACI code, stiffness.

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656 3D Dynamic Modeling of Transition Zones

Authors: Edina Koch, Péter Hudacsek

Abstract:

In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: Culvert, dynamic load, HS small model, railway transition zone.

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655 The Development of Chulalongkorn University's SAE Student Formula's Space Frame

Authors: Chartree Sithananun, Teekayu Limchamroon, Tanawat Limwathanagura, Thanyarat Singhanart

Abstract:

The objective of this paper is to present the development of the frame of Chulalongkorn University team in TSAE Auto Challenge Student Formula and Student Formula SAE Competition of Japan. Chulalongkorn University's SAE team, has established since year 2003, joined many competitions since year 2006 and became the leading team in Thailand. Through these 5 years, space frame was the most selected and developed year by year through six frame designs. In this paper, the discussions on the conceptual design of these frames are introduced, focusing on the mass and torsional stiffness improvement. The torsional stiffness test was performed on the real used frames and the results are compared. It can be seen that the 2010-2011 frame is firstly designed based on the analysis and experiment that considered the required mass and torsional stiffness. From the torsional stiffness results, it can be concluded that the frames were developed including the decreasing of mass and the increasing torsional stiffness by applying many techniques.

Keywords: SAE Student Formula, Space Frame, Torsional Stiffness

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654 Arterial Stiffness Detection Depending on Neural Network Classification of the Multi- Input Parameters

Authors: Firas Salih, Luban Hameed, Afaf Kamil, Armin Bolz

Abstract:

Diagnostic and detection of the arterial stiffness is very important; which gives indication of the associated increased risk of cardiovascular diseases. To make a cheap and easy method for general screening technique to avoid the future cardiovascular complexes , due to the rising of the arterial stiffness ; a proposed algorithm depending on photoplethysmogram to be used. The photoplethysmograph signals would be processed in MATLAB. The signal will be filtered, baseline wandering removed, peaks and valleys detected and normalization of the signals should be achieved .The area under the catacrotic phase of the photoplethysmogram pulse curve is calculated using trapezoidal algorithm ; then will used in cooperation with other parameters such as age, height, blood pressure in neural network for arterial stiffness detection. The Neural network were implemented with sensitivity of 80%, accuracy 85% and specificity of 90% were got from the patients data. It is concluded that neural network can detect the arterial STIFFNESS depending on risk factor parameters.

Keywords: Arterial stiffness, area under the catacrotic phase of the photoplethysmograph pulse, neural network

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653 Backcalculation of HMA Stiffness Based On Finite Element Model

Authors: Md Rashadul Islam, Umme Amina Mannan, Rafiqul A. Tarefder

Abstract:

Stiffness of Hot Mix Asphalt (HMA) in flexible pavement is largely dependent of temperature, mode of testing and age of pavement. Accurate measurement of HMA stiffness is thus quite challenging. This study determines HMA stiffness based on Finite Element Model (FEM) and validates the results using field data. As a first step, stiffnesses of different layers of a pavement section on Interstate 40 (I-40) in New Mexico were determined by Falling Weight Deflectometer (FWD) test. Pavement temperature was not measured at that time due to lack of temperature probe. Secondly, a FE model is developed in ABAQUS. Stiffness of the base, subbase and subgrade were taken from the FWD test output obtained from the first step. As HMA stiffness largely varies with temperature it was assigned trial and error approach. Thirdly, horizontal strain and vertical stress at the bottom of the HMA and temperature at different depths of the pavement were measured with installed sensors on the whole day on December 25th, 2012. Fourthly, outputs of FEM were correlated with measured stress-strain responses. After a number of trials a relationship was developed between the trial stiffness of HMA and measured mid-depth HMA temperature. At last, the obtained relationship between stiffness and temperature is verified by further FWD test when pavement temperature was recorded. A promising agreement between them is observed. Therefore, conclusion can be drawn that linear elastic FEM can accurately predict the stiffness and the structural response of flexible pavement.

Keywords: Asphalt pavement, falling weight deflectometer test, field instrumentation, finite element model, horizontal strain, temperature probes.

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652 Evaluation of Soil Stiffness and Strength for Quality Control of Compacted Earthwork

Authors: A. Sawangsuriya, T. B. Edil

Abstract:

Microstructure and fabric of soils play an important role on structural properties e.g. stiffness and strength of compacted earthwork. Traditional quality control monitoring based on moisturedensity tests neither reflects the variability of soil microstructure nor provides a direct assessment of structural property, which is the ultimate objective of the earthwork quality control. Since stiffness and strength are sensitive to soil microstructure and fabric, any independent test methods that provide simple, rapid, and direct measurement of stiffness and strength are anticipated to provide an effective assessment of compacted earthen materials’ uniformity. In this study, the soil stiffness gauge (SSG) and the dynamic cone penetrometer (DCP) were respectively utilized to measure and monitor the stiffness and strength in companion with traditional moisture-density measurements of various earthen materials used in Thailand road construction projects. The practical earthwork quality control criteria are presented herein in order to assure proper earthwork quality control and uniform structural property of compacted earthworks.

Keywords: Dynamic cone penetrometer, moisture content, relative compaction, soil stiffness gauge, structural property.

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651 Dependence of Shaft Stiffness on the Crack Location

Authors: H. M. Mobarak, Helen Wu, Chunhui Yang

Abstract:

In this study, an analytical model is developed to study crack breathing behavior under the effect of crack location and unbalance force. Crack breathing behavior is determined using effectual bending angle by studying the transient change in closed area of the crack. The status of the crack of a balanced shaft is symmetrical about shaft rotational angle and the duration of each crack status remains unchanged. The global stiffness of the balanced shaft is independent of crack location. Different crack breathing behavior for the unbalanced shaft has been observed. The influence of crack location on the unbalanced shaft stiffness can be divided into three regions. When the crack is located between 0.3L and 0.8335L, where L is the total length of the shaft, the unbalanced shaft is less stiff and when located outside this region it is stiffer than the balanced shaft. It was also found that unbalanced shaft stiffness has a maximum value with a crack at 0.1946L, a minimum value at 0.8053L and same value as balanced shaft at 0.3L and 0.8335L.

Keywords: Cracked shaft, crack location, shaft stiffness, unbalanced force.

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650 Determination of Regimes of the Equivalent Generator Based On Projective Geometry: The Generalized Equivalent Generator

Authors: A. A. Penin

Abstract:

Requirements that should be met when determining the regimes of circuits with variable elements are formulated. The interpretation of the variations in the regimes, based on projective geometry, enables adequate expressions for determining and comparing the regimes to be derived. It is proposed to use as the parameters of a generalized equivalent generator of an active two-pole with changeable resistor such load current and voltage which provide the current through this resistor equal to zero.

Keywords: Equivalent generator, geometric circuits theory, circuits regimes, load characteristics, variable elements.

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649 The Frame Analysis and Testing for Student Formula

Authors: Tanawat Limwathanagura, Chartree Sithananun, Teekayu Limchamroon, Thanyarat Singhanart

Abstract:

The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.

Keywords: Space Frame, Student Formula, Torsional Stiffness, TSAE Auto Challenge

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648 Influence of Wall Stiffness and Embedment Depth on Excavations Supported by Cantilever Walls

Authors: Muhammad Naseem Baig, Abdul Qudoos Khan, Jamal Ali

Abstract:

Ground deformations in deep excavations are affected by wall stiffness and pile embedment ratio. This paper presents the findings of a parametric study of a 64-ft deep excavation in mixed stiff soil conditions supported by cantilever pile wall. A series of finite element analysis has been carried out in Plaxis 2D by varying the pile embedment ratio and wall stiffness. It has been observed that maximum wall deflections decrease by increasing the embedment ratio up to 1.50; however, any further increase in pile length does not improve the performance of the wall. Similarly, increasing wall stiffness reduces the wall deformations and affects the deflection patterns of the wall. The finite element analysis results are compared with the field data of 25 case studies of cantilever walls. Analysis results fall within the range of normalized wall deflections of the 25 case studies. It has been concluded that deep excavations can be supported by cantilever walls provided the system stiffness is increased significantly.

Keywords: Excavations, support systems, wall stiffness, cantilever walls.

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647 A Novel Cold Asphalt Concrete Mixture for Heavily Trafficked Binder Course

Authors: A. Dulaimi, H. Al Nageim, F. Ruddock, L. Seton

Abstract:

This study aims at developing a novel cold asphalt concrete binder course mixture by using Ordinary Portland Cement (OPC) as a replacement for conventional mineral filler (0%-100%) with new by-product material (LJMU-A2) used as a supplementary cementitious material. With this purpose, cold asphalt concrete binder course mixtures with cationic emulsions were studied by means of stiffness modulus whereas water sensitivity was assessed by measuring the stiffness modulus ratio before and after sample conditioning. The results indicate that a substantial enhancement in the stiffness modulus and a considerable improvement of water sensitivity resistance is achieved by adding LJMU-A2 to the cold asphalt mixtures as a supplementary cementitious material. Moreover, the addition of LJMU-A2 to those mixtures leads to a stiffness modulus after 2-day curing compared to that obtained with Portland cement, which occurs after 7-day curing.

Keywords: Binder course, cold mix asphalt, cement, stiffness modulus, water sensitivity.

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646 On Chromaticity of Wheels

Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: Chromatic Polynomial, Chromatically Equivalent, Chromatically Unique, Wheel.

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645 Polymer Aerostatic Thrust Bearing under Circular Support for High Static Stiffness

Authors: S. W. Lo, C.-H. Yu

Abstract:

A new design of aerostatic thrust bearing is proposed for high static stiffness. The bearing body, which is mead of polymer covered with metallic membrane, is held by a circular ring. Such a support helps form a concave air gap to grasp the air pressure. The polymer body, which can be made rapidly by either injection or molding is able to provide extra damping under dynamic loading. The smooth membrane not only serves as the bearing surface but also protects the polymer body. The restrictor is a capillary inside a silicone tube. It can passively compensate the variation of load by expanding the capillary diameter for more air flux. In the present example, the stiffness soars from 15.85 N/μm of typical bearing to 349.85 N/μm at bearing elevation 9.5 μm; meanwhile the load capacity also enhances from 346.86 N to 704.18 N.

Keywords: Aerostatic, bearing, polymer, static stiffness.

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644 Retrofitting of Beam-Column Joint Using CFRP and Steel Plate

Authors: N. H. Hamid, N. D. Hadi, K. D. Ghani

Abstract:

This paper presents the retrofitting of beam-column joint using CFRP (Carbon Fiber Reinforced Polymer) and steel plate. This specimen was tested until failure up to 1.0% drift. This joint suffered severe damages and diagonal cracks at upper crack at upper column before retrofitted. CFRP were wrapped at corbel, bottom and top of the column. Steel plates with bonding were attached to the two beams and the jointing system. This retrofitted specimen is tested again under lateral cyclic loading up 1.75% drift. Visual observations show that the cracks started at joint when 0.5% drift applied at top of column. Damage of retrofitted beam-column joint occurred inside the CFRP and it cannot be seen from outside. Analysis of elastic stiffness, lateral strength, ductility, hysteresis loops and equivalent viscous damping shows that these values are higher than before retrofitting. Therefore, it is recommended to use this type of retrofitting method for beam-column joint with corbel which suffers severe damage after the earthquake.

Keywords: Beam-Column joint, ductility, stiffness, retrofitting.

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643 Impact of Out-of-Plane Stiffness of the Diaphragm on Deflection of Wood Light-Frame Shear Walls

Authors: M. M. Bagheri, G. Doudak, M. Gong

Abstract:

The in-plane rigidity of light frame diaphragms has been investigated by researchers due to the importance of this subsystem regarding lateral force distribution between the lateral force resisting system (LFRS). Where research has lacked is in evaluating the impact of out-of-plane raigidity of the diaphragm on the deflection of shear walls. This study aims at investigating the effect of the diaphragm on the behavior of wood light-frame shear walls, in particular its out-of-plane rigidity was simulated by modeling the floors as beam. The out of plane stiffness of the diaphragm was investigated for idealized (infinitely stiff or flexible) as well as “realistic”. The results showed reductions in the shear wall deflection in the magnitude of approximately 80% considering the out of plane rigidity of the diaphragm. It was also concluded that considering conservative estimates of out-of-plane stiffness might lead to a very significant reduction in deflection and that assuming the floor diaphragm to be infinitely rigid out of plan seems to be reasonable. For diaphragms supported on multiple panels, further reduction in the deflection was observed. More work, particularly at the experimental level, is needed to verify the finding obtained in the numerical investigation related to the effect of out of plane diaphragm stiffness.

Keywords: Deflection of light-frame wood shear walls, out-of-plane stiffness of the diaphragm, initial stiffness.

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642 The Small Strain Effects to the Shear Strength and Maximum Stiffness of Post-Cyclic Degradation of Hemic Peat Soil

Authors: Z. Adnan, M. M. Habib

Abstract:

The laboratory tests for measuring the effects of small strain to the shear strength and maximum stiffness development of post-cyclic degradation of hemic peat are reviewed in this paper. A series of laboratory testing has been conducted to fulfil the objective of this research to study the post-cyclic behaviour of peat soil and focuses on the small strain characteristics. For this purpose, a number of strain-controlled static, cyclic and post-cyclic triaxial tests were carried out in undrained condition on hemic peat soil. The shear strength and maximum stiffness of hemic peat are evaluated immediately after post-cyclic monotonic testing. There are two soil samples taken from West Johor and East Malaysia peat soil. Based on these laboratories and field testing data, it was found that the shear strength and maximum stiffness of peat soil decreased in post-cyclic monotonic loading than its initial shear strength and stiffness. In particular, degradation in shear strength and stiffness is more sensitive for peat soil due to fragile and uniform fibre structures. Shear strength of peat soil, τmax = 12.53 kPa (Beaufort peat, BFpt) and 36.61 kPa (Parit Nipah peat, PNpt) decreased than its initial 58.46 kPa and 91.67 kPa. The maximum stiffness, Gmax = 0.23 and 0.25 decreased markedly with post-cyclic, Gmax = 0.04 and 0.09. Simple correlations between the Gmax and the τmax effects due to small strain, ε = 0.1, the Gmax values for post-cyclic are relatively low compared to its initial Gmax. As a consequence, the reported values and patterns of both the West Johor and East Malaysia peat soil are generally the same.

Keywords: Post-cyclic, strain, shear strength, maximum stiffness.

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