SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS

 Jonah McKinney
 11 months ago
 Views:
Transcription
1 SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS de Aguiar, José M., Faculdade de Tecnologia de São Paulo, FATECSP Centro Estadual de Educação Tecnológica Paula Souza. CEETEPS Praça Coronel Fernando Prestes, 30  Bom Retiro  São PauloSP  CEP de Aguiar, João B., Universidade Federal do ABC, Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas. Av. dos Estados, 5501 Bangu Santo Andre, SP  Brasil Abstract. The development of composite beams for structural purposes have been investigated in the past. Composite beams made of soft core materials, lie foams, have been used. However, high compressive loads commom in structural applications have led to failure of these materials. New developments using glass fiber reinforced polymer sins and high strength core materials are showing promissing future. Experimental results characterizing some sandwich composite beams developed in Australia have been published, though sin plies layup details have not. The objective of this study is to model laminated sandwich composite beams using experimental results as reference. The proposed fem model analysis is based on an article about the ASTM C fourpoint bending test of composite sandwiches beams developed by Van Erp and Roger. Several composed ply combinations were modelled using the reported mechanical properties of the glass fiber sin and core material. The fem results relating midspan deflections, load capacity and stress distributions on layers were obtained. The numerical simulation have produced close results compared to the experimental flexural behavior reported. In addition, the stresses in the layers seem to explain the observed failure scenario Keywords: sandwich, composite, bending, beam, fem 1. INTRODUCTION Several approaches on sandwich composite beam fabrication for structural usages have been considered over the past years. Foam and soft materials (wood, plastic for example) were used as core materials, in order to produce a lightweight composite structure. Honeycomb, truss structures were investigated too. Though they mae a lightweight structure, soft core materials are not adequate to hold mechanical connectors. These limitations seem to be better handled by using strong thin layers bonded to high strength thic core. The fibre composite sandwich developed by Van Erp, and Roger (2008) is an example. 2. MATERIAL CHARACTERIZATION The laminated sandwich composites tested by Manalo et al. (2009), were made of modified phenolic material (core material) bonded to biaxial glass fiber sins. They used a resin obtained from plants to bond the materials. The mechanical properties, in the main direction, of the materials used in the beam fabrication are reproduced in Tab. 1. Table 1. Mechanical properties of sin and core materials. Property Sin Core Young s Module (MPa) Maximum tensile stress (MPa) Maximum compressive stress (MPa) Thicness (mm) The sandwich composite beams were submitted to a fourpoint bending test in accordance to ASTM C standard. The distance between supports was L = 400 mm and the specimens were 500 mm long. The loaddeflection static curves, development of cracs, delamination, etc. were reported. Details about the number of plies, angular orientation of glass fibers of the sin layers were not available Principle of virtual wor and governing equations The principle of virtual wor (Gibson, R. (2007)) done by the actual forces acting on a solid involves the virtual strain energy δ the virtual external wor and corresponds to the balance equation: U int δ and V ext δ U int δv = 0 (1) + ext
2 March 2408, 2014, Santiago, Chile Let f = f(x) be the transverse load acting on a beam. Let us consider a rectangular beam with crosssection ( b, h) where x is the axial direction, y is along the width direction and z along the height direction. The length of the beam is L.The transverse load will produce internally normal and shear stresses ( σ ; ). Let δ w be a virtual xx τ xz transversal displacement along z coordinate direction, and δψ be the virtual section rotation. The external wor produced by the acting load on a virtual transversal displacement is given by L δ Vext = fδwdx (2) 0 When the beam undergoes a virtual transversal displacement and virtual rotation, the internal stresses produce a virtual strain energy given by: δ where int L = 0 A σ σ : δε dadx; σ = ; τ ε ε = γ U (3) δε xx and xz δγ are the normal and shear strains associated with the virtual displacement and rotations. Integration is taen over all the section, and will depend on the composite section model, 1 or 2. If it assumed that the core region is in plane strain conditions, while the sin is always in plane stress conditions, then in the first case, whereas for the second. Matrices and are the constitutive matrices for elastic behavior. Integrating the virtual strain energy expression through the sandwich beam thicness, layer by layer, the virtual strain energy becomes: 5 δ U = δε CεdAdx (4) int = 1 L A Upon introduction of discretization into finite elements, vector of strains may be written in terms of the vector of lateral displacements by means of an interpolation matrix, so that for each layer: T K = B C BdAdx (5) L A is the layer stiffness matrix. As the sin layers are made of an anisotropic material, rotation matrix results to the main axes directions. This matrix is set equal to the identity matrix for the core material. is used to refer Introduction of the above results into the expression of the principle of virtual wor, Eq. (1) leads to: (6) Being the vector of applied loading. Details are available in Reddy, J. (1993), Reddy, J. (2004). 3. RESULS AND DISCUSSION 3.1 Flat position failure mode Composite materials mechanical behavior is dependent on several factors, i.e, fiber and matrix bonding, plies stacing sequence, plies thicnesses and orientations, angular directions with respect to layup reference directions, etc. The fem model was constructed using the mechanical properties shown in Tab. 1. The biaxial fiber sins were modeled by plies with ply angles (±45) 2, sequenced by the core material. The core material occupied the middle of the beam. The model can be described by [(±45) 2 /0] s. Different number of plies and orientations were verified, however the [(±45/0] s was the simplest to show good agreement with reported results.
3 Fem models were created using Abaqus software for sandwich composite beams. Sin layers were placed in horizontal position (flat) as well as in vertical one (edge position). Figure 1 is a schematic representation of the four point bending test of the laminated sandwich composite using the 100 N universal testing machine.. P/2 P/2 0.4L 0.2L 0.4L L Horizontal sin layers model. Vertical sin layers model. Figure 1. Schematic representation of a four point bending test. Manalo et al. (2009) presented the load and midspan deflection experimental results for the beams of rectangular crosssections tested in the flat and edge positions. Figure 2. Vertical displacements of composite sandwich. The midspan deflection of horizontal beam (Fig. 1: horizontal sin layers) tested in the flat position increased linearly until a load around 4550 N was reached. The corresponding reported midspan deflection was 24 mm. An Abaqus 3D deformable solid model was used to represent the rectangular beam subjected to the fourpoint bending test. The beam dimensions were 50x20 mm. Model 1 had sin layers placed horizontally on the top and bottom of the beam. The total thicness of the sin layers were 1.92 mm. Figure 2 shows results of the vertical displacement distribution (U2) for the composite solid model of the laminates sandwich beam [(±45) 2 /0] s. The displacements are in meters. The fem maximum vertical displacement result for a fourpoint bending test simulation was 21.8 mm.
4 March 2408, 2014, Santiago, Chile Figure 3. Principal stress distribution on composite sandwich core layer. Flat position Figure 4. Principal stresses distribution on composite sandwich bottom sin layer. Flat position. Stresses in the core layer are represented in Fig. 3. Figure 4 shows stresses for the bottom sin layer. The stress distribution for the top layer is shown in Fig. 5. The stresses are in SI units (N/m 2 ). Experimental observations report that some tension cracs were observed at the bottom part of the core material. The fem maximum principal stresses in the core materials are at 13.4 MPa (Fig. 3), thus very close to the maximum tensile stresses for the core material (14 MPa). The fem results (Fig. 3) could explain the observed tension cracs at the bottom of the core material. However, it was observed also that core cracs did not cause the final failure. The failure was due to compressive sin stresses followed by delamination between the core and sin materials. There were no shear stresses properties on the report in order to verify the claim by the simulation.
5 The stresses in the bottom sin layer (Fig. 4) are about 12% below the maximum tensile stress for the sin materials (Tab. 1.). The maximum stresses happen in the region between the loads. However, we cannot reach a conclusion without first observing the scenario of the top sin layer. The stresses in the top sin layers are compressive stresses. The maximum compressive stresses of the central region are at MPa (Fig 5.). These stresses are 1% below the maximum compressive stress of the sin material which is 211 MPa (Tab. 1). It should explain the reason why the specimen failed due to compressive failure of composite sins. Figure 5. Principal stresses distribution on composite sandwich top sin layer. Flat position Edge position failure mode Laminated sandwich composite rectangular beams placed on the vertical position, edge position, are also setched in Fig. 1. The sin layers are placed in vertical position at the vertical sides of the rectangle. An abaqus 3D deformable composite solid model was constructed. The solid beam model had dimension 20x50 mm. Model 2 assumes four vertical sin layers at each side of the core layer, with a total 1.92 mm for the sin thicness [(±45) 2 /0] s. The experimental investigation mentions the edgewise rectangular beam bending test results. Load and deflection increased linearly until 5000 N during the experiment. Cracs were observed appearing in the core material leading to slope reduction of load against deflection curve, ie, different mechanical properties. Next, the loading increased until 5500 N and the deflections reached 8 mm. However, the deflections progressed even further without an increase in the applied load. The failure occurred with an approximate 14 mm deflection. The Figure 6 shows the vertical beam displacement under a 5500 N load obtained by the fem model simulation. The displacements in the pure bending region are mm. (0.4L)[4(0.4L) 2 3L 2 ] The maximum displacement formula w max = P corresponding to the four bending test 24EI 3 3 H t s H t c settings turns w max = 9.06 mm, with EI = Es + Ec being H=beam height, t= beam thicness, E= Young s module; s= sin material and c=core material. The results are in good agreement with the fem model simulation ones.
6 March 2408, 2014, Santiago, Chile Figure 5. Vertical displacements of composite sandwich. Edge Position. The stresses in the vertical core material are represented in Fig. 6. Figure 7 shows the stresses in the leftmost sin layer. It can be observed that the maximum stress level (Fig. 6) in core material (+14.5 MPa) is higher than the maximum tensile core stress level (Tab. 1). Figure 6. Principal stresses on composite sandwich core layer. Edge Position This stress level explains the appearance of tensile cracs in core material. However, the load deflection experimental curve shows an increase in the amount of deflection without any increase of the applied load. Certainly, the mechanical properties available (Tab. 1) would not the material behavior changes. Figure 7 shows the principal stresses reached in the leftmost sin layer material. The sin tensile and compressive stresses are approximately 30% below the maximum stress levels (Tab. 1). Based on the core stress level, expect outcome would be a failure of the core material. The experimental observation mentions that the core tensile cracs did not progress due to the presence of vertical sin layers. The constant loaddeflection plateau represents a stress
7 redistribution leading to progressive compressive and tensile sin failure. Additional mechanical properties are needed to simulate the nonlinear behavior. We can conclude that the fem models predict close enough the experimental observations. However, the models would need more mechanical properties to characterize the delamination and other experimental measures. 4. REFERENCES Figure 7. Principal stresses on composite sandwich leftmost sin layer. Edge Position Manalo, A.C., Aravinthan, T., Karunasena, W, Flexural Behaviour of Laminated Fibre Composite Sandwich Beams. The Second Official International Conference of International Institute for FRP in Construction for Asia Pacific Region. APFIS, South Korea, December, 2009 Van Erp, G, Rogers, D A highly sustainable fiber composite building panel Proceeding of the International Worshop on Fibre Composites in Civil Infrastructure Past, Present and Future. December 2008, University of Southern Queensland, Toowomba, Queensland, Australia. Islam, M.M., Aravinthan, T., Van Erp, G., Behaviour of Innovative Fibre Composite Sandwich Panels under Point Load. The Second Official International Conference of International Institute for FRP in Construction for Asia Pacific Region. APFIS, South Korea, December, 2009 Reddy, J An introduction to the finite element method.. McGrawHill, Inc. Reddy, J Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press. Gibson, R Principle of Composite Materials Mechanics. CRC Press 5. RESPONSIBILITY NOTICE The author(s) is (are) the only responsible for the printed material included in this paper.
QUESTION BANK Composite Materials
QUESTION BANK Composite Materials 1. Define composite material. 2. What is the need for composite material? 3. Mention important characterits of composite material 4. Give examples for fiber material 5.
More informationJournal of Composite Materials. Behaviour of hollow pultruded GFRP square beams with different shear spantodepth ratios
Behaviour of hollow pultruded GFRP square beams with different shear spantodepth ratios Journal: Manuscript ID: Draft Manuscript Type: Original Manuscript Date Submitted by the Author: n/a Complete List
More informationTESTING AND ANALYSIS OF COMPOSITE SANDWICH BEAMS
TESTING AND ANALYSIS OF COMPOSITE SANDWICH BEAMS I. M. Daniel, J. L. Abot, and K. A. Wang Walter P. Murphy Professor, Departments of Civil and Mechanical Engineering, Robert R. McCormick School of Engineering
More informationCOMPUTER AIDED DESIGN IN CASE OF THE LAMINATED COMPOSITE MATERIALS
6 th International Conference Computational Mechanics and Virtual Engineering COMEC 15 1516 October 15, Braşov, Romania COMPUER AIDED DESIGN IN CASE OF HE LAMINAED COMPOSIE MAERIALS Camelia Cerbu ransilvania
More informationMECHANICS OF MATERIALS
Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:
More informationASPECTS CONCERNING TO THE MECHANICAL PROPERTIES OF THE GLASS / FLAX / EPOXY COMPOSITE MATERIAL
5 th International Conference Advanced Composite Materials Engineering COMAT 2014 1617 October 2014, Braşov, Romania ASPECTS CONCERNING TO THE MECHANICAL PROPERTIES OF THE GLASS / FLAX / EPOXY COMPOSITE
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationISSN: ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 2, Issue 4, July 2013
Delamination Studies in FibreReinforced Polymer Composites K.Kantha Rao, Dr P. Shailesh, K. Vijay Kumar 1 Associate Professor, Narasimha Reddy Engineering College Hyderabad. 2 Professor, St. Peter s Engineering
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis StressStrain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationBending of Simply Supported Isotropic and Composite Laminate Plates
Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto GutierrezMiravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,
More information3. BEAMS: STRAIN, STRESS, DEFLECTIONS
3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets
More informationDegree Thesis Flexural Rigidity (D) in Beams. Author: Zious Karis. Instructor: Rene Herrmann
Degree Thesis Flexural Rigidity (D) in Beams Author: Zious Karis Instructor: Rene Herrmann Degree Thesis Materials Processing Technology 2017 DEGREE THESIS Arcada University of Applied Sciences, Helsinki,
More informationDetermination of the Shear Buckling Load of a Large Polymer Composite ISection Using Strain and Displacement Sensors
Sensors 2012, 12, 1602416036; doi:10.3390/s121216024 Article OPEN ACCESS sensors ISSN 14248220 www.mdpi.com/journal/sensors Determination of the Shear Buckling Load of a Large Polymer Composite ISection
More informationFracture Mechanics of Composites with Residual Thermal Stresses
J. A. Nairn Material Science & Engineering, University of Utah, Salt Lake City, Utah 84 Fracture Mechanics of Composites with Residual Thermal Stresses The problem of calculating the energy release rate
More informationBIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS
BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS H. Kumazawa and T. Takatoya Airframes and Structures Group, Japan Aerospace Exploration Agency 6131, Ohsawa, Mitaka,
More informationTHE ROLE OF DELAMINATION IN NOTCHED AND UNNOTCHED TENSILE STRENGTH
THE ROLE OF DELAMINATION IN NOTCHED AND UNNOTCHED TENSILE STRENGTH M. R. Wisnom University of Bristol Advanced Composites Centre for Innovation and Science University Walk, Bristol BS8 1TR, UK M.Wisnom@bristol.ac.uk
More informationTHE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE
Journal of Applied Mathematics and Computational Mechanics 013, 1(4), 131 THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE Jolanta Błaszczuk
More informationTensile behaviour of antisymmetric CFRP composite
Available online at www.sciencedirect.com Procedia Engineering 1 (211) 1865 187 ICM11 Tensile behaviour of antisymmetric CFRP composite K. J. Wong a,b, *, X. J. Gong a, S. Aivazzadeh a, M. N. Tamin b
More informationVALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED  PART 2 )
VALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED  PART 2 ) Graham D Sims and William R Broughton Composites Design Data and Methods, Centre for Materials
More informationChapter 5 Elastic Strain, Deflection, and Stability 1. Elastic StressStrain Relationship
Chapter 5 Elastic Strain, Deflection, and Stability Elastic StressStrain Relationship A stress in the xdirection causes a strain in the xdirection by σ x also causes a strain in the ydirection & zdirection
More informationA review on the mechanical behaviour of curvilinear fibre composite laminated panels
A review on the mechanical behaviour of curvilinear fibre composite laminated panels Pedro Ribeiro, Hamed Ahavan IDMEC/DEMec, Faculdade de Engenharia, Universidade do Porto Porto, Portugal Andrzej Teter,
More informationPLAT DAN CANGKANG (TKS 4219)
PLAT DAN CANGKANG (TKS 4219) SESI I: PLATES Dr.Eng. Achfas Zacoeb Dept. of Civil Engineering Brawijaya University INTRODUCTION Plates are straight, plane, twodimensional structural components of which
More informationLAMINATION THEORY FOR THE STRENGTH OF FIBER COMPOSITE MATERIALS
XXII. LAMINATION THEORY FOR THE STRENGTH OF FIBER COMPOSITE MATERIALS Introduction The lamination theory for the elastic stiffness of fiber composite materials is the backbone of the entire field, it holds
More informationEnhancing Prediction Accuracy In Sift Theory
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Enhancing Prediction Accuracy In Sift Theory J. Wang 1 *, W. K. Chiu 1 Defence Science and Technology Organisation, Fishermans Bend, Australia, Department
More informationStatic and Time Dependent Failure of Fibre Reinforced Elastomeric Components. Salim Mirza Element Materials Technology Hitchin, UK
Static and Time Dependent Failure of Fibre Reinforced Elastomeric Components Salim Mirza Element Materials Technology Hitchin, UK Introduction Fibre reinforced elastomers are used in many applications,
More informationMaterials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationMATERIAL ELASTIC ANISOTROPIC command
MATERIAL ELASTIC ANISOTROPIC command.. Synopsis The MATERIAL ELASTIC ANISOTROPIC command is used to specify the parameters associated with an anisotropic linear elastic material idealization. Syntax The
More informationMacroscopic Elastic Constitutive Relationship of CastinPlace HollowCore Slabs
Macroscopic Elastic Constitutive Relationship of CastinPlace HollowCore Slabs JingZhong Xie 1 Abstract: The macroscopic Poisson ratio and elastic moduli of the castinplace hollowcore slab are researched
More informationMaterials and Structures. Indian Institute of Technology Kanpur
Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 16 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More informationCHEMC2410: Materials Science from Microstructures to Properties Composites: basic principles
CHEMC2410: Materials Science from Microstructures to Properties Composites: basic principles Mark Hughes 14 th March 2017 Today s learning outcomes To understand the role of reinforcement, matrix and
More informationNumerical simulation of delamination onset and growth in laminated composites
Numerical simulation of delamination onset and growth in laminated composites G. Wimmer, C. Schuecker, H.E. Pettermann Austrian Aeronautics Research (AAR) / Network for Materials and Engineering at the
More informationReview of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis
uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods
More informationFinite element modelling of infinitely wide Angleply FRP. laminates
www.ijaser.com 2012 by the authors Licensee IJASER Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Finite element modelling of infinitely wide Angleply FRP laminates
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationBone Tissue Mechanics
Bone Tissue Mechanics João Folgado Paulo R. Fernandes Instituto Superior Técnico, 2016 PART 1 and 2 Introduction The objective of this course is to study basic concepts on hard tissue mechanics. Hard tissue
More informationPRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses
OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 241002
More informationCalculation of Energy Release Rate in Mode I Delamination of Angle Ply Laminated Composites
Copyright c 2007 ICCES ICCES, vol.1, no.2, pp.6167, 2007 Calculation of Energy Release Rate in Mode I Delamination of Angle Ply Laminated Composites K. Gordnian 1, H. Hadavinia 1, G. Simpson 1 and A.
More informationComposite Laminate Modeling
omposite Laminate Modeling White Paper for Femap and NX Nastran Users Venkata Bheemreddy, Ph.D., Senior Staff Mechanical Engineer Adrian Jensen, PE, Senior Staff Mechanical Engineer WHAT THIS WHITE PAPER
More informationMECHANICS OF MATERIALS. Analysis of Beams for Bending
MECHANICS OF MATERIALS Analysis of Beams for Bending By NUR FARHAYU ARIFFIN Faculty of Civil Engineering & Earth Resources Chapter Description Expected Outcomes Define the elastic deformation of an axially
More informationCRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES
S. Kakay et al. Int. J. Comp. Meth. and Exp. Meas. Vol. 5 No. (017) 116 14 CRACK FORMATION AND CRACK PROPAGATION INTO THE COMPRESSION ZONE ON REINFORCED CONCRETE BEAM STRUCTURES SAMDAR KAKAY DANIEL BÅRDSEN
More informationModeling of the Bending Stiffness of a Bimaterial Beam by the Approximation of OneDimensional of Laminated Theory
. FloresDomínguez Int. Journal of Engineering Research and Applications RESEARCH ARTICLE OPEN ACCESS odeling of the Bending Stiffness of a Bimaterial Beam by the Approimation of OneDimensional of Laminated
More informationIf the number of unknown reaction components are equal to the number of equations, the structure is known as statically determinate.
1 of 6 EQUILIBRIUM OF A RIGID BODY AND ANALYSIS OF ETRUCTURAS II 9.1 reactions in supports and joints of a twodimensional structure and statically indeterminate reactions: Statically indeterminate structures
More informationFEM Modeling of a 3D Printed Carbon Fiber Pylon
FEM Modeling of a 3D Printed Carbon Fiber Pylon I. López G.*, B. Chiné, and J.L. León S. Costa Rica Institute of Technology, School of Materials Science and Engineering, Cartago, Costa Rica *Corresponding
More informationMESH MODELING OF ANGLEPLY LAMINATED COMPOSITE PLATES FOR DNS AND IPSAP
16 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MESH MODELING OF ANGLEPLY LAMINATED COMPOSITE PLATES FOR DNS AND IPSAP Wanil Byun*, Seung Jo Kim*, Joris Wismans** *Seoul National University, Republic
More informationSTRUCTURAL OPTIMIZATION OF A MATERIAL EXHIBITING NEGATIVE STIFFNESS
International Conference on Engineering Vibration Ljubljana, Slovenia, 70 September 05 STRUCTURAL OPTIMIZATION OF A MATERIAL EXHIBITING NEGATIVE STIFFNESS Zuzana Dimitrovová*, Jan Heczo, Helder C. Rodrigues
More informationModule 4 : Deflection of Structures Lecture 4 : Strain Energy Method
Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under
More informationFASTENER PULLTHROUGH FAILURE IN GFRP LAMINATES
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS FASTENER PULLTHROUGH FAILURE IN GFRP LAMINATES G. Catalanotti 1*, P.P. Camanho 1, P. Ghys 2, A.T. Marques 1 1 DEMec, Faculdade de Engenharia, Universidade
More informationBilinear Quadrilateral (Q4): CQUAD4 in GENESIS
Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The Q4 element has four nodes and eight nodal dof. The shape can be any quadrilateral; we ll concentrate on a rectangle now. The displacement field in terms
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationMECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola
MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the
More informationPlane Strain Test for Metal Sheet Characterization
Plane Strain Test for Metal Sheet Characterization Paulo Flores 1, Felix Bonnet 2 and AnneMarie Habraken 3 1 DIM, University of Concepción, Edmundo Larenas 270, Concepción, Chile 2 ENS  Cachan, Avenue
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
More informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationA Study on the Tube of Integral Propeller Shaft for the Rearwheel Drive Automobile Using Carbon Composite Fiber
A Study on the Tube of Integral Propeller Shaft for the Rearwheel Drive Automobile Using Carbon Composite Fiber Kibong Han Mechatronics Department, Jungwon University, 85 Munmuro, Goesangun, South Korea.
More informationAn investigation of the mechanical behaviour of carbon epoxy cross ply cruciform specimens under biaxial loading
An investigation of the mechanical behaviour of carbon epoxy cross ply cruciform specimens under biaxial loading A. Makris, C. Ramault, D. Van Hemelrijck Department of Mechanics of Materials and Constructions,
More informationDeflections and Strains in Cracked Shafts due to Rotating Loads: A Numerical and Experimental Analysis
Rotating Machinery, 10(4): 283 291, 2004 Copyright c Taylor & Francis Inc. ISSN: 1023621X print / 15423034 online DOI: 10.1080/10236210490447728 Deflections and Strains in Cracked Shafts due to Rotating
More informationSeismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design
Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department
More informationTHEORY OF PLATES AND SHELLS
THEORY OF PLATES AND SHELLS S. TIMOSHENKO Professor Emeritus of Engineering Mechanics Stanford University S. WOINOWSKYKRIEGER Professor of Engineering Mechanics Laval University SECOND EDITION MCGRAWHILL
More informationSOME RESEARCH ON FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS
Mechanical Testing and Diagnosis ISSN 2247 9635, 2012 (II), Volume 3, 7985 SOME RESEARCH ON FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS Valeriu DULGHERU, Viorel BOSTAN, Marin GUŢU Technical University
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain  Axial Loading Statics
More informationMarch 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE
Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano
More informationSIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE
SIMPLIFIED METHOD FOR PREDICTING DEFORMATIONS OF RC FRAMES DURING FIRE EXPOSURE M.A. Youssef a, S.F. ElFitiany a a Western University, Faculty of Engineering, London, Ontario, Canada Abstract Structural
More informationExternal Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is
Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the
More informationChapter 2: Deflections of Structures
Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2
More informationA PROPOSAL OF DESIGN PROCEDURE FOR FLEXURAL STRENGTHENING RC BEAMS WITH FRP SHEET
N. Kishi, E89, 1/8 A PROPOSAL OF DESIGN PROCEDURE FOR FLEXURAL STRENGTHENING RC BEAMS WITH FRP SHEET Yusuke Kurihashi Norimitsu Kishi Hiroshi Mikami Sumiyuki Sawada Civil Engrg. Research Muroran Inst.
More informationLecture 1617, Sandwich Panel Notes, 3.054
Sandwich Panels Two stiff strong skins separated by a lightweight core Separation of skins by core increases moment of inertia, with little increase in weight Efficient for resisting bending and buckling
More informationFinite Element Analysis of Dynamic Properties of Thermally Optimal Twophase Composite Structure
Vibrations in Physical Systems Vol.26 (2014) Finite Element Analysis of Dynamic Properties of Thermally Optimal Twophase Composite Structure Abstract Maria NIENARTOWICZ Institute of Applied Mechanics,
More informationA FINITE ELEMENT MODEL TO PREDICT MULTI AXIAL STRESSSTRAIN RESPONSE OF CERAMIC MATRIX COMPOSITES WITH STRAIN INDUCED DAMAGE
A FINITE ELEMENT MODEL TO PREDICT MULTI AXIAL STRESSSTRAIN RESPONSE OF CERAMIC MATRIX COMPOSITES WITH STRAIN INDUCED DAMAGE Daxu Zhang and D. R. Hayhurst School of Mechanical, Aerospace and Civil Engineering,
More informationA NEW REFINED THEORY OF PLATES WITH TRANSVERSE SHEAR DEFORMATION FOR MODERATELY THICK AND THICK PLATES
A NEW REFINED THEORY OF PLATES WITH TRANSVERSE SHEAR DEFORMATION FOR MODERATELY THICK AND THICK PLATES J.M. MARTÍNEZ VALLE Mechanics Department, EPS; Leonardo da Vinci Building, Rabanales Campus, Cordoba
More informationSIMULATION OF PROGRESSIVE FAILURE PREDICTION OF FILAMENT WOUND COMPOSITE TUBES SUBJECTED TO MULTIPLE LOADING WITH MEMBRANEFLEXION COUPLING EFFECTS
VOL. 5, NO. 4, APRIL 010 ISSN 18196608 006010 Asian Research Publishing Network (ARPN). All rights reserved. SIMULATION OF PROGRESSIVE FAILURE PREDICTION OF FILAMENT WOUND COMPOSITE TUBES SUBJECTED TO
More informationEvaluation of Flexural Stiffness for RC Beams During Fire Events
3 rd International Structural Specialty Conference 3 ième conférence internationale spécialisée sur le génie des structures Edmonton, Alberta June 69, 202 / 6 au 9 juin 202 Evaluation of Flexural Stiffness
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More informationMechanical Design in Optical Engineering
OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:
More informationEFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS
EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS Atsuhiko MACHIDA And Khairy H ABDELKAREEM SUMMARY Nonlinear D FEM was utilized to carry out inelastic
More informationIMPACT ON LAMINATED COMPOSITE PLATES: COMPARISON OF TEST AND SIMULATION RESULTS OBTAINED WITH LMS SAMTECH SAMCEF
V ECCOMAS Thematic Conference on the Mechanical Response of Composites COMPOSITES 015 S.R. Hallett and J.J.C. Remmers (Editors) IMPACT ON LAMINATED COMPOSITE PLATES: COMPARISON OF TEST AND SIMULATION RESULTS
More informationNonconventional Glass fiber NCF composites with thermoset and thermoplastic matrices. F Talence, France Le Cheylard, France
20 th International Conference on Composite Materials Copenhagen, 1924th July 2015 Nonconventional Glass fiber NCF composites with thermoset and thermoplastic matrices. Thierry Lorriot 1, Jalal El Yagoubi
More informationThe Accuracy of Characteristic Length Method on Failure Load Prediction of Composite Pinned Joints
, June 30  July 2, 2010, London, U.K. The Accuracy of Characteristic Length Method on Failure Load Prediction of Composite Pinned Joints O. Aluko, and Q. Mazumder Abstract An analytical model was developed
More informationJeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA UNESCO EOLSS
MECHANICS OF MATERIALS Jeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA Keywords: Solid mechanics, stress, strain, yield strength Contents 1. Introduction 2. Stress
More informationUNIAXIAL COMPRESSION TEST OF STEEL PLATE BONDED VARIOUS FRP SHEETS
UNIAXIAL COMRESSION TEST OF STEEL LATE BONDED VARIOUS FR SHEETS Takeshi MIYASHITA Specially appointed associate professor Nagaoka University of Technology 1631 Kamitomioka, Nagaoka, Niigata, Japan mtakeshi@vos.nagaokaut.ac.jp*
More information2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?
IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at
More informationEngineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati
Engineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati Module 3 Lecture 6 Internal Forces Today, we will see analysis of structures part
More informationA Suggested Analytical Solution for Vibration of Honeycombs Sandwich Combined Plate Structure
International Journal of Mechanical & Mechatronics Engineering IJMMEIJENS Vol:16 No:04 9 A Suggested Analytical Solution for Vibration of Honeycombs Sandwich Combined Plate Structure Muhsin J. Jweeg College
More informationLecture 4: PRELIMINARY CONCEPTS OF STRUCTURAL ANALYSIS. Introduction
Introduction In this class we will focus on the structural analysis of framed structures. We will learn about the flexibility method first, and then learn how to use the primary analytical tools associated
More informationCHAPTER 6: ULTIMATE LIMIT STATE
CHAPTER 6: ULTIMATE LIMIT STATE 6.1 GENERAL It shall be in accordance with JSCE Standard Specification (Design), 6.1. The collapse mechanism in statically indeterminate structures shall not be considered.
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationUNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.
UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude
More informationEVALUATION OF DAMAGE DEVELOPMENT FOR NCF COMPOSITES WITH A CIRCULAR HOLE BASED ON MULTISCALE ANALYSIS
THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS EVALUATION OF DAMAGE DEVELOPMENT FOR NCF COMPOSITES WITH A CIRCULAR HOLE BASED ON MULTISCALE ANALYSIS T. Kurashiki 1 *, Y. Matsushima 1, Y. Nakayasu
More informationMechanics of Irregular Honeycomb Structures
Mechanics of Irregular Honeycomb Structures S. Adhikari 1, T. Mukhopadhyay 1 Chair of Aerospace Engineering, College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK Sixth International
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationFinite Element Analysis of Composite Laminate By Using ABDH Matrix(Stiffness Matrix)
Finite Element Analysis of Composite Laminate By Using ABDH Matrix(Stiffness Matrix) Nikhil J. Chaudhari 1 Post Graduate Student Department of Mechanical Engineering Veermata Jijabai Technological Institute
More informationAnálisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas
San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo
More informationISO 178 INTERNATIONAL STANDARD. Plastics Determination of flexural properties. Plastiques Détermination des propriétés en flexion
INTERNATIONAL STANDARD ISO 178 Fifth edition 20101215 Plastics Determination of flexural properties Plastiques Détermination des propriétés en flexion Reference number ISO 178:2010(E) ISO 2010 PDF disclaimer
More informationAnalysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method
Analysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method V.M.F. Nascimento Departameto de ngenharia Mecânica TM, UFF, Rio de Janeiro
More information14. *14.8 CASTIGLIANO S THEOREM
*14.8 CASTIGLIANO S THEOREM Consider a body of arbitrary shape subjected to a series of n forces P 1, P 2, P n. Since external work done by forces is equal to internal strain energy stored in body, by
More informationDEVELOPMENT OF A METHOD TO ANALYZE STRUCTURAL INSULATED PANELS UNDER TRANSVERSE LOADING HEMING ZHANG ALWIN
DEVELOPMENT OF A METHOD TO ANALYZE STRUCTURAL INSULATED PANELS UNDER TRANSVERSE LOADING By HEMING ZHANG ALWIN A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
More informationDiscontinuous Distributions in Mechanics of Materials
Discontinuous Distributions in Mechanics of Materials J.E. Akin, Rice University 1. Introduction The study of the mechanics of materials continues to change slowly. The student needs to learn about software
More informationFailure Mode Predictions in the Compressive Response of Laminated Composites
Structures, Structural Dynamics, and Materials and Colocated Conferences April 811, 2013, Boston, Massachusetts 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference AIAA
More informationAnisotropic modeling of short fibers reinforced thermoplastics materials with LSDYNA
Anisotropic modeling of short fibers reinforced thermoplastics materials with LSDYNA Alexandre Hatt 1 1 Faurecia Automotive Seating, Simplified Limited Liability Company 1 Abstract / Summary Polymer thermoplastics
More information