Presented By: EAS 6939 Aerospace Structural Composites

 Rosalyn Thomas
 9 months ago
 Views:
Transcription
1 A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1
2 Introduction Composite beams have become very common in applications like Automobile Suspensions, Hip Prosthesis etc. Unlike beams of Isotropic materials, Composite beams may exhibit strong coupling between: Extensional Flexural & Twisting modes of Deformation. There is a need for simple and efficient analysis procedures for Composite beam like structures. 2
3 Beam Theories EULERBERNOULLI BEAM THEORY Assumptions: 1. Crosssections which are plane & normal to the longitudinal axis remain plane and normal to it after deformation. 2. Shear Deformations are neglected. 3. Beam Deflections are small. EulerBernoulli eq. for bending of Isotropic beams of constant crosssection: where: w(x): deflection of the neutral axis q(x): the applied transverse load 3
4 Beam Theories TIMOSHENKO BEAM THEORY Basic difference from EulerBernoulli beam theory is that Timoshenko beam theory considers the effects of Shear and also of Rotational Inertia in the Beam Equation. So physically, Timoshenko s s theory effectively lowers the stiffness of beam and the result is a larger deflection. Timoshenko s eq. for bending of Isotropic beams of constant crosssection: where: A: Area of Crosssection G: Shear Modulus : Shear Correction Factor 4
5 Beam Theories TIMOSHENKO BEAM THEORY(Contd.) Shear Correction Factor Timoshenko Defined it as: Significance of Shear Correction Factor : Multilayered plate and Shell finite elements have a constant shear distribution across thickness. This causes a decrease in accuracy especially for sandwich structures. This problem is overcome using shear correction factors. 5
6 Objective Derivation of a Beam Theory for Laminated Composites and Application to Torsion problems The solution procedure is indicated for the case of a Cantilever Beam subjected to end loads. A closed form solution is derived for the problem of Torsion of a Specially Orthotropic laminated beam (Coupling Matrix [B] = 0, A 16 = A 26 = D 16 = D 26 = 0). 6
7 Derivation of a Composite Beam Theory A Beam Theory for Laminated Composite Beams is derived from the shear deformable laminated plate theory. The equilibrium equations are assumed to be satisfied in an average sense over the width of the beam. The Principle of Minimum Potential Energy is applied to derive the Equilibrium equations and Boundary conditions. i.e Beam cross sections normal to the xaxis do not undergo any inplane deformations. 7
8 Derivation of a Composite Beam Theory 8
9 Steps Followed for the Derivation The displacement field in the Beam is derived by retaining the First order terms in the Taylor Series expansion for the plate midplane deformations in the width coordinate. E.g. where U(x) is the displacement of points on the longitudinal axis of the beam The laminate constitutive relation is expressed in simple terms as: {F} = [C] {E} where: {F} : Vector of Force and Moment Resultants [C] : Laminate Stiffness Matrix {E} : Vector of MidPlane Deformations A new set of Force and Moment Resultants for the Beam are defined as: 9
10 Steps Followed for the Derivation The strain energy per unit area of the laminate : The strain energy per unit length of the beam : The Strain Energy in the Beam : The Principle of Minimum Potential Energy is applied to derive the Equilibrium equations and Boundary conditions. Force and Moment resultants t are substituted t in the differential equations of Equilibrium in terms of displacement variables to obtain differential equations of equilibrium. These differential equations are then solved for the particular case of a Cantilevered beam of Rectangular cross section subjected to end loads only. 10
11 Steps Followed for the Derivation Principle of Minimum Potential Energy According to the Principle of Minimum Potential energy, a structure or body shall deform or displace to a position that minimizes i i the total potential energy. The total potential energy,, is the sum of the elastic strain energy,, stored in the deformed body and the potential energy,,of the applied forces. 11
12 Torsion of Specially Orthotropic Laminated Beams Specially Orthotropic Laminated Beams: The property of Specially Orthotropic Laminated Beams used for this derivation is that they have no coupling effects. i.e. Coupling Matrix [B] = 0, A 16 = A 26 = D 16 = D 26 = 0 Actually Specially orthotropic Laminates is another name given to Symmetric Balanced Laminates. For a Specially Orthotropic Cantilever Beam Subjected to an End Torque T, Angle of Twist ( ) is derived as: where: ; ; 12
13 Results For the purpose of comparison with available results we introduce a Nondimensional tip Rotation defined as: So our solution for the tip rotation takes the form: The first term on the right corresponds to classical theory solution for isotropic beams. The shear deformations effects are reflected in the second and third term The third term represents the effect of restrained end at x=0, where warping is prevented. In Figure 2, is plotted as a function of. It shows that restrained end effects are only felt for. Further, the restrained effects are less pronounced as the ratio increases. 13
14 Figure 2: Results The results obtained can be compared with 2 available results: 1. If we ignore shear deformation i.e. let : This result is identical for an isotropic beam (Boresi, Sidebottom, Seely and Smith, 1978) 2. If we ignore the restrained end effects by letting : This result can be compared with that of (Tsai, Daniel and Yaniv, 1990) for a 0 0 Unidirectional Composite Beam. The Maximum difference between the results is about 11% 14
15 Conclusions A beam theory for Laminated Composites has been derived. A closed form solution is derived for the problem of Torsion of a Specially Laminated Orthotropic Laminate. The result for Angle of Twist compare well with available soultions. 15
16 References B.V. Sankar (1993) "A Beam Theory for Laminated Composites and Application to Torsion Problems", Journal of Applied Mechanics, 60(1):
Bending 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 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 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 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 informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. BernoulliEuler Beams.
More informationFlexure of Thick Cantilever Beam using Third Order Shear Deformation Theory
International Journal of Engineering Research and Development eissn: 7867X, pissn: 788X, www.ijerd.com Volume 6, Issue 1 (April 13), PP. 914 Fleure of Thick Cantilever Beam using Third Order Shear
More informationFinite element modelling of structural mechanics problems
1 Finite element modelling of structural mechanics problems Kjell Magne Mathisen Department of Structural Engineering Norwegian University of Science and Technology Lecture 10: Geilo Winter School  January,
More informationChapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements
CIVL 7/8117 Chapter 12  Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module  01 Lecture  11
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Module  01 Lecture  11 Last class, what we did is, we looked at a method called superposition
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 informationDue Monday, September 14 th, 12:00 midnight
Due Monday, September 14 th, 1: midnight This homework is considering the analysis of plane and space (3D) trusses as discussed in class. A list of MatLab programs that were discussed in class is provided
More informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
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 informationEE C245 ME C218 Introduction to MEMS Design
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy
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 informationGeneric Strategies to Implement Material Grading in Finite Element Methods for Isotropic and Anisotropic Materials
University of Nebraska  Lincoln DigitalCommons@University of Nebraska  Lincoln Engineering Mechanics Dissertations & Theses Mechanical & Materials Engineering, Department of Winter 1292011 Generic
More information7.4 The Elementary Beam Theory
7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be
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 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 informationEFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING
Journal of MECHANICAL ENGINEERING Strojnícky časopis, VOL 67 (217), NO 1, 522 EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Arnab Choudhury 1,
More informationA Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers H. Ozbasaran
Vol:8, No:7, 214 A Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers H. Ozbasaran Abstract IPN and IPE sections, which are commonly used European I shapes, are widely used
More informationMacaulay s method for a Timoshenko beam
Macaulay s method for a Timoshenko beam N. G. Stephen School of Engineering Sciences, Mechanical Engineering, University of Southampton, Highfield, Southampton SO7 BJ, UK Email: ngs@soton.ac.uk Abstract
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 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 informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationFlexural Analysis of Deep Aluminum Beam
Journal of Soft Computing in Civil Engineering 1 (018) 7184 journal homepage: http://www.jsoftcivil.com/ Fleural Analysis of Deep Aluminum Beam P. Kapdis 1, U. Kalwane 1, U. Salunkhe 1 and A. Dahake
More information4. SHAFTS. A shaft is an element used to transmit power and torque, and it can support
4. SHAFTS A shaft is an element used to transmit power and torque, and it can support reverse bending (fatigue). Most shafts have circular cross sections, either solid or tubular. The difference between
More informationIntroduction to Finite Element Method. Dr. Aamer Haque
Introduction to Finite Element Method 4 th Order Beam Equation Dr. Aamer Haque http://math.iit.edu/~ahaque6 ahaque7@iit.edu Illinois Institute of Technology July 1, 009 Outline EulerBernoulli Beams Assumptions
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 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 informationMechanics of Materials and Structures
Journal of Mechanics of Materials and Structures EXACT CLOSEDFORM SOLUTION OF THE DYNAMIC COUPLED THERMOELASTIC RESPONSE OF A FUNCTIONALLY GRADED TIMOSHENKO BEAM Mostafa Abbasi, Mehdy Sabbaghian and M.
More informationBUTT SPLICE HINGING. KEVIN COLE, PhD Senior Web Handling Development Engineer Optimation Technology Incorporated
BUTT SPLICE HINGING BY KEVIN COLE, PhD Senior Web Handling Development Engineer Optimation Technology Incorporated Introduction Splicing is a process used to join the tail of an expiring roll to the start
More informationUnit 15 Shearing and Torsion (and Bending) of Shell Beams
Unit 15 Shearing and Torsion (and Bending) of Shell Beams Readings: Rivello Ch. 9, section 8.7 (again), section 7.6 T & G 126, 127 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering
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 informationBeam Models. Wenbin Yu Utah State University, Logan, Utah April 13, 2012
Beam Models Wenbin Yu Utah State University, Logan, Utah 8434130 April 13, 01 1 Introduction If a structure has one of its dimensions much larger than the other two, such as slender wings, rotor blades,
More informationInfluence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes
October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:
More informationFlexuralTorsional Buckling of General ColdFormed Steel Columns with Unequal Unbraced Lengths
Proceedings of the Annual Stability Conference Structural Stability Research Council San Antonio, Texas, March 2124, 2017 FlexuralTorsional Buckling of General ColdFormed Steel Columns with Unequal
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of aterials Science and Engineering A 6 (12) (2016) 3542 doi: 10.17265/21616213/2016.12.005 D DAVID PUBLISHIG Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K
More informationCOURSE STE6289 Modern Materials and Computations (Moderne materialer og beregninger 7.5 stp.)
Narvik University College (Høgskolen i Narvik) EXAMINATION TASK COURSE STE6289 Modern Materials and Computations (Moderne materialer og beregninger 7.5 stp.) CLASS: Master students in Engineering Design
More informationModule 3. Analysis of Statically Indeterminate Structures by the Displacement Method
odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 14 The SlopeDeflection ethod: An Introduction Introduction As pointed out earlier, there are two distinct methods
More informationGyroscopic matrixes of the straight beams and the discs
Titre : Matrice gyroscopique des poutres droites et des di[...] Date : 29/05/2013 Page : 1/12 Gyroscopic matrixes of the straight beams and the discs Summarized: This document presents the formulation
More informationSeismic design of bridges
NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour
More informationFree Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation Method. Eric A. Butcher and Ma en Sari
Free Vibration Analysis of Kirchoff Plates with Damaged Boundaries by the Chebyshev Collocation Method Eric A. Butcher and Ma en Sari Department of Mechanical and Aerospace Engineering, New Mexico State
More informationFor more Stuffs Visit Owner: N.Rajeev. R07
Code.No: 43034 R07 SET1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH  I SEMESTER REGULAR EXAMINATIONS NOVEMBER, 2009 FOUNDATION OF SOLID MECHANICS (AERONAUTICAL ENGINEERING) Time: 3hours
More informationDEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS
DEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS THE INFLUENCE OF THE FORM OF A WOODEN BEAM ON ITS STIFFNESS AND STRENGTHI (REPRINT FROM NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS REPORT
More informationModule 10: Free Vibration of an Undampened 1D Cantilever Beam
Module 10: Free Vibration of an Undampened 1D Cantilever Beam Table of Contents Page Number Problem Description Theory Geometry 4 Preprocessor 6 Element Type 6 Real Constants and Material Properties 7
More informationVIBRATION AND ACOUSTIC PERFORMANCE OF INPLANE HONEYCOMB SANDWICH PANELS
Clemson University TigerPrints All Theses Theses 801 VIBRATION AND ACOUSTIC PERFORMANCE OF INPLANE HONEYCOMB SANDWICH PANELS Xiao Gong Clemson University, xiaog@clemson.edu Follow this and additional
More informationGeometrydependent MITC method for a 2node isobeam element
Structural Engineering and Mechanics, Vol. 9, No. (8) 33 Geometrydependent MITC method for a node isobeam element PhillSeung Lee Samsung Heavy Industries, Seocho, Seoul 37857, Korea HyuChun Noh
More informationUSER BULLETIN 3: DETERMINATION OF UNSUPPORTED LENGTH RATIO L/Db
USER BULLETIN 3: DETERMINATION OF UNSUPPORTED LENGTH RATIO L/Db The unsupported length ratio (L/Db) is calculated by the automatic Sectional modeler spreadsheet using Dhakal and Maekawa [1]. This method
More informationME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2)
ME 582 Advanced Materials Science Chapter 2 Macromechanical Analysis of a Lamina (Part 2) Laboratory for Composite Materials Research Department of Mechanical Engineering University of South Alabama, Mobile,
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 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 informationDavid A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan
Session: ENG 03091 Deflection Solutions for Edge Stiffened Plates David A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan david.pape@cmich.edu Angela J.
More informationSteel Post Load Analysis
Steel Post Load Analysis Scope The steel posts in 73019022, 73019024, and 73019025, are considered to be traditional building products. According to the 2015 International Building Code, this type of product
More informationStructural Analysis III Compatibility of Displacements & Principle of Superposition
Structural Analysis III Compatibility of Displacements & Principle of Superposition 2007/8 Dr. Colin Caprani, Chartered Engineer 1 1. Introduction 1.1 Background In the case of 2dimensional structures
More informationBending Analysis of a Cantilever Nanobeam With End Forces by Laplace Transform
International Journal of Engineering & Applied Sciences (IJEAS) Vol.9, Issue (Special Issue: Composite Structures) (07) 03 http://.doi.org/0.407/ijeas.34635 Int J Eng Appl Sci 9() (07) 03 Bending Analysis
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 informationThesis. Submitted to. The School of Engineering of the UNIVERSITY OF DAYTON. In Partial Fulfillment of the Requirements for.
FLEXURAL ANALYSIS AND COMPOSITE BEHAVIOR OF PRECAST CONCRETE SANDWICH PANEL Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The
More informationEE C245 ME C218 Introduction to MEMS Design Fall 2010
EE C245 ME C218 Introduction to MEMS Design Fall 2010 Prof. Clark T.C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture EE C245:
More informationContinuum mechanics of beamlike structures using onedimensional finite element based on Serendipity Lagrange crosssectional discretisation, Mayank Patni, Prof. Paul Weaver, Dr Alberto Pirrera Bristol
More informationMethod of elastic line
Method of elastic line To study the method of elastic line we shall first consider a beam of infinite length with a constant cross section (fig. 5.34). This beam rests on elastic soil and the deflection
More informationAn Evaluation and Comparison of Models for Maximum Deflection of Stiffened Plates Using Finite Element Analysis
Marine Technology, Vol. 44, No. 4, October 2007, pp. 212 225 An Evaluation and Comparison of Models for Maximum Deflection of Stiffened Plates Using Finite Element Analysis Lior Banai 1 and Omri Pedatzur
More informationInternational Journal of Advanced Engineering Technology EISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationTHE BENDING STIFFNESSES OF CORRUGATED BOARD
AMDVol. 145/MDVol. 36, Mechanics of Cellulosic Materials ASME 1992 THE BENDING STIFFNESSES OF CORRUGATED BOARD S. Luo and J. C. Suhling Department of Mechanical Engineering Auburn University Auburn,
More informationTorsional Analysis of
Steel Design Guide Series Torsional Analysis of Structured Steel Members Steel Design Guide Series Torsional Analysis of Structural Steel Members Paul A. Seaburg, PhD, PE Head, Department of Architectural
More informationC:\Users\whit\Desktop\Active\304_2012_ver_2\_Notes\4_Torsion\1_torsion.docx 6
C:\Users\whit\Desktop\Active\304_2012_ver_2\_Notes\4_Torsion\1_torsion.doc 6 p. 1 of Torsion of circular bar The crosssections rotate without deformation. The deformation that does occur results from
More informationNATURAL FREQUENCIES OF A HONEYCOMB SANDWICH PLATE Revision F. A diagram of a honeycomb plate crosssection is shown in Figure 1.
NATURAL FREQUENCIES OF A HONEYCOMB SANDWICH PLATE Revision F By Tom Irvine Email: tomirvine@aol.com August 5, 008 Bending Stiffness of a Honeycomb Sandwich Plate A diagram of a honeycomb plate crosssection
More informationSLOPEDEFLECTION METHOD
SLOPEDEFLECTION ETHOD The slopedeflection method uses displacements as unknowns and is referred to as a displacement method. In the slopedeflection method, the moments at the ends of the members are
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 informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationChapter 2  Macromechanical Analysis of a Lamina. Exercise Set. 2.1 The number of independent elastic constants in three dimensions are: 2.
Chapter  Macromechanical Analysis of a Lamina Exercise Set. The number of independent elastic constants in three dimensions are: Anisotropic Monoclinic 3 Orthotropic 9 Transversely Orthotropic 5 Isotropic.
More informationChapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )
Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress
More informationSample Problems for Exam II
Sample Problems for Exam 1. Te saft below as lengt L, Torsional stiffness GJ and torque T is applied at point C, wic is at a distance of 0.6L from te left (point ). Use Castigliano teorem to Calculate
More informationLAMINATED COMPOSITE PLATES
LAMINATED COMPOSITE PLATES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 February 10, 2000 Introduction This document is intended
More informationDynamic Model of a Badminton Stroke
ISEA 28 CONFERENCE Dynamic Model of a Badminton Stroke M. Kwan* and J. Rasmussen Department of Mechanical Engineering, Aalborg University, 922 Aalborg East, Denmark Phone: +45 994 9317 / Fax: +45 9815
More informationINTRODUCTION TO PIEZO TRANSDUCERS
PIEZO SYSTEMS, INC. 65 Tower Office Park Woburn, MA 01801 USA Tel: 781 933 4850 Fax: 781 933 4743 email: sales@piezo.com Find Search for a product or category HOME PRODUCTS CUSTOM OEM CATALOG TECHNICAL
More informationAalto University School of Engineering
Aalto University School of Engineering Kul4.4 Ship Structural Design (P) ecture 6  Response of Webframes, Girders and Grillages Kul4.4 Ship Structures Response ecture 5: Tertiary Response: Bending
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 informationTHE EFFECT OF FIBER ORIENTATION AND LAMINATE STACKING SEQUENCES ON THE TORSIONAL NATURAL FREQUENCIES OF LAMINATED COMPOSITE BEAMS
IJRET: International Journal of Research in Engineering and Technology eissn: 3191163 pissn: 317308 THE EFFECT OF FIBER ORIENTATION AND LAMINATE STACKING SEQUENCES ON THE TORSIONAL NATURAL FREQUENCIES
More information11 Locate the centroid of the plane area shown. 12 Determine the location of centroid of the composite area shown.
Chapter 1 Review of Mechanics of Materials 11 Locate the centroid of the plane area shown 650 mm 1000 mm 650 x 1 Determine the location of centroid of the composite area shown. 00 150 mm radius 00 mm
More informationMINIMUM WEIGHT STRUCTURAL SANDWICH
U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WIS. In Cooperation with the University of Wisconsin U.S.D.A. FOREST SERVICE RESEARCH NOTE Revised NOVEMBER 1970 MINIMUM
More informationDYNAMIC ANALYSIS OF CANTILEVER BEAM AND ITS EXPERIMENTAL VALIDATION
DYNAMIC ANALYSIS OF CANTILEVER BEAM AND ITS EXPERIMENTAL VALIDATION A Thesis submitted in partial fulfillment of the requirements for the Degree of Bachelor of Technology In Mechanical Engineering By Subhransu
More informationEXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFFAXIS GFRP LAMINATES
20 th International Conference on Composite Materials Copenhagen, 1924 th July 2015 EXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFFAXIS GFRP LAMINATES Esben Lindgaard 1 and Brian
More informationGerald Allen Cohen, 83, passed away Oct. 1, 2014, at his home in Laguna Beach.
Dr Gerald Allen Cohen (19312014) Ringstiffened shallow conical shell designed with the use of FASOR for NASA s Viking project in the 1970s. (from NASA TN D7853, 1975, by Walter L. Heard, Jr., Melvin
More informationNonlocal material properties of single walled carbon nanotubes
Nonlocal material properties of single walled carbon nanotubes J. V. Araújo dos Santos * and C. M. Mota Soares IDMEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal Av. Rovisco Pais,
More informationDynamic Stability of Uncertain Laminated Beams Subjected to Subtangential Loads
Dynamic Stability of Uncertain Laminated Beams Subjected to Subtangential Loads by Vijay Kumar Goyal Dissertation submmitted to the Faculty of Virginia Polytechnic Institute and State University in partial
More information6.1 Formulation of the basic equations of torsion of prismatic bars (St. Venant) Figure 6.1: Torsion of a prismatic bar
Module 6 Torsion Learning Objectives 6.1 Formulation of the basic equations of torsion of prismatic bars (St. Venant) Readings: Sadd 9.3, Timoshenko Chapter 11 e e 1 e 3 Figure 6.1: Torsion of a prismatic
More informationACCURATE FREE VIBRATION ANALYSIS OF POINT SUPPORTED MINDLIN PLATES BY THE SUPERPOSITION METHOD
Journal of Sound and Vibration (1999) 219(2), 265 277 Article No. jsvi.1998.1874, available online at http://www.idealibrary.com.on ACCURATE FREE VIBRATION ANALYSIS OF POINT SUPPORTED MINDLIN PLATES BY
More informationNonlinear Response of Functionally Graded Panels with stiffeners in Supersonic Flow
ASDJournal (2017), Vol. 5, No. 1, pp. 1 16 1 Nonlinear Response of Functionally Graded Panels with stiffeners in Supersonic Flow (Received: September 24, 2016. Revised: October 26, 2016. Accepted: January
More informationKirchhoff Plates: Field Equations
20 Kirchhoff Plates: Field Equations AFEM Ch 20 Slide 1 Plate Structures A plate is a three dimensional bod characterized b Thinness: one of the plate dimensions, the thickness, is much smaller than the
More informationDesign of reinforced concrete sections according to EN and EN
Design of reinforced concrete sections according to EN 199211 and EN 19922 Validation Examples Brno, 21.10.2010 IDEA RS s.r.o. South Moravian Innovation Centre, U Vodarny 2a, 616 00 BRNO tel.: +420511
More informationBeam Bending Stresses and Shear Stress
Beam Bending Stresses and Shear Stress Notation: A = name or area Aweb = area o the web o a wide lange section b = width o a rectangle = total width o material at a horizontal section c = largest distance
More information7.5 Elastic Buckling Columns and Buckling
7.5 Elastic Buckling The initial theory of the buckling of columns was worked out by Euler in 1757, a nice example of a theory preceding the application, the application mainly being for the later invented
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads
More information2
Analysis of Laminated Structures Course of Lectures Rolands Rikards Riga Technical University Riga, 1999 2 Preface Among the modern structural materials, the history of ber reinforced composites is only
More informationNow we are going to use our free body analysis to look at Beam Bending (W3L1) Problems 17, F2002Q1, F2003Q1c
Now we are going to use our free body analysis to look at Beam Bending (WL1) Problems 17, F00Q1, F00Q1c One of the most useful applications of the free body analysis method is to be able to derive equations
More informationMECHANICAL PROPERTIES OF SOLIDS
Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small nonzero constant value. 9. The maximum load a wire
More informationdv dx Slope of the shear diagram =  Value of applied loading dm dx Slope of the moment curve = Shear Force
Beams SFD and BMD Shear and Moment Relationships w dv dx Slope of the shear diagram =  Value of applied loading V dm dx Slope of the moment curve = Shear Force Both equations not applicable at the point
More informationFLEXURE OF STRUCTURAL SANDWICH CONSTRUCTION
FLEXURE OF STRUCTURAL SANDWICH CONSTRUCTION December 1951 INFORMATION REVIEWED AND REAFFIRMED 1958 LOAN COPY Please return to: Wood Engineering Research Forest Products Laboratory Madison, Wisconsin 53705
More information(laod No \' V,R A " FI 1 4, <4. ELASTIC STABILITY Of CYLINDRICAL SANDWICH SHELLS UNDER AXIAL AND LATERAL LOAD. July 1955
ELASTIC STABILITY Of CYLIDRICAL SADWICH SHELLS UDER AXIAL AD LATERAL LOAD (laod o. 1852 July 1955 This Report is One of a Series Issued ha Cooperation with the AC23 PAEL O SADWICH COSTRUCTIO of the Departments
More information