E1. Column subjected to bending and axial action, Non-dissipative material
|
|
- Evelyn Bell
- 5 years ago
- Views:
Transcription
1 E1. Column subjected to bending and axial action, Non-dissipative material Problem definition In this exercise, calculate roughly the maximum load, due to the material behavior, of a column structure made of a common railway steel, as shown in the Figure below. s the Figure, indicates, the column structure is loaded in both axial and transversal directions. The cross section of the column is singly symmetric around the z-axis. Figure 1: Column problem considered, use H 10 h, b u h, b l h 3 and h 5mm in the assignment. Based in the Euler-Bernoulli beam theory, the uniaxial strain of each "beamfiber" can be expressed as a linear function in terms of the strain 0 due to the uniaxial elongation of the beam and the beam curvature. We thus obtain the linear relationship z 0 z Buwith B 1, z and u 0 where B is the strain displacement transformation and u is the generalized strain measure (comprising both the uniaxial strain and the curvature) of the cross section. The stress resultants of the beam consists of the bending moment and the axial force which are defined in the usual as h z N z b z z z h z M z z zb z z z where is the uniaxial stress. The material behavior is described by the experimentally determined cyclic stress-strain curve shown in the Figure below. In the present example we are not interested in the actual cyclic material behavior. Instead, we extract data from the first monotonic loading branch up to the uniaxial strain e=0.9%. non-linear elastic law, named the modified Ramberg-Osgood law, is used to pick up the material behavior. This law defines the non-linear elastic stress-strain relationship E 1 bs 0 n 1 n with 0 0 E
2 2 CE1.nb where the material parameters 0 and n have been used to calibrate the material parameters as shown in the Figure below. The material parameters in the elastic law are obtained after manual curve fitting as: MPa, n 2.66, with E MPa It may be shown that the tangent stiffness E t can be written as E t d d E 1 bs 0 n 1 n n Figure 1: Cyclic behavior of a typical railway steel in strain-controlled uniaxial test. Results taken from Johan hlström, Birger Karlsson, Wear 258, , (2005). s MPa e Figure 2: Non-linear elastic response of modified Ramberg-Osgood law, calibrated from the first branch of the experimental curve above. Exercise problems s alluded to in the problem definition, let us consider the assignment problems è Calculate roughly the maximum load of the column with respect to the non-linear material law. è Discuss possible deficiencies of the proposed material modelling. What will happen if the loading is removed? How about the behavior at cyclic loading? How can the residual stress state be modeled, etc.? è Extra problem (for those of you who are specially interested) consider the same analysis using the standard Ramberg-Osgood law written in a flexibility format as
3 CE1.nb 3 E 0 bs 0 n Sign s MPa e Figure 2: Non-linear elastic response of true Ramberg-Osgood law, calibrated from the first branch of the experimental curve shown above. The following paramters where used: MPa, n 11.2, E , 1, Numerical procedures ü Equilibrium condition The equilibrium conditions for the considered problem may be formulated as the balance relation of internal forces b u and external forces f t defined as g u b u f t 0 with b 1 z B t N u M u, f N 0 M 0 and u 0 where N u and M u are the stress resultants of the internal stress state in the cross section, and N 0 10 P t and M 0 P t H are the prescribed stress resultants due to equilibrium of the column in the Figure above. The problem is to find the total "displacement" (or total generalized strain measure) u 0, so that g u 0. To this end, the nonlinear solution strategy is used as discussed below. ü Spatial discretization of beam cross section In order to integrate numerically the stress resultants involved in the vectort b, the beam cross is discretized into "nlay" number of finite slabs z at distances z i from the geometrical center so that the stress resultants can the integrated numerically as b N M 1 nlay z 1 z z i b z i z i i i 1 where it is assumed that the stress z i is constant within each lamella z i. The adopted spatial discretization of the beam cross section is shown in the Figure below.
4 4 CE1.nb ü Non-linear solution strategy - Newton's method In order to solve the non-linear problem, let us consider the balance of internal and extermal forces for each given time step as g u b u f t 0 with u n u v t and t n 1 t where n u is the displacement from the previous time step n t and v is the "displacement" velocity pertinent to the current time step t n 1 t. For each time t n 1 t, consider the algorithm defined as: for each iterate i, evaluate the improved displacement increment i 1 from the Newton step t i K i 1 g n u i v t, i 1 v i v i 1 where K is the Jacobian (or tangent stiffness) matrix of the beam cross section. It is defined from the linearization dg u db u tkdv with K b u E t B t B The spatial discretization of the iteration matrix becomes and E t 1 K E t z z z 2 nlay E t z i i 1 1 z i z i z i 2 b z i z i ü Prelimimary results Preliminary result from the analyses are given the figures below in terms "bending moment" versus curvature and stress distribution aling the z-axis of the beam cross section. M t Bending moment versus curvature k t
5 CE1.nb 5
6 6 CE1.nb Implementation: Pseudo code ü Pseudo code of main module h 10; H 10 h; bu h; bl h ; 3 gp bl, bu, h ; geometry parameters array ; E ; n 2.66; mp E, 0, n ; material parameters array nlay 100; number of layers for integration of cross section dz h nlay ; cg 2bl bu h ; geometrical center of gravity 3 bl bu z Range dz,h, h cg; define vector with z values based on dz 2 nlay mtim 150; number of timesteps T 1; t T mtim; define time step size defining "displacement" increment P xx; M0 0; dm0 PH mtim; define bending moment and axialforce N0 0; dn0 10 P mtim; sig = Constantrray[0, nlay];(*zero initial continuum stress state*) = Constantrray[0, mtim];(*curvature for output*) u = {0, 0};(*total displacement*) v = {0, 0};(*displacement velocity*) Do[(*for all time steps {itim=1, mtim}*) {M0 = itim dm0; N0 = itim dn0;(*increment the load*) pra[mp, gp, t, nlay, z, dz, N0, M0];(*Evaluate stress state in cross section for given load N0, M0*) u += tv;(*update total displacement*) [itim] = u[2]}(*save curvature for data representation*), {itim, 1, mtim} ]
7 CE1.nb 7 ü Pseudo code of non-linear solver module pra mp, gp, t, nlay, zval, dz, N0, M0 : Module mite 10; 10 4 ; bl, bu, h gp; Do for all Newton iterations iite 1,mite S Constantrray 0, 2, 2 ; N 0; M 0; Do for all layers ilay 1,nlay z zval ilay ; sig ilay, E t praa mp, u tv,z ; Stress and tangent stiffness in layer sig ilay ; cg z bl cg h z bu b ; h N bdz;m zbdz; S t E t Outer Times, 1, z, 1, z dz b, ilay, 1, nlay ; g N N0, M M0 ; out of balance forces or residual error Norm g ; If iite 1, ref error ; reps error ;If reps, Break ; ref Inverse S.g; Evaluate the iterative improvement v ; update improved solution, iite, 1, mite ; ü Pseudo code of stress evaluation module praa mp,u,z : Module E, 0, n mp; 1, z.u; calculate total fiber strain at the actual layer 0 0 ; E ; establish the stress E t ; establish the tangent stiffness
Course in. Geometric nonlinearity. Nonlinear FEM. Computational Mechanics, AAU, Esbjerg
Course in Nonlinear FEM Geometric nonlinearity Nonlinear FEM Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity it continued
More informationSensitivity and Reliability Analysis of Nonlinear Frame Structures
Sensitivity and Reliability Analysis of Nonlinear Frame Structures Michael H. Scott Associate Professor School of Civil and Construction Engineering Applied Mathematics and Computation Seminar April 8,
More informationForce-based Element vs. Displacement-based Element
Force-based Element vs. Displacement-based Element Vesna Terzic UC Berkeley December 211 Agenda Introduction Theory of force-based element (FBE) Theory of displacement-based element (DBE) Examples Summary
More informationLarge Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties
Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties DR. ŞEREF DOĞUŞCAN AKBAŞ Civil Engineer, Şehit Muhtar Mah. Öğüt Sok. No:2/37, 34435 Beyoğlu- Istanbul,
More informationChapter 5 Structural Elements: The truss & beam elements
Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations
More informationEFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 1498 EFFECTS OF CONFINED CONCRETE MODELS ON SIMULATING RC COLUMNS UNDER LOW-CYCLIC LOADING Zongming HUANG
More informationSTRAIN ASSESSMENT USFOS
1 STRAIN ASSESSMENT IN USFOS 2 CONTENTS: 1 Introduction...3 2 Revised strain calculation model...3 3 Strain predictions for various characteristic cases...4 3.1 Beam with concentrated load at mid span...
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationNon-linear and time-dependent material models in Mentat & MARC. Tutorial with Background and Exercises
Non-linear and time-dependent material models in Mentat & MARC Tutorial with Background and Exercises Eindhoven University of Technology Department of Mechanical Engineering Piet Schreurs July 7, 2009
More informationBiaxial Analysis of General Shaped Base Plates
Biaxial Analysis of General Shaped Base Plates R. GONZALO ORELLANA 1 Summary: A linear model is used for the contact stresses calculation between a steel base plate and a concrete foundation. It is also
More informationM5 Simple Beam Theory (continued)
M5 Simple Beam Theory (continued) Reading: Crandall, Dahl and Lardner 7.-7.6 In the previous lecture we had reached the point of obtaining 5 equations, 5 unknowns by application of equations of elasticity
More informationUltralight Cellular Composite Materials with Architected Geometrical Structure. Maryam Tabatabaei and Satya N. Atluri
Ultralight Cellular Composite Materials with Architected Geometrical Structure Maryam Tabatabaei and Satya N. Atluri Center for Advanced Research in the Engineering Sciences Institute for Materials, Manufacturing,
More informationMethods of Analysis. Force or Flexibility Method
INTRODUCTION: The structural analysis is a mathematical process by which the response of a structure to specified loads is determined. This response is measured by determining the internal forces or stresses
More informationEsben Byskov. Elementary Continuum. Mechanics for Everyone. With Applications to Structural Mechanics. Springer
Esben Byskov Elementary Continuum Mechanics for Everyone With Applications to Structural Mechanics Springer Contents Preface v Contents ix Introduction What Is Continuum Mechanics? "I Need Continuum Mechanics
More informationNUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS
NUMERICAL SIMULATION OF THE INELASTIC SEISMIC RESPONSE OF RC STRUCTURES WITH ENERGY DISSIPATORS ABSTRACT : P Mata1, AH Barbat1, S Oller1, R Boroschek2 1 Technical University of Catalonia, Civil Engineering
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationDEVELOPMENT OF A CONTINUUM PLASTICITY MODEL FOR THE COMMERCIAL FINITE ELEMENT CODE ABAQUS
DEVELOPMENT OF A CONTINUUM PLASTICITY MODEL FOR THE COMMERCIAL FINITE ELEMENT CODE ABAQUS Mohsen Safaei, Wim De Waele Ghent University, Laboratory Soete, Belgium Abstract The present work relates to the
More informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationLecture 7: The Beam Element Equations.
4.1 Beam Stiffness. A Beam: A long slender structural component generally subjected to transverse loading that produces significant bending effects as opposed to twisting or axial effects. MECH 40: Finite
More informationElasto-plastic concrete beam analysis by 1-dimensional Finite Element Method
AALBORG UNIVERSITY MASTER S THESIS Elasto-plastic concrete beam analysis by 1-dimensional Finite Element Method Authors: Niels F. Overgaard Martin B. Andreasen Supervisors: Johan Clausen Lars V. Andersen
More informationMechanics PhD Preliminary Spring 2017
Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n
More information6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS
6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under in-plane loads. The displacement
More information3-dimensional joint torque calculation of compression sportswear using 3D-CG human model
3-dimensional joint torque calculation of compression sportswear using 3D-CG human model Akihiro Matsuda, University of Tsukuba Hirokazu Tanaka, University of Tsukuba Hitoshi Aoki, University of Tsukuba
More information7. Hierarchical modeling examples
7. Hierarchical modeling examples The objective of this chapter is to apply the hierarchical modeling approach discussed in Chapter 1 to three selected problems using the mathematical models studied in
More informationLecture notes Models of Mechanics
Lecture notes Models of Mechanics Anders Klarbring Division of Mechanics, Linköping University, Sweden Lecture 7: Small deformation theories Klarbring (Mechanics, LiU) Lecture notes Linköping 2012 1 /
More informationChapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship
Chapter 5 Elastic Strain, Deflection, and Stability Elastic Stress-Strain Relationship A stress in the x-direction causes a strain in the x-direction by σ x also causes a strain in the y-direction & z-direction
More informationInfluence of residual stress on the carrying-capacity of steel framed structures. Numerical investigation
Stability and Ductility of Steel Structures (SDSS'99) D.Dubina & M. Ivany (editors) Elsevier Science Pub. Pages 317-324 Influence of residual stress on the carrying-capacity of steel framed structures.
More informationLecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2
Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2 This semester we are going to utilize the principles we learnt last semester (i.e the 3 great principles and
More informationENGN2340 Final Project: Implementation of a Euler-Bernuolli Beam Element Michael Monn
ENGN234 Final Project: Implementation of a Euler-Bernuolli Beam Element Michael Monn 12/11/13 Problem Definition and Shape Functions Although there exist many analytical solutions to the Euler-Bernuolli
More informationNonlinear Modeling of Fiber-Reinforced Elastomers and the Response of a Rubber Muscle Actuator
Nonlinear Modeling of Fiber-Reinforced Elastomers and the Response of a Rubber Muscle Actuator Larry D. Peel, Ph.D.* Department of Mechanical & Industrial Engineering Texas A&M Univ. - Kingsville David
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, two-dimensional structural components of which
More informationThe CR Formulation: BE Plane Beam
6 The CR Formulation: BE Plane Beam 6 Chapter 6: THE CR FORMUATION: BE PANE BEAM TABE OF CONTENTS Page 6. Introduction..................... 6 4 6.2 CR Beam Kinematics................. 6 4 6.2. Coordinate
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems
The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems Prof. Dr. Eleni Chatzi Dr. Giuseppe Abbiati, Dr. Konstantinos Agathos Lecture 1-21 September, 2017 Institute of Structural Engineering
More informationLab Exercise #5: Tension and Bending with Strain Gages
Lab Exercise #5: Tension and Bending with Strain Gages Pre-lab assignment: Yes No Goals: 1. To evaluate tension and bending stress models and Hooke s Law. a. σ = Mc/I and σ = P/A 2. To determine material
More informationDecember 10, PROBLEM NO points max.
PROBLEM NO. 1 25 points max. PROBLEM NO. 2 25 points max. B 3A A C D A H k P L 2L Given: Consider the structure above that is made up of rod segments BC and DH, a spring of stiffness k and rigid connectors
More information. D CR Nomenclature D 1
. D CR Nomenclature D 1 Appendix D: CR NOMENCLATURE D 2 The notation used by different investigators working in CR formulations has not coalesced, since the topic is in flux. This Appendix identifies the
More informationUNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES
UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES A Thesis by WOORAM KIM Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the
More informationOn Nonlinear Buckling and Collapse Analysis using Riks Method
Visit the SIMULIA Resource Center for more customer examples. On Nonlinear Buckling and Collapse Analysis using Riks Method Mingxin Zhao, Ph.D. UOP, A Honeywell Company, 50 East Algonquin Road, Des Plaines,
More informationRole of Force Resultant Interaction on Ultra-High Performance Concrete
First International Interactive Symposium on UHPC 216 Role of Force Resultant Interaction on Ultra-High Performance Concrete Author(s) & Affiliation: Titchenda Chan (1), Kevin R. Mackie (1), and Jun Xia
More informationNUMERICAL SIMULATION OF STEEL CATENARY RISER
SIMMEC/EMMCOMP 214 XI Simpósio de Mecânica Computacional II Encontro Mineiro de Modelagem Computacional Juiz De Fora, MG, 28-3 de Maio De 214 NUMERICAL SIMULATION OF STEEL CATENARY RISER Marcus V. S. Casagrande
More informationStresses in Curved Beam
Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions:
More informationUnit 13 Review of Simple Beam Theory
MIT - 16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 10-15 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics
More information2D Kirchhoff Thin Beam Elements
2D Kirchhoff Thin Beam Elements General Element Name Y,v X,u BM3 2 3 1 Element Group Element Subgroup Element Description Number Of Nodes 3 Freedoms Node Coordinates Geometric Properties Kirchhoff Parabolically
More informationUnit 18 Other Issues In Buckling/Structural Instability
Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your leisure ) Ch. 15, Ch. 16 Theory of Elastic Stability
More information6. Bending CHAPTER OBJECTIVES
CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where
More informationComputational Inelasticity FHLN05. Assignment A non-linear elasto-plastic problem
Computational Inelasticity FHLN05 Assignment 2017 A non-linear elasto-plastic problem General instructions A written report should be submitted to the Division of Solid Mechanics no later than October
More informationNonlinear Static - 1D Plasticity - Isotropic and Kinematic Hardening Walla Walla University
Nonlinear Static - 1D Plasticity - Isotropic and Kinematic Hardening Walla Walla University Professor Louie L. Yaw c Draft date January 18, 2017 Copyright is reserved. Individual copies may be made for
More informationMATERIAL PROPERTIES. Material Properties Must Be Evaluated By Laboratory or Field Tests 1.1 INTRODUCTION 1.2 ANISOTROPIC MATERIALS
. MARIAL PROPRIS Material Properties Must Be valuated By Laboratory or Field ests. INRODUCION he fundamental equations of structural mechanics can be placed in three categories[]. First, the stress-strain
More informationGeneral method for simulating laboratory tests with constitutive models for geomechanics
General method for simulating laboratory tests with constitutive models for geomechanics Tomáš Janda 1 and David Mašín 2 1 Czech Technical University in Prague, Faculty of Civil Engineering, Czech Republic
More informationMODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Class Meeting #5: Integration of Constitutive Equations
MODELING OF CONCRETE MATERIALS AND STRUCTURES Kaspar Willam University of Colorado at Boulder Class Meeting #5: Integration of Constitutive Equations Structural Equilibrium: Incremental Tangent Stiffness
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 2-dimensional structures
More informationFinite Element Modelling with Plastic Hinges
01/02/2016 Marco Donà Finite Element Modelling with Plastic Hinges 1 Plastic hinge approach A plastic hinge represents a concentrated post-yield behaviour in one or more degrees of freedom. Hinges only
More informationComparison of Structural Models for Seismic Analysis of Multi-Storey Frame Buildings
Comparison of Structural Models for Seismic Analysis of Multi-Storey Frame Buildings Dj. Ladjinovic, A. Raseta, A. Radujkovic & R. Folic University of Novi Sad, Faculty of Technical Sciences, Novi Sad,
More informationSlender Structures Load carrying principles
Slender Structures Load carrying principles Basic cases: Extension, Shear, Torsion, Cable Bending (Euler) v017-1 Hans Welleman 1 Content (preliminary schedule) Basic cases Extension, shear, torsion, cable
More informationAdvanced Structural Analysis EGF Section Properties and Bending
Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear
More information1 Nonlinear deformation
NONLINEAR TRUSS 1 Nonlinear deformation When deformation and/or rotation of the truss are large, various strains and stresses can be defined and related by material laws. The material behavior can be expected
More informationENGN 2290: Plasticity Computational plasticity in Abaqus
ENGN 229: Plasticity Computational plasticity in Abaqus The purpose of these exercises is to build a familiarity with using user-material subroutines (UMATs) in Abaqus/Standard. Abaqus/Standard is a finite-element
More informationRigid Pavement Mechanics. Curling Stresses
Rigid Pavement Mechanics Curling Stresses Major Distress Conditions Cracking Bottom-up transverse cracks Top-down transverse cracks Longitudinal cracks Corner breaks Punchouts (CRCP) 2 Major Distress Conditions
More informationME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING
ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING PURPOSE 01 January 2000 / mgj The purpose of this exercise is to study the effects of end conditions, column length, and material properties
More informationMECHANICS OF MATERIALS
STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental
More informationIndeterminate Analysis Force Method 1
Indeterminate Analysis Force Method 1 The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Primary objective of the force method is to
More informationModule 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur
Module 11 Design of Joints for Special Loading Version ME, IIT Kharagpur Lesson Design of Eccentrically Loaded Welded Joints Version ME, IIT Kharagpur Instructional Objectives: At the end of this lesson,
More informationBoundary Nonlinear Dynamic Analysis
Boundary Nonlinear Dynamic Analysis Damper type Nonlinear Link Base Isolator type Nonlinear Link Modal Nonlinear Analysis : Equivalent Dynamic Load Damper type Nonlinear Link Visco-Elastic Damper (VED)
More informationLecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012
Lecture Slides Chapter 4 Deflection and Stiffness The McGraw-Hill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration
More informationAnalysis of a portal steel frame subject to fire by use of a truss model
Analysis of a portal steel frame subject to fire by use of a truss model P. G. Papadopoulos & A. Mathiopoulou Department of Civil Engineering, Aristotle University of Thessaloniki, Greece Abstract A plane
More informationVirtual Work and Variational Principles
Virtual Work and Principles Mathematically, the structural analysis problem is a boundary value problem (BVP). Forces, displacements, stresses, and strains are connected and computed within the framework
More informationGEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE
GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of Civil Engineering, IIT Bombay, Powai, Mumbai 400076, India. Tel.022-25767328 email: cejnm@civil.iitb.ac.in Module-13 LECTURE-
More informationNonlinear Theory of Elasticity. Dr.-Ing. Martin Ruess
Nonlinear Theory of Elasticity Dr.-Ing. Martin Ruess geometry description Cartesian global coordinate system with base vectors of the Euclidian space orthonormal basis origin O point P domain of a deformable
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 informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:
More informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationNonlinear static analysis PUSHOVER
Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC Structural
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 informationAppendix G Analytical Studies of Columns
Appendix G Analytical Studies of Columns G.1 Introduction Analytical parametric studies were performed to evaluate a number of issues related to the use of ASTM A103 steel as longitudinal and transverse
More informationGapping effects on the lateral stiffness of piles in cohesive soil
Gapping effects on the lateral stiffness of piles in cohesive soil Satyawan Pranjoto Engineering Geology, Auckland, New Zealand. M. J. Pender Department of Civil and Environmental Engineering, University
More informationComputational Inelasticity FHLN05. Assignment A non-linear elasto-plastic problem
Computational Inelasticity FHLN05 Assignment 2018 A non-linear elasto-plastic problem General instructions A written report should be submitted to the Division of Solid Mechanics no later than November
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 informationStructural Analysis. For. Civil Engineering.
Structural Analysis For Civil Engineering By www.thegateacademy.com ` Syllabus for Structural Analysis Syllabus Statically Determinate and Indeterminate Structures by Force/ Energy Methods; Method of Superposition;
More informationEDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d
Institute of Industrial Science, University of Tokyo Bulletin of ERS, No. 48 (5) A TWO-PHASE SIMPLIFIED COLLAPSE ANALYSIS OF RC BUILDINGS PHASE : SPRING NETWORK PHASE Shanthanu RAJASEKHARAN, Muneyoshi
More informationBending Stress. Sign convention. Centroid of an area
Bending Stress Sign convention The positive shear force and bending moments are as shown in the figure. Centroid of an area Figure 40: Sign convention followed. If the area can be divided into n parts
More informationModelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations
Modelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations W. Van Paepegem *, I. De Baere and J. Degrieck Ghent
More informationMEASURMENT OF BENDING PROPERTIES OF RHIZOPHORA TROPICAL WOOD. Sarawak, Malaysia. Engineering & Technology, Dhaka, Bangladesh
AJSTD Vol. 26 Issue 2 pp. 73-84 (2010) MEASURMENT OF BENDING PROPERTIES OF RHIZOPHORA TROPICAL WOOD Sinin Hamdan* a, Mahbub Hasan b and Yoann Nohe c a Faculty of Engineering, Universiti Malaysia Sarawak,
More informationA HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS
A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,
More informationEngineering Science OUTCOME 1 - TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1 - TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationFire Analysis of Reinforced Concrete Beams with 2-D Plane Stress Concrete Model
Research Journal of Applied Sciences, Engineering and Technology 5(2): 398-44, 213 ISSN: 24-7459; E-ISSN: 24-7467 Maxwell Scientific Organization, 213 Submitted: April 29, 212 Accepted: May 23, 212 Published:
More informationLecture 11: The Stiffness Method. Introduction
Introduction Although the mathematical formulation of the flexibility and stiffness methods are similar, the physical concepts involved are different. We found that in the flexibility method, the unknowns
More informationGEOMETRIC NONLINEAR ANALYSIS
GEOMETRIC NONLINEAR ANALYSIS The approach for solving problems with geometric nonlinearity is presented. The ESAComp solution relies on Elmer open-source computational tool [1] for multiphysics problems.
More informationInternational Journal of Advanced Engineering Technology E-ISSN
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 information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Problem Set
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 informationDynamic Analysis Contents - 1
Dynamic Analysis Contents - 1 TABLE OF CONTENTS 1 DYNAMIC ANALYSIS 1.1 Overview... 1-1 1.2 Relation to Equivalent-Linear Methods... 1-2 1.2.1 Characteristics of the Equivalent-Linear Method... 1-2 1.2.2
More informationCHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES
CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES 14.1 GENERAL REMARKS In structures where dominant loading is usually static, the most common cause of the collapse is a buckling failure. Buckling may
More informationSSNS106 Damage of a reinforced concrete plate under requests varied with model GLRC_DM
Titre : SSNS106 - Endommagement d une plaque plane sous so[...] Date : 01/03/2013 Page : 1/67 SSNS106 Damage of a reinforced concrete plate under requests varied with model GLRC_DM Summarized: This test
More informationFURTHER RESEARCH ON CHORD LENGTH AND BOUNDARY CONDITIONS OF CHS T- AND X-JOINTS
Advanced Steel Construction Vol. 6, No. 3, pp. 879-89 (1) 879 FURTHER RESEARCH ON CHORD LENGTH AND BOUNDARY CONDITIONS OF CHS T- AND X-JOINTS G.J. van der Vegte 1, * and Y. Makino 1 Delft University of
More informationME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.
ME 323 - Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2
More informationEffect Of Material Nonlinearity On Submarine Pipeline During Laying
Effect Of Material Nonlinearity On Submarine Pipeline During Laying Dr. Hakim Saeed Muhammed, Dr. Karim Radhi Obead, Anwar Sabah Abd Alameer Abstract: The main causes of nonlinearity are the large deformations
More informationPRACTICAL THREE-DIMENSIONAL EFFECTIVE STRESS ANALYSIS CONSIDERING CYCLIC MOBILITY BEHAVIOR
PRACTICAL THREE-DIMENSIONAL EFFECTIVE STRESS ANALYSIS CONSIDERING CYCLIC MOBILITY BEHAVIOR Hiroyuki Yoshida 1, Kohji Tokimatsu 2, Tatsuya Sugiyama 3 and Tadahiko Shiomi 4 1 Member, Arch. & Struct. Eng.
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M - N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More informationSoftware Verification
PROGRAM NAME: SAFE 014 EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 16-1 depicts a plot of the uncracked and cracked conditions, 1 State 1, and, State,
More information