five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture


 Francis Lawrence
 1 years ago
 Views:
Transcription
1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics of materials Mechanics of Materials 1
2 Mechanics of Materials MECHANICS MATERIALS Mechanics of Materials 2
3 Mechanics of Materials external loads and their effect on deformable bodies use it to answer question if structure meets requirements of stability and equilibrium strength and stiffness other principle building requirements economy, functionality and aesthetics Mechanics of Materials 3
4 Knowledge Required material properties member cross sections ability of a material to resist breaking structural elements that resist excessive deflection deformation Mechanics of Materials 4
5 Problem Solving 1. STATICS: equilibrium of external forces, internal forces, stresses 2. GEOMETRY: cross section properties, deformations and conditions of geometric fit, strains 3. MATERIAL PROPERTIES: stressstrain relationship for each material obtained from testing Mechanics of Materials 5
6 Stress stress is a term for the intensity of a force, like a pressure internal or applied force per unit area P stress f A Mechanics of Materials 6
7 Design materials have a critical stress value where they could break or yield ultimate stress yield stress compressive stress fatigue strength (creep & temperature) acceptance vs. failure Mechanics of Materials 7
8 Design (cont) we d like f actual F allowable stress distribution may vary: average uniform distribution exists IF the member is loaded axially (concentric) Mechanics of Materials 8
9 Scale Effect model scale material weights by volume, small section areas structural scale much more material weight, bigger section areas scale for strength is not proportional: 3 L L 2 L Mechanics of Materials 9
10 Normal Stress (direct) normal stress is normal to the cross section stressed area is perpendicular to the load f t or c P A Mechanics of Materials 10
11 Shear Stress stress parallel to a surface P P f v ave A td Mechanics of Materials 11
12 Bearing Stress stress on a surface by contact in compression P P f p A td Mechanics of Materials 12
13 Bending Stress normal stress caused by bending Mc M f b I S Mechanics of Materials 13
14 Torsional Stress shear stress caused by twisting f v T J Mechanics of Materials 14
15 Structures and Shear what structural elements see shear? beams bolts splices slabs footings walls wind seismic loads connections V Mechanics of Materials 15
16 Bolts connected members in tension cause shear stress connected members in compression cause bearing stress Mechanics of Materials 16
17 Single Shear seen when 2 members are connected P P Mechanics of Materials 17 f v A d 2 4
18 Double Shear seen when 3 members are connected two areas F= f v P P P 2 2 2A A 2 d 4 Mechanics of Materials 18
19 Bolt Bearing Stress compression & contact projected area F= P P f p A projected td Mechanics of Materials 19
20 Strain materials deform axially loaded materials change length bending materials deflect STRAIN: change in length over length + UNITLESS Mechanics of Materials 20 strain L L
21 Shearing Strain deformations with shear parallelogram change in angles stress: strain: unitless (radians) s L s L tan Mechanics of Materials 21
22 Shearing Strain deformations with torsion twist change in angle of line stress: strain: unitless (radians) L Mechanics of Materials 22
23 Load and Deformation for stress, need P & A for strain, need & L how? TEST with load and measure plot P/A vs. Mechanics of Materials 23
24 Material Behavior every material has its own response 10,000 psi L = 10 in Douglas Fir vs. steel? Mechanics of Materials 24
25 Behavior Types ductile  necking true stress f engineering stress (simplified) f P A P A o Mechanics of Materials 25
26 Behavior Types brittle semibrittle Mechanics of Materials 26
27 Stress to Strain important to us in  diagrams: straight section LINEARELASTIC recovers shape (no permanent deformation) f Mechanics of Materials 27
28 Hooke s Law straight line has constant slope Hooke s Law f f E E E Modulus of elasticity Young s modulus units just like stress 1 Mechanics of Materials 28
29 Stiffness ability to resist strain f u steels same E different yield points different ultimate strength Mechanics of Materials 29
30 Isotropy & Anisotropy ISOTROPIC materials with E same at any direction of loading ex. steel ANISOTROPIC materials with different E at any direction of loading ex. wood is orthotropic Mechanics of Materials 30
31 Elastic, Plastic, Fatigue elastic springs back plastic has permanent deformation fatigue caused by reversed loading cycles Mechanics of Materials 31
32 Plastic Behavior ductile at yield stress Mechanics of Materials 32
33 Lateral Strain or what happens to the cross section with axial stress x f f y z f x E 0 strain in lateral direction negative equal for isometric materials y z Mechanics of Materials 33
34 Poisson s Ratio constant relationship between longitudinal strain and lateral strain lateral strain axial strain f x y z E y x z x sign! Mechanics of Materials 34
35 Calculating Strain from Hooke s law substitute f E P A E L get PL AE Mechanics of Materials 35
36 Orthotropic Materials nonisometric directional values of E and ex: plywood laminates polymer composites Mechanics of Materials 36
37 Stress Concentrations why we use f ave increase in stress at changes in geometry sharp notches holes corners Mechanics of Materials 37
38 Maximum Stresses if we need to know where max f and f v happen: F P 0 cos 1 f max A o 45 cos sin 0.5 Mechanics of Materials 38 f vmax P 2A o f 2 max
39 Maximum Stresses Mechanics of Materials 39
40 Deformation Relationships physical movement axially (same or zero) rotations from axial changes 20 kn aluminum steel relates to P PL AE Mechanics of Materials 40
41 Deformations from Temperature atomic chemistry reacts to changes in energy solid materials can contract with decrease in temperature can expand with increase in temperature linear change can be measured per degree Mechanics of Materials 41
42 Thermal Deformation  the rate of strain per degree UNITS :, F C length change: thermal strain: T T T T L no stress when movement allowed Mechanics of Materials 42
43 Coefficients of Thermal Expansion Material Mechanics of Materials 43 Coefficients () [in./in./f] Wood 3.0 x 106 Glass 4.4 x 106 Concrete 6.0 x 106 Cast Iron 6.1 x 106 Steel 6.5 x 106 Wrought Iron 6.7 x 106 Copper 9.3 x 106 Bronze 10.0 x 106 Brass 10.4 x 106 Aluminum 12.8 x 106
44 Stresses and Thermal Strains if thermal movement is restrained stresses are induced 1. bar pushes on supports 2. support pushes back 3. reaction causes internal stress P f E A L Mechanics of Materials 44
45 Superposition Method can remove a support to make it look determinant replace the support with a reaction enforce the geometry constraint Mechanics of Materials 45
46 Superposition Method total length change restrained to zero p sub: f PL AE PL AE constraint: P A P T T L 0 T T T E L 0 Mechanics of Materials 46
47 Design of Members beyond allowable stress... materials aren t uniform 100% of the time ultimate strength or capacity to failure may be different and some strengths hard to test for RISK & UNCERTAINTY f u P u A Mechanics of Materials 47
48 Factor of Safety accommodate uncertainty with a safety factor: allowable load ultimate load F. S with linear relation between load and stress: F. S ultimate load allowable load ultimate stress allowable stress Mechanics of Materials 48
49 Load and Resistance Factor Design loads on structures are not constant can be more influential on failure happen more or less often UNCERTAINTY R u D R D L R L R n  resistance factor  load factor for (D)ead & (L)ive load Mechanics of Materials 49
five mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS
RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SUMMER 2014 Mechanics o Materials MECHNICS MTERIS lecture ive mechanics o materials www.carttalk.com Mechanics o Materials 1 rchitectural
More informationtwo structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS
APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture two structural analysis (statics & mechanics) Analysis 1 Structural Requirements strength serviceability
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More information4.MECHANICAL PROPERTIES OF MATERIALS
4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stressstrain diagram
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
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 informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM1(15A01303) Year & Sem: IIB.Tech & ISem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
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 informationOutline. TensileTest Specimen and Machine. StressStrain Curve. Review of Mechanical Properties. Mechanical Behaviour
TensileTest Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress  true strain (flow curve) mechanical properties:  Resilience  Ductility  Toughness  Hardness A standard
More informationStrength of Material. Shear Strain. Dr. Attaullah Shah
Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume
More informationStressStrain Behavior
StressStrain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
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 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 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 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 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 informationChapter 26 Elastic Properties of Materials
Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic
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 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 informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
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 informationHow materials work. Compression Tension Bending Torsion
Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons () B. Neutral charge, i.e., # electrons = #
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 informationUnit M1.5 Statically Indeterminate Systems
Unit M1.5 Statically Indeterminate Systems Readings: CDL 2.1, 2.3, 2.4, 2.7 16.001/002  Unified Engineering Department of Aeronautics and Astronautics Massachusetts Institute of Technology LEARNING OBJECTIVES
More information1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.
Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
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 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 informationElastic Properties of Solid Materials. Notes based on those by James Irvine at
Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonineeducation.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationMECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I
MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I Engineering Mechanics Branch of science which deals with the behavior of a body with the state of rest or motion, subjected to the action of forces.
More informationMECH 344/X Machine Element Design
1 MECH 344/X Machine Element Design Time: M 14:4517:30 Lecture 2 Contents of today's lecture Introduction to Static Stresses Axial, Shear and Torsional Loading Bending in Straight and Curved Beams Transverse
More informationSolid Mechanics Homework Answers
Name: Date: Solid Mechanics Homework nswers Please show all of your work, including which equations you are using, and circle your final answer. Be sure to include the units in your answers. 1. The yield
More informationA concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0.
2011 earson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 8 1. 3 1. concrete cylinder having a a diameter of of 6.00
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 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 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 informationFCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering
FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress
More informationExperiment Two (2) Torsional testing of Circular Shafts
Experiment Two (2) Torsional testing of Circular Shafts Introduction: Torsion occurs when any shaft is subjected to a torque. This is true whether the shaft is rotating (such as drive shafts on engines,
More informationCivil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7
Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...
More informationPLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder
16 PLATE GIRDERS II 1.0 INTRODUCTION This chapter describes the current practice for the design of plate girders adopting meaningful simplifications of the equations derived in the chapter on Plate Girders
More informationMECHANICS OF MATERIALS
CHAPTER 2 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Lecture Notes: J. Walt Oler Texas Tech University Stress and Strain Axial Loading 2.1 An Introduction
More informationSTATICALLY INDETERMINATE STRUCTURES
STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal
More informationARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13
ARC241 Structural Analysis I Lecture 10: MM1.3 MM1.13 MM1.4) Analysis and Design MM1.5) Axial Loading; Normal Stress MM1.6) Shearing Stress MM1.7) Bearing Stress in Connections MM1.9) Method of Problem
More informationStructural Metals Lab 1.2. Torsion Testing of Structural Metals. Standards ASTM E143: Shear Modulus at Room Temperature
Torsion Testing of Structural Metals Standards ASTM E143: Shear Modulus at Room Temperature Purpose To determine the shear modulus of structural metals Equipment TiniusOlsen LoTorq Torsion Machine (figure
More informationCONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS
Chapter 9 CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS Figure 9.1: Hooke memorial window, St. Helen s, Bishopsgate, City of London 211 212 CHAPTR 9. CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS 9.1 Mechanical
More informationCOLUMNS: BUCKLING (DIFFERENT ENDS)
COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pinconnected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43
More information6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and
6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile
More informationSOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling.
SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. Find: Determine the value of the critical speed of rotation for the shaft. Schematic and
More informationMECH 401 Mechanical Design Applications
MECH 401 Mechanical Design Applications Dr. M. O Malley Master Notes Spring 008 Dr. D. M. McStravick Rice University Updates HW 1 due Thursday (11708) Last time Introduction Units Reliability engineering
More information22 Which of the following correctly defines the terms stress, strain and Young modulus? stress strain Young modulus
PhysicsndMathsTutor.com Which of the following correctly defines the terms stress, strain and Young modulus? 97/1/M/J/ stress strain Young modulus () x (area) (extension) x (original length) (stress) /
More informationBE Semester I ( ) Question Bank (MECHANICS OF SOLIDS)
BE Semester I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)
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 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 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 informationFailure in Flexure. Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas
Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE VIII Dr. Jason E. Charalambides Failure in Flexure!
More informationPressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials
Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials Pressure Vessels: In the previous lectures we have discussed elements subjected
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 informationChapter 1 Introduction Concept of Stress
hapter 1 Introduction oncept of Stress INTRODUTION Review of Statics xial Stress earing Stress Torsional Stress 14 6 ending Stress W W L Introduction 11 Shear Stress W W Stress and Strain L y y τ xy
More informationLab Exercise #3: Torsion
Lab Exercise #3: Prelab assignment: Yes No Goals: 1. To evaluate the equations of angular displacement, shear stress, and shear strain for a shaft undergoing torsional stress. Principles: testing of round
More informationBOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE 2 ND YEAR STUDENTS OF THE UACEG
BOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE ND YEAR STUDENTS OF THE UACEG Assoc.Prof. Dr. Svetlana LilkovaMarkova, Chief. Assist. Prof. Dimitar Lolov Sofia, 011 STRENGTH OF MATERIALS GENERAL
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 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 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 informationMECHANICS OF MATERIALS
Fifth SI Edition CHTER 1 MECHNICS OF MTERILS Ferdinand. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Introduction Concept of Stress Lecture Notes: J. Walt Oler Teas Tech University Contents
More informationGlossary Innovative Measurement Solutions
Glossary GLOSSARY OF TERMS FOR TRANSDUCERS, LOAD CELLS AND WEIGH MODULES This purpose of this document is to provide a comprehensive, alphabetical list of terms and definitions commonly employed in the
More informationtwo loads, forces and vectors ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2017 lecture ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2017 lecture two y x z loads, forces and vectors Forces 1 Structural Design planning preliminary structural configuration
More informationExternal Pressure... Thermal Expansion in unrestrained pipeline... The critical (buckling) pressure is calculated as follows:
External Pressure... The critical (buckling) pressure is calculated as follows: P C = E. t s ³ / 4 (1  ν ha.ν ah ) R E ³ P C = Critical buckling pressure, kn/m² E = Hoop modulus in flexure, kn/m² t s
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 informationDetermine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.
E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct
More informationFailure from static loading
Failure from static loading Topics Quiz /1/07 Failures from static loading Reading Chapter 5 Homework HW 3 due /1 HW 4 due /8 What is Failure? Failure any change in a machine part which makes it unable
More informationME 202 STRENGTH OF MATERIALS SPRING 2014 HOMEWORK 4 SOLUTIONS
ÇANKAYA UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 202 STRENGTH OF MATERIALS SPRING 2014 Due Date: 1 ST Lecture Hour of Week 12 (02 May 2014) Quiz Date: 3 rd Lecture Hour of Week 12 (08 May 2014)
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 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 informationMARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.
Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL
More informationFundamentals of Durability. Unrestricted Siemens AG 2013 All rights reserved. Siemens PLM Software
Fundamentals of Durability Page 1 Your single provider of solutions System simulation solutions 3D simulation solutions Testbased engineering solutions Engineering services  Deployment services Troubleshooting
More informationRigid pavement design
Rigid pavement design Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Overview 1 1.1 Modulus of subgrade reaction.......................... 2 1.2 Relative stiffness
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 postyield behaviour in one or more degrees of freedom. Hinges only
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 informationRoadway Grade = m, amsl HWM = Roadway grade dictates elevation of superstructure and not minimum free board requirement.
Example on Design of Slab Bridge Design Data and Specifications Chapter 5 SUPERSTRUCTURES Superstructure consists of 10m slab, 36m box girder and 10m Tgirder all simply supported. Only the design of Slab
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 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 informationDETAILED SYLLABUS FOR DISTANCE EDUCATION. Diploma. (Three Years Semester Scheme) Diploma in Architecture (DARC)
DETAILED SYLLABUS FOR DISTANCE EDUCATION Diploma (Three Years Semester Scheme) Diploma in Architecture (DARC) COURSE TITLE DURATION : Diploma in ARCHITECTURE (DARC) : 03 Years (Semester System) FOURTH
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending
EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:
More informationLecture 7, Foams, 3.054
Lecture 7, Foams, 3.054 Opencell foams StressStrain curve: deformation and failure mechanisms Compression  3 regimes  linear elastic  bending  stress plateau  cell collapse by buckling yielding
More informationRESEARCH PROJECT NO. 26
RESEARCH PROJECT NO. 26 DETERMINATION OF POISSON'S RATIO IN AD1 TESTING BY UNIVERSITY OF MICHIGAN REPORT PREPARED BY BELA V. KOVACS and JOHN R. KEOUGH \ MEMBER / / DUCTILE IRON \ SOCIETY Issued by the
More informationChapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson
STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. Elkashif Civil Engineering Department, University
More information**********************************************************************
Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 333 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235
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 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 informationDEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8  PART 3 PROVISIONS
DEFORMATION CAPACITY OF OLDER RC SHEAR WALLS: EXPERIMENTAL ASSESSMENT AND COMPARISON WITH EUROCODE 8  PART 3 PROVISIONS Konstantinos CHRISTIDIS 1, Emmanouil VOUGIOUKAS 2 and Konstantinos TREZOS 3 ABSTRACT
More informationStatic Equilibrium; Elasticity & Fracture
Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with
More informationMechanics of Materials
Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics
More informationSERVICEABILITY LIMIT STATE DESIGN
CHAPTER 11 SERVICEABILITY LIMIT STATE DESIGN Article 49. Cracking Limit State 49.1 General considerations In the case of verifications relating to Cracking Limit State, the effects of actions comprise
More informationChapter 13 ELASTIC PROPERTIES OF MATERIALS
Physics Including Human Applications 280 Chapter 13 ELASTIC PROPERTIES OF MATERIALS GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions
More informationREVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002
REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental
More informationLecture 8 Viscoelasticity and Deformation
HW#5 Due 2/13 (Friday) Lab #1 Due 2/18 (Next Wednesday) For Friday Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, μ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force
More information