CHAPTER MECHANICS OF MATERIALS


 Amanda Chambers
 1 years ago
 Views:
Transcription
1 CHPTER 4 Pure MECHNCS OF MTERLS Bending
2 Pure Bending Pure Bending Other Loading Tpes Smmetric Member in Pure Bending Bending Deformations Strain Due to Bending Stress Due to Bending Beam Section Properties Bending of Members Made of Several Materials Reinforced Concrete Beams Unsmmetric Bending 4 
3 MECHNCS OF MTERLS Pure Bending Pure Bending: Prismatic members subjected to equal and opposite couples acting in the same longitudinal plane 43
4 Pure/NonPure Bending 44
5 Other Loading Tpes Eccentric Loading: xial loading which does not pass through section centroid produces internal forces equivalent to an axial force and a couple Transverse Loading: Concentrated or distributed transverse load produces internal forces equivalent to a shear force and a couple Principle of Superposition: The normal stress due to pure bending ma be combined with the normal stress due to axial loading and shear stress due to shear loading to find the complete state of stress
6 Smmetric Member in Pure Bending nternal forces in a cross section are equivalent to a couple moment, i.e., the section bending moment. Couple moment is same about an axis perpendicular to the plane of the couple. Due to smmetr of loading and smmetr of crosssection, beam bends uniforml into arc of circle and plane sections remain plane. 46
7 Terminologies/ssumptions 47
8 Phsical meaning of assumptions. ssumption that plane sections remain plane and perpendicular to deflection curve after deformation implies shear strain γ = 0. Thus Hooke s law gives shear stress τ = 0. This is exactl true in pure bending (since no Shear force). f plane sections remain plane but not perpendicular to deflection curve after deformation, γ (hence τ ) is nonero but constant through depth (direction). f plane sections don t remain plane or perpendicular to deflection curve after deformation, γ (hence τ ) is nonero and varies through depth (direction). This is what we will obtain later when we find shear stresses. 48
9 Longitudinal Strain 49
10 Normal Stress 410
11 Resultant of Normal Stress Distribution 411
12 Resultant Force 41
13 Resultant Moment 413
14 Relationship between Bending Stress and Moment 414
15 rea Moments of nertia 415 d d d d d d d tan axes, principal i.e., 0, For sin sin cos sin cos sin cos sin d ; cos sin ; sin cos axes : Rotation of )d )( ( Similarl,. 0 d use expand,, d ) ( d axes : of Translation 0 d d so axes, centroidal are,, Here ; d ; d ; d C=centroid
16 rea centroids and rea Moments of nertia 416
17 rea centroids and rea Moments of nertia 417
18 Deformations in a Transverse Cross Section Recall: deformation due to bending moment M is quantified b curvature of neutral surface 1 x x E M E lthough cross sectional planes remain planar when subjected to bending moments, inplane deformations are nonero, x x So expansion occurs above neutral surface and contraction below it, causing inplane curvature, 1 anticlastic curvature 418
19 Section Modulii 419
20 Doubl Smmetric Shape Larger the section modulus lower the max normal stress Review Calculations of Centroid & for various crosssections ppendix, Beer and Johnston c h c d For two rectangular beams with same area, the one with larger depth is better S bh 6 h 6 40
21 Square Vs. Circular CrossSection 41
22 Design of Beams for Bending The largest normal stress is found at the surface where the maximum bending moment occurs. m M max c M max S Safe design requires that maximum normal stress be less than allowable stress for material used. This leads to determination of minimum acceptable section modulus. S m min all M max all mong beam section choices which have an acceptable section modulus, the one with smallest weight per unit length or cross sectional area will be least expensive and hence best choice. See ppendix C of BJ book. 5 
23 Design of Beams in Bending 43
24 Example 5.1 Castiron machine part, acted upon b 3 knm couple. E = 165 Gpa, neglect effects of fillets, determine (a) max tensile and compressive stresses, (b) radius of curvature. 44
25 Example 5.1 SOLUTON: Based on cross section geometr, calculate location of section centroid and moment of inertia. 1 rea, mm , mm 50 0, mm Y x mm 3 d 1 bh d mm m
26 Example 5.1 ppl the elastic flexural formula to find the maximum tensile and compressive stresses. m B Mc M c M c 3 kn m0.0m mm 3 kn m0.038m mm B B 76.0 MPa MPa Calculate the curvature 1 M E 3 kn m 165 GPa m m m 46
27 Example
28 MECHNCS OF MTERLS Example
29 MECHNCS OF MTERLS Example
30 MECHNCS OF MTERLS Example
31 Example 5.4 Simpl supported steel beam is to carr loads as shown. llowable normal stress for steel used is 160 Mpa. Select the wideflange shape that should be used (section properties of wide flange sections are given). 531
32 Example 5.4 Determine reactions at and D. M F D 0 D 58.0 kn kn 5m 60kN1.5m 50kN4m 58.0 kn 60kN 50kN Develop shear force diagram and determine maximum bending moment. V V V B B V 8kN 5.0 kn area under load curve 60kN Maximum bending moment occurs at V = 0 or x =.6 m. M max area under shear curve, to E 67.6 kn 53
33 Example 5.4 Determine minimum acceptable section modulus. S min M max all kn m 160MPa 6 m mm 3 Shape W W W W W S 10 3, 69, , , , , 5880 Choose best standard section which meets this criteria. W
34 Bending of Members Made of Several Materials Consider a composite beam formed from two materials with E 1 and E. Normal strain (still) varies linearl (cannot violate kinematics). x Piecewise linear normal stress variation. E E x E x E Neutral axis does not pass through section centroid of composite section. x 1 M x n x Elemental forces on the section are df E E d 1 d df d 1 d 1 Define a transformed section such that ne1 E1 E df d n d n E
35 lternate derivation  neutral axis for composite beam F n d 0 1 E 1 E 1 E 1 x1 d d E 1 E E x 1 d E 1 d d n E E 1 x1 d d E x d So neutral axis is centroid of 1 n Note: widening ( n 1 ) or narrowing ( n 1 ) done parallel to neutral axis, so that and hence remain unaltered. x 435
36 Example 5.5 SOLUTON: Transform to an equivalent cross section made entirel of (sa) brass Evaluate cross sectional properties of transformed section Calculate maximum stress in transformed section. This is the correct maximum stress for brass portion of the bar. Bar made from bonded pieces of steel (E s = 00 GPa) and brass (E b = 100 GPa). Determine maximum stress in steel and in brass when a moment of 4.5 KNm is applied. Determine the maximum stress in steel portion of b multipling maximum stress for transformed section b the modular ratio. Don t forget this important step!! 436
37 Example 5.5 SOLUTON: Transform to equivalent brass section. E n E b Evaluate transformed cross sectional properties T 10 mm 18 mm 10 mm 56 mm 1 1 s b b T h 00GPa 100GPa mm75 mm 6.0 mm Calculate maximum stresses m Mc Nm m m MPa b max m b 85.7 MPa max n 85.7 MPa MPa s max m s max 437
38 Reinforced Concrete Beams Concrete beams subjected to bending moments are reinforced b steel rods. The steel rods assumed to carr the entire tensile load below neutral axis (since concrete is weak in tension). Upper part of the concrete beam carries the compressive load. n the transformed section, cross sectional area of steel, s, replaced b equivalent area n s where n = E s /E c. To determine the location of the neutral axis, x bx n d x 0 s 1 b x n x n d s s The normal stress in the concrete and steel x c M x s n x
39 Example 5.6 Concrete floor slab reinforced with 16 mmdiameter steel rods. Modulus of elasticit is 00 GPa for steel and 5 GPa for concrete. pplied bending moment is 4.5 knm per 0.3 m width of slab. Find maximum stress in concrete and in steel
40 Example 5.6 SOLUTON: Transform to section made entirel of concrete. n n s E E s c GPa 5 GPa mm mm Evaluate geometric properties of transformed section. x 300x x 0 x 36.8mm mm 36.8mm 316mm 63. mm mm Check: F s = F c Calculate maximum stresses. Mc Nm0.0368m c m Mc 4500 Nm m s n m c s 9.9 MPa 17.61MPa 440
41 Example
42 Unsmmetric Bending Thus far analsis of pure bending limited to members subjected to bending couples acting in a plane of smmetr. Members remain smmetric and bend in the plane of smmetr. Neutral axis of cross section coincides/parallel with axis of couple Now consider situations in which bending couple does not act in a plane of smmetr. Cannot assume that member will bend in the plane of the couples. n general, neutral axis of section will not coincide with axis of couple. 44
43 Unsmmetric Bending 0 or 0 F xd x d E d neutral axis passes through centroid Wish to determine conditions under which neutral axis of section of arbitrar shape coincides with axis of couple, as shown above. M M or M E d E x, defines stress distribution moment of inertia Resultant force and moment from the stress distribution in the section must satisf: F x 0 M M M appliedcouple 0 M or 0 d x d product of So couple vector must be directed along a principal centroidal axis. M d inertia 443
44 Unsmmetric Bending Superposition applied to determine stresses in the most general case of unsmmetric bending. Resolve couple vector into components along principle centroidal axes. M M cos M M sin Superpose stresses due to M and M M x M long neutral axis we have, M cos sin tan tan M M M x
45 Example Nm couple applied to rectangular wooden beam in a plane at 30 deg. to vertical. Find (a) maximum stress in beam, (b) angle that neutral axis makes with horiontal plane
46 Example 5.7 Resolve couple vector along principal axes and calculate corresponding maximum stresses. M M 180 Nmcos Nmsin m0.09m 0.09 m0.04 m The largest tensile stress due to M Nm m.4310 The largest tensile stress due to M M M 90 Nm0.0 m Nm 90 Nm m m m m 4 4 occurs along.89 MPa occurs along 3.75 MPa Largest tensile stress due to combined M and M occurs at. B D max max MPa 446
47 Example 5.7 Determine angle of neutral axis m tan tan m.9 tan 30 o
48 MECHNCS OF MTERLS Example
49 Example
50 Example
51 General Case of Eccentric xial Loading Consider straight member subject to equal and opposite eccentric forces. Eccentric force equivalent to sstem comprising centric force and two couples. P M centric force Pa M Pb B principle of superposition, combined stress distribution is x P M M f neutral axis lies on section, it is found from P M M
52 Example 5.9 Openlink chain obtained b bending lowcarbon steel rods into shape shown. For 700 N load, find (a) maximum tensile and compressive stresses, (b) distance between section centroid and neutral axis 45
53 Example 5.9 Normal stress due to a centric load c mm P 6. MPa 6 mm 700 N m Equivalent centric load and bending moment P 700 N M Pd 11. Nm 700 N m Normal stress due to bending moment m mm 1 4 c Mc 4 66 MPa mm Nm m m
54 Example 5.9 Maximum tensile and compressive stresses t c m m t c 7. MPa 59.8MPa Neutral axis location P M0 0 P 0 M mm Pa Nm 1 m
55 Sample Problem 5.10 Largest allowable stresses for cast iron link are 30 MPa in tension and 10 MPa in compression. Determine largest force P which can be applied Y 0.038m m 9 m
56 Sample Problem 5.10 Determine equivalent centric load & bending moment. d m P centric load M Pd 0.08P bending moment Superpose stresses due to P and M, Mc P 0.08 P0.0 Evaluate critical loads for allowable stresses. B B P 377 P 1559P P Mc 310 P MPa 10MPa P P 79.6 kn P 77.0 kn P 1559P Largest allowable load is P 77.0 kn 456
57 MECHNCS OF MTERLS Example 5.11 lso locate N
58 Example
Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t
Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a loadcarrying
More informationStresses in Beam (Basic Topics)
Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and
More informationSection 16: Neutral Axis and Parallel Axis Theorem 161
Section 16: Neutral Axis and Parallel Axis Theorem 161 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about yaxis All parts
More informationLecture 4: Basic Review of Stress and Strain, Mechanics of Beams
MECH 466 Microelectromechanical Sstems Universit of Victoria Dept. of Mechanical Engineering Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams 1 Overview Compliant Mechanisms Basics of Mechanics
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following.
MECHANICS OF SOLIDS  BEAMS TUTOIAL 1 STESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS
MECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.
More informationBending of Beams with Unsymmetrical Sections
Bending of Beams with Unsmmetrical Sections Assume that CZ is a neutral ais. C = centroid of section Hence, if > 0, da has negative stress. From the diagram below, we have: δ = α and s = αρ and δ ε = =
More informationStructural Axial, Shear and Bending Moments
Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants
More informationThe following sketches show the plans of the two cases of oneway slabs. The spanning direction in each case is shown by the double headed arrow.
9.2 Oneway Slabs This section covers the following topics. Introduction Analysis and Design 9.2.1 Introduction Slabs are an important structural component where prestressing is applied. With increase
More informationSTRESSSTRAIN RELATIONS
STRSSSTRAIN RLATIONS Strain Strain is related to change in dimensions and shape of a material. The most elementar definition of strain is when the deformation is along one ais: change in length strain
More informationProblem 1: Computation of Reactions. Problem 2: Computation of Reactions. Problem 3: Computation of Reactions
Problem 1: Computation of Reactions Problem 2: Computation of Reactions Problem 3: Computation of Reactions Problem 4: Computation of forces and moments Problem 5: Bending Moment and Shear force Problem
More informationINTRODUCTION TO BEAMS
CHAPTER Structural Steel Design LRFD Method INTRODUCTION TO BEAMS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural Steel Design and Analysis
More informationReinforced Concrete Design SHEAR IN BEAMS
CHAPTER Reinforced Concrete Design Fifth Edition SHEAR IN BEAMS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part I Concrete Design and Analysis 4a FALL 2002 By Dr.
More informationTorsion Testing. Objectives
Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials
More informationOptimum proportions for the design of suspension bridge
Journal of Civil Engineering (IEB), 34 (1) (26) 114 Optimum proportions for the design of suspension bridge Tanvir Manzur and Alamgir Habib Department of Civil Engineering Bangladesh University of Engineering
More informationBending Stress in Beams
93673600 Bending Stress in Beams Derive a relationship for bending stress in a beam: Basic Assumptions:. Deflections are very small with respect to the depth of the beam. Plane sections before bending
More informationIntroduction, Method of Sections
Lecture #1 Introduction, Method of Sections Reading: 1:12 Mechanics of Materials is the study of the relationship between external, applied forces and internal effects (stress & deformation). An understanding
More informationSolid Mechanics. Stress. What you ll learn: Motivation
Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS
EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering
More informationDeflections. Question: What are Structural Deflections?
Question: What are Structural Deflections? Answer: The deformations or movements of a structure and its components, such as beams and trusses, from their original positions. It is as important for the
More information8.2 Elastic Strain Energy
Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS
MECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.
More informationObjectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.
Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity
More informationUnit 48: Structural Behaviour and Detailing for Construction. Chapter 13. Reinforced Concrete Beams
Chapter 13 Reinforced Concrete Beams Concrete is a material strong in its resistance to compression, but very weak indeed in tension. good concrete will safely take a stress upwards of 7 N/mm 2 in compression,
More informationENGINEERING COUNCIL CERTIFICATE LEVEL
ENGINEERING COUNCIL CERTIICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL  BASIC STUDIES O STRESS AND STRAIN You should judge your progress by completing the self assessment exercises. These may be sent
More informationAnalysis of Stresses and Strains
Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we
More informationMATERIALS AND MECHANICS OF BENDING
HAPTER Reinforced oncrete Design Fifth Edition MATERIALS AND MEHANIS OF BENDING A. J. lark School of Engineering Department of ivil and Environmental Engineering Part I oncrete Design and Analysis b FALL
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQF LEVEL 3 OUTCOME 2  STRESS AND STRAIN
EDEXCEL NATIONAL CERTIICATE/DIPLOMA URTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQ LEVEL 3 OUTCOME  STRESS AND STRAIN TUTORIAL 1  SHEAR CONTENT Be able to determine the stress in structural
More informationIntroduction to Mechanical Behavior of Biological Materials
Introduction to Mechanical Behavior of Biological Materials Ozkaya and Nordin Chapter 7, pages 127151 Chapter 8, pages 173194 Outline Modes of loading Internal forces and moments Stiffness of a structure
More informationENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those
More informationMECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN
MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES O STRESS AND STRAIN This tutorial is essential for anyone studying the group of tutorials on beams. Essential prerequisite knowledge
More informationIntroduction to Plates
Chapter Introduction to Plates Plate is a flat surface having considerabl large dimensions as compared to its thickness. Common eamples of plates in civil engineering are. Slab in a building.. Base slab
More informationSTRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION
Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general threedimensional solid deformable
More informationStatics and Mechanics of Materials
Statics and Mechanics of Materials Chapter 41 Internal force, normal and shearing Stress Outlines Internal Forces  cutting plane Result of mutual attraction (or repulsion) between molecules on both
More informationReinforced Concrete Design to BS8110 Structural Design 1 Lesson 5
Lesson 5: Deflection in reinforced concrete beams Content 4.1 Introduction 4. Definitions 4..1 Tension 4.. Compression 4.3 Initial sizing 4.3.1 Worked example 4.4 Reinforcement details 4.5 Anchorage at
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS
ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,
More informationCOMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN
COMPLX STRSS TUTORIAL COMPLX STRSS AND STRAIN This tutorial is not part of the decel unit mechanical Principles but covers elements of the following sllabi. o Parts of the ngineering Council eam subject
More informationsuperimposing the stresses and strains cause by each load acting separately
COMBINED LOADS In many structures the members are required to resist more than one kind of loading (combined loading). These can often be analyzed by superimposing the stresses and strains cause by each
More informationDESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,
DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared
More informationStress Strain Relationships
Stress Strain Relationships Tensile Testing One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. These properties relate the stresses to the
More informationMECHANICS OF MATERIALS
T dition CHTR MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University Stress and Strain xial oading  Contents Stress & Strain: xial oading
More informationBeam Deflections: SecondOrder Method
10 eam Deflections: SecondOrder Method 10 1 Lecture 10: EM DEFLECTIONS: SECONDORDER METHOD TLE OF CONTENTS Page 10.1 Introduction..................... 10 3 10.2 What is a eam?................... 10 3
More informationTechnical Notes 3B  Brick Masonry Section Properties May 1993
Technical Notes 3B  Brick Masonry Section Properties May 1993 Abstract: This Technical Notes is a design aid for the Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 40292) and Specifications
More informationThe Mathematics of Simple Beam Deflection
The Mathematics of Simple Beam Laing O Rourke Civil Engineering INTRODUCTION Laing O Rourke plc is the largest privately owned construction firm in the UK. It has offices in the UK, Germany, India, Australia
More informationAluminium systems profile selection
Aluminium systems profile selection The purpose of this document is to summarise the way that aluminium profile selection should be made, based on the strength requirements for each application. Curtain
More informationB.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) TermEnd Examination December, 2011 BAS010 : MACHINE DESIGN
No. of Printed Pages : 7 BAS01.0 B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) CV CA CV C:) O TermEnd Examination December, 2011 BAS010 : MACHINE DESIGN Time : 3 hours Maximum Marks : 70 Note : (1)
More informationDesign Analysis and Review of Stresses at a Point
Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to
More informationMechanics of Materials. Chapter 5 Stresses In Beams
Mechanics of Materials Chapter 5 Stresses In Beams 5.1 Introduction In previous chapters, the stresses in bars caused by axial loading and torsion. Here consider the third fundamental loading : bending.
More informationMCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements
MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.
More informationMECHANICAL BEHAVIOR OF REINFORCED CONCRETE BEAMCOLUMN ASSEMBLAGES WITH ECCENTRICITY
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 16, 2004 Paper No. 4 MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BEAMCOLUMN ASSEMBLAGES WITH ECCENTRICITY Tomohiko KAMIMURA
More information16. BeamandSlab Design
ENDP311 Structural Concrete Design 16. BeamandSlab Design BeamandSlab System How does the slab work? L beams and T beams Holding beam and slab together University of Western Australia School of Civil
More informationME111 Lecture 16 1. ME111 Instructor: Peter Pinsky Class #16 November 1, 2000
Toda s Topics ME111 Instructor: Peter Pinsk Class #16 November 1, 2000 Introduction to linear elastic fracture mechanics (LEFM). Problem 3 A centercracked plate of AII 1144 steel ( C = 115MPa m ) has
More informationDetailing of Reinforcment in Concrete Structures
Chapter 8 Detailing of Reinforcment in Concrete Structures 8.1 Scope Provisions of Sec. 8.1 and 8.2 of Chapter 8 shall apply for detailing of reinforcement in reinforced concrete members, in general. For
More informationNew approaches in Eurocode 3 efficient global structural design
New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beamcolumn FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural
More informationModule 3. Limit State of Collapse  Flexure (Theories and Examples) Version 2 CE IIT, Kharagpur
Module 3 Limit State of Collapse  Flexure (Theories and Examples) Lesson 4 Computation of Parameters of Governing Equations Instructional Objectives: At the end of this lesson, the student should be able
More informationShear Forces and Bending Moments
Chapter 4 Shear Forces and Bending Moments 4.1 Introduction Consider a beam subjected to transverse loads as shown in figure, the deflections occur in the plane same as the loading plane, is called the
More informationFinite Element Formulation for Beams  Handout 2 
Finite Element Formulation for Beams  Handout 2  Dr Fehmi Cirak (fc286@) Completed Version Review of EulerBernoulli Beam Physical beam model midline Beam domain in threedimensions Midline, also called
More informationCHAP 4 FINITE ELEMENT ANALYSIS OF BEAMS AND FRAMES INTRODUCTION
CHAP FINITE EEMENT ANAYSIS OF BEAMS AND FRAMES INTRODUCTION We learned Direct Stiffness Method in Chapter imited to simple elements such as D bars we will learn Energ Method to build beam finite element
More informationShaft Design. Shaft Design. Shaft Design Procedure. Chapter 12
Shaft Design Chapter 1 Material taken from Mott, 003, Machine Elements in Mechanical Design Shaft Design A shaft is the component of a mechanical device that transmits rotational motion and power. It is
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS
MECHANICS OF SOLIDS  BEAMS TUTORIAL THE DEECTION OF BEAMS This is the third tutorial on the bending of beams. You should judge your progress by completing the self assessment exercises. On completion
More informationMechanical Properties  Stresses & Strains
Mechanical Properties  Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =
More informationDesign of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column
Design of reinforced concrete columns Type of columns Failure of reinforced concrete columns Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend
More informationThe elements used in commercial codes can be classified in two basic categories:
CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for
More informationSECTION 3 DESIGN OF POST TENSIONED COMPONENTS FOR FLEXURE
SECTION 3 DESIGN OF POST TENSIONED COMPONENTS FOR FLEXURE DEVELOPED BY THE PTI EDC130 EDUCATION COMMITTEE LEAD AUTHOR: TREY HAMILTON, UNIVERSITY OF FLORIDA NOTE: MOMENT DIAGRAM CONVENTION In PT design,
More informationChapter 5 Bridge Deck Slabs. Bridge Engineering 1
Chapter 5 Bridge Deck Slabs Bridge Engineering 1 Basic types of bridge decks Insitu reinforced concrete deck (most common type) Precast concrete deck (minimize the use of local labor) Open steel grid
More informationDESIGN OF BEAMCOLUMNS  I
13 DESIGN OF BEACOLUNS  I INTRODUCTION Columns in practice rarely experience concentric axial compression alone. Since columns are usually parts of a frame, they experience both bending moment and axial
More informationF. P. Beer et al., Meccanica dei solidi, Elementi di scienza delle costruzioni, 5e  isbn 9788838668579, 2014 McGrawHill Education (Italy) srl
F. P. Beer et al., eccanica dei solidi, Elementi di scienza delle costruzioni, 5e  isbn 9788888579, 04 cgrawhill Education (Italy) srl Reactions: Σ = 0: bp = 0 = Pb Σ = 0: ap = 0 = Pa From to B: 0
More informationSTRUCTURAL DESIGN 2 RIBBED (JOIST), HOLLOW POT & WAFFLE SLAB DESIGN TO BS 8110
LECTURE 4: 1.0 RIBBED SLAB 1.0.1 INTRODUCTION 1.0.2 PRESENTATION OF RIBBED FLOOR PLAN 1.0.3 ADVANTAGES & DISADVANTAGES OF RIBBED SLAB 1.0.4 SIZING OF SLAB AND RIBS 1.0.5 DESIGN METHODOLOGY 1.0.6 SUMMARY
More informationREVIEW PROBLEMS & SOLUTIONS JAMES M. GERE BARRY J. GOODNO
REVIEW ROEMS & SOUTIONS JMES M. GERE RRY J. GOODNO ppendix FE Exam Review roblems R1.1: plane truss has downward applied load at joint and another load applied leftward at joint 5. The force in member
More informationHardened Concrete. Lecture No. 14
Hardened Concrete Lecture No. 14 Strength of Concrete Strength of concrete is commonly considered its most valuable property, although in many practical cases, other characteristics, such as durability
More informationMechanics of Materials Summary
Mechanics of Materials Summary 1. Stresses and Strains 1.1 Normal Stress Let s consider a fixed rod. This rod has length L. Its crosssectional shape is constant and has area. Figure 1.1: rod with a normal
More information4 Shear Forces and Bending Moments
4 Shear Forces and ending oments Shear Forces and ending oments 8 lb 16 lb roblem 4.31 alculate the shear force and bending moment at a cross section just to the left of the 16lb load acting on the simple
More informationSheet metal operations  Bending and related processes
Sheet metal operations  Bending and related processes R. Chandramouli Associate DeanResearch SASTRA University, Thanjavur613 401 Table of Contents 1.QuizKey... Error! Bookmark not defined. 1.Bending
More informationConcrete Frame Design Manual
Concrete Frame Design Manual Turkish TS 5002000 with Turkish Seismic Code 2007 For SAP2000 ISO SAP093011M26 Rev. 0 Version 15 Berkeley, California, USA October 2011 COPYRIGHT Copyright Computers and Structures,
More informationType of Force 1 Axial (tension / compression) Shear. 3 Bending 4 Torsion 5 Images 6 Symbol (+ )
Cause: external force P Force vs. Stress Effect: internal stress f 05 Force vs. Stress Copyright G G Schierle, 200105 press Esc to end, for next, for previous slide 1 Type of Force 1 Axial (tension /
More informationModule 4. Analysis of Statically Indeterminate Structures by the Direct Stiffness Method. Version 2 CE IIT, Kharagpur
Module Analysis of Statically Indeterminate Structures by the Direct Stiffness Method Version CE IIT, haragpur esson 7 The Direct Stiffness Method: Beams Version CE IIT, haragpur Instructional Objectives
More informationPart 1. Dimensions and Properties. Load and Resistance Factor Design, 3 rd Editioni. Most widely used section. Two flanges held apart by a web
Manual of Steel Construction Load and Resistance Factor Design, 3 rd Editioni Part 1 Dimensions and Properties C. C. Fu, Ph.D., P.E. University of Maryland at College Park 1 Wideflange (W) Shapes Most
More informationSECTION 3 DESIGN OF POST TENSIONED COMPONENTS FOR FLEXURE
SECTION 3 DESIGN OF POST TENSIONED COMPONENTS FOR FLEXURE DEVELOPED BY THE PTI EDC130 EDUCATION COMMITTEE LEAD AUTHOR: TREY HAMILTON, UNIVERSITY OF FLORIDA NOTE: MOMENT DIAGRAM CONVENTION In PT design,
More informationFOOTING DESIGN EXAMPLE
County: Any Design: BRG Date: 10/007 Hwy: Any Ck Dsn: BRG Date: 10/007 FOOTING DESIGN EXAMPLE Design: Based on AASHTO LRFD 007 Specifications, TxDOT LRFD Bridge Design Manual, and TxDOT Project 04371
More informationHOW TO DESIGN CONCRETE STRUCTURES Beams
HOW TO DESIGN CONCRETE STRUCTURES Beams Instructions for the Members of BIBM, CEMBUREAU, EFCA and ERMCO: It is the responsibility of the Members (national associations) of BIBM, CEMBUREAU, EFCA and ERMCO
More informationIntroduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams
Introduction to Beam Theory Area Moments of Inertia, Deflection, and Volumes of Beams Horizontal structural member used to support horizontal loads such as floors, roofs, and decks. Types of beam loads
More informationFall 12 PHY 122 Homework Solutions #8
Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i  6.0j)10 4 m/s in a magnetic field B= (0.80i + 0.60j)T. Determine the magnitude and direction of the
More informationChapter Outline. Mechanical Properties of Metals How do metals respond to external loads?
Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility
More informationSTEEL BUILDINGS IN EUROPE. MultiStorey Steel Buildings Part 10: Guidance to developers of software for the design of composite beams
STEEL BUILDINGS IN EUROPE MultiStorey Steel Buildings Part 10: Guidance to developers of software for the design of MultiStorey Steel Buildings Part 10: Guidance to developers of software for the design
More information5 G R A TINGS ENGINEERING DESIGN MANUAL. MBG Metal Bar Grating METAL BAR GRATING MANUAL MBG 53412 METAL BAR GRATING NAAMM
METAL BAR NAAMM GRATNG MANUAL MBG 53412 5 G R A TNG NAAMM MBG 53412 November 4, 2012 METAL BAR GRATNG ENGNEERNG DEGN MANUAL NAAMM MBG 53412 November 4, 2012 5 G R A TNG MBG Metal Bar Grating A Division
More informationDesign of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. Fig. 7.21 some of the trusses that are used in steel bridges
7.7 Truss bridges Fig. 7.21 some of the trusses that are used in steel bridges Truss Girders, lattice girders or open web girders are efficient and economical structural systems, since the members experience
More informationModeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method
Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method Yungang Zhan School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang,
More informationMechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied
Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the
More informationReinforced Concrete Beam
Mecanics of Materials Reinforced Concrete Beam Concrete Beam Concrete Beam We will examine a concrete eam in ending P P A concrete eam is wat we call a composite eam It is made of two materials: concrete
More informationEUROPEAN ORGANISATION FOR TECHNICAL APPROVALS
E TA TECHNICAL REPORT Design of Bonded Anchors TR 29 Edition June 27 EUROPEAN ORGANISATION FOR TECHNICAL APPROVALS TABLE OF CONTENTS Design method for bonded anchors Introduction..4 1 Scope...2 1.1 Type
More informationCH 6: Fatigue Failure Resulting from Variable Loading
CH 6: Fatigue Failure Resulting from Variable Loading Some machine elements are subjected to static loads and for such elements static failure theories are used to predict failure (yielding or fracture).
More informationNonlinear Models of Reinforced and Posttensioned Concrete Beams
111 Nonlinear Models of Reinforced and Posttensioned Concrete Beams ABSTRACT P. Fanning Lecturer, Department of Civil Engineering, University College Dublin Earlsfort Terrace, Dublin 2, Ireland. Email:
More informationFinite Element Formulation for Plates  Handout 3 
Finite Element Formulation for Plates  Handout 3  Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the
More informationNumerical modelling of shear connection between concrete slab and sheeting deck
7th fib International PhD Symposium in Civil Engineering 2008 September 1013, Universität Stuttgart, Germany Numerical modelling of shear connection between concrete slab and sheeting deck Noémi Seres
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Analysis of Statically Indeterminate Structures by the Matrix Force Method esson 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be able
More informationExamples of New version for Designing members of Reinforced Concrete, Steel or Timber according to Eurocode 2, Eurocode 3 and Eurocode 5
Examples of New version for Designing members of Reinforced Concrete, Steel or Timber according to Eurocode 2, Eurocode 3 and Eurocode 5 Copyright RUNET Software www.runetsoftware.com 1 1. Examples 1.1
More informationTorsion Tests. Subjects of interest
Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test
More informationLecture 8 Bending & Shear Stresses on Beams
Lecture 8 Bending & hear tresses on Beams Beams are almost always designed on the asis of ending stress and, to a lesser degree, shear stress. Each of these stresses will e discussed in detail as follows.
More informationBEAMS: SHEAR FLOW, THIN WALLED MEMBERS
LECTURE BEAMS: SHEAR FLOW, THN WALLED MEMBERS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering 15 Chapter 6.6 6.7 by Dr. brahim A. Assakkaf SPRNG 200 ENES
More informationDesign of Fibre Reinforced Concrete Beams and Slabs
Design of Fibre Reinforced Concrete Beams and Slabs Master of Science Thesis in the Master s Programme Structural Engineering and Building Performance Design AMMAR ABID, KENNETH B. FRANZÉN Department of
More information