P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures


 Ralf Simon
 1 years ago
 Views:
Transcription
1 4 Stress and Strain Dr... Zavatsky MT07 ecture 3 Statically Indeterminate Structures Statically determinate structures. Statically indeterminate structures (equations of equilibrium, compatibility, and forcedisplacement; use of displacement diagrams) olts and turnbuckles. Temperature effects. Misfits and prestrains. 1
2 Statically Determinate Structures Reactions and internal forces can be determined solely from freebody diagrams and equations of equilibrium. Results are independent of the material from which the structure has been made. 5 kn Unknowns reaction forces + bar forces ( + 1) Independent equations [equilibrium in x & y directions at each joint] (number of joints) (8) kn Doublecheck structure for internal mechanisms, etc.
3 Statically Indeterminate Structures Reactions and internal forces cannot be found by statics alone (more unknown forces than independent equations of equilibrium). Results are dependent on the material from which the structure has been made. R C a unknown forces Only 1 useful equation of equilibrium b R + R 0 R Need to find another equation 3
4 R Flexibility or Force Method 1 a R static redundant C + b R 1 released structure Equation of compatibility expresses the fact that the change in length of the bar must be compatible with the conditions at the supports
5 Write the forcedisplacement relations. These take the mechanical properties of the material into account. b and E 1 R E Substituting into the equation of compatibility gives: R b R + 0 E E b *Note that flexibilities (b/e) and (/E) appear in this equation. Hence, this approach is called the flexibility method. Substituting into the equilibrium equation gives: R R a *Note that we have solved for forces. Hence, this approach is also called the force method. 5
6 Stiffness or Displacement Method R R C a C + R b R C1 C R Equation of equilibrium (forces at C must balance) R + R Equation of compatibility (at point C) C C1 C R 6
7 Write the forcedisplacement relations and solve for the forces. R C1 Ra E C1E a and and C R Rb E CE b Substituting into the equilibrium equation gives: E a E b C 1 C + *Note that stiffnesses (E/a) and (E/b) appear in this equation. Hence, this approach is called the stiffness method. Using the compatibility condition (displacements equal) gives: ab E a C ab ( + b) E *Note that we have solved for displacement. Hence, this approach is also called the displacement method. 7
8 Finally, substituting into the expressions for forces gives: R R ab E ab E E a E b b a So, both the flexibility method and the stiffness method give the same result. The choice of approach will depend on the problem being solved. 8
9 Use of Displacement Diagrams in Statically Indeterminate roblems (based on Example 3, page 70, Gere & Timoshenko) C CD C 5 sinα sinα α 1 D α ar D is supported by two wires, CD and C. load is applied at. The wires have axial rigidity E. Disregarding the weight of the bar, find the forces in the wires. 9
10 R y T CD T C α 1 α R x Equilibrium Horizontal Direction F x Rx TCD cosα1 TC cosα 0 Vertical Direction F y Ry + TCD sinα1 + TC sin α 0 Moments about (ccw +) ( T α ) + ( T sinα ) ( ) M CD sin 1 C 0 4 unknown forces, only 3 equations 10
11 Compatibility We can relate the tensions in the two wires by considering the extensions of the wires. D D C D CD Displacement diagram CD C D sinα sinα 1 D sinα 11
12 Forcedisplacement relations TCDCD and E CD C TC E C Using the equilibrium moment equation, the compatibility equation, and the forcedisplacement relations, it is possible to solve for the forces in the wires. We find that T C 1.15 and T CD
13 Elastoplastic nalysis of a Statically Indeterminate Structure (based on Example 19 from Gere) ar 1 ar (a) (b) b b b Horizontal beam is rigid. Supporting bars 1 and are made of an elastic perfectly plastic material with yield stress σ Y, yield strain ε Y, and Young s modulus E σ Y / ε Y. Each bar has crosssectional area. (c) Find the yield load Y and the corresponding yield displacement Δ Y at point. Find the plastic load and the corresponding plastic displacement Δ at point. Draw a loaddisplacement diagram relating the load to the displacement Δ of point. 13
14 R y F 1 F R x b b b Moment Equilibrium (ccw +) M 1 F + F 3 1 Compatibility 1 ( F ) b + ( F ) b ( 3b) Forcedisplacement 1 1 and E F F E 0 F F ar will yield first, since F > F 1. 14
15 F Y 6Y σ Y 5 5σ Y (a) 6 The corresponding elongation of bar is: F F σ Y E E E The downward displacement of the bar at point is: Δ Y 3 3σ Y E When the plastic load is reached, both bars will be stretched to the yield stress, and F 1 F σ Y. From equilibrium, F 1 + F 3 (b) σ Y (a) 15
16 The corresponding elongation of bar 1 (which has just reached yield) is: F F σ Y E E E The downward displacement of the bar at point is: ar yields Δ 3 1 ar 1 yields 3σ E Y (b) Note that / Y 6/5 and Δ /Δ Y Y oth bars plastic ar plastic, bar 1 elastic Δ Y Δ (c) Δ 16
17 olts and Turnbuckles The simplest way to produce a change in length. Nut and olt Distance travelled by the nut n p n number of turns (not necessarily an integer) p pitch of the screw (units mm / turn) Turnbuckle Righthand screw efthand screw Distance travelled n p Often used to tension cables 17
18 ased on Gere, Example 9 Steel cable Turnbuckle Rigid plate Copper tube The slack is removed from the cables by rotating the turnbuckles until the assembly is snug but with no initial stresses (do not want to stretch the cables and compress the tube). Find the forces in the tube and cables when the turnbuckles are tightened by n turns, and determine the shortening of the tube. 18
19 If the turnbuckles are rotated through n turns, the cables will shorten by a distance 1 n p s c s The tensile forces in the cables s and the compressive force in the tube c must be such that the final lengths of the cables and tube is the same. 19
20 Equilibrium (forces must balance) s 0 c Compatibility (shortening of tube must equal shortening of cable) 3 1 Forcedisplacement 1 np s E 3 s c s c E c With these equations, we can solve for the forces in the tube and cables and for the shortening of the tube. 0
21 Temperature Effects Changes in temperature produce expansion or contraction of structural materials. When heated, the block expands in all three directions: x, y, z. For most structural materials, ε T α (ΔT) ε T thermal strain α coefficient of thermal expansion (HT, units 1/K or 1/ C) ΔT change in temperature The change in length of the block in NY direction can be found using T ε T α (ΔT), where is one of the block s dimensions. 1
22 Expansion is positive; contraction is negative. relatively modest change in temperature produces about the same magnitude of strain as that caused by ordinary working stresses. This shows that temperature effects can be important in engineering design. For mild steel, α 11 x 106 K 1 (HT, page 39) Thermal strain: ε T α (ΔT) 11 x 106 K 1 (40 K) με Yield strain: ε Y σ Y / E (40 x 10 6 a)/(10 x 10 9 a) με Ordinary working stress might be 50% of the yield stress, giving 570 με Thermal strains are USUY reversible.
23 Free expansion or contraction occurs when an object rests on a frictionless surface or hangs in open space. Then no stresses are produced by a uniform temperature change, but there are strains. In statically determinate structures, uniform temperature changes in the members produce thermal strains (and corresponding changes in length) without producing any corresponding stresses. statically indeterminate structure may or may not develop thermal stresses, depending on the character of the structure and the nature of the temperature changes. C D Since D can move horizontally, no stresses are developed when the entire structure is heated uniformly. If only some bars are heated, thermal stresses will develop. 3
24 Example: The temperature of the bar is raised by ΔT. Find the reactions at the supports. R R R T ΔT + ΔT R Equilibrium: R + R 0 Compatibility: T + R 0 or T  R 4
25 Using temperaturedisplacement and forcedisplacement relations: T R α ( ΔT ) R E Substituting in to the compatibility condition gives: α R ( ΔT ) R E E α ( ΔT ) (compression) Substituting into the equilibrium equation gives: R R E α ( ΔT ) 5
26 Misfits and restrains When a member is manufactured with a length slightly different from its prescribed length, the member will not fit into the structure as planned and the geometry of the structure will be different from what was planned. Such situations are misfits. Some misfits are created intentionally to introduce strains into the structure at the time it is built. ecause these strains exist before any loads are applied, they are called prestrains. long with the prestrains are usually prestresses. Examples: spokes in bicycle wheels, pretensioned faces of tennis racquets, shrinkfitted machine parts, prestressed concrete beams 6
27 If a structure is statically determinate, small misfits in one or more members will not produce strains or stresses, although the initial configuration will depart from the theoretical. Here, having CD longer than expected will not induce prestrains or prestresses. can rotate to accommodate the length change. C D In a statically indeterminate structure, misfits cannot be accommodated without prestresses. 7
28 C E D F ssume that CD is slightly longer than prescribed. Then to assemble the structure, CD must be compressed by external forces (or EF must be stretched by external forces). The bars can then be fitted into place and the external loads released. s a result, the beam will deform and rotate. If CD is put into compression, EF will be in tension. So, prestrains will exist and the structure will be prestressed, although no external loads are acting. When a load is added, additional stresses and strains will result. 8
MECHANICS 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 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 informationP4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections
4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear
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 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 informationWelcome to the first lesson of third module which is on thinwalled pressure vessels part one which is on the application of stress and strain.
Strength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture 15 Application of Stress by Strain Thinwalled Pressure Vessels  I Welcome
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 informationStiffness Methods for Systematic Analysis of Structures (Ref: Chapters 14, 15, 16)
Stiffness Methods for Systematic Analysis of Structures (Ref: Chapters 14, 15, 16) The Stiffness method provides a very systematic way of analyzing determinate and indeterminate structures. Recall Force
More informationd B = PL Ans. = m = 1.59 mm d A = PL AE = 12(10 3 )(3) Ans. = m = 6.14 mm Ans:
4 5. The assembly consists of a steel rod and an aluminum rod, each having a diameter of 12 mm. If the rod is subjected to the axial loadings at and at the couling, determine the dislacement of the couling
More informationChapter 5: Indeterminate Structures Force Method
Chapter 5: Indeterminate Structures Force Method 1. Introduction Statically indeterminate structures are the ones where the independent reaction components, and/or internal forces cannot be obtained by
More information4.2 Free Body Diagrams
CE297FA09Ch4 Page 1 Friday, September 18, 2009 12:11 AM Chapter 4: Equilibrium of Rigid Bodies A (rigid) body is said to in equilibrium if the vector sum of ALL forces and all their moments taken about
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 informationENGR1100 Introduction to Engineering Analysis. Lecture 13
ENGR1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREEBODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a freebody
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 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 informationStructural Displacements. Structural Displacements. Beam Displacement. Truss Displacements 2
Structural Displacements Structural Displacements P Beam Displacement 1 Truss Displacements The deflections of civil engineering structures under the action of usual design loads are known to be small
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 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 informationChapter 7: Forces in Beams and Cables
Chapter 7: Forces in Beams and Cables 최해진 hjchoi@cau.ac.kr Contents Introduction Internal Forces in embers Sample Problem 7.1 Various Types of Beam Loading and Support Shear and Bending oment in a Beam
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 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 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 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 informationMECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS. On completion of this tutorial you should be able to do the following.
MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following.
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 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 informationActivity 2.3b Engineering Problem Solving Answer Key
Activity.3b Engineering roblem Solving Answer Key 1. A force of 00 lbs pushes against a rectangular plate that is 1 ft. by ft. Determine the lb lb pressure in and that the plate exerts on the ground due
More informationFric3. force F k and the equation (4.2) may be used. The sense of F k is opposite
4. FRICTION 4.1 Laws of friction. We know from experience that when two bodies tend to slide on each other a resisting force appears at their surface of contact which opposes their relative motion. The
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 informationAnalyzing the Effectiveness of the Turnbuckle Exterior Post Tensioning as a Structural Retrofitting Method Using SAP2000
Presented at the DLSU Research Congress 15 Analyzing the Effectiveness of the Turnbuckle Exterior Post Tensioning as a Structural Retrofitting Method Using SAP Bernardo Lejano 1, Kenneth Toral 2,*, Dustin
More informationCopyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass
Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of
More information2.2 Losses in Prestress (Part II)
2.2 Losses in Prestress (Part II) This section covers the following topics Friction Anchorage Slip Force Variation Diagram 2.2.1 Friction The friction generated at the interface of concrete and steel during
More informationThermal Stress & Strain. 07 Thermal Stress and Strain Copyright G G Schierle, 200105 press Esc to end, for next, for previous slide 3
Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G Schierle, 200105 press Esc to end, for next, for previous slide 3 Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G
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 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 informationThe Free Body Diagram. The Concurrent System
T A B The Free Body Diagram The Concurrent System Free Body Diagrams Essential step in solving Equilibrium problems Complex Structural systems reduced into concise FORCE systems WHAT IS A FREE BODY DIAGRAM?
More informationENGINEERING MECHANICS STATIC
EX 16 Using the method of joints, determine the force in each member of the truss shown. State whether each member in tension or in compression. Sol Freebody diagram of the pin at B X = 0 500 BC sin
More informationStress 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 informationStatics of Structural Supports
Statics of Structural Supports TYPES OF FORCES External Forces actions of other bodies on the structure under consideration. Internal Forces forces and couples exerted on a member or portion of the structure
More informationPLANE TRUSSES. Definitions
Definitions PLANE TRUSSES A truss is one of the major types of engineering structures which provides a practical and economical solution for many engineering constructions, especially in the design of
More informationInterconnected Rigid Bodies with Multiforce Members Rigid Noncollapsible
Frames and Machines Interconnected Rigid Bodies with Multiforce Members Rigid Noncollapsible structure constitutes a rigid unit by itself when removed from its supports first find all forces external
More informationStatics of Structural Supports
Statics of Structural Supports TYPES OF FORCES External Forces actions of other bodies on the structure under consideration. Internal Forces forces and couples exerted on a member or portion of the structure
More informationENGI 8673 Subsea Pipeline Engineering Faculty of Engineering and Applied Science
GUIDANCE NOTE LECTURE 12 THERMAL EXPANSION ANALYSIS OVERVIEW The calculation procedure for determining the longitudinal pipeline response can be formulated on the basis of strain. The longitudinal strain
More informationProblem P5.2: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable?
Problem P5.: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable? Find the cross sectional area in terms of diameter using Equation (5.1). Calculate the tensile stress
More informationAnnouncements. Moment of a Force
Announcements Test observations Units Significant figures Position vectors Moment of a Force Today s Objectives Understand and define Moment Determine moments of a force in 2D and 3D cases Moment of
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 informationTUTORIAL FOR RISA EDUCATIONAL
1. INTRODUCTION TUTORIAL FOR RISA EDUCATIONAL C.M. Uang and K.M. Leet The educational version of the software RISA2D, developed by RISA Technologies for the textbook Fundamentals of Structural Analysis,
More informationTesting Anchors in Cracked Concrete
Testing Anchors in Cracked Concrete Guidance for testing laboratories: how to generate cracks BY ROLF ELIGEHAUSEN, LEE MATTIS, RICHARD WOLLMERSHAUSER, AND MATTHEW S. HOEHLER ACI Committee 355, Anchorage
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 informationChapter 18 Static Equilibrium
Chapter 8 Static Equilibrium 8. Introduction Static Equilibrium... 8. Lever Law... Example 8. Lever Law... 4 8.3 Generalized Lever Law... 5 8.4 Worked Examples... 7 Example 8. Suspended Rod... 7 Example
More informationMechanics of Materials. Chapter 4 Shear and Moment In Beams
Mechanics of Materials Chapter 4 Shear and Moment In Beams 4.1 Introduction The term beam refers to a slender bar that carries transverse loading; that is, the applied force are perpendicular to the bar.
More informationChapter 9 Statics. Review of Forces: Ex 1. Review of Forces: Ex 2. Two 50 lb. children sit on a seesaw. Will they balance in all three cases?
Two 50 lb. children sit on a seesaw. Will they balance in all three cases? Chapter 9 Statics Review of Forces: Ex 1 A dentist places braces on a person s teeth that exert 2.00 N in each direction as shown.
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 informationNonlinear analysis and formfinding in GSA Training Course
Nonlinear analysis and formfinding in GSA Training Course Nonlinear analysis and formfinding in GSA 1 of 47 Oasys Ltd Nonlinear analysis and formfinding in GSA 2 of 47 Using the GSA GsRelax Solver
More informationW2L2 Problems 11, 13
W2L2 roblems 11, 13 Bulk Stress and Bulk Modulus (French pg 5759 This considers changes in the total volume associated with a uniform stress in the form of a pressure change think of a piston pushing
More informationStatically Indeterminate Structure. : More unknowns than equations: Statically Indeterminate
Statically Indeterminate Structure : More unknowns than equations: Statically Indeterminate 1 Plane Truss :: Determinacy No. of unknown reactions = 3 No. of equilibrium equations = 3 : Statically Determinate
More informationσ = F / A o Chapter Outline Introduction Mechanical Properties of Metals How do metals respond to external loads?
Mechanical Properties of Metals How do metals respond to external loads? and Tension Compression Shear Torsion Elastic deformation Chapter Outline Introduction To understand and describe how materials
More informationCourse 1 Laboratory. Second Semester. Experiment: Young s Modulus
Course 1 Laboratory Second Semester Experiment: Young s Modulus 1 Elasticity Measurements: Young Modulus Of Brass 1 Aims of the Experiment The aim of this experiment is to measure the elastic modulus with
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 informationEQUILIBRIUM AND ELASTICITY
Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none
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 informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationDesign MEMO 60 Reinforcement design for TSS 102
Date: 04.0.0 sss Page of 5 CONTENTS PART BASIC ASSUMTIONS... GENERAL... STANDARDS... QUALITIES... 3 DIMENSIONS... 3 LOADS... 3 PART REINFORCEMENT... 4 EQUILIBRIUM... 4 Date: 04.0.0 sss Page of 5 PART BASIC
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 informationDesign MEMO 54a Reinforcement design for RVK 41
Page of 5 CONTENTS PART BASIC ASSUMTIONS... 2 GENERAL... 2 STANDARDS... 2 QUALITIES... 3 DIMENSIONS... 3 LOADS... 3 PART 2 REINFORCEMENT... 4 EQUILIBRIUM... 4 Page 2 of 5 PART BASIC ASSUMTIONS GENERAL
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 informationMECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES
MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential
More informationFatigue Testing. Objectives
Laboratory 8 Fatigue Testing Objectives Students are required to understand principle of fatigue testing as well as practice how to operate the fatigue testing machine in a reverse loading manner. Students
More informationAN EXPLANATION OF JOINT DIAGRAMS
AN EXPLANATION OF JOINT DIAGRAMS When bolted joints are subjected to external tensile loads, what forces and elastic deformation really exist? The majority of engineers in both the fastener manufacturing
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 informationME 215 Engineering Materials I
ME 215 Engineering Materials I Chapter 3 Properties in Tension and Compression (Part III) Mechanical Engineering University of Gaziantep Dr. A. Tolga Bozdana www.gantep.edu.tr/~bozdana True Stress and
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 informationStructural Analysis  II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  02
Structural Analysis  II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  02 Good morning. Today is the second lecture in the series of lectures on structural
More informationCHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS
CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.1 Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a freebody diagram),
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 informationCHAPTER 6 SIMPLY SUPPORTED BEAMS
CHPTE 6 SIMPLY SUPPOTED BEMS EXECISE 40, Page 87 1. Determine the moment of a force of 5 N applied to a spanner at an effective length of 180 mm from the centre of a nut. Moment, M = force distance = 5
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 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 informationStatically determinate structures
Statically determinate structures A statically determinate structure is the one in which reactions and internal forces can be determined solely from freebody diagrams and equations of equilibrium. These
More informationPHYS101 The Laws of Motion Spring 2014
The Laws of Motion 1. An object of mass m 1 = 55.00 kg placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m 2
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 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 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 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 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 informationLesson 4 Rigid Body Statics. Taking into account finite size of rigid bodies
Lesson 4 Rigid Body Statics When performing static equilibrium calculations for objects, we always start by assuming the objects are rigid bodies. This assumption means that the object does not change
More informationThe Influence of Magnetic Forces on the Stability Behavior of Large Electrical Machines
The Influence of Magnetic Forces on the Stability Behavior of Large Electrical Machines Dr. H. Sprysl, Dr. H. Vögele, ABB Kraftwerke AG, CH5242 Birr Dr. G. Ebi, SENSOPLAN GmbH, D79801 Hohentengen a.h.
More informationApproximate Analysis of Statically Indeterminate Structures
Approximate Analysis of Statically Indeterminate Structures Every successful structure must be capable of reaching stable equilibrium under its applied loads, regardless of structural behavior. Exact analysis
More informationUnit 1: Fire Engineering Science (A/505/6005)
L3D1 THE INSTITUTION OF FIRE ENGINEERS Founded 1918 Incorporated 1924 IFE Level 3 Diploma in Fire Science and Fire Safety (VRQ) Unit 1: Fire Engineering Science (A/505/6005) Friday 13 March 2015 10:15
More informationStress Analysis Verification Manual
Settle3D 3D settlement for foundations Stress Analysis Verification Manual 00701 Rocscience Inc. Table of Contents Settle3D Stress Verification Problems 1 Vertical Stresses underneath Rectangular Footings
More informationSince the Steel Joist Institute
SELECTING and SPECIFYING Wesley B. Myers, P.E. An insider s guide to selecting and specifying Kseries, LH, DLHseries joists and joist girders Since the Steel Joist Institute adopted the first standard
More informationIntroduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1
Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1 In this tutorial, we will use the SolidWorks Simulation finite element analysis (FEA) program to analyze the response
More informationExperimentation and Analysis of an Automatic Can/Plastic Bottle Crusher Machine
IJIRST International Journal for Innovative Research in Science & Technology Vol. 1, Issue 2, July 2014 ISSN(online): 23496010 Experimentation and Analysis of an Automatic Can/Plastic Bottle Crusher Machine
More informationChapter 9 CONCRETE STRUCTURE DESIGN REQUIREMENTS
Chapter 9 CONCRETE STRUCTURE DESIGN REQUIREMENTS 9.1 GENERAL 9.1.1 Scope. The quality and testing of concrete and steel (reinforcing and anchoring) materials and the design and construction of concrete
More informationProperties of Matter
Mr. Patrick J Camilleri B.Ed (Hons) M.Ed Science (Sheffield) Department of Physics JC Malta Properties of Matter Basics You Should Know Elasticity. Young modulus 1. Hooke's law. Extension α tension (force
More informationQuestion 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm
14:440:407 Ch6 Question 6.3: A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
More 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 informationMODULE 3 ANALYSIS OF STATICALLY INDETERMINATE STRUCTURES BY THE DISPLACEMENT METHOD. Version 2 CE IIT, Kharagpur
ODULE 3 ANALYI O TATICALLY INDETERINATE TRUCTURE BY THE DIPLACEENT ETHOD LEON 19 THE OENT DITRIBUTION ETHOD: TATICALLY INDETERINATE BEA WITH UPPORT ETTLEENT Instructional Objectives After reading this
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 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 information