ME 201 Engineering Mechanics: Statics
|
|
- Tabitha Sparks
- 5 years ago
- Views:
Transcription
1 ME 0 Engineering Mechanics: Statics Unit 9. Moments of nertia Definition of Moments of nertia for Areas Parallel-Axis Theorem for an Area Radius of Gyration of an Area Moments of nertia for Composite Areas
2 Moments of nertia The Moment of nertia,, represents the relative capacity of a section to resist bending or buckling in a direction perpendicular to the neutral axis Based on shape, not on material Also referred to as nd Moment Area x Ay y Ax
3 Moment of nertia of Simple Shapes Rectangle h b x c xc bh Suppose we have a x. Which orientation poses the greater resistance to bending? x c x c xc.67 in xc 0.67 in
4 Moment of nertia of Simple Shapes Triangle h Circle r b x c x c xc xc bh 6 r d 6 Semi-Circle r c y x xc r 8
5 Moment of nertia about Another Axis The Moment of nertia may be computed about another axis using the Parallel Axis Theorem (also called Transfer Formula) x c Ad
6 Parallel Axis Theorem h xc b bh x c x x xc bh bh Ad h bh bh bh
7 Finding of Composite Areas Procedure Divide into numbered, simple areas Find composite centroid Find c of each of each area Use parallel axis theorem to find composite y x
8 Example Problem of Composite Area 0 00 Find: x about centroid 0 0
9 00 0 Find: x about centroid Solution: Find Centroid Example Problem Solution 0 0 A y 0* / 5 A y 0* / 50 X Shape y A ya mm ( by symmetry) ~ ya 6000 Y A 7600 mm
10 00 0 Find: x about centroid Solution: Find Centroid Example Problem Solution 0 0 y y Y 5 x xc Ad mm 0*0 0*00 (600)(5 80.8) (000)( ).E6 mm
11 Radius of Gyration s defined as the distance from its moment of inertia axis at which the entire area could be considered as being concentrated without changing its moment of inertia A compressive member tends to buckle in the direction of its least radius of gyration k A What are the units? in in in
12
13 Centroid Review Find the centroid, y of the shaded area: A.. m B.. m C..57 m D..8 m E. None of the above
14 Moments of nertia The Moment of nertia,, represents the relative capacity of a section to resist bending or buckling in a direction perpendicular to the neutral axis Based on shape, not on material Also referred to as nd Moment Area x Ay y Ax
15 Moment of nertia of Simple Shapes The Moment of nertia for simple geometric shapes about the Centroidal Axis of the shape is shown in the next series of slides Moments of nertia may also be computed about other axes.
16 Moment of nertia of Simple Shapes Rectangle h b x c xc bh Suppose we have a x. Which orientation poses the greater resistance to bending? x c x c xc.67 in xc 0.67 in
17 Moment of nertia of Simple Shapes Triangle h Circle r b x c x c xc xc bh 6 r d 6 Semi-Circle r c y x xc r 8
18 Moment of nertia about Another Axis The Moment of nertia may be computed about another axis using the Parallel Axis Theorem (also called Transfer Formula) x c Ad
19 Parallel Axis Theorem h xc b bh x c x x xc bh bh Ad h bh bh bh
20 Finding of Composite Areas Procedure Divide into numbered, simple areas Find c of each of each area Find composite centroid Use parallel axis theorem to find composite y x
21 Example Problem of Composite Area 0 00 Find: x about centroid 0 0
22 00 0 Find: x about centroid Example 0 0
23 00 0 Find: x about centroid Solution: Find Centroid Example Problem Solution 0 0 A y 0* / 5 A y 0* / 50 X Shape y A ya mm ( by symmetry) ~ ya 6000 Y A 7600 mm
24 00 0 Find: x about centroid Solution: Find Centroid Example Problem Solution 0 0 y y Y 5 x xc Ad mm 0*0 0*00 (600)(5 80.8) (000)( ).E6 mm
25 Radius of Gyration s defined as the distance from its moment of inertia axis at which the entire area could be considered as being concentrated without changing its moment of inertia A compressive member tends to buckle in the direction of its least radius of gyration k A What are the units? in in in
26 n Class Exercise Find: xc & yc (about centroid)
27 Find: xc & yc (about centroid) Solution
28 Find: xc & yc (about centroid) Solution
29 Find: xx, yy k xx, k yy n Class Exercise
30 Find: xx, yy, k xx, k yy Solution
31 Find: xx, yy, k xx, k yy Solution
10.5 MOMENT OF INERTIA FOR A COMPOSITE AREA
10.5 MOMENT OF NERTA FOR A COMPOSTE AREA A composite area is made by adding or subtracting a series of simple shaped areas like rectangles, triangles, and circles. For example, the area on the left can
More informationMoment of Inertia and Centroid
Chapter- Moment of nertia and Centroid Page- 1. Moment of nertia and Centroid Theory at a Glance (for ES, GATE, PSU).1 Centre of gravity: The centre of gravity of a body defined as the point through which
More informationStatics: Lecture Notes for Sections
0.5 MOMENT OF INERTIA FOR A COMPOSITE AREA A composite area is made by adding or subtracting a series of simple shaped areas like rectangles, triangles, and circles. For example, the area on the left can
More informationProperties of Sections
ARCH 314 Structures I Test Primer Questions Dr.-Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body
More informationh p://edugen.wileyplus.com/edugen/courses/crs1404/pc/b03/c2hlch...
n this appendix we discuss... 1 of 4 16-Sep-12 19:35 APPENDIX C In this appendix we discuss how to calculate the moment of inertia of an area. 1 The moment of inertia of an area was first introduced in
More informationChapter 6: Cross-Sectional Properties of Structural Members
Chapter 6: Cross-Sectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross
More informationHong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 2 SECTION PROPERTIES
Section Properties Centroid The centroid of an area is the point about which the area could be balanced if it was supported from that point. The word is derived from the word center, and it can be though
More informationProperties of surfaces II: Second moment of area
Properties of surfaces II: Second moment of area Just as we have discussing first moment of an area and its relation with problems in mechanics, we will now describe second moment and product of area of
More informationChapter 9 Moment of Inertia
Chapter 9 Moment of Inertia Dr. Khairul Salleh Basaruddin Applied Mechanics Division School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) khsalleh@unimap.edu.my PARALLEL-AXIS THEOREM,
More informationAPPENDIX 1 MODEL CALCULATION OF VARIOUS CODES
163 APPENDIX 1 MODEL CALCULATION OF VARIOUS CODES A1.1 DESIGN AS PER NORTH AMERICAN SPECIFICATION OF COLD FORMED STEEL (AISI S100: 2007) 1. Based on Initiation of Yielding: Effective yield moment, M n
More informationDEFINITION OF MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA
DEFINITION OF MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the moment of inertia
More informationMAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPPALLI Distinguish between centroid and centre of gravity. (AU DEC 09,DEC 12)
MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAPPALLI 621213 Sub Code: GE 6253 Semester: II Subject: ENGINEERING MECHANICS Unit III: PROPERTIES OF SURFACES AND SOLIDS PART A 1. Distinguish between centroid and
More informationStatics: Lecture Notes for Sections 10.1,10.2,10.3 1
Chapter 10 MOMENTS of INERTIA for AREAS, RADIUS OF GYRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the MoI for an area by integration.
More informationMoments of Inertia. Notation:
RCH 1 Note Set 9. S015abn Moments of nertia Notation: b d d d h c Jo O = name for area = name for a (base) width = calculus smbol for differentiation = name for a difference = name for a depth = difference
More informationME 141. Lecture 8: Moment of Inertia
ME 4 Engineering Mechanics Lecture 8: Moment of nertia Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil679@gmail.com Website: teacher.buet.ac.bd/sshakil
More informationSecond Moments or Moments of Inertia
Second Moments or Moments of Inertia The second moment of inertia of an element of area such as da in Figure 1 with respect to any axis is defined as the product of the area of the element and the square
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 informationCH. 4 BEAMS & COLUMNS
CH. 4 BEAMS & COLUMNS BEAMS Beams Basic theory of bending: internal resisting moment at any point in a beam must equal the bending moments produced by the external loads on the beam Rx = Cc + Tt - If the
More informationCentroid & Moment of Inertia
UNIT Learning Objectives Centroid & Moment of Inertia After studying this unit, the student will be able to Know what is centre of gravity and centroid Calculate centroid of geometric sections Centre of
More informationEngineering Science OUTCOME 1 - TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1 - TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
More informationSub:Strength of Material (22306)
Sub:Strength of Material (22306) UNIT 1. Moment of Inertia 1.1 Concept of Moment of Inertia (Ml). Effect of MI in case of beam and column. 1.2 MI about axes passing through centroid. Parallel and Perpendicular
More information[8] Bending and Shear Loading of Beams
[8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight
More informationDistributed Forces: Moments of Inertia
Distributed Forces: Moments of nertia Contents ntroduction Moments of nertia of an Area Moments of nertia of an Area b ntegration Polar Moments of nertia Radius of Gration of an Area Sample Problems Parallel
More information2. Supports which resist forces in two directions. Fig Hinge. Rough Surface. Fig Rocker. Roller. Frictionless Surface
4. Structural Equilibrium 4.1 ntroduction n statics, it becomes convenient to ignore the small deformation and displacement. We pretend that the materials used are rigid, having the propert or infinite
More informationFUNDAMENTALS OF ENGINEERING CIVIL EXAM TOPICS. Computer-Based Test (CBT)
FUNDAMENTALS OF ENGINEERING CIVIL EXAM TOPICS Computer-Based Test (CBT) Total Number of Questions: 110 Time: 6 hours The new Civil FE Computer Based Test (CBT) consists of 110 multiple choice questions
More informationMOI (SEM. II) EXAMINATION.
Problems Based On Centroid And MOI (SEM. II) EXAMINATION. 2006-07 1- Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R. 2- State the parallel axis theorem.
More informationBending Stress. Sign convention. Centroid of an area
Bending Stress Sign convention The positive shear force and bending moments are as shown in the figure. Centroid of an area Figure 40: Sign convention followed. If the area can be divided into n parts
More informationSTATICS. Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Ninth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
N E 9 Distributed CHAPTER VECTOR MECHANCS FOR ENGNEERS: STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Teas Tech Universit Forces: Moments of nertia Contents ntroduction
More informationENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 4 COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those studying
More informationENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AND STRUCTURAL ENGINEERING C105 TUTORIAL 1 - MOMENTS OF AREA
ENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AN STRUCTURAL ENGINEERING C105 TUTORIAL 1 - MOMENTS OF AREA The concept of first and second moments of area is fundamental to several areas of engineering
More informationSTATICS. Distributed Forces: Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
007 The McGraw-Hill Companies, nc. All rights reserved. Eighth E CHAPTER 9 VECTOR MECHANCS FOR ENGNEERS: STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University
More information(Refer Slide Time: 2:08 min)
Applied Mechanics Prof. R. K. Mittal Department of Applied Mechanics Indian Institute of Technology, Delhi Lecture No. 11 Properties of Surfaces (Contd.) Today we will take up lecture eleven which is a
More informationSTATICS. Moments of Inertia VECTOR MECHANICS FOR ENGINEERS: Seventh Edition CHAPTER. Ferdinand P. Beer
00 The McGraw-Hill Companies, nc. All rights reserved. Seventh E CHAPTER VECTOR MECHANCS FOR ENGNEERS: 9 STATCS Ferdinand P. Beer E. Russell Johnston, Jr. Distributed Forces: Lecture Notes: J. Walt Oler
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationSemester: BE 3 rd Subject :Mechanics of Solids ( ) Year: Faculty: Mr. Rohan S. Kariya. Tutorial 1
Semester: BE 3 rd Subject :Mechanics of Solids (2130003) Year: 2018-19 Faculty: Mr. Rohan S. Kariya Class: MA Tutorial 1 1 Define force and explain different type of force system with figures. 2 Explain
More informationSamantha Ramirez, MSE
Samantha Ramirez, MSE Centroids The centroid of an area refers to the point that defines the geometric center for the area. In cases where the area has an axis of symmetry, the centroid will lie along
More informationAREAS, RADIUS OF GYRATION
Chapter 10 MOMENTS of INERTIA for AREAS, RADIUS OF GYRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine the MoI for an area by integration.
More informationCIVL Statics. Moment of Inertia - Composite Area. A math professor in an unheated room is cold and calculating. Radius of Gyration
CVL 131 - Statics Moment of nertia Composite Areas A math professor in an unheated room is cold and calculating. Radius of Gration This actuall sounds like some sort of rule for separation on a dance floor.
More informationCOURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES -I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More informationChapter 10: Moments of Inertia
Chapter 10: Moments of Inertia Chapter Objectives To develop a method for determining the moment of inertia and product of inertia for an area with respect to given x- and y-axes. To develop a method for
More informationME 201 Engineering Mechanics: Statics. Final Exam Review
ME 201 Engineering Mechanics: Statics inal Exam Review inal Exam Testing Center (Proctored, 1 attempt) Opens: Monday, April 9 th Closes : riday, April 13 th Test ormat 15 Problems 10 Multiple Choice (75%)
More informationPESIT- Bangalore South Campus Dept of science & Humanities Sub: Elements Of Civil Engineering & Engineering Mechanics 1 st module QB
PESIT- Bangalore South Campus Dept of science & Humanities Sub: Elements Of Civil Engineering & Engineering Mechanics 1 st module QB Sub Code: 15CIV13/23 1. Briefly give the scope of different fields in
More informationBEAMS: SHEAR AND MOMENT DIAGRAMS (FORMULA)
LETURE Third Edition BEMS: SHER ND MOMENT DGRMS (FORMUL). J. lark School of Engineering Department of ivil and Environmental Engineering 1 hapter 5.1 5. b Dr. brahim. ssakkaf SPRNG 00 ENES 0 Mechanics
More informationCOURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5
COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5 TIME SCHEDULE MODULE TOPICS PERIODS 1 Simple stresses
More informationSTATICS Chapter 1 Introductory Concepts
Contents Preface to Adapted Edition... (v) Preface to Third Edition... (vii) List of Symbols and Abbreviations... (xi) PART - I STATICS Chapter 1 Introductory Concepts 1-1 Scope of Mechanics... 1 1-2 Preview
More informationThe minus sign indicates that the centroid is located below point E. We will relocate the axis as shown in Figure (1) and take discard the sign:
AOE 304: Thin Walled Structures Solutions to Consider a cantilever beam as shown in the attached figure. At the tip of the beam, a bending moment M = 1000 N-m is applied at an angle θ with respect to the
More informationREVOLVED CIRCLE SECTIONS. Triangle revolved about its Centroid
REVOLVED CIRCLE SECTIONS Triangle revolved about its Centroid Box-in Method Circle Sector Method Integrating to solve I, Ax, and A for a revolved triangle is difficult. A quadrilateral and another triangle
More informationStress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 4 ME 76 Spring 017-018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a
More informationUNIT- I Thin plate theory, Structural Instability:
UNIT- I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and in-plane loading Thin plates having
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any cross-section of a beam may consists of a resultant normal force,
More information: APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE
COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Simple stresses
More informationSample Question Paper
Scheme I Sample Question Paper Program Name : Mechanical Engineering Program Group Program Code : AE/ME/PG/PT/FG Semester : Third Course Title : Strength of Materials Marks : 70 Time: 3 Hrs. Instructions:
More informationENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01
ENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01 3. Multiple Integration This chapter provides only a very brief introduction to the major topic of multiple integration. Uses of multiple
More informationBASIC MATHS TUTORIAL 7 - MOMENTS OF AREA. This tutorial should be skipped if you are already familiar with the topic.
BASIC MATHS TUTORIAL 7 - MOMENTS OF AREA This tutorial should be skipped if you are already familiar with the topic. In this section you will do the following. Define the centre of area. Define and calculate
More informationMoment Of Inertia Solutions Meriam File Type
We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with moment of inertia solutions
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING. BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS
TW21 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS MODULE NO: CIE4011 Date: Wednesday 11 th January 2017 Time:
More informationME 101: Engineering Mechanics
ME 0: Engineering Mechanics Rajib Kumar Bhattacharja Department of Civil Engineering ndian nstitute of Technolog Guwahati M Block : Room No 005 : Tel: 8 www.iitg.ernet.in/rkbc Area Moments of nertia Parallel
More informationThe plastic moment capacity of a composite cross-section is calculated in the program on the following basis (BS 4.4.2):
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002 COMPOSITE BEAM DESIGN BS 5950-90 Technical Note Composite Plastic Moment Capacity for Positive Bending This Technical Note describes
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 17
ENGR-1100 Introduction to Engineering Analysis Lecture 17 CENTROID OF COMPOSITE AREAS Today s Objective : Students will: a) Understand the concept of centroid. b) Be able to determine the location of the
More informationCO~RSEOUTL..INE. revisedjune 1981 by G. Frech. of..a.pqij~t(..~ttsa.fidteconol.q.gy. Sault ",Ste'...:M~ri,e.: SAUl. ir.ft\,nl~t';~l' G ". E b:.
-/ 1/ /.. SAUl. ir.ft\,nl~t';~l' G ". E b:.~~~~~, of..a.pqij~t(..~ttsa.fidteconol.q.gy. Sault ",Ste'...:M~ri,e.: ',' -.\'~. ~ ;:T.., CO~RSEOUTL..INE ARCHITECTURAL ENGINEERING II ARC 200-4 revisedjune 1981
More informationFIXED BEAMS CONTINUOUS BEAMS
FIXED BEAMS CONTINUOUS BEAMS INTRODUCTION A beam carried over more than two supports is known as a continuous beam. Railway bridges are common examples of continuous beams. But the beams in railway bridges
More informationOutline: Centres of Mass and Centroids. Beams External Effects Beams Internal Effects
Outline: Centres of Mass and Centroids Centre of Mass Centroids of Lines, Areas and Volumes Composite Bodies Beams External Effects Beams Internal Effects 1 Up to now all forces have been concentrated
More information2.6 Force reacts with planar object in fluid
2.6 Force reacts with planar object in fluid Fluid surface Specific weight (γ) => Object sinks in fluid => C is center of gravity or Centroid => P is center of pressure (always under C) => x axis is cross
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationMECE 3321: Mechanics of Solids Chapter 6
MECE 3321: Mechanics of Solids Chapter 6 Samantha Ramirez Beams Beams are long straight members that carry loads perpendicular to their longitudinal axis Beams are classified by the way they are supported
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST
More informationAdditional Mathematics Lines and circles
Additional Mathematics Lines and circles Topic assessment 1 The points A and B have coordinates ( ) and (4 respectively. Calculate (i) The gradient of the line AB [1] The length of the line AB [] (iii)
More informationAdvanced Structural Analysis EGF Section Properties and Bending
Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear
More 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 informationJUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 10 (Second moments of an arc) A.J.Hobson
JUST THE MATHS UNIT NUMBER 13.1 INTEGRATION APPLICATIONS 1 (Second moments of an arc) by A.J.Hobson 13.1.1 Introduction 13.1. The second moment of an arc about the y-axis 13.1.3 The second moment of an
More informationLocal Buckling. Local Buckling in Columns. Buckling is not to be viewed only as failure of the entire member
Local Buckling MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE V Dr. Jason E. Charalamides Local Buckling in Columns Buckling is not to e viewed only as failure of the entire memer
More informationneeded to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns.
CHAPTER OBJECTIVES Discuss the behavior of columns. Discuss the buckling of columns. Determine the axial load needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods
More informationAnna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions.
Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions 1. Find the resultant force and its direction for the given figure 2. Two forces are acting at a point O as shown in
More informationUnit Workbook 1 Level 4 ENG U8 Mechanical Principles 2018 UniCourse Ltd. All Rights Reserved. Sample
Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 8: Mechanical Principles Unit Workbook 1 in a series of 4 for this unit Learning Outcome 1 Static Mechanical Systems Page 1 of 23 1.1 Shafts
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 informationCritical Load columns buckling critical load
Buckling of Columns Buckling of Columns Critical Load Some member may be subjected to compressive loadings, and if these members are long enough to cause the member to deflect laterally or sideway. To
More informationMechanics of Structure
S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI
More informationENGI Multiple Integration Page 8-01
ENGI 345 8. Multiple Integration Page 8-01 8. Multiple Integration This chapter provides only a very brief introduction to the major topic of multiple integration. Uses of multiple integration include
More informationMOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION
MOMENTS OF INERTIA FOR AREAS, RADIUS OF GYRATION OF AN AREA, & MOMENTS OF INTERTIA BY INTEGRATION Today s Objectives: Students will be able to: a) Define the moments of inertia (MoI) for an area. b) Determine
More informationUNSYMMETRICAL BENDING
UNSYMMETRICAL BENDING The general bending stress equation for elastic, homogeneous beams is given as (II.1) where Mx and My are the bending moments about the x and y centroidal axes, respectively. Ix and
More information4. BEAMS: CURVED, COMPOSITE, UNSYMMETRICAL
4. BEMS: CURVED, COMPOSITE, UNSYMMETRICL Discussions of beams in bending are usually limited to beams with at least one longitudinal plane of symmetry with the load applied in the plane of symmetry or
More informationSTATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.
STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle
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 informationCHAPTER -6- BENDING Part -1-
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER -6- BENDING Part -1-1 CHAPTER -6- Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationStrength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in Beams-I
Strength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in Beams-I Welcome to the first lesson of the 6th module which is on Stresses in Beams
More informationTwo small balls, each of mass m, with perpendicular bisector of the line joining the two balls as the axis of rotation:
PHYSCS LOCUS 17 summation in mi ri becomes an integration. We imagine the body to be subdivided into infinitesimal elements, each of mass dm, as shown in figure 7.17. Let r be the distance from such an
More informationChapter 3. Load and Stress Analysis. Lecture Slides
Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
More informationFE Sta'cs Review. Torch Ellio0 (801) MCE room 2016 (through 2000B door)
FE Sta'cs Review h0p://www.coe.utah.edu/current- undergrad/fee.php Scroll down to: Sta'cs Review - Slides Torch Ellio0 ellio0@eng.utah.edu (801) 587-9016 MCE room 2016 (through 2000B door) Posi'on and
More informationQuestions from all units
Questions from all units S.NO 1. 1 UNT NO QUESTON Explain the concept of force and its characteristics. BLOOMS LEVEL LEVEL 2. 2 Explain different types of force systems with examples. Determine the magnitude
More information3/31/ Product of Inertia. Sample Problem Sample Problem 10.6 (continue)
/1/01 10.6 Product of Inertia Product of Inertia: I xy = xy da When the x axis, the y axis, or both are an axis of symmetry, the product of inertia is zero. Parallel axis theorem for products of inertia:
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationStrength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee
Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Lecture - 28 Hi, this is Dr. S. P. Harsha from Mechanical and
More informationSAULT COLLEGE OF APPLIED ARTS & TECHNOLOGY SAULT STE. MARIE, ONTARIO COURSE OUTLINE STRENGTH OF MATERIALS MECHANICAL TECHNOLOGY
(/.- SAULT COLLEGE OF APPLIED ARTS & TECHNOLOGY SAULT STE. MARIE, ONTARIO COURSE OUTLINE Course Title: Code No.: Program: Semester: Date: Author: STRENGTH OF MATERIALS MCH 202 MECHANICAL TECHNOLOGY THREE
More informationSOLUTION Determine the moment of inertia for the shaded area about the x axis. I x = y 2 da = 2 y 2 (xdy) = 2 y y dy
5. Determine the moment of inertia for the shaded area about the ais. 4 4m 4 4 I = da = (d) 4 = 4 - d I = B (5 + (4)() + 8(4) ) (4 - ) 3-5 4 R m m I = 39. m 4 6. Determine the moment of inertia for the
More informationIntro Vectors 2D implicit curves 2D parametric curves. Graphics 2011/2012, 4th quarter. Lecture 2: vectors, curves, and surfaces
Lecture 2, curves, and surfaces Organizational remarks Tutorials: Tutorial 1 will be online later today TA sessions for questions start next week Practicals: Exams: Make sure to find a team partner very
More informationNYIT Instructors: Alfred Sanabria and Rodrigo Suarez
NYIT Instructors: Alfred Sanabria and Rodrigo Suarez Massive stone columns, used from Stonehenge to Ancient Greece were stabilized by their own work With steel and concrete technology columns have become
More informationMTE 119 STATICS FINAL HELP SESSION REVIEW PROBLEMS PAGE 1 9 NAME & ID DATE. Example Problem P.1
MTE STATICS Example Problem P. Beer & Johnston, 004 by Mc Graw-Hill Companies, Inc. The structure shown consists of a beam of rectangular cross section (4in width, 8in height. (a Draw the shear and bending
More informationMECHANICS OF MATERIALS Sample Problem 4.2
Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A cast-iron machine part is acted upon by a kn-m couple.
More informationmportant nstructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may
More information