Beam Bending Stresses and Shear Stress


 Christiana West
 1 years ago
 Views:
Transcription
1 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 rom the neutral axis to the top or bottom edge o a beam d = calculus symbol or dierentiation = depth o a wide lange section dy = dierence in the y direction between an area centroid ( ) and the centroid o the composite shape ( ) DL = shorthand or dead load E = modulus o elasticity or Young s modulus b = bending stress c = compressive stress max = maximum stress t = tensile stress v = shear stress Fb = allowable bending stress Fconnector = shear orce capacity per connector h = height o a rectangle = moment o inertia with respect to neutral axis bending x = moment o inertia with respect to an xaxis L = name or length LL = shorthand or live load M = internal bending moment = name or a moment vector y ŷ n = number o connectors across a joint n.a. = shorthand or neutral axis (N.A.) O = name or reerence origin p = pitch o connector spacing P = name or a orce vector q = shear per length (shear low) Q = irst moment area about a neutral axis Qconnected = irst moment area about a neutral axis or the connected part R = radius o curvature o a deormed beam S = section modulus Sreq d = section modulus required at allowable stress tw = thickness o web o wide lange = internal shear orce longitudinal = longitudinal shear orce T = transverse shear orce w = name or distributed load x = horizontal distance y = vertical distance y = the distance in the y direction rom a reerence axis (n.a) to the centroid o a shape = the distance in the y direction rom a reerence axis to the centroid o a composite shape = calculus symbol or small quantity = elongation or length change = strain = arc angle = summation symbol ŷ 185
2 Pure Bending in Beams With bending moments along the axis o the member only, a beam is said to be in pure bending. Normal stresses due to bending can be ound or homogeneous materials having a plane o symmetry in the y axis that ollow Hooke s law. y Maximum Moment and Stress Distribution x n a member o constant cross section, the maximum bending moment will govern the design o the section size when we know what kind o normal stress is caused by it. For internal equilibrium to be maintained, the bending moment will be equal to the M rom the normal stresses the areas the moment arms. Geometric it helps solve this statically indeterminate problem: 1. The normal planes remain normal or pure bending.. There is no net internal axial orce. 3. Stress varies linearly over cross section. 4. Zero stress exists at the centroid and the line o centroids is the neutral axis (n. a) 186
3 Relations or Beam Geometry and Stress Pure bending results in a circular arc delection. R is the distance to the center o the arc; is the angle o the arc (radians); c is the distance rom the n.a. to the extreme iber; is a length change; max is the maximum normal stress at the extreme iber; y is a distance in y rom the n.a.; M is the bending moment; is the moment o inertia; S is the section modulus. L R M i A i My b L R M max c y i A i max Now: or a rectangle o height h and width b: E y A y c c S ½ c R L y ½ Mc max 3 bh bh S 1 h 6 M S RELATONS: 1 * M R E My b S c b max Mc M S S required M F b *Note: y positive goes DOWN. With a positive M and y to the bottom iber as positive, it results in a TENSON stress (we ve called positive) Transverse Loading in Beams We are aware that transverse beam loadings result in internal shear and bending moments. We designed sections based on bending stresses, since this stress dominates beam behavior. There can be shear stresses horizontally within a beam member. t can be shown that horizontal vertical 187
4 Equilibrium and Derivation n order or equilibrium or any element CDD C, there needs to be a horizontal orce H. D da C da Q is a moment area with respect to the neutral axis o the area above or below the horizontal where the H occurs. Q is a maximum when y = 0 (at the neutral axis). longitudinal T Q x q is a horizontal shear per unit length shear low Shearing Stresses q longitudinal x T Q v ave = 0 on the beam s surace. Even i Q is a maximum at y = 0, we don t know that the thickness is a minimum there. v A b x vave Q b Rectangular Sections occurs at the neutral axis: vmax then: 3 bh 1 Q Q 1 8 bh 3 v 3 b 1 bh b bh 1 Ay b h 1 h bh 3 v A 8 188
5 Webs o Beams n steel W or S sections the thickness varies rom the lange to the web. d We neglect the shear stress in the langes and consider the shear stress in the web to be constant: tw vmax 3 A A web vmax t d web Webs o beams can ail in tension shear across a panel with stieners or the web can buckle. Shear Flow Even i the cut we make to ind Q is not horizontal, but arbitrary, we can still ind the shear low, q, as long as the loads on thinwalled sections are applied in a plane o symmetry, and the cut is made perpendicular to the surace o the member. Q q The shear low magnitudes can be sketched by knowing Q. 189
6 Connectors to Resist Horizontal Shear in Composite Members Typical connections needing to resist shear are plates with nails or rivets or bolts in composite sections or splices. The pitch (spacing) can be determined by the capacity in shear o the connector(s) to the shear over the spacing interval, p. x y 4.43 ya low p p p where p = pitch length longitudinal Q n = number o connectors connecting the connected area to the rest o the cross section F = orce capacity in one connector p nf connector Q connected area longitudinal p Q p Qconnected area = Aconnected area yconnected area yconnected area = distance rom the centroid o the connected area to the neutral axis Connectors to Resist Horizontal Shear in Composite Members Even vertical connectors have shear low across them. p p p The spacing can be determined by the capacity in shear o the connector(s) to the shear low over the spacing interval, p. nf p Q connector connected area Unsymmetrical Sections or Shear the section is not symmetric, or has a shear not in that plane, the member can bend and twist. the load is applied at the shear center there will not be twisting. This is the location where the moment caused by shear low = the moment o the shear orce about the shear center. 190
7 Example 1 (pg 37) 191
8 Example * (pg 377), and evaluate the shear stress i F v = 95 psi. Roo: Snow +DL = 00 lb/t Walls: 400 lb on nd loor beams Railing: 100 lb on beam overhang Second Floor: DL + LL = 300 lb/t (including overhang) Roo: *ALSO select the most economical steel section or the secondloor when S req d is 165 in 3 and evaluate the shear stress when = 60 k. Second Floor: 19
9 Example 3 (pg 386) ALSO: Determine the minimum nail spacing required (pitch) i the shear capacity o a nail (F connector) is 50 lb
10 y= 4.5" ARCH 331 Note Set 10.1 Su016abn Example 4 (pg394 Q = Ay = (9")(½")(4.5")+(9")(½")(4.5")+(1.5")(3.5")(8.5") = 83.8 in 3 3 (, 600 #)( 83. 8in. ) 181. psi vmax ( 1, 0. 6in. )( " ") (n) (n) (n) (n)f p (n)f p 194
Beam Stresses Bending and Shear
Beam Stresses Bending and Shear Notation: A = name or area A web = area o the web o a wide lange setion b = width o a retangle = total width o material at a horizontal setion = largest distane rom the
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 informationtwo structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS
APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture two structural analysis (statics & mechanics) Analysis 1 Structural Requirements strength serviceability
More informationChapter 6: CrossSectional Properties of Structural Members
Chapter 6: CrossSectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross
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 informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationCHAPTER 6: Shearing Stresses in Beams
(130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.
More informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More 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 crosssection of a beam may consists of a resultant normal force,
More information7.4 The Elementary Beam Theory
7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be
More informationfive mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS
RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SUMMER 2014 Mechanics o Materials MECHNICS MTERIS lecture ive mechanics o materials www.carttalk.com Mechanics o Materials 1 rchitectural
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More information6. Bending CHAPTER OBJECTIVES
CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where
More information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shearstress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationSymmetric Bending of Beams
Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications
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 informationUNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.
UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude
More informationChapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )
Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress
More informationFor more Stuffs Visit Owner: N.Rajeev. R07
Code.No: 43034 R07 SET1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH  I SEMESTER REGULAR EXAMINATIONS NOVEMBER, 2009 FOUNDATION OF SOLID MECHANICS (AERONAUTICAL ENGINEERING) Time: 3hours
More informationMarch 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE
Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
More informationMECH 401 Mechanical Design Applications
MECH 401 Mechanical Design Applications Dr. M. O Malley Master Notes Spring 008 Dr. D. M. McStravick Rice University Updates HW 1 due Thursday (11708) Last time Introduction Units Reliability engineering
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M  N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationMECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola
MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the
More information6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and
6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile
More informationMechanics of Materials
Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics
More informationSTATICALLY INDETERMINATE STRUCTURES
STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal
More informationBE Semester I ( ) Question Bank (MECHANICS OF SOLIDS)
BE Semester I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)
More informationUnit III Theory of columns. Dr.P.Venkateswara Rao, Associate Professor, Dept. of Civil Engg., SVCE, Sriperumbudir
Unit III Theory of columns 1 Unit III Theory of Columns References: Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength of Materials", Tata
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending
EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:
More informationMECHANICS OF MATERIALS
CHAPTER 6 MECHANCS OF MATERALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Lecture Notes: J. Walt Oler Texas Tech University Shearing Stresses in Beams and Thin Walled Members
More informationMECHANICS OF MATERIALS. Analysis of Beams for Bending
MECHANICS OF MATERIALS Analysis of Beams for Bending By NUR FARHAYU ARIFFIN Faculty of Civil Engineering & Earth Resources Chapter Description Expected Outcomes Define the elastic deformation of an axially
More informationMaterials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationChapter 7: Bending and Shear in Simple Beams
Chapter 7: Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are generally applied transverse (perpendicular) to its longitudinal axis.
More information2014 MECHANICS OF MATERIALS
R10 SET  1 II. Tech I Semester Regular Examinations, March 2014 MEHNIS OF MTERILS (ivil Engineering) Time: 3 hours Max. Marks: 75 nswer any FIVE Questions ll Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 1
MECE 3321 MECHANICS O SOLIDS CHAPTER 1 Samantha Ramirez, MSE WHAT IS MECHANICS O MATERIALS? Rigid Bodies Statics Dynamics Mechanics Deformable Bodies Solids/Mech. Of Materials luids 1 WHAT IS MECHANICS
More informationCH. 5 TRUSSES BASIC PRINCIPLES TRUSS ANALYSIS. Typical depthtospan ratios range from 1:10 to 1:20. First: determine loads in various members
CH. 5 TRUSSES BASIC PRINCIPLES Typical depthtospan ratios range from 1:10 to 1:20  Flat trusses require less overall depth than pitched trusses Spans: 40200 Spacing: 10 to 40 on center  Residential
More informationPLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder
16 PLATE GIRDERS II 1.0 INTRODUCTION This chapter describes the current practice for the design of plate girders adopting meaningful simplifications of the equations derived in the chapter on Plate Girders
More information2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?
IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationEvaluation of Scantlings of Corrugated Transverse Watertight Bulkheads in NonCSR Bulk Carriers Considering Hold Flooding
(1997) (Rev.1 1997) (Rev.1.1 Mar 1998 /Corr.1) (Rev. Sept 000) (Rev.3 eb 001) (Rev.4 Nov 001) (Rev.5 July 003) (Rev.6 July 004) (Rev.7 eb 006) (Corr.1 Oct 009) (Rev.8 May 010) (Rev.9 Apr 014) Evaluation
More informationNow we are going to use our free body analysis to look at Beam Bending (W3L1) Problems 17, F2002Q1, F2003Q1c
Now we are going to use our free body analysis to look at Beam Bending (WL1) Problems 17, F00Q1, F00Q1c One of the most useful applications of the free body analysis method is to be able to derive equations
More informationIf the number of unknown reaction components are equal to the number of equations, the structure is known as statically determinate.
1 of 6 EQUILIBRIUM OF A RIGID BODY AND ANALYSIS OF ETRUCTURAS II 9.1 reactions in supports and joints of a twodimensional structure and statically indeterminate reactions: Statically indeterminate structures
More informationEngineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati
Engineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati Module 3 Lecture 6 Internal Forces Today, we will see analysis of structures part
More information8.3 Design of Base Plate for Thickness
8.3 Design o Base Plate or Thickness 8.3.1 Design o base plate or thickness (Elastic Design) Upto this point, the chie concern has been about the concrete oundation, and methods o design have been proposed
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain  Axial Loading Statics
More informationDECLARATION. Supervised by: Prof Stephen Mutuli
DECLARATION The work presented in this project is the original work, which to the best of our knowledge has never been produced and presented elsewhere for academic purposes... EYSIMGOBANAY K. J F18/1857/006
More informationMARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.
Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL
More informationMECHANICAL PROPERTIES OF SOLIDS
Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small nonzero constant value. 9. The maximum load a wire
More informationSeismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design
Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department
More informationDEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS
DEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS THE INFLUENCE OF THE FORM OF A WOODEN BEAM ON ITS STIFFNESS AND STRENGTHI (REPRINT FROM NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS REPORT
More informationStrength of Material. Shear Strain. Dr. Attaullah Shah
Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume
More informationCIVL222 STRENGTH OF MATERIALS. Chapter 6. Torsion
CIVL222 STRENGTH OF MATERIALS Chapter 6 Torsion Definition Torque is a moment that tends to twist a member about its longitudinal axis. Slender members subjected to a twisting load are said to be in torsion.
More informationCHAPTER 5 Statically Determinate Plane Trusses
CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS TYPES OF ROOF TRUSS ROOF TRUSS SETUP ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse
More informationStatic Equilibrium; Elasticity & Fracture
Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with
More informationCHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS
CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS 1 TYPES OF ROOF TRUSS ROOF TRUSS SETUP 2 ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse
More informationThis Technical Note describes how the program checks column capacity or designs reinforced concrete columns when the ACI code is selected.
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI31899 Technical Note This Technical Note describes how the program checks column capacity or designs reinforced
More informationChapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson
STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. Elkashif Civil Engineering Department, University
More informationMechanical Design in Optical Engineering
OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:
More informationChapter 2: Deflections of Structures
Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2
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 informationTHE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE
Journal of Applied Mathematics and Computational Mechanics 013, 1(4), 131 THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE Jolanta Błaszczuk
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationA. Objective of the Course: Objectives of introducing this subject at second year level in civil branches are: 1. Introduction 02
Subject Code: 0CL030 Subject Name: Mechanics of Solids B.Tech. II Year (Sem3) Mechanical & Automobile Engineering Teaching Credits Examination Marks Scheme Theory Marks Practical Marks Total L 4 T 0 P
More information4. SHAFTS. A shaft is an element used to transmit power and torque, and it can support
4. SHAFTS A shaft is an element used to transmit power and torque, and it can support reverse bending (fatigue). Most shafts have circular cross sections, either solid or tubular. The difference between
More informationOutline. Organization. Stresses in Beams
Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of
More informationChapter 5 Elastic Strain, Deflection, and Stability 1. Elastic StressStrain Relationship
Chapter 5 Elastic Strain, Deflection, and Stability Elastic StressStrain Relationship A stress in the xdirection causes a strain in the xdirection by σ x also causes a strain in the ydirection & zdirection
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
More informationCHAPTER 6: ULTIMATE LIMIT STATE
CHAPTER 6: ULTIMATE LIMIT STATE 6.1 GENERAL It shall be in accordance with JSCE Standard Specification (Design), 6.1. The collapse mechanism in statically indeterminate structures shall not be considered.
More informationInfluence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes
October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis StressStrain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationPLAT DAN CANGKANG (TKS 4219)
PLAT DAN CANGKANG (TKS 4219) SESI I: PLATES Dr.Eng. Achfas Zacoeb Dept. of Civil Engineering Brawijaya University INTRODUCTION Plates are straight, plane, twodimensional structural components of which
More 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 informationfive moments ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture five moments Moments 1 Moments forces have the tendency to make a body rotate about an axis http://www.physics.umd.edu
More informationSteel Post Load Analysis
Steel Post Load Analysis Scope The steel posts in 73019022, 73019024, and 73019025, are considered to be traditional building products. According to the 2015 International Building Code, this type of product
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad 00 04 CIVIL ENGINEERING QUESTION BANK Course Name : STRENGTH OF MATERIALS II Course Code : A404 Class : II B. Tech II Semester Section
More informationExplanatory Examples for Ductile Detailing of RC Buildings
Document No. :: IITKGSDEQV3.0 Final Report ::  Earthquake Codes IITKGSD Project on Building Codes Explanatory Examples or Ductile Detailing o RC Buildings by Dr. R. K. Ingle Department o pplied echanics
More informationCivil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7
Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...
More informationChapter 26 Elastic Properties of Materials
Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic
More informationLECTURE 14 Strength of a Bar in Transverse Bending. 1 Introduction. As we have seen, only normal stresses occur at cross sections of a rod in pure
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 14 Strength of a Bar in Transverse Bending 1 ntroduction s we have seen, onl normal stresses occur at cross sections of a rod in pure bending. The corresponding
More informationModule 7 Design of Springs. Version 2 ME, IIT Kharagpur
Module 7 Design of Springs Lesson 1 Introduction to Design of Helical Springs Instructional Objectives: At the end of this lesson, the students should be able to understand: Uses of springs Nomenclature
More informationMECHANICS OF SOLIDS Credit Hours: 6
MECHANICS OF SOLIDS Credit Hours: 6 Teaching Scheme Theory Tutorials Practical Total Credit Hours/week 4 0 6 6 Marks 00 0 50 50 6 A. Objective of the Course: Objectives of introducing this subject at second
More informationFCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering
FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress
More informationLecture 8 Viscoelasticity and Deformation
HW#5 Due 2/13 (Friday) Lab #1 Due 2/18 (Next Wednesday) For Friday Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, μ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force
More informationSection Downloads. Section Downloads. Handouts & Slides can be printed. Other documents cannot be printed Course binders are available for purchase
Level II: Section 04 Simplified Method (optional) Section Downloads Section Downloads Handouts & Slides can be printed Version.0 Other documents cannot be printed Course binders are available for purchase
More informationMECHANICS OF MATERIALS
009 The McGrawHill Companies, nc. All rights reserved. Fifth S E CHAPTER 6 MECHANCS OF MATERALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Lecture Notes: J. Walt Oler Texas
More informationDegree Thesis Flexural Rigidity (D) in Beams. Author: Zious Karis. Instructor: Rene Herrmann
Degree Thesis Flexural Rigidity (D) in Beams Author: Zious Karis Instructor: Rene Herrmann Degree Thesis Materials Processing Technology 2017 DEGREE THESIS Arcada University of Applied Sciences, Helsinki,
More information14. *14.8 CASTIGLIANO S THEOREM
*14.8 CASTIGLIANO S THEOREM Consider a body of arbitrary shape subjected to a series of n forces P 1, P 2, P n. Since external work done by forces is equal to internal strain energy stored in body, by
More informationRigid and Braced Frames
RH 331 Note Set 12.1 F2014abn Rigid and raced Frames Notation: E = modulus of elasticit or Young s modulus F = force component in the direction F = force component in the direction FD = free bod diagram
More informationThe Local Web Buckling Strength of Coped Steel IBeam. ABSTRACT : When a beam flange is coped to allow clearance at the
The Local Web Buckling Strength of Coped Steel IBeam Michael C. H. Yam 1 Member, ASCE Angus C. C. Lam Associate Member, ASCE, V. P. IU and J. J. R. Cheng 3 Members, ASCE ABSTRACT : When a beam flange
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 informationME 176 Final Exam, Fall 1995
ME 176 Final Exam, Fall 1995 Saturday, December 16, 12:30 3:30 PM, 1995. Answer all questions. Please write all answers in the space provided. If you need additional space, write on the back sides. Indicate
More informationLongitudinal strength standard
(1989) (Rev. 1 199) (Rev. Nov. 001) Longitudinal strength standard.1 Application This requirement applies only to steel ships of length 90 m and greater in unrestricted service. For ships having one or
More informationBTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5
BTECH MECHANICAL PRINCIPLES AND APPLICATIONS Level 3 Unit 5 FORCES AS VECTORS Vectors have a magnitude (amount) and a direction. Forces are vectors FORCES AS VECTORS (2 FORCES) Forces F1 and F2 are in
More informationDetermine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.
E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct
More informationFundamentals of Structural Design Part of Steel Structures
Fundamentals of Structural Design Part of Steel Structures Civil Engineering for Bachelors 133FSTD Teacher: Zdeněk Sokol Office number: B619 1 Syllabus of lectures 1. Introduction, history of steel structures,
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More information