Shear Center in Thin-Walled Beams Lab

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Shear Center in Thin-Walled Beams Lab"

Transcription

1 Shear Center in Thin-Walled Beams Lab Shear flow is developed in beams with thin-walled cross sections shear flow (q sx ): shear force per unit length along cross section q sx =τ sx t behaves much like a flow, especially at junctions in cross section shear flow acts along tangent (s) direction on cross section there is a normal component, τ nx, but it is very small e.g., because it must be zero at ±t/2 shear force: q sx ds (acting in s direction) Shear flow arises from presence of shear loads, V y or V z needed to counter unbalanced bending stresses, σ x to determine, must analyze equilibrium in axial (x) direction Shear center: resultant of shear flow on section must equal V y and V z moment due to q sx must be equal to moment due to V y and V z shear center: point about which moment due to shear flow is zero not applying transverse loads through shear center will cause a twisting of the beam about the x axis AE3145 Shear Center Lab (S2k) Slide 1

2 Approach for Lab Apply transverse loading to tip of a cantilever thin-walled beam use cross-arm at tip to apply both a lateral force and twisting mom. measure bending deflection measure twisting vary location of load point along cross-arm repeat for beam rotated 90 deg. about x axis Data analysis record deflections using LVDT plot twisting versus load position on cross-arm determine location on cross-arm where load produces no twisting Compare the measured shear center with theoretical location shear flow calculations used to compute shear center consider both y axis and z axis loading (rotated 90 deg) AE3145 Shear Center Lab (S2k) Slide 2

3 Review from AE2120 (2751), AE3120 Bending of beams with unsymmetrical cross sections bending stress depends on I y, I z and I yz neutral surface is no longer aligned with z or y axes Shear stresses are computed from axial force equilibrium shear stress needed to counter changing σ x analysis strictly correct for rectangular sections only Thin-walled cross sections thin walls support bending stress just like a solid section (no change) thin walls support shear stress in tangential direction transverse shear component is negligable... because it must vanish at the free surfaces (edges of cross section) shear flow: τ xs t (force/unit length along section) shear flow must be equivalent to V y and V z so it must: produce same vertical and horizontal force (V x and V y ) produce same mumoment about any point in cross section point about which no moment is developed: SHEAR CENTER lateral load must be applied through SC to avoid twisting beam twisting loads will cause section to twist about SC (center of rotation) AE3145 Shear Center Lab (S2k) Slide 3

4 Test Configuration Cantilever Cantilever with with thinwalled thinwalled C section section LVDT LVDT measures measures tip tip deflection deflection on on cross-arm cross-arm cross arm LVDT weight Lab Apparatus Small Small weight weight used used to to apply apply load load at at point point on on cross-arm cross-arm AE3145 Shear Center Lab (S2k) Slide 4

5 Lab Procedure 1. Determine the beam material properties from reference material (e.g., referenced textbooks or MIL Handbook 5 which can be found in the GT Library). 2. Find the centroid of the given beam cross-section. 3. Determine Iz, I y, I yz for the given section. 4. Determine the shear flow distribution on the cross-section for a V y shear load. 5. Determine the shear flow distribution on the cross-section for a V z shear load. 6. Determine the shear center for the cross-section. 7. Using data from the lab, determine the measured location of the shear center and compare this with the location determined in step 6 above. AE3145 Shear Center Lab (S2k) Slide 5

6 Beam Cross Section 1.353in. Use Use single single line line approx approx for for 1.330in. cross cross section section (t<<b,h) (t<<b,h) 0.420in. Centroidal Axes: 0.050in. 0 = 0 = A A zda yda Area Moments (of Inertia): 2 z da A 2 y da A AE3145 Shear Center Lab (S2k) Slide 6 I I I yy zz yz = = = yzda A

7 Bending of Beam with Unsymmetrical Cross Section q General: σ x Acts over cross section Symmetric cross section, M z =0: x ( yi zi ) M + ( yi zi ) M = σ = ym I zz A 1 yy yz z yz zz y 2 Izz Iyy Iyz z But But also also consider consider equilibrium equilibrium of of segment segment A 1 (see 1 (see next next slide!) slide!) AE3145 Shear Center Lab (S2k) Slide 7

8 Shear Stresses and Shear Flow σ x q sx s Complementary Complementary q sx acts sx acts on on A 1 in 1 in opposite opposite direction direction A 1 σ x +dσ x Axial force equilibrium for element: X F da q dx da A1 A1 0 = x = σ x + sx σ x x+ dx x AE3145 Shear Center Lab (S2k) Slide 8

9 Shear Flow Result for q sx : V y V z qsx = 2 Iyy yda Iyz zda + 2 Izz zda Iyz yda Iyy Izz I yz A1 A I 1 yy Izz I yz A1 A1 s Shear flow: q sx (s) AE3145 Shear Center Lab (S2k) Slide 9

10 Shear Center Moment Moment due due to to V y y must must be be equal equal to to M 0 0 V y s e z Shear flow: q sx (s) Therefore: Therefore: Shear Shear center center lies lies distance distance e z from z from origin origin where: where: M 0 =V 0 =V y e y z z Moment, Moment, M 0, 0, at at origin origin due due to to shear shear flow, flow, q sx sx AE3145 Shear Center Lab (S2k) Slide 10

11 Examples of Shear Centers V y V y q sx Shear Center lies on y axis Shear Center q sx Section Symmetric about about y axis: axis: Angle Angle Section: Shear Shear center center must must lie lie on on y y axis axis (similar (similar argument argument for for z z axis axis symmetry) symmetry) Shear Shear center center must must lie lie at at vertex vertex of of legs legs (regardless (regardless of of orientation orientation of of section) section) AE3145 Shear Center Lab (S2k) Slide 11

12 Shear Center Must Lie Outside C B q sx V y e q sx h/2 Shear Center A h/2 q sx Sum moments from q sx about A: =force in each flange x h/2 Must equal moment from V y about A: =V y x e e must must be be positive positive for for q sx as sx as shown shown so so shear shear center center lies lies to to left left of of section section AE3145 Shear Center Lab (S2k) Slide 12

13 Data Acquisition Use PC data acquisition program to acquire deflection and strain data and test machine load Use 2 LVDT displacement gages Measure vertical displacements at ends of cross arm Use to determine vertical deflection and cross arm rotation Use single weight but move to different locations on cross arm Cross arm Replace dial gages with LVDT s Loading system AE3145 Shear Center Lab (S2k) Slide 13

14 Data Reduction Acquired data is voltage from transducers convert to inch units Determine vertical displacement per applied load Determine rotation per applied load Plot rotation vs cross arm location: 0 point defines shear center or: plot both displacements: crossing point defines shear center Example (next slide) AE3145 Shear Center Lab (S2k) Slide 14

15 AE 3145 Lab - Fall 99 Lab name=lab#7 Shear Center Group name = Monday1 Load Position Channel 1 Channel 2 Excitation Voltage 0.00E E E E E E E E E E E E E+00 Convert -7.04E E E E+00 Convert voltages -6.15E+00 voltages to to displacement -3.75E E+00 displacement using 2.50E E+00 using LVDT LVDT -3.38E E+00 calibration 3.00E+00 calibration data -3.87E+00 data -3.67E E E E E E E E E E+00 Cal: Position LVDT 1 LVDT 2 Deflection Rotation Sample Data Reading (inch or radian) Shear Shear Center Center is is point point where where Rotation Rotation = = 0 0 or or point point where where LVDT1=LVDT2 LVDT1=LVDT2 LVDT 1 LVDT 2 Rotation Position Plot Plot your your data! data! Compute Compute avg avg deflection deflection and and rotation rotation from from geometry geometry AE3145 Shear Center Lab (S2k) Slide 15

Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

More information

BEAMS: SHEAR FLOW, THIN WALLED MEMBERS

BEAMS: SHEAR FLOW, THIN WALLED MEMBERS LECTURE BEAMS: SHEAR FLOW, THN WALLED MEMBERS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering 15 Chapter 6.6 6.7 by Dr. brahim A. Assakkaf SPRNG 200 ENES

More information

Introduction, Method of Sections

Introduction, Method of Sections Lecture #1 Introduction, Method of Sections Reading: 1:1-2 Mechanics of Materials is the study of the relationship between external, applied forces and internal effects (stress & deformation). An understanding

More information

Section 16: Neutral Axis and Parallel Axis Theorem 16-1

Section 16: Neutral Axis and Parallel Axis Theorem 16-1 Section 16: Neutral Axis and Parallel Axis Theorem 16-1 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about y-axis All parts

More information

New approaches in Eurocode 3 efficient global structural design

New approaches in Eurocode 3 efficient global structural design New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beam-column FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural

More information

Figure 1- Different parts of experimental apparatus.

Figure 1- Different parts of experimental apparatus. Objectives Determination of center of buoyancy Determination of metacentric height Investigation of stability of floating objects Apparatus The unit shown in Fig. 1 consists of a pontoon (1) and a water

More information

8.2 Elastic Strain Energy

8.2 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 information

MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS

MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.

More information

EML 5526 FEA Project 1 Alexander, Dylan. Project 1 Finite Element Analysis and Design of a Plane Truss

EML 5526 FEA Project 1 Alexander, Dylan. Project 1 Finite Element Analysis and Design of a Plane Truss Problem Statement: Project 1 Finite Element Analysis and Design of a Plane Truss The plane truss in Figure 1 is analyzed using finite element analysis (FEA) for three load cases: A) Axial load: 10,000

More information

MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements

MCE380: 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 information

Deflections. Question: What are Structural Deflections?

Deflections. 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 information

MECHANICS 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 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 information

Stresses in Beam (Basic Topics)

Stresses 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 information

Chapter 2: Load, Stress and Strain

Chapter 2: Load, Stress and Strain Chapter 2: Load, Stress and Strain The careful text- books measure (Let all who build beware!) The load, the shock, the pressure Material can bear. So when the buckled girder Lets down the grinding span,

More information

Structural Axial, Shear and Bending Moments

Structural 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 information

Lab for Deflection and Moment of Inertia

Lab for Deflection and Moment of Inertia Deflection and Moment of Inertia Subject Area(s) Associated Unit Lesson Title Physics Wind Effects on Model Building Lab for Deflection and Moment of Inertia Grade Level (11-12) Part # 2 of 3 Lesson #

More information

Analysis of Stresses and Strains

Analysis of Stresses and Strains Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we

More information

Introduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams

Introduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams Introduction to Beam Theory Area Moments of Inertia, Deflection, and Volumes of Beams Horizontal structural member used to support horizontal loads such as floors, roofs, and decks. Types of beam loads

More information

Torsion Testing. Objectives

Torsion Testing. Objectives Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials

More information

Design Analysis and Review of Stresses at a Point

Design 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 information

Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 23 Bending of Beams- II

Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 23 Bending of Beams- II Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 23 Bending of Beams- II Welcome to the second lesson of the fifth module which is on Bending of Beams part

More information

MECHANICS 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 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 information

Bending of Beams with Unsymmetrical Sections

Bending of Beams with Unsymmetrical Sections Bending of Beams with Unsmmetrical Sections Assume that CZ is a neutral ais. C = centroid of section Hence, if > 0, da has negative stress. From the diagram below, we have: δ = α and s = αρ and δ ε = =

More information

CASE HISTORY #2. APPLICATION: Piping Movement Survey using Permalign Laser Measurement System

CASE HISTORY #2. APPLICATION: Piping Movement Survey using Permalign Laser Measurement System CASE HISTORY #2 APPLICATION: Piping Movement Survey using Permalign Laser Measurement System EQUIPMENT: Dresser-Clark Hot Gas Expander (Turbine), 60-inch Inlet Flange HISTORY: Piping support modifications

More information

Mechanics of Materials Summary

Mechanics 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 cross-sectional shape is constant and has area. Figure 1.1: rod with a normal

More information

Problem 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 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 information

Torsion Tests. Subjects of interest

Torsion 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 information

Structures and Stiffness

Structures and Stiffness Structures and Stiffness ENGR 10 Introduction to Engineering Ken Youssefi/Thalia Anagnos Engineering 10, SJSU 1 Wind Turbine Structure The Goal The support structure should be optimized for weight and

More information

STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION

STRESS 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 three-dimensional solid deformable

More information

Notes on the Linear Analysis of Thin-walled Beams

Notes on the Linear Analysis of Thin-walled Beams Notes on the Linear Analysis of Thin-walled Beams Walter D. Pilkey and Levent Kitiş Department of Mechanical Engineering University of Virginia Charlottesville, Virginia c August 1996 Contents Chapter

More information

M x (a) (b) (c) Figure 2: Lateral Buckling The positions of the beam shown in Figures 2a and 2b should be considered as two possible equilibrium posit

M x (a) (b) (c) Figure 2: Lateral Buckling The positions of the beam shown in Figures 2a and 2b should be considered as two possible equilibrium posit Lateral Stability of a Slender Cantilever Beam With End Load Erik Thompson Consider the slender cantilever beam with an end load shown in Figure 1. The bending moment at any cross-section is in the x-direction.

More information

Stiffness Methods for Systematic Analysis of Structures (Ref: Chapters 14, 15, 16)

Stiffness 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 information

bi directional loading). Prototype ten story

bi directional loading). Prototype ten story NEESR SG: Behavior, Analysis and Design of Complex Wall Systems The laboratory testing presented here was conducted as part of a larger effort that employed laboratory testing and numerical simulation

More information

Certification of Discontinuous Composite Material Forms for Aircraft Structures

Certification of Discontinuous Composite Material Forms for Aircraft Structures Certification of Discontinuous Composite Material Forms for Aircraft Structures Paolo Feraboli (UWAA), Mark Tuttle (UW), Larry Ilcewicz (FAA), Bill Avery (Boeing), Bruno Boursier, Dave Barr (Hexcel) JAMS

More information

Unit 6 Plane Stress and Plane Strain

Unit 6 Plane Stress and Plane Strain Unit 6 Plane Stress and Plane Strain Readings: T & G 8, 9, 10, 11, 12, 14, 15, 16 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems There are many structural configurations

More information

Introduction to Mechanical Behavior of Biological Materials

Introduction to Mechanical Behavior of Biological Materials Introduction to Mechanical Behavior of Biological Materials Ozkaya and Nordin Chapter 7, pages 127-151 Chapter 8, pages 173-194 Outline Modes of loading Internal forces and moments Stiffness of a structure

More information

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

More information

Finite Element Formulation for Beams - Handout 2 -

Finite Element Formulation for Beams - Handout 2 - Finite Element Formulation for Beams - Handout 2 - Dr Fehmi Cirak (fc286@) Completed Version Review of Euler-Bernoulli Beam Physical beam model midline Beam domain in three-dimensions Midline, also called

More information

ENGINEERING 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 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 information

Impact Load Factors for Static Analysis

Impact Load Factors for Static Analysis Impact Load Factors for Static Analysis Often a designer has a mass, with a known velocity, hitting an object and thereby causing a suddenly applied impact load. Rather than conduct a dynamic analysis

More information

Hydrostatic Force on a Submerged Surface

Hydrostatic Force on a Submerged Surface Experiment 3 Hydrostatic Force on a Submerged Surface Purpose The purpose of this experiment is to experimentally locate the center of pressure of a vertical, submerged, plane surface. The experimental

More information

Shear Force and Moment Diagrams

Shear Force and Moment Diagrams C h a p t e r 9 Shear Force and Moment Diagrams In this chapter, you will learn the following to World Class standards: Making a Shear Force Diagram Simple Shear Force Diagram Practice Problems More Complex

More information

The elements used in commercial codes can be classified in two basic categories:

The 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 information

Høgskolen i Narvik Sivilingeniørutdanningen

Høgskolen i Narvik Sivilingeniørutdanningen Høgskolen i Narvik Sivilingeniørutdanningen Eksamen i Faget STE66 ELASTISITETSTEORI Klasse: 4.ID Dato: 7.0.009 Tid: Kl. 09.00 1.00 Tillatte hjelpemidler under eksamen: Kalkulator Kopi av Boken Mechanics

More information

Bending Stress and Strain

Bending Stress and Strain Bending Stress and Strain DEFLECTIONS OF BEAMS When a beam with a straight longitudinal ais is loaded by lateral forces, the ais is deformed into a curve, called the deflection curve of the beam. We will

More information

Mechanics of Materials. Chapter 5 Stresses In Beams

Mechanics of Materials. Chapter 5 Stresses In Beams Mechanics of Materials Chapter 5 Stresses In Beams 5.1 Introduction In previous chapters, the stresses in bars caused by axial loading and torsion. Here consider the third fundamental loading : bending.

More information

22.302 Experiment 5. Strain Gage Measurements

22.302 Experiment 5. Strain Gage Measurements 22.302 Experiment 5 Strain Gage Measurements Introduction The design of components for many engineering systems is based on the application of theoretical models. The accuracy of these models can be verified

More information

Plane-Shear Measurement with Strain Gages

Plane-Shear Measurement with Strain Gages Micro-MeasuremeNTs Strain Gages and Instruments e TN-5- Introduction Loading a specimen as shown in Figure a produces shear stresses in the material. An initially square element of the material, having

More information

Chapter 5: Distributed Forces; Centroids and Centers of Gravity

Chapter 5: Distributed Forces; Centroids and Centers of Gravity CE297-FA09-Ch5 Page 1 Wednesday, October 07, 2009 12:39 PM Chapter 5: Distributed Forces; Centroids and Centers of Gravity What are distributed forces? Forces that act on a body per unit length, area or

More information

Unit M4.3 Statics of Beams

Unit M4.3 Statics of Beams Unit M4.3 Statics of Beams Readings: CD 3.2-3.6 (CD 3.8 -- etension to 3-D) 16.003/004 -- Unified Engineering Department of Aeronautics and Astronautics Massachusetts Institute of Technology EARNING OBJECTIVES

More information

MATERIALS AND MECHANICS OF BENDING

MATERIALS AND MECHANICS OF BENDING HAPTER Reinforced oncrete Design Fifth Edition MATERIALS AND MEHANIS OF BENDING A. J. lark School of Engineering Department of ivil and Environmental Engineering Part I oncrete Design and Analysis b FALL

More information

BEAMS: SHEAR AND MOMENT DIAGRAMS (GRAPHICAL)

BEAMS: SHEAR AND MOMENT DIAGRAMS (GRAPHICAL) LECTURE Third Edition BES: SHER ND OENT DIGRS (GRPHICL). J. Clark School of Engineering Department of Civil and Environmental Engineering 3 Chapter 5.3 by Dr. Ibrahim. ssakkaf SPRING 003 ENES 0 echanics

More information

Lateral Buckling of Singly Symmetric Beams

Lateral Buckling of Singly Symmetric Beams Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold- Formed Steel Structures (1992) - 11th International Specialty Conference on Cold-Formed Steel Structures

More information

Reinforced Concrete Design SHEAR IN BEAMS

Reinforced Concrete Design SHEAR IN BEAMS CHAPTER Reinforced Concrete Design Fifth Edition SHEAR IN BEAMS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part I Concrete Design and Analysis 4a FALL 2002 By Dr.

More information

Chapter 5: Tool Dynamometers

Chapter 5: Tool Dynamometers Chapter 5: Tool Dynamometers LEARNING OBJECTIVES Different types of transducers used in Dynamometers Design Requirements Types of Dynamometers ---------------------------------------------------------------------------------------------------------------------

More information

A beam is a structural member that is subjected primarily to transverse loads and negligible

A beam is a structural member that is subjected primarily to transverse loads and negligible Chapter. Design of Beams Flexure and Shear.1 Section force-deformation response & Plastic Moment (M p ) A beam is a structural member that is subjected primarily to transverse loads and negligible axial

More information

INTRODUCTION TO BEAMS

INTRODUCTION 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 information

Calibration and Use of a Strain-Gage-Instrumented Beam: Density Determination and Weight-Flow-Rate Measurement

Calibration and Use of a Strain-Gage-Instrumented Beam: Density Determination and Weight-Flow-Rate Measurement Chapter 2 Calibration and Use of a Strain-Gage-Instrumented Beam: Density Determination and Weight-Flow-Rate Measurement 2.1 Introduction and Objectives This laboratory exercise involves the static calibration

More information

FLC Ch 1 & 3.1. A ray AB, denoted, is the union of and all points on such that is between and. The endpoint of the ray AB is A.

FLC Ch 1 & 3.1. A ray AB, denoted, is the union of and all points on such that is between and. The endpoint of the ray AB is A. Math 335 Trigonometry Sec 1.1: Angles Definitions A line is an infinite set of points where between any two points, there is another point on the line that lies between them. Line AB, A line segment is

More information

TUTORIAL FOR RISA EDUCATIONAL

TUTORIAL FOR RISA EDUCATIONAL 1. INTRODUCTION TUTORIAL FOR RISA EDUCATIONAL C.M. Uang and K.M. Leet The educational version of the software RISA-2D, developed by RISA Technologies for the textbook Fundamentals of Structural Analysis,

More information

Rear Impact Guard TEST METHOD 223. Standards and Regulations Division. Issued: December 2003

Rear Impact Guard TEST METHOD 223. Standards and Regulations Division. Issued: December 2003 Transport Canada Safety and Security Road Safety Transports Canada Sécurité et sûreté Sécurité routière Standards and Regulations Division TEST METHOD 223 Rear Impact Guard Issued: December 2003 Standards

More information

8.2 Shear and Bending-Moment Diagrams: Equation Form

8.2 Shear and Bending-Moment Diagrams: Equation Form 8.2 Shear and ending-oment Diagrams: Equation Form 8.2 Shear and ending-oment Diagrams: Equation Form Eample 1, page 1 of 6 1. Epress the shear and bending moment as functions of, the distance from the

More information

m i: is the mass of each particle

m i: is the mass of each particle Center of Mass (CM): The center of mass is a point which locates the resultant mass of a system of particles or body. It can be within the object (like a human standing straight) or outside the object

More information

Course 1 Laboratory. Second Semester. Experiment: Young s Modulus

Course 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 information

Trench Tutorial. 1. Bring soil layers to equilibrium. 2. Install a pile on the high side of the trench

Trench Tutorial. 1. Bring soil layers to equilibrium. 2. Install a pile on the high side of the trench Trench Tutorial 17-1 Trench Tutorial In this tutorial, Phase2 is used to simulate the excavation of a trench into a sloped embankment. The trench is supported by soldier piles and struts. The model is

More information

When a user chooses to model the surface component using plate elements, he/she is taking on the responsibility of meshing.

When a user chooses to model the surface component using plate elements, he/she is taking on the responsibility of meshing. Concrete slab Design: Yes, you can design the concrete slab using STAAD, with plate elements and meshing it appropriately. But it is best practice to take the analysis results from the STAAD and do the

More information

Stress: The stress in an axially loaded tension member is given by Equation (4.1) P (4.1) A

Stress: The stress in an axially loaded tension member is given by Equation (4.1) P (4.1) A Chapter 4. TENSION MEMBER DESIGN 4.1 INTRODUCTORY CONCEPTS Stress: The stress in an axially loaded tension member is given by Equation (4.1) P f = (4.1) A where, P is the magnitude of load, and A is the

More information

CEEN 162 - Geotechnical Engineering Laboratory Session 7 - Direct Shear and Unconfined Compression Tests

CEEN 162 - Geotechnical Engineering Laboratory Session 7 - Direct Shear and Unconfined Compression Tests PURPOSE: The parameters of the shear strength relationship provide a means of evaluating the load carrying capacity of soils, stability of slopes, and pile capacity. The direct shear test is one of the

More information

Worked Examples of mathematics used in Civil Engineering

Worked Examples of mathematics used in Civil Engineering Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial - Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced

More information

EXPERIMENT NO. 1. Aim: - To verify strain in an externally loaded beam with the help of a strain gauge indicator and to verify theoretically.

EXPERIMENT NO. 1. Aim: - To verify strain in an externally loaded beam with the help of a strain gauge indicator and to verify theoretically. EXPERIMENT NO. 1 Aim: - To verify strain in an externally loaded beam with the help of a strain gauge indicator and to verify theoretically. Apparatus: - Strain gauge Indicator, weights, hanger, scale,

More information

Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

More information

Standard Terminology for Vehicle Dynamics Simulations

Standard Terminology for Vehicle Dynamics Simulations Standard Terminology for Vehicle Dynamics Simulations Y v Z v X v Michael Sayers The University of Michigan Transportation Research Institute (UMTRI) February 22, 1996 Table of Contents 1. Introduction...1

More information

End Restraint and Effective Lengths of Columns

End Restraint and Effective Lengths of Columns CHAPTER Structural Steel Design LRFD Method Third Edition INTRODUCTION TO AXIALLY LOADED COMPRESSION MEMBERS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II

More information

Composite Sections and Steel Beam Design. Composite Design. Steel Beam Selection - ASD Composite Sections Analysis Method

Composite Sections and Steel Beam Design. Composite Design. Steel Beam Selection - ASD Composite Sections Analysis Method Architecture 324 Structures II Composite Sections and Steel Beam Design Steel Beam Selection - ASD Composite Sections Analysis Method Photo by Mike Greenwood, 2009. Used with permission University of Michigan,

More information

EQUILIBRIUM STRESS SYSTEMS

EQUILIBRIUM STRESS SYSTEMS EQUILIBRIUM STRESS SYSTEMS Definition of stress The general definition of stress is: Stress = Force Area where the area is the cross-sectional area on which the force is acting. Consider the rectangular

More information

Bending Stress in Beams

Bending Stress in Beams 936-73-600 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

Finite Element Formulation for Plates - Handout 3 -

Finite Element Formulation for Plates - Handout 3 - Finite Element Formulation for Plates - Handout 3 - Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the

More information

W2L3. Stresses in Engineering Components (problems 14, 15, 16) (Courseware pg 43-46) τda

W2L3. Stresses in Engineering Components (problems 14, 15, 16) (Courseware pg 43-46) τda Stresses in Engineering Components (problems 14, 15, 16) (combining elastic moduli with geometry elastic behaviour) W2L3 (Courseware pg 43-46) Free Body Analysis: common technique to develop stress equations

More information

Mathematics 1. Lecture 5. Pattarawit Polpinit

Mathematics 1. Lecture 5. Pattarawit Polpinit Mathematics 1 Lecture 5 Pattarawit Polpinit Lecture Objective At the end of the lesson, the student is expected to be able to: familiarize with the use of Cartesian Coordinate System. determine the distance

More information

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.)

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.) ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University it of Maryland Compression Members Following subjects are covered:

More information

Chapter 4: Summary and Conclusions

Chapter 4: Summary and Conclusions Chapter 4: Summary and Conclusions 4.1 Summary Three different models are presented and analyzed in this research for the purpose of studying the potential of using post-buckled or pre-bent elastic struts

More information

Module 6 : Design of Retaining Structures. Lecture 28 : Anchored sheet pile walls [ Section 28.1 : Introduction ]

Module 6 : Design of Retaining Structures. Lecture 28 : Anchored sheet pile walls [ Section 28.1 : Introduction ] Lecture 28 : Anchored sheet pile walls [ Section 28.1 : Introduction ] Objectives In this section you will learn the following Introduction Lecture 28 : Anchored sheet pile walls [ Section 28.1 : Introduction

More information

Advanced Structural Analysis. Prof. Devdas Menon. Department of Civil Engineering. Indian Institute of Technology, Madras. Module - 5.3.

Advanced Structural Analysis. Prof. Devdas Menon. Department of Civil Engineering. Indian Institute of Technology, Madras. Module - 5.3. Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module - 5.3 Lecture - 29 Matrix Analysis of Beams and Grids Good morning. This is

More information

MENG 302L Lab 4: Modulus of Elasticity and Poisson s Ratio

MENG 302L Lab 4: Modulus of Elasticity and Poisson s Ratio MENG 302L Lab 4: Modulus of Elasticity and Poisson s Ratio Introduction: In Lab 4 we will measure the two fundamental elastic constants relating stress to strain: Modulus of Elasticity and Poisson s Ratio.

More information

2. Axial Force, Shear Force, Torque and Bending Moment Diagrams

2. Axial Force, Shear Force, Torque and Bending Moment Diagrams 2. Axial Force, Shear Force, Torque and Bending Moment Diagrams In this section, we learn how to summarize the internal actions (shear force and bending moment) that occur throughout an axial member, shaft,

More information

physics 111N rotational motion

physics 111N rotational motion physics 111N rotational motion rotations of a rigid body! suppose we have a body which rotates about some axis! we can define its orientation at any moment by an angle, θ (any point P will do) θ P physics

More information

Learning Module 1 Static Structural Analysis

Learning Module 1 Static Structural Analysis LM-ST-1 Learning Module 1 Static Structural Analysis What is a Learning Module? Title Page Guide A Learning Module (LM) is a structured, concise, and self-sufficient learning resource. An LM provides the

More information

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS

A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The

More information

Unit 3 (Review of) Language of Stress/Strain Analysis

Unit 3 (Review of) Language of Stress/Strain Analysis Unit 3 (Review of) Language of Stress/Strain Analysis Readings: B, M, P A.2, A.3, A.6 Rivello 2.1, 2.2 T & G Ch. 1 (especially 1.7) Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering

More information

Nonlinear analysis and form-finding in GSA Training Course

Nonlinear analysis and form-finding in GSA Training Course Nonlinear analysis and form-finding in GSA Training Course Non-linear analysis and form-finding in GSA 1 of 47 Oasys Ltd Non-linear analysis and form-finding in GSA 2 of 47 Using the GSA GsRelax Solver

More information

Mechanics of Materials. Chapter 6 Deflection of Beams

Mechanics of Materials. Chapter 6 Deflection of Beams Mechanics of Materials Chapter 6 Deflection of Beams 6.1 Introduction Because the design of beams is frequently governed by rigidity rather than strength. For example, building codes specify limits on

More information

Lecture 8 Bending & Shear Stresses on Beams

Lecture 8 Bending & Shear Stresses on Beams Lecture 8 Bending & hear tresses on Beams Beams are almost always designed on the asis of ending stress and, to a lesser degree, shear stress. Each of these stresses will e discussed in detail as follows.

More information

EXPERIMENT: MOMENT OF INERTIA

EXPERIMENT: MOMENT OF INERTIA OBJECTIVES EXPERIMENT: MOMENT OF INERTIA to familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in

More information

Precision Miniature Load Cell. Models 8431, 8432 with Overload Protection

Precision Miniature Load Cell. Models 8431, 8432 with Overload Protection w Technical Product Information Precision Miniature Load Cell with Overload Protection 1. Introduction The load cells in the model 8431 and 8432 series are primarily designed for the measurement of force

More information

EQUILIBRIUM AND ELASTICITY

EQUILIBRIUM 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 information

BEAM THEORIES The difference between Euler-Bernoulli and Timoschenko

BEAM THEORIES The difference between Euler-Bernoulli and Timoschenko BEAM THEORIES The difference between Euler-Bernoulli and Timoschenko Uemuet Goerguelue Two mathematical models, namely the shear-deformable (Timoshenko) model and the shearindeformable (Euler-Bernoulli)

More information

6 1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft.

6 1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft. 06 Solutions 46060_Part1 5/27/10 3:51 PM Page 329 6 1. Draw the shear and moment diagrams for the shaft. The bearings at and exert only vertical reactions on the shaft. 250 mm 800 mm 24 kn 6 2. Draw the

More information

Overhang Bracket Loading. Deck Issues: Design Perspective

Overhang Bracket Loading. Deck Issues: Design Perspective Deck Issues: Design Perspective Overhang Bracket Loading Deck overhangs and screed rails are generally supported on cantilever brackets during the deck pour These brackets produce an overturning couple

More information

Optimising plate girder design

Optimising plate girder design Optimising plate girder design NSCC29 R. Abspoel 1 1 Division of structural engineering, Delft University of Technology, Delft, The Netherlands ABSTRACT: In the design of steel plate girders a high degree

More information

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20 Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

More information