MENG 302L Lab 6: Stress Concentration
|
|
- Sydney Baker
- 6 years ago
- Views:
Transcription
1 Introduction 1 : The purpose of this experiment is to demonstrate the existence of stress and strain concentration in the vicinity of a geometric discontinuity in a cantilever beam, and to obtain an approximate measure of the elastic (theoretical or geometric) stress concentration factor, K t. 2 In this case, the discontinuity is simply a circular hole, drilled through the beam on its centerline. Figure 1: Stress Concentration in a Cantilever Beam The presence of any geometric irregularity in the shape of a loaded mechanical part or structural member impedes the orderly flow of stress trajectories, causing them to crowd together, and locally increasing the stress above the nominal level as calculated by conventional mechanics of materials formulas. Such an irregularity or discontinuity is referred to as a stress-raiser. Figure 1 shows the stress distribution at two sections of a cantilever beam and illustrates the presence of stress concentration. 1 This lab is based on E-104 STRESS AND STRAIN CONCENTRATION, Vishay Measurements Group, Inc., 1982, printed March Portions of this text were taken verbatim from that document. 2 K t - stress concentration factor. This is not to be confused with K t strain gage transverse sensitivity. Page 1 of 10
2 At section A, the stress is uniform across the width of the beam, and calculable from the following relationship: (1) where: σ = stress, psi (N/m), M = bending moment, in-lbs (mn), I = moment of inertia on beam cross section, in 4 (m 4 ), c = half-thickness of beam, in (m), P = load, lbs, (N) At section B, the nominal stress, based upon the net area of the section is: If the location of the hole is selected so that (2) (3) the nominal stress at section B is the same as that at section A. The maximum stress at section B, however, is much greater, due to the stress concentration effect. As shown in the sketch, the maximum stress exists at the edge of the hole, on the transverse diameter, and the stress decreases rapidly with distance from the hole. By definition, the stress concentration factor, K t, is the ratio of the maximum stress at the stress-raiser to the nominal stress at the same point. That is, (4) Since the nominal stress at both sections of the beam and the peak stress at the edge of the hole are all uniaxial, the strain and stress are proportional if the proportional limit of the beam material is not exceeded in the experiment. Thus, the stress concentration factor is equal to the ratio of the maximum to nominal strains at section B. Therefore, (5) Equipment and Supplies: - Vishay Flexor cantilever flexure frame - High-strength aluminum alloy beam, 1/4 x 1 x 12 ½ (3.2 x 25 x 318 mm), outfitted with preinstalled strain gages and a ¼ diameter stress concentration hole. - Vishay P3 Strain Indicator Page 2 of 10
3 Pre-Lab: A) The Flexor loading micrometer will be used to load the beam. Calculate the micrometer motion necessary to induce 2000 µϵ at the location of gage 4: Deflection in a cantilever beam b inches wide by t inches thick is: (6) where: y = deflection (in), P = force, lbs, L = clamp to micrometer distance (10.0 in), E = Young s modulus for aluminum (10.4E6 psi), t = beam thickness (0.25 in). Strain at strain gage 4 (section A) is given by: (7) where: x = micrometer to gage 4 distance (9.0 in). P, b and t are as defined above. Using equations (6) and (7) above, determine the deflection required to induce 2000 µϵ in the beam at gage 4. (Do your work in the space provided below.) y(pre-lab): Micrometer deflection required for 2000 µϵ: (in) B) Engineering texts and handbooks often include tables of stress concentration factors. Use one of these tables to determine the theoretical stress concentration for a ¼ diameter hole drilled through the center of a ¼ x 1 rectangular beam in simple bending. Kt Source Page 3 of 10
4 Procedure General: In this experiment, the beam will be loaded with the Flexor until a predetermined nominal axial strain level of 2000 µϵ is reached at section B (see Figure 1). As described in the introduction, the nominal strain at section B will be measured, not at that point on the beam, but instead at section A, where the measurement can be made more conveniently and accurately. It is important not to exceed a nominal strain of 2000 µϵ, since the actual strain at the edge of the hole is much higher than the nominal, and excessive strain could produce local yielding. The actual strains in the region of stress concentration will be measured with three very small strain gages placed in section B at varying distances from the hole, with one of the gages directly adjacent to the edge. The strains indicated by the three gages will be plotted on the graph sheet (included in the Appendix of this experiment) at the locations of the respective gage centerlines. A smooth curve can be drawn through the resulting three data points to show the strain distribution in the vicinity of the hole. Since the centerline of the closest gage to the hole cannot physically coincide with the edge of the hole, it is necessary to extrapolate the data to the edge to obtain an approximate value for the technique given in the Analysis and Presentation of Data section. The ratio of the maximum to the nominal strain at section B is the strain concentration due to the disruptive presence of the hole. If the proportional limit of the beam material has not been exceeded during the experiment, the stresses are proportional to the strains, and the same ratio represents the stress concentration factor, K t. In measuring stress concentration with a strain gage, it must be kept in mind that the gage tends to indicate the average strain in the area covered by the grid. Since the strain in the immediate vicinity of a stress-raiser decreases very steeply with distance, it is obviously necessary to select the smallest practicable strain gage and bond it in place as close as possible to the edge of the stress-raiser in order to minimize the error in sensing the peak strain. Even with this technique, the strain indicated by the gage may be significantly lower than the peak strain. The three gages selected for measurements in the steeply varying strain field near the hole should have grids no larger than x in. Ideally, gage grid dimensions should be 10% or less of the radius represented by the stress concentration configuration. The 4 th gage, which is located at section A, remote from the hole, and out of the region of steep strain gradient, can be considerably larger. At a distance along the beam from the stress raiser, the axial strain is essentially uniformly distributed across the width of the beam, and varies linearly along the length. The average strain indicated by the gage at section A is thus equal to the strain at the center of the grid. Because of the relationship expressed by Eq. (3) in the introduction, this is also equal to the nominal axial strain at section B. Micro-Measurements foil strain gages employed on the pregaged beam are intrinsically temperature compensated for use on the material from which the beam is made. Because of this, the four gages can be connected to the P3 Strain Indicator individually in quarterbridge arrangements, completing the bridge circuit each time with the precision resistors built into the instrument. For quarter bridge operation, a three-wire circuit is ordinarily used with each gage in order to obtain compensation for temperature-induced resistance changes in the leadwires by placing equal lengths of leadwire in adjacent arms of the bridge Page 4 of 10
5 circuit. It is often convenient in minimizing the lead and connection requirements to combine the leads from one solder tab of each strain gage into a common lead. When threewire circuitry is used, this becomes a pair of leads which is common to every gage in the system (see Wiring Diagram included in the Appendix). Acquisition of Data: The gages will be connected (via the flexor cable) to the strain indicator one at a time, first with the beam undeflected, and again with the beam deflected. An initial reference reading of the strain indicator readout will be obtained for each gage with the beam undeflected, and a final reading with the beam deflected. The differences in these two sets of readings will give the strains at the respective gage locations. 1) Record gage factor G and resistance Ω for all four gages: G Gages 1 thru 3 Gage 4 Ω 2) Install the beam in the flexor with gages facing up on the clamp end. Make sure the micrometer is clear of the beam and that the beam is as far in as it will go. 3) Connect the leads from the beam to the flexor terminals and gage 1 to Channel 1 on the P3 indicator as shown in the Appendix. 4) Turn on the P3. Set it for Channel 1 active, Channels 2-4 inactive, quarter bridge. 5) Set the gage factor to that for gage 1. 6) Balance the gage and save settings. 7) Record the initial reading for gage 1 (0 µϵ) in the Data Table. 8) Connect gage 2 in place of gage 1. (Swap leads 3 and 4, leaving 1 and 2 alone.) 9) Record the gage 2 initial reading in the Data Table. 10) Connect gage 3 in place of gage 2. (Swap leads 4 and 5.) 11) Record the gage 3 initial reading in the Data Table. 12) Connect gage 4 in place of gage 3. (Swap leads 5 and 6.) 13) Record the gage 4 initial reading in the Data Table. 14) Turn the loading micrometer clockwise until the strain indication just begins to change. Record the micrometer reading as y(initial) in the table below. 15) Turn the loading micrometer clockwise until gage 4 reads 2000 µϵ plus the initial value recorded in step ) Record the micrometer reading as y(final) in the table below. Calculate the error as follows: 100% y initial y final y pre-lab Error (%) in in in 17) Record the gage 4 final reading in the Data Table and backtrack steps 12 through 7 to get final readings for gages 3, 2 and 1. Page 5 of 10
6 18) Back the loading micrometer clear of the beam. The gage 1 strain indication should return within a few µϵ of the initial reading. Record the reading here: The pregaged beams used in this experiment have been tested for gage stability at the time of manufacture, and should perform in a highly repeatable manner unless one or more of the gages has been damaged. If the zero-beam-deflection readings of the strain indicator fail to repeat well, the binding post connections may not have been snug enough to avoid small contact resistance changes. Binding post connections should be snug enough to allow a wiggle test of the leadwires without a zero balance shift. Analysis and Presentation of Data The strain indicated by gage 4 can be corrected for gage factor (if different from the gage factor of gages 1, 2 and 3 and the instrument gage factor setting) by the following relationship: (8) The result of this calculation is the nominal strain at Sections A and B of the beam, and should be entered in the Worksheet. The strains sensed by gages 1, 2 and 3 can be calculated by subtracting the initial reading from the final reading in each case. These numbers should be entered in the Data Table. Even though the centerline of gage 1 is only inch from the edge of the hole, the average strain sensed by this gage is considerably lower than the peak strain. A satisfactory estimate of the peak strain can be obtained by extrapolating curvilinearly to the edge of the hole. Assume that the strain distribution can be approximated by an expression of the following form: (9) Where R is the radius of the hole, X is the distance from the center of the hole to any point on the transverse centerline, and A, B and C are coefficients to be determined from the measured strains at three different points along the transverse centerline. Thus, Page 6 of 10
7 ( ) (10) Noting that: R = in, X 1 = in, X 2 = in, and X 3 = in and solving Eqs. (10) simultaneously for C, B, and A,.. (11).. (12).. (13) Substituting the measured strains from the worksheet table into Eq. (11) gives C, which can then be used in Eq. (12) to solve for B, etc. Since 1 at the edge of the hole, the peak strain is: (14) The strain (and stress) concentration factor is then: (15) where = the strain indication at gage 4, corrected for gage factor. Plot the strains ϵ 0, ϵ 1, ϵ 2, and ϵ 3, versus the corresponding dimensionless distance X/R on the accompanying graph sheet to visualize the stress distribution in the vicinity of the hole. Write-up: (Worksheet) - The executive summary should include a brief description of the experiment and your value for. - The Results consist of the completed handout. - In the discussion, compare your value for to that found in the pre-lab. Your value is probably considerably smaller than the published value. Discuss possible causes. How did your pre-lab value for the 2000 µϵ deflection compare to the actual value? Mention anything else you deem worthwhile. - For the conclusion, recap everything in 50 words or less. Page 7 of 10
8 Appendix: Wiring Diagram Page 8 of 10
9 Worksheet: Date: Lab Partners: Data Table Gage Initial Reading Final Reading Strain 1 0 µϵ µϵ 1) Correct strain ϵ 4 for gage factor per Eq. (8) and enter the value here: 2) Compute extrapolation coefficients A, B and C per Eqs. (13), (12) and (11) and enter the values here: Extrapolation Coefficients A B C 3) Compute the maximum strain at the edge of the hole,, per Eq. (14), and the stress concentration factor,, per Eq. (15), and enter the values here:, and, 4) Plot the strains ϵ 0, ϵ 1, ϵ 2, and ϵ 3, versus the corresponding dimensionless distance X/R on the accompanying graph sheet. Draw a smooth curve through the points. Page 9 of 10
10 Figure 2: Strain Distribution Plot Page 10 of 10
Experiment Five (5) Principal of Stress and Strain
Experiment Five (5) Principal of Stress and Strain Introduction Objective: To determine principal stresses and strains in a beam made of aluminum and loaded as a cantilever, and compare them with theoretical
More informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationLab Exercise #5: Tension and Bending with Strain Gages
Lab Exercise #5: Tension and Bending with Strain Gages Pre-lab assignment: Yes No Goals: 1. To evaluate tension and bending stress models and Hooke s Law. a. σ = Mc/I and σ = P/A 2. To determine material
More informationCE 320 Structures Laboratory 1 Flexure Fall 2006
CE 320 Structures Laboratory 1 Flexure Fall 2006 General Note: All structures labs are to be conducted by teams of no more than four students. Teams are expected to meet to decide on an experimental design
More informationWheatstone Bridge Nonlinearity
Index: Nonlinearity Wheatstone Bridge Nonlinearity Introduction General Considerations The "Unbalanced" Circuit The Unbalanced Circuit Table of Contents Output & Nonlinearity with Various Bridge/Strain
More informationMET 301 EXPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES
MET 301 EPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES 1. Objective To understand the working principle of bonded strain gauge and to study the stress and strain in a hollow cylindrical shaft under bending,
More informationENSC387: Introduction to Electromechanical Sensors and Actuators LAB 3: USING STRAIN GAUGES TO FIND POISSON S RATIO AND YOUNG S MODULUS
ENSC387: Introduction to Electromechanical Sensors and Actuators LAB 3: USING STRAIN GAUGES TO FIND POISSON S RATIO AND YOUNG S MODULUS 1 Introduction... 3 2 Objective... 3 3 Supplies... 3 4 Theory...
More informationME411 Engineering Measurement & Instrumentation. Winter 2017 Lecture 9
ME411 Engineering Measurement & Instrumentation Winter 2017 Lecture 9 1 Introduction If we design a load bearing component, how do we know it will not fail? Simulate/predict behavior from known fundamentals
More informationExcerpt from the Proceedings of the COMSOL Conference 2010 Boston
Excerpt from the Proceedings of the COMSOL Conference 21 Boston Uncertainty Analysis, Verification and Validation of a Stress Concentration in a Cantilever Beam S. Kargar *, D.M. Bardot. University of
More informationStrain Measurements. Isaac Choutapalli
Note that for axial elongation (Eaxiai > 0), Erransverse (from Equation C.6), and therefore Strain Measurements Isaac Choutapalli Department of Mechanical Engineering The University of Texas - Pan American
More informationMEMS Report for Lab #3. Use of Strain Gages to Determine the Strain in Cantilever Beams
MEMS 1041 Report for Lab #3 Use of Strain Gages to Determine the Strain in Cantilever Beams Date: February 9, 2016 Lab Instructor: Robert Carey Submitted by: Derek Nichols Objective: The objective of this
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 & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationMET 487 Instrumentation and Automatic Controls. Lecture 13 Sensors
MET 87 nstrumentation and utomatic Controls Lecture Sensors July 6-9, 00 Stress and Strain Measurement Safe Load Level monitoring Force (indirect measurement by measuring strain of a flexural element Pressure
More information1 Force Sensing. Lecture Notes. 1.1 Load Cell. 1.2 Stress and Strain
Lecture Notes 1 Force Sensing 1.1 Load Cell A Load Cell is a structure which supports the load and deflects a known amount in response to applied forces and torques. The deflections are measured to characterize
More informationBy Dr. Mohammed Ramidh
Engineering Materials Design Lecture.6 the design of beams By Dr. Mohammed Ramidh 6.1 INTRODUCTION Finding the shear forces and bending moments is an essential step in the design of any beam. we usually
More informationStrain Gage Calibration Factors for Constant Room Temperature Conditions. Gage Resistance, Gage Factor and Transverse Sensitivity Coefficient)
Strain Gage Calibration Factors for Constant Room Temperature Conditions (Or equivalently, measurement of the room temperature (Or equivalently, measurement of the room temperature Gage Resistance, Gage
More informationMechatronics II Laboratory EXPERIMENT #1: FORCE AND TORQUE SENSORS DC Motor Characteristics Dynamometer, Part I
Mechatronics II Laboratory EXPEIMENT #1: FOCE AND TOQUE SENSOS DC Motor Characteristics Dynamometer, Part I Force Sensors Force and torque are not measured directly. Typically, the deformation or strain
More informationAE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF HOOP STRESSES FOR A THIN-WALL PRESSURE VESSEL
Objective AE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF OOP STRESSES FOR A TIN-WA PRESSURE VESSE This experiment will allow you to investigate hoop and axial stress/strain relations
More informationSTRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING
STRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING 1 YEDITEPE UNIVERSITY ENGINEERING FACULTY MECHANICAL ENGINEERING LABORATORY 1. Objective: Strain Gauges Know how the change in resistance
More informationTrueStructures TM Strain Analysis System
TrueStructures TM Strain Analysis System Operator's Manual and Sample Lab Procedures TrueStructures TM Strain Analysis System shown with I-Beam, Torsion Tube and Airfoil Test Sections. Copyright March
More informationMECHANICS LAB AM 317 EXP 3 BENDING STRESS IN A BEAM
MECHANICS LAB AM 37 EXP 3 BENDING STRESS IN A BEAM I. OBJECTIVES I. To compare the experimentally determined stresses in a beam with those predicted from the simple beam theory (a.k.a. Euler-Bernoull beam
More informationMechatronics II Laboratory EXPERIMENT #1 MOTOR CHARACTERISTICS FORCE/TORQUE SENSORS AND DYNAMOMETER PART 1
Mechatronics II Laboratory EXPEIMENT #1 MOTO CHAACTEISTICS FOCE/TOQUE SENSOS AND DYNAMOMETE PAT 1 Force Sensors Force and torque are not measured directly. Typically, the deformation or strain of some
More informationErrors Due to Transverse Sensitivity in Strain Gages
Index: Transverse Sensitivity Errors Due to Transverse Sensitivity in Strain Gages Introduction Transverse Sensitivity Table of Contents Transverse Sensitivity Errors & Their Corrections Errors Corrections
More informationDESIGN AND APPLICATION
III. 3.1 INTRODUCTION. From the foregoing sections on contact theory and material properties we can make a list of what properties an ideal contact material would possess. (1) High electrical conductivity
More informationStrain Measurement MEASUREMENT EXPERIMENT
Strain Measurement MEASUREMENT EXPERIMENT 1. OBJECT The objective of this experiment is to become familiar with the electric resistance strain gage techniques and utilize such gages for the determination
More informationExperiment Two (2) Torsional testing of Circular Shafts
Experiment Two (2) Torsional testing of Circular Shafts Introduction: Torsion occurs when any shaft is subjected to a torque. This is true whether the shaft is rotating (such as drive shafts on engines,
More informationStructures - Experiment 3B Sophomore Design - Fall 2006
Structures - Experiment 3B 1.101 Sophomore Design - Fall 2006 Linear elastic behavior of a beam. The objectives of this experiment are to experimentally study the linear elastic behavior of beams under
More informationStrain Measurement. Prof. Yu Qiao. Department of Structural Engineering, UCSD. Strain Measurement
Strain Measurement Prof. Yu Qiao Department of Structural Engineering, UCSD Strain Measurement The design of load-carrying components for machines and structures requires information about the distribution
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 informationAERO 214. Lab II. Measurement of elastic moduli using bending of beams and torsion of bars
AERO 214 Lab II. Measurement of elastic moduli using bending of beams and torsion of bars BENDING EXPERIMENT Introduction Flexural properties of materials are of interest to engineers in many different
More information1.105 Solid Mechanics Laboratory Fall 2003
1.105 Solid Mechanics Laboratory Fall 2003 Eperiment 6 The linear, elastic behavior of a Beam The objectives of this eperiment are To eperimentally study the linear elastic behavior of beams under four
More informationWhat is a Strain Gauge? Strain Gauge. Schematic View Of Strain Gauge
( ) : 1391-92 92 What is Strain? Strain is the amount of deformation of a body due to an applied force. More specifically, strain (ε) is defined as the fractional change in length. Strain can be positive
More informationChapter Objectives. Design a beam to resist both bendingand shear loads
Chapter Objectives Design a beam to resist both bendingand shear loads A Bridge Deck under Bending Action Castellated Beams Post-tensioned Concrete Beam Lateral Distortion of a Beam Due to Lateral Load
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 informationENGINEERING TRIPOS PART IIA 3C7: EXPERIMENTAL STRESS ANALYSIS
ENGINEERING TRIPOS PART IIA 3C7: EXPERIMENTAL STRESS ANALYSIS Experiment takes place in BNB-06 (follow downward stairs opposite Baker Building reception). OBJECTIVES To develop an appreciation of two different
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 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 informationLaboratory 4 Topic: Buckling
Laboratory 4 Topic: Buckling Objectives: To record the load-deflection response of a clamped-clamped column. To identify, from the recorded response, the collapse load of the column. Introduction: Buckling
More informationMechanical Properties Rev 5.0
McMaster Faculty of Engineering Hamilton Ontario Canada Materials 2H04 Measurement and Communications 2005-2006 Introduction Mechanical Properties Rev 5.0 Tasks 5, 6 Lab tasks 5,6 link closely to the course
More informationME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING
ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING PURPOSE 01 January 2000 / mgj The purpose of this exercise is to study the effects of end conditions, column length, and material properties
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 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 informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More information1.1 To observe, evaluate and report on the load deflection relationship of a simply supported beam and a cantilever beam.
I. OBJECTIVES 1.1 To observe, evaluate and report on the load deflection relationship of a simply supported beam and a cantilever beam. 1.2 To determine the modulus of elasticity of the beam and what the
More informationLaboratory 7 Measurement on Strain & Force. Department of Mechanical and Aerospace Engineering University of California, San Diego MAE170
Laboratory 7 Measurement on Strain & Force Department of Mechanical and Aerospace Engineering University of California, San Diego MAE170 Megan Ong Diana Wu Wong B01 Tuesday 11am May 17 th, 2015 Abstract:
More information3 Hours/100 Marks Seat No.
*17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full
More information= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200
Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength
More informationExperimental Stress Analysis of Curved Beams Using Strain Gauges
Experimental Stress Analysis of Curved Beams Using Strain Gauges Srinivasa Prasad K S 1, Roshaan Subramanian 2, Sanjay Krishna 3, Prashanth S 4 1 Assistant Professor, Department of Mechanical Engineering,
More informationARTICLE A-8000 STRESSES IN PERFORATED FLAT PLATES
ARTICLE A-8000 STRESSES IN PERFORATED FLAT PLATES Delete endnote 18, which says "Express metric values in exponential form" A-8100 INTRODUCTION A-8110 SCOPE (a) This Article contains a method of analysis
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 informationME C85/CE C30 Fall, Introduction to Solid Mechanics ME C85/CE C30. Final Exam. Fall, 2013
Introduction to Solid Mechanics ME C85/CE C30 Fall, 2013 1. Leave an empty seat between you and the person (people) next to you. Unfortunately, there have been reports of cheating on the midterms, so we
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationPrincipal Stress Separation in PhotoStress Measurements
PhotoStress Instruments Principal Stress Separation in PhotoStress Measurements TN-708-.0 Introduction Or, In addition to its unique capability as a full-field technique for visualizing stress distribution,
More information1.105 Solid Mechanics Laboratory
1.105 Solid Mechanics Laboratory General Information Fall 2003 Prof. Louis Bucciarelli Rm 5-213 x3-4061 llbjr@mit.edu TA: Attasit Korchaiyapruk, Pong Rm 5-330B x 3-5170 attasit@mit.edu Athena Locker: /mit/1.105/
More informationEXPERIMENTAL TECHNIQUES STRESS ANALYSIS
EXPERIMENTAL TECHNIQUES STRESS ANALYSIS DEPARTMENT OF MECHANICAL ENGINEERING FACULTY OF ENGINEERING Dr Martin Muscat 005 Stress analyses lab STUDENTS ACTIITY This lab work will be carried out as a group
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 informationHomework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004
Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. 1. A beam is loaded as shown. The dimensions of the cross section appear in the insert. the figure. Draw a complete free body diagram showing an equivalent
More informationForce and Displacement Measurement
Force and Displacement Measurement Prof. R.G. Longoria Updated Fall 20 Simple ways to measure a force http://scienceblogs.com/dotphysics/200/02/diy_force_probe.php Example: Key Force/Deflection measure
More informationExperimental Lab. Principles of Superposition
Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you
More informationGlossary Innovative Measurement Solutions
Glossary GLOSSARY OF TERMS FOR TRANSDUCERS, LOAD CELLS AND WEIGH MODULES This purpose of this document is to provide a comprehensive, alphabetical list of terms and definitions commonly employed in the
More information5. What is the moment of inertia about the x - x axis of the rectangular beam shown?
1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment
More informationStrain Gage Rosettes: Selection, Application and Data Reduction
Micro-MeasuremeNTs Strain Gages and Instruments e TN-55 Strain Gage Rosettes: Selection, Application and Data Reduction.0 Introduction A strain gage rosette is, by definition, an arrangement of two or
More information1.105 Solid Mechanics Laboratory Fall 2003
1.105 Solid Mechanics Laboratory Fall 200 Experiment 7 Elastic Buckling. The objectives of this experiment are To study the failure of a truss structure due to local buckling of a compression member. To
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 informationLoad Cell Design Using COMSOL Multiphysics
Load Cell Design Using COMSOL Multiphysics Andrei Marchidan, Tarah N. Sullivan and Joseph L. Palladino Department of Engineering, Trinity College, Hartford, CT 06106, USA joseph.palladino@trincoll.edu
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 informationPOE Practice Test - Materials
Class: Date: POE Practice Test - Materials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A student weighs 150 lbs and is standing on a beam which spans
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 13
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras (Refer Slide Time: 00:25) Module - 01 Lecture - 13 In the last class, we have seen how
More informationSTRENGTH AND STIFFNESS REDUCTION OF LARGE NOTCHED BEAMS
STRENGTH AND STIFFNESS REDUCTION OF LARGE NOTCHED BEAMS By Joseph F. Murphy 1 ABSTRACT: Four large glulam beams with notches on the tension side were tested for strength and stiffness. Using either bending
More informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationSAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE
SAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE STRENGTH OF ~1ATERIALS MCH 103-3 revised June 1981 by W.J. Adolph ------- STRENGHT OF MATERIALS MCH 103-3 To'Cic Periods Tooic Description
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 informationNAME: Given Formulae: Law of Cosines: Law of Sines:
NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.
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 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 information[5] Stress and Strain
[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law
More informationMCE 403 MACHINERY LABORATORY EXPERIMENT 10
1 1.OBJECTIVE The objective of this experiment is to become familiar with the electric resistance strain gauge techniques and utilize such gauges for the determination of unknown quantities (such as strain,
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 informationDEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).
DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)
More informationStrain Gages. Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, Shear Modulus, (S) N/m 2
When you bend a piece of metal, the Strain Gages Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, 1979 Material Young's Modulus, (E) 10 11 N/m 2 Shear Modulus,
More informationCOPPER FOR BUSBARS CHAPTER 4: SHORT-CIRCUIT EFFECTS
European Copper Institute COPPER FOR BUSBARS CHAPTER 4: SHORT-CIRCUIT EFFECTS David Chapman August 2011 ECI Available from www.leonardo-energy.org Document Issue Control Sheet Document Title: Publication
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 informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More informationElectric Field Mapping
Electric Field Mapping Objectives To determine the equipotential lines and the corresponding electric field lines for a variety of arrangements of conductors in a plane. Theory The concept of an electric
More informationCHAPTER II EXPERIMENTAL INVESTIGATION
CHAPTER II EXPERIMENTAL INVESTIGATION 2.1 SCOPE OF TESTING The objective of this research is to determine the force distribution between the column web and stiffener when the column flanges are subjected
More informationIntroduction to Structural Member Properties
Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I): a mathematical property of a cross-section (measured in inches 4 or in 4 ) that gives important information
More informationFig. 1. Two common types of van der Pauw samples: clover leaf and square. Each sample has four symmetrical electrical contacts.
15 2. Basic Electrical Parameters of Semiconductors: Sheet Resistivity, Resistivity and Conduction Type 2.1 Objectives 1. Familiarizing with experimental techniques used for the measurements of electrical
More informationSimulation of Geometrical Cross-Section for Practical Purposes
Simulation of Geometrical Cross-Section for Practical Purposes Bhasker R.S. 1, Prasad R. K. 2, Kumar V. 3, Prasad P. 4 123 Department of Mechanical Engineering, R.D. Engineering College, Ghaziabad, UP,
More information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shear-stress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationLecture 19. Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity
MECH 373 Instrumentation and Measurements Lecture 19 Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity Measuring Accepleration and
More informationPrinciples Of Engineering. Part A
Principles Of Engineering Final Examination Part A Fall 2007 Student Name: Date: Class Period: Total Points: /40 Converted Score: /50 Page 1 of 11 Directions: Circle the letter of the response that best
More informationExperimental Approach to Determine the Stress at a Section of Semi Circular Curved Beam Subjected to Out-Of-Plane Load Using Strain Rosette
Experimental Approach to Determine the Stress at a Section of Semi Circular Curved Beam Subjected to Out-Of-Plane Load Using Strain Rosette Rakshith N 1, Dr. D S Ramakrishna 2, Srinivasa K 3, Md Nadeem
More information2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C
CE-1259, Strength of Materials UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS Part -A 1. Define strain energy density. 2. State Maxwell s reciprocal theorem. 3. Define proof resilience. 4. State Castigliano
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 informationPES Institute of Technology
PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject
More information1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6
1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine MIT Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 COMPRESSION TESTING AND ANISOTROPY OF WOOD Purpose: Reading: During this laboratory
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 informationMeasurement of Bone Strength and Stiffness using 3-Point Bending
BME 315 Biomechanics, U. Wisconsin Adapted by R. Lakes from D. Thelen and C. Decker, 09, adapted from Lakes 06 Experimental Details I. Laboratory equipment The load frame that we will use to perform our
More informationStrain and Force San José State University A. Mysore Spring 2009
Strain and Force Strain Gage Measures strain as a change in length L, observed by change in resistance R, for a given resistivity ρ and cross-sectional area A. For elastic materials that follow Hooke s
More informationMECHANICS OF MATERIALS
Third CHTR Stress MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University and Strain xial oading Contents Stress & Strain: xial oading Normal
More information