# A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS

Save this PDF as:

Size: px
Start display at page:

Download "A PROTOCOL FOR DETERMINATION OF THE ADHESIVE FRACTURE TOUGHNESS OF FLEXIBLE LAMINATES BY PEEL TESTING: FIXED ARM AND T-PEEL METHODS"

## Transcription

2 2 2 FIXED ARM PEEL TEST. 2.1 ANALYSIS OF THE FIXED ARM PEEL TEST. Peel arm (thickness h Peel force P Laminate of width b θ Peel angle Fixed arm of laminate Figure 1 Fixed arm peel test Figure 1 shows the peel of a laminate at a peel angle of θ with a force P acting on the peel arm (width b, thickness h. In order to peel one laer of the laminate from the other, it is necessar to provide energ in the form of external work to the laminate. The energ contributions to a fixed arm peel procedure can be described b a global energ analsis [1]. The input energ to the peel test needs to be resolved into the various deformational energies, elastic, plastic and adhesive fracture energies, at least. G A du ext du s du dt du db = ( 1 bda bda bda bda where G A is the adhesive fracture toughness, U is energ with subscripts ext, s, dt and db referring to external work, strain energ, dissipated tensile energ and dissipated bending energ, respectivel. b is the specimen width and da the peel fracture length. This approach has been applied to a fixed arm peel test [1, 2] in order to convert peel strength (P/b to adhesive fracture toughness: G = G ( 2 A G P G is the input energ after correction for tensile elastic and plastic deformation in the peel arm and G P is the plastic work in bending the peel arm. The tensile corrections are often negligible [1] and then input energ is given b: P G = ( 1 cosθ (3 b θ is the peel angle. In order to calculate the plastic deformation energ associated with the peel arm, it is first necessar to have knowledge of the tensile stress-strain characteristics of the peel arm material. This will include an initial elastic deformation but also a subsequent work hardening, plastic, deformation. The plastic bending in the peel tests ma then be

3 3 modelled using large-displacement beam theor with modifications for plastic bending. Solutions have been formulated for three cases: (i Digitised, where the stress-strain behaviour of the peel arm is digitised and a numerical analsis is used to calculate G P [3]. (ii Bilinear, where a bilinear fit is given to the stress-strain curve and an analtical calculation of G P [4,5]. (iii Power law, where an linear elastic-power law plastic fit is given to the stress-strain curve and an analtical calculation of G P [4,5]. For the bilinear and power law curve fits, the details are as follows where a number of parameters from the stress-strain fits are calculated. N is a constant, α is the ratio of plastic modulus to elastic modulus i.e. E 2 /E 1, σ is ield stress and ε is ield strain. N and α are the respective work hardening coefficients for power law and linear work hardening. When ε ε, σ = Eε ( 3 in both cases, and whenε >, N ε ε σ = σ ( ( 4 ε in the power law work hardening model, and σ = σ + αe( ε ε ( 5 for the bilinear model. For laminates where the adhesive laer thickness (h A is ver small, h A 0, there is no requirement to consider the deformation in the adhesive in conducting the calculations of adhesive fracture toughness [4]. However, when h A >0 the deformation in the adhesive laer should be included in the analsis for which it will be necessar to have knowledge of the modulus of the adhesive material (E A. In all, these various calculations can be complex and whilst a theoretical analsis is given in reference [4], software (ICPeel that can be used to conduct the calculations is available on the Imperial College London website [6]. The digitisation of the stress-strain behaviour also requires a software package as does the subsequent numerical analsis for calculation of G P. This is also provided on the Imperial College London website [6] where the package is called ICPeel (Digitised. In principle, the digitised approach should be the most accurate but it is also the most cumbersome and time-consuming approach. However, the digitised package is quite quick if an approximate solution is used first. This is based on using the stress-strain parameters form the curve fitting procedures prior to conducting an accurate analsis. Therefore, it is necessar to run ICPeel first and ICPeel (Digitised next. Consequentl, it is helpful to use the results from all three cases in the determination of G P and G A. The website includes instructions on how to run the packages. In order to determine G A without neglecting an of the elastic or plastic deformations, two experiments are required:

4 4 (a The peel test with a control of the peel angle. (b A tensile stress-strain measurement of the peel arm up to fracture or at least to a strain magnitude that exceeds the maximum strain in the peel test (this is given in ICPeel and is tpicall 6%. Experimental requirements for both of these measurements are given in section 2.2 and Straight line fitted to elastic curve True Stress (MPa Straight line fitted to initial plastic curve Interception of these lines provides the ield co-ordinates True Strain Figure 2 Definition of ield co-ordinates A critical issue in analsing these curves concerns the definition of the ield co-ordinates (ε, σ. These are obtained from the experimental data b fitting a straight line to the linear elastic region of the curve and a straight line to the initial plastic region of the curve, as shown in Figure 2. The straight line fitted to the initial plastic curve should start beond an approximate ield point and end at approximatel 10 times the ield strain, again as shown in Figure 2. The interception of these two lines defines the ield co-ordinates. The measured stress-strain curve is then modelled to either a bilinear form, as shown in Figure 3 or a power law form as shown in Figure 4. Both fits should be conducted for the purpose of calculation of G P and G A, but also for the ICPeel (Digitised analsis. The fitted curves must compl with these ield co-ordinates (as equations 3-5 indicate. Therefore, once the ield co-ordinates are defined from the experimental curve, then the linear elastic portion for both models is the line between the origin and these co-ordinates. The plastic region then starts beond the ield co-ordinates but for both tpes of model, the fitted curve must pass through the ield co-ordinates. In general, net stress (force/original cross sectional area and net strain (increase in length/gauge length are used. However, if the strain exceeds 10% then a true stress should be used (true stress = net stress [1+ strain].

5 5 250 True Stress (MPa Experimental curve E 1 E 2 Yield co-ordinates (ε,σ True Strain Figure 3 Tensile stress versus strain plot for a peel arm illustrating a bilinear elasticplastic fit and the definition of E 1, E 2 and ield strain 200 True Stress (MPa Experimental curve Yield co-ordinates (ε,σ True Strain Figure 4 An illustration of an elastic region followed b a power law fit for work hardening. Adhesive fracture toughness is determined according to equation 2. Ideall, the corrections for plastic deformation should not be too large otherwise errors for the determination of

6 6 adhesive fracture toughness will become significant. The size of this correction is given b G ( P x100% ; the smaller this correction the better [2]. G These considerations appl equall to the T-peel analsis but can onl be determined for each peel arm separatel. 2.2 EXPERIMENTAL PROCEDURES IN THE FIXED ARM PEEL TEST. Specimens for conducting peel strength should be in the form of rectangular specimens where the two parts of the laminate have alread been adhered but where there is a region of unadhered material (of nominal length 30 mm. The overall dimensions of a peel specimen need not be rigidl defined but for man tests we have found that a length of 100 mm and width 20 mm proves to be quite satisfactor. Three specimens should be tested for each set of conditions. The choice of peel jig is not unique but the apparatus should incorporate a number of facilities. A successful kit is shown schematicall in Figure 5. First, the apparatus should be able to select the peel angle in the range up to 180. Second, the jig is attached to an Instron or similar universal testing machine such that as peel occurs the peel angle is maintained constant b the jig moving along a low friction linear bearing sstem. Third, onl one side of the laminate is allowed to be the peel arm in the test. Of course, the laminate can be reversed so changing the peel arm material in another but separate test. (Consequentl, the composition of the adherends ma or ma not be the same. Adhering one side of the laminate to the peel table is a critical issue. If this laer can separate from the table during the test then the energ involved in that process will increase the measured adhesive fracture toughness value to an erroneousl high level. The means of gluing the laer to the table should be reported. The material used for the peel arm (substrate should be reported, as should the length, width and thickness dimensions of the specimen (h and h A where h is the thickness of the substrate alone (i.e. without an coating of adhesive and h A is the thickness of the adhesive. The peel angle needs to be selected on the basis of ensuring that the peel force is large compared with the resolution of the load cell and the frictional forces in the test. For purposes of the protocol it will be necessar to conduct the test at a range of peel angles between 45 o and 135 o but the peel angle 90 o δ should alwas be one of the angles. A peel test speed ( t of 10 mm/min can be used as a standard speed with the 90 o. However, the peel angle will a influence the peel crack speed (. t δ a = (1 cos θ (6 t t Therefore, when conducting tests over a range of peel angles it us necessar to select a common peel crack speed.

7 7 Figure 5 Fixed arm peel fixture with linear bearing sstem showing a peel angle of 45 o. The force versus displacement curve to initiate and propagate a peel fracture should be recorded. At least 30 mm of peel fracture should be established. The average peel force should then be determined as shown in Figure 6A. If there is a combination of adhesive and cohesive fracture or stick-slip (as illustrated in Figure 6B, then for these occasions, both the mean lowest and the mean highest stead propagation peel force values should then be used to determine the adhesive and cohesive fracture toughness values, respectivel. 400 Peel force (N Onset of peel Average peel force Displacement (mm Figure 6A: Illustrative peel force versus displacement demonstrating how to average the peel force.

8 8 2.5 Cohesive peel force Force N mm Deflection Adhesive peel force Figure 6B Peel force versus deflection in a fixed arm peel test. The higher peel forces relate to cohesive fracture; the lower peel forces relate to adhesive fracture In order to conduct the corrections summarised in equations 2-5 it is necessar to obtain a tensile stress - strain plot on the material of the peel arm. (This should be the substrate material alone i.e. it should not be the substrate with a coating of adhesive material. In order to accommodate current analtical methods for the determination of the plastic work in bending the peel arm, this stress-strain plot will need to be described either as a bilinear function or as a linear elastic-power law plastic function or as a digitised function. The tensile test should be conducted at the same test speed as the peel test and in order to obtain sufficient accurac the test specimen should be a rectangular strip of width 10 mm and length 100 mm. In addition, an extensometer will be required to measure the strain deformations necessar to define the elastic deformations. The extensometer, ideall, should be of a non-contacting tpe, since the peel arms are likel to be of low stiffness. The tensile test should continue in order to enable a clear definition of the plastic region of the deformations b continuing the test to fracture. The comments preceding Figure 3 provide instructions for fitting a bilinear elastic-plastic fit for the stress-strain curve. Five parameters should be obtained, namel E 1, E 2, α (E 2 /E 1, ε and σ. The elastic modulus (E 1 is defined as the slope of the stress-strain curve at small deformations and before ielding has occurred. In order to define the plastic modulus (E 2 it is helpful to allow the tensile specimen to continue extension for as long as possible. If it transpires that the "work hardening" portion of the stress-strain curve exhibits a negative slope, then values of α and E 2 should be made zero (and not negative. In order to construct a linear elastic region followed b a power law work hardening region, the scheme shown in the text preceding Figure 4 should be used. The definition of the elastic region is as above and the power law fit should onl be made for post ield data. The parameters that should be obtained from the analsis are E 1, N, ε and σ. The co-ordinates at ield (as defined in an earlier section are given b the intercept of the elastic line and the plastic region for the experimental curve. Therefore, if the general power law gives N σ = Aε (7 The elastic region is

9 9 σ = E1ε (8 At ield, the stress (σ is σ and the strain (ε is ε. Therefore eliminating σ from equations 7 and 8 gives an expression for ield strain, 1 A 1 N = ( E1 ε (9 and ield stress is σ = E ε ( TEST REPORT FOR THE FIXED ARM PEEL TESTS The following information is required in the test report. General information Name of Laborator Description of laminate Material of peel arm Adhesive used for gluing one arm to the peel table Test equipment Data from tensile test on the peel arm material Test speed (mm/min Bilinear fit Low strain modulus (E 1 (GPa Power law fit Low strain modulus (E 1 (GPa N Yield strain (% High strain modulus (E 2 (GPa Yield strain (% Alpha (E 2 /E 1 Yield stress (MPa Yield stress (MPa Data from the peel test Peel angle ( o Test speed (mm/min Specimen dimensions L (mm b (mm Peel arm thickness h (µm (substrate onl Thickness of adhesive laer h A (µm (if h A > 0 then conduct calculations for two cases h A = 0 and the actual value for h A Value ascribed to the modulus of the adhesive E A (GPa Peel strength (P/b (N/mm Derived results b calculations (for each of the three fits to the stress-strain data G (J/m 2 G P (J/m 2

10 10 G A (J/m 2 Correction factor (% Results should be presented for each specimen. The report should include a plot of the peel curve (i.e. force versus displacement in the peel test. The length of peel growth should be marked on this curve together with a clear indication as to how the peel force used to determine the peel strength is derived from the plot. (Figure 6 shows an illustration of the requirement. In addition, the tensile stress-strain plots with the bilinear and/or power law fits should be reported 3 T-PEEL TEST 3.1 ANALYSIS OF THE T-PEEL TEST. Figure 7 shows the specimen configuration during a T-peel test. When the stiffness of the peel arms is different the peel angles will be φ and θ (rather than 90 o. In Figure 7 the stiffer arm is peel arm 2, therefore φ<90 and θ>90. The analsis proceeds along similar lines to that in the fixed arm peel test (see section 2.1, except that there are now two peel arms to accommodate. However, onl one of the peel angles needs to be considered since φ = π θ:- P G = (1 + cos (6 b 1 φ P G = (1 cos (7 b 2 φ Where the super scripts 1 and 2 refer to the two peel arms, respectivel. The peel toughness terms for elastic corrections are then similar to those in equation (3, except that there are two terms. In a similar manner, there will be two terms for the dissipated energ. Consequentl, there will be two forms for equations (2:- G = G G (8 ( A 1 1 ( P 1 G = G G (9 ( A 2 2 ( P 2

11 11 Peel force P Peel arm Specimen of width b θ φ Peel arm 2 Figure 7: T-Peel Specimen During a Test. The adhesive fracture toughness (G A from the T-peel test is then the sum of the terms from equations (8 and (9, namel:- G + A ( GA 1 ( GA 2 = ( EXPERIMENTAL PROCEDURES IN THE T- PEEL TEST. Specimens for conducting peel strength should be in the form of rectangular specimens where the two parts of the laminate have alread been adhered but where there is a region of unadhered material (of nominal length 30 mm. The overall dimensions of a peel specimen need not be rigidl defined but for man tests we have found that a length of 100 mm and width 20 mm proves to be quite satisfactor. Three specimens should be tested for each set of conditions and care should be taken to ensure that no part of the peel arms can touch the test equipment. There are two configurations for conducting the T-peel tests, as shown in Figure 8. Configuration A has the stiffer peel arm at the bottom, whilst configuration B has the stiffer peel arm at the top. It is likel that the small peel angle for these configurations will not be the same since the stiffer peel arm, which could contain more mass than the less stiff peel arm, will hang differentl. Three specimens tested in either configuration A or B should be conducted and the configuration tpe recorded.

12 12 Peel arm 1 Stiffer arm Peel arm 2 Configuration A Configuration B Figure 8 Specimen configurations for T-peel The materials of the peel arms ma or ma not be the same. The test machine should have the usual capabilities for sufficient resolution of force. Once the peel arms are in tension, the specimen configuration will be similar to one of those shown in Figure 8. During the course of peeling it is necessar to measure one of the peel angles (φ or ϕ and at least three measurements should be made throughout the 30 mm peel fracture; one near the start, one in the middle and one near the end. The average value for the peel angle can then be determined and used in the calculations. A peel test speed of 10 mm/min can be used as a standard. However, if there are large variations in measured peel angle (e.g. > 30 o between specimens or samples then equation 6 should be used to adjust to a common crack speed. (This will be a retrospective judgement. The force versus displacement curve to initiate and propagate a peel fracture should be recorded. At least 30 mm of peel fracture should be established. The average peel force should then be determined unless there is a combination of adhesive and cohesive fracture or stick-slip (as illustrated in Figure 6. For these occasions, the mean lowest and the mean highest stead propagation peel force values should then be used to determine the adhesive and the cohesive fracture toughness values, respectivel. In order to conduct the corrections summarised in equations 6-10, it is necessar to measure tensile stress - strain plots on the material of the peel arms. (Two tensile stress-strain plots will be required if the materials of the peel arms are different. Establishing digitised, bilinear and elastic-power law plastic descriptions of the tensile stress-strain behaviour of the peel arms should be done as previousl described in the section on fixed arm tests. Calculation of the various adhesive fracture toughness terms is then done for each peel arm as described in the section on the fixed arm peel. 3.3 TEST REPORT FOR THE T-PEEL TESTS The information required in a test report is similar to that for the fixed arm test. However, for the T-peel test there will be two peel arms to report and two possible specimen configurations (A and B as well as the measured peel angle. However, there is no requirement to test both tpes of configuration. The information required is as follows:

13 13 General information Name of Laborator Description of laminate Material of peel arm Adhesive used for gluing one arm to the peel table Test equipment Data from tensile test(s on the peel arm material(s This should be provided for both peel arms (1 and 2 if different. Test speed (mm/min Bilinear fit Power law fit Low strain modulus (E 1 (GPa Low strain modulus (E 1 (GPa Yield strain (% N High strain modulus (E 2 (GPa Yield strain (% Alpha (E 2 /E 1 Yield stress (MPa Yield stress (MPa Data from the peel test Specimen configuration (A or B Measured peel angle ( o [The smaller angle should be quoted] Test speed (mm/min Specimen dimensions L (mm b (mm Peel arm thickness h (µm (substrate onl Thickness of adhesive laer h A (µm (if h A > 0 then conduct calculations for two cases h A = 0 and the actual value for h A Value ascribed to the modulus of the adhesive E A (GPa Peel strength (P/b (N/mm Derived results b calculations (for each of the three fits to the stress-strain data To be quoted for each peel arm G (J/m 2 G P (J/m 2 G A (J/m 2 Correction factor (% Overall results G A =(G A 1 +(G A 2 CONCLUDING COMMENTS It would be helpful to use both test methods in order to determine the adhesive fracture toughness. Provided that the correction factor is not too large, then it can be hoped that the values will be the same for both test methods. It is recommended that the software source used for the calculations is quoted in all reports.

14 14 REFERENCES 1 Kinloch, A.J., Lau, C.C. and J G Williams, Int. J. Fract., 66, ( Moore, D.R., Williams, J.G., Fracture of Polmers, Composites and Adhesives, ESIS pub 32, ISBN: , Elsevier, L. F. Kawashita The Peeling of Adhesive Joints PhD thesis Universit of London Georgiou, I., Hadavina, H., Ivankovic, A., Kinloch, A.J., Tropsa, V., Williams, J. G., The Journal of Adhesion, 79, 1-27 ( Lau, C. C., PhD Thesis, Universit of London ( Imperial College London Website,

### Available online at ScienceDirect. Energy Procedia 55 (2014 )

Available online at www.sciencedirect.com ScienceDirect Energy Procedia 55 (214 ) 331 335 4th International Conference on Silicon Photovoltaics, SiliconPV 214 The mechanical theory behind the peel test

### Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double cantilever beam (DCB) specimens.

a). Cohesive Failure b). Interfacial Failure c). Oscillatory Failure d). Alternating Failure Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double

### Project PAJ2 Dynamic Performance of Adhesively Bonded Joints. Report No. 3 August Proposed Draft for the Revision of ISO

NPL Report CMMT(A)81 Project PAJ2 Dynamic Performance of Adhesively Bonded Joints Report No. 3 August 1997 Proposed Draft for the Revision of ISO 11003-2 Adhesives - Determination of Shear Behaviour of

### Int. J. Fracture, 119, 2003, 25-46

Int. J. Fracture, 119, 003, 5-46 THE USE OF A COHESIVE ZONE MODEL TO STUDY THE FRACTURE OF FIBRE COMPOSITES AND ADHESIVELY-BONDED JOINTS Blackman, B.R.K., Hadavinia, H., Kinloch, A.J. and Williams, J.G.

### TOUGHNESS OF PLASTICALLY-DEFORMING ASYMMETRIC JOINTS. Ford Research Laboratory, Ford Motor Company, Dearborn, MI 48121, U.S.A. 1.

TOUGHNESS OF PLASTICALLY-DEFORMING ASYMMETRIC JOINTS M. D. Thouless, M. S. Kafkalidis, S. M. Ward and Y. Bankowski Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann

### Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives

Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline

### Using ABAQUS Cohesive Elements to Model Peeling of an Epoxy-bonded Aluminum Strip: A Benchmark Study for Inelastic Peel Arms

Using ABAQUS Cohesive Elements to Model Peeling of an Epoxy-bonded Aluminum Strip: A Benchmark Study for Inelastic Peel Arms Ted Diehl DuPont DuPont Engineering Technology, Chestnut Run, Bldg 722, Wilmington,

### Proceedings of the 28th Risø international symposium on materials science, 3-6 Sept 2007.

Proceedings of the 28th Risø international symposium on materials science, 3-6 Sept 27. INFLUENCE OF TEMPERATURE ON COHESIVE PARAMETERS FOR ADHESIVES Anders Biel 1 and Thomas Carlberger 2 1 University

### CHARACTERIZING ADHESION OF PSA TAPES USING THE SHAFT LOADED BLISTER TEST

.. CHARACTERIZING ADHESION OF PSA TAPES USING THE SHAFT LOADED BLISTER TEST Emmett O'Brien Graduate Student Dept. of Chemical Engineering Virginia Tech Blacksburg, VA Shu Guo Graduate Student Dept. of

### Figure 1. Simply-supported beam nomenclature with single point load. Typical shear and moment diagrams are also shown.

CE0L Student Lab Manual Wood Flexural Strength Introduction This section outlines the steps necessar to perform the Wood Flexural Strength lab experiment. The purpose of the lab is to determine the Modulus

### MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.

### A SELF-INDICATING MODE I INTERLAMINAR TOUGHNESS TEST

A SELF-INDICATING MODE I INTERLAMINAR TOUGHNESS TEST P. Robinson The Composites Centre, Department of Aeronautics, Imperial College London South Kensington, London, SW7 2AZ, UK p.robinson@imperial.ac.uk

### Adhesive Joints Theory (and use of innovative joints) ERIK SERRANO STRUCTURAL MECHANICS, LUND UNIVERSITY

Adhesive Joints Theory (and use of innovative joints) ERIK SERRANO STRUCTURAL MECHANICS, LUND UNIVERSITY Wood and Timber Why I m intrigued From this to this! via this Fibre deviation close to knots and

### Mode II Delamination Analysis of Asymmetrical Four Point Bend Layered Beams with Considering Material Non-linearity

TECHNSCHE ECHANK, 7,, (07), 8-7 submitted: November 7, 0 ode Delamination Analsis of Asmmetrical Four Point Bend Laered Beams with Considering aterial Non-linearit V. Rizov An analtical stud is performed

### The science of elasticity

The science of elasticity In 1676 Hooke realized that 1.Every kind of solid changes shape when a mechanical force acts on it. 2.It is this change of shape which enables the solid to supply the reaction

### A Direct Derivation of the Griffith-Irwin Relationship using a Crack tip Unloading Stress Wave Model.

A Direct Derivation of the Griffith-Irwin Relationship using a Crack tip Unloading Stress Wave Model. C.E. Neal-Sturgess. Emeritus Professor of Mechanical Engineering, The Universit of Birmingham, UK.

### 1.103 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

### ME 2570 MECHANICS OF MATERIALS

ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation

### Laboratory 4 Bending Test of Materials

Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective

### Stress-Strain Behavior

Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

### Geometric Stiffness Effects in 2D and 3D Frames

Geometric Stiffness Effects in D and 3D Frames CEE 41. Matrix Structural Analsis Department of Civil and Environmental Engineering Duke Universit Henri Gavin Fall, 1 In situations in which deformations

### Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP

Proceedings of the World Congress on Engineering 21 Vol II WCE 21, June 2 - July 1, 21, London, U.K. Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP Lihua Huang,

### Introduction to Engineering Materials ENGR2000. Dr. Coates

Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed

### Flexural properties of polymers

A2 _EN BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF POLYMER ENGINEERING Flexural properties of polymers BENDING TEST OF CHECK THE VALIDITY OF NOTE ON

### Outline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour

Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard

### FREE EDGE DELAMINATION ONSET CRITERION

FREE EGE ELAMINATION ONSET CRITERION G. MARION now, 2, formerl 3, R. HARRY 2, and F. LECUYER MEYSYS, 29 rue J. Rostand, 9873 ORSAY CEEX, FRANCE 2 Laboratoire de Génie Mécanique, IUT Bordeaux I, 3345 TALENCE

### The objective of this experiment is to investigate the behavior of steel specimen under a tensile test and to determine it's properties.

Objective: The objective of this experiment is to investigate the behavior of steel specimen under a tensile test and to determine it's properties. Introduction: Mechanical testing plays an important role

### FRACTURE MECHANICS OF COMPOSITES WITH RESIDUAL STRESSES, TRACTION-LOADED CRACKS, AND IMPERFECT INTERFACES

Proc. 2 nd ESIS TC4 Conference on Polymers and Composites, in press, 1999 Author prepared reprint FRACTURE MECHANICS OF COMPOSITES WITH RESIDUAL STRESSES, TRACTION-LOADED CRACKS, AND IMPERFECT INTERFACES

### Mixed-Mode Fracture Toughness Determination USING NON-CONVENTIONAL TECHNIQUES

Mixed-Mode Fracture Toughness Determination USING NON-CONVENTIONAL TECHNIQUES IDMEC- Pólo FEUP DEMec - FEUP ESM Virginia Tech motivation fracture modes conventional tests [mode I] conventional tests [mode

### NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

### MECHANICS OF 2D MATERIALS

MECHANICS OF 2D MATERIALS Nicola Pugno Cambridge February 23 rd, 2015 2 Outline Stretching Stress Strain Stress-Strain curve Mechanical Properties Young s modulus Strength Ultimate strain Toughness modulus

### ICM11. Simulation of debonding in Al/epoxy T-peel joints using a potential-based cohesive zone model

Available online at www.sciencedirect.com Procedia Engineering 10 (2011) 1760 1765 ICM11 Simulation of debonding in Al/epoxy T-peel joints using a potential-based cohesive zone model Marco Alfano a,, Franco

### ME 323 Examination #2 April 11, 2018

ME 2 Eamination #2 April, 2 PROBLEM NO. 25 points ma. A thin-walled pressure vessel is fabricated b welding together two, open-ended stainless-steel vessels along a 6 weld line. The welded vessel has an

### Bending 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

### AERO 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

### Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced

### EMA 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:

### STRESSES AROUND UNDERGROUND OPENINGS CONTENTS

STRESSES AROUND UNDERGROUND OPENINGS CONTENTS 6.1 Introduction 6. Stresses Around Underground Opening 6.3 Circular Hole in an Elasto-Plastic Infinite Medium Under Hdrostatic Loading 6.4 Plastic Behaviour

### A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS

Journal of the Chinese Institute of Engineers, Vol. 9, No. 6, pp. 191-197 (6) 191 Short Paper A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS Der-Gue Lin and Zheng-Yi Feng* ABSTRACT This paper presents raft-pile-soil

### Survey of Wave Types and Characteristics

Seminar: Vibrations and Structure-Borne Sound in Civil Engineering Theor and Applications Surve of Wave Tpes and Characteristics Xiuu Gao April 1 st, 2006 Abstract Mechanical waves are waves which propagate

### NCHRP FY 2004 Rotational Limits for Elastomeric Bearings. Final Report APPENDIX E. John F. Stanton Charles W. Roeder Peter Mackenzie-Helnwein

NCHRP -68 FY 4 Rotational Limits for Elastomeric Bearings Final Report APPENDIX E John F. Stanton Charles W. Roeder Peter Mackenzie-Helnwein Department of Civil and Environmental Engineering Universit

### STANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius

MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen

### American Society for Testing and Materials (ASTM) Standards. Mechanical Testing of Composites and their Constituents

Mechanical Testing of Composites and their Constituents American Society for Testing and Materials (ASTM) Standards Tests done to determine intrinsic material properties such as modulus and strength for

### Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina

Module III - Macro-mechanics of Lamina Lecture 23 Macro-Mechanics of Lamina For better understanding of the macromechanics of lamina, the knowledge of the material properties in essential. Therefore, the

### MEASUREMENT METHODS FOR OBTAINING VOLUMETRIC COEFFICIENTS FOR HYPERELASTIC MODELLING OF FLEXIBLE ADHESIVES

MEASUREMENT METHODS FOR OBTAINING VOLUMETRIC COEFFICIENTS FOR HYPERELASTIC MODELLING OF FLEXIBLE ADHESIVES by Louise Crocker and Bruce Duncan Project PAJex2 - Flexible Adhesives PAJex2 Report No 3 January

### Geometric and Material Property Effects on the Strength of Rubber-Toughened Adhesive Joints

Geometric and Material Property Effects on the Strength of Rubber-Toughened Adhesive Joints Altering the geometry of a bonded joint will invariably cause changes to occur in the stress and strain distribution

### Massachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139

Massachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139 2.002 Mechanics and Materials II Spring 2004 Laboratory Module No. 6 Fracture Toughness Testing and Residual

### Effect of Bi-axial Residual Stresses on the Micro-Indentation Behaviour of Bulk Materials

Effect of Bi-axial Residual Stresses on the Micro-Indentation Behaviour of Bulk Materials Prakash Jadhav Department of Mechanical Engineering CMR Institute of Technolog, Bangalore, India Prakash.k@cmrit.ac.in

### BOUNDARY EFFECTS IN STEEL MOMENT CONNECTIONS

BOUNDARY EFFECTS IN STEEL MOMENT CONNECTIONS Koung-Heog LEE 1, Subhash C GOEL 2 And Bozidar STOJADINOVIC 3 SUMMARY Full restrained beam-to-column connections in steel moment resisting frames have been

### ISO 178 INTERNATIONAL STANDARD. Plastics Determination of flexural properties. Plastiques Détermination des propriétés en flexion

INTERNATIONAL STANDARD ISO 178 Fourth edition 2001-12-15 Plastics Determination of flexural properties Plastiques Détermination des propriétés en flexion Reference number ISO 2001 PDF disclaimer This PDF

### Chapter 7. Highlights:

Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true

### Mechanical Properties of Materials

Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of

### ADHESIVE TAPE. Nives Bonačić University of Zagreb, Physics department, Croatia

ADHESIVE TAPE Nives Bonačić University of Zagreb, Physics department, Croatia Abstract This paper focuses on determining the force necessary to remove a piece of adhesive tape from a horizontal surface

### Evaluation of in-plane orthotropic elastic constants of paper and paperboard

Evaluation of in-plane orthotropic elastic constants of paper and paperboard T. Yokoyama and K. Nakai Department of Mechanical Engineering, Okayama University of Science - Ridai-cho, Okayama 7-5, Japan

### MECHANICS OF MATERIALS REVIEW

MCHANICS OF MATRIALS RVIW Notation: - normal stress (psi or Pa) - shear stress (psi or Pa) - normal strain (in/in or m/m) - shearing strain (in/in or m/m) I - area moment of inertia (in 4 or m 4 ) J -

### MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING

MCHANICS OF SOLIDS - BAMS TUTOIAL 1 STSSS IN BAMS DU TO BNDING This tutorial covers elements of the following sllabi. o Part of dexcel HNC Mechanical Principles UNIT 21722P outcome2. o Parts of the ngineering

### Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

5.4 Beams As stated previousl, the effect of local buckling should invariabl be taken into account in thin walled members, using methods described alread. Laterall stable beams are beams, which do not

### Physical Properties Testing Technical Bulletin

Technical Bulletin MANUFACTURER Raven Lining Systems 13105 E. 61 st Street, Suite A Broken Arrow, OK 74012 (918) 615-0020 TENSILE TESTING OF PLASTICS ASTM D638, ISO 527 Tensile tests measure the force

### Limit analysis of brick masonry shear walls with openings under later loads by rigid block modeling

Limit analysis of brick masonry shear walls with openings under later loads by rigid block modeling F. Portioli, L. Cascini, R. Landolfo University of Naples Federico II, Italy P. Foraboschi IUAV University,

### Chapter 5: Ball Grid Array (BGA)

Chapter 5: Ball Grid Array (BGA) 5.1 Development of the Models The following sequence of pictures explains schematically how the FE-model of the Ball Grid Array (BGA) was developed. Initially a single

### Introduction to Fracture

Introduction to Fracture Introduction Design of a component Yielding Strength Deflection Stiffness Buckling critical load Fatigue Stress and Strain based Vibration Resonance Impact High strain rates Fracture

### ME 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

### ME 243. Mechanics of Solids

ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

### Back Calculation of Rock Mass Modulus using Finite Element Code (COMSOL)

Back Calculation of Rock Mass Modulus using Finite Element Code (COMSOL) Amirreza Ghasemi 1. Introduction Deformability is recognized as one of the most important parameters governing the behavior of rock

### INTRODUCTION (Cont..)

INTRODUCTION Name : Mohamad Redhwan Abd Aziz Post : Lecturer @ DEAN CENTER OF HND STUDIES Subject : Solid Mechanics Code : BME 2033 Room : CENTER OF HND STUDIES OFFICE H/P No. : 019-2579663 W/SITE : Http://tatiuc.edu.my/redhwan

### EFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A SPHERE AGAINST A RIGID FLAT A FINITE ELEMENT STUDY

Proceedings of the International Conference on Mechanical Engineering 2009 (ICME2009) 26-28 December 2009, Dhaka, Bangladesh ICME09- EFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A

### Numerical analysis of the energy contributions in peel tests: a steady-state multilevel finite element approach

Int. J. Adhesion and Adhesives, vol 28, 2008, 222-236 Numerical analysis of the energy contributions in peel tests: a steady-state multilevel finite element approach Ph. Martiny a, *, F. Lani a, A.J. Kinloch

### COMELD TM JOINTS: A NOVEL TECHNIQUE FOR BONDING COMPOSITES AND METAL

COMELD TM JOINTS: A NOVEL TECHNIQUE FOR BONDING COMPOSITES AND METAL F.J. Guild *, P.J. Hogg + and W. Tu School of Engineering and Materials Science, Queen Mary, University of London, London E1 4NS, UK

### A Compression-Loaded Double Lap Shear Test: Part 1, Theory

International Journal of Adhesion and Adhesives, submitted A Compression-Loaded Double Lap Shear Test: Part 1, Theor D.-A. Mendels, S.A. Page, J.-A. E. Månson Laboratoire de Technologie des Composites

### CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS

CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.1 Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a free-body diagram),

### A CRITERION OF TENSILE FAILURE FOR HYPERELASTIC MATERIALS AND ITS APPLICATION TO VISCOELASTIC-VISCOPLASTIC MATERIALS

MTS ADHESIVES PROGRAMME 1996-1999 PERFORMANCE OF ADHESIVE JOINTS Project: PAJ1; Failure Criteria and their Application to Visco-Elastic/Visco-Plastic Materials Report 2 A CRITERION OF TENSILE FAILURE FOR

### Experimental Uncertainty Review. Abstract. References. Measurement Uncertainties and Uncertainty Propagation

Experimental Uncertaint Review Abstract This is intended as a brief summar of the basic elements of uncertaint analsis, and a hand reference for laborator use. It provides some elementar "rules-of-thumb"

### 4.MECHANICAL PROPERTIES OF MATERIALS

4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stress-strain diagram

### Advanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay. Lecture 27

Advanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay Lecture 27 Last time we considered Griffith theory of brittle fracture, where in it was considered

### Laboratory 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

### Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2BX. UK.

Engineering Fracture Mechanics, vol. 7, 005, 877-897 The determination of the mode II adhesive fracture resistance, G IIC, of structural adhesive joints: An effective crack length approach. B.R.K. Blackman

### EXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFF-AXIS GFRP LAMINATES

20 th International Conference on Composite Materials Copenhagen, 19-24 th July 2015 EXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFF-AXIS GFRP LAMINATES Esben Lindgaard 1 and Brian

### MODELING OF THE WEDGE SPLITTING TEST USING AN EXTENDED CRACKED HINGE MODEL

Engineering MECHANICS, Vol. 21, 2014, No. 1, p. 67 72 67 MODELING OF THE WEDGE SPLITTING TEST USING AN EXTENDED CRACKED HINGE MODEL Tomáš Pail, Petr Frantík* The present paper describes a semi-analytical

### INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT

INTERFACE SHEAR TRANSFER FOR HIGH STRENGTH CONCRETE AND HIGH STRENGTH REINFORCEMENT 641 Susumu KONO 1 And Hitoshi TANAKA SUMMARY The shear transfer at construction joints for members with high strength

### Plastic Hinge Rotation Capacity of Reinforced Concrete Beams

Plastic Hinge Rotation Capacit of Reinforced Concrete Beams Ali Kheroddin 1 and Hosein Naderpour 2 Downloaded from ijce.iust.ac.ir at 21:57 IRDT on Monda September 10th 2018 1 Associate Professor, Department

### Delamination in fractured laminated glass

Delamination in fractured laminated glass Caroline BUTCHART*, Mauro OVEREND a * Department of Engineering, University of Cambridge Trumpington Street, Cambridge, CB2 1PZ, UK cvb25@cam.ac.uk a Department

### DESIGN OF BEAM-COLUMNS - II

DESIGN OF BEA-COLUNS-II 14 DESIGN OF BEA-COLUNS - II 1.0 INTRODUCTION Beam-columns are members subjected to combined bending and axial compression. Their behaviour under uniaxial bending, biaxial bending

### Experimental and numerical study on GFRP-glass adhesively bonded joints

Challenging Glass 4 & COST Action TU0905 Final Conference Louter, Bos, Belis & Lebet (Eds) 2014 Taylor & Francis Group, London, ISBN 978-1-138-00164-0 Experimental and numerical study on GFRP-glass adhesively

### ASPECTS CONCERNING TO THE MECHANICAL PROPERTIES OF THE GLASS / FLAX / EPOXY COMPOSITE MATERIAL

5 th International Conference Advanced Composite Materials Engineering COMAT 2014 16-17 October 2014, Braşov, Romania ASPECTS CONCERNING TO THE MECHANICAL PROPERTIES OF THE GLASS / FLAX / EPOXY COMPOSITE

### 6.4 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

### Int. J. Fracture, vol. 173, 2012, A multiscale parametric study of mode I fracture in metal-to-metal low-toughness adhesive joints

Int. J. Fracture, vol. 173, 2012, 105-133 A multiscale parametric study of mode I fracture in metal-to-metal low-toughness adhesive joints Ph. Martiny a, F. Lani a,c, A.J. Kinloch b, T. Pardoen c* a Cenaero,

### A RESEARCH ON NONLINEAR STABILITY AND FAILURE OF THIN- WALLED COMPOSITE COLUMNS WITH OPEN CROSS-SECTION

A RESEARCH ON NONLINEAR STABILITY AND FAILURE OF THIN- WALLED COMPOSITE COLUMNS WITH OPEN CROSS-SECTION H. Debski a*, J. Bienias b, P. Jakubczak b a Faculty of Mechanical Engineering, Department of Machine

### Modeling the elastic properties of paper honeycomb panels using the finite element method

Proceedings of the XXVI th International Conference Research for Furniture Industry Modeling the elastic properties of paper honeycomb panels using the finite element method Viktor UTASSY, Levente DÉNES

### Friction of Extensible Strips: an Extended Shear Lag Model with Experimental Evaluation

Friction of Extensible Strips: an Extended Shear Lag Model with Experimental Evaluation Ahmad R. Mojdehi 1, Douglas P. Holmes 2, Christopher B. Williams 3, Timothy E. Long 4, David A. Dillard 1 1 Department

### Nigerian Journal of Technology, Vol. 26, No. 2, June 2007 Edelugo 37

Nigerian Journal of Technology, Vol. 26, No. 2, June 2007 Edelugo 37 APPLICATION OF THE REISSNERS PLATE THEORY IN THE DELAMINATION ANALYSIS OF A THREE-DIMENSIONAL, TIME- DEPENDENT, NON-LINEAR, UNI-DIRECTIONAL

### EMA 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

### NON-LINEAR FRACTURE BEHAVIOR OF DOUBLE CANTILEVER BEAM

Engineering MECHANICS, Vol., 015, No., p. 95 10 95 NON-LINEAR FRACTURE BEHAVIOR OF DOUBLE CANTILEVER BEAM Viktor Rizov* This article describes a theoretical study of non-linear fracture behavior of the

### DYNAMIC DELAMINATION OF AERONAUTIC STRUCTURAL COMPOSITES BY USING COHESIVE FINITE ELEMENTS

DYNAMIC DELAMINATION OF AERONAUTIC STRUCTURAL COMPOSITES BY USING COHESIVE FINITE ELEMENTS M. Ilyas, F. Lachaud 1, Ch. Espinosa and M. Salaün Université de Toulouse, ISAE/DMSM, 1 avenue Edouard Belin,

### On characterising fracture resistance in mode-i delamination

9 th International Congress of Croatian Society of Mechanics 18-22 September 2018 Split, Croatia On characterising fracture resistance in mode-i delamination Leo ŠKEC *, Giulio ALFANO +, Gordan JELENIĆ

### Pullout Tests of Geogrids Embedded in Non-cohesive Soil

Archives of Hydro-Engineering and Environmental Mechanics Vol. 51 (2004), No. 2, pp. 135 147 Pullout Tests of Geogrids Embedded in Non-cohesive Soil Angelika Duszyńska, Adam F. Bolt Gdansk University of

### D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.

D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having

### Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

### 3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture,

3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture, 09.21.07 1. In the beam considered in PS1, steel beams carried the distributed weight of the rooms above. To reduce stress on the beam, it