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Assessing the Behavior of Balsa Wood in Three-point Bend Testing to Fulfill ABET Outcome (b)

Wayne L. Elban

Department of Engineering Loyola University Maryland Baltimore, Maryland 21210

COPYRIGHT: Edmonds Community College 2015 This material may be used and reproduced for non-commercial educational purposes only. This module provided by MatEdU, the National Resource Center for Materials Technology Education, http://materialseducation.org/. ABSTRACT: A procedure is described for materials engineering students, functioning in two- to four-member teams, to fulfill the four elements of Accreditation Board for Engineering and Technology (ABET) Outcome (b) as the capstone activity in an experimental methodology course. An experiment is designed and executed using a linear variable differential transformer (LVDT) to measure the center deflection of a balsa wood beam subjected to three-point bending. Data analysis was accomplished using a spreadsheet and accompanying plotting capability to determine Young’s modulus for balsa wood for comparison with literature values. KEY WORDS: Design of experiment, three-point bend (flexure) testing, LVDT, Young’s modulus, balsa wood, ABET Outcome (b) PREREQUISITE KNOWLEDGE: Students should have an understanding of mechanical properties of materials and possible experimental issues present in their determination at the level provided in an introductory materials science course (and accompanying laboratory course as needed). OBJECTIVES: (a) Experimental Goals:

1. To measure any deflection present in a three-point bend testing apparatus in order to correct deflection data obtained when testing a sample;

2. To measure the deflection of a balsa wood beam in three-point bend testing in order to determine Young’s modulus; and

3. To assess whether the maximum center deflection allowance desired in a laboratory bridge fabricated with balsa wood beams is satisfied.

(b) Learning Goals:

1. To be able to create an open-ended, non-statistical design of experiment and to execute the procedure;

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2. To be able to contribute to a team activity and distribute/accomplish technical work assignments; and

3. To be able to use engineering planning and experimental methods to provide a quantitative assessment of technical issues.

TYPE OF MODULE: Laboratory experiment TIME REQUIRED: Instrumentation assessment and flexural measurements occur in one laboratory session scheduled to last two hours and 40 minutes. MODULE LEVEL: Advanced; developed to be suitable as a junior-level undergraduate experience MatEd CORE COMPETENCIES COVERED:

0.A Demonstrate good communication skills 0.B Prepare tests and analyze data 1.A Carry out measurement of dimensions and of physical properties 1.C Demonstrate laboratory skills 1.D Apply electrical phenomena to physical measurements 2.B Demonstrate proper use of units and conversions 3.A Practice appropriate computer skills and uses 3.B Demonstrate use of computer applications 4.A Demonstrate effective work with teams 6.A Apply basic concepts of mechanics 8.A Demonstrate the planning and execution of materials experiments 8.B Apply mechanical testing processes to solid materials 8.G Perform appropriate tests of wood 12.A Describe the properties and testing processes for wood

TABLE OF CONTENTS Abstract 1 Objectives 1 Module data 2 MatEd core competencies covered 2 Materials and equipment required 3 Process for fulfilling ABET Outcome (b) 3 Part I Design the experiment 3 Part II Conduct the experiment 5 Part III Analyze experimental data 5 Part IV Interpret the analyzed experimental data 5 Part V Reporting 6 Appendix A: Guidance for preparing a punch list 7 Punch list for designing three-point experiment 8 Appendix B: Experimental procedure 9

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Appendix C: Data analysis 10 Appendix D: Sample analysis results with comments 11 Appendix E: Written report grading criterion 12 Instructor notes 13 References 14 Sources of Supplies 16 Acknowledgments 17 About the author 17 Tables and figures 18 Evaluation packet 23 EQUIPMENT AND MATERIALS: (1) LVDT [direct current (DC)-operated and spring- loaded] -- Measurement Specialties GCD-125, Reference [1] (formerly Lucas Schaevitz designated GCD-121-125) with mounting fixture; (2) Lab jack with stabilizing weights; (3) Gage blocks: Mitutoya 0.020", 0.050", 0.1001", and 0.200"; (4) Protoboard (Global Specialties Model 203A), supplying +15 V DC or alternative power supply with the same DC voltage capability; (5) Digital multimeter (Fluke model 45); (6) Three-point bend test apparatus (American Instrument Co. cat. no. 4-3900); (7) Set of 8 brass masses (Central Scientific Co. cat no. 09600); (8) Steel beam (16 mm wide x 10 mm thick x 115 mm long); (9) Balsa wood beam (19.0 mm wide x 6.27 mm thick x 254 mm long); and (10) Metric dial caliper. PROCESS FOR FULFILLING ABET OUTCOME (b): An ability to design and conduct experiments, as well analyze and interpret data [2] Part I: Design the Experiment (Instructor Note 1) General Background: Flexure (bend) testing is often used to determine mechanical properties of ceramic materials, for example, which are brittle and subject to experimental artifacts due to misalignment issues when tested in tension. To circumvent this, one standard arrangement is the three-point bend test involving two rounded (e.g., cylindrical to minimize stress concentration) supports beneath the sample and a rounded (e.g., cylindrical) member to provide an applied load to the top of the sample located halfway between the bottom supports (Fig. 6.14, Shackelford [3], p. 166). When this occurs, the bottom surface is placed in tension while the top surface simultaneously goes into compression. Initially, the sample is elastically loaded, but plastic deformation and fracture result when the load exceeds the sample’s elastic limit. In addition, bend testing at various scales (from fractional to full) can be used for a variety of non-brittle materials when it is desired to simulate real service conditions for such structural members as I-beams and bridge deck planks. Young's modulus or the modulus of elasticity, E, for a beam loaded in three-point bending is calculated using: E = L3m / 4bh3, (1) where L is the span length between bottom supports; m is the slope of the applied load − deflection plot;

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b is the beam width; and h is the beam thickness. (Eq. 6.14, Shackelford [3], p. 168) A schematic of the three-point bend test apparatus is given in Figure 1. Originally, the test apparatus incorporated a dial indicator to measure sample deflection. This is now accomplished using a linear variable differential transformer (LVDT) briefly described in the next paragraph. However, the dial indicator remains an integral part of the apparatus, providing vertical positioning and alignment of the loading nose (Figure 1, Reference [4]). Once a sample has been positioned in the apparatus, various applied masses are placed on a circular load platform. Rather than contacting the platform near its circumference as drawn however, a short cantilever arm is attached to the platform so there is sufficient room for the LVDT not to be disturbed as the masses are added. An LVDT [5,6] is a widely used electromechanical transducer that converts linear displacement, sensed by the movement of the device's core (Figure 4-50, Holman [7], p. 231), into a DC signal that can be detected, for example, by a digital multimeter (DMM) set to measure DC voltages. Referring to the position of the LVDT in Figure 1, the sample and test apparatus are effectively in series. During loading, any apparatus displacement is included in the LVDT output and must be accounted for when determining the desired sample displacement.[8] This is demonstrated in the schematic data plot in Figure 2. Student Problem Statement (Instructor Note 2): As part of your first engineering work assignment, your employer asks you to design a scale-model bridge truss with balsa wood beams for the roadbed (as planking). First, it is necessary to determine experimentally the Young's modulus of balsa wood using the beam. Second, one of the design specifications requires that a center deflection of no more than 0.45 mm occurs when the beam experiences an applied load of 5.4 N.(Instructor Note 3) In constructing the model truss, the span length of the beam is specified to be 8". After examining a sample of the balsa wood planking to be used in the model and the three-point bend tester, design an experimental procedure to determine Young's modulus for the sample provided and to address the maximum center deflection specification issue.(Instructor Note 4) Follow the procedural guidelines that are detailed in Table 2-8, Holman [7], p. 49. Implement this procedure during the following week. Include in the lab report your evaluation as to whether the balsa wood beam plank that was tested will meet the deflection specification. Based on your experience with the tester, also indicate specific improvements to the experiment you would make for a revised (“second generation”) test. Research: Utilize the remaining time in lab when the experiment is not being conducted by your team and out-of-lab time to delegate/distribute the work to perform research using textbooks, reference books, and especially the internet to investigate the following topics in particular: 1. Three-point bend testing; 2. Three-point bend tester design; and 3. Mechanical properties of balsa wood.

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The information obtained will be useful in preparing your written report, providing background and possible insights regarding the performance of the balsa wood beam.

Equipment: Open; to be determined/specified by student teams from any/only items used

throughout the semester Schedule: At the end of prior lab session, review problem statement and examine three-point

bend tester and balsa wood sample. Hold one or more team meetings where each team works separately to design an experimental procedure in detail. Each team provides a completed “punch list” (Appendix A) for the design of the experiment for instructor evaluation and to assure availability of equipment when the experiment is to be performed. (Instructor Note 5) Part II: Conduct the Experiment Record measurements and any relevant observations in a laboratory notebook with appropriate drawings. Perform experiment that was designed taking into account comments and suggestions provided on the punch list by the instructor. {Note: A step-by-step procedure is provided in Appendix B adapted from Reference [9]. (Instructor Note 6)} Conduct research on the properties of balsa wood and three-point bend testing. Repeat experiment as necessary after performing data analysis. Part III: Analyze Experimental Data Perform a spreadsheet analysis of the data obtained in order to determine Young’s modulus for the beam and respond to the deflection design limit issue. Any figures and tables to be included are at the discretion of students. {Note: A step-by-step procedure is provided in Appendix C adapted from Reference [9]. (Instructor Note 6)} Part IV: Interpret the Analyzed Experimental Data Balsa Wood Beam Deflection Report values for Young’s modulus in units of GPa and the center deflection in units of mm for an applied load of 5.4 N.

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Uncertainty Analysis As part of your uncertainty analysis, quantitatively determine the uncertainty in the displacement measurement on the balsa wood beam resulting when loaded with 5.4 N, involving a difference in two voltage measurements and applying Eq. [3-2], Holman [7], p. 64. Be sure to factor this calculation into your evaluation of the beam’s ability to satisfy the design specification. Next, identify any non-quantitative issues that contribute to experimental uncertainty. Comparison with Published Values of Young’s Modulus for Balsa Wood Compare the value determined for Young’s modulus for the balsa wood beam with values found in the literature and on the Internet. Design Improvements Identify any improvements to be made both in the design of the tester and the experimental procedure. {Note: A summary of representative data with comments addressing each of these issues appears in Appendix D adapted from Reference [9]. (Instructor Note 6)} Part V: Reporting (Instructor Note 7) A maximum of 2 word-processed pages of text is allowed as a team (group) reporting effort. Relevant tables and figures (graphs) should be incorporated at the end of the report and do not count as text. (Instructor Note 8) The following subjects to be covered in the report: Objective(s) Experimental Procedure Experimental Results (from Analysis of Experimental Data) Uncertainty Analysis Brief Discussion of Results and Uncertainty Analysis Summary and Conclusions Appendix (does not count toward the two-page limit): Sample Calculations It is important to adhere to the report section headings/format listed above. All sections should be provided in paragraph form. Written reports are due on the day and time specified by the instructor. {Note: The grading criterion form is given in Appendix E.}

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Appendix A: Guidance for Preparing a Punch List for Experimentally Assessing the Behavior of Balsa Wood in Three-point Bending

Due date/time specified by the instructor Description: A “punch list” is widely used in the construction industry to provide the set of tasks needing to be completed in order to satisfy the terms of a given contract. The basic format has been adopted for other purposes such as to document findings from a safety inspection and their resolution. Here, a punch list is being used to ensure that the necessary elements in designing the experiment are considered and detailed to facilitate executing the experiment in an efficient manner. Elements in the punch list are taken from the generalized experiment procedure appearing in Table 2-8, Holman [7], p. 49. The following comments are offered to guide the experiment design and completion of the list appearing on the next page. Experiment design constraints: 1. Must only specify equipment used this semester. 2. Useful data must be obtained in the time allotted (two hours and 40 min. max.). Rules of engagement: 1. As a group effort, each team is responsible to submit a carefully prepared punch list for instructor evaluation by the indicated deadline before the experiment is performed. Team success is determined by how carefully the experiment is designed and how thoroughly the punch list is prepared. Since this is an open-ended design of experiment, instructor input may be limited during the laboratory session, particularly for each team’s first attempt. 2. If needed or if the data is deemed unsatisfactory, teams may re-attempt the experiment the following week.

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Punch List for Designing Three-Point Bend Experiment

Name: _____________________________ on Team #______ Date: ___________________ Partners: ______________________________________________________________________ (5 Points) Technical objective(s): (5 Points) Primary variable(s) to be measured: (10 Points) Complete list of equipment and any other items needed to perform experiment, including specifying the choice of LVDT from three available (GCD-050, -125, or -250): (10 Points) Detailed experimental procedure, including any controls being used: (10 Points) Detailed data analysis procedure, including what and how software will be used, if needed: (10 Points) Uncertainty issues:

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Appendix B: Experimental Procedure 1. Using the 0.020, 0.050, 0.1001, and 0.200" gage blocks, perform a calibration of the

LVDT to be used with the three-point bend test apparatus (Instructor Note 2). To gain an additional gage block length, combine the 0.020 and 0.050" gage blocks by rubbing them together until they stick. Likewise, combine the 0.020 and 0.1001" gage blocks; then the 0.050 and 0.1001" gage blocks; and finally the 0.020, 0.050, and 0.1001" gage blocks. Before beginning the calibration procedure, adjust the height of the LVDT against a smooth rigid surface (e.g., steel beam placed on laboratory bench top) until the DMM reads 0.0 ± 0.2 VDC.

2. Determine the displacement of the apparatus by testing the steel beam, having a 3" span

support length (Instructor Note 9). With the LVDT contacting the load platform of the three-point bend test apparatus (Instructor Note 10), adjust the initial height of the LVDT until the DMM reads between +8 and +9 VDC. Successively load the beam in a gentle manner with 50, 100, 150, 250, 350, and 550 gf. Record the output voltage for each loading.

3. Determine the deflection of the balsa wood beam for a span support length of 8". Adjust

the LVDT to yield a DMM reading between +8 and +9 VDC. Load this beam as done previously. Record the output voltage for each loading. Repeat the process several times to assess repeatability.

4. Measure the thickness of the balsa wood beam and its width with a dial caliper. The span

support length can be read directly off of the three-point bend test apparatus.

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Appendix C: Data Analysis 1. Adjust the gage block data so that zero displacement equals zero volts. Plot LVDT

output voltage, V, as a function of gage block thickness, in, for all of the gage blocks used. Perform a computer least-squares fit analysis on the data that is appropriate (not departing from linearity) to determine the slope.

2. Adjust the steel loading data so that zero displacement equals zero volts. The value

generated for each mass should be tabulated for possible use in correcting [8] the deflection data of the material being tested.

3. Adjust the balsa wood loading data so that zero displacement equals zero volts. This data

possibly has two components. The major portion is the actual balsa wood deflection. There may be a minor contribution to the measured deflection data coming from the displacement of the apparatus itself. This can be evaluated quantitatively from the steel loading data since the steel bar that was used is a rigid body (i.e., undergoes no deflection) to a very good approximation for the masses used to load it. The apparatus displacement needs to be removed from the total deflection data for each mass to yield only the material response. This is accomplished using the relation

Vs = Vm - Va , (2)

where Vs is sample deflection voltage; Vm is measured total deflection voltage; and Va is apparatus displacement voltage.

Plot applied force, N, as a function of deflection, mm, of the balsa wood during loading. Although this graph will probably exhibit some scatter, perform a computer least-squares fit analysis on the plotted values to determine the slope.

4. Compute Young’s modulus in units of GPa for balsa wood using Eq. (1).

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Appendix D: Sample Analysis Results with Comments SAMPLE DATA SHEETS AND PLOTS: The LVDT calibration was repeated several times. Six balsa wood beams were each tested a total of six times verifying that the results were reasonably reproducible. The data sets appearing in this section are considered to be representative. LVDT Operation/Calibration Verification: A plot of zero-adjusted output voltages as a function of gage block thickness as the LVDT was exercised with thicknesses ranging from 0.020 to 0.200 in appears in Figure 3. The least-squares fit analysis yielded a slope of 83.8 V/in, comparing favorably with the scale factor = 83.513 V/in provided by the manufacturer. Test Apparatus Displacement: Appearing in the second column of Table 1 are the zero-adjusted output voltages obtained as the LVDT detected the displacement of the three-point bend test apparatus itself while loading a rigid steel beam with applied masses ranging from 0 to 550 g. Balsa Wood Beam Deflection: The first column in Table 1 provides the zero-adjusted output voltages resulting when balsa wood beam sample NB #1 (designated NB #1-5 for run 5) was loaded in the apparatus. Net voltages, corresponding to sample deflection, are given in the third column by subtracting the voltages associated with apparatus deflection. Figure 4 shows a plot of the variation of applied force, in units of N, as a function of beam deflection in units of mm obtained using the manufacturer’s scale factor. A slope of 12.9 N/mm was obtained by least-squares fit analysis corresponding to E = 5.78 GPa. The measured center deflection was 0.420 mm which is below the stated design specification requirement even when measurement uncertainty is considered (below). Table 2 provides a summary of the balsa wood results for all of the samples tested and shows considerable variability in the values for Young’s modulus and center deflection. The average E for six samples was 5.02 GPa (standard deviation = 0.74 GPa), and the corresponding average center deflection when experiencing an applied load of 5.4 N was 0.449 mm (standard deviation = 0.075 mm). Table 3 provides a comparison of the current average Young’s modulus value with those reported elsewhere [10-14], and the current determination is reasonable given the large variability in the other values (Instructor Note 11). Figure 5 shows the non-linear variation of center deflection (at 5.4 N applied load) with Young’s modulus in reasonable agreement with the expected (1/Young’s modulus) dependency [15]. Uncertainty: The calculation of the uncertainty in an LVDT displacement measurement depends on the uncertainty specified by the DMM manufacturer for the DC voltage scale used. The Fluke model 45 has a stated uncertainty of ±[0.025%(reading) + twice least count]. Referring to Table 1 for NB #1-5, a force of 5.4 N causes a deflection of 0.420 mm, corresponding to a net voltage reading of 1.38 VDC with a calculated uncertainty of ±0.02√2 VDC. This corresponds to a displacement uncertainty of ±0.009 mm. There are also non-quantitative issues such as repeatability of the placement and stacking of the applied loads and how carefully and gently this is done so as not to disturb the LVDT or dynamically load the beam. (Instructor Note 12)

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Appendix E: Written Report Grading Criterion Objectives (10) Experimental Procedure (10) Experimental Results (20) Uncertainty Analysis (20) Brief Discussion (20) Summary and Conclusions (20) Rewrite Needed: Yes or No Over Two-Page Maximum (-10) Late (-5 per day; due by course start time)

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INSTRUCTOR NOTES: 1. This experiment was originally introduced at the National Educators’ Workshop: Update 93 as a sophomore-level materials science experiment.[9] Now, the experiment has been adapted to fulfill ABET Outcome (b) involving student teams of two to four members. For a given laboratory session, each team is given their own balsa wood beam. The beams were all procured at the same time from the same vendor and have been designated OB (old beam to indicate being used in the 1993 study) and NB (new beam to indicate being recently introduced). To enhance the experiment, a punch list format has been introduced to guide student teams in their design of the experiment, open-ended Web-based student activities have been included, and a large amount of additional experimental results were obtained. Six repeat experiments on each of six balsa wood beams were performed. These results are presented in summary form to underscore the known sample-to-sample variability [12] encountered in the mechanical properties of (balsa) wood. Setting the ABET accreditation issue aside, this experiment provides an orderly method to step through the process of designing and executing an experiment to obtain reliable material property data and to have their uncertainties characterized. This method is not limited to flexural testing and can be readily used for a wide variety of material property experiments. 2. In order to call attention to and improve students’ ability with the conversion of units, the problem statement and equipment used involves mixed units which are still encountered in the workplace. 3. The particular center deflection was chosen to be approximately the mean value for the average determinations of the six balsa wood samples tested. Thus depending on the sample provided a given student team, it could either pass or fail the criterion. 4. In addition to Reference [9], the current experiment relates to several previous National Educators' Workshop papers on various aspects of materials bend testing [16-20] and on the properties and testing of wood [16,19,21,22]. 5. The punch list appearing in Appendix A has a condensed format to save space. Students are provided an expanded three-page electronic version to complete and submit. 6. While the experimental procedure and sample data acquisition and analysis with appropriate plots are available in Reference [9], these elements are provided in somewhat modified form as a series of appendices as a convenience. 7. The written report is intended to resemble closely technical progress reports that entry- or intermediate-level engineers are called upon to prepare either weekly, bi-weekly, or monthly. In these reports, emphasis is given to providing a concise description of what was to be achieved, what approach was taken, what results were obtained, what uncertainty exists in the results, and what can be summarized and concluded from the work to date.

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8. To maximize the amount of information contained in any technical report, it is necessary to rely heavily on tables and figures (graphs). Attention should be given to preparing tables and figures (graphs) that can "stand alone" essentially as separate entities without extensive reference to the accompanying text. As such, each table and figure (graph) must have a well-composed title or caption that clearly describes what is being shown. Providing descriptive column headings for tabulated information and data is a necessity. Consideration should also be given to the use of footnotes at the bottom of tables to describe further the information/data being displayed. Line drawings and graphs should also be well-labeled. Tables and figures (graphs) should be numbered 1 to n consecutively as they are introduced in the text to facilitate referring to them (i.e., Table 1, Table 2, ..., Table n and Figure 1, Figure 2, ..., Figure n). Care must be taken to include appropriate, consistent units in tables and figures (graphs) as well as throughout the report. 9. A 3" span support length for the steel beam was chosen because of material availability, but this length is considered valid to relate to testing balsa wood beams with an 8" span because the steel beam is rigid for the applied loads being used. 10. Care must be taken to handle the dial indicator gently as it is easily damaged. 11. Since wood is a natural product, a number of factors affect its mechanical properties including tree-to-tree variation associated with growing conditions (e.g., soil type and content, rainfall, and tree spacing) and moisture content, density, and grain orientation of harvested (processed) wood.[12] 12. A major source of uncertainty in the earlier experiment [9] was slight tilting of the platform for placing the applied loads because of how the platform was attached to the dial indicator (simple butt joint secured with a flathead machine screw as per Figure 1). To eliminate this issue in the current work, a single-piece platform with an underneath, tight-fitting sleeve that slips over the top end of the dial indicator rod was used, being secured with the same screw. Now, the stack of applied loads can be placed in the center of the platform. REFERENCES: [1] Online Sensors Information Resource – “GCD Series – DC Operated Gage Heads,”

Measurement Specialties Technical Paper. Web. 6/2/2015. <http://meas-spec.com/downloads/GCD-Series.pdf>.

[2] Online Information Resource – “Outcome (b) an ability to design and conduct

experiments, as well as analyze and interpret data,” Report. Web. 2/10/2015. <http://www.foundationcoalition.org/home/keycomponents/assessment_eval/outcome_b.html>.

[3] Shackelford, J.F.: Introduction to Materials Science for Engineers. 8th Edition, Pearson,

Upper Saddle River, New Jersey, 2015.

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[4] “Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials (Metric),” Designation D 790M-86, 1989 Annual Book of ASTM Standards, Volume 08.01 Plastics (I). ASTM, pp. 290-298.

[5] Online Sensors Information Resource – “The LVDT: construction and principles of

operation,” Measurement Specialties Technical Paper. Web. 5/14/2015. <http://www.meas-spec.com/downloads/Principles_of_the_LVDT.pdf>.

[6] Online Sensors Information Resource – “MEAS LVDT,” Measurement Specialties

Application Note. Web. 5/14/2015. <http://www.meas-spec.com/downloads/LVDT_Technology.pdf>.

[7] Holman, J.P.: Experimental Methods for Engineers. 8th Edition, McGraw-Hill Inc., New

York, 2012. [8] Tegart, W.J.M.: Elements of Mechanical Metallurgy. The Macmillan Co., New York,

1966, pp. 25-29. [9] Elban, W.L.: Three-point Bend Testing of Poly (methyl methacrylate) and Balsa Wood,

in National Educators’ Workshop: Update 93, NASA Conference Publication 3259, 1994, pp. 373-390. Web accessible at http://www.materialsinstem.org/docs/archive/1993.pdf

[10] Easterling, K.E.; Harrysson, R.; Gibson, L.J.; and Ashby, M.F.: On the Mechanics of

Balsa and Other Woods, Proceedings of the Royal Society London, Volume A383, 1982, pp. 31-41.

[11] Ashby, M.F.; and Jones, D.R.H.: Engineering Materials 2. Pergamon Press, Oxford,

1986, p. 255. [12] Online Materials Information Resource – “Chapter 5: Mechanical Properties of Wood,”

D.E. Kretschmann, Forest Products Laboratory Report. Web. 5/14/2015. < http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr190/chapter_05.pdf>. Appears in Wood Handbook: Wood as an Engineering Material, Centennial Edition, Forest Products laboratory General Technical Report FPL_GTR-190, April 2010.

[13] Online Materials Information Resource – “Balsa Class 4 Wood: Slightly Durable,”

Matbase. Web. 5/21/2015. < http://www.matbase.com/material-categories/composites/polymer-matrix-composites-pmc/wood/class-4-wood-slightly-durable/material-properties-of-balsa-wood.html#properties >.

[14] Online Materials Information Resource – “Balsa,” The Wood Database. Web.

12/11/2014. <http://www.wood-database.com/lumber-identification/hardwoods/balsa/>.

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[15] Dowling, N.E.: Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue. 4th Edition, Pearson, Upper Saddle River, New Jersey, 2013, pp. 152-153.

[16] Gorman, T.M.: Observing and Modeling Creep Behavior in Wood, in National

Educators’ Workshop: Update 94, NASA Conference Publication 3304, 1995, pp. 343-349. Web accessible at http://www.materialsinstem.org/docs/archive/1994.pdf

[17] Griffin, R.B.; and Cornwell, L.R.: Measurement of the Modulus of Elasticity Using a Three-Point Bend Test, in National Educators’ Workshop: Update 97, NASA Conference Publication 208726, 1998, pp. 73-80. Web accessible at http://www.materialsinstem.org/docs/archive/1997.pdf

[18] Griffin, R.B.; Cornwell, L.R.; Yapura, Y., Krishnan, S.; and Hollford, J.: Use of a Four-point Bend Apparatus to Determine the Modulus of Elasticity, in National Educators’ Workshop: Update 98, NASA Conference Publication 209549, 1999, pp. 153-163. Web accessible at http://www.materialsinstem.org/docs/archive/1998.pdf

[19] Abramowitz, H., Bennett III, R.E.; Bennett, J.; Hendrickson, R.J.; Koultourides, C; Tredway, B.W.; and Kuchariski, W.: Load Testing of Temporary Structural Platforms, in National Educators’ Workshop: Update 2001, NASA Conference Publication 211735, 2002, pp. 413-434. Web accessible at http://www.materialsinstem.org/docs/archive/2001.pdf

[20] Griffin, R.B.; Klosky, L.; and Vander Schaaf, R.: Beams in Bending: An Instrumented Classroom Demonstrator, in National Educators’ Workshop: Update 2002, NASA Conference Publication 212403, 2003, pp. 483-490. Web accessible at http://www.materialsinstem.org/docs/archive/2002.pdf

[21] Gorman, T.M.: Designing, Engineering, and Testing Wood Structures, in National Educators’ Workshop: Update 91, NASA Conference Publication 3151, 1992, pp. 121-128. Web accessible at http://www.materialsinstem.org/docs/archive/1991.pdf

[22] Gorman, T.M.: Relationship Between Moisture Changes and Dimensional Changes in Wood, in National Educators’ Workshop: Update 97, NASA Conference Publication 208726, 1998, pp. 87-95. Web accessible at http://www.materialsinstem.org/docs/archive/1997.pdf

SOURCES OF SUPPLIES: The LVDT is available from Measurement Specialties Inc., 1000 Lucas Way, Hampton, VA 23666 for $598.00 (2015 price). The three-point bend test apparatus was originally manufactured by the American Instrument Co. (AMINCO) which is no longer in business. It is not known whether this particular apparatus is still being made by another company. However, an apparatus could be machined and incorporate a replacement original dial indicator (model 262J) purchased for $126.00 (2015 price) from B.C. Ames Inc., 1644 Concord

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Street, Framingham, MA 01701. The type of back mount on the indicator must be specified depending on the apparatus design. Dr. Yanko Kranov, Loyola University Maryland, Department of Engineering, machined and fabricated four testers closely based on the AMINCO instrument using a considerably less expensive dial indicator (item no. 303-3112) available from Shars Inc., 840 Equity Drive, St. Charles, IL and costing $15.95 (2015 price). Details concerning this replacement tester are available on request. Alternatively since the dial indicator is not being used to measure displacement, it could be replaced with a newly-designed and machined fixture for the load platform/loading nose assembly. Balsa wood can be obtained at hobby and model making-shops or at internet sites (e.g., http://www.nationalbalsa.com/). ACKNOWLEDGEMENTS: The identification of any manufacturer and/or product does not imply endorsement or criticism by the author or Loyola University Maryland. ABOUT THE AUTHOR: Wayne L. Elban Since 1985, Professor Elban has taught engineering courses at Loyola College (now Loyola University Maryland), including introductory materials science, materials science lab, mechanical properties of materials, transformations in solids, and engineering materials and manufacturing processes. He received a BChE with distinction ('69) and a PhD in Applied Sciences: Metallurgy ('77) from the University of Delaware and a MS in Engineering Materials ('72) from the University of Maryland, College Park. From 1969-1985, he was a research engineer at the Naval Surface Warfare Center, White Oak Laboratory, Silver Spring, Maryland. In 1992, he was a Fulbright scholar at the University of Strathclyde (Glasgow), Department of Pure and Applied Chemistry. From 2001-2003, he was a working visitor at the Smithsonian Center for Materials Research and Education, Silver Hill, Maryland. From 2008-2011, he was a guest worker at the National Institute of Standards and Technology, Gaithersburg, Maryland. He is a member of ASM International and the Society of Manufacturing Engineers.

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Figure 1. Side view of three-point bend apparatus instrumented with a linear variable differential transformer (LVDT) -- after Reference [9].

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Figure 2. Schematic plot of force-deflection data corrected to account for apparatus displacement occurring during loading in a three-point bend test.

Figure 3. Highly linear plot of LVDT voltage as a function of gage block thickness together with two data points revealing saturation outside the measurement range of the LVDT -- after Reference [9].

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Table 1. Measured raw (LVDT) and corrected voltage levels with corresponding deflections obtained for balsa wood beam sample designated NB #1-5. Total Voltage,

VDC Voltage Tester,

VDC Net Voltage,

VDC Force,

gf Deflection,

mm Force,

N 0.00 0.00 0.00 0 0 0 0.16 0.01 0.15 50 0.046 0.49 0.25 0.02 0.23 100 0.070 0.98 0.39 0.02 0.37 150 0.113 1.47 0.62 0.03 0.59 250 0.179 2.45 0.91 0.04 0.87 350 0.265 3.43 1.44 0.06 1.38 550 0.420 5.40

Figure 4. Elastic response of balsa wood beam sample designated NB #1-5 tested in three-point bending having a slope of 12.9 N/mm corresponding to a Young’s modulus of 5.78 GPa.

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Table 2. Average Young’s modulus and average center deflection values obtained from six determinations on each sample beam. Sample Beam Designation Average Young’s Modulus

(Standard Deviation), GPa Average Center Deflection (Standard Deviation), mm

OB #1 4.87 (0.13) 0.449 (0.017) OB #2 5.23 (0.19) 0.421 (0.019) OB #3 5.99 (0.20) 0.370 (0.015)

NB #1 5.31 (0.13) 0.421 (0.013) NB #2 3.73 (0.08) 0.591 (0.017) NB #3 4.99 (0.30) 0.443 (0.036)

Table 3. Comparison of Young’s modulus values for balsa wood reported in the literature with that determined in the current work.

Young’s Modulus, GPa Comments Reference 0.903 Density = 0.078 g/cm3 [10] 2.87 Density = 0.127 g/cm3 [10] 3.33 Density = 0.160 g/cm3 [10] 5.90 Density = 0.218 g/cm3 [10] 4.0 ±20% (parallel to grain) [11] 3.40 12% moisture [12]

1.13 min. – 6.00 max. [13] 3.71 [14] 5.03 Standard deviation = 0.74

GPa for six determinations on each of six beam samples

Current work

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Figure 5. Non-linear variation of average center deflection at 5.4 N applied load with average Young’s modulus obtained for six balsa wood beam samples tested six times each in three-point bending.

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EVALUATION PACKET: Student evaluation questions (discussion or quiz):

1. Discuss the basic elements (features) of a three-point bend tester. 2. Discuss the state of surface stress in a beam sample placed in three-point bending. 3. Discuss the value of using a planning document such as a “punch list” in designing and

executing an experiment. 4. What are the essential elements in a successful design of experiment? 5. What does an applied force-deflection plot look like for a beam sample elastically loaded

in three-point bending? 6. In addition to obtaining the slope of the applied force-deflection plot, what additional

measurements are needed to determine Young’s modulus for a beam sample loaded in three-point bending?

Instructor evaluation questions:

1. At what educational level was this module used? 2. Was the level and rigor of the module what you expected? If not, how can it be

improved? 3. Did the lab work as presented? Did it add to student learning? Please note any problems

or suggestions. 4. Was the background material provided sufficient for your background? Sufficient for

your discussion with the students? Comments? 5. Did the lab generate interest among the students? Explain. 6. Please provide your input on how this module can be improved, including comments or

suggestions concerning the approach, focus, and effectiveness of this activity in your context.

Course evaluation questions (for the students):

1. Was the lab write-up clear and understandable? 2. Was the instructor’s explanation comprehensive and thorough? 3. Was the instructor interested in your questions? 4. Was the instructor able to answer your questions? 5. Was the methodology for designing an experiment, including use of a punch list, made

clear? 6. What was the most interesting thing that you learned?