MEEN 3210 MEASUREMENTS LABORATORY Spring 2023 Instructions and Samples for Technical Report The grade sheet must be attached to the front of each written laboratory report. The sample report cover sheet and grade sheets are included in this document. The report will be graded on two parts: technical content, and writing style and format. Report Sections Grade Sheet: See Sample Cover Sheet: Abstract: Table of Content: Nomenclature: Introduction: Objectives: Apparatus: Theory: (if needed) Results: Discussion: Conclusions: Citations: Appendix: Format and Style See Sample 200-300 words, no citation, no detail results Each Section and corresponding page number, no leading character for page number Symbols and units, Alphabetical (Upper, then lower), Greek, Sub and Super-scripts Brief description of the lab, problem statement List the main objectives of the lab List/Tabulate the equipments and instruments used for the lab Gives a short summary of theory and equations used Raw data collected during the lab, sample calculation (in Appendix), final results Discuss the results in terms of accuracy, agreement with theory, achievement of objectives, experimental errors final thoughts on experiments and results, recommendations for improvements Use the style in the textbook. Sample calculation Write in third person past tense, and present tense. Use a standard font and font size, e.g. Times New Roman 11 points. Check spelling and grammar, usage of words, repetition, redundancy, etc. Arrange sections to improve readability. Include page numbers. Number each equation and define the symbols in Nomenclature. Caption tables and label figures. Label each axis clearly in a figure and include unit of the variables. Include Legends in graphs if there is more than one data set. Show only data points, unless there is a trend line (least-square-fit) involved. If the trend line is used, include the goodness of fit measure (R or R²) and the regression equation of the line. SAMPLE GRADE SHEET FOR A LAB REPORT MEEN 3210 MEASUREMENTS LABORATORY SPRING 2023 Grade Sheet Name: John Doe Lab No. and Title: Laboratory 4 Strain Measurement Content (70%) Abstract Table of Contents Nomenclature Introduction Objectives Experimental Apparatus Results Raw Data Sheet Sample Calculation Final Results Points Allocated Point Received 10 10 1555i5 Discussion Conclusion 10 55595 Format and Style (30%) Heading, Citations, Readability 10 Grammar, Usage 10 Tables/Figures 10 100 TOTAL Instructor's Comment: SAMPLE COVER SHEET FOR A LAB REPORT MEEN 3210 Measurements Laboratory Department of Mechanical Engineering Lab 4 Strain Measurement Laboratory John Doe Date of Experiment: 02/--/2023 Date of Submission: 02/--/2023/nTable 1: Dimensions of the Beams Dimensions (unit) Steel Beam Material Aluminum Brass Width in Tin Lin Length Height Location of a strain 15.8 10.75 in 21.8 Convert 403 P.25 0.125 0.2 S gauge from an open end 9.06 in 5.5 in 11.25 in Table 2: Strain Measurements of Three Beams Brass Steel Nico Aluminum Weight Strain Weight Strain Weight Strain (unit) (E) X/9 (unit) (με) Χιο (unit) (H) x/ 500 gm 31 100 gm 50 200 gm 46 1000 gm 69 200 gm 100 400 gm 90 1500 gm 2000 gm 2500 gm 300 gm 151 600 gm 133 136 400 gm 201 800 gm 176 174 500 gm 252 1000 gm 225 Table 3: Comparison of Experimental and Theoretical Stress Values Material Stress from the book do calelution no Result Experimental Theoretical (unit) (unit) Error (unit) Error (%) Aluminum from the Steel Brass Table 4: Comparison of Experimental and Textbook Values of Modulus of Elasticity Material for each material Modulus of Elasticity Experimental (unit) Aluminum Eeel ass Result Textbook Error book Error (%) (unit) (unit) ba/nProcedure 1. Select the beam to be used and record the strain gage factor for future reference. 2. Measure the dimensions of the beam and record data in Table 6. 3. Place the beam onto the support bars and level it. 4. Connect the strain gage wires to the P3500 strain gage indicator and calibrate the indicator as shown on the inside of the lid of the indicator unit. 5. Apply the weights at the designated distance (mid-point of the beam) and record data (strain and deflection) in Table 7. 6. Compare the measured values of defection with the theoretical values obtained using Eq. (7). I of incre در calcate Sthin σε Mc I PL³ d = 48EL is lood Eq. (7) Strain Jraph 7. Discuss the differences between theoretical and experimental results. Possible discussions: Does experimental and theoretical values of deflection agree with each other? What are the sources of errors? Table 6: Dimensions of the Beams Dimensions (unit) Width Beam Material Steel 34 in Length Height 34 in 0.25 in defection 61 Location of a strain gauge Table 7: Strain and Deflection Measurements for the Beam 0.001 Load (in lb) Load (in gm) Strain Deflection 61-49 (unit) 2 0907.18 gm 16 12 in 4 1814.37 gm 33 26 6 2721.55 gm 50 40 8 3628.74 gm 67 54 Table 8: Comparison of Experimental and Theoretical Deflection Values Material Load (unit) Deflection (unit) Experimental Theoretical Steel from text book grap/n MEEN 3210 MEASUREMENTS STRAIN MEASUREMENT LABORATORY Robert Benton and Kendrick Aung Introduction Experimental determination of stress is important when designing components with complex geometry and/or loading. To verify a given design, nondestructive tests of a prototype may be performed using strain gages. Once strain is determined experimentally, the stress may be calculated using the stress-strain relationship for the material. Although there are various failure theories for the ductile and brittle materials subjected to static and dynamic loads, each of these theories predicts failure when the stress in a given material exceeds various predetermined values. As such, stress is a major consideration in design of mechanical components. Analytical methods exist for relatively simple and common geometric cases such as shafts, beams, and cylinders. However for cases with stress concentration or other complex geometry, these analytical methods are not accurate. Numerical methods such as finite element analysis (FEA) may be applied in such cases. However, finding the appropriate FEA model (or mesh) for a given situation can be more of an art than an exact science. As such, strain measurements should be used to verify stresses in physical prototypes of the design. Strain Measurement Three common tools are available for experimental determination of stress and strain, namely, photoelasticity, stress coat application, and strain gage application. Photoelasticity Although photoelasticity is most easily applied in cases of two-dimensional components, techniques also exist for more complex geometry. When polarized light is passed through a transparent material, visible bands appear as contour lines within the material to indicate the level of stress in the material. This is because the speed of light in the medium is a function of stress. Determination of stress using photoelasticity requires relatively expensive equipment when compared to the methods described below. In addition, prototypes of the part must be prepared especially for photoelastic measurement. Stress Coat Application The application of a stress coat is a fairly simple concept for which students should have an intuitive sense. A stress coat is used to determine the principal stress directions by observation. A brittle lacquer is applied to the surface of the prototype (note: the stress coat is applied in liquid form and allowed to dry). Because the coating is brittle, the coating will crack perpendicular to the direction of maximum tensile stress (maximum principal stress). Strain Gage Application Strain gages may be applied to any free surface of a prototype component. In many cases, the component may be tested in service with the strain gages applied. The main limitations include environmental limitations required to avoid corrosion motion limitations due to the requirement that wire leads be connected between the strain gages and measurement instruments (for example, rotating components would present a challenge). In these cases, service conditions should be simulated on the prototype during strain gage experiments. Strain gage measurements are based on small changes in resistance of the gage when strained. As such, a bridge circuit is employed to measure change in resistance. Although the bridge can be cheaply constructed from scratch using precision resistors, specialized bridge-balancing units and strain indicators are most often used in practice to ensure precise measurements. Specialized analog-to-digital- conversion (AD) cards may also be purchased with built-in bridge circuits for dynamic strain gage measurement and data logging via personal computer (PC). Because strain gage resistance and prototype/gage strain are functions of temperature, temperature is an important consideration in strain gage application. If used to determine stress, the thermal growth in the component should not be measured by the strain-gage bridge circuit. Bridges with more than one strain gage leg may be used to aid in temperature compensation. In addition, self-temperature compensation gages are commonly available for application with steel and aluminum alloys (designated 06 and 13, respectively). Resistors in the bridge will also change resistance with temperature. Once the gage system is connected, temperature tests can be performed to determine error due to temperature in the measurement system. During any experiment where environmental factors may affect the results, temperature variation and other environmental conditions should be recorded along with strain measurements for future analysis. Theory The resistance in a wire in Equation (1) PL R = Eq. (1) where p is the wire material's resistivity, L is the wire's length, and A is the wire's cross sectional area. When a strain is placed on the wire, its resistance changes due to changes in resistivity, length, and cross-sectional area. As a result, measurement of the wire's resistance can be used to indicate strain. A strain gage is a specially designed metallic element that is very sensitive to strain in a given direction (see discussion and figures in [1], [2], and [3]). Strain gage application procedures are described on pages 17-23 of [1], which should be read at this time. Once the gage is applied and connection wires have been made, the gage must be placed in a bridge circuit in order to measure changes in the gage's resistance (see page 24 of [1]). For this lab, specially designed strain gage instruments described in [1] will be used to implement the bridge circuits. Often, specially oriented sets of strain gage “rosettes” are applied to measure strain in various directions at a single location (see pages 31 and 32 of [1] for examples of various strain gages and strain gage rosettes). Juvinal [3] gives equations necessary to find principal strains from measured strains in chapter 5. Objectives The main objectives of the laboratory are: 1. To familiarize students with industry standard strain measurement techniques 2. To determine Modulus of Elasticity of three materials using a cantilever beam 3. To compare experimental and theoretical values of Modulus of Elasticity 4. To compare experimental and theoretical deflection values Experiment 1: Application of a Strain Gage on a beam Required Equipment and Supplies Bulletin 309D: Student Manual for Strain Gage Technology [1] Student Strain Gage Application Kit " ◉ Sandpaper Degreaser ◉ M-Prep Conditioner A " M-Prep Neutralizer 5A Gauze and Cotton Swabs • ◉ Cellophane tape M-Bond 200 Kit M-Coat A Leadwire Drafting tape Soldering Station with Soldering Supplies Student Strain Gage Practice Patterns and Student Strain Gages Steel or Aluminum Bar Stock Procedure 1. Select a piece of steel or aluminum bar stock. 2. Prepare the surface of the bar stock as described on pages 18 and 19 of [1]. 3. Obtain a student strain gage practice pattern from the instructor and practice the strain gage application procedure described on pages 20 and 21. Special care should be taken to replace the caps on all chemicals to avoid spillage or evaporation. 4. Repeat steps 2 and 3 until the practice pattern in successfully applied to the bar stock surface. 5. Obtain a student strain gage from the instructor and repeat the procedures described on pages 18-21. STRAIN GAUGE LT-1 CSM-1 Figure 1 Materials and Soldering Station for Strain Gage Mounting Possible discussions: Why is the cleaning process before mounting the strain gage important? Experiment 2: Strain Measurement and Application Required Equipment and Supplies • Model P-3500 Portable Digital Strain Indicator Connecting wires Beam with Strain Gage Calipers and/or Ruler Test Weights Procedure 1. Select a beam with strain gage (record the strain gage resistance and gage factor for future reference). 2. Clamp the beam to the table or place the beam in a vice. Note that care should be taken to clamp the beam far enough from the strain gage to minimize the strain induced by the clamping forces. Recall that the vice forces may induce strain due to the effects of Poisson's ratio. 3. Measure the dimensions of the beam required to calculate the stress at the location of the strain gage. Record data in Table 1. 4. Connect the wires to the P-3500 Portable Digital Strain Indicator as indicated inside the lid of the Indicator unit. 5. Use the procedure inside the lid of the P-3500 unit to set the appropriate gage factor for the strain gage(s). 6. With no weight attached to the beam, use the procedure inside the lid of the P-3500 unit to balance the bridge circuit. To avoid unnecessary wear on the equipment, please unlock the balance control knobs before attempting to adjust the knob positions. 7. Once the bridge is balanced, lock the balance control knob on the P-3500 unit and do not attempt to adjust the knob for the remainder of the lab period. 8. Apply weights supplied by instructor to the beam made of steel and record the strain for each weight. Record data in Table 2. 9. Repeat the measurements in step 8 using the beam made of Plexiglas. Record the measured data in Table 2. C 000 Figure 2 An Experimental Setup for Measuring Strain Results and Discussions Result I: Comparison of Stress Using the Published Value of Young's Modulus 1. Use the stress strain relationship (Hooke's law) to calculate the experimental stress (σexp) using the measured strain and Young's Modulus of the beam material from the Machine Design text book. σ = E. exp text * E exp Eq. (2) where, σexp is the experimental stress, Etext is the value of modulus of elasticity from the textbook and Ɛexp is the experimental strain.

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MEEN 3210 MEASUREMENTS LABORATORY Spring 2023 Instructions and Samples for Technical Report The grade sheet must be attached to the front of each written laboratory report. The sample report cover sheet and grade sheets are included in this document. The report will be graded on two parts: technical content, and writi