UWM CE203 Lab Manual_updated

University of Wisconsin-Milwaukee Civil Engineering 203 Introduction to Solid Mechanics Laboratory Manual 2022

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 i CONTENTS Laboratory Report Format .............................................................................................................. 1 I. Title Page ...................................................................................................................... 1 II. Objective ....................................................................................................................... 1 III. Questions ....................................................................................................................... 1 IV. Conclusions ................................................................................................................... 1 V. References ..................................................................................................................... 1 Additional Formatting Guidelines .................................................................................................. 2 I. General .......................................................................................................................... 2 II. Values ........................................................................................................................... 2 III. Calculations ................................................................................................................... 2 IV. Data ............................................................................................................................... 3 V. Tables ............................................................................................................................ 3 VI. Graphs ........................................................................................................................... 3 VII. Conclusions ................................................................................................................... 4 VIII. References ..................................................................................................................... 4 Lab #1: Stress Strain Curves of Steel and Aluminum in Tension .................................................. 5 I. I. Objective and Background ........................................................................................ 5 A. Terminology ....................................................................................................... 5 II. Laboratory Procedure .................................................................................................... 7 III. Recorded Data ............................................................................................................... 9 A. Tension Test of Steel .......................................................................................... 9 B. Tension Test of Aluminum ................................................................................. 9 IV. Questions ....................................................................................................................... 9 V. Conclusions ................................................................................................................. 10 VI. References ................................................................................................................... 10 Lab #2: Stress Strain Curves of Concrete and Wood in Compression ......................................... 11 I. Objective and Background .......................................................................................... 11 A. Terminology ..................................................................................................... 11 II. Laboratory Procedure .................................................................................................. 12 III. Recorded Data ............................................................................................................. 13 IV. Questions ..................................................................................................................... 16 V. Conclusions ................................................................................................................. 16 VI. References ................................................................................................................... 16 Lab #3: Stress Concentrations ...................................................................................................... 17 I. Objective and Background .......................................................................................... 17 A. Terminology ..................................................................................................... 18 II. Laboratory Procedure .................................................................................................. 18 III. Recorded Data ............................................................................................................. 20 IV. Questions ..................................................................................................................... 21 V. Conclusions ................................................................................................................. 24 VI. References ................................................................................................................... 24 Lab #4: Torsion Test for Material Properties in Shear ................................................................. 25

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 1 of 36 LABORATORY REPORT FORMAT I. Title Page Include Name and Number of Lab, Your Name, and the Date II. Objective Write a brief (1-2 sentences) statement of the objectives and key concepts of the lab. Please write this in your own words and do not copy directly from the lab manual. III. Questions Answer each question in the “Calculations” section of the laboratory manual. Please number each question as in the lab manual , and leave adequate space between questions to distinguish one question and answer from the next. Usually, some questions will ask for “data,” so you do not need to have a separate section on data. SHOW ALL WORK for each problem. In some cases, it may be appropriate to generate calculations with a spreadsheet in which the same calculation is repeated many times. In such cases, show a sample calculation and explain how you encoded the spreadsheet formulae. IV. Conclusions Summarize what the basic results of the lab were, what errors may have occurred, what you learned, whether the experimental results were expected, and what new questions you have. You must supply evidence for your reasons. For example, a statement such as “I think that human error was responsible for some of our errors” is insufficient. You should explain which human error affected which measurement, and how significant the error was by providing an error analysis computation. V. References Cite any sources you referenced. All citations must include at least Title, Author, Publisher, and Date. Bare URLs are never sufficient.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 2 of 36 ADDITIONAL FORMATTING GUIDELINES I. General Format your lab reports with a word processor, use a spreadsheet or similar program to report data, and generate graphs electronically. If you are neat, you may hand write your sample calculations. Please see the instructor if you need assistance using electronic formatting. Work in groups of 3-4, and hand in single lab report per group. Each group should have at least one person who is skilled with Excel or some other data-processing software. The laboratory manual has been carefully written to alert you to which data is “recorded,” and which is “calculated.” Please be clear about this when you do your labs. II. Values If you are reporting some value, such as yield stress, that might have already been published elsewhere, you should also include that published number, with a suitable reference, and discuss how the number you measure or calculate compares to the published value. If you refer to a published number, you should show what that number is and provide a valid reference for it. An extremely useful comparison is percent difference. III. Calculations All calculations performed should be demonstrated with symbols and then sample numbers from the data you collect, as shown below Stress:   2 2 4 4 100 lb 2037 psi 0.25 in F F A d        If you cannot use an equation editor, as in the example above, then in many cases, especially with fractions, neat hand writing is preferable to simply entering the equation in one long single line. For example, consider the following, equivalent statements: A. (123 lb + 127 lb)/((0.5 in)(0.5 in)) = 500 lb/in^2 B. 2 123 lb 127lb lb 500 (0.5in.)(0.5in.) in   Each is correct, but A is more difficult to read. You are encouraged to write in the style B. You may do this either by handwriting or using the equation editor. Note that in all cases, variables should be in italics, but numbers, mathematical operators ( x , +, etc.), parentheses, and units should not be italicized.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 4 of 36 All graphs should have a title, and both axes should have labels that indicate the variable or property plotted along that axis units of that variable or property. Any graph with only one set of data should not have a legend, even though the default Excel behavior is to show a legend. If the legend contains only one entry, you should delete it. Figure 1: Example stress strain curves If the property being plotted could reasonably be interpolated between two data points, such as with deflection under load, connect them with straight lines that go through all data points. If not, as some property you measure from similar samples, do not. For example, it is reasonable to assume that the stress value for the strain 0.015 lies somewhere between the stress values for strains of 0.01 and 0.02, but it is not reasonable to assume that the diameter of sample 1.5 lies between the diameters of samples 1 and 2. The former should be graphed as a lines, and the later should be graphed as points. Resize the default Excel symbol to be small enough to allow distinguishing data points. Pick different symbols so that different data sets can be distinguished on the same graph in black and white, if you are going to print your report in black and white. Do not show Excel’s canned trend line equation. It is not Young’s Modulus or whatever else you might be trying to convey. With a y intercept and no units, it is merely gibberish. VII. Conclusions Do not simply state what your values are and what someone else’s values are. This belongs in a table, ideally with a percent difference, and then it can be found there. Instead, you should discuss similarities and differences, and explain why they exist and/or what they mean. VIII. References If you report a number that you did not record or did not calculate from numbers you recorded, you must indicate where you found it. 0 10000 20000 30000 40000 50000 60000 0 0.02 0.04 0.06 0.08 0.1 Stress (psi) Strain (in./in.) Aluminum Tue 8 am Tue 11 am Thur 8 am Thu 11 am 0.2% offset

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 5 of 36 LAB #1: STRESS STRAIN CURVES OF STEEL AND ALUMINUM IN TENSION I. I. Objective and Background The objective of this lab is to determine basic mechanical properties of steel and aluminum. Many important engineering material properties can be determined by testing materials and generating stress-strain curves. In this set of experiments, we will generate stress- strain curves by applying and measuring axial force and displacement. While a variety of test methods and specimen types exist for obtaining these values, all methods share some basic features. First, there must be a means of applying and measuring axial load to a test specimen. The engineering stress can then be computed as the axial load divided by the cross sectional area of the original specimen. Second, the change of length of the specimen must be measured. Then the strain can be calculated as the change in length ( deformation ) divided by the initial length of the specimen. Since strains are typically very small quantities, it is necessary sometimes to take average measurements over long specimens. Some important engineering material properties, such as the Young’s Modulus (modulus of elasticity) are measured from data points at which the strain is very small. Other material properties are measured from data points at which the strain is very large. For example, the strain at which the material ruptures may be several hundred times larger than the strains used to measure the modulus of elasticity. Therefore, it is often necessary to generate at least two stress-strain plots to display fully all of the critical details of the material behavior. One plot would detail small strain measurements, while the other would detail measurements at larger strains. A. Terminology Proportional Limit: Farthest point on stress-strain curve to which proportionality of stress and strain extends. Modulus of Elasticity: Slope of proportional or the linear part of the Stress vs. Strain curve. Calculated as E =  /  , were E = modulus of elasticity,  = stress up to the proportional limit, and  = strain up to the proportional limit. Yield Point: Point at which there begins to be an appreciable yielding of the material without any corresponding increase of load. The yield point is sometimes identifiable by a sharp corner in the stress-strain diagram. However, if no such point exists, draw a line with slope E through the point 0.2% (or 0.002 in./in.) on the strain axis. The yield point is where this line intersects the stress-strain curve. Ultimate Stress: Largest (engineering) stress experienced by test specimen.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 7 of 36 II. Laboratory Procedure The following table and figures summarize the materials, specimen sizes, and instrumentation that will be used in this lab. The accompanying figures display images of the specimens and some testing equipment. Figure 2: INSTRON Testing Machine Figure 3: Standard Dimensions of Steel Sample Used in Tensile Test Figure 4: Standard Dimensions of Aluminum Sample Used in Tensile Test For both steel and aluminum, inscribe gage marks onto the sample using the punching device. Next, measure the original width, diameter or thickness and gage length of the test sample. Mount the specimen between the two grips of the INSTRON testing machine. To start the test use Instron Bluehill Software as directed by your lab instructor. The output displacement and force data will be saved in a comma separated values file (.csv), keep a copy of this file for future data processing. Testing Machine INSTRON 3369 Capacity 11K Measuring Device Load Cell Gage Length 2"

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 8 of 36 Figure 5: Electronic Extensometer Figure 6: Steel Tensile Test Setup Figure 7: Aluminum Tensile Test Setup Figure 8: Ruptured Aluminum Specimen

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 10 of 36 a. Send a digital copy of the data recorded to your instructor. b. Calculate stress-strain values from the recorded data (note that a reasonable conversion factor may be needed to obtain a correct diagram, your instructor should provide you with an actual stress-strain data that you will use to find this factor.) c. Plot the Stress-Strain Diagram and show the following items on it: Yield Stress, Proportional Limit, Ultimate Strength, Breaking Stress, Moduli of Elasticity, Resilience and Rupture. 2. Using the data you collected in the lab, complete the following chart of mechanical properties. Show all work, but also summarize all results in a chart of this format. In particular, clearly describe which data points you are using to base your calculations. Aluminum Steel Proportional Limit Yield Strength Ultimate Strength Modulus of Elasticity Modulus of Resilience Modulus of Rupture Percent Elongation Percent Area Reduction 3. Which material will deform the most if stressed to 50% of its yield strength? How is this conclusion reached? V. Conclusions Write a concluding statement according to the lab format guidelines. VI. References

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 11 of 36 LAB #2: STRESS STRAIN CURVES OF CONCRETE AND WOOD IN COMPRESSION I. Objective and Background The objective of this lab is to determine basic mechanical properties of wood and concrete. Many important engineering material properties can be determined by testing materials and generating stress-strain curves. In this set of experiments, we will generate stress- strain curves by applying and measuring axial force and displacement. While a variety of test methods and specimen types exist for obtaining these values, all methods share some basic features. First, there must be a means of applying and measuring axial load to a test specimen. The engineering stress can then be computed as the axial load divided by the cross sectional area of the original specimen. Second, the change of length of the specimen must be measured. Then the strain can be calculated as the change in length ( deformation ) divided by the initial length of the specimen. Since strains are typically very small quantities, it is necessary to sometimes take average measurements over long specimens. Some important engineering material properties, such as the Young’s Modulus (modulus of elasticity) are measured from data points at which the strain is very small. Other material properties are measured from data points at which the strain is very large. For example, the strain at which the material ruptures may be several hundred times larger than the strains used to measure the modulus of elasticity. Therefore, it is often necessary to generate at least two stress-strain plots is necessary to fully display all of the critical details of the material behavior. One plot would detail small strain measurements, while the other would detail measurements at larger strains. A. Terminology Proportional Limit: Farthest point on stress-strain curve to which proportionality of stress and strain extends. Modulus of Elasticity: Slope of proportional or the linear part of the Stress vs. Strain curve. Calculated as E =  /  , were E = modulus of elasticity,  = stress up to the proportional limit, and  = strain up to the proportional limit. Yield Point: Point at which there begins to be an appreciable yielding of the material without any corresponding increase of load. The yield point is sometimes identifiable by a sharp corner in the stress-strain diagram. However, if no such point exists, draw a line with slope E through the point 0.2% (or 0.002 in./in.) on the strain axis. The yield point is where this line intersects the stress-strain curve. Ultimate Stress: Largest (engineering) stress experienced by test specimen.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 13 of 36 Figure 4: Standard Dimensions of Wood Sample Used in Compression Test Figure 5: Standard Dimensions of Concrete Sample Used in Compression Test Record dial indicator reading at zero load for the sample. Begin to apply load. Record the dial readings on both sides of the specimen at intervals of 10,000 lb for the concrete and 2500 lb for the wood. Repeat this process until the instructor has determined that it is no longer safe to conduct this experiment with the dial indicators mounted on the sample. Remove the dial indicators, so that they are not damaged, and continue to increase load on the sample until failure . The maximum load at failure should be recorded. III. Recorded Data Record the data from the lab in the tables given on the following pages. Be sure to note that much of the data in the tables is calculated, and not recorded. 12 in. 6 in. Gage length 2.5 in. 2.5 in. 12 in. 6 in. 6 in. Gage length 6 in.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 14 of 36 Compression Test of Wood General Data Sample length Gage length: Cross section width Cross section area Ultimate load: 1 2 3 4 5 6 7 8 Load (lb) Displacement Readings (in.) Displacement Readings (Absolute) (in.) Avg Disp. δ avg (in.) Stress σ (psi) Strain  ( μ in./in.) Front Rear Front Rear 0 0 0 -- 0 0 2500 5000 7500 10000 12500 15000 17500 20000 22500 25000 27500 30000 32500 35000  = δ avg /6" and σ = P/A 0 Notes:  Data is recorded in columns 1-3 and calculated in the rest.  The absolute displacement is determined by subtracting the first reading from all other readings.

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 16 of 36 IV. Questions SHOW ALL WORK AS DESCRIBED IN LAB FORMAT 1. Stress-Strain Curves (Wood) a. Provide a copy of the data tables recorded and calculated for both concrete and wood. Remember that you need to show, at least, a sample calculation of everything you do. b. Plot the Stress-Strain Diagram and show the following items on it: Yield Stress, Ultimate Strength, Breaking Stress, Moduli of Elasticity, Resilience and Rupture. Note: use the 0.2% offset method to find the yield stress. 2. Using the data you collected in the lab, complete the following chart of mechanical properties. Show all work, but also summarize all results in a chart of this format. In particular, clearly describe which data points you are using to base your calculations. Wood Concrete Yield Strength Ultimate Strength Modulus of Elasticity Modulus of Resilience Modulus of Rupture 3. Which material will deform the most if stressed to 50% of its yield strength? How is this conclusion reached? V. Conclusions Write a concluding statement according to the lab format guidelines. VI. References

CivEng Introduction to Solid Mechanics UWM 203 Lab Manual 2022 Page 17 of 36 LAB #3: STRESS CONCENTRATIONS I. Objective and Background The purpose of this lab experiment is to determine changes in the stress level caused by geometric irregularities such as notches and holes in an axially loaded bar (Figure 1). If a solid plate of constant cross section is loaded along its axis with a force P , the state of stress in the plate at points away from the ends is uniaxial . The stress distribution is uniform at any cross section, and has value  = P/A . For sufficiently small strain, Hooke’s Law can be used to relate stress and strain:  = E  ,  =  /E When a geometric discontinuity is present, e.g. a hole or a fillet is cut out from the plate as shown in the plate below; a rise in stress develops in the immediate vicinity of the hole and the fillet. The state of stress near the fillet and hole becomes biaxial , and the relations between stress and strain are now the following (plane stress case): ) ( 1 2 y x x E        , ) ( 1 y x x E      ) ( 1 2 y x y E        , ) ( 1 x y y E      Sample Material Steel Testing Machine INSTRON 3369 Capacity 11K Measuring Device Load Cell Figure 1 Standard Dimensions of the Steel Sample and Location of Gages r = 0.5 in. r = 0.25 in. 2 in. 0.25 in. z y x 2 1 3 4 5 6 8 7 9 10