UWM CE203 Lab Manual_updated

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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 ii I. Objective and Background .......................................................................................... 25 A. Terminology ..................................................................................................... 26 II. Laboratory Procedure .................................................................................................. 27 III. Recorded Data ............................................................................................................. 28 IV. Results and Calculations ............................................................................................. 29 V. Conclusions ................................................................................................................. 30 VI. References ................................................................................................................... 30 Lab #5: Flexure of Beams ............................................................................................................. 31 I. Objective and Background .......................................................................................... 31 A. Terminology ..................................................................................................... 31 II. Laboratory Procedure .................................................................................................. 31 III. Recorded Data ............................................................................................................. 32 IV. Questions ..................................................................................................................... 33 Appendix A ................................................................................................................................... 36 I. Factorial Design of Experiments ................................................................................ 36 A. Response ........................................................................................................... 36 B. Factors .............................................................................................................. 36 C. Levels ............................................................................................................... 36 D. Null Outcome ................................................................................................... 36 E. Main Effects ..................................................................................................... 36 F. Interaction Effects ............................................................................................ 36 II. 2 k Factorial Design of Experiments ............................................................................ 37 III. 2 2 Factorial Design of Experiments ............................................................................ 37 IV. Statistical Analysis ...................................................................................................... 37 V. Conclusions ................................................................................................................. 37 VI. References ................................................................................................................... 37

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 3 of 36 As a rule of thumb, the reader should be able to reproduce each of your calculations easily from your examples. IV. Data Do not show the numbers of machine recorded data, such as force and displacement automatically recorded every second by the Instron testing machine. Instead, they belong in a graph. Any number that you collect by hand, that is you see it with your eyes and record it with your hand and a writing implement or a keyboard, should be displayed in the report. You must know and include the units for the data that you use. If the machine records force in pounds, and you treat it as stress in psi, you are creating gibberish. V. Tables By the time you include 3 numbers in a sentence, such as the yield stress of aluminum, brass, and steel, you should take them out and put them in a table. To the extent possible and practical, combine separate tables of similar values, such as yield stress and failure stress for different materials into a single table. This facilitates comparisons and improves comprehension for the reader and the writer. Tables should have a 2D arrangement of values. Listing all the numbers in a single column makes them nearly as difficult to read as they were when they were in a sentence. Units should not take up an entire row or column of a table. Include them in a column or row title. For example: Poor example section material value Units 011 brass 0.125 in. steel 0.124 in. 012 brass 0.123 in. steel 0.125 in. 013 brass 0.127 in. steel 0.126 in. Good example section brass (in.) steel (in.) 011 0.125 0.124 012 0.123 0.125 013 0.127 0.126 In reporting data, you should be consistent with the precision, lining up all decimal points. This may violate principles of significant figures in some cases, but it vastly improves readability and facilitates comparisons. VI. Graphs Always graph the independent variable on the horizontal axis and the dependent variable, the variable that depends upon the independent variable, on the vertical axis. For example, in the case of stress vs strain, the Instron machine creates a deflection that you specify and from which you calculate strain, and then it measures the force created by that deflection, from which you calculate stress. Thus, strain is the independent variable that belongs on the horizontal axis, and stress is the dependent variable that belongs on the vertical axis.

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