Engineering 202 Laboratory Manual StAtics And Strength of MAteriAls (Read before attending lab.) Fall 2002 , Spring 2003 This manual has evolved over the years. Contributors in the past two decades include: Kenneth Bhalla, Jason Cortell, Jill Evensizer, Richard Lance, Jamie Manos, Dan Mittler, Francis Moon, Leigh Phoenix, James Rice, Andy Ruina, and Alan Zehnder. Revised July 2002 Department of Theoretical and Applied Mechanics Cornell University Ithaca, New York TAM 202 LAB MANUAL Introduction 1 THEORETICAL AND APPLIED MECHANICS 202 STATICS AND STRENGTH OF MATERIALS Revised: July 2002 INTRODUCTION PURPOSE These laboratories are designed to complement the lectures, text, and homework. They should help you gain a physical feel for some of the basic concepts in statics and strengths of solids: force, stress, deflection, strain, yield, failure and buckling. You will also get exposure to equipment which you may use in the future. Some mathematics from MATH 192 and 293 will be used, helping you make the tie between mathematics and physical reality that is essential to most engineering. The labs may come either before or after you cover the relevant material in lecture. Thus, they can be either a motivation for the lecture material or an application of what you have learned, depending on the timing. Lab groups are small enough (1 or 2 people) that you can get direct experience with the instruments and equipment. Both you and your lab partner should learn how to do all aspects of the lab. The laboratory teaching assistants will have scheduled office hours in the laboratories so that you can return to use the facilities independently, or ask questions. These hours will be posted on the door of the laboratory. You may also ask the lab TA about other course material if time allows. CONTENT There are four labs and one assignment which require write-ups: 0) Error Analysis (handed in with the Lab 1 report) 1) Truss 2) Tension Test 3) Beam 4) Compression It is essential that you read through the lab (especially the procedure section) and answer the pre-lab questions before coming to lab. The reading for Lab 1 is quite long and may look a bit intimidating, but the rest are short. In addition to the regular labs, there are some demonstrations set up for you to experiment with, if enough time is available. Some of the labs may also include extra topics for you to research, or ask you to develop a small experiment of your own. LOCATION The laboratories are in Thurston 101A. 2 Introduction TAM 202 LAB MANUAL SCHEDULING Each of the four labs is taught for two weeks. You will be scheduled to attend lab during one week of the two. The meeting dates for your laboratory section will be posted in the hallway around the corner from room 101A Thurston, during the first week of classes. In general, you will have a lab once every three weeks, but be aware that this may vary due to exam and break schedules. (Summer session lab schedules will differ.) See the Secretary in Kimball 212 if you have problems with your lab schedule. You'll need to get her approval for any changes, so that the lab sections do not become overly full. Turning in a course change form to the registrar is not enough. TURNING IN YOUR LAB REPORT Lab reports are due one week from the day you performed the lab, at 8:00 in the morning, unless your TA specifies another time. Turn in reports to the boxes in the Don Conway room on the first floor of Thurston Hall. Be sure to put your report in the correct box corresponding to the TA in charge of your lab section. MISSED LAB AND LATE REPORT POLICY All make-up labs must be arranged with your TA and the Secretary in 212 Kimball Hall. If you know in advance that you'll be gone, you should sign up with her at least one week prior to the scheduled lab. This gives you a better chance to sign up for a convenient time, and there's no point penalty. If you miss your lab without arranging a make-up lab in advance, you should still try to arrange a new time. However, a one- point lab report penalty will be imposed, unless you were ill, etc. You should arrange to make up a missed lab as soon as possible, since the lab setups are changed after a lab is finished. In special circumstances, labs may be made up at the end of the semester; sign up with the Secretary in 212 Kimball Hall and your TA. If you show up for lab after it is under way, your lab instructor may ask you to leave, and to perform the lab another time. The testing machines used in ENGRD 202 are potentially dangerous and quite expensive, and should not be used without proper training. Note also that answers to pre-lab questions are due at the beginning of lab, and will not be accepted for credit later. Reports turned in late will be marked down 2 points, and 4 points if they are more than a week late. Maximum late penalty is 4 points. Late reports may be handed in until one week after the last regularly scheduled lab of the semester. Exceptions to the above policies may be made in the case of documented illness or other emergency. Talk to your lab TA about late reports; see your TA and the Secretary in 212 Kimball about making up a lab. PRE-LAB QUESTIONS Each lab has pre-lab questions which should be answered before you come to lab. These questions encourage you to read through the laboratory procedure prior to attending the lab, and gain an understanding of what will be done during the laboratory period. Because of this policy your answers must be turned in at the start of the lab if you want to receive credit for them. TAM 202 LAB MANUAL Introduction 3 ACADEMIC INTEGRITY Your pre-lab answers and lab reports should be in your own words, based on your own understanding and your own calculations. You are encouraged to discuss the material with other students, friends, TAs, or faculty. Any help you receive from such discussion must be acknowledged on the cover of your lab report, including the name of the person or persons and the exact nature of the help. Violations of this policy will be reported to the academic integrity board. You may, however, do a joint report with your lab partner (turn in one report for two people). Both partners get the same grade. When you are through in the lab, you must have your TA sign one of your data sheets. This sheet must include the name of your lab partner, if you had one, and the time and date the lab was performed. The TA will not sign this sheet until your work station is clean and all equipment is accounted for. No lab reports will be accepted without this signed sheet. CREDIT AND GRADING Each lab is graded from 0-15. At the end of the semester the grades will be rescaled so that the average grade given by each TA is the same. This grade will be given to your recitation TA. Grading: You must attend the lab and turn in a report to get credit for the lab. +2 points for pre-lab questions. +5 points for attendance, competent in-lab performance, and a minimally passable report. +5 points for clear, neat report that is mostly correct. +3 points for perfectly correct report. +? points for observations that go beyond the direct questions. -? points for penalties (see the missed lab and late report policy). PROBLEMS AND COMPLAINTS 1) Your teaching assistant. The lab TA's job is to help you. See your TA if you have problems with the pre-lab questions, lab, or lab report. In-lab office hours will be available if you need to redo some part of the lab, or want to collect additional data (For this you can see any of the lab TAs.) 2) Dan Mittler, 218 Kimball (5-9172), [email protected]. See Dan if you have problems with equipment operation. You may also arrange with him to redo part of a lab, or perform additional lab work. 3) Andy Ruina, 309 Kimball (5-7108), [email protected]. See Professor Ruina about problems with laboratory content or policy. 4) Secretary , 212 Kimball (5-5062), [email protected]. See her if you have problems with your lab schedule, or need to make up a missed lab (read the policy, above). 4 Introduction TAM 202 LAB MANUAL LABORATORY NOTES A rule of laboratory work is to keep a neat, complete record of what has been done, why it was done, how it was done, and what the result was. The success or failure of an experiment in a research laboratory often depends critically upon the record made of the experiment. The outcome of a poorly documented experiment becomes a matter of personal recollection, which is not reliable enough to serve as a basis for further work, especially by someone else. You should take copious notes. If in doubt, WRITE IT DOWN. One can ignore what is written, but one can not resurrect that which was never recorded. Similarly, NEVER erase in your lab notes. If an erroneous reading was made, strike it out with a single line and record the new data. You may later decide that it was not in error. All lab notes, in their original form, must be submitted with your report. THE LAB REPORT Your laboratory report should be neatly printed or typed. Do not crowd your writing. Make sure there is room for comments by your TA. The report should communicate clearly and convincingly what was demonstrated or suggested by the lab work. Your TA is looking for evidence of thought and understanding on your part. Your logic and methods are as important as results or “correct” answers. It is essential that you provide information and calculations which indicate how you arrived at your conclusions. It is permissible (and a good idea if you want a very good grade) to discuss observations and material relevant to the lab which are not specifically asked about in the questions. Format: The lab reports should contain the following material in the order specified. I) Cover page: A plain sheet, firmly attached to the rest of the report with staples or another binder. The cover should contain the following (with appropriate substitutions for the words in quotes): “NAME OF THE LAB” TAM 202 By: “Your name and your signature (both partners if a joint report)” Performed: “Date" Performed with: “Name of person(s) with whom you performed the lab” Discussed lab with: “Names of people with whom you discussed the lab, and nature of the discussions” TA: “Laboratory Teaching Assistant's name” TA signed the data on page: “Page #” II) Procedure: (1/2 page maximum) This section should be included only when you deviate from the procedure specified in the lab manual. This section will be needed when there are problems with malfunctioning equipment, or if you develop your own procedure. TAM 202 LAB MANUAL Introduction 5 III) Answers to questions: Concisely answer the questions that are asked and number them as they are numbered in the lab manual. Include any necessary plots, data or calculations. Your answers should be self-contained and presented in an orderly fashion (i.e., the reader of the report should not have to refer back to the questions that are asked, nor should he or she have to hunt through the report to find your answers). While many questions require that you perform calculations, written explanations of what you are doing and sketches can be very helpful. Show all calculations that you perform in arriving at your answers. If you are performing repetitive calculations, you need show only one sample calculation. IV) Observations and conclusions: If you did anything or observed anything in the lab which was not covered in your answers to questions, this is the place to discuss it. This is optional. V) Supplemental procedures and questions: If there are multiple parts to the lab, repeat sections II, III, and IV for each topic. VI) Mistakes and suggestions: This is an optional section. Point out errors in any of the documentation or oral information you were given. Make suggestions for changes in the lab procedure, instructions, content, etc. Please put this section on a separate page, so that it may be kept by the TA for future reference. VII) Appendix: Append ALL notes and records taken in the laboratory (including data sheets signed by your TA). If you have used an x− y plot or data table in your previous answers to questions you need not include it here again. DATA ANALYSIS AND PRESENTATION [Read this section carefully. See Lab 0 for further comments.] I) Significant figures: When reporting numerical data, an appropriate number of significant figures should always be used. Large numbers should be written in scientific notation, so that the number of significant figures is not ambiguous. The numbers 3.840, 0.003840, and 3.840×105each have four significant figures. When multiplying two numbers together, the general rule of thumb is to write the answer using the same number of digits as the multipliers. When the multipliers have different numbers of significant digits the smallest is used. Thus 0.3526×1.2=0.42 (not 0.42312). This same method should be used for division. Addition is different. Consider the example: 0.2056+14.25+576.1=593.1. An answer of 593.1276 is not appropriate because the last three digits (.0276) add nothing to the accuracy of the results, since one of the numbers being added (576.1) is accurate only to tenths. Subtraction should be done in a similar manner. II) Percentage difference calculation: Percentage difference calculations can be used to quantify how well experimental results agree with theoretical or expected values. Rather than writing “the experimental results agree very well with the theoretical calculations,” this phrase can be changed to make a quantifiable statement; “the experimental results are within 5 percent of the theoretical calculations.” Percentage difference is calculated as: 100% * (Value being compared -Reference value)/(Reference value) Formal error analysis should only be used if it is necessary to make a point, but for full credit your answers should include some discussion of the type and relative importance of errors in your data. 6 Introduction TAM 202 LAB MANUAL III) Units: The dimensions of all physical quantities should be clearly presented in all calculations, tables and graphs. IV) Graphs: Figure i.1 is an example of how your graphs should appear in lab reports. The following is a checklist of the items your graph should include. • Use graph paper or computer. • Curves should be drawn with rulers or french curves (not sketched). • Graph title. • Both axes should be titled, with the appropriate units listed in parentheses. • Numerical values on the axes should be at reasonable intervals and scales be chosen so that all of the data points can be displayed on the graphs. • On graphs with more than one curve a legend should be used to identify the curve. Data points can be enclosed by some symbol (i.e. circle, rectangle, etc.) to distinguish different data sets. • The independent variable should be placed on the horizontal axis. • All labels, symbols, etc... should be neat and readable. • When plotting with a computer, the considerations of labeling axes, etc., still apply. FIGURE i.1 TAM 202 LAB MANUAL Introduction 7 V) Linear, semi-log and log-log plot interpretation: • Linear: a straight-line plot on linear graph paper indicates a relationship of the general formy = mx+b, where m is the slope and b is the y-axis intercept. Choose two points along the line(x ,y ),(x ,y ), preferably well separated. Then 1 1 2 2 y − y m = 2 1 x −x 2 1 Since y = mx +b, 1 1 b = y −mx 1 1 Sometimes it is useful to plot a function of x and/or y, instead of plotting x and y directly. For example, if y² is proportional to x, you could plot y² vs. x, and obtain a straight line. The slope of the line then gives you the constant of proportionality. If you don't have (or don't want to use) semi-log or log-log graph paper, you can plot ln y vs. x or ln y vs. ln x, respectively. (Logs to other bases will also work.) This is often very useful with computer-generated graphs. The procedure to obtain an equation from the graph is similar to the one described above. For a graph of ln y vs. ln x which forms a straight line, ln y = m(lnx)+b. Find two well-separated points on the line, and write (lny) −(lny) m = 2 1 (lnx) −(lnx) 2 1 since( ln y) = m( ln x) + b, 1 1 b = ( ln y) - m( ln x) . 1 1 Then eln y = em(ln x)+b = ebeln(xm), and therefore y = ebxm, a power-law relationship (eb is just a constant). 8 Introduction TAM 202 LAB MANUAL • Semi-log: a straight-line plot on semi-log paper indicates an exponential relationship of the general form y = aecx. Choose two points along the line, as above, reading the values from the graph paper scales. Then ln(y )−ln(y) c = 2 1 . x −x 2 1 Sincey = aecx1, 1 y a = 1 ecx1 If you want to plot your data on a computer, use a log scale for the y axis, or plot lnyvs. xwith linear scales, as described earlier. • Log-log: a straight-line plot on log-log paper indicates a power-law relationship of the general formy =axn. Choose two points along the line, as above, reading the values from the graph paper scales. Then ln(y )−ln(y ) n = 2 1 . ln(x )−ln(x ) 2 1 Since y = axn, 1 1 y a = 1 xn 1 If you want to plot your data on a computer, use log scales for both axes, or plot lny vs. lnxwith linear scales, as described earlier. TAM 202 LAB MANUAL Error Analysis 1 LABORATORY 0 ERROR ANALYSIS Revised: July 2002 This laboratory assignment is to be done during the first few weeks of the semester, before you do Laboratory I, and turned in along with your report for Laboratory I. INTRODUCTION The collection of data is an important part of all laboratory work, and interpreting the data is the major part of a laboratory report. Laboratory 0 presents a brief overview of techniques and concepts needed to estimate and analyze the errors inherent in experimental work. Although formal error analysis is optional for laboratory reports in this class, you will need to be familiar with its basic principles while writing your reports. Concepts you should be familiar with (and apply when needed) include accuracy and precision, systematic and random error, error propagation, absolute and relative error, and significant figures. If you would like a more detailed discussion of error analysis, a good reference is An Introduction to Error Analysis by John R. Taylor. EXPERIMENTAL ERROR Error (or uncertainty) is defined as the difference between a measured or estimated value for a quantity and its true value, and is inherent in all measurements. Knowledge of the type and degree of error likely to be present is essential if data are to be used wisely, whether the data being considered were measured personally or merely read from manufacturer's data sheets for a material or component. In medical research, biology, and the social sciences, the plan for the data acquisition and analysis is the heart of the experiment. Engineers also need to be careful; although some engineering measurements have been made with fantastic accuracy (e.g., the speed of light is 299,792,458 ±1 m/sec.), for most an error of less than 1 percent is considered good, and for a few one must use advanced experimental design and analysis techniques to get any useful data at all. Making measurements and analyzing them is a key part of the engineering process, from the initial characterization of materials and components needed for a design, to testing of prototypes, to quality control during manufacture, to operation and maintenance of the final product. Reported experimental results should always include a realistic estimate of their error, either explicitly, as plus/minus an error value, or implicitly, using the appropriate number of significant figures. Furthermore, you need to include the reasoning and calculations that went into your error estimate, if it is to be plausible to others. An explicit estimate of the error may be given either as a measurement plus/minus an absolute error, in the units of the measurement; or as a fractional or relative error, expressed as plus/minus a fraction or percentage of the measurement. The advantage of the fractional error format is that it gives an idea of the relative importance of the error. A 10-gram error is a tiny 0.0125% of the weight of an 80-kg man, but is 33.3% of the weight of a 30-g mouse. Errors may be divided roughly into two categories: Systematic error in a measurement is a consistent and repeatable bias or offset from the true value. This is typically the result of miscalibration of the test equipment, or problems with the experimental procedure. On the other hand, variations between successive measurements made under apparently identical experimental conditions are called random errors. Random variations can occur in either the physical quantity being measured, the measurement process, or both. We will outline statistical procedures for handling this type of error.