Final Report for the LITRE project Web Based Observation and Control of an Undergraduate Civil Engineering Laboratory Experiment Submitted by Vernon Matzen, Jim Nau and Abhinav Gupta Department of Civil, Construction and Environmental Engineering July 20, 2006 The project description contained the following items: An existing experiment in CE 324, Structural Behavior Measurements, will be modified so that it can be controlled and observed remotely using web based tools. In the web-based setup, a controller with a stepper motor will be used to operate the screw actuator and the strains will be monitored, recorded and displayed using a PC-based data acquisition system. The research will investigate appropriate ways to o protect the experiment from overloading and internet / PC malfunctions o set up procedures for scheduling, access and security. The write-up in the lab manual for this experiment will be o modified to describe the web-based operation and then o posted online so that the students will have a complete web-based experience. The TAs will be trained in the remote operation of the experiment so that they can give assistance as needed Two related projects were going on concurrently with the LITRE project. Here is how they were related, as well as a list of other funding sources: The NSF project dealt with the conversion of two laboratory experiments - a shake table experiment and a soil consolidation test – to a web based format. The original scope of the project included the wide flange experiment that was the focus of this LITRE project, but the NSF budget was cut, and this experiment was deleted from that project. The DELTA project included enhancements to the shake table experiment to include web security and web based scheduling. In addition, we obtained some funding from the Engineering Online program, from the Civil Engineering Department’s Education and Technology Funds (ETF), and from other Departmental accounts. Tasks completed as of June 30, 2006: Supported RA Jerry Bridges ($ 4,824) Purchased the following equipment (total of $3,176) o Stepper motor ($825 from LITRE) o National Instruments data acquisition hardware ($6,426 from various nonLITRE funds) o Computer to act as a proxy server ($1675 from LITRE, $1617 from nonLITRE funds) o High speed Basler digital video camera ($11,451 from non-LITRE funds) o Lens for digital video camera ($676 from LITRE, $2522 from non-LITRE funds) o Heavy duty tripod and pan-tilt tripod head ($2300 from non-LITRE funds) o Lighting for video camera ($645 from non-LITRE funds) Modified the wide flange beam experiment for web-based operation (modify the screw actuator so it could be actuated by the stepper motor rather then by hand; change the data recording procedure from manual strain indicators to data acquisition modules.) Modified the lab manual for web-based experiment. APPENDICES I (introduction), II (original write-up), III (new write-up) Beta tested the experiment with a group of visiting students in the Summer of 2005. Completed web based scheduling, access and security procedures. Ported lab write up to the web for the Spring 2006 lab offering. Develop assessment questions for the experiment. o What could be done to improve the online lab to make it a better teaching tool? o Are the instructions adequate, and the lab theory understandable and clear? o Is the remote experimentation a good alternative to use in the lab, or is in class better suited for laboratory learning? Please explain. Trained two new instructors in the web-based approach (TA Preston Royer and faculty member Abhinav Gupta) Implement the web based experiment in the CE 324 lab in the Fall of 2005 (shake down runs) and the Spring of 2006 (half of each section performed the experiment remotely). Performed assessment in the Spring of 2006. The full results are given in APPENDIX IV, and the results (22 responses) are summarized below: o What could be done to improve the online lab to make it a better teaching tool? 7 students said that web access was a problem (some thought that signing up 24 hours in advance was too long; others had difficulty with the access) 5 students said that a better written/web explanation was needed since a TA was not available. 3 students said they had difficulty with or didn’t understand the EXCEL data sheet. 2 students each had the following comments: It would be useful if there were one or more graphics to illustrate the loading and set up and labeling the components; 2 students each had the following comments: An online forum would be useful; The experiment was slow and boring; It would be useful to run the experiment both in class and remotely. o Are the instructions adequate, and the lab theory understandable and clear? 21 students said that the instructions were adequate (although several said that the theory was not as well explained.) One of these students said that it would help to be able to see the entire set up. 1 student said that the instructions were not clear. o Is the remote experimentation a good alternative to use in the lab, or is in class better suited for laboratory learning? Please explain. 18 students said that the in class lab experience is preferred. 4 students said they preferred the web based version Results from the final exam: o Question pertaining to this experiment: Web based group Section 1: 17.8 out of 25 points Section 2: 18.1 out of 25 points In class group Section 1: 19.2 out of 25 points Section 2: 19.5 out of 25 points o Overall exam averages Web based group 68.3% In class group 75.0% Summary and conclusions: All of the tasks associated with this LITRE project were completed: One experiment in the CE 324 lab was converted to a web based environment; access, scheduling and security software was written and implemented; the instructions for this experiment were modified for web usage; instructors were trained; the experiment was implemented partially in the Fall of 2005 and more fully in the Spring of 2006; and an assessment was made of the effectiveness of the web based experiment. The results of the assessment were not a surprise. The responses to the first question about improvements that could be made pointed out that we still need to improve the web access and the data spreadsheet. The lab manual can also be made clearer. The online forum is an interesting idea and one we will consider implementing. This may be useful for the in class experiments, also. The responses to the question about the clarity of the manual show that, while the instructions on conducting the lab were clear enough, the write up on the theory was not. The responses to the last question are the most interesting and, perhaps, indicate that we need to modify the write up for distance to clearly indicate the subtle difference in objectives between the remotely conducted lab and the one done in the lab itself. We apparently didn’t make it clear that the rationale for conducting the lab remotely was not just to save us all from having to spend 3 hours in the lab, but to illustrate that the remote technology does work, and that the results can be just as good as those obtained during the hands-on version of the lab. The results from the final exam are a bit disappointing. We had hoped that the students performing the experiment remotely would learn as much as those performing it in the lab while, at the same time, learning how to use modern technology to conduct experiments remotely. Even though the differences in grades are not great, we believe they should be much lower; i.e. there should be little difference if any between the students performing the experiment remotely and those performing it in the lab. Future work: We will modify the lab write-up in accordance with the comments above, and implement this remote experiment again in the Fall. We will reduce the sign up wait period from 24 hours to some smaller number. We will modify the assessment questions to better reflect the actual objectives of the experiment. APPENDIX I Introduction to the lab manual Lab Introduction I. II. III. IV. V. Objectives…………………………………………………………………2 Lab Policies………………………………………………………….........2 Safety……………………………………………………………………...3 Laboratory Equipment and Instrumentation………………………………3 A. Transduction…………………………………………………………7 B. Measurement and Recording Devices……………………………….8 Frequently Asked Questions………………………………………………13 Experiments 1. Strain and Deflection Measurements in a Cantilever Beam 2. Elastic Buckling 3. Torsion Test of a Hollow Tube 4. Free and Forced Vibrations of a Single Story Shear 5. Indeterminate Beam Behavior 6. Normal and Shearing Strains in a Wide-Flange Beam I. OBJECTIVES 1. Provide the student with a “feel” of the response quantities such as displacements, strains, forces etc. as observed in actual physical behavior of structural members such as beams, columns etc. 2. Compare response quantities from actual physical behavior of structural elements with those obtained from theory. 3. Learn to use modern instrumentation to measure the response quantities and understand the principles of its working. 4. Prepare technical reports to describe the nature of the experiment and its outcome. The objective of this Lab course is to make the student familiar with the real behavior of structural elements as observed in field of work. It will also provide an insight into the order of magnitude for different response quantities, thus enabling the student to verify theoretical results and the assumptions of the theory. II. LAB POLICIES 1. DO NOT WEAR OPEN TOED SHOES! You will be asked to leave the lab and you may not be able to make up the missed lab. 2. Attendance of ALL labs is required in order to receive a grade in this course. 3. If you must miss a lab due to an excused absence, you will need to reschedule the missed lab to coincide with another session (if you are a section “B” student then rescheduling for the section “A” time of the previous week will be necessary!). 4. The lab reports are to be turned in within one week of the period in which the experiment was performed. 5. The penalty for late reports is 10% per school day, up to a maximum of 50% with a maximum of 10 days to turn the lab in. After 10 days you will receive a zero. 6. The NCSU honor code will be followed in both letter and spirit. http://www2.ncsu.edu/prr/student_services/student_conduct/POL445.00.1.htm Although you will work in pairs during lab, you are expected to do your own work for the report. This policy applies to everything included in your reports. DO NOT copy someone else’s work! Any breach of this policy will result in severe penalties. 7. Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for students at 1900 Student health Center, Campus Box 7509, 515-7563. http://www.ncsu.edu/provost/offices/affirm_action/dss/ For more information on NC State’s policy on working with students with disabilities, please see http://www.ncsu.edu/provost/hat/current/appendix/appen_k.html III. SAFETY 1. 2. 3. 4. Absolutely no horseplay. No bare feet, sandals, flip-flops, or other abbreviated footwear. Exercise appropriate caution in use of electrical equipment. Fire alarm procedure: turn off equipment; gather up personal valuables; exit calmly but promptly. Exit route: turn left, then right, exit at the back door at the southeast corner of Mann Hall. Gather at the planter just outside the door for further instructions. 5. Be careful with the weights that you will be using to conduct the experiment. 6. No food or drinks. 7. No smoking or use of other tobacco products. 8. Keep work area neat. Leave personal items on shelf or hooks near door. 9. Notify the lab instructor immediately in the event of an accident. 10. Refer to the lab safety manual for further questions. SAFETY TRAINING OUTLINE IN CASE OF EMERGENCY CALL PUBLIC SAFETY AT 515-3333 Safety training will be conducted by the Principal Investigator or their designate(s) prior to the use of the lab. Following is a list and brief description of the main topics to be covered in safety training: 1. 2. 3. 4. 5. 6. Appropriate Clothing and Personal Items Eye Protection Housekeeping Rules Electrical Hazards Fire Extinguishers First Aid This training must be documented in writing using the form following the next page. This document will be archived in the Department Personnel File. 1. Appropriate Clothing and Personal Items: Shoes that cover the entire foot must be worn whenever in the laboratory. Sandals, flip-flops, or other abbreviated footwear is not allowed. While hazards in the lab are few, individuals are urged to wear clothing which protects as much of the body as possible. It is recommended that older, expendable clothing be worn while in the lab, since grease (from the screw actuators) and other substance might stain or otherwise cause unsightly damage to new clothing. 2. Eye Protection: In CE 324 lab, conditions do not warrant the use of safety glasses, and hence they are not required. However, safety glasses are required for the application of strain gages, which may be necessary in research activities. Strain gage application is the only procedure in this laboratory which warrants and requires the use of eye protection. 3. Housekeeping Rules: There will be no eating or drinking in the laboratory. There will be no smoking or consumption of other tobacco products in the laboratory. Horseplay of any kind is never permitted in the laboratory. Safety clothing and other protective devices are generally nor required in the lab. However, eye protection is required for the application of strain gages (see Eye Protection). Open-toed shoes and sandals are not permitted, nor are bare feet, because of the potential danger posed by objects (especially slotted weights) which may fall if not handled and applied carefully. Ties, scarves, and loose clothing should be removed or secured with appropriate fasteners. Loose or hanging jewelry should also be removed. Long hair should be carefully restrained (see Clothing and Personal Items). Bench tops should be kept clear of any personal items, devices, or materials not directly involved in the experiment in progress. This minimizes the chances of an accident and diminishes the severity of any accident which might occur. 4. Electrical Hazards No significant electrical hazards exist in the lab. Most of the frequently used electrical equipment is battery-operated. Some instrumentation requires 120volt AC power, which is provided in the lab with grounded electrical outlets. The instruments using this power are equipped with a three-pronged plug. The condition of the wiring, plugs, cords, and related equipment is periodically inspected for electrical hazards. 5. Fire Extinguishers One dry-chemical fire extinguisher is located on the wall in Room 112, as shown on the Evacuation Plan Map. Should additional equipment be required, the Evacuation Plan Map shows the location of larger dry-chemical extinguishers in the hallway outside the lab. Fire extinguishers should only be used by those who feel competent and comfortable given their formal training and previous experience. Even in the case of a small fire, the pull alarm in the main hallway outside the lab should be activated immediately, since a timely response by fire fighters is critical to ensure the safety of all occupants of the building. 6. First Aid A basic first-aid kit containing bandages is provided in the laboratory. Following any first aid, a nurse of physician at the nearest medical facility should provide further examination and treatment, if warranted. Someone knowledgeable about the accident should always accompany the injured person. On _______________________________, I ____________________________ was dates of instruction printed full name instructed by ______________________________________________ on the hazards printed name(s) of Instructor(s) present in Rooms 112 and 112D Mann Hall, and the proper safety procedures to follow when working there as outlined in the Safety Plan for that area. I understand these hazards and accept them as a necessary part of my work. I will follow the proper safety procedures in my work in this area at all times. ___________________________ Student’s Signature __________________________ Date Attested by Instructor: ___________________________ Instructor’s Signature __________________________ Date IV. LABORATORY EQUIPMENT AND INSTRUMENTATION A. TRANSDUCTION One of the most important concepts in instrumentation is transduction, which is the process of converting one variable which is difficult to measure into another which is more easily read. Fore example tire pressure is usually measured with a dial gage. The pressure has been converted into the mechanical response of a gauge needle. 1. Displacements: Displacement is always measured relative to some reference frame. Magnitudes of displacements can be determined in only two ways: a. By direct comparison, e.g. with a ruler. But how was the ruler calibrated? By comparing its length to a known standard. b. By “transduction”, for example by relating the displacement to the rotation of a dial gage needle. But, how was the dial gage calibrated? Again, by using a known standard. In both cases, a standard length must be used. In high quality devices, the standard is traceable to the National Institute of Standards and Technology (NIST). 2. Strain: Engineering strain is defined as a change in length over the original length. In most applications, the change in length is too small to measure directly. There are several practical ways of measuring strain, but the most common is to use a bonded electrical resistance strain gage. The gage is bonded to the surface of the specimen and is configured so that as the strain in the gage strains, its resistance changes by a predictable amount. The ratio of the change in resistance to the strain is defined as the Gage Factor. That is R R G.F. R R L L (2) Modern strain indicators measure (∆R/R) very accurately and incorporate a user specified Gage Factor to compute and display strain. The reading is in micro (10-6) inches per inch, often called microstrain and denoted µε. Stain gage manufacturers provide gage factors which have been determined by applying known strains to sample gages. The known strains are referenced to standards which are traceable to the NIST 3. Force: As with displacements, the magnitude of force can be measured in two ways: a. by comparison, e.g. using a pan balance b. by transduction, e.g. using a spring cable But again, the question remains: how is the balance or the scale calibrated? In this lab you will use two methods to apply loads: (a) calibrated weights (with calibrated 1pound weight hanger), and (b) a screw actuator with a device called a “load cell”. The load cell is a stiff spring element that is inserted between the loading mechanism and the structure. It has four or more strain gages attached to it, and the indicated strain output can be related to the applied load. The load cell is calibrated using a precision resister. B. MEASUREMENT AND RECORDING DEVICES 1. Digital Multi-Meter (DMM). Digital Multi-Meters give digital readouts of AC voltage, DC voltage, amperage, and resistance. They are battery operated, so turn them off when they are not in use. Directions on how to use the DMMs will be provided in the lab. See figure 1 below . Figure 1 Digital Multimeter 2. Digital Strain Indicator. When a strain gage is wired to a Digital Strain Indicator (DSI), the DSI measures a change in voltage across a Wheatstone bridge induced by a change in resistance in that gage. By varying the gage factor, this change in voltage can be converted into a change in resistance (G.F. = 1.000), strain (G.F. from manufacturer, 2.080 for example), stress, load, moment, and so on. We use this concept when calibrating the load cells. . Figure 2 P-3500 Digital Strain Indicator The DSIs that we use in this course are the model P-3500 (see figure 2 on the previous page) from the Instruments Division of the Measurements Group, Inc., Wendell, NC. The instructions for use are on the inside of the lid and are self explanatory (quarter bridges assume a 3-lead wire method which we always use in this lab). 3. Switch and Balance Unit. These units, Measurements Group Model SB10, enable up to ten strain gages to be connected to a single P-3500 digital strain indicator. Each gage can be balanced and the strain displayed by selecting the appropriate channel via the selector knob. 4. Digital Outside Micrometer Caliper. These micrometers (see figure 3) measure outside distances up to one inch with a readability of one tenthousandth of an inch (0.0001”). Micrometers are very fragile. Never lay one down near an edge where it may be knocked onto the floor. Vernier Thimble Sleeve Figure 3 Micrometer Vernier, 0.0001 inches 20 10 15 5 0 0 10 1 2 3 Reading on sleeve Reading on thimble Reading on vernier 0.400 inches 0.003 inches 0.0005 inches Final Reading 0.4035 inches 4 5 0 Sleeve, 0.025 inches Thimble, 0.001 inches Figure 4 Reading a Micrometer 5. Vernier Caliper. The vernier calipers can measure inside and outside distances up to 6” to a readability of one one-thousandth of an inch (0.001”) or one one-fiftieth of a millimeter (0.02 mm). These, too, are fragile instruments so treat them with great care. Figure 5, shows a typical vernier caliper and figure 6 shows how to read the caliper vernier scale. Locking Screw Inside Calipers Vernier Scale 0.001 inches Beam Scale 0.025 inches Outside Calipers Figure 5 Vernier Caliper Reading on beam scale Reading on vernier Scale 0.950 inches 0.008 inches Final Reading 0.958 inches Figure 6 Reading a Vernier Caliper 6. Linear Variable Differential Transformer. An LVDT is an electromechanical device that produces an electrical output proportional to the displacement of a separate movable core. It consists of a primary coil and two secondary coils symmetrically spaced on a cylindrical form. A free-moving rod-shaped magnetic core inside the coil assembly provides a path for the magnetic flux linking the coils. The LVDTs we have are made by TRANS-TEK, INCORPORATED Ellington, CT and are actually DC-DC LVDTs, that is both the input and output voltages are DC. The relationship between the voltage output and the displacement of the core is found through calibration. You will learn how to calibrate LVDT as part of one of the experiments. Figure 7 shows a photo of both the power supply and the LVDT. Figure 8 on the next page shows how to connect the LVDT wires to power supply and to the DMM. Figure 7 Power Supply and LVDT The LVDTs are held in place for an experiment with a MAGNETIC BASE and a wooden holder. The magnetic bases can be placed at different heights from the table using the steel risers with threaded rods. They can be attached to the aluminum reaction fame using special steel plates. Be very careful with the core when the LVDT is in the vertical position. If you are moving the specimen, either remove the core or rotate the LVDT into the horizontal position. The testing tables are quite stiff, but they are not rigid. When using an LVDT be careful not to stand on the table or touch the specimen. On/Off -V DMM Com Power Supply +V Black (-) Red (+) Red (+input) Black (-input) Blue (+output) Green (-output) LVDT Figure 8 Wiring an LVDT into the Power Supply and DMM 7. Accelerometer. There are many types of accelerometers commercially available. We will use a piezoelectric type on the vibration experiment. It gives a voltage output that is proportional to the acceleration. The relation between the acceleration and the voltage is called the calibration constant. It will be provided. 8. Oscilloscope. We will use a Digital Storage Oscilloscope (DSO) software package with a PC-based data acquisition system as the readout device for accelerometers. V. FREQUENTLY ASKED QUESTIONS How can I get an A in this lab course? The obvious answer is to do well on the lab reports, study sheets and on the final. To do this, we recommend the following: Read this introduction carefully to find out what you are supposed to learn in the lab. Read each lab write-up before you come to lab so that, when you arrive, you will know what you are supposed to be doing and what questions to ask. Complete the study sheet associated with that days lab. Review the theory related to the experiment you will be working. Ask enough questions in lab so that you know what is happening and why. Is this Manual the only textbook? Yes. However, you will probably want to refer to your textbooks from Solids, Structures, or Dynamics (as appropriate) while you are in lab. Assumptions, theory, and equations are not repeated in this manual, but reference is made to the appropriate material in one of these other textbooks. Will there be a lecture before each lab? Yes, but it will be short. The first lab will be conducted as a group, with the instructor demonstrating each step before the students attempt it. There will be ample time for questions and discussion, and suggestions will be given on how lab reports should be written. For the other experiments, there will be a brief explanation of the procedure at the beginning, and then the groups will work independently. There will, of course, be an instructor available to assist you in all of the labs. How long will each lab take? You will usually be in the lab the full 2 hours and 50 minutes. You won’t necessarily be performing the experiment the entire time – of the time will be spent reducing data and making typical calculations. By knowing how your results turn out before you leave the lab, you can catch any problems you may have with your data, and you will find that your lab reports are easier to write and take less time. Can I use old lab reports? No. The cliché “You only get out something what you put into it” is true in this lab. The more work you do on your own and the more thought you give to the experiments, the more you will get out of the lab. And, of course, there is the final. We will not intentionally make it difficult, but we will try to find out if you understood what was going on in the six experiments. Can I quote the lab manual in my lab report? Quotation is permitted, but plagiarism is not. The objective of writing a lab report is not to rewrite the lab manual but to attain a working understanding of the theories tested. From this understanding, you will be able to make quality conclusive lab reports. Is there a final lab exam? Yes, there will be one on Thursday evening on the last week of classes. The questions will be related to the fundamental concepts covered during the semester (state of stress at a point, relationship between stress and strain, transduction, calibration, and so on). Tips on reading the Vernier calipers -Place object snugly between the jaws, do not squeeze the jaws too tightly on the specimen as it may yield an inappropriate reading and/or damage the device. -Identify the beam and Vernier scales -Remember the smallest division on the beam scale is 0.025 inch and the smallest division on the Vernier scale is 0.001 inch. -Note the value on the beam scale which just precedes the zero mark on the Verniew, say X. -Note the value (say Y) on the Vernier scale which precisely (not very close, but PRECISELY) aligns with a division on the beam scale. -Add X to the product of the Y time 0.001 inch for the final measurement. Tips on reading the Micrometer Calipers -Place object snugly between the spindle, do not overtighten the micrometer on the specimen as it may damage this expensive device. -Identify the sleeve scale value which just precedes the edge of the thimble (say A). -Identify the value on the thimble which just precedes the horizontal mark on sleeve (say B). -Identify the value on the Vernier scale which most closely aligns with a horizontal division on the sleeve (say C). -Multiply B by 0.001 inch and C by 0.0001 inch and add these products to A to yield the final reading. Setting up a ±0.5 inch Linear Voltage Differential Transformer for the deflection measurement 1) The first step is to calibrate the LVDT as instructed by the instructor. When this is done, DO NOT disconnect the wires! 2) Determine the section of the structural element where the displacement needs to be measured. 3) Secure the magnetic base on the steel table such that the LVDT can be aligned vertically over the specimen. 4) Readjust the LVDT, with the core in place, in the clamp until the voltage displayed on the DMM is between +17 and -17 Volts. Unless a good deal of displacement is expected, it is usually convenient to start at close to zero volts. 5) Check to insure that the LVDT is secure in its clamp. 6) Check that the LVDT is acting correctly by gently depressing the member up and down. 7) Begin your experiment and take readings as instructed. 8) Compare your displacements with the theoretical predictions (if possible) and make certain nothing unseemly has occurred. Get the instructor to verify your results once you are satisfied. 9) Carefully disconnect the LVDT and place it back in the kit. Setting up a P-3500 Digital Strain Indicator to read strains from a single gage 1. Depress the amp zero switch and adjust it to zero with the appropriate knob. It will very likely be at zero and require no adjustment. 2. Set the unit to a quarter-bridge setting, if not already set, using the far right hand switch. 3. Hook up the gage wires to the correct terminals. Connect the red wire to the P+ terminal, the white wire to the D-120 terminal and the black wire to the S- terminal. 4. Depress the gage factor switch and adjust as necessary according to the gage in use (usually around 2.0 to 2.1). 5. Depress the run switch and adjust the balance knob until the reading is zero. Steps to Calibrating a 2-kip Load Cell with a P-3500 Strain Indicator 1) Find the appropriate calibration certificate for your load cell and copy down the value of the compressive load, which coincides with the 60kΩ resistance. 2) Plug the load cell into the P-3500. 3) Turn on the P-3500 and adjust the amp to zero. 4) Set the P-3500 to a FULL bridge setting. 5) Set the P-3500 to RUN mode and balance the unit to zero. 6) Place the 60kΩ resistor across the P+ and S- terminals. 7) While in RUN mode adjust the Gage Factor knob until the display matches the compression load from the calibration certificate. NOTE: The G.F. may need to be in the 2.3 to 4.5 range to do this. 8) Remove the resistor from the P+ and S- terminals, balance to zero and apply a test load. APPENDIX II Lab manual for the Wide Flange Beam Experiment Experiment #6 Study Sheet All questions relate to the T-section below 1500 lb A 5.00” 1.00” 4.00” 48” 32” 1.00” A E = 10.0 x 106 psi V = 0.32 1. Find the normal strain (in microstrains) at the top and bottom of the beam at section A-A. 2. Calculate the shearing strains (in microstrains) at the following points. a. at the top of the flange, b. at the bottom of the flange, c. at the top of the web, d. at the neutral axis, and e. at the bottom of the web. 3. Sketch both the normal and shearing strain distribution over the cross section at A-A. 4. Is the one-dimensional form of Hooke’s Law for normal strain applicable for converting normal stress to normal strain in this beam? Explain. Department of Civil Engineering North Carolina State University Raleigh, North Carolina CE324 STRUCTURAL BEHAVIOR MEASUREMENTS LABORATORY EXPERIMENT NUMBER 6: NORMAL AND SHEARING STRAINS IN A WIDE FLANGE BEAM NAME___________________________ OTHER MEMBERS OF GROUP: __________________________ __________________________ __________________________ SECTION_________GROUP________ DATE EXPERIMENT PERFORMED_____________________________ DATE REPORT TURNED IN______________________________ I. Reference: CE 313 textbook II. Objective: To find the normal and shearing strain distribution in the web of a cantilevered wide-flange beam. III. Specimen: A five foot long 5 x 5 wide flange aluminum beam is welded to a base plate which is in turn bolted to the column of a test frame. Vertical loading is applied with a screw actuator to the end of the beam. Five rectangular rosette strain gages are mounted across the web in a vertical line approximately halfway between the load and the support. A single uniaxial strain gage is mounted on the top of the flange in line with the rosette gages. IV. Background: One of the assumptions of Bernoulli-Euler beam theory is that the beam is under pure bending, that is, no shear. Under these conditions, the normal stress is related to the bending moment through the equation: ( y) My I (1) The normal strain can be obtained using the one-dimensional form of Hooke’s law as in lab 1. ( y) ( y) E My EI (2) In most applications, however, shearing forces are present. For beams that are long and slender, say the length is more than three to four times the depth, the effect of shear on the overall deformation will be small. Thus Bernoulli-Euler beam theory is considered to be valid to engineering accuracy. Using this theory it can be shown that the distribution of shearing stresses has the form: ( y) VQ( y ) It ( y ) where, (y) is the shearing stress at a distance y from the neutral axis, V is the shearing force at the cross section, Q(y) is the first moment of area above y about the neutral axis, I is the moment of inertia of the entire cross section about the neutral axis, and t(y) is the width of the section a distance y from the neutral axis. (3) The shearing strain can be obtained using the shear modulus, G, as follows: ( y) VQ( y ) GIt ( y ) (4) where G is related to E through the equation: E 2(1 ) G (5) If the cross section is rectangular, the shearing strain distribution is parabolic as shown in figure 1. The normal strain is linear for every cross section as long as the beam closely satisfies the Bernoulli-Euler beam assumptions. y y h b e Figure 1. Strain Distributions in a beam with Rectangular Cross Section In this case the shearing stress equation is found as follows: h A( y ) y b; 2 y 1 h 2 2 y ; I bh 3 ; 12 2 h 1 h b h Q( y ) A( y ) y y b y y 2 ; 2 2 2 2 2 V VQ( y ) ( y) It ( y ) 2 b h 2 y 2 2 bh3 b 12 6V 3 bh h 2 2 y 2 t(y) = b (6) (7) (8) The shearing stress is zero at the extreme fibers and a maximum at the neutral axis. For the rectangular cross section, the maximum shearing stress is: max 3V 3 avg 2A 2 (9) where A = bh, the entire area of the rectangular cross section. Since the thickness of the cross section is not uniform for the wide flange cross section, the vertical shearing stress (and hence the shearing strain) distribution will not be parabolic. Considering only the thickness, it is clear that the thickness of the web is much smaller than the thickness of the flange (meaning the flange width) and, hence, the shearing stress will be much smaller in the flange than in the web. The contribution of the vertical shearing stress resultant in the two flanges is small compared to the total vertical shearing force and hence, to engineering accuracy, it is usually neglected. The normal stress distribution remains linear. Figure 2 shows the distribution of both shearing and normal strains in the wide flange section. Figure 2. Shearing and Normal Strain Distributions in a Wide Flange Beam. V. Experimental Background Strain measurement: Normal strains in the x-direction can be measured directly by using a gage that is aligned with that axis. Shearing strains, on the other hand, cannot be measured directly with strain gages. A rosette gage, has three strain gages, describes completely the state of strain at a point and hence the shearing strains can be found by using the information gathered from the uniaxial strains measured by the three elements. Mohr’s circle for strain provides a convenient way to do this. The rosette gage we use is in a rectangular pattern, meaning that the three elements are 45o apart. Figure 3 shows a rectangular rosette strain gage (greatly enlarged) in the orientation we use. Notice that the middle gages, B is aligned with the x-axis. To derive the equation for the shearing strain, look first at the stress block in figure 3 which, in this case, is above the neutral axis. Mohr’s circle for the state of strain corresponding to this state of stress can now be drawn. The notation used here for shearing strain is that the shearing stress shown in figure 3 is positive and, hence, the shearing strain is positive. The primary difference between Mohr’s circle for stress and strain is that, for strain, the vertical axis (for shearing strain) is half that of the horizontal axis (for normal strain). Notice, also, that the positive shearing strain axis is down. P yx x C x xy B A y = -x x = Ex y = -x Figure 3. Stress Block and Strain Gage Rosette on a Cantilever Beam Points A, B, and C on the Mohr’s circle in figure 4 correspond to elements A, B, and C in figure 3. Since the elements on the rosettes gage are 45o apart, the points on the Mohr’s circle are 90o apart. The coordinates of B, which locates the x-axis on the circle, are (x, xy/2). The geometric proof given below provides the relationship between the normal strains at A and C (which can be measured) and the shearing strains (which cannot be measured). C D E 90o F G 90o B A xy Figure 4. Mohr’s Circle for Strain point G = B = x point D =A point F =C distance GB = xy/2 triangle ADE = triangle CFE = triangle EGB therefore DE = EF = GB DF = C – A = 2GB = 2(xy/2) therefore xy = C - A VI. Experimental Procedure Calculating the moment of inertia, I, using section measurements. Because of the shape of the section, it is clear that we will not be able to use a simplified equation to calculate the moment of inertia. We will need to divide the section into discrete pieces for which a moment of inertia can be readily calculated using the parallel axis theorem. Then we will combine these values to generate a moment of inertia for your composite section. The most important thing to remember is to generate a discretization that will be simply solved. For instance, consider figure 5 which is a representation of a T-section with tapered flanges. Figure 6 represents two possible methods of discretization. Both are perfectly allowable, but the one on the right is much simpler to calculate and is only slightly less accurate. 11 pieces Figure 5 Figure 6 2 pieces For our purposes, we will divide the wide flange section in a fashion to the simpler example of figure 6. Thus, our section will be comprised of 3 pieces. An approximation of this shape can be observed in figure 7 below. b1 bavg t2 t3 t1 tavg t4 w1 d1 d2 w2 davg wavg w3 t5 t8 t6 tavg t7 bavg b2 Figure 7. Wide Flange Approximation Upon measurement of the appropriate dimensions, calculate the contribution of each piece to the moment of inertia and sum them all to obtain the total composite moment of inertia. Remember that the parallel axis theorem states that the contribution of each piece should be equal to I cgi Ai d i 2 (10) where Icgi is the moment of inertia about that segments centroid, Ai is the area of that segment, and di is the distance from the section’s centroid to the segment’s centroid. thus the total moment of inertia from the three pieces should be equal to I 3 1 cgi Ai d i 2 (11) The normal strain due to bending can be readily calculated using equation 2 assuming the other necessary parameters are known. Calculation of Q(y) for the composite section to calculate shearing strain The calculation of Q(y) must be completed for each rosette gage location. Using the composite section, this should be a relatively simple process. The equation for the first moment of area states that Q( y ) yda (12) For this section, we can simplify the equation to n Q ( y ) Ai d i (13) 1 where di is the distance from the centroid to the center of that segment. For our purposes this calculation of Q would normally need to be done five times, but from symmetry we can show that the two outer gages and the inner two gages are equivalent. Thus, only three calculations will need to be made here. Upon completion of these calculations, the shearing strain may be calculated using equation 4, assuming the other parameters have been determined. Measurement of normal and shearing strains Because of the complexity of this procedure, only one specimen will be used for the entire lab. The necessary measurements and gage locations will be given during the course of the exercise. See figure 8 for a photo of the specimen and gage layout.. Rosette Gage Layout Strain Gage Locations “Fixed End” Specimen 2-kip Load Cell SB-10’s and P3500’s Figure 8. Specimen and Rosette Gage Photo There are a total of sixteen individual strain gages which will be measured. Three on each of the five rosettes and a single uniaxial gage mounted on top of the beam in line with the rosettes. The rosettes have been symmetrically mounted to simplify the calculation procedure. Each gage is wired into an SB-10 terminal as in lab 3. Each SB10 is in turn wired into a P-3500. The individual gage measurements can be observed by selecting the appropriate channel on the SB-10. In addition, there is a 2-kip load cell which is also plugged into a P-3500. Using these devices, the appropriate measurements can be taken during the loading process. For this exercise, an ultimate load of 1000 lbs will be applied. The load will be applied with no intermediary steps. Linearity will be checked by monitoring the top-mounted uniaxial gage through a second loading and unloading cycle to 1000 lbs in 500 lb increments. The shearing strains can be approximately checked by back-calculating the shear stress and then back-calculating the shear force. VII. Report a) Plot the normal strain distribution (Exp and theoretical) (Strain on x-axis and distance from neutral axis on the y-axis) b) Plot shearing strains distributions (Exp and theoretical) (Strain on x-axis and distance from neutral axis on the y-axis) These plots should resemble the sketches on figure 2. Plot the theoretical values connected with a line and experimental as discreet points. Be sure to scale the shear strain plot such that the strain axis goes all the way to zero i.e. x-axis starts from zero. Otherwise EXCEL will likely choose a scale that greatly exaggerates the curvature of the plot. c) Plot the linearity check from the uniaxial gage data. A single experimental sketch will suffice, but include sub-sketches of the gage locations. Include in your discussion of results: What do you think a test of deflection for this wide flange beam would have resulted in, if loads were to be applied at the end of the beam to obtain deflection and then compared using theoretical equation of PL3/3EI and why. Some interesting simple checks of the data may be performed if you are interested. For instance, you may check the approximate shear in the section by back calculating the shear stress and then calculating the resultant shear force in each region by multiplying this stress by the area over which it acts. By summing these values over the five regions you can get an estimate of the total shear force. Also, you can do a “better” job of calculating the moment of inertia of the section by dividing the flanges into rectangles and triangles (for the tapered portion). The moment of inertia and centroid of a triangle can be found using the appendix of your mechanics text. All of these “checks” can be done very quickly using EXCEL. DATA SHEETS Specimen measurements and predicted strains Material 6061 T6 Aluminum Young’s Modulus: Poisson’s Ratio: Shear Modulus psi psi Dimensions (Refer Fig. 7) t1 (in) w1 (in) d1 (in) t2 (in) w2 (in) d2 (in) t3 (in) w3 (in) t4 (in) t5 (in) t6 (in) t7 (in) b1 (in) t8 (in) b2 (in) Average measurements tavg (in) wavg (in) davg (in) bavg (in) Moment of inertia calculations (Eq’s 10 & 11) Icg Ipa I1 (in4) (in4) I2 (in4) (in4) I3 (in4) (in4) Itotal (in4) First moment of area calculations, Q (Eq. 13) Distance between gages Q5 (in3) Q4 (in3) Q3 (in3) Q2 (in3) Q1 (in3) (in) Distance from load to rosette gages (in) Theoretical strains at 1000 lbs Gage x () xy () A () B () C () x () xy () A () B () C () x () xy () y (in) Uniaxial 5 4 3 2 1 Experimental Strains Zero pounds uniaxial 5 4 3 2 1 1000 pounds uniaxial 5 4 3 2 1 Zero pounds A () uniaxial 5 4 3 2 1 Uniaxial Gage Linearity Check Load(lb) 0 500 1000 500 0 Strain() B () C () x () xy () APPENDIX III Instructions for the web based lab Procedure for Running Remote Experiment 1.) Read over the lab sheets. Understanding the mechanics behind the experiment is most important. The discussion is very straight forward and not at all complicated. For reference during the experiment see “Mechanics of Materials”, by James Gere. This is as good a reference that can be found on the subject of mechanics. Refer to section 1.6, 5.15.5, 5.8, and 5.10, also the discussion of Mohr’s circle in chapter 7 is excellent especially if you do not understand the proof given in the lab sheets as to how the rossette gages can be used to determine shearing strain. 2.) Calculate the moment of inertia and first moment of area (Q) from the cross sectional dimensions given in the data sheets. For help with these calculations see chapter 12 in Gere. In the data sheets Icg refers to the inertia of the individual pieces about their centroid (i.e. bh3/12) while IPA refers to the inertia calculated with the parallel axis theorem, or transformed moment of inertia. Also there are examples in chapter 5 on calculating the first moment (Q). 3.) Calculate the theoretical values from Bernoulli-Euler beam theory that you will compare your experimental findings to. ( y) ( y) E My EI ( y) VQ( y ) GIt ( y ) 4.) Make sure your default web browser is microsoft internet explorer. Then select the labview link to download the viewer so you can run the experiment. 5.) Next select the link to run the experiment, you will see the experiment page as shown below. 6.) You will need to log in with your unity ID and password, and you will probably have to run through several pop-ups, but do not cancel any of these. Navigate through the menu’s. If you have not scheduled a timeslot to control the experiment you need to do so at least 24 hours before you plan on running the experiment. Select the menu to schedule a time to control and follow the instructions given. Come back to the website at the time you have scheduled to control the experiment. 7.) The following page will be displayed when you enter the experiment to control it. 1.) Press Run button 2.) Press to turn on lights View video below, may need to resize window to view 3.) Select load from pull down menu 4.) Read strains and load from the boxes labeled at the left You will first need to hit the run button at the top of the picture. Then you will turn on the lights by pressing the button that says lights. Next use the drop down scroll bar to select the load to apply to the beam. Once the load has been reached read off the strains for each gage and record in your data sheet. Once you are done loading make sure you unload the beam and remember to turn off the light before you hit the stop button that is located at the top to the page. Once this has been done you can simply close your web page. APPENDIX IV Assessment questionnaire and responses 1) What could be done to improve the online lab to make it a better teaching tool? • One thing that could be done is to maybe somehow find a way to put something up to show how the load acts and how the beam deflects more accurately. Besides that, materially, it is explained very well, and the study sheet really helps you prepare adequately for the actual experiment. • One thing that could be done to improve the online lab would include fixing the excel data sheet (that is sent to the user’s email account) so that it is properly labeled. I had a hard time figuring out what the values represented. • To improve the online lab the excel spreadsheet could be made easier to understand or maybe a legend with it to explain the columns. • The only thing I thought that could have been improved to make this lab better would be to allow you to do the lab even if you did not sign up to 24 hours in advance. If a time was open and no one was performing the experiment then I did not see why you could not just log in and do the lab right then. • To improve the online laboratory I would first work out all the bugs to make sure it would let everyone in. I heard form several classmates that they were unable to get in and actually do the lab. Also, an online forum might make it easier for classmates to chat and discuss concepts, which would make it similar to a lab setting in which they can interact and even the instructor could be present. • This lab could be improved by making it easier to access. I know that I had trouble getting on the website and having to make it work for me. I ended up having to go up to a TA’s computer to do the experiment. Otherwise, it was pretty straightforward and just required time. There’s nothing we could have done in terms of errors or mistakes, so there wasn’t much difference between just being given the numbers or running this experiment and watching it give you the numbers. • Explain a little better what exactly needs to be included in the lab report. • The internet did not work properly for some people in my group. If you could make the lab compatible with other browsers it would be better. • The actual loading of the specimen took an extremely long amount of time. It was actually very boring to watch the load increase. I lost my interest by the time it reached 1000 lbs. Is there anyway to load it faster. • The online lab could be improved by making the data which I emailed to myself more interpretable and useful. I received 17 columns and almost 17000 rows of unlabeled numbers and it took me some time to realize what any of them meant. In the end, I did not make any use of them. • One thing that could improve the online lab would be to do the lab in teams with a TA or professor available. Some things are not easily understood without a TA present. • I feel that the lab could be improved in several ways. I think that students should have more access to the labs than having to sign up a day in advance then go through multiple sign in problems. Most students have a hard enough time as it is finding time to set aside to do it but may be able to just decide to sit down and do it. • I think that more class discussion of the aspects of the lab would have made the online lab more helpful. • The online lab could be a better teaching tool if the T.A. was ore directly involved in the process, to field questions in determining values and utilizing data obtained from the experiment. • I think that you need to find an undisturbed place where the camera and equipment can be setup and not be touched until the experiment time is over. • Need a couple of in class sessions to explain the methodology of using the tools, also inclusion of the ability to do the lab online and hands on to better understand. • I think that having a labeled diagram of the items that are being recorded during the lab would be helpful in understanding the lab. • The lab is adequate, but a shorter signup time would be helpful. • By completing the lab over the internet, I found it more difficult to complete and understand the lab. While the convenience of not coming to campus for lab was nice, the absence of an instructor and the tangible learning experience made it more challenging. • The main problem with the online lab was that it gave technical difficulties. If those could be worked out then it would be a great way to conduct a lab. • One thing that could improve the online lab would be to have it done in teams rather than doing it individually. • The online lab seems to be a good teaching tool. As long as the students give themselves enough time to become acclimated to the procedure, it is easy to understand and run the experiment. 2) Are the instructions adequate, and the lab theory understandable and clear? • The instructions are adequate because they are laid out before you very directly, step by step. The theory, for the most part, is understandable, except that there are so many equations, and it seems like some of them don’t have a very good explanation (i.e. equations 6, 7, and 8). There probably shouldn’t be more of a write up about them, but possibly just a little more explanation in the lab. However, it isn’t extremely necessary, as long as you take a good look at it. • Yes, the instructions seem to be adequate. It was easy to download the software needed and to carry out the experiment. • The instructions are pretty clear and the lab theory is understandable. • I think the instructions were adequate and very easy to follow. • The instructions are clear and adequate but the theory is not completely clear, which I feel the online forum, as suggested above, could help with the understanding. • The instructions were clear and it was easy to follow. There were no tricks that were hidden that you may have had to know. I think that anyone could have run the experiment. • The instructions are clear, but the theory was not fully described. • The theory was not as clear as it could be. Without the TA present, we got confused. • I believe that the instructions for the lab were very adequate. The only other thing that might have been interesting to see, would be how the actual instrumentation was set up, seeing that we were not actually in the laboratory to set it up. • The instructions were adequate and the lab theory was understandable and clear. • The instructions are adequate, but the theory is a little hard to understand. It is hard to compare the formulas in the theory to the lab data sheet we are provided. • I think that the lab theory was very understandable and clear to what we were doing. Going over the basic principles in class definitely helped. The instructions and all the different links on the website were a little confusing at first, but as long as you read them all it is very easy to understand. • I believed the instructions on how to run the lab were very understandable and clear. • The instructions are adequate, and the lab theory did make sense, although there were a few points where some of the wording in the text is vague, with regard to equations. • The instructions and theory are both very understandable. I understood what I was supposed to be doing and what I was supposed to learn. • The instructions were adequate when explained by the TA thoroughly. The lab theory however was difficult to grasp with just handouts. A time to come in and discuss questions would be good to include as an optional event. • The instructions were helpful in understanding how to conduct the lab and the lab theory was understandable. • It is understandable, but I think it would work better if the class could get in front of computers and do the lab together. That way, we still get the online experience, but it is easier to have questions answered. The process is hard to remember when you have only a small presentation of how to do everything. • The instructions were enough to complete the lab, although probably not enough to fully understand it. • Yes, the instructions were clear. I would spend a few more minutes in class explaining exactly what is needed. • The instructions are adequate, but the theory is a little hard to understand. It is hard to compare the formulas in the theory to the lab data sheet we are provided. • The instructions are very clear and lead you through the lab in a timely manner. 3) Is remote experimentation a good alternative to use in the lab, or is in class better suited for laboratory learning? Please explain. • First off, in class is always the best way to learn in the lab, just because it truly is “hands on.” However, remote experimentation is very interesting, and it does provide another way to learn the material, but it’s not as good of an option as actual in class experimentation. In class experimentation makes everything easy to see, in comparison to remote experimentation, partly because group work is encouraged more in class experiments as well. • I think for this lab, the remote experiment is a good alternative to being in the classroom. The lab itself is very easy to explain and carry out and with the remote application the experiment can be performed at anytime as many times needed. • I think remote experimentation is a good alternative to use in the lab. I would like the option of attending a lab if I really didn’t understand the material. • I think the remote experiment was a great experience and a neat way to do a lab which I had never done before. It was also good because it gave you the flexibility to perform the experiment whenever you wanted to. • I feel that in its current setup, I would prefer an in person lab, mostly because I would have an instructor and classmates to ask questions to and help get a full grasp of everything. But I can definitely see the online lab being a better alternative in the future, because of its convenience to a time schedule. • I like the lab setup better just because of the variation in numbers and actually doing something manually, rather than watching it on a computer screen. I just feel like I get more out of it when I can see what is going on and being a part of it. • It’s interesting and all, but I feel that I learn more about the subject at hand when we meet to do the lab. • I think maybe individual teams working on the lab with the TA would work better. • I believe that this takes away from the laboratory experience. Sure, it was nice to not have to stay in the lab for an hour or so, but you lose something when the answer is just a click away. There’s no setup, no group work, and there’s nothing to compare your results to. In the lab, we usually are able to compare our results to other groups, where here, we have nothing but our own work to compare to. I believe that the online system turns a lab experiment into something like a homework problem. You might as well have gave us the numbers and told us to write a report on it. • I think, in general, in class labs are better for learning the material, by doing the entire lab hands on. Having the experience of doing a lab remotely once was also useful, but I think I would have learned a lot less if all or most of the labs had been performed remotely. • I do not think there is anything really wrong with the remote experiment. However, I think an in class lab is better suited for learning. The lab would be easier to understand if you are working with others and you have the lab TA there to help you through any problems that may arise. • I think that all labs are always better suited in the classroom. This lab was very easy to perform and it was very useful to know how to remotely control the experiment, but the classroom allows you hands on and the ability to learn more and ask questions. • Personally I prefer the in class lab, because I like to have a hands on feel and like to be able to speak to the instructor if I have any questions. • I definitely believe in class is the preferred alternative for laboratory leaning, for the value of working had on with a project, and having someone there who can field questions regarding the lab. • I think that in class is the better way to learn because I like to actually have hands on experience with my peers when doing these labs. It is just a learning preference for me but online labs were effective in a minimal way. • I believe the in class experience is good to continue to do because it will allow you to visibly see what is going on and how the things work. In addition, you will be able to see where you sources of error can come from. However, more complex computer oriented labs are better suited online. I believe the inclusion of both in the curriculum is the best option for laboratory learning. • I do not think that remote experimentation is a good alternative, but I definitely think it is a useful tool that should be used in conjunction with the lab. For easier labs such as this one, where the actual conducting of the lab report is not so difficult, the remote alternative saves everyone time and effort. • I like in lab learning better. • I feel that the remote experimentation is not a good alternate to the in class lab. It seems the online actions take away from the whole purpose of the laboratory classes hands on experience. • Remote experimenting is a good way to implement a lab. The theory was nothing out of the ordinary and it really made it an easy lab to complete, while still getting the same learning effect and understanding of what’s going on. • I think an in class lab is better suited for learning because you are working with others and you have the lab TA there to help you through misunderstandings. • In my opinion, I prefer labs that are run in the class setting. Questions may come up that can be answered right away and it is easier to understand exactly how the experiment is set up. Exam Questions Prestons Lab Points missed on question pertaining to remote lab: Remote group: -7.2/25 Non-remote group: -5.8/25 Average Exam grade: Remote group: 66.25 Non-remote group: 64.25 Jerrys Lab Points missed on question pertaining to remote lab: Remote group: -6.9/25 Non-remote group: -5.5/25 Average Exam grade: Remote group: 68.3 Non-remote group: 75 Nothing very unusual, looks like the remote users did slightly worse on the question but nothing significant. From both lab sections the non-remote group scored 1.4 points better on the question than did the remote group.