1.105 Solid Mechanics Laboratory

Transcription

1 1.105 Solid Mechanics Laboratory General Information Fall 2003 Prof. Louis Bucciarelli Rm x TA: Attasit Korchaiyapruk, Pong Rm 5-330B x attasit@mit.edu Athena Locker: /mit/1.105/ Class: Section B01 Tuesday, 14:00-17:00 Room Section B02 Thursday 14:00-17:00 Room Subject Description: In Solid Mechanics Laboratory, 1.105, you will have the opportunity to assemble and test a variety of structural elements. You will subject them to loading, observe and measure their behavior using both crude and relatively sophisticated instruments. Foci include: Testing of statements made and conclusions derived in the companion subject, 1.050; Study force/displacement, stiffness behavior of structural elements; Failure modes and mechanisms; Introduction to instrumentation, resolution, range, transducer response, signal conditioning; Coping with uncertainty; methods of data analysis; Experiment design; Report writing. Laboratory Conduct Each lab session will begin with an orientation. The lab instructor will respond to questions and convey essential, tacit, knowledge re the smooth conduct of the experiment. The lab instructor will be available throughout the three hours to provoke your thinking in response to questions that you pose. The laboratory exercise is not a test. It is a hands-on experience meant to show the relevance of theoretical concepts to understanding the behavior of real hardware and instrumentation and, at the same time, reveal how non-ideal conditions and some very un-theoretical events can obscure the theoretical behavior. There are four test frames in the lab. You will work in groups of two or three. While you are to collaborate in setting-up and running the experiments, each of you individually will be responsible for a report of your experiences. Procedures for each experiment, other than the first, are to be read before the start of lab even though these can only sketch out what needs to be done to effect a measurement. Certain constraints are printed in bold within these descriptions. These constraints are to be strictly observed. In part this is for safety reasons, in part because we do not want to fail a test specimen or overload an instrument. If you are not sure, ask your lab instructor. The most successful experiments in science and engineering are those in which you know what the outcome will be. Indeed, you cannot design an experiment without knowing something about the range of possible deflections, a safe loading of the structure, an instruments sensitivity to some external, disturbance, and the like. So while the experiment is in progress, one of your team should do a rough data reduction and sketch out the behavior e.g., load vs. deflection, as you go along. Make the most of your time to ensure that you have quality data by checking it with expectations. At the same time you must resist letting your expectations color or bias your readings; if your reading looks 10% low, don t try to reduce the difference; on the other hand if it is off by a factor of 10, you had better stop everything and check your experimental setup, your theoretical deductions, or your data analysis procedures.

2 Report Content and Format You will record your activities in the lab in a lab notebook. You are to use ink, make no erasures. Draw a line through that text which you find faulty or erroneous. Sketches of apparatus may be made in pencil. Make sure you record all relevant dimensions, variables, settings, (don t neglect to record the units) and information that will enable you to write the report without coming back to the lab to check up on the value of a critical parameter. If you use a laptop computer to record data, you must still print out pages to paste into your lab notebook. The report should include the following: Summary - A one page summary of purpose, method and main results Introduction - including objectives. Experimental Procedure Results Conclusions Appendices. The amount of detail to include in these sections varies depending upon your audience. For our purposes, think of your audience as a fellow student who has not yet done the experiment but will do so within a few days. You can assume they are familiar with the theoretical concepts of With respect to instrumentation, assume this student is aware of the basic principle of operation of the transducer but is not familiar with the particular application you are making. Results should not include excessive detail. Put the full data record in the appendices. Appendices are also the place for background theory, manufacturer s specifications and the like. Grading: This is a 6 unit subject. There are seven in-lab experiments. Experiment # 5 10% The remaining six experiments 15% each There is no final exam.

3 Experiment 1 We determine the failure strain of a strand of spaghetti and test the validity of Euler s theory for the large deflections of an elastic lamina. Those are the objectives. The educational objectives are to introduce the concept of uncertainty in measurement and to learn something about strain in bending. Experiment 2 Cable In this experiment we verify the consequences of static equilibrium for a weight suspended from a cable. In a second part, you will determine the force/deflection relationship for a redundant structure built up with two cables under pretension. In contrast to the first part, we will not provide the theory for the second experiment until later in the course. A W A θ L x C W B W B L/2 Experiment 3 Tension Test Our objective is to measure the Elastic Modulus of steel. The experiment comes in two parts. In the first part of the experiment, you will subject a ordinary steel reinforcing rod to a tension test using a testing machine designed specifically for that purpose. The BLH machine dates from the fifty s but its mechanical subsystems still function well enough for our purposes. In the second part you will do a tension test of a stainless steel rod, loading the specimen using the dead weights available in the lab but measuring displacement using the LVDT, Linearly Variable Differential Transformer. Experiment 4 Truss Deflection We will load a truss structure vertically at various pairs of joints (symmetrically disposed with respect to the length) and measure the vertical displacements of two or three joints. Our objective is to compare the results obtained from analyses which model the structure as a truss (i.e., with friction-less pinned joints), with experiment. fixed LVDT W fixed d c i b h a g f e

4 Experiment 5 Strength, compressive and tensile, of Concrete. We conduct a compressive test on a cylinder of concrete to observe its force/deformation behavior and determine its strength. A second test gives, indirectly, the tensile strength. Experiment 6 Beam Deflection and Stresses The objective is to verify the predictions of engineering beam theory in so far as that theory defines the centerline deflection and extreme values of the normal stress. We will determine the relative stiffness of two aluminum beam test specimens of equal cross sectional area but different cross-sectional shape and see how they conform to theory. W, strain gage strain gage Experiment 7 Elastic Buckling. The objective is to demonstrate local elastic buckling within a truss structure and to compare experimental results with Euler buckling theory.

5 1.105 Solid Mechanics Laboratory Fall 2003 Prof. L. L. Bucciarelli DATE CLASS TOPIC READ LABORATORY TOPIC W 09/03 Introduction Chpt. 1 Tr 09/04 Use of Spread Sheet F 09/05 Concept of Force 2.1 M 09/08 Concept of Moment 2.2 T 09/09 Lab #1 Pasta Uncertainty W 09/10 Static Equilibrium Requirements Tr 09/11 Design Exercise #1 Lab #1 Pasta Uncertainty F 09/12 Truss Structures 3.1 M 09/15 T 09/16 Lab #2 Cable Structures W 09/17 Beam Structures 3.2 Tr 09/18 Lab #2 Cable Structures F 09/19 M 09/22 Student Holiday T 09/23 Design Exercise #2 W 09/24 Torsion of circular shafts 3.3 Tr 09/25 F 09/26 Thin Cylinder under Pressure 3.4 M 09/27 Concept of Stress 4.1 T 09/30 Lab #3 Uniaxial Tension W 10/01 Stress Component Transformation Tr 10/02 Lab #3 Uniaxial Tension F 10/03 Stress Fields 4.2 M 10/06 Indeterminate Systems 5.1 T 10/07 W 10/08 Compatibility of Deformation Tr 10/09 F 10/10 Quiz #1 M 10/13 Columbus Day T 10/14 Truss Matrix Analysis 5.2 Lab #4 Truss Structures W 10/15 Tr 10/16 Design Exercise #3 Lab #4 Truss Structures F 10/17 Concept of Strain 6.1 M 10/20 Strain Component Transformation 6.2 T 10/21

6 DATE CLASS TOPIC READ W 10/22 Materia Properties/Stress-Strain Reln Tr 10/23 F 10/24 Modes of Failure 7.4 M 10/27 Stress/Deflections Shafts in Torsion Chpt. 8 T 10/28 Design Exercise #4 W 10/29 Stresses - Beams in Bending LABORATORY TOPIC Tr 10/30 Lab #5 Concrete Failure F 10/31 M 11/03 Shear Stresses in Beams 9.4 T 11/04 Lab #5 Concrete Failure W 11/05 Tr 11/06 F 11/07 Quiz #2 M 11/10 Veterans Day Vacation T 11/11 W 11/12 Stresses in Composite Beams 9.5 Tr 11/13 Design Exercise #5 Lab #6 Beam Bending F 11/14 M 11/17 Deflections Due to Bending 10.1 T 11/18 Lab #6 Beam Bending W 11/19 Tr 11/20 Lab #7 Buckling F 11/21 Buckling of Beams 10.2 M 11/24 T 11/25 Design Exercise #6 Lab #7 Buckling W 11/26 Tr 11/27 Thanksgiving Vacation F 11/28 M 12/01 Frame Matrix Analysis 10.3 T 12/02 W 12/03 Some Special Methods 5.3, 10.4 Tr 12/04 F 12/05 M 12/08 T 12/ NO REQUIREMENTS DUE ZONE W 12/10

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