AE3145 Strain Gage Rosette Experiment Using Cantilever Beam (S02) Page 1 of 2 GEORGIA INSTITUTE OF TECHNOLOGY School of Aerospace Engineering AE3145 Laboratory Strain Gage Rosette Experiment Using Cantilever Beam Purpose: The purpose of this lab experiment is to gain additional experience using resistance strain gages, strain gage techniques, and strain gage rosette analysis. The lab will examine the behavior of a thin rectangular cantilever beam subjected to either a tip load or a tip displacement. Several strain gages, including a rosette gage, have been applied to the upper and lower surfaces of the beam near the root end. These will be used to measure the state of strain on the upper and lower surfaces of the beam, and from this strain state, the state of stress will be estimated and compared to elementary beam theory. Lab Work The lab apparatus consists of a small (approximately 12 inches long) cantilever beam and a support fixture that allows either a tip load or force to be applied. A strain rosette and possibly several extensional strain gages are bonded to locations near the root of the cantilever (the TA’s will either furnish dimensions or you will have to measure them directly in the lab). A manual strain indicator and switching and balancing unit (SBU) will be used to read the strains in the individual gages and rosette gages. You will apply tip loads to the beam and record the strains in all gages and them repeat this for applied tip displacements instead of loads. The lab class will be broken into smaller groups and each group will be given a separate beam setup; each setup will have slightly different beam and strain gage configurations and each specimen will be identified by a name or number. You will then complete the following: 1 Measure all strains in all gages on the beam for tip loads from 0 to 1.5 lbs. and for tip displacements ranging from 0 to 0.25 inches. 2 Plot all data to show trends and any evidence on irregular behavior. 3 Determine the principal strains and their directions as a function of applied tip load or applied tip displacements. Analysis: Your analysis of the results must consider the following specific questions along with any other points that are raised in the lab session itself. You should also make use of your textbooks and class notes for the development of beam theory (bending and deflection) as well as the supplementary lab notes on strain gage rosettes (Strain Gage Rosette Theory and Problems). Check your units. Using the data from the rosette strain gage:AE3145 Strain Gage Rosette Experiment Using Cantilever Beam (S02) Page 2 of 2 1. Determine the principal strains and directions for each loading condition applied to the beam. Plot your results in two figures, principal strains versus the load (P) and the principal strains versus tip deflection (d). Hint: this is easy to do using a spreadsheet. 2. Does the material behave in a linear manner? Do the principal directions change with load? Why/why not is this like you would expect from basic beam theory? 3. From the above results, determine approximately the equivalent spring stiffness of the beam. You will have to consider the data from your two experiments, the one with applied tip loads and the other with applied tip displacements (question #1). Hint: Check your units. 4. Explain qualitatively the presence of a compressive strain in a direction transverse to the beam axis. 5. What is the maximum shear strain developed in the beam? Along which axis did it act? Express this as strain per unit applied load /and tip displacement. Note: this is the shear strain on the upper beam surface and NOT the shear stress on the cross section (which we cannot easily measure directly). 6. Using E and ν from your text or any other source (e.g., you must reference your source(s) in your lab write-up), determine the principal stresses and their directions for the two experiments. (as in # 1,2). Do the results confirm the assumption of a uniaxial stress state for beam bending? 7. Assume that you have only the rosette gage data and that the stress state is uniaxial (e.g., only σx is nonzero). For the tip loaded experiment, estimate (average) a value for E and ν from your data. Are these reasonable values? Hint: Find a relation between σx and load P in your notes. 8. Finally, from the tip deflected beam: Using the Young’s modulus found in step #7, determine the load versus deflection for this material (the relation between the deflection and load can be found in your text book or any other source). Lab Report You are required to submit a formal lab report for this tensile coupon testing portion of the lab assignment. Use the format and tips provided in the first lab and try to incorporate any suggestions that the TA’s may have made on returned