University of Texas at Arlington MAE 3183, Measurements II Laboratory Strain Measurement 1 Experiment #6 Strain MeasurementUniversity of Texas at Arlington MAE 3183, Measurements II Laboratory Strain Measurement 2 Motivation The main idea of this experiment is to revise the concept of stress, strain, their relation to the applied load in different types of structures, idea of stress and strain transformation, methods to calculate the strain in any required direction generated by the loads in direction different from the required one. Before performing this lab you MUST be familiar with 1. Basic notion of stress and strain. 2. Plain stress and plain strain. Principal normal and shear stresses. Relation between Principal stresses and stresses at any other orientation. 3. Strain gage and its working principle. 4. Strain rosette and its utility. 5. Plain stress and strain transformation. 6. Mohr’s Circle for stress and strain. 7. Transformation from stress to strain in 1-D, 2-D and 3-D. 8. Working principal of wheat-stone bridge. INDIVIDUALLY submit the solution of following problem in the pre-lab report and before you start the experiment. Original stress state is as under σx – σy – τxy - θ = mm – dd – yy – 30+dd (your date of birth mm-dd-yy (last two digits for year) ) 1. Transform it at the angle defined above using stress transformation equations 2. Draw Mohr’s circle for stress and use this to find the transformed stresses. 3. Calculate the original longitudinal strains. 4. Calculate longitudinal strains in new transformed orientation Introduction A short lived engineer would be one that never considered stress or strain. Stress is present in all structures either static or dynamic, at least on earth anyway. Stress is typically a key element that dictates every design. Strain is the resulting deformation that a structure experiences under a given stress. For most materials considered in mainstream engineering, stress is directly proportional to strain. Within the design process a preliminary survey produces likely candidates for use as materials and the expected stress-strain quantities are calculated. At this point two key problems exist. These problems are (1) How is the stress calculated for complex shapes such as curved areas? and (2) How are the strains measured once the structure has been built? To attack the first problem, analytical solutions are available for almost every type of structure imaginable. These equations produce equations normal or shear stress as a function of loading and geometry. The equations are based entirely upon geometric quantities and don't depend on empirical data for a solution. In this experiment, we challenge those equations. Given various structures, loads are applied andUniversity of Texas at Arlington MAE 3183, Measurements II Laboratory Strain Measurement 3 measurements are made that will either coincide or diverge from values produced using theoretically derived equations. Now all that's left to find is a means to measure strain. Most people, with the aid of a ruler, can measure 1/32 of an inch within +/- 1/64. That's fine for extremely high loadings or extremely weak materials, but many materials might fail at say 3500 strain, which would be well below 1/20 of the resolution of a ruler. To solve this problem several instruments can be used, one of which is the strain gage/Wheatstone bridge. This instrument combination allows measurements, in some cases, as low as +/- 1strain. With resolution this good the question arises "Is this minute quantity significantly useful in most applications?" Typically, this resolution is not needed and the closest desired resolution may be +/- 5strain. In this experiment the student loads actual structures then examines the strains produced by the loading. Later, the student calculates the strains expected by geometrically derived equations and compares the difference in the two values. In the end, the student can provide evidence if the equations can accurately predict strains present in a structure and also if the strain gage/strain box combination is useful in the measurement of these strains. Theory Foil strain gages are essential elements in the measurement of small displacements of materials. Strain gages are constructed from a thin plastic film coated with a copper film layer. The copper film layer is etched away in a certain pattern to give the strain gage lines of conductive material. The direction of these conductive lines is the direction in which the strain is to be measured. The strain gage is mounted to a material with some type of adhesive. This can be epoxy, cyanoacrilate, or numerous other bonding agents depending on the host material. Strain gauges are mounted with the plastic film backing next to the material that is being measured. Once again, the lines of conductive material run in the direction of the strain that is to be measured. When the host material is elongated (or compressed) the lines of copper are stretched as well. With Poisson effects in mind it is easy to image the cross sectional area of the lines getting smaller and the overall length of the gage increasing. These two effects give a change in resistance to the strain gage. The change is resistance (strain) allows the transformation of a physical quantity into an electrical quantity. The change in strain typically may be only 1/10 Ohm at most. This presents a big challenge if one was to simply use an Ohm meter to gauge strain. A Wheatstone bridge, shown in figure 1, can be used in order to make this change in resistance meaningful. The gage is inserted in one “leg” of the bridge. The bridge is assumed to be balanced at a “no strain condition.” From there, when strain is applied, the complementary leg of the bridge is adjusted in order to re-balance the bridge. The amount of change in resistance used to re-balance the bridge is directly proportional to the strain that is being applied to the test material. Figure 1, Wheatstone bridge with strain gage in place.University of Texas at Arlington MAE 3183, Measurements II Laboratory Strain Measurement 4 RRRR4213 (1) Equation (1) gives the relationship to R4 as a function of the remaining resistor. In most bridge configurations, R3 is made close to R4 and R1 is made close to R2. It's easy to imagine that by correct selection of the resistors, R1 and R2 that a multiplier effect occurs in