the properties of the material as well so knowing the geometry of the system knowing the geometry of the cross-section knowing the material properties and knowing the theory from twenty-three-twelve you will be able to predict the stresses normal stresses shear stresses at this cross section where you have bending would shear at this cross section where you have pure bed now the purpose of an experiment is to verify to measure and use the measurements to verify a theory so since we can predict stresses the idea would be took to measure stresses and compare predicted and measured stresses
well the problem is that we can predict stress but we cannot measure stress right we cannot measure stress we don't have a way to measure stress particularly for a complex situation such as this there's no stress familiar but there's astronomical right you just learned how to measure strength so here's what we're gonna do knowing the state of strain stress predicting the state of stress you will be able to manage the predictor at any point on the cross-section strength so at any point you're going to be able to predict the strains now let me get into
that for just a second and make things very clear if you have let me start cutter if you have this I mean robot it is typical for beam bending to consider this to be the x-axis it is typical to consider this to be the y-axis and then in order for the system to be right-handed and Cartesian the z-axis goes this way therefore you have this plane being the X of Y plane this plane being the XZ plane and this plane which is the plane of the cross section itself is the y ou set point this
is the cross-sectional so when we measure strains or where they predict strains on this face which plane are we talking about and the answer if you are here should be its the xs/s point so the strains measure for the stress and strains that you predict and measure on this space are going to be in the XZ plane which means they're going to be X epsilon xx epsilon Zed Zed gamma XZ those are the meet them in the strains that you can measure at the point on the six when you talk about this space the lateral
face what plane is this well this would be like X or Y so this is X or Y which means that you're going to be measuring epsilon X X or predicting epsilon xx epsilon YY gamma X Y and then if you go on the bottom face it's going to be the same situation as here that's going to be still an Excel set plane and you're going to be able to predict so when using these equations you need to be careful and understand very clearly what stresses and what strains are you predicting on each particular face
so here's the battle one we're gonna have a beam made out of an aluminum alloy you're gonna learn what it is the cross-sectional dimensions are going to be provided the geometry of the entire setup is going to be provided the testing machine is going to be used to apply for point bending and we're going to show you in a second the specific configuration as a result of the application of load the beam is going to be subject to four point bending which means that in a center region there's going to be only pure bending in
the side regions you're going to have bending which shoots the stresses in each of these regions can be predicted using what you learn in 23:12 be careful which components you're predicting from the stresses that you predict you can use Hookes law and predict the strains okay so what are you going to have to for each of these two cross sections of the beam bending which shear and pure bending you're going to have into the follow you're gonna be awesome do this you're gonna be awesome predict just rains at three locations the first location will be
cute along the midline at the top the second location will be here at the middle of this face on the side and the third location will be on the bottom here so top center on the side bottom that those are going to be places where you're gonna need to predict predict the state of strength that's your prediction based on the theory of 23:12 and these locations we're also going to place some strain gauge rosettes and this is not a color that shows up very well so I'm going to use white again so there's going to
be one strain gauge rosette installed here one strain gauges the things falling here one strain gauge rosette installed on the bottom that's for each cross sections and again there are two such cross sections 1 corresponding to pure bending one corresponding to bending which you so you're going to measure here epsilon a epsilon B where X M epsilon C and C fact the labels are one two and three so you're gonna measure epsilon 1 epsilon 2 and epsilon 3 here you're gonna measure epsilon 1 epsilon 2 and epsilon 3 and here you're gonna make measure epsilon
one two and three top center and bottom top Center one for the cross section that has bending that is with shear or for the cross section that has pure better you're gonna be able to predict the corresponding shear strains here here and here for the two cases and you're gonna be able to measure these during the experiment you're gonna have to compare prediction and measure and by comparing prediction and mesh you're going to be able to draw a conclusion as to how correct how good are your prediction capabilities are your prediction is verified by experiment
does the experiment confirm support what your the theories that you learn in 2312 predict now before we go into the details of how you specifically do let me discuss something else how do you compare two states of strength let's say that we have a state of strain that is predicted and the same state of strain that is measured how will you compare two states of strangers you would say compare component by component right good in principle there's no problem with doing that but here's where things get tricky if you take this approach of comparing two
states of strength it's predicted that measured component by component you can end up drawing the wrong conclusions for the following simple reason you predict by assuming the particular reference system X or Y and you assumed that your measurements are performed precisely in the exact same reference system X ly in other words you presume you assume that you have glued your strain gauges perfectly aligned with the reference system that you used for prediction guess what there is no marking anywhere on the specimen as to the reference system that you use it your predictions and the small
misalignment that you may make may lead you to their own conclusions because if you rotate the two coordinate system by even something like five degrees three or four or five degrees you're gonna get different set of values you're going to get what looks like two very different states of strength so that's a problem so for that reason there is another technique that is being used and that is based on the concept of principle strength you remember from twenty-three-twelve that every single state of strains has a number of invariants some properties that do not depend on
change with the orientation of the reference system as you change the coordinate system the components of strain change but the invariants of strain don't and in fact principle strains are invariants so what you're going to do in order to perform a meaningful comparison between the two from these predicted
