00013

all right continuing now so we covered the aspect of measurement of stress which in fact is not the measurement of stress with youth rather an estimation of stress a calculation of stress based on Sigma is equal to PI over eight which requires as I was pointing out before the break that the area of the specimen stays constant in the gauge section that the specimen is straight and that the load is applied at the centroid of the cross section so that covers the aspect of stress measurement or stress estimation during the experiment the testing machine will

apply tension the tensile force to the specimen that is connected between the grips and by so doing it will develop a stress the specimen of a stress that the program the software will estimate based on this formula by the testing machine measuring the force using the load cell and you providing the cross section of your specimen as input to the program before the test starts let me now switch over the aspect of strength which should be simple and straightforward to begin with let me ask the following question one of erasing the board what is strength

and this is the point where I'd like you to make you pause and fall back on your textbook first of all fall back on what is already in your mind and that may be on the textbook it is necessary to remember or to read and learn what is strength all right I assume that you did that I assume that all of you have a definition of strain so I will offer you the definition of strain from my perspective strength is a measure a measure not a single measure but one measure of deformation so in order

to have strain one needs to have the information now you will remember that there are two kinds of strain normal strain which reflects change in size and shear strain which let's the changing shape so if I have for example a spherical ball the time that made out of say for example a rubber the time inflating as even as the result of applying internal pressure the sphere is going to become larger that's a change in size the shape remains the same so the strain that that's reducing is going to be normal strength on the other hand

if I have a slice of jell-o and you can imagine that I have a slice of jell-o in my hands and I apply a tangential load on the top so I'm producing a shearing effect then I'm gonna have a change of angle the slice of jell-o that we support on the ground when I apply shear force as this way will deform in this shape so that represents a change in shape or a change in angles that is associated with shear strength now let's go back and for the purpose of this experiment we only need to

be concerned with normal strain we're going to come back to shear strain in the next lecture it is very important but for now we're simply dealing with normal strength so you will remember I'm sure that epsilon is equal to Delta L divided by L is the definition of normal strength Engineering normal strength the change in length divided by the original length or the final length minus the initial length divided by the initial length right that's the definition of normal strength so you would think and you know that's the normal thought process that you could measure

strain by simply applying the definition you could measure the initial length of a part you could measure the final length of a part compute the difference to get Delta L divided by the initial length there's your answer and that in principle is very true however power this is the point where we're going to commit with the uncertainty discussion during lab number one and what you're gonna notice is that for this class time again we're gonna build upon previously acquired knowledge we're gonna use every single lab as a stepping stone for the next one so you

remember that if we perform a measurement using any of the methodologies you wish the ruler were using vernier caliper or using the micrometer there's going to be some uncertainty in fall so in fact when you measure the initial length what you're going to measure is the nominal DV which stands for initial length of that the nominal reading plus or minus ha because the SS the smallest scale division which represents the uncertainty in reading when we are going to measure the final days we're gonna get also the nominal reading to find the length whatever that is

which will stand for an actual final length equals through their reading plus or minus 1/2 SSD again these values represent the actual initial length and the actual final length which are the reading plus the uncertainty the reading plus the answer plus or minus the answer so that means that we need to compute Delta L in fact what they're gonna have to compute this L final plus or minus 1 over to SSD - le needle plus the minus 1 over to SSD which can be written as L final minus initial which is Delta L the difference

in length between the readings the nominal values and here we're gonna have plus or minus and we have to take into account the worst case scenario so the worst case scenario is plus plus plus half with the other half is one full SS e if you take minus minus it also has a plus half 1 SSD so what you see here is that the app and certainties in the worst case scenario whether to plus or without - add up so the uncertainty in the computed bail file are gonna be twice as large so the problem

here becomes the father right here that when I compute epsilon I'm gonna get Delta L divided by L initial which is also affected by plus or minus one over two SSD which is going to be L final the final the reading of the final length - they're reading like the initial length plus or minus 1 SS V divided by L initial plus or minus 1 over to ssleep this is the result for the strain that we're going to be measured now this up to this point everything is strictly correct there's an equal sign further we're

going to say the following this is approximately equal to and we're going to make the observation that typically compared to this to the nominal length this is a very small quantity let's say that the length that were you trying to measure the strain over is which is called the base length or thin gauge length the base length or the gauge length is not your one inch using a good instrument and we always try to use a good instrument which has very high precision this is going to be on the order of 1 over 100,000 h1

over 1,000 or 1 over 10,000 of an inch so this is going to be much small B I'm certain here is going to be much smaller than the base length as the consequence this can be neglected and the approximate answer that we get is LS minus L by the readings that this has between the readings divided by the original reading plus or minus one SSB divided by the original reading now this is the only approximate after here to the left everything is strictly correct to the right it's approximately true but the closer the smaller the

SSD is compared to the lie the more this is close to being true this here represents epsilon nominal the nominal reading of strain as computed by LS by the the difference in readings divided by the original reading whereas this here represents the uncertainty infection now let's see how large is that uncertainty and before we can go there and discuss that uncertainty in Epsilon let's first of all try to give a sense for what values of strain actually mean so first of all we said that epsilon is Delta L divided by that which is measured in

inches per inch or meters per meter or mile per mile so strain is non-dimensional there are no units first rate that's the first thing that I hope you remember the second thing in terms of numerical value epsilon is equal to 1 what does that mean the value of strain equal to 1 well that means that Delta L is equal to L or L final minus L initial value in other words L initial is equal to 2 times sorry L final is equal to 2 times L initial so a strain of 1 means that the final

length is twice the initial length that's the kind of thing that you would expect to be able to see from a rubber band you can take a rubber band with the given length put on it you double its length Robert can do that so the strain of 1 is something that you can measure