In this class, we are going to discuss about some numericals on noise, vibration and data acquisition. As by now, we would have understood the fundamentals of vibration, then little introduction into noise and of course, we need to acquire data so that we can analyze them on the computer. So, in this class, I am just going to give you six example problems, which normally we encounter while doing machinery condition monitoring and this through these examples, I will tell you certain simple tricks of the trade which has to be used while doing a machinery condition monitoring. So, the first problem is actually a very simple problem like what is the sound pressure level in decibel or dB of a plane wave at the end of 1 meter, if it is excited by a sound source of one Pascal at the other end. So, let me explain you this problem in the sense we have a duct, this is a long duct it could be of any length L. So, usually to give a source at one end, which is a plane wave source because the diameter of this duct D such that the frequency below which the plane waves propagate are given by this equation. So, 0.86 times speed of sound by the diameter of the duct. So, for example, our typical duct of diameter about 35 mm, this close comes to about 4000 hertz, this is typical. So, that means if I have a plane wave tube of duct diameter 35 mm. So, for any source whose frequency is less than 4000, I will be having plane waves travelling in this waveform, by plane waves I mean they are longitudinal, they are one directional. So, pressure at any cross section is the same, any point in the cross section is the same. So, this is a little tricky problem in the sense the sound wave, plane wave if it is propagating in a duct as long as the duct diameter satisfies this equation and the frequencies are less than 4000 hertz, I am going to have plane waves at the other end. So, this is the other end and thus the pressure will be the same if the inlet pressure is equal to one Pascal and the out load pressure p outlet will be also equal to one Pascal. So, in order now to express this Pascal's in decibel way you will use the formula as P L is nothing but 20 logarithm to the base 10 of P by P reference. So, P reference is 2 into 10 to the power minus 5 Pascal, if I plug P as one Pascal in this equation I will come up with an value of 94 decibel. This has a practical significance in the sense that in any problem or any special duct applications for example, I have an HVAC system where I have a blower giving in a conditioned air to a point say inside a room I have diffuser. So, if this diameter of this duct obeys this relationship that plane waves will propagate. So, any pressure here in Pascal will be the same sound pressure here in terms of this P is the sound pressure. So, we do not require any complication complicated formula to estimate the sound pressure level at the end of the duct as long as we know that it is a plane wave and plane wave conditions are being satisfied. The reason I told you about this problem is many a times in the industry we will come across such scenarios where noise is generated at one end and then we have to guess or estimate what is the sound pressure level at the other end and if you just by measuring the diameter of will ensure that the these equations obeyed where see the speed of sound in air at 20 degree Celsius I will know that this if these 35 mm and you can somehow calculate f is 4000 hertz. So, this can be calculated ok. So, now we will move over to the second problem which is again a very simple problem. This is an handheld accelerometer calibrator provides 10 meters per second square of peak vibration in terms of acceleration at a circular frequency of 1000 radians per second calculate the linear frequency and the RMS amplitudes of velocity and displacement provided by the calibrator. Usually to calibrate an accelerometer in the field it is actually mounted on a calibrator this is the handheld calibrator and this will give certain voltage or charge signal corresponding to this mechanical vibration is subjected and this vibration is typically about 10 meters per second square at a circular frequency of 1000 radians per second. The question is what is the velocity and what is the acceleration? As you know this is a pure tone of 1000 radians per second its frequency omega is sorry frequency linear frequency f is equal to nothing, but omega by 2 pi and this comes down to about 159.1 hertz ok. But I know the velocity magnitude for a harmonic wave is nothing, but the acceleration magnitude divided by omega and the displacement magnitude is nothing, but the velocity magnitude divided by omega R which is equal to the acceleration magnitude divided by omega square ok. So in this case we have our acceleration magnitude is 10 meters per second square and it says it is peak. So that means and if I was to plot the time history of such a signal. So this value a is nothing, but 10 meters per second square this is the acceleration waveform ok. So in this case the velocity is will be nothing, but 10 divided by omega is 1000. So this will come to meters per second. So this will correspond to 10 millimeter per second. So I am putting them in the box to explain to you later and similarly the displacement magnitude will be nothing, but 10 divided by 1000 into 1000 meters that is equal to 10 micro meter. So if my acceleration magnitude is 10 meters per second square for the same calibrator at 1000 radians per second I have velocity as 10 millimeters per second displacement as 10 kilometers. So to remember a good rule of thumb in the field is this is 10 this is 10 this is 10 only thing that we have to be careful about the units 1 is in meters per second square other is in millimeters per second another is in micron. So this problem has a second problem as to calculate the RMS amplitude and we know for a harmonic wave any general x is equal to A sin omega t the RMS amplitude x RMS is nothing, but A by root 2 that is 0.707 A. So to answer the second part of the problem find out the RMS amplitudes of velocity and displacement provided by the calibrator the V RMS would be therefore 0.707 times 10 millimeters per second that is 7.07 millimeters per second and the displacement RMS A RMS is equal to nothing, but 0.707 times 10 micron that is 7.07 micron. This is a certain handy numbers to remember in the field for example whenever we go to the field with this handheld calibrator which I had shown in one of my previous classes as to how this calibrator is actually used to calibrate accelerometers in the field all we know is we give a mechanical signal of 10 meters per second square at 1000 radians per second. We will just see the voltage output from this accelerometer and if we are going to calibrate in the displacement mode or in the velocity mode or in the accelerometer mode we will apply these actual mechanical values to this signal. So as to calibrate what is the voltage level corresponding to or what is the mechanical value corresponding to a particular voltage we would have obtained. Now we will move over to the next problem question 3 which says for a machinery having 90 decibel of sound power level compute the sound pressure level in dB and Pascal at a distance of 1 meter in the free field condition ok. Usually sound pressure level is denoted by SPL and sound power level by SWL and the general equation for the sound pressure level as with relation with sound power level is given by this equation that SPL is equal to SWL plus 10 logarithm based on of q theta by 4 pi r square plus 4 by r r c. This is a very important formula and I will explain you what these terms mean here. This is the sound pressure level we all know that this is the sound power level theta naught or q theta is the directivity r is the distance from the source r c is the room constant which depends on the amount of sound absorption in the room. So r c is given by this formula as alpha average by 1 minus alpha average in meter square where s is the total surface area of the room alpha average is the average sound absorption coefficient of the room. So in a room suppose I take a wall and I divide them into small patches and each one has a different alpha i and area of this is s i. So the average alpha average is nothing but s i alpha i is equal to 1 to n and then or the total area ok. Now this could be of different materials and they all could be having different alpha i for example this could be gypsum, this could be fiberglass, this could be jute of course nowadays you know we have found out that jute and its derivatives are good sound absorbers also. So anyway just to come back to the problem which we are discussing so we can have the room constant like this. So if the room was totally absorbing or there was no sound which is generated so for example this is a room and I have a sound source and these are walls which are treated with sound absorbers and then we have a good amount of absorption in this walls. So and this was in the center of the room a typical case in this case your absorption is the maximum so your RC is actually close to infinite ok. So the second term 4 by RC because the room constant actually disappears in a case where it is totally absorbing that means there are no echoes or an anechoic condition have been obtained and this is essentially what is known as the free field condition. So only in the case of a free field condition this problem will become so SPL will become SWL plus 10 log 10 q theta by 4 pi r square plus 4 by RC. So this will become 0 in the case of for free field condition and if it is in the center of the room if the source is in the center of a room if it is here in the center of the room q theta is equal to 1 in the center of the room is equal to 2 in on the floor of the center of the room is equal to 4 if it is on the center of the this is 2 this is 4 this is 1 floor this is on the center of edge between wall and floor and this is equal to 8 it is the corner between walls and floor. So by this I mean the vice versa also you would have realized in because from the reciprocity relationship suppose you are standing in sorry suppose you are standing in a room in the center of a room I will just draw one plane suppose you are standing here and I move your loud speaker to this location here the directivity will increase and you will hear it to be louder then I put it in the middle of the room because of the directivity issues you know this is just explain. So in other words if I come back to this problem in this case SPL is equal to SWL plus 10 log 10 q theta by 4 pi r square plus 4 by r c it has been told this is free field condition. So free field condition means this this will vanish and the center of the room if I take so q theta will be equal to 1 excuse me in the center of the room excuse me and at the distance r r is equal to 1 1 meter my expression will come up to SPL is equal to SWL minus 10 log 10 of 4 pi. Now some of the important things we have to observe from this case because here I have taken q theta is equal to 1 so log of 1 is actually 0 so it will disappear and this value will be approximately equal to 10 decibel. Again a good rule of thumb, thumb rule which we should follow is in any free field condition now what are typical examples of free field conditions one is an echoic chamber other is here. An open field in fact many times we do lot of noise destructing in open field wherein we do not have any reflection there has to be no reflections. So you can pretty much understand the SPL at 1 meter away from the source will be actually SWL minus 10 decibel is equal to SPL. So SPL is something constant to a particular machine it is the inherent noise quality of the machine which is fixed. So at 1 meter away from the sound pressure level from the source the sound pressure level will be whatever the value you have in SWL in decibels you have to subtract it by 10 dB ok. Of course, we have to keep in mind the SWL dB and SPL dB they have different references and there is something you have to find out. So SWL is actually 10 log 10 of W by W reference where W reference is actually 10 power minus 12 watts you have to keep this in mind. So in this problem the machinery was having 90 dB as SWL the SPL would be close to about 80 decibel in free field conditions at distance of 1 meter. So through this example I just introduce it to few concepts of room constants which is very important in machinery environment as to we will be called to monitor the noise of machines which are having certain defects. So we have to be careful about the what conditions in which we measure the sound pressure level because if the environment changes the sound pressure level will obviously change like we saw it depends on the directivity it depends on the room constant. So whenever we want to monitor the health of a machine by noise monitoring it is always recommended that we actually always do the measurements in the same noise environment otherwise there will be no apple to apple or orange to orange comparison unless we follow the simple rule. And that is why through this example I just showed you how the room constant the distance from the source and the directivity does affect the sound pressure level which have been measured. Now we will move over to the next problem this is again a simple problem on vibration that is question number 4. A machine can be modeled as a single degree of freedom spring mass dash pod system if the machine is operating at 1200 rpm and has a mass of 100 kg and is supported on 4 linear springs each of stiffness 25 Newton per meter and an overall damping ratio of 0.03 determine the damped natural frequency of the machine. See this is a machine a mass and supported on 4 springs I am just showing a 2D plane view so I am not showing the other 2 springs. So the effective springs because there are 4 springs k effective nothing but 4 times k and the value of k is 100. So this becomes 400 Newton per meter and the natural frequency of this system omega n is equal to root over k by n and that happens to be 400 and mass is also I just did a mistake here this will be actually k is 25 so this is 100 so 4 times 25 so this will be 100 divided by 100 so this will be 1 radians per second. So now the damped natural frequency of the system is given by this expression so we have found out the natural frequency as 1 radians per second so damped natural frequency is 1 times 1 minus 0.03 square and this will be somewhere close to about 0.95 radians per second. It is a very simple example where we are just used the formula to find out the natural frequency of a system and the damped natural frequency of the system. Now many a times what happens that of course there is a fact that in this machine was running at 1200 rpm. So if this machine is running at 1200 rpm the forcing frequency omega forcing is nothing but the frequency of forcing frequency is nothing but 1200 by 60 Hertz 20 Hertz and omega is 2 pi into 20 this is 40 pi radians per second. Many a times just by estimating the mass of a machine and estimating the springs the stiffness of the springs we can get some idea as to what is the natural frequency of the machine. Particularly in many machinery condition monitoring situations the defects occur because unknowingly or unknowingly while I would say unknowingly somebody is operating the machine at its resonant frequency or the designers did not take care of certain issues in mounting which would have been introduced. So that the stiffness change the damping change and then the natural frequency of the system happens to be close to the forcing frequency and then a condition of resonance occurs and because of resonance will have large motions and then there will be failure in the machine. So a good way to estimate the natural frequency of a system is through experimental model analysis which we would have discussed in one of these lectures. But just by knowing the mass stiffness and usually some guess on the damping we can estimate the natural frequency because vibration is such a phenomenon which is dependent on these three parameters and we cannot neglect it and the phenomena of vibration is actually very much frequency dependent. This is the dynamic magnificence in factor x by x naught and r is nothing but omega by omega n where omega could be the forcing frequency and this is the natural frequency. So the dynamic magnification factor is always given by 1 by 1 minus r square whole square plus twice zeta r square where zeta is the damping ratio. In this case zeta was given as 0.03. As you see the phenomena of damping is very much dependent on r and r is nothing but the forcing frequency ratio of the forcing frequency and the natural frequency. So these simple formula helps you know the dynamic response of a machine knows helps you to estimate the damped natural frequency and you can also see how the machine is going to behave as a function of frequency by plotting the dynamic magnification factor. So these are simple things which one needs to keep in mind while doing machinery condition monitoring or doing machinery fault detection. So just to summarize you know we just saw two examples each from the classes of vibration and noise as to how simple equations gives us insight into handling few numbers be it in noise be it in vibration and how these numbers can help us do a better estimation or better assessment of the machine's health condition. And these are a very very preliminary and rudimentary problem which one needs to be absolutely sure about because later on in machinery condition monitoring we will be building on some of these very very simple equations and if you remember this you know this will help you go a long way in doing actually machinery troubleshooting. Now we will come to two different other classes of problem which is this on computer aided data acquisition in the acquisition. So coming to the fifth problem this says a pure tone signal of 2200 hertz is to be digitally acquired by a 16 bit computer aided data acquisition system. So what is the minimum amount of onboard RAM that is random access memory required to store the digital data in the digital data acquisition system so that the frequency resolution of one hertz can be obtained by performing analysis on the acquired time domain signal. As you know this equation there are two three concepts which are being in this problem we require two three concepts to solve this problem. For example, I have a pure tone by a pure tone I mean a signal of a single frequency and this pure tone signal is of 200 hertz. So by Shannon's sampling theorem without worrying about over sampling and all that my sampling frequency f s should be equal to at least twice of f max. So in this case it is 400 hertz is my sampling frequency because that is something I have to keep in mind and in the next part of the system it is a 16 bit computer that means one digital data point will be stored in 16 bit spaces or that corresponds to 2 bytes because 8 bit is equal to 1 byte ok. Now the question is this signal pure tone signal which has been sampled will be processed digitally into the frequency domain so that the frequency domain resolution delta f is equal to one hertz ok. But we know there is a relationship between the delta f and the block of time data which you have taken because this data which has been digitized so I take this digital data I take n data points this total time is nothing but n times delta t where delta t is nothing but one of the one by the sampling frequency this is known as the sampling interval this value is delta t. So in the frequency resolution or in the frequency spectrum because this is a pure tone these values we get certain digital value and then we join them. So typical spacing between any two consecutive point is delta f certain amplitude ok. So there is a inverse relationship between the time and frequency and that is the most fundamental relationship this is a very very important relationship.  Here of course we have done an assumption which is normally not true that we have just f f t on one block of data because no information is given whether we are going to take more blocks of data and so on. So just assuming that one block of data is being used we have to take 400 data points. So each data point requires two bytes of space so total space total space is equal to twice two times 400 that is equal to 800 bytes but as you know memory is available in 2 to the power some power. So the closest highest power will be actually 2 to the power 12 or 2 to the power 10 that will be 1000 to 4 bytes or which we known as 1 kilobyte. So to analyze such a signal I will require 1 kilobyte of RAM space many times in a students give answer as 800 bytes and I would normally prefer that the answer is actually 1 kilobyte and close not one not 800 bytes but 1 kilobyte because you will not get 800 bytes of memory to my in the market. So this is how you can decide on the number of the RAM requirement and you would have known in the FFT analysis if we buy the signal analyzer they are sometimes specified by the lines of FFT. So you say 400 lines 800 lines ok this actually correspond to 400 by 2.56 this corresponds to about times 2.56 about 1024 data points. So more lines in more data points means more memories and you would have seen when you buy of course nowadays you know we have system with 6400 lines available the present day systems. So many times some of these FFT analyzers are actually on chips or on IC chips or processors thus this kind of an example helps us understand what is the numerical requirement in terms of the memory storage for data equation. As you know in data equation system two most important parameters are the one is the sampling frequency the resolution of the card in terms of you know whether it is 16 bit 12 bit etcetera. So this are very important I mean if you have a mistake in the sampling frequency you have erroneous sampling frequency you have the problem of signal aliasing and if you have do not have a adequate resolution you have what is known as the quantization error. So looking back to the this previous problem so this means if you want to have one hertz resolution we have to have more spaces. Next question is suppose I wanted to have 0.1 hertz you will see how your memory size will increase n is equal to FS by delta F. So in this case it will 400 by 0.1 so this will increase by about 4000 ok. If you want better resolution we have to have more memory space ok so this will this is what is going to change isn't it. So we have to keep that in mind ok. So better resolution means more memory space and these are there deleted. Now I will come to the next and the last problem on this topics that is what is the gain in a signal conditioning analog amplifier required so that a 12 bit data equation system with a maximum input analog voltage range of 10 volt can acquire a signal of 1 micro volt amplitude. So this comes the problem because see I have a machine I put a sensor and it gives me some analog voltage ok voltage. Now I have a A to D system and then which gives me digital data which goes into a computer. Now obviously this A to D system has a minimum voltage which it can sense that is known as the resolution and this resolution is given by what is known as the maximum voltage it can sense the range by 2 to the power bit size where this is the bit size. So that is the lowest voltage it can sense. So in this case if this range is 10 volts I have the bit size as 12 so 2 to the power 12 and this corresponds to about 2.44 and 10 to the power minus 3 volt that is 2.44 milli volt. So in other words a 12 bit DAQ system with 10 volt range can only sense or detect minimum of 2.44 milli volt. So I have a big problem in hand my I have been asked to acquire 1 micro volt that is my actual analog signal a very low temperature thermocouple signal will give you this kind of a value and suppose you want to detect such a system and you want to acquire it remotely or through a computer aided data processing the problem is is your 12 bit system good enough to sense it. Obviously you see because to 1 micro volt is much much less than 2.44 milli volt it cannot sense. There are couple of ways we can do it I can increase the bit size instead of 2 to the power 12 I can make it 2 to the power 24 in a 24 bit system that calls of course for a new hardware new DAQ system sometimes that may not be possible but nowadays 24 bit DAQ systems are available and so to have good enough amplitude resolutions I have to always increase the bit size if that is not possible in between what I can do is I can have a very nice analog amplifier with high signal to noise ratio so that I give my 1 micro volt and I make it at least 2.44 milli volt or more. So, I have to amplify I have to multiply with some gain. So, this analog amplifier the question is what is this gain so that a 12 volt system is going to register 1 micro volt obviously. So, the gain of the amplifier would be nothing gain of the amplifier is nothing but 2.44 into 10 to the power minus 3 volt divide by 1 micro volt 10 to the power minus 6. So, this is equal to 2.44 into 10 to the power 3 is 2444. So, this is the gain. That means, if I have a 1 micro volt signal I multiply with this value of gain I will get 2.44 into 10 to the power sorry this is plus 3 minus 3 volt which can be detected and sensed by the DAQ. So, we have to keep this in mind while we have to select on a certain data acquisition system. So, in summary on this class we just looked into 6 example problems typical example problems couple of them from noise couple of them from vibration and couple of them from DAQ system as to making us familiar on some of the important concepts on data acquisition signal aliasing quantization error conversion of SPL to in P Pascals to decibel. How do you relate sound pressure level to an estimate sound pressure level from sound power level? What is the meaning of dynamic magnification factor? How do you estimate natural frequency damp natural frequency? So, with this kind of an understanding we are ready to go to the field to do some actually troubleshooting and in the subsequent classes actually will be discussing about how machine monitoring is done through vibration how faults are detected by vibration monitoring. Thank you.


I'm sorry. I could find a good time. If I turn my... I actually... I know somebody who can. I will come. He will be 99. Okay, no problem. He made a big difference in my application. She's also... Really? She should be there for six months. All right. Okay, everybody's here. All right. Good afternoon. Welcome to the Durham City Council Planning Commission. The members of the Durham Planning Commission have been appointed by the City Council and the County Board of Commissioners as an advisory board to the elected officials. You should know that the elected officials will have the final say of any issue before us tonight. If you wish to speak to an item tonight, please go to the table on my left and sign up to speak. For those who wish to speak, please state your name and your address clearly when you come to the podium. Please speak clearly into the microphone because you'll be in televised. Each side, those speaking in favor of an item and those speaking in opposition to an item will have 10 minutes to present for each side. The time will be divided among all persons wishing to speak. Finally, all motions are stated in the affirmative, so if a motion fails or ties, the recommendation to the elected body is for the now. Thank you. Could we have the roll call, please? Mr. Alturt. Mr. Brun. Mr. Busby. Ms. Freeman. Mr. Gosh. Mr. Gibbs. Mr. Harris. Ms. Hyman. Mr. Johnson. Mr. Kinchin. Mr. Miller. Mr. Van. Mr. Whitley. We have a quorum. Thank you. Are there any adjustments to the agenda? Yes, Mr. Chairman. If I may suggest, it's my understanding that in our agenda item 7, the Creekside Commons case, we have a simple procedural request. Just looking at the audience, it is my assumption that there are a great many people here who have come to hear that case. Would it be convenient for them and for us to go ahead and hear that procedural request and dispose of that before we do go into our regular cases in item 6? Is that a motion? That's a motion. Is there a second? Second. The motion is to move item 7 before item 6. Move item 7 before item 6. Are there any comments or questions? Yes. I understand the point, although there are a lot of people here to speak on that topic, I mean, we do have a case in front of it and they are in front of it because they were presumably filed first or whatever, and I wouldn't want to make those applicants wait until the end of our Creekside Commons hearing. I'm assuming that the people here do want to speak on it. That makes sense. Actually, my motion was based upon the assumption that they wouldn't speak if they were to be wrong. Okay, the motion on the 4 is to move item 7 before item 6 or the additional comments. If not all in favor of that motion, please raise your right hand. That's 9. All opposed. Motion carries 9 to 5. Okay, and one additional thing under announcements which you don't have under new business, that's address November the 8th which is election day and our meeting day. So let the board address that. Okay. The chair will now entertain a motion to approve the agenda as modified. Mr. Chair, I make a motion to move the agenda as modified. Second. Second by commissioner Friedman. All those in favor say aye. Aye. Opposed? Aye. The next item on the agenda is approval of it August the 9th meeting minutes comments. If I may, Mr. Chairman. My comments and I believe perhaps Ms. Hyman's comments were left out of the material. Not this time. My comments were left out and my only concern is that going forward those comments be included in the materials that we send to the council and staff is assured me that those are there even if they are not in the packet we are voting on tonight. Is that correct? That is correct. Thank you, Mr. Chairman. I'm satisfied. Okay, I'm there. No more comments. Yes. I just wanted to move approval of the minutes as presented. Mr. Chairman, I do have a change. Okay, it's been motioned seconded that we approve the minutes as presented and we have a comment from Commissioner Gibbs. Well, my note re-elected should be changed to re-evaluated. It's on the first page my vote. Gibbs voted for development. Entire 100 plus acres should be re-evaluated. Thank you, Mayor. Okay, the motion will you accept an amendment? Yes. While we're at it, my name is spelled wrong on the same page. Okay, did you get that? Okay, would you with a maker of the motion I mean his motion to include the corrections? I move the adoption of the minutes as corrected. Motion is seconded that the minutes be received and approved as corrected. All those in favor say aye. Opposed? Aye. Okay, the next item on our agenda is item number 7. The public hearing will open the public hearing for the zoning map change request for Creekside Commons Z 16 quadruple 01. And we have a new staff member during the presentation. Bear with me. Yes, please bear with me. Steve Medlin with the planning department. I am filling in for my entire staff which happens to be in Asheville this evening at a national, I mean a statewide conference. Yeah, fortunately they get to go and I don't. This case is case Z1601 which is Creekside Commons which is a request by NDR Ryan Holmes Stephen Freeman to rezone the current site from RS 20 to a PDR 6.302. Earlier today the staff received a request and I think the planning commission received a request from the applicant to consider a 30 day deferral of this item. Staff obviously has no issue with a deferral being granted for this case in order for the applicant to modify their development plan and to potentially work with the adjacent property owners and citizens in the area to address some of their concerns. Staff will be glad to answer any questions that you may have at this point but we're going to reserve our full presentation until this item potentially this issue is decided. Thank you. I have two people wishing to speak in favor of this item and five people wishing to speak against. Okay. I understand the applicant may have a motion to for consideration. Good evening Mr. Chairman members of the planning commission my name is Ken Spaulding. I represent the applicant in there. I was just brought into this case last week and so was Mr. Stan Jel and we saw that there was some needs to meet with the residents again as well as some cleaning up some issues in regard to our commitment, our committed elements to clear that up with staff. I would like to reserve any further presentation unless or until we have to go further based on you all's vote but I think it's very important for us to make sure that we have met with the residents again since we are now involved with this and to hear them out completely and to see what if anything we can do to address their concerns. It's clear from some emails I've read it's very important to them about some issues. We need to understand the issues better and we need to be able to explain the situation better and to get as much input to make any modifications if they're going to be possible. So I would respectfully request that and move that this be continued over deferred over for 30 days. Thank you very much. Commissioner Bryan. Is we open to discussion on this? We have not closed the public hearing. Okay. Before we bring before the commissioners he's making a request he's not making a motion the motion will have to come from someone up here. So he's making a request for a continuance for 30 days. Now before I close the public hearing there were five people from the community that signed up to speak and against. If the motion is granted the request is granted. They're going to have 30 day continuance in other words it will come back in October. If the motion is granted and moved upon we will not make any decision on it tonight. And my question to the five people that signed up to speak and against is there anyone that just would like to speak tonight with reference to this or wait until October to speak after the full presentation has been made from both staff and the applicant. Come to it Mike please. And state your name and address. As Michael. Greetings. Greetings members of the planning commission. My name is Mike Cutlip. I'm a resident at nine T House court in South Durham. My only question is not to speak necessarily to the proposed development but to the possibility of 30 days not being enough time to meet with the residents in the area and address the concerns that they have. I don't know if there could be a motion for possibly 60 days. You can request a 60 day continuance. I would like to request a 60 day continuance instead of 30 days. Thank you. So we have two requests. We have a request from the applicant for 30 day continuance. We have a request from the community for 60 day continuance. So if no one else wishing to speak I'll close the public hearing and bring it back before the commissioners and hear what the commissioners commissioner Brian. I agree with the community based on what I've read so far from the neighbors and looking at the plan for 60 days is going to be even pushing it to really get this cleaned up if it's even possible to clean it up. So I'm going to move that we reopen the public hearing and continue it for 60 days. It's had a motion for continuance for 60 days. I have a second from commissioner Miller. Is there any other discussion? Commissioner Whitley. Is it possible who's here for transportation? Bill Judge. Creeside Elementary School in the mornings and the evenings the cause are in a parking lot.  Let me ask one question. The discussion the motion on the floor is for continuance. You're asking about the project. You're speaking to the project. I'm wondering whether I know it doesn't fit the criteria for transportation but you're still asking about the project and not the motion is on the floor. The motion on the floor is whether to grant a continuance or not.  Mr. Chairman, I wanted to get some business done in the 60 days. Are there other comments? Commissioner Goesch. Thank you, Chair Harris. My comment is that without I know we all received emails and have read the report and all of that but without opening the public hearing I don't know how we can make a determination that 60 days would be required rather than 30 days and I think just from a practical standpoint if they are not able to resolve the issues in 30 days then they would come back and ask for another continuance which they would be able to do. So I'm inclined to not vote for a 60 day but to vote for a 30 day continuance because it is possible that they would be able to meet with the neighbors and address their concerns in that amount of time and I don't see any reason to push it out 60 days if they can do it in 30. Thank you. Commissioner Freeman. Can I ask the question of the representative that was speaking? Is it speaking to the motion or is it speaking to the project? Specifically to the motion. I just want to know if you think the property owner or whoever is working on this project would be amenable to 60 days rather than 30 days and it doesn't matter whether he is amenable or not. We say 60 is 60. I just spoke with the developer and he truly feels we can get it done in 30 days but that's it. May he just respond to that person? Sure. My name is Britt Spivey and I'm an applicant. The only reason I think that 30 days is reasonable is that there's actually been a meeting with the homeowners already that took place and actually some of the text commitments came from that meeting. We also have people here in support of the project too that would rather see it happen sooner than later so I'm willing to act as quickly as possible with West and Downs to have a second meeting. Do you have meeting dates already lined up? I do not. So I think that the 60 days might probably work better then. If 30 days does not work, I agree. Thank you. Any other comments? If not, the motion on the floor. Commissioner Johnson. I'm just curious to the resident who requested the 60 days could he provide insight as to why he doesn't feel that 30 days is enough time? Let me do that. They have to have information in for the agenda two weeks prior to the meeting so right now from tonight they would have like a week or a week and a half to get the information in to staff for the October meeting and so even if they had the meetings already lined up it would still be tight and pushing it in order to get the material into the staff in time enough for the October meeting. They only have about a week and a week and a half. That's very helpful. Thanks. Any other comments? Can I speak one more time? Yes. We're fine with 60 days. If that's what it takes to make the council happy and to give the neighborhood a chance to schedule a meeting then we're fine with that. Thank you. It's for case number Z16 to have a 60-day continuous to our November meeting. Whatever day that is. It may not be 60, it may be but to our November meeting so all those in favor of this motion please raise their right hand. Thank you. And thank you neighbors for coming and thank you for granting us this lead way. And I also thank the people from Ellis Road Townhouses for allowing us to do this. Mr. Chairman. Yes. Now would be the time for me to talk about the possibilities between here and the 60 days. Okay, ma'am you need to speak up. You're being televised. I want to ask a question about getting a staff evaluation of traffic right there by Creeside Elementary School that backs up and creates a one name traffic instead of two lanes. Bill. Bill Judge with transportation the only thing I can really answer is that the ordinance has very specific criteria for when we can threshold for when we can require a traffic impact analysis. This site is currently presented is under that criteria so there's no basis for us to require any additional traffic impact analysis or study. If in conversations with the neighbors or the commissioners and ultimately the city council those are concerns and those are certainly things that the applicant can volunteer and provide but there's no ordinance requirement for it. Mr. Chairman I came from Chapel Hill Creeside Elementary School to come here and there's no way they can do that project without some traffic calming. Mr. Commissioner again I'm going to rule you out of order because you're speaking to something that's not on the floor right now. I'll bring it back in 60 days. Okay the next item is public hearing open the public hearing for Ellis Road Townhouse A16 Quadruple 03 and Z16 Quadruple 04 Good evening I'm Laura Woods with the planning department I'll be presenting both cases this evening and these cases were previously before the commission on July 12th 2016 the case was deferred two cycles because the applicant a new commitment at that time so we're bringing back the cases this evening my presentations will be slightly different this evening since you've seen the full presentations before I'm going to present a slightly abbreviated version hopefully you will remember the case well enough that if you do not and would prefer me to pull up the PowerPoints from July we can certainly do that to look at the maps Case 1600 003 Ellis Road Town Homes is a proposed amendment to the comprehensive plan for four parcels comprising 25.6 acres generally located in southeast Durham at 2511 Ellis Road it's directly east of the southern rail corridor in north of Ellis Road as I stated this case and the associated zoning case were deferred two cycles owing to some issues that have been resolved I'll touch on this more fully when I discuss the zoning case subject side is presently designated low density residential that's four dwelling units or less per acre the applicant Ellis Road residential to LP request a designation of low-medium density residential that would raise the density to four to eight under the intended land use as a town home community to the north of the site is recreation and open space to the east is single family residential and town homes to the south is vacant a single family residence and multi-family residential and to the west the aforementioned rail corridor and vacant land as staff concluded in July when we did the full presentation we find the proposal consistent with the four criteria for plan amendments those being the proposed change would be consistent with intent the intent goals and policies of adopted plans the proposed change would be compatible with surrounding land uses and future designated land uses the proposed change would not create substantial adverse impacts in the adjacent in the adjacent area and the subject site is of adequate shape and size to accommodate the proposed use therefore staff recommends approval of the plan amendment that concludes my presentation on the plan amendment we will now move to the next case the associated zoning case Z16 00 004 here the applicant is requesting a change from a residential suburban 20 to PDR or plan development residential 7.55 a voluntary and accession petition has been submitted in conjunction with this request the case is clear of comments at this point and the applicant and city have agreed the extension agreement the development plan associated with this request includes the following following commitments it will be townhomes to a maximum of 165 dwelling units the new commitment in the development plan is that units containing garages shall utilize a decorative garage door design including but not limited to windows or carriage style doors I believe that was a point of contention in July so they have addressed that there are four access points on the development plan there are three preservation areas and a maximum on pervious surface of 60% text commitments include widening of Ellis Road for an eastbound lane and continuous three lane cross section from Taylor Ridge Drive to the proposed site access number three four feet of additional asphalt on Ellis Road for accommodation of a bicycle lane a bus shelter and design commitments staff determined that the proposals meet the requirements of the unified development ordinance and should the plan amendment be passed it would meet the comprehensive plan as well that concludes my presentation thank you very much I'll turn it back over to the board Susan can I get your sign up sheet and she came to get back okay we have three people signed up to speak all is in favor of the project so I will entertain three minutes each or roughly four minutes each for each of you to present Lara Holman thank you members of the planning commission again my name is Lara Holman with Spalding and Norris representing the applicant thank you very much for allowing us to come back here this evening in just a response from the earlier agenda item 60 days was very helpful so thank you we take away from the last planning commission meeting as the staff member stated we were able to work out and finalize the utility extension agreement with the city that has been done and is finalized and is poised to move forward with rezoning and annexation to city council so we're all finalized there the second item on the list was to work with staff to work out a design commitment speaking to a decorative garage door and as the staff member stated we have done that as well that has been stated and added to our published and finalized development plan so that has been done as well thank you very much Steven William Stevens good evening Mr. Chair and also members of the commission my name is William Stevens I've been serving as the pastor of the south side church since 1982 we are located on Elmira Avenue where we also house a private elementary school that provides affordable education to the community when we purchased the property on Ellis Road we did so with the intent of developing the 25 acres to help meet some of the needs we saw that existed in that community however due to reasons beyond our control of the property on the market when we were approached by the builders we had no idea who they really were after speaking with the representatives of the Halley Company it became clear that their intent for the property is similar to the vision we had in mind except for church building and school I discovered they have a great reputation and what they are doing in that part of the community they have done projects in Apex as well as Holly Springs a project different from the one they have in mind I do believe housing options are important in this area with this close proximity to the RTP these townhomes will complement the existing residents as well as professional office and campuses nearby my understanding is the project is meeting all development requirements by agreeing to everything the city has asked in terms of roadway improvements on Ellis Road as you told the extensions in my honest opinion this will greatly improve that area thank you very much thank you and Isaac Woods Isaac Woods is anyone else in the audience that wants to speak to this item if not then we will close the public hearing and bring it back before the commissioners that we have commissioners wishing to speak we have commissioners wishing to speak Commissioner Goosh just quickly I want to thank you guys for making the changes and working to finalize your utility extension agreement with the city I know those were the primary outstanding issues that we had when it was before us two months ago so I commend your efforts in getting those things resolved and I plan to vote in favor of this whenever a motion comes available okay if this Commissioner Miller I have a question if I may of the developer if you could come to the mic I'd appreciate it it looks like your building envelope line is co-equal with the railway 200 foot right of way line if the railway were to expand in that right of way is there any plan or anything to provide any kind of planning from your property to protect your residents from the potentiality of an expanded railway usage inside that right of way sure I understand your question we have talked about that and of course you know we delve into that when we get into our level four site plan but certainly there is we believe some area some variation where we can provide some sort of buffer for that I don't have a lot of experience with railway rights of way it seems like 200 feet 100 feet is a lot and I don't know what they're playing whether they plan to expand the tracks or usage in there so that was just a concern I had then the last question I have if I may Mr. Chairman is I see that you have a potential crossing point for that creek or stream that runs through there would you carry your roadway over like on a culvert or as a bridge what have you got in mind for that culvert yes culvert thank you that's all I have any other comments questions if not to entertain a motion Commissioner Bryan please don't leave are you planning to have any amenities for the residents of these townhomes yes there will be some sort of amenity it may be a playground area but it certainly will be a developed amenity feature for the residents because you have no commitment on your development plan for any amenities so you can state what you just said at the public hearing but there's no way to enforce it no I mean I would certainly be able to comment that when we get to site plan and see what's actually before you at that time we don't see the site plan right I understand and the pastor said something about a mixture of housing in the area and everything will any affordable housing be part of this development for sale market rate townhomes no affordable housing thank you any more comments Mr. Chairman then I move that we send case A16 quadruple zero three forward to the city council with a favorable recommendation second second by Commissioner Miller second by Commissioner Bryan that we send to the elected body with a favorable recommendation all those in favor please raise the right hand all those in opposition in zoning case if I may Mr. Chairman I move that we send case Z16 quadruple zero four forward to the city council with a favorable recommendation and Mr. Medlin before I finish my motion this case does go to the city council with a favorable recommendation all right thank you we send it forward to the city council with a favorable recommendation motion by Miller second by Commissioner Whitley that we send Z16 quadruple zero four forward to the city council with a favorable recommendation all those in favor please raise the right hand all those in opposition okay the next thing on our agenda is the election of chair and vice chair for the next year and according to our bylaws that's done by the planning director or his designee good evening again Steve Medlin with the planning department at this time I'd like to open the four for nominations for the chair I nominate Commissioner Hyman for chair second have a motion to second any other nominations hearing none all those in favor please signify by saying aye aye any opposed but the record reflected was unanimous vote that Ms. Hyman has been elected chair vice chair vice chair now elect vice chair I understand I'm not leaving yet just pick it up my favor at this time I'll open the floor for nominations for vice chair I nominate Mr. Busby for vice chair any further nominations hearing none all those in favor of Mr. Busby please indicate by saying aye any opposed let the record reflect that was unanimous vote of Mr. Busby for vice chair congratulations congratulations to the both of you okay the next item on the agenda is new business and I added the November the 8th how the commission want to address that do we want to move it out a week yeah yeah I'd like Mr. Chair if I may I'd like to hear the staff's recommendation but I would strongly like to not have our meeting on election night especially while the polls are still open but I'm open to when we we move it it is solely the board's decision as to when you want to have the meeting we just need to know well in advance to ensure that we can secure the venue and also make sure that we do all proper notice according to general statute we haven't noticed anything already we have not so at this point we are we're two months out so we have plenty of time to work through the logistics in terms of preference obviously the staff would prefer either a Tuesday or Wednesday night just simply because it doesn't conflict with other boards and commissions that we may be serving that evening whether you want to move it to the Wednesday following the election or the following week certainly or whatever is the discretion of the body Commissioner Miller I was wondering if anybody on the commission had any strenuous objections to proceeding on the 9th which is the closest day to our regular schedule I have in mind that we have continued that one K 60 days with the gracious consent of the developer who wanted 30 and I thought that one day's delay would be more acceptable to them under the circumstances in a full week no problem motion it I just wanted to make sure it was if somebody on the commission really had a strenuous objection that we okay I was just going to ask if it might be possible to move up a week to like the first and similar to your thought process and shorten in the 60 days a little bit I don't know if that works for everyone but so that would be the second that would be the November 1st that doesn't cause any problems from the staff perspective to move it up a week if I may then Mr. Chairman I move that we move our regularly scheduled planning commission meeting from November 8th to November 1st at 5 30 in these chambers if they are available and if they are not available on that day that we instead have a ready alternate for the staff to work with that we move that November 8th meeting to the 9th to these chambers at 5 30 p.m. let me have one motion you did a compound motion and I'm not going to accept that well I just think that since we are not coming back and if the staff can't get the chambers they might like to have two dates to work with one is a primary and one is a secondary so if I may interject Mr. Chair I think it's certainly reasonable for staff to assume that we will be able to find a venue whether it's this room or another venue within city hall or even the county building that would suffice though we may not be able to broadcast if we don't get this venue but we certainly can work to get a proper venue for your meeting on the first under those circumstances Mr. Chairman I withdraw my motion and move that we move our November 8th meeting to November 1st at a venue that the staff finds for us 5 30 p.m. Second. Motion is seconded that we move our November meeting from election night to a week earlier which would be November 1st any additional discussion all in favor please raise the right hand that was an opposition 13 to 1 so we had one no vote right Johnson no vote Mr. Whitley I did not get Mr. Johnson's vote yeah that's no vote so it was 12 12 to 2 okay so the motion carries so is there any other new business whether you have what's coming up next month sadly I don't really have an answer versus the staff going commission of middle Mr. Chairman with Mr. Judge still here and I think perhaps consistent with where Mr. Whitley was going with regard to the case 16 quadruple 0 1 the Creekside Commons case it would be great I would like to know in preparation for that case to know if there are reasonably current traffic counts for Farrington in the area and Ephesus Church Road in the area to have that information whenever you can make it available between now and the first and if you foresee a problem with using that information and evaluating this case tell me what that is so I'll be armed certainly right now the information in the packet is the best information we have available however as you probably noticed it is 2013 data and generally by about this time of year we usually have the 2015 so we're expecting it any day so certainly if we get it between now and the November meeting we'll update those numbers and those figures not only for this case we do that routinely for every case is it never mind thank you very much Susan I do have one additional item for new business and I would like to move to the mic to read a resolution of appreciation for Mr. David Harris Mr. Harris if you will join me please this is a resolution of appreciation of Mr. David Harris whereas Mr. David Harris acted as chair of the Durham Planning Commission from September of 2014 through September of 2016 and whereas the Durham Planning Commission and the citizens and city of Durham and the county of Durham have benefited from the dedicated efforts that he displayed while serving as a member of the Durham Planning Commission and whereas this commission desires to express its appreciation for the public of a job well done now therefore be it resolved by the Durham Planning Commission one that this commission does hereby express its sincere appreciation for the service rendered by Mr. Harris to the citizens of this community and number two that the clerk of the commission is hereby directed to spread this resolution in its entirety upon the official minutes of this commission and this resolution is hereby presented to Mr. Harris as a token of the high esteem held for him adopted this 13 day of September 2016 and I would just like to say personally to this individual who has sat next to me I have appreciated all that he has done his guidance his leadership and that we it is a rare opportunity that individuals step forward and give their time to the community it is so much appreciated and at this time I know we'd like to hear from Mr. Harris thank you and the chair will now entertain a motion for Jeremy no actually Mr. Chairman given the date that's been appended to that resolution I move the resolution second it has been moved and properly second that the resolution be adopted by this body and so are we ready for the question let it be known by saying aye all opposed the ayes have it and Mr. Harris we thank you so very much and now I move to adjourn


Our national central bureaus, or NCEBs, are the essential nodes of Interpol's global early warning system. They are our foundation for operational support and the stepping stones for Interpol's response to the world security challenges. This is why meetings such as the heads of NCEBs are so important. It is an opportunity for direct exchange of expertise and experience between all our member countries. Interpol is unique in that we connect law enforcement across 194 countries, each with its own crime priorities in addition to regional and global threats. It is through our network that they can communicate instantly and effectively and also have access to our 17 global databases and the 91 million police records they contain. The heads of NCEBs meeting is also an opportunity for me to speak with the police chiefs from around the world to make sure that Interpol is responding to their needs and to gain a stronger insight into their day-to-day activities.


I don't expect it to take too long, but you have the time. It actually had been three problems before, but I knocked it back to two for you tomorrow. So I think you'll have plenty of time, but you've got to let little extra in you since everybody can stay and all kicked out. Other than the fact that class comes in after that, but that's like an hour after, right? So it should be okay. All right, any questions or a go? Remember to open book, open notes. All right, we're working on a problem on Friday for some of you there should remain a problem. Everybody look at it over the weekend? I'll take bite of your snort. That means no. There's no football. You still hung over from last week? Sometimes those things can take a while. All right, we had a simple stand of some kind that when loaded must remain level. The trouble being that two legs were not the same length. Now, we know from what we've been looking at so far, which is new to us this term. It's nothing we had to look at last term. In fact, let's look at this as we would have looked at it last term. We don't know what this placement is, and so we would have set up our equations. We would have summed the forces, know that they summed to zero. So a free body diagram of the beam itself gives us that the two reaction forces must equal the load. Sum the moments, maybe about B, who told us what, that F, A, which we don't know yet, times its moment arm, oh, remember this was three meters, must equal the load times its moment arm, which is three minus X meters. No slap so far. You guys could have done that this much in your sleep. We have three unknowns, the two Fs and the X, so we need another equation. Last fall, we would have pulled in that other equation, being just the sum of the moments about some other point. A is as easy as any. Could do it about the load itself, but so the reaction at B times its moment arm has got to equal the load times its moment arm, just the X. And that would have done it for us last fall. Everybody did that, I think. If we just thought about it for a split second or two, we would have just put the load dead center. There's a trouble with that, that we didn't have, now that we're looking at real engineering materials and how they deform under loads. We have a problem with just using our statics analysis from last fall, which then makes FA and FB equal. So we'll say here, from last fall, that gives us a symmetric load. Well, it depends. If that's what you did, that's all you did, just took what we did from last fall, yeah, you get a symmetric load, and there's a trouble with that. Who did it this way, found the load to be symmetric, and placed the load dead center? Something like this, something to be in the arrow of both terms, X, the load, X is one. X is one? Yeah. Where we're here? Yeah. You got that from this? Yeah. Because with just this alone, that should have put the load right in the center. So this is what we would have seen last fall. Load right in the center, and two reactions out of that. And this would put the load, DJ, what'd you do? Put it right in the center. DJ, what'd you do? This is the one from last Friday we're taking out again. I was having a hard time solving this on the AISC, and they got a cancel out of the AISC. Okay, Pat? I didn't get that. Divide each over three, add them together, solve for X. Divide what? Bite three? Divide it, move this FAA and FB, take the three out for another side, about three meters. So you have everything in terms of X, and then put both of those in there. Yeah, and you get X. All right, so that's A divided by three, one minus X over three. That's this one divided by three, and put it ready there. Plus this one divided by the side of the three, which is 80X over three, equals 80. Right, that's these two put into there. These two divided by three, and put it in there. Is that okay? Let's see the 80 cancels. If we can multiply by three now, make it easier. We get one minus X over three, plus X equals three. What do we get? Two-thirds X equals... Okay, well this is algebra now, though, right? If I made a mistake, X equals three. X equals three. This doesn't work either. That puts it right there. So that must be some movement somewhere. Okay, well you get 1.5 just by inspection. So there must be an algebra error in there somewhere. Multiply by three. So that's just this. Oh, multiply by three, are in the truck. So this is one minus X over three. That's the... Oh, yeah. No, it's okay. That's the 80's canceled, and then multiplied by three. And this was 80 canceled, so that's one multiplied by three X three. Is that okay? Yeah, same thing I had. If you carry the one over, we get minus X over three, plus three X over three equals two. Now how do we get the three out of that? Two-thirds X equals two. Times the big three halves of both sides. Times the big X equals three again. Yeah, that's the same thing we had. Well, I don't make any sense either. Something's wrong somewhere. And then eight, is this distance... That's three minus X. That's 80 times three minus X. You have to do it really fast. You get 240 minus 80 X plus 80 X, all over three. What? You just distribute it really fast. You get 80 times three is 240 minus 80 X, and then plus 80 X. So 80 X is canceled, so it's 240 divided by three equals... Okay. 80. 80. But what that sounds like, what you're reading that to me, blah, blah, blah, blah, blah, blah, blah. I'm just figuring out my mistake. Well, what's our mistake then? I don't know where it is on there. But it's 1.5? I don't have the answer now. Fv times three, 80 times X. Well, anyway, in here, A plus Fv... Just distribute the 80s versus the 90s, then by three. And that's how it equals to the other one. And 240 divided by three is 80. So that's all for today. It's just canceled. Yeah, it's not that bad. Anyway, so... You have to get 5.8, that's 3.2, and you get like 4.6, 4.8, something like that. Yeah. And those, then you just double that, and you divide your 80 by that, and you'll work with mine. A lot of that. Now I can see why math is not taught over the telephone. All right, so this is okay. There was just some algebra error, and there was given us the X over three. How do you get that by inspection now? How can you just assume that it's 1.5? Well, the symmetry of it, if this is moved over, then... Well, I guess we could solve it, but I mean, that's certainly the simplest of the solutions. The trouble is that this ignores the deformation that we've been studying, and remember the requirement was that the beam remain level. And we haven't taken that into account. So there's some kind of deformation here, del A and some there, del B, that in fact must be equal, which means, well, those are equal. That's really just a single unknown. We now have four unknowns, not three. So we need a fourth equation. Now that we're looking at other things, now that we're looking at the deformation of the materials, there's got to be other unknowns. What's our fourth equation then to find this unknown? There's four unknowns, and now these, they're equal, so it's really only one unknown. The left stream. All right, how do I write it? So that, okay, now there's a fifth unknown. We need to set this requirement sometimes, since it was a restriction on the problem. And you're right on the edge of what you need anyway. Set the two deformations equal. That's then what? Strain and A. Well, let's see if the easier way to do it is I'll make sure I've got the algebra right this time. That is del of A. The other equation has bala in it anyway, I think. That doesn't happen often enough. And then there's the same equation for Fv, Lv over. A lot of those things cancel out. The area of the two is the same. Remember, they both have the same diameter. They were also the same material, huh? I don't have it up there, but it was the same for both of them. Oh, that's 22. Now with that then, we have enough to solve for everything. And it doesn't change things a lot, but it's still something we needed to add that we hadn't had before. There's a slight shift of that load slightly past the halfway point, which makes sense because post A is longer, which means it'll take less force to make it deform as much as post B is. It's got to be a little bit less. And Fv is, the deformation in A and the platform remains level. From this, you can also find the deformation in the two of them. That's what I got when I solved this, isn't it in that equation? When you have a system set of equations, every unknown doesn't necessarily appear in every equation. Now I double-checked this one last night where my algebra went wrong. And then there was one other little piece that required to find your member final diameter after loading. Where would that come from? Once loaded, its natural response is to sort of bulge out like that. Lausanne's ratio, which we know because we know what the material was. I think it was .35? Yeah. Stress and strain in the radial direction over that in the axial direction. In the axial stress, we have that number. It's the, which we can get from here. That's full eight nulls here. And Frank, you did that. You thought that this needed to be in there and got a number, something like that? Yeah. All right, so the deformation of these materials brings in other unknowns. But they do respond in predictable ways. So it allows us to engineer for these things, which we couldn't have done last fall. All right, one last thing we need to bring up. Now let me double-check now that everybody's here. Everybody can stay afterwards tomorrow if need be. I don't think it will be actually short of the test from last year. But I don't want some to stay if someone can. This is not fair. So everybody can stay if need to. All right, so it's optional. If you want to stay and work a little bit more. If nothing else, just help take the pressure off a little bit. It's easy enough just to make simple algebra errors when you're under the gun. All right. Well, we've got two things in particular we've looked at as far as material properties. The Young's modulus. Let's see. That's the load over the area and the deformation over the length. Both the area and the length were original values, remember? Unloaded values. So these two things here are just constants of the geometry of the piece we're looking at which makes this essentially then the load we apply over the material that the structural members response to that. Young's modulus is essentially the material's response to a given load in a very predictable way that we can use. It might make sense to think, well, what if we have the same kind of thing not for the normal loading that we do but the shear loading we do? What if we have a shear stress divided by the shear response? Let's see if we remember what that is. Imagine we've got a piece of something like this. We've got some kind of shearing load on it like that. The real response to that is something like that. Remember we looked at that? The shear strain. What did we call this? This response to that? That's the shear strain, but what was the symbol? Yeah. So if we have the same type of thing here where we had the normal stress over the normal strain, now we have the shear stress over the shear strain. It might make sense that we have the same type of thing, some characteristic of the material that's load over response, which is just what this would be. The load over the response. Well, we can't really write that in the same type of way that we could here. This is indeed a material characteristic that we call G. It's called the modulus of rigidity that these two moduli are actually related function given there. We'll see that later. I don't know that we'll actually cover that. It's derived in the book. It's a simple derivation, but we can use it now if we wish. Is that a Poisson-Zerchian book? Yeah, that's Poisson-Zerchian. So we have a new material characteristic. I believe it's in the back of the book. Anybody that you've got there's just real handy. Never mind, Jake. Double check. G is in there? In our tables? It's a material property just like the modulus of elasticity is. And we can use it in the same kind of way. So we'll look at it quick, see how we can do that. Two rigid plates fastened to some elastic material. This kind of thing is sometimes termed a shear block. I can actually use a sort of a shock absorber as a load is applied to the plates. The material will respond, can serve as a shock absorber for the material. Jake, how are you doing? Bob, you wouldn't have no trouble with these if you stuck with the technical free-hand sketching. Notice that the material actually responds a little bit different than we've been sketching in reality because of our assumption of perfect bonding of the material to those plates. But what we've always looked at before when we looked at this shear strain is we looked at the average and not necessarily worried about what the strain was individually at each plate. Specifically looking just what the slopes were at these two different places because the strain is different there than it is in the material and the interior of the material. But then we have to start looking at things like bonding strength and other considerations that are beyond the scope of this cluster right now. So let's put some numbers on there. Original dimensions, 50 millimeters back, 40 millimeters high, 160 long. Those are the original dimensions all in millimeters. Given that this material has a modulus of rigidity of 600 megapascals, find the load that would give a deformation we need to limit the deformation of this shear block to 0.8 millimeters. Maybe it'd be conflict with some other part of the machinery that it's a component of. So we need to find what load is possible. Be at that level or less. Let's see, that's going to come from, come from, let's see, well, if we knew the, or this is the shearing stress, we've got the area. Do we have this? Not, not specifically, but we certainly have enough information to find that, especially if we use the average values here. So we can get the load from the modulus of rigidity and the shear stress. Sorry, shear strain. So we've got G, the shear strain we can pull out. The area, you've got to make sure you've got the right area here. There's sort of several to choose from, as there are often in these three-dimensional problems more through the day for coming prepared. A little bit of algebra, mostly just getting used to the numbers, also making sure that you're using the proper area of that calculation. Millimeters and megapascals and things are getting, a lot of big things, a lot of small things, all mixed together. You've got to watch it and get it very carefully. The use of the same area is one of the easy places. It's the area over which that shear is being exerted. It's the 50 by the 160. What about gamma? What did you put in for gamma itself? This is the main process that I had too. Nothing yet? Still in conflict? You need to arm wrestle? That's the arc tangent of the 0.8 over the 40. That's where you got the 0.02? What is those two just divided straight? Which, if you remember, in radians the tangent is essentially equal to the angle. And we are talking about very small angles here. We have to exaggerate them greatly to the drawing. The 50 by 160 give us meters squared cans a week. We'll have newtons. Now we have radians. This only holds, it probably holds for zero degrees, but beyond that, that approximation is true only in radians. But another try, this is the problem I took off of tomorrow's test. We'll see if I should have left it on or not. It's very similar. Sure. Can I send it to the printer yet? And I haven't put it up on the board yet. In fact, good idea. Very similar problem. And shear block. There are classes that you can take that will worry about just how you do this bonding such that the failure is not there, assuming that I'm buying stuff from Earl. Add a little bit of free dimensionality to it. We're going to need that. We need the area which that plate's attached. That plate's loaded. Then with some load p causing the shear block to deform. We'll again now just look at the average response to form something like that. Since A piece there is B, the depth into the board is B, we need to find that deformation, that displacement there, the dimensions, the size of the load itself that can affect how far it's going to deform. But also then the material characteristic modulus of region. So it's not terribly unlike what we just did. They bungled it so. No, in terms of those, you'll have del as some fairly simple function of these five variables. On this plate, straight down. So how is it shifting when you're out? It's not shifting now. The whole piece just goes like that. It's a lot of impact. I told you, I don't want to do three dimensional things, but you guys make it. We can make this here. Get out of class question. The units, check out. You can check your units, because you know these are all going to be units of length. P is going to be in units of force. G is going to be in units of force per area. You can check your units. Once you've got del in there, this is all properties of the object, or the load, and the object itself. There's no... You're solving four. Del. You should have del as some function where the units work out in about very small angles. So, yeah, you've got that. Did you just take the tan part on there? Nope. Did the units work on that? Yeah, I guess they would. G is defined as the shear stress over the shear response. The shear stress is P over the area over which it acts, which is VH. Gamma now uses a small-angle approximation, which essentially, if you've got a tan, you just take it out. Yeah, being radiant, you can solve for P... Oh, no. I'll have to solve for del. That's the only way you've got for the alarm.


How to earn more money? Five ways to boost your income. To achieve financial freedom, you have to earn more money and save more money. Saving more money, however, can be difficult and slightly insignificant if your earning potential is low. For instance, consider someone who earns $50 monthly and saves 50% of what he earns. Imagine a second person who earns $150 and saves just 30% of his monthly income. Which of both parties will generate more money at the end of the year? Of course, the man who earns more, even though he saves less, hence the need to boost one's earning potential and passive income. According to American author T. Harve Ecker, you become financially free when your passive income exceeds your expenses. Saving more money will help you become financially free, before you know it, especially if you know how best to manage your income. Anyway, in this video, I'll share with you how to earn more money, five ways to boost your income. This, I believe, will help you become a successful person. If you're new here, consider subscribing so that you won't miss other interesting videos like this. 1. Pick up a side business Side businesses are businesses that you can launch on the side while working your full-time job. For instance, you can pick up becoming an Uber driver or you can become a product vendor for different brands and earn money on every item you sell or every referral that gets converted into a purchase. Some businesses might require your time while others will require your resources for the smooth running of the business. Depending on the flexibility of your full-time job, it is advisable to pick a side business that won't interfere with your current job while providing you with the extra cash that you need. Ensure that you are not putting more money into the business than you are getting out of it, since it is a side business. Stephen C. Hogan, a social entrepreneur, producer and writer said, you can't have a million-dollar dream with a minimum wage work ethic. If you truly want to make more money, then you should be ready to put in more work or at least spend more money to generate some more. 2. Consider Freelancing Thinking of writing or blogging, vlogging, coding and the likes? One thing that they have in common is that they can all be done or created from any location in the world. The most important thing is to get a result that is excellent and satisfying. There are a couple of online businesses that you can lay your hands on as a freelancer. For instance, you can consider writing for different websites or become a business strategist or digital marketer for any brand of your choice. In the case of starting a side business, you are entirely responsible for the growth of the business. But in freelancing, you are working for someone else to help build their business. You are an employee as far as the business is concerned. The only difference is that unlike your full-time job that requires your presence to function, working as a freelancer doesn't require you to be present. Also, the expectations are different from your full-time job. Here you are employed to work on different projects per time, not concerning yourself with the functioning of the entire organization or an entire unit. Three, make money with your hobbies and social media. Have you heard of influencer marketing? According to marketing schools.org, influencer marketing involves marketing products and services to those who have a sway over the things people buy. This market influence typically stems from an individual's expertise, popularity, or reputation. When a reputable or popular person or an expert of a field recommends a product, people tend to make purchasing decisions easily than when they just depend on random ads thrown here and there by marketers, especially in the world saturated by advertising and producers or makers lanehold to ridiculous claims. What does this have to do with you? I'll tell you. Say you like cooking or you enjoy reading books and doing a review. You can turn this hobby into a money-making opportunity by teaching people how to make different delicacies online or posting reviews of different books that you have read. As soon as brands in your industry start noticing the quality of your work and how well you are attracting and engaging with your followers and social media, they'll begin to pay to have you promote their brand or promote a product that they made. This method of earning money might take a little longer than the others, but when done properly, will earn you quite a lot of money. Four, become a business coach. If you've been in a particular field for a while and you can provide valuable insight and guidance to less experienced people or those who want to break into your field, you can offer your services online or offline. For instance, you can host a training class or lessons from time to time for those interested at a particular rate. Five, be bold enough to ask for a raise or a promotion. This is one option majority look away from in the request to increase their income perhaps for fear of being turned down. However, before you consider asking for a raise, you should have a valid reason for a raise. For example, you recently completed a major project that made your company a lot of money. You've been putting in a lot of extra hours or you've been receiving rave reviews from customers. Also, you don't want to be asking for a raise every month.  Considering that it has been a while since you last got something rewarding. However, if after all these your boss says no, remember to be professional. Thank them for their time and ask how you might be able to secure a raise in the future. You never know. Maybe they'll recommend asking again after tax time or in the next quarter. Now you can start earning more money. Thank you very much for watching our videos. We'll like to give you another interesting video for you to enjoy next. But before then, our team will be very happy if you can like this video and share it with your friends on social media. If you're new here, don't forget to subscribe so you won't miss other interesting videos like this. Look at your screen now to see two other videos we handpicked for you to enjoy next. We love you.


Hello and welcome to the session. I am Aasha and I am going to help you with the following question that says the length L of a copper rod is a linear function of its Celsius temperature C in an experiment if L is equal to 124.942 when C is 20 and L is equal to 125.134 when C is equal to 110 express L in terms of C. Let us now begin with the solution and they are given that L is a linear function of its Celsius temperature therefore L is equal to AC plus B since any linear function is of the form AX plus B is equal to 0 this is a general form of linear equation and here we are given that L is a linear function of its Celsius temperature therefore L is equal to AC plus B. Now the first case is L is equal to 124.942 when C is equal to 20 so this equation can be further written as 124.942 is equal to A into 20 plus B so this is equation number one. Second we are given that L is equal to 125.134 when C is equal to 110 therefore we have 125.134 is equal to A into 110 plus B so this is equation number two. Now subtracting one from two we have 125.134 is equal to 110 into A plus B and 124 plus 942 is equal to 20 into A plus B. Now solving it B cancels up with minus B 110 A minus 20 A is 98 and subtracting 124.942 from 125.134 we get 0.192 so this implies A is equal to 0.192 upon 90 let this be equation number three. Now as we know L is equal to AC plus B therefore this implies that B is equal to L minus AC and now substituting the value of B in equation number one which is 124.942 is equal to 20 times of A plus B and B is L minus AC therefore this implies that L is equal to 124.942 plus C minus 20. Now substituting the value of A so we have L is equal to 124.942 plus 0.192 upon 90 into C minus 20 therefore L can be expressed in the terms of C as 0.192 upon 90 into C minus 20 plus 124.942 this is the answer hope you have understood it take care and have a good day.


At Audiology Associates at Prestonsburg, you can live your life the way you want and find the freedom of better hearing. You'll experience patient care that is specific to you with exceptional follow-up care that ensures your hearing and balance needs are being met. Audiology Associates at 1428 Northlake Drive in Prestonsburg. With construction season and full swing, Kentucky Transportation Cabinet wants to remind travelers to be mindful of work zones as construction begins on a few projects this summer. So if you can plan a head that helps you know exactly if you want to encounter a work zone. And then two, you always need to slow down and pay attention and obey the signage in the area. Sometimes we will have stationary signs that you'll see and then in different areas we may have flaggers on site. Each one of our construction zones is unique. And so sometimes we may have a temporary daytime closure for crews or just working during daytime hours. And you'll need to pay attention for equipment and things that are parked in the work zone day and night. Sometimes I don't think people realize that we still have to have equipment there in the evenings. So you'll want to be very vigilant about paying attention. Also avoid distractions. So that means stay off the phone and pay attention to the zone. So the more attention that you can pay in these areas, the safer it is for you and the safer it is for our crews, you know, as well.  And lastly, and I always talk about this, buckle up. As the Kentucky Transportation Cabinet reminds travelers to watch for construction zones, they would also like to notify travelers of ongoing projects within the district. These would include repair to Kentucky 1056 around Blackberry, Kentucky 2061 around Cowpen and more. And last but not least, we have Ridgeline Road. We've been working on that for several weeks and things and we've got a couple more weeks left to have that finished up. And that's Kentucky 3418. So we're diligently trying to get the work done in several different areas, you know, throughout our district. And lastly, with ongoing construction, Kentucky Transportation Cabinet reminds travelers to obey signs even when crews aren't active. For construction information, you can visit transportation.ky.gov. For Mountain Top News, I'm Joel Hodgell.


My fellow Americans, recent economic reports confirm our economy is moving smartly ahead with solid expansion in the job market and inflation being held down. Our future looks good, but one group is still having difficulty. Far too many farmers are seeing hard times. Prices for corn, wheat and soybeans have been weak and getting weaker. Demand for exports has dropped as production here and in other countries has steadily increased and foreign suppliers have filled markets that once were ours. Our great success in bringing down inflation has helped farmers by ending double digit price increases for fuel, fertilizer and other supplies. But there's been a downside. Many farmers took out loans in the late 70s when inflation was soaring, assuming the value of the land they were pledging as collateral would keep on rising. Unfortunately, the opposite happened. When inflation plunged, land values plunged too. And when inflation stayed down, defying the expert's predictions, those loans farmers were carrying became more and more difficult to finance. How can we not open our hearts to these people in distress who mean so much and give so much to America? We know that while farmers account for only 3% of the workforce, farming and related industries generate $660 billion a year or almost 18% of a gross national product. We know that these industries are responsible for 21 million workers, nearly 20% of the workforce. We can be thankful that agriculture, one of the few industries with a strong positive trade balance, provides employment for 630,000 non-farm workers through its yearly exports. These facts and figures are convincing in their own right. Yet facts and figures don't tell the whole story. They don't convey the strength and nobility of values, the deep faith in God, and love of freedom and independence, the many years of hard work and caring for friends and neighbors that began on the farm and made America the greatest nation on earth. Farming is hard work, maybe the hardest. The strength of our farmers has always been the strength of their dreams for the future. Dreams that a son or a daughter working the fields, tending the herds, might decide to stay on that farm and be able to make a go of it. There is no price tag on traditions like these. Only the stark realization that to lose our farmers would be to lose the best part of ourselves, the heart and soul of America. Well, we cannot let that happen. We cannot permit the dreams of our farmers to die. We must have compassion for these men, women and their families so important to all of us. I'm asking Congress to join me in planting fresh seeds of hope for America's farmers. We might begin by seeing and avoiding the one threat that could make today's problems far worse. Some 300 protectionist bills await action in Congress. To enact them would be to invite certain retaliation against our farm exports, heightening the risk of a farm catastrophe which would send shockwaves throughout our economy. Believe me, protectionism is farmers' enemy number one, and that enemy is stalking our gate. Let us work aggressively for freer and fairer markets. But more than that, let us have the courage to urge that more countries start doing what America has begun doing so well. Go for growth by adopting low-tax, free-market policies that will increase jobs, raise their people's standard of living, thereby strengthening demand for our products. Nations which have stagnated their economies with high taxes are weak importers, and this problem must be recognized. We do not seek an America that is closed to the world. We seek a world that is open to America. We do not dream of protecting America from other success. We seek to include everyone in the success of the American Dream. I'm asking Congress to unite with me for intelligent policies that provide farmers needed help without doing harm to the budget limitations adopted by Congress, and greater freedom for them to grow and sell their crops in the marketplaces of the world. By working in this spirit, we can avoid budget-busting legislation which repeats the mistakes of the past. Legislation I would not hesitate to veto. We must meet our responsibility to America's farmers and pass a farm bill that provides hope, not measured doses of despair. Until next week, thanks for listening, and God bless you. Actually came from England, and the story that the English were telling was of this man who lost his dog. And he put an ad on the papers promising a very handsome reward for this, and described it as a large shaggy dog. And a fellow in America read the story, and he went out and found the shaggiest dog he could find, and then got a job in a cattle boat to take the dog and get himself to England. Getting to England, he made his way to this great manor house there, rang the bell and the butler came to the door, and he said to him, your master advertised her for a lost shaggy dog. And the tagline is the butler looked at him and he says, not that shaggy. That's the shaggy dog story. Okay. Only the English would laugh. Good day. Bye bye. This is Ravens.


Monotony is not life. Monotony is the nature of the mind. That is if you left your mind loose without knowing how to employ it. So if you do not know how to use it, mind will use you on consumption. So the whole spiritual process is just that.  Every moment if you look up, you're seeing a new piece of the sky. It's very exciting. The earth is spinning all the time. Not one moment, same old thing anywhere. Everything is changing. If you're alive to life, you will never know any monotony in your life. If you're not alive to life, but you just live in your mind, then everything will be monotonous because mind is repetitive in nature. People who are just bored and dejected and suffering the monotony of life, people come to just a week-long or weekend program and suddenly everything looks fresh for them because the cataract on their eyes has been cleared. So the cataracted mind has been cleared and suddenly they find everything is beautiful for them all of a sudden. Particularly people who go through the Bhavasplanana, for them they go out and suddenly they're excited about everything and the same old things. So what is old essentially comes because of your mind. Otherwise there's nothing old in existence. Modern science is proving to you beyond any doubt. There is no such thing as old anywhere. Everything is reverberating and creating itself all the time and the rock is pulsating with new life every moment. But the old exists only in the mind because mind functions out of past memory. Once your mind is repetitive you will neither know peace nor joy nor wisdom in your life. It's time you meditate and go beyond the step to do this.