Snaps are very polarizing and really you can say that about any package management system that is trying to be universal whether it's flat pack snaps or app images but for whatever reason snaps seem to get a very large amount of flack for any number of reasons and I wanted to go through and talk about a few reasons why snaps are just so hated by a lot of people and see if I can come up with at least a few reasons why people should like them so if you watch the channel for any amount of time you'll know that I just can't stand snaps I try to avoid them as much as possible I'm pretty sure I have some snaps on my computer right now if I open up a terminal I think I have no I don't have any snaps installed right now I actually thought that I did but I don't I have seven flat packs so there you go the thing is I've always just like snaps and there's just some reasons why that is true so I wanted to start off there and because most of the reasons why I hate snaps at least I feel are the reasons why a lot of other people hate snaps as well so the first reason why people seem to hate snaps and one of the reasons why I hate snaps the most is because they're very slow upon a cold boot now basically what that means is when you've never opened up the application before in your current session when you first load that application it takes a significant amount of time and I'm talking multiple tens of seconds to actually load that application and the reason why this it actually happens is because of the way snap packages stuff there's extra steps that it has to go through in order to launch the application specifically things like uncompressing the file and all this stuff because it's just the way it's packaged it's very much more tech technical than that but just that's the reason why when you say launch up Firefox on the latest version of Ubuntu it takes some time for Firefox to load that first time and it's always going to that's just the nature of snaps now once you've had this that application open at least once the startup time is actually just normal it's not any longer than normal at all or at least it's not noticeably slower I should say so this speed difference between a snap package and a non snap package is something that a lot of people notice and it's probably the number one criticism of snap packages and for good reason people don't like waiting I know I don't I would one of the things that bother me the most about audacity is that when you start up audacity it takes at least a good 10 15 seconds for it to load it's doing stuff in the background that enables it to grab control of the audio system and it takes time to do that snaps are kind of the same way they have a reason why they're so slow but frankly I don't care why that is I just want my application to start up when I hit the button you know call it American impatience but it's just the case you know so that's the number one reason another reason why I don't like snaps and I feel a lot of people don't like snaps and this isn't so much of a big reason anymore it used to be a lot worse but sometimes snaps don't follow the theme that you've set for GTK now theming itself is a another controversial topic that depending on whether you're a developer or not your views probably change but for normal people a lot of people like to theme their desktops even if you're not the racing aficionado that I am chances are you've probably sets your GTK theme you're not sticking with whatever the developer has given you and sometimes snaps don't follow the GTK theme that you've set they stay with the default or they break completely like I said it used to be a lot bigger problem than it is now I've actually noticed that flat pack has this problem as well so it's just a kind of a nature of the beast kind of thing but it does happen and it bothers me because it makes that application stand out like a sore thumb against all the other GTK themes that actually do follow the theme now the next one is one that whether or not you care about is probably going to be depending on how in the open source software you are some people just use Linux because they don't want to use Windows some people use Linux because they're really into free and open-source software it doesn't really matter to me which side of that spectrum you're on but for the people who are really into FOS the fact that the back end for snaps isn't open source really drives them crazy and I can understand this personally it probably doesn't matter to me that much but I can understand it and it does bug me a little bit because canonical is this corporation that kind of champions open-source software and Linux and all this stuff and then it has the their proprietary package management system it doesn't really make sense if you listen to people in the development community for Ubuntu and snaps you'll know that they have reasons for keeping the back end for snaps proprietary and not bringing open source and that reason seems to be that they don't want the PPA system to become this thing again so for those of you who don't know the PPA system allows you to basically anyone to host their own repository and then that can be added into a Debian or Ubuntu based system and it's a mess because people create their repositories and they abandon all the software in those repositories some of those software things are either not updated at all or become broken or become security threats it's a mess and we nobody likes PPA's like nobody does and the people behind snaps don't want the snap back end to become another PPA system where anybody can host their own snap store and then abandon it and have those applications become security threats just like the PPA stuff kind of did so the argument behind it is I can understand their point personally I think that there are ways to mitigate that but like I said I can see their point so it if you are the kind of person who doesn't want to use something that's based on proprietary software snaps are probably something that bug you quite a lot and that kind of leads me to the next one is that they're kind of being forced on you if you use Ubuntu you have to use snaps as far as I'm aware and I might be wrong on this I don't use Ubuntu from what I've read you can actually take snaps out of Ubuntu that easily like they've kind of forced so many snaps into Ubuntu you'd have to remove quite a few packages in order for snaps to actually be removed from your system and that means that you're going to just have to put up with snaps unless you want to go through that work and that's not a great thing right it's not if you you have to use Ubuntu but you don't want snaps on it chances are you're gonna just have to stumble your way through removing them and being forced to use something just isn't that great an experience now the argument against this obviously is that if you can use something different and you know you should just do that you know use Linux Mint which doesn't use snaps I think one of the Ubuntu flavors actually doesn't use snaps as well I don't I can't remember which one but that's the solution for that one at least and that one leads into the next one which is they're not as universal as they really want you to think so the idea behind snaps is that they can be like a universal package manager where they can be used no matter what distro you're on and that's true you can use snaps on any Linux distribution it's fairly easy on the vast majority of them so for example if you're on Arch you can do pseudo pac-man dash capital S snap D and you'll have install snap very simple but on some distros where they are protesting against the idea of snaps themselves for example Linux Mint using snaps is actually a lot harder because they put barriers in front of the usage of them so that you actually have to to basically confirm that you want to install snap and that's you know it's a choice obviously and whether you agree or don't agree with that choice it's still something that you kind of have to put up with and there are a lot of distributions that just don't like snaps they prefer flat packs some distros don't include either so that this I don't want to call it a war between package you know formats but it kind of is that because which distro you choose is very much going to determine what package formats you're going to be using and that while that's always kind of in the case because if you use an Ubuntu based distro you use apt if you use Arch you use pac-man and so on and so forth it kind of dilutes the argument for actually using snaps in the first place if they're not as universal as the developers claim they should be so the next one is my personal pet peeve so everybody knows that I consider the home directory sacred and right now my home directory is kind of a mess but I'm working on it but the point is when you install snaps on a distro that doesn't support them out of the box it installs a folder in your home directory and that's just the way it is you can't remove it unless you install snaps I hate this like I it drives me absolutely bonkers out of all these things that I've listed so far this is the one that drives me the the most crazy because I don't want to see a snap folder in my home directory I just don't and it's a pain in the ass it's a stupid thing to care about I understand but the thing is we know that they can fix this because if there's not a snap folder on Ubuntu like Ubuntu has snaps install a lot of the box and there's no snap folder some distros are the same way if they come with snaps pre-installed you don't have a snap folder but if you install it explicitly yourself it's gonna install that snap folder and to pay in the ass and it's ugly and I don't want it to be there it needs to go away but that's probably the most superfluous reason to hate snaps I can help it it's just one of the things that I dislike so the last one for the reasons why I personally dislike snaps is because they're not necessarily secure as you think now you gotta remember I'm not the most well read on security issues and how these things interact with security but from the things that I have read snaps aren't necessarily as secure as we think so one of the promises behind snaps is that they're kind of sandbox that they are pre-packaged containers that protect you from from that application having access to your system in unusual ways but this isn't actually true for for snaps or flatbacks they both have or can have unregulated access to your home directory so for example if you install a music player from the snap store that particular music player will probably have access to your musical directory which is in your home directory it's not as sandboxed as they want you to believe now the thing about sandbox apps is that they do sometimes need that access but and we know that from like the mobile phone sphere where if they want access to stuff chances are on your phone like on Android they're gonna tell you hey this application has access to this stuff would you like it to continue to have access same thing on on the iPhone where if it's gonna access say your microphone or something it says hey would you like to have all this app to have access and that's kind of the promise behind snaps and flat packs but they're not there yet a lot of applications just assume that they have access to your home directory and if snaps said hey no that application would be broken so I know that they're trying to fix this I know that it's a pain in the ass for the developers and stuff like that but it's another one of those things that you kind of have to keep in mind if you use snaps that they may not be as secure as they might supposed to be so I know I've gone through and talked about a whole lot about negative things about why people hate snaps but I wanted to include three or four things that give me hope that snaps could be a good thing in the future so kind of playing off that last one is this sandbox apps can be a good idea if we can get to the point where they're actually sandbox and then the only time they have permission to do things outside of their container is when you explicitly give them permission to do so that's a good thing now I wouldn't want all of my apps to be this way there are some applications where I just want them to work I don't care what permissions they have so for example like a terminal doesn't I'm not gonna I don't need to give that thing permission that's always going to have permission to do the things that it can do and then if it needs root permission you know you can use sudo or do as or whatever you know it has that thing you wouldn't want to have to go through every single time and say hey I have all this thing to have access to the internet or whatever you know you just want to do that but for certain things that you download and try out or whatever it'd be nice to have that granular control of what that particular app has access to on your system your camera your microphone things like that that'd be cool but I think that that is kind of far down the future we're not there yet so one of the things that snaps and flat packs are good at now is that they can be packaged and maintained independent of other dependencies so for example let's just say you have a we'll take our music player for example again you have a music player it has a dependency of some random 32-bit library whatever it's not maintained anymore but it needs it by being able to package both the music player and the dependency together you can ensure that that dependency is always available and you can also ensure that the version number doesn't change so if that music player depends on that particular version of that library it won't break when that library is updated outside of the sandbox so that's a really good thing because the number of times you've updated an application and then had a problem where the dependency that you have installed is an older version than what the application is looking for that happens all the time especially on rolling releases it just if the main package is updated and then the dependency is not updated but it's looking for a specific version number it can be a real mess snaps kind of get around that by packaging the exact dependency that is needed inside the package with the actual application the other one that is really cool is kind of similar is that they can go through and be packaged based on the maintainers wishes so for example things like OBS can be packaged and compiled with certain plugins enabled out of the box so if you install things OBS on arch you're just gonna get vanilla OBS that's just the way it is if you install the snap version however you get a ton of plugins and certain settings that are enabled by default in that snap package that you don't get basically anywhere else you'd have to go through and set all those things together so it allows a maintainer to kind of create a package that is different than the norm because it can include other things specifically dependencies that would probably otherwise have to be installed separately so I think the bottom line is that snaps are controversial for good reason they're not perfect now we don't expect perfection in the Linux community we shouldn't expect it we should strive for it but we shouldn't expect it no but nothing is ever going to be the perfect package management system it's just not as much as I like Pac-Man on arch it's not the perfect package manager it's not there's not a perfect perfect package manager so we can admit and acknowledge that snap has problems and that there are good reasons why people this like snaps and I think for me personally the reason why I hate snaps the most are the first and like the fourth reason is whatever one day I don't like that I don't remember the numbers but the first one was that the snaps are slow to start on a cold boot I don't like that at all if they're faster that eliminate that argument against snaps and they are faster than they used to be but they're still really slow and then that whole home directory thing if they didn't put the snap directory in the home directory if they at least hit it like if they put a period in front of it and made it hidden I still wouldn't be happy about it but it'd be better than having it just there it those are the two reasons out of all the ones I saw talked about that are the biggest deal for me so in the comment section below I would love to hear why you like or just like snaps I'd really like to know make sure you hit the like button and the subscribe button if you like this kind of content you can follow me on Twitter at the Linuxcast you can support me on patreon at patreon.com slash Linuxcast before I go I would like to take a moment to thank my current patrons said a Devon Chris East Coast Web Gentoo's fun to Patrick Oh Primus Marcus Maclin Jackson Poole Steve a cyber guy Linux Mitchell Arson our amateurs carbon dated merit camp dr. Lee J dog to be sees rock eater a crucible thanks everybody for watching I'll see you next time


Unless you have agreed that your relationship with him is exclusive, he should not be grilling you about your friendships with your male friends. I agree with what the Arabi said, yes. That he comes over with no notice hoping to catch you cheating is more than a little sick. Well that's like Ralph Crandon when he used to go aha with Alice you know he found the glove you know. And what he pulled during this midnight prowl is off the charts. It's important that you understand the only way he will ever overcome his insecurities and inability to trust will be with professional help. He is so messed up that you could enter a convent and he would mount a security camera on the back door. Oh that is very true but they never so apparently they never had, they never decided on an exclusive relationship. Well she doesn't even know if he loves her. She doesn't know where she stands with this man. Right. She just knows her own. He said she loves him. She just knows her own feelings. Yeah. Okay. Yeah.  Hasn't it occurred to you that this may be the reason two wives left him? Maybe he drove them nuts. I would say. He drove them stark raving mad. I would say. I would say. Okay. That's it. That's it. Thank you for joining us for this week's Progressive Discussions. I don't even know if I announce the name of our show. I don't remember. Well it's called Progressive Discussions and thank you for joining us on All Hallows Eve 2015 and the next couple days you know we're going to have All Saints Day and then the day of the dead on the second, November 2nd. So have a good and safe above all and fun-filled Halloween week. Don't drink and drive. Don't eat too much candy because the sugar is toxic and there's also other things that are not good for you that are put into today's candy. It's not healthy at all. I like dark chocolate and I like nuts. So candy that are composed of both is what I like you know. I know it's not a health food but baby Ruth, Snickers, I'm enjoying mounds. Actually I'm enjoying mounds are way too sweet. I don't know why they put so much damn sugar in it. There's 11 carbs in the small ones. Well I know the mounds that doesn't have an almond is dark chocolate. It's the mounds. And the almond joy is milk. You like this interrupting banter thing. I'm not crazy about it. The almond joy is milk chocolate with an almond. That's great. But I mean the coconut inside is sweet as hell. It's a very very sweetened coconut. But then again the American food industry wants people to get addicted to refined carbs and sugar. You know it's part of their their divine plan to get you. They're the same thing with big pharma. They're glorified legal drug dealers. You might as well call them. Okay we'll see you next time. And so and this guy also says so long. All right the Republican Republican party the true face of the Republican party the true face of the Republican party this has been a mega life 21 production


The first event during Baltops 2015 was a photo ex where the ships come together in various formations in order to get a Photograph as they sail from the harbor in Gdynia, Poland lieutenant commander George Storten Navigations officer board the HMS ocean spent long hours coordinating the event It was day one of the exercise So we hadn't really worked together up to that point and also lots of different classes of ships I think there were there were 30 different classes of ships Everyone has different propulsion systems different command chains and different ways of operating So we had to take all of that into account. There were a lot of late nights researching different types of ships Which we got together and we got everyone in formation in a roughly even size and shape This exercise involves precise movements that require constant communication to pull off safely and effectively It was a fantastic day and all the ships achieved everything they needed to achieve We've got the photographs and more importantly we got the formation and we got the exercise off to the right start So bolt-ups 2015 started with every ship being formed up within a few hundred yards of each other bolt-ups is an annual multinational exercise designed to enhance flexibility and interoperability as well as demonstrate Resolve among allied and partner forces to defend the Baltic region from the USS San Antonio. I'm semen Luke ask you


Have you ever driven across our state and wondered why in some places the soil like this appears to be white? The soil is white because of a high concentration of salt. These areas are called alkali flats. Alkali flats typically occur at low elevations on fine textured soils that have developed from highly saline materials. With little precipitation and soil that does not readily allow water in, the salts are never washed away. Because of a high salt content, high pH level and low precipitation, the plants that grow here must adapt in order to survive these extreme conditions. One of these adaptations is the ability to extract water from salty soils. If the salt content of the soil water is higher than that of a plant cell, the plant will not be able to take in water. Plants like this grease would adapt by concentrating salt in their leaves. This keeps the salt content higher in the plant than the soil and allows water uptake. While alkali flats may look barren and uninviting, the plants that are found here are able to thrive because of their ability to adapt to harsh conditions and survive on limited resources. From the University of Wyoming Cooperative Extension Service, I'm Barton Stamm.


Welcome, folks. We had the Dow Industrial's finish down 13, NASDAQ, flat S&Ps down three. And what you have out here, folks, you have a failure on price as well as volume. We get open. We take a look at the S&Ps, but you're going to see first, we look at the spy. You're going to see you got to the higher high, did 50 million shares. Yesterday, we bottom line, you did 60 million, you're going into 127 million. NDX100, same type of setup inside the NDX, when you had the three Qs, you got to a price point out here of 185.40, you close at 183.40. Yesterday, we did 41 million shares, you did 37 today, that's going into 67. Small caps, small caps out of the weakest indices, NDX100 a second as that weakest meaning, and then the spy. Small caps just gave it up, small caps, got to 153.23, get over that high of 153.14. From yesterday, did 14 million shares versus 18, and the small caps are actually going into 26. Gold contract, gold contract, a bottom line rejected lower price, ended up closing up a couple bucks at that 13.30, silver, same setup, rejected lower price, up 19 cents, $14.73, notes and bonds are the ones that really set it all. You had the 10-year note, flat, 126.23, that rejected lower price, lighter volume, 30 year, up to 6, 153.17, also rejected lower price, went topside, and then good old King Dollar. King Dollar bottom line, rejected higher price, had lighter volume, that wants lower price. King Dollar got up to a price point today of 96.860, did 19,000 contracts, yesterday I believe we did 24 going into 28, I believe, yeah, 24, we're going into 28, bottom line, good old King Dollar can't handle higher price, you're at 96.660, I expect what we're going to see here is that baby is going to try to make its way down into that 95 to 94 area. Bottom line, market wise, setting up building cars for the next leg down inside this market. We got to take a look at that gold contract, gold wants higher price, we had a nice rejection of lower price out here today. Stay right there folks, three numbers coming out after the close to recap, and the oil numbers, oil numbers are going to be coming out at 430, recap, we had the Dow Industries down at 14, NASDAQ, flat S&Ps down at 2.5 will come right back.


Hi and welcome to the session. Let us discuss the following question. Question says in figure 6.18 if Ln is parallel to Cb and Ln is parallel to Cb prove that a m upon a b is equal to a n upon a d. This is the figure 6.18. First of all let us understand basic proportionality theorem. Basic proportionality theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points the other two sides are divided in the same ratio. That is if we are given a triangle abc in which d e is a line parallel to bc, clearly we can see d e is intersecting ab and ac at distinct points d and e. So this line will divide ab and ac in the same ratio. So we can say if in triangle abc d e is parallel to bc then by basic proportionality theorem we get a d upon db is equal to a upon ac. This is the key idea to solve the given question. Let us now start with the solution. Now in figure 6.18 we are given Lm is parallel to bc and Ln is parallel to Cd. So first of all let us consider triangle abc. In triangle abc Lm is parallel to bc or we can say Lm is parallel to Cd. This is given in the question.  Now let us consider triangle adc. In triangle adc Ln is parallel to Cd. This is given in the question.  Now in this triangle a n upon n d is equal to a l upon lc and in this triangle m upon mv is equal to a l upon lc.  So these two ratios must be equal. Now let us name this expression as 1 and this expression as 2. So from 1 and 2 we get a m upon mv is equal to a n upon n d. Now taking reciprocal of both the ratios we get mv upon m is equal to n d upon n. Now adding 1 on both the sides we get mv upon m plus 1 is equal to n d upon n plus 1. Now we will add these two terms by taking their LCM. We get mv plus m upon m is equal to similarly here we will add these two terms by taking their LCM. So we get mv plus a n upon n on right hand side. Now clearly we can see mv plus m is equal to a b. So we can write a b upon m here this is equal to we know n d plus a n is equal to a d. So on right hand side we can write a d upon a n. Now taking reciprocal of both the ratios we get m upon a b is equal to a n upon a d. This is our required answer. We were required to prove this only. So this completes the session. Hope you understood the session. Take care and have a nice day.


Live from Barcelona, Spain, it's theCUBE, covering KubeCon CloudNativeCon Europe 2019. brought to you by Red Hat, the CloudNative Computing Foundation and ecosystem partners. Welcome back. This is theCUBE's coverage of KubeCon CloudNativeCon 2019. I'm Stu Miniman with Corey Quinn as my co-host, even though he says KubeCon. And joining us on this segment, we're not going to debate how we pronounce certain things, but I will try to make sure that I get Bridget Cromhout correct. She's a principle cloud advocate at Microsoft. Thank you for coming back to theCUBE. Thank you for having me again. This was fun. First of all, I do have to say, the bizazzled shirt is quite impressive. We always love the sartorial view that we get at a show like this because there's some really interesting shirts and there's one guy in a three-piece suit. There is. It's the high style, got to have that. Oh, absolutely. Bring in some class to the joint. Wearing a scoot is my primary skill. I will tell you that, yes, they sell this shirt on the Microsoft company store and yes, it's only available in unisex fitted, which is to say much like Alice Goldfuss likes to put it, ladies is gender neutral. So all of the gentlemen who say, but I have too much dad bod to wear that shirt. I say, well, you know, get your bedazzlers out. I say it's not dad bod, it's a father figure, but I digress. Exactly. All right. So Bridget, you're doing some speaking at the conference. You've been at the show, you know, a few times. Tell us, it gives a little bit of overview what you're doing here and your role at Microsoft these days. Sure, absolutely. So my talk is tomorrow and I think that I'm going to go with it's a vote of confidence that they put your talk on the last day at 2 p.m. instead of the, oh gosh, are they trying to bury it? But no, it's, I have scheduled enough conferences myself that I know that you have to put some stuff on the last day that people want to go to or they're just not going to come. And my talk is about, and I'm co-presenting with my colleague Jessica Dean and we're talking about Helm 3, which is to say, I think a lot of times with these open source shows, people say, oh, why do you have to have a lot of information about the third release of your, you know, third major release of your project? Why? I mean, it's just an iterative release. It is, and yet there are enough significant differences that it's kind of valuable to talk about, at least the end user experience. Yeah, so they actually got an applause in the keynote, you know, there's certain shows where people are hooting in hollering for every, you know, you know, different compute instance that that has released and you look at a little bit funny. But in the keynote, there was a singular moment where it was the removal of Tiller, which Corey and I have been trying to get feedback from the community as to what this all means. From my perspective, it seemed like a very strange thing. It's we added this, yay, we added this other thing, yay, we're taking this thing, ripping it out and throwing it right into the garbage and the crowd goes nuts. And my two thoughts are first, that probably doesn't feel great if that was the thing you spent a lot of time working on. But secondly, I'm not as steep in the ecosystem as perhaps I should be. And I don't really know what it does. So what does it do and why is everyone super happy to consign it to the rubbish bin of history? Right, exactly. So first of all, I think it's 100% impossible to be an expert on every single vertical in this ecosystem and look around. KubeCon has 7,000 plus people about a zillion vendor booths. They're all doing something that sounds slightly overlapping and it's very confusing. So in the helm, if people want to look or we can say there's a link in the show notes but people can go read on helm.sh slash blog. We have a seven part, I think, blog series about exactly what the history and the current release is about. But the TLDR, too long didn't follow the link, is that helm one was pretty limited in scope. Helm two was certainly more ambitious and it was born out of a collaboration between Google actually and a few other project contributors and Microsoft. And the tiller came in with the Google folks and it really served a need at that specific time. And it was a server side component. And this was an era when the role-based access control in Kubernetes was well-nigh non-existent. And so there were a lot of security components that you kind of had to bolt on after the fact. And once we got to, I think it was like Kubernetes 17, 118 maybe, the security model had matured enough that instead of it being great to have this extra component, it became burdensome to try to work around the extra component. And so I think that's actually a really good example of it's like you were saying, people get excited about adding things. People sometimes don't get excited about removing things but I think people are excited about the work that went into removing this particular component because it ends up reducing the complexity in terms of the configuration for anyone who's using the system. It felt very spiritually aligned in some ways with the announcement of open telemetry where you're taking two projects and combining them into one. Where it's, oh, thank goodness, one less thing that I have to think about or deal with instead of A or B, I just mix them together. And hopefully it's a chocolate and peanut butter moment. Delicious. One of the topics that's been pretty hot in this ecosystem for the last, I'd say two years now has been service mesh and talk about some complexity and, you know, I talked to, it's like, which one of these are you using? Oh, I'm using all three of them and this is how I use them in my environment. So there was an announcement spearheaded by Microsoft, the service mesh interface. Give us the high level what this is. So first of all, the SMI acronym is hilarious to me because I got to tell you, as a nerdy teenager, I went to math camp in the summertime as one did and it was named SMI. It was like Summer Mathematics Institute. And I'm like, awesome. Now we have a work project that's named that. Happy memories of lots of nerdy math. But in my first Unix system that I played with. So, but what's great about that, what's great about that particular project, and you're right that this is very much aligned with you're an enterprise. You would very much like to do enterprisey things like being a bank or being an airline or being an insurance company. And you super don't want to look at the very confusing CNCF project map and go, oh, I think we need something in that quadrant. And then, you know, set your ships for that direction and hopefully you'll get to what you need. And it's especially when you said that you mentioned that this, it basically standardizes it such that whichever projects you want to use, whichever of the end. And we used to joke about JavaScript framework for the week, but I'm pretty sure the service mesh project of the week has outstripped it in terms of like speed of, you know, new projects being released all the time. And like a lot of end user companies would very much like to start doing something and have it work. And if the adorable startup that had all the stars on GitHub and the two contributors ends up, and I'm not even naming a specific one. I'm just saying like, there are many projects out there that are great technically and maybe they don't actually plan on supporting your LTS. And that's fine. But if we end up with this interface such that whatever service mesh, that's a hard word. Whatever service mesh technology you choose to use, you can be confident that you can move forward and not have a horrible disaster later. Right. And I think that's something that a lot of developers went left to our own devices. And in my particular device, the devices are pretty crappy. It becomes a, I want to get this thing built and up and running and working. And then when it finally works, I do a happy dance. And no one wants to see that, I promise. It becomes a very different story when, okay, now how do you maintain this? How do you responsibly keep this running? And it's, well, I just got it working. And what do you mean maintain it? I'm done. My job is done. I'm going home now. It turns out that when you have a business that isn't being the most clever person in the room, you sort of need to have a longer-term plan around that. And it's nice to see that level of maturation being absorbed into the ecosystem. I think the ecosystem may finally be ready for it. And this is, I feel like it's easy for us to look at examples of the past. People kind of shake their heads at open stack as a cautionary tale of sprawl and whatnot. But this is a thriving, which means growing, which means changing, which means very busy ecosystem.  To an enterprise, just because this got launched in 2014, okay, June 2014, that sounds kind of new. Like we're still running that mainframe that is still producing business value. And actually that's fine. I mean, I think this maybe is one of the great things about a company like Microsoft is we are our customers. Like we also respect the fact that if something works, you don't just yolo a new thing out into production to replace it for what reason? What is the business value of replacing it? And I think that's why this kind of Unix philosophy of the very modular pieces of this ecosystem, and we were talking about how them a little earlier, but there's also draft, brigade, et cetera. Like the Porter, the CNAD spec implementation stuff and the cloud native application bundles, which that's a whole mouthful. Well, no disrespect to your sparkly shirt, but chasing the shiny thing and this is new and exciting is not necessarily a great thing. I've heard some of the shiny squad that were on the show floor earlier complaining a little bit about the keynotes that, well, there haven't been a whole lot of new service and feature announcements. And my opinion on that is feature not bug. It turns out most of us have jobs that aren't keeping up with every new commit to an open source project. This is the, I think what you were talking about before, this idea of, I'm the developer. I yoloed this out into production. It is definitely production grade as long as everything stays on the happy path and nothing unexpected happens and I probably have error handling. And yay, we had the launch party. We're drinking and eating and we're happy and we don't really care that somebody is getting paged and it's probably burning down and a lot of human misery is being poured in to keeping it working. I like to think that, considering that we're paying attention to our enterprise customers and their needs, they're pretty interested in things that don't just work on day one, but they work on day two and hopefully day 200 and maybe day 2000. And that doesn't mean that you ship something once and you're like, okay, we don't have to change it for three years. It's like, no, you ship something, then you keep iterating on it. You keep both fixing. You keep, sure, you want features, but stability is a feature. And customer value is a feature. I'm glad you brought that up. Last thing I want to ask you, because Microsoft's a great example. If you say as a customer, if you're an Azure customer, I don't ask you what version of Azure you're running or whether you've done the latest security patch that's in there because Microsoft takes care of you. Now, your customers that are pulled between their two worlds is, oh wait, I might have gotten rid of Patch Tuesdays, but I still have to worry and maintain that environment. How are they dealing with kind of that new world and still have certain things that are going to stay the old way that they have been since the 90s or longer? I mean, obviously it's a very broad question and I can really only speak to the Kubernetes space, but I will say that the customers really appreciate, and this goes for all the cloud providers, when there is something like the dramatic CVE that we had in December, for example, it's like, oh, every Kubernetes cluster everywhere is horribly insecure. That's awesome. I guess your API gateway is also an API welcome mat for everyone who wants to do terrible things to your clusters. All of the vendors, Microsoft included, had their managed services patched very quickly. They're probably just like your heart bleeds of the world. If you're rolled your own, you are responsible for patching, maintaining, securing your own. And this is, really that's that tension, that's that continuum we always see our customers on. Like, they probably have a data center full of, you know, vSphere and sadness and they would very much like to have managed happiness. And that doesn't mean that they can easily pick up everything in the data center that they have a lease on and move it instantly, but we can work with them to make sure that, hey, say you want to run some Kubernetes stuff in your data center and you also want to have some AKS. Hey, there's this open source project that we instantiated that we worked on with other organizations called Virtual Kubelet. There was actually a talk about it happening, I think like in the last hour, so people can watch the video of that. But we have now, we now have virtual node, our product version of it in GA. And I think this is kind of that continuum is like, yes, of course your early adopters want the open source to play with. Your enterprises want it to be open source so that they can make sure that their security team is happy having reviewed it. But like you're saying, they would very much like to consume a service so that they can get to business value. Like they don't necessarily want to take, you know, Kelsey's wonderful Kubernetes the hard way tutorial and put that in production. It's like, probably not because they can't. These are smart people. They absolutely could do that. But then they spent their, you know, innovation tokens as the McFundley blog post puts it, the, you know, it's like choose boring technology. It's not wrong. It's not that boring is the goal, it's that you want the exciting to be in the area that is producing value for your organization. Like that's where you want most of your effort to go. And so if you can use well vetted open source that is cross industry standard, stuff like SMI that is going to help you use everything that you chose wisely or not so wisely and integrate it and hopefully not spend a lot of time redevelop it. If you redevelop the same applications you already had, it's like, I don't think at the end of the quarter anybody is getting their VP level up if you waste time. So I think that is like one of the things that Microsoft is so excited about with this kind of open source stuff is that our customers can get to value faster and everyone that we collaborate with in the other clouds and with all of these vendor partnerships you have the show floor can keep the ecosystem moving forward because I don't know about you but I feel like for a while we were all building different things. I mean, like instead of, for example, managed services for something like Kubernetes. I mean, a few jobs ago I was at a startup that we built our own custom container platform as one did in 2014. And we assembled it out of all the Legos.  It's always a lie. There's definitely bash in there. They may or may not be checking exit codes but like we all were doing that for a while and we were all building container orchestration systems because we didn't have a great industry standard. Awesome, we're here at KubeCon. Obviously, Kubernetes is a great industry standard but everybody who wants to chase the shiny is like, but service meshes. If I review talks for, I think I review talks for KubeCon and Copenhagen and it was like 50 or 60 almost identical service mesh talk proposals.  Like you don't have sensation to them, which is great. You still have them. I think that that hype train is going to keep happening and what we need to do is make sure that we keep it usable for what the customers are trying to accomplish. Does that make sense? It does and unfortunately we're going to have to leave it there. Thank you so much for sharing everything with our audience here. For Corey, I'm Stu. We'll be back with more coverage. Thanks for watching theCUBE.


A little bit of a summary of where we get going and just where we've gotten so far. We were looking at objects under simple axial tension or compression. I have to draw one or the other. I can't really draw both. So as often as not, I just happen to draw something under tension. But what we're looking at now is at the response internally of that material as if we again put one of our imaginary cuts through this material. And then as we look at what's happening inside, we came to appreciate the other day the fact that these internal forces are spread over some cross-sectional area that for the normal stress that we talk about is that cross-sectional area that's normal to that force that's over that face, over that area. Occasionally we'll put a little end there. If we don't, we're generally applying the normal stress. But we had that normal stress, the force divided by the area that's withstanding it, which kind of makes sense. As the force goes up, the stress is going to go up. As the area goes down, the stress is again going to go up. So it makes sense that we do this ratio. And the general units on this, typically kilopascals, maybe even mega, occasionally even as far as gigapascals. But we're talking about generally structural solids that can maintain an awful lot of force over sometimes very small areas. And this can be done with cables and very thin members that withstand an awful lot of weight. So we had that as our first look at the possible type of loading and the stresses associated with that internally to the material. It's the material's ability to withstand these stresses that tells us whether or not we're going to have some kind of catastrophic failure. We also then had the other possibility of not axial loading of some kind, but transverse loading. Could be, as we find with the distributed loads we saw in statics low those many months ago. But again, as we look at the internal response of the material to those loads. And it doesn't matter if it's a distributed load or not, what matters is the internal response of the material to that load. In this case we have a force that's now parallel to the cross-sectional area rather than normal to it. And then we call the average shear stress. So we had the normal stress and if we don't say anything before the word stress, that's the stress we're typically talking about. And then this being the shear stress. And in this case for both of these quantities, these are average values. They are not constant over the cross-section. But we're not going to worry, at least not at this time about the fact that these force distributions across these areas aren't uniform. We're going to treat them as if they're uniform. And so these are average values unless we say otherwise. One other little piece we hadn't quite gotten to and we will look at it as we wrap up this piece, the problem we were looking at on the board. And that's that sometimes one member is simply bearing on the surface of another member at that interface where they connect. Which in this case is this base piece here. At that interface where they connect, there's a bearing force as one member presses on the other. We know that again that this is a load F of some kind. This is a total load F. It's also force acting on the area that's withstanding that force. In this case, it's one object bearing on another. So this is an average bearing stress. Same units, same general size as the other, but can lead to a very different type of failure. I don't know about you. You can go downstairs in my basement at home where I have the columns in the basement supporting the floor above. And you'll see little minor cracking in the concrete below that column. And that's bearing stress starting to cause the concrete to break apart. Well, the builder who happens to live next door swears that it's nothing to worry about, no trouble. I personally think that snakes are coming up through those cracks, but he says they aren't. So I'll have to trust him. But that's a bearing stress. It's not a failure. It's just a response to the material to that stress. But that's the type of thing that we talk about bearing stresses. So that's a little bit of a summary, plus a little extra thrown in. The type of thing we started with on Monday. So any questions with that as you started to look at some of the problems? We'll finish up. We'll look at a little bit of the bearing stress on one of the parts of this member and then we'll move on from it. All right then. Let's refocus our attention on this pin A. This member AB is in compression. So that member is pushing on the pin A. Then the pin A itself is pushing on the bracket at A. So if we take part of a cross-sectional view of that bracket, this course is wonderful for your drawing skills. So I hope they're up to speed. So there's a little bit of the cross-sectional view of the bracket. Then here is the wall to which it's attached. And then the pin itself, pin A, is in the hole that I have represented here. And then the member AB is in compression, so pressing on this pin A. So it's going to be something like the member AB is pressing on the pin there. So we have a bearing stress from member AB on the middle of the pin. And then the bracket is pushing back. It's hard to draw it on the back side of that pin back there. And the pin itself is pressing on this bracket as if it's in the piece there. Now, again, that's just the bearing stress is the force divided by the area that's withstanding that force. For this bracket, things are a little bit different. I'm going to change the view some. We're going to look straight down on the bracket there. It's a little bit easier to draw. Remember, this is a cross-section of the bracket where I'm looking at just the bearing stress of the pin on the interior surface of that bracket where it meets. It's not a uniform force distribution, not in magnitude or direction as it presses on the interior surface here. It changes a little bit with position. We have sort of a circular force distribution where that total force is, of course, actually it's F over 2 because there's two surfaces where this bearing is going on. This is the force coming from the member. So F over 2 is at the two different bearing surfaces. So this is really F over 2. It's still a resultant force in just that direction because the little side components on the left have an equal and opposite side component on the right that cancels each other. So all the sideways components all have equal and opposite opponents to them on the other side. It gives us a net of this F over 2 straight on. But how do we calculate, how do we figure what the area is? It's actually quite simple. And you'll remember this very same type of thing from your statics working in Physics 2. The area we use because of this circular distribution is just simply this cross-sectional area of the opening itself. And that's the area we use to calculate the bearing stress or each bearing stress. In this case, it's F over 2 over A where A is this blue cross-sectional area which is the same as that area there which is what's the diameter of the pin 25 by the thickness of the bracket which is another 25 in this case. And so you can take those known values and fairly simply figure out what the bearing stress is along a curved surface even without a uniform force distribution across it either in magnitude or direction. It all integrates to be just the total force through the... It's not really the cross-sectional area. It's sort of an exposed area sometimes. Same thing you did if you took... Did you do fluid statics in Physics 2? Did this kind of thing figure out the force on an inclined surface, the pressure force on an inclined surface? Sure. Well, it's in your book so if you didn't cover it, it's in there. But we're not going to be doing very much with it. The thing is the reason we can sort of gloss over this as we need to is generally these stresses are not the sources of the catastrophic failure we're worried about. It's much more likely that these objects, these structures are going to fail either in normal stress failure or shear stress failure or some combination of the two. So we're not as worried about the bearing stress. Often anyway it's not as difficult to see because it's a little bit more straightforward but this was one where it wasn't quite as straightforward but the calculation of it does come out to be quite simple in the end. Harder to visualize than calculate actually. Alright, so that will wrap things up for that little diagram. We can put the projector to bed for a bit here. Unless there are any more questions on that structure, there's a lot of pieces in there and if you were designing that, you'd have to take care of every single little part of it to make sure none of it failed because any one of those pieces failed anywhere. If any of the members failed or any of the connections failed or any of the brackets failed, the structure itself is going to fail. One thing we will have to concern ourselves with in a little bit, probably on Monday we'll start with it, is that the failure doesn't necessarily mean that the piece breaks apart and can no longer maintain any forces. It could be that the structure elastically deforms enough so it no longer serves its purpose. It could be that under load some of these members deform enough that other parts in the structure don't match quite and then the piece won't quite work. Same kind of thing if you're putting in a new door and you don't mount it tightly enough that under the load of the door it deforms enough itself that it doesn't even open or close properly. So it's not necessary that things need to catastrophically fail. It might be enough that they just deform until the entire thing itself fails in some way. All right, so we're going to change gears a little bit here as we look at not just simply what's going on internally but take another bit of a view towards it as we look what happens if we're not looking at the stressors on a normal cross-section but on an oblique cross-section where we have a cross-section taken at some angle to the normal direction. So I've drawn such an oblique angle there for us to take a look at. That's our imaginary cut plane through the piece because it's set back at some arbitrary angle theta and then this piece is loaded with some force P. And we'll pull away this front part, look at just the back part here because that will expose for us then that oblique phase now set back at some arbitrary angle theta. Of course it's still true because of the force balance that we need on anything here that it's still force P but that force P is now acting over a slightly different area. We'll call this a theta where a zero is the original phase from which we would have calculated the original stress. So if we look at the original normal stress and by original I just mean what we've been looking at since the first day. It's the load and it's supported by a normal cross-sectional area A0. Let's look at this one then a little bit differently. Let's look at this oblique phase now. We have this force on it say a force P but we can break that into two components. The normal component of that force acting normally to the surface we might call F and then a transverse component that acts parallel to the surface and we can call that V because that is a shear stress so that's our rather common for us to use that as the designator for a shear stress or a transverse force. So I'll cross out that force P because I've broken it into two components. I don't have three forces there. I have either the original force P or the two component forces F and V. I don't have all three. L, this is V. And this is again acting over this area A theta because this is the inclined phase. Imaginary cut through the piece inclined at an angle theta. So this angle as well is that angle theta. So we know that this force F is P cosine theta and it's acting on an area A theta. A theta, the inclined area exposed, remember, imaginarily exposed by that area is the original area A0 also divided by cosine theta. So if we put those two together to see what the internal normal stress is at an arbitrary angle theta, so I'll call this sigma theta it's F over A theta which is P cosine theta, that's F divided now, oh sorry, this is A theta there, not A0, divided by the area A theta which is the original area divided by the cosine so I get P cosine squared theta over the original area. No, this is A0 because now I have cosine squared from here. If I put these two together, I get the cosine squared on top. What's nice about that is that it allows us to compare the normal stresses at an arbitrarily inclined angle interior to the piece compare it to the original normal stress that we were observing and because cosine is never greater than one cosine squared is certainly never greater than one we find that we always have a normal stress at an inclined angle less than the normal stress we have experienced at the regular axial direction as we originally had. So that tells us at off angles at oblique angles we don't expect there to be greater normal stresses than we would have found in the original look at the normal stress anyway. Let's see if that same kind of thing holds true for the shear stress. So the shear stress, let's see, that's the load times sine theta so the shear stress, the average shear stress at some plane, imaginary plane at some arbitrary angle theta is V over the area over which it acts which is V over A theta but V is P sine theta divided by A theta which is A zero over cosine theta and so I get a new then shear stress internal on some arbitrary oblique angle that is sine theta over cosine theta. So what we need to do now is look at what those are in terms of theta to see if there are other places there might be trouble that we would not have seen before if we had looked at some arbitrary angle theta internal to the piece. So if we just look at theta over maybe what I'll call the shear ratio which is I'll look at the ratio of these two sigma theta to sigma zero is cosine squared theta just to normalize it so I can compare the two at an angle of zero degrees which was our original look at the strictly cross-sectional piece this is our member on edge we're looking remember oblique angles of theta so if theta equals zero we're at our original situation we looked at when we opened things on Monday and that's just been simply a shear ratio of one and from there to a maximum of 90 degrees which means we're longitudinally cutting all the way down the piece which is in its own right a bit absurd we get a relationship between the shear ratio and the imaginary angle of our oblique plane to be something like that we see that the worst possible situation is the original one that we've looked at this angle is that's not it can't even drop because it's zero that's where we're going to find the maximum normal stress any other angle from there the normal stress drops and remember this is the normal stress normal at all times to whatever face we're looking at it's not that there's more forces it's just that as we go to oblique angles the original force has different components to it that we have to account for when we look at the shear force however across that face and do the same kind of thing with it we did previously so t theta I'm sorry tau theta over tau zero is sine theta cosine theta that has a bit of a different response to it does something like this where at 45 degrees it reaches a maximum which also happens to be the place where it crosses the other shear stress or shear ratio curve that being the normal response this being the shear stress response we see it does reach a maximum at a place at 45 degrees so at an oblique angle of 45 degrees we see we have the maximum shear response and we're still at a significant normal of about a half at least half of what it was originally so this is a we'll call this sigma one half for some other reason no other reason than just to call it something question John this is in general I assume that once you know material you're working with what we have not talked about at all is what is the material limits on these stresses that we're finding there's no point looking at any of the materials and how they can withstand these stresses until we know how to figure out what the stresses are themselves so this actually turns out to be the critical situation this is an angle of 45 degrees and you will find and in fact I've hosted two videos where they actually do these type of tests and you can see what the failure looks like if you take a test piece and pull it apart when it fails it doesn't fail straight across the piece in a nice clean break it tends to fail something like something very much more like this when the two pieces pop apart you'll see that there's a a semi-irregular surface that's now been exposed where the piece broke it's only semi-irregular because it tends to look sort of like a 45 degree cone that formed on one end as it popped out of the other kind of like a socket to each other but this is at approximately 45 degrees because of the materials inability to withstand the maximum shear at that oblique angle remember our look at all of this was at an imaginary we determined that the maximum shear response was at an oblique angle of about 45 degrees and that's indeed where the material tends to fail it's also true and maybe you've seen this if you've ever overloaded a a column on a deck or some kind of structural piece that was meant to carry more weight than it could it tends to fail something like that and if you I've posted two videos one that shows a tensile test to failure and you'll see sort of this type of surface forming and I've also got a piece of wood in compression to failure and you'll see that it splits in very much this type of way and this is fairly close to that 45 degrees of course this assumes a completely homogeneous material which is not the case naturally we have especially with wood there's differences in the material throughout it's not a homogeneous material perfectly which is why it's not exactly 45 degrees but that is where we predicted a sheer failure and that's just what's seen when the piece does go to failure so on Angel go to check out those two videos they're not even a minute long I don't think you have to watch them closely because what you can't tell is that as soon as the video starts the test has already begun and there's no sound that indicates that there's actually stress and if anybody happens to have an extra $50,000 to buy us one of these test machines we could have done this ourselves so John if you stop wasting your money on little toys on your computer you could buy us a stress test machine we'll talk about that very test probably on Monday so we just had a chance to look at the internal stress at arbitrary angles now we're going to take a more general look at what we might call generalized stresses and again we're really only looking at the two stresses that we've talked about so far well we talked about three but we're not going to talk about a bearing stress here we're just talking about the normal and the sheer stress and again for the most part we're assuming the part to be homogeneous by that I mean a uniform throughout it's not like a piece of wood is where it's very different in one place than it is in another we're just assuming it's a perfect piece of material and the force is uniform over the surface so we have some object we're concerned of and I'll even keep its shape under some kind of loading and again just to illustrate how very arbitrary any of this can be so that we do indeed get a very generalized situation we have some object we don't care what its size, shape, or purpose is it's under some kind of load and we're not even concerned with what that load is all we'll do again is take an imaginary cut through the piece and expose the interior of it so maybe it'll look something like that it looks like a Christmas ham that's what that looks like and we'll put a a cornet system on it just to help us orient things and we'll put the origin of that cornet system just to make things nice and easy for us so we'll call that the X that the Y and that the Z direction so now that we've done that and taken all of these forces, figured out what the resultant is we know that there will be some component of that resultant force right down the X axis normal to the face that's just the nature of the resultant comes out to be we could resolve one component of it to be in the X direction so we'll also imagine that to be acting on a little piece of area we'll call delta A and then the other component of the resultant force no matter where it points it's going to have some component of shear well let me draw it in even a more arbitrary direction because we don't can't possibly know where it's going to be so often some direction parallel to that face is some shear component and it's the two of those together that came from the resultant force of all of these original forces acting on it so since they're both acting on the same area we can make the components not the force components themselves but we'll make them the shear components because they're both divided by the same area so we have that normal component of stress whatever it is whatever magnitude we do know its direction we purposely resolve the resultant into an X component but the Y component the shear component could lie in any direction along that face so what we'll do is make things very simple on ourselves we'll take this exposed face with this coordinate system conveniently located on the center of our our piece there we've got this normal component of the stress in the X direction and remember there could be compression it depends on what the forces were originally and where I made this imaginary cut but I have to draw something so I drew tension and then we'll take this shear component and go ahead and break it into the two pieces in our X sorry, Y and Z directions and then we are able to figure out all pieces we had before so I need sort of a system of writing this thing down so I'm going to use this system here for the shear stresses I'm going to have a two letter subscript to it the first letter is the face that the shear is on and by that I mean a cut like this particularly the X direction we call an X face so this is tau sub X and then the second letter in the subscript is going to be the direction the coordinate direction that that shear component lies in so this would be a tau X, Y, shear a shear stress on an X face in the Y direction so this piece down here is a shear stress and then what would the two letters be that describe what shear stress that is X it's still on the X face that's the only face I've exposed right now is a face in the X direction it's a cut that's normal to the X direction and that one happens to be the component that's in the Z direction so I have a piece that looks just like that so that no matter what my loading is no matter where I actually have this cut we can resolve the resultant force calculate the resulting stresses both normal and shear and draw them in something like that kind of designation remember the actual directions of these is arbitrary they draw something so I just happen to draw them all in that direction we can then do that in the five other directions we can do it on the back of the face we can also do two Y cuts and two Z cuts and come down to all those cuts together expose just a big cube again with the coordinate directions conveniently located at the center of the cube and that exposes the shear stresses the internal shear stress sorry the internal stresses both normal and shear on all of the faces so the ones I've already drawn there I have a sigma X we'll call it a normal stress in the X direction and then I've got those two shear stresses their direction is arbitrary and then there's exact copy of that kind of thing on the back face that I'm not going to draw it's just too difficult to draw behind the board and then on this wide face I've got the same kind of thing it might be tension, it might be compression but there's still going to be some stress along that face I'll just arbitrary choose to draw all of these in the X direction there's a shear stress that will be exposed along that face what should I call it tau it's on the Y face on A Y face we have two Y faces there's one on the bottom as well tau Y face but it's in the X direction and then I might have a component in that direction as well it's on the Y face in the Z direction and again the very same type of thing on the bottom of this cube that we've imaginarily exposed with our cuts through the material and then there's also a normal stress to the Z faces a shear stress on these Z faces one in the X direction and one in the Y direction and then again of course on the back side on the back Z face I'm just not going to bother drawing in total then we've got nine stress components in a generalized case generalized meaning for any arbitrary loading and any arbitrary orthogonal directions we can break down any problem we have nine stress components the nine that you see and then those are each mirror image on the back but not to the point where we have 18 stress components because on the back for example the normal stress in the X direction we have to have the exact same normal stress in the X direction on the back side as well why is that? it must be maintained at all times all of the forces sum to zero these stresses are called these X stresses are caused by X forces so for every X force in that direction we have an equal in the back direction so those aren't new components we only have then the nine stress components exposed and don't forget that the moments must also sum to zero so we're going to generalize things even a little bit farther make things a little bit easier to us we're going to actually look at the force balance on these things so let's imagine our cube has a length a on the side we're only going to look at it in two dimensions we've done this in so many of our other classes where we look at two dimensions rather than all three because what happens in the third dimension is not necessarily any more instructed but it sure complicates the drawings so we can draw the forces on this we'll take just the X, Y plane view of this type of thing we'll ignore the Z direction it comes out of the board at us and so on this X face now first face we drew I'll draw not the stresses but the forces on that piece because I need to do a force balance on this so the force on that face is sigma X acting over an area delta A remember that was the size of the element that I first exposed and of course on the back side we know there must be an equal and opposite load on the back side and again arbitrarily drawn as tension and the sigma Y forces sigma Y delta A and an equal and opposite member to that sigma Y delta A so automatically by virtue of that we've already got the force balance satisfied at least for the normal stresses for the shear stresses I'll draw them something like that to remind us this is across the face remember we're looking down the Z direction we're looking along this X face with this drawing we're just doing there so that's tau and an area delta A remember we're doing a force balance here so I want the forces not the stresses it's not going to be a big concern all these delta A's are the same anyway and this is on the back face so this is tau also on the next face also on the Y direction also acting on an area delta A so that's tau X Y delta A as well force balance there as well and then I have the same type of thing with the shear stresses on the Y faces so that's tau Y X delta A and down here in the opposite direction as it must be because I need to balance that force on the top I have tau X delta A there as well alright we automatically have our force balance satisfied so it gets a big happy check mark because I drew it that way we know it must be that way so it's not like I'm assuming anything we know that we have static equilibrium on all these pieces so I just drew it that way right from the start so I don't need to do anything more with the force balance there that especially works for all the normal stresses all the stresses perpendicular normal to the faces especially because not only are those automatically satisfied force balance those forces are also automatically satisfying a moment balance as well because not only are they equal there's no moment caused by any of those so at least for the normal forces we also have a moment balance satisfied that's not true of the shear forces though because they're equal and opposite but they're not collinear they're separated by a distance A so we need to satisfy a moment balance here with the shear stresses so we'll take this couple first tau x y delta A that's the magnitude of the forces in this couple this is the couple of these two shear forces on the x faces but what's the magnitude of the couple this is just the forces in the couple how do we calculate the magnitude of a couple divided by two forces we have two equal and opposite forces separated by a distance that causes a moment causes a couple the magnitude of that couple is the magnitude of the forces times the distance between the two remember this was a cube of sine A so the magnitude of the couple caused by the shear stresses on the x faces is that so that's the x face there's also a couple caused by the forces on the y faces as well and we know that those must be equal and opposite so that they sum to zero so I'll assume it's equal and opposite turns out I drew it that way anyway so no great trouble with that sorry this is tau yx not xy I'm working with this couple now caused by these shear stresses the forces is the shear stress times the area over which it acts times the distance between the two forces that make up the couple so that's the y face couple and I know they must be equal and opposite but they sum to zero and I drew the minus sign because I actually have them drawn in the opposite direction each other so just taking that into account the x face couple happens to be counter clockwise the y face couple happens to be clockwise so that's the minus sign between the two notice how this simplifies things for us specifically because the a's cancel the delta a's cancel not only is delta xy equal to delta yx but I can do this on the other faces as well and I get delta xz tau xz equals tau zx tau yz equals tau zy as well makes things terrifically easier for us down to not nine stress components we're now down to six stress components we have the two stress components in our x and y direction again I stress upon intended that I'm arbitrarily drawing these as tensile forces tensile stresses we're going to see lots of situations where either or compression I have those two I have a third in the z direction and I have shear stresses that must be drawn in that relationship to each other or we don't have a force balance two on adjacent sides must either point towards each other or point away from each other depending on which corner you're looking at and it's not even important anymore what I designate them I'll just call them the shear stress tau because they're the same on all of the faces because I can do this in any directions I can do this all the way around the cube all of the shear stresses must be the same and they must orient themselves in this way we could have the possibility that any or all of them are in the opposite direction as drawn but then the relationship between the shear stresses must still be like this that they tend to point to opposite corners or they tend to go away from opposite corners depending on what the actual loading is remember it's the external loading that determines the magnitude and the directions of any of these things we'll look at problems that do exactly that very shortly so now we're down to six stress components the sigma the normal stresses in those directions and then the three different parts of the stresses in those directions if I did need to concern myself with the z direction I might further the designation tau xy but all four of these have the very same magnitude they must or we don't satisfy both the force balance and the moment balance if we happen to look at any of the other two directions we just take into account the other two possibilities for the shear stress so that's six components three stresses three normal stresses and the three possible shear stresses we're down now to just six stress components for an entire 3D analysis of the stress on a structural member no assumptions going in here I didn't assume that these would be the same well I did initially assume these would be in the directions shown we'd have the opposite directions of each but it turned out that that's the way it indeed had to be so we get down to this not with any assumptions it's just the reality of the nature of the three dimensional stresses on a solid okay so let's put this together with something we just did earlier again what we're looking at so far is simple axial loading some load on a cross sectional area if we look at some small elemental piece in the member itself remember we of course do not actually expose any of these areas because we can't do that in a structural piece for a simple axial load all we're going to have is normal stresses there in that situation there's no possibility of any shear stresses because I have no transverse component to the stress to the force so I'm not going to have a transverse component to the stresses if we take the very same situation this is not a different situation it's the exact same one we're just going to look at in this way now if I look at an elemental piece not oriented in this way but oriented that way in fact let's let's make it nice and regular make it at 45 degrees I know from the oblique plane study we did to open class that I have shear normal stresses all of the phases now before I only had them on one I only had an axial force on the member I'm only going to have axial forces in resultant but when we took a side look at these we got extra components on the other faces plus I'm going to have shear stresses now exposed on those faces with the oblique plane we open class with we saw that it off angles we get shear stresses across the faces we also know that those will be at their maximum in this piece we also know though now from what we just looked at our generalized case that they must be oriented in that fashion in relation to each other so we've been able to combine view with an oblique orthogonal view where we know now from what we looked at earlier that things are at a maximum at 45 degrees you know I'm sorry if I think about it if I think about it I've actually happened to draw the shear stresses in the wrong direction for this tensile loading because their components are going to be in that direction not as I drew here so let's fix that and those these sigmas remember are not necessarily the same so maybe I'll call those x prime and y prime just to indicate we're at an oblique angle but we do know if that angle happens to be 45 degrees that that is the maximum that we're going to see anything other than that we're going to see less shear stress remember what the magnitude of these shears were the normal shears were to the original normal shear it was half of the original in fact those two would be the same sigma original divided by 2 I guess if they're going to be the same we don't need any kind of subscript on them okay any questions as we go through these things remember that the shear stresses must be oriented in relation to each other in this way they might be in opposite directions but if one's in an opposite direction they all are and no matter what the angle all four of those are the same magnitude or we don't have a static equilibrium on an element which we must for any element any parts any total structure that we might look at questions Phil good the shear on the bottom left hand side is this supposed to be going the other way oh yeah it's too hard to draw talk see I'm in three different time periods I'm saying one thing and I'm thinking what's coming up next good catch, thank you Phil they must always be there they're either pulling the piece this way or they're pulling the piece that way in fact we'll look at that specific deformation caused by those next week