Unsolved Jbeam properties compared to real world physical properties

Discussion in 'Mod Support' started by crashmaster, Nov 4, 2019.

  1. crashmaster

    crashmaster
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    Hey everyone!

    Today ive got a really big question/discussion that id like to start with the forum.

    Over the past few years ive been doing a lot of different jbeam related stuff, ive been able to know how jbeaming works, aka the language itself and the conditions in which you should write code. The syntax in other words haha.

    But my biggest question thats been stopping me since i started modding is the relation between the numbers we give the jbeam and real world data.

    Im currently studying in technical design (3d solidworks stuff)
    and in those 2 years ive had a few different classes related to materials and such.

    Quick warning before we start in some technical stuff, the numbers i give might be off or simply completely wrong, im no engineer and i know little about this stuff but this is stuff that is easy to learn when the right person comes in and explains this stuff.
    Lets say that i dont have a technical specs sheet of every material on earth so im just gonna give out examples to know what i should do if i end up needing to calculate the weight/mass and force of certain items.

    Hopefully with this thread, a lot of experienced modder could pitch in a explain about how they calculate such things to get a realistic acting jbeam.

    Lets say ive got a 2x2x1/8inch square tubing that i wanna make a frame with in beamng.
    if i know that for every 1m cube of steel it weights 3.47lb/ft how would i go about in jbeaming something that is equal of the strength of the material i want to simulate?

    I know how to calculate the weight of an item given its size/total volume and weight per cubic meter.
    But in the jbeam you can have a 1m cube and it could weight 100000kg just as much as 1kg but behind that is the beam spring/damp/strength and etc other properties that jumps in with the suspension springs.
    A 1m steel cube doesnt have the same weight and strength as a 1m titanium cube. How would you go about to jbeam a realistic jbeam according to real world data?

    Every material has a different bending stress and different strength. this is what i want to "decode" with you guys in this post.

    Lets develop a thread where we can learn and explain how jbeam works in relation with real life material properties. Hopefully this thread willl help people who wants to mod in the future. Since this is the whole point of this thread.

    Thank you for your cooperation. :)
     
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  2. Capkirk

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    Jbeam properties primarily use Nm as their units. It should be pretty easy to look up the yield stress/ Young’s modulus of the material you want, calculate how much force would be required to deform it (elastically and plastically), and use that as your Jbeam settings. This will only really work for simple shapes, but it should work.
     
  3. crashmaster

    crashmaster
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    Yeah but as you said, simple shapes.
    Im looking for everything from simple shapes formulas to actual 3 dimensional assemblies.

    Im talking developing formulas here on the forum to help people calculate what beam spring they would need for certain things.


    I also got another question regarding this.
    Seeing how relatively easy it could be figuring it out the jbeam for a single linear tube, how would i go about to make the proper jbeam corners?
    This has to do with trigonometry somewhere in there too right?

    If i have a 3d box with 8 nodes, the cross beams going between all of those nodes should have a different spring then the ones going x/y/z (linear)
    How to figure those out. thats my question.
    Isnt there a way to formulate in a mathematical equation how much beam spring/damp we need depending on the molecular weight/strength of a material?
    Honestly just having a baseline to work with will get me started just enough

    Honestly, if this thread can end up somewhere, id love to develop an excel spreadsheet which i could use to calculate a more stable jbeam without having to do trial and errors for years without success. and then release this spreadsheet on the forum for everyone to have a better idea of how to modify the jbeam to have better results.

    Modding is what expands beamng, but modding is also the hardest thing to do in beamng due to the realism behind it. If together (the forum/experienced modder/devs) we could develop a tool to help us create a more stable jbeam this would most likely improve the overall mods quality. (at least id hope so)

    People wanna start modding and its fun starting with a trash can and all but how do you get to a stable non vibrating jbeam with dev like quality stuff?
    None of us has experience behind the engineering world (or at least very few has experience) and just having a tool like this could help sooooo sooo much in creating quality content.
    And forget trial and error. its what humanity has been doing for thousands of years. im not gonna trial and error my way into perfection if i got no idea where to even start. this is very complex, and for everyone to have to trial and error their way to success, we see less and less mods. If we could develop something like this to calculate the jbeam spring'ness im sure it would aid everyone who wants to create mods for this game.

    This is honestly all that im after, quality content.

    I couldve gave up and released my mods years ago but i keep researching and trying to find a way to make quality stuff but im getting nowhere with my knowledge. im missing a key ingredient somewhere and i cant really get anywhere because of that.

    Ive started learning how to mod this game as early as the 1st official release of this game back in 2013 and ive already came a very long way. the learning curve has been steep but even where i am at now, the learning curve is still extremely steep because ive got no idea what im doing(physics wise). yeah sure i can copy paste official values from another jbeam to another but that doesnt make it stable or even remotely close to realistic.

    I am fascinated by the quality of the official vehicles and i want to be able to create stuff that is near that quality. but as ive been saying, im missing a link between real life material properties and jbeam.
     
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  4. Mad Genexixs

    Mad Genexixs
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    I Completely agree; This would help modders a lot, even me, I was wondering the same thing aswell; how to create a perfect stable jbeam like dev. quality? I did a lots of research, after those two years researching I am able to make a car from scratch, but like half of it is either copied or random placed values.
     
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  5. NOCARGO

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    Very interesting thread ! I am no expert whatsoever on the matter but my first opinion goes like this :

    As I am no scientist at all, imo science is the primary driver to understand most of all technical issues.
    I've been studying the core files for nearly a year now (and only for the time able to spend on it) and I conclude
    that the core of the matter is very scientific. Simpler said, behind the creation of the core are people with scientific
    degrees without a doubt. The right formulas are used (imo) as far as the engine can handle them. So, the engine ?
    Right, here we end up at the Torque3d engine itself, so next thing to consider is how the T3d engine is constructed.

    Again, I'm not really experienced in scientifical matter at all ( and I'm even not native English speaking) but don't the
    jbeam properties can go as far as the T3d engine can handle them ?

    On the side of mass/acceleration ( Newton, followed by Einstein ? ) isn't the node weight ( jbeam ) accounting for
    the most if not all for that ? I don't know, but I know it's strange but the beams don't represent any weight right ?
    If I'm right that means the mass can only be distributed thru out the nodes.

    Also remember that real simulation of real matter still requires supercomputers and doesn't fit in the realm of today's
    home computer at all. On the other hand code gets more and more refined ( in a pleasant complicated way ) and
    this gets us closer to beating the ratios of Moore's Law. :D

    About the beam properties ( like springiness factor or strength and damp etc ) I would say if no one is able or willing to unveil the formula ( which I doubt cause if one goes about learning the Torque engine ) then there are at least
    two options to consider. One, experimenting on the lowest level by comparison with real world actions and then
    work your way up from there, two, wright your own jbeam variables in relation to the engine. I understand the latter
    is far fetched and complicated ( and without any sense imo ). Let me suggest that everyone is one the same side
    here whatsoever, devs, active members and modders and whole humanity as far as I'm concerned. We all want to
    improve Moore's Law, right ? ( or is it 'More' I don't remember right now :) )

    If I'm exaggerating or just dumb feel free to remind me or to clarify :p
     
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  6. ThreeDTech21

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    a list of relative material strengths and node beam values to match would be awesome.

    Eample

    2'x2' quater inch steel Sheet
    {"beamSpring":300800,"beamDamp":1600},
    {"beamDeform":15000,"beamStrength":320000},

    4'x4' quater inch steel sheet
    {"beamSpring":62000800,"beamDamp":1200},
    {"beamDeform":12000,"beamStrength":440000},

    2'x2' half inch windshield glass
    {"beamSpring":72000800,"beamDamp":19000},
    {"beamDeform":24000,"beamStrength":"FLT_MAX"},
     
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  7. NOCARGO

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    Ok, but let's not forget that most things that mankind produces are copies or improved copies of a certain concept :
    "I baked a cookie, mm tastes nice.. Let's bake another one !" :p
     
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  8. crashmaster

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    Well, if beamng tries to simulate real life physics as close to possible and follows the laws of physics (Moores law) that means i should be able to take engineering specs of a certain material (density per m cube) and (im still learning, there are a lot of different words for scientific data on material strength. so take what i say with a grain of salt, since it may not even make sense just because i dont know the right words) take the tensile strength and somehow figure out that if i got a material weighting a certain amount and it can bend a certain amount. knowing all that, technically with numbers we should be able to formulate something that will give us the numbers we need for the jbeam.

    But how do you convert tensile strength to spring damp and deform?

    For college i had to buy a massive Machinery book. (for those interested, this is the book im talking about https://books.industrialpress.com/machinery-s-handbook-30th-edition-toolbox-edition.html)
    In this book, well its basically the bible of machinist stuff.
    There is a lot of info on pretty much anything. but being a 3000 page book i need to read a lot and find what i need first.
    But seeing how i can have the atomic weight of every material, and have their strength both tensile, sheer, yeild strength, elastic limit and wayyyy much more data on physical properties of material, mass and basically all im looking for.

    Somewhere, in all of that physics, there has to be a way to formulate real world data and incorporate them in a jbeam. if not, how does the devs go about to create their jbeams?
    around what data do they make EVERYTHING basically. how can you say something is realistic if none of what we see can be translated to real world data? and vise versa.

    There is technically something to start with in some of the jbeam.

    Autobello front springs/torsion bars
    //10mm 187.4
    //11mm 274.3
    //11.5mm 327.7
    //12mm 388.5
    but this is for the spring itself.
    the current one is 327.7 spring with damp:10, deform:2000
    so technically a 11.5mm thick (steel? aluminium?) rod has 327.7 spring and 2000 deform.

    Im sure we could find other similar stuff in some of the official jbeam.

    Im not the best person at all when it comes to math but im trying a lot of stuff lately since its been fascinating me and all i want to do is figure out the jbeam mysteries to create good mods.

    Honestly i keep searching for numbers i could somewhat convert to real numbers, aka if that steel rod has 327 spring and 2000 deform. if i want titanium rod, what conversion factor should i calculate those with if i know the density of titanium?
    I might be looking further then i need but ive started looking into atomic weights and maybe try some stuff through that. but i need to figure out the whole conversion factor and its a process im currently learning/working on.

    If i know how heavy an item is that figures out the node weight. but what about the rest?
    How does the piano weight and act the way it does? was it done by trial and error or the devs knew the strength of wood and made the piano appropriate for that material.

    Its easy saying "wood weights that much" but there is xyz different kind of wood with their own properties. same goes for aluminium and titanium. there is different strength/density depending on their composition and temperature and etc etc etc.

    True. but when ive started a scratch made jbeam i want to have to calculate the strength of my current project to get something appropriate to what im making.
    Not the front suspension of a subaru ported to a chassis half made from the body of a pigeon and a covet, and the roof of a d series.



    A very interesting topic and i hope we can find out this mystery together hahaha.
     
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  9. atv_123

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    Alright... I will admit that I am leaving this comment here basically just to stick myself in here so I can find it again... but I will try to add some useful information as well.

    Take caution with that initial assumption of 327.7 for the spring... in that particular case we are talking about torsional rigidity... not compression tension or shear. That makes a big difference.

    The torsional spring rate is found via the formula (it's times like these I wish we had a math addon on these forums...)

    Θ = (T*L)/(K*G)

    Θ = Angle of Twist
    T = Twisting moment (basically torque)
    K = Torsional rigidity multiplier for the particular geometric cross section (our case... a circular cross section)
    G = Modulus of Rigidity

    Now this may seem like a mess, but it's really not that bad...

    I was gonna go through the math... but I am kinda at work... if anyone wants to see me work it out, I guess I can oblige later... right now though, use this. http://www.gtsparkplugs.com/Sway-Bar-Calculator.html

    This is basically a spring rate calculator for a sway bar... it's pretty self explanatory, however, when you get done, make sure you convert from lbs/in to N/m as I believe that is what Beam is measured in.

    Ok... I am gonna say some stupid stuff, but keep bugging me for more information... I need to write all this down for everyone to see, but right at this moment I am at work and I don't want to forget to come back and update this with more information. This is kinda my time to shine and I don't have time right this moment to do all the explaining I want to do... so for this next bit I will try to keep this brief as I have to get back to work (my computer is crunching numbers now, so I am good)

    Ok... you mentioned a box right?

    upload_2019-11-5_10-4-16.png

    Le box

    Now the JBeam of said empty box is a little lacking at the moment...

    upload_2019-11-5_10-5-17.png

    This, as anyone that has any modding experience will tell you, will just collapsed into a pile on the floor. So we beef it up a bit.

    upload_2019-11-5_10-7-34.png

    This, as we can all agree, will stand on its own... now there are only surface cross braces... nothing internal. What we have made here is essentially a crate (kinda) but let's go solid for this first example.

    upload_2019-11-5_10-9-32.png

    Alright... now... all the corners are connected (as you can see I have one pair highlighted here) right through the cube... this would basically be what we could do if we were, for whatever reason, simulating a solid cube... lets say... of steel. We are simulating a solid cube of 1mX1mX1m of steel.

    So... what do we do for our properties and why?

    Well I am glad you asked.

    I said this was the simplest example, and that is because it is. A solid cube will exert the same forces all the way through itself no matter the direction that the force is applied... it is dealing with the same amount of material no matter what...

    Granted... even in this simple state... where do we get our numbers?

    Well we now have to do a little math, don't worry though, it's not too hard.

    Now 3 numbers we are going to need are the Yield strength and the Ultimate tensile strength and density.

    I am gonna use structural ASTM A36 Steel because it is the first one in the list on Wikipedia, so we are just gonna roll with it. https://en.wikipedia.org/wiki/Ultimate_tensile_strength

    Our numbers:
    YS = 250MPa
    UTS = 400-550MPa
    Density = 7.8g/cm^3

    Now that we have some numbers, let's do some math... first off, node weight. Since this is a cube, it's pretty easy, however we are in the wrong units... it would be much easier if it were in kg/m^3... so let's do that. 1g/cm^3 = 1000kg/m^3, so our total density is 7800kg/m^3... multiply that by 1m^3, cancel units, and we get 7800kg as our final weight... divide that by 8 as we have 8 evenly spaced nodes and we get 975kg per node. Dis gonna be one chunky boi...

    Alright, next we need to get MPa into something a little more usable by our math... first we shall just drop from MPa to Pa... that is 1MPa = 1000000Pa. Next we convert from Pa to N/m^2 to get it into more recognizable units... but the funny thing is is that Pa IS N/m^2... so 1Pa = 1N/m^2... easy peasy.

    So... now that we have units we can use, what do they mean? Well, this number is in terms of force (N) per cross sectional area of our part (m^2) so... if we multiply by our cross sectional area that each beam is responsible for, we should be about to get our strengths!

    Alright...

    upload_2019-11-5_10-52-55.png

    Pardon my terrible mouse usage...

    Anyways, in one single loading direction, we will have 4 cross sectional areas taken up by 4 beams... each area is 0.5mX0.5m or 0.25m^2. From here it's just simple math (or is it? I will have to get to that part at another time) anyways... our YS is 250MPa or 250,000,000N/m^2 * 0.25m^2. Cancel out the units and we get 62,500,000 N. For out UTS we will use the middle ground of 400 and 550 at 475MPa. So 475MPa = 475,000,000N/m^2 * 0.25m^2 = 118,750,000 N. Cool... whats that stand for though?

    Well, these are our beamDeform and beamStrength. YS is equal to beamDeform and UTS is equal to beamStrength. That means our beamDeform is 62500000 and our beamStrength is 118750000.

    Now the astute of you will notice I didn't take into account any of the diagonal beams helping out... and your right... this is a basic calculation to get close... I will have to come back to break down exactly how you would get even more realistic numbers for all the beams... but for now I am running out of time, so that will have to do.

    Finally, for that spring rate, we need the Youngs Modulus which for this steel is:

    200 GPa = 200,000,000,000 Pa = 200,000,000,000 N/m^2

    Now the equation for stiffness in materials along a single axis (no buckling or anything like that... and technically under tension) is:

    k = (E*A)/Lo

    k = Spring rate/Stiffness (what we want)
    E = Youngs Modulus
    A = Cross Sectional area again
    Lo = the original length of said specimen

    Now this is supposed to be used for wires under tension... but it should still work in this case... would need some testing to verify though...

    Time to plug and chug...

    (200,000,000,000 N/m^2 * 0.25m^2)/(1m (this is the full length of our block)) = 50,000,000,000 N/m^2

    Now again... this is being helped by other beams... I will attempt to take those into account later, but right now I just don't have the time... but anyways, that's how you calculate the spring force for a solid cube of steel... next I will try to add to the calculations to show how to incorporate the diagonal beams, or, if no one is interested in solid blocks, we can skip right to the question at hand which is about calculating for hollow structures...

    That will give much more normal numbers that you are used to... like around the 5,000,000N/m to 50,000,000N/m mark...

    Like I said, make sure to tag me with exactly what you want so I can come back to add more information.
     
    #9 atv_123, Nov 5, 2019
    Last edited: Nov 5, 2019
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  10. crashmaster

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    This is already more then i couldve figured out by myself weeks at a time. (prob in years too by now haha)
    Seriously thank you for writing this post.
    Im currently at college and kinda missing explanations just because im more fascinated by how this all works together instead of creating a firepit hahaha.
    Its gonna have to wait until i get home, but trust me im gonna go run some numbers and tests of my own based on what you wrote here. this is already a great beginning to start with just because you explained and showed me the actual numbers you used and converted.
    I kept seeing Gpa and a bunch of other force related stuff but i had no idea where to even place those numbers.
    This was exactly the explanation i needed. thank you so much for this.

    I might not be the best at math, but honestly if you keep explaining stuff like you just did, with the addition of computer aided calculating, i know what to do now. This is actually all of the missing links i am currently talking about.
    I keep saying im not that great at math. what i more precisely mean by that is, i wont be the one whos gonna find a new formulas because i have a hard time placing my numbers. but over the time ive been able to do some pretty nice math related stuff. skills are getting somewhere but ever since highschool ive been more slow then others at doing math, but at the end of the day i usually end up with decent results. Aka i can manage when i understand hahaha. it just takes a bit of time.

    I understand you cant properly explain the whole process yet, but take your time. as much of this might seem complex, as much as we need to get this sort of information out here on the forum for everyone to read and be able to understand how to create stuff properly. this is a big missing piece for a lot of modders.

    It seems math heavy because it is. but its somewhat basic stuff still. we arent going in crazy math territory ya know. i find this stuff manageable so its all going good.

    I really appreciate the time you put into writing this. thank you very much for this great addition. this is already extremely helpful for me.
    Ill come back later, hopefully i wont be bugging you too much for answers haha.
     
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  11. atv_123

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    No no no... do bug me... that's kinda the point... the more information we get out there the better everyone can benefit from it. This is going to require all sorts of information that I would love to go about explaining, I just need to remember to come back here and do it.
     
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  12. ThreeDTech21

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    is there a website that list all the scientific specs of metal and other materials? We could get all the specs and break it down into tables and run math on it to get the correct beam settings, kind of like an input converter, it converts various inputs into correct beam settings, that would be epic!

    Heres a search for tables: https://www.google.com/search?rlz=1...TlAhVgThUIHYAsAG0QsAR6BAgHEAE&biw=958&bih=878
     
  13. NOCARGO

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    Now you see, it's people like @atv_123 in the dev team :)

    Another thing : Moore's Law = the rate at which the computational power of computers increases over time.
    Knowing that will make my point a bit more clear I guess :)

    Also would like to add that conversion tables and calculation standards etc can be found in a few places
    among the core files. Not sure, but there might be clues of how BeamNG handles some jbeam constants and the like.
    Not sure if jbeam calculations can be found, I haven't got to the point of finding out.

    And I would like to repeat my statement about Torque3d. Isn't Torque playing a key role factor when it comes to
    getting to the full technical details of the simulation process ?

    Anyway, @atv_123's approach is quite sensational indeed so far !
     
  14. crashmaster

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    Yes that would be nice.
    But just take note that i said tensile strength but the tensile strength is the strength of a material stretching apart.
    There is also the compressive strength. but seeing how materials deforms differently in any direction it gets complicated.
    I did a quick google for tensile strength and they talked about ultimate tensile strength.

    But if someone would want to go in depth, and have horizontal beams act as compressive strength and a vertical beam act as tensile strength? idk if its worth it or if it even makes sense to do it like that. So maybe its better to follow only the Ultimate tensile strength of a material.

    I think ill have to go look in the core files some more. i have been looking around in them but mostly in the vehicle lua's and not much else.
    Ive been slowly learning lua and ive been tempted to try to write my own stuff but beamng seems to handle the lua a little bit in a unique way. i honestly dont know. its a long process.

    I dont have the actual quote but i remember seeing the devs talk about this a bit.
    I might say something completely false here but i just know the devs has been taking out parts of torque 3d and it was basically just used as a base to start their own game engine.
    But torque 3d is still a factor in the game engine itself. It would be nice to have a dev explain this a bit in detail once and for all.
     
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  15. NOCARGO

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    For instance, the devs have written their own LUA modules to act upon how the lua code functions in the game.
    They are like 'pre-tables' and there are quite bit of them and on a few different levels too if I'm correct. :)

    + 1 :)
     
  16. alex1dp

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    Sorry for the bump, but it would be interesting to know the formulas for both diagonal beams and hollow structures @atv_123
     
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  17. atv_123

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    I am so sorry, I completely forgot about this :rolleyes:

    I'll have to go back through and read my post so I can make sure to give you all proper numbers and maths as I don't remember what I was carrying on about ;)
     
  18. crashmaster

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    I didnt forget about this. but i was waiting for a time more appropriate for me to really get into this.

    I did try to go thru what you said already but i already had difficulty getting the same numbers are you.
    I get confused with numbers, computers helps a lot but it still takes me more time to learn the big complex stuff.

    I know its something that is time consuming and the purpose of this thread wasnt even to be answered within a week. your response was already quite detailed and overwhelming and i loved it. Its exactly what we needed.
    But this stuff is time consuming for whoever works on it, so as i said, even if it takes months to get to an actual working formula, or a response. if after a few years we finally get something good out of this its really going to be helpful for whoever really wants to take the notch up a little bit on the quality of their mods, but have no idea how to.
    im just finishing up college in a few months and kinda getting on track with starting my life so modding has kinda just been on hold for a while now.

    Thank you for the time you put into this already. its been a very helpful bunch of information.
    i still managed to make some research and now i have somewhat of a better idea about what we are talking about. Its very helpful stuff.
     
  19. Taza

    Taza
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    So basically, if you need values for your own jbeam, find the closest match in terms of material, structure and weight from the game files, and copy those values. If needed, lower until shaking stops.
     
  20. atv_123

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    Alright, so I will tag my previous post to make sure that everyone is with me when we go about these calculations… that way we can all be on the same page.

    I had typed up this nice long post… and then it went and deleted itself… so I might accidently cut some stuff out… if it isn’t understandable, please just DM me about it and I will come back and fix it properly… There was like 4 hours of typing and it is all just gone.

    So anyways, with our cube, we left off with a vertical force of 50,000,000,000 N/m^2

    In our cube, we have this force being spread across 4 different beams. The perfectly vertical beam, the corner node to corner node beam on face one, the corner node to corner node beam on face two, and then the corner to corner node beam across the interior of our cube.

    Beams in BeamNG are basically just springs, so the nice thing about springs is that when they are calculated in parallel, their spring rates can just be added together.

    Spring calculations have x for the position, F for the force, and k for the spring rate. The equation for a spring is F = k*x. This leaves us with:

    x = x1 = x2 ---> F = F1 + F2 ---> kx = k1x + k2x ---> kx = (k1 + k2)x ---> k = k1 + k2

    This means that spring rates for our 4 beams can literally be 50,000,000,000 / 4.

    That gives us 12,500,000,000 N/m^2 per beam per node… but this isn’t the whole story. While that is the proper value, that is only the proper value for our straight side beams. We have beams at angles as well that also have to support that same force. So how do we get that?

    Triangles.

    Alright… so basically we have 2 different triangles in this cube. One with the hypotenuse across each of the faces that have 2 sides equal to 1m (since our cube is just 1m x 1m x 1m) and we have another that has 1 side equal to 1m, and the other side equal to the hypotenuse of the other triangle. To find these sides we need the pythagorean theorem.

    Basically C^2 = A^2 + B^2 or C = √(A^2 + B^2)

    You can get a pretty good breakdown of everything here:

    https://www.calculator.net/right-tr...taunit=d&cv=&hv=&areav=&perimeterv=&x=50&y=17

    They do it pretty well, and I did break everything down before, but I don’t feel like typing that all again right now.

    The important things to know are that our face corner to corner beams are a perfect 45°, 45°, 90° triangle, which means that 2 of the sides will be exactly the same length… so if you know even one of those sides, you immediately know the hypotenuse as it will always be one of the sides multiplied by the √2. Your side is 3m and it's a 45°, 45°, 90° triangle? Your hypotenuse is 3*√2… solid.

    So that takes care of the length on the cross beams on the face of the cube, but what about the interior of the cube? Well… that has a base length of one of the cross beams that we just calculated, and then a height of just the cube itself. This gives us a triangle with the side lengths of 1m and √2m. Now we just plug and chug.

    C = √(1m^2 + √(2)m^2) = √(1m^2 + 2m^2) = √(3m^2) = √3 m

    So C = √3 m… lovely.

    So why do I bring all this up… well, luckily forces can be calculated in the exact same manner. Soooooooo our 1m side has a spring rate of 12,500,000,000 N/m^2. Fantastic… so now that we figured out or side lengths with our triangle, we can use those to find our spring rates. We basically just use our main spring rate and use it in our pythagorean theorem. Granted, since the spring rate is also on the side of the triangle that is length 1, we can literally just multiply the spring rate by the length of the hypotenuse.

    That leaves us with a the material properties of:
    Node weight of 975kg
    beamDamp of ~0.001
    Vertical beams properties
    beamSpring of 12,500,000,000 N/m^2
    beamDeform of 12,625,000 N
    beamStrength of 29,687,500 N
    Corner to corner face beams properties
    beamSpring of 17,677,500,000 N/m^2
    beamDeform of 17,854,274 N
    beamStrength of 41,984,063 N
    Corner to corner interior beams properties
    beamSpring of 21,651,250,000 N/m^2
    beamDeform of 21,867,763 N
    beamStrength of 51,421,719 N

    These numbers are found all the same way… take the vertical beams properties, and then just find their adjusted values for each of the differences.

    Now unfortunately, since this is a completely solid block of steel, it ends up being way too stiff for Beam to really work well with it, so without over adjusting the weight way above what it should ideally be to be realistic… it ends up exploding. But beam is more supported to being able to deal with the stiffness of hollow structures.

    Fortunitally I can still test this to prove my point and show that the numbers still work out by just adjusting the node weights…. Get them high enough and it becomes stable and it might as well just be putting a weight on top of it.

    So for 62,500,000 N/m^2 (our YS) we need to support:

    F = m*g ---> 62,500,000 N/m^2 = m * 9.81 m/s^2 ---> 6,371,050 kg (through some unit reduction) per node.

    So from this we can see when it would collapse like this.
    Node weight of 60,000 kg
    screenshot_2020-05-04_21-01-25.png

    Node weight of 600,000 kg
    screenshot_2020-05-04_21-02-26.png

    Node weight of 6,000,000 kg
    screenshot_2020-05-04_21-05-30.png

    Node weight of 6,371,050 kg fails as it is right at the yield strength
    screenshot_2020-05-04_21-06-30.png
    screenshot_2020-05-04_21-06-33.png
    screenshot_2020-05-04_21-06-38.png

    So... this is for solid blocks....

    I will come back on again and do hollow structures next...
     
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