i have a question. I understand everything about Young's Modulus but, when they say a material has for example 210000 N/mm^2 , what do they mean? that it can handle 210000N/mm^2 in the elastic region? and then it goes to the plastic?
Young's modulus, yield strength (the stress at which a material goes plastic) and ultimate strength (the stress at which a material fractures) all have the same units. So it doesn't make sense to say "a material has 210000 N/mm^2", without specifying which parameter we are talking about. 210 GPa is a typical Young's modulus value for steel, so it is likely that in this case the 210000 N/mm^2 is Young's modulus.
No - it means that the slope of this material's stress-strain curve in the elastic region is equal to 210000 N/mm^2. So for example for an applied stress of 210 MPa, we would get a strain of 0.1%.
@@whitelight32 no, it means that you need 210 GPa stress in material to deform it by 100%, of course it will fail because Young modulus is only appropriate (linear) in elastic range of the material. Simply saying, Young modulus is the number that helps you transform stresses to strains and vice versa but only in the elastic range of the material, for concrete it is 0,20% for compression, for reinforcing steel it is up to ~0.24% in tension
I get amazed at the wealth of information available to us now. It's fascinating how physics, one of the broadest subjects, is so widely accessible and easier to understand if explained by independent creators rather than by mainstream school teachers. Amazing video, btw!
Wikipedia is my book… I find myself having a deep spiritual thought next thing you know I’m clicking on all the blue words looking at the facts of words like sound, it really is amazing
Very useful and simple refresher. I had forgotten these stuff from my college days. I was doing some project with my driveway to eliminate lateral stress on a retaining wall thereby extending its life. I was stuck at a point. I could get the vertical stress figured out but horizontal is what mattered. This video refresher cleared everything and I am at completion of my project. Thank you for the educational videos.
This is a clear and comprehensible explanation. The sounds in this video are sooo pleasing and captions are perfectly timed. It is evident that you have really put an effort into making everything great. Thank you :)
This is a really great straight forward video. As a Metallurgist, this was a really good introduction. You explained it way better than my professors did. I don't wanna be that guy that tells you why your video is wrong. But around 5:30, you show that carbon replaces the iron atoms in your model. In reality, carbon goes in between the iron atoms in the interstitial space. This is hopefully a video that you could do in the future talking about until cells and Crystal structures. Keep up the good work!
Thank you for your kind comments Jon. You are of course correct about the interstitial nature of steel - my mistake. Hopefully the animation still illustrates the point without being too misleading. A video on unit cells would be really interesting - thanks for the idea!
@pyropulse As an engineer with quite some work experience i must say the following: The stuff with the atoms is nice and everything but it should have been left out of a beginners introduction video entirely. The only thing that has to stick in the head of an efficient engineer is that E is a material constant that represents the slope of sigma and epsilon and is different for different materials. It is also commonly used in combinations like EI and EA. For the advanced theoretical engineer the atom part is important of course ;)
@@a1mforthetop I don't think so, I am a high school student and I get way more intuition if I understand how things work at the atomic level and then use the non-descriptive formulae.
Bro the background music in disturbing the concentration. Please upload it with a smooth and lighter music like in your stress strain demonstration video. Thanks
It feels sad that you have very less subscribers. But I must say the way you explain concepts is awesomeeeee..... Looking for many more concepts from you ....
Everything is great about this video, the explanation is top-notch supported by equally great animations and designs. This is the first video I am seeing on your channel. Looking forward to watching other videos and understanding my concepts better.
I wish I had these videos before solids and egineering experinentation courses. Incredibly well done. Ill be sure to lead other people your way when they are introduced to these concepts.
Thank you so much bro I got an engineering final today this helped quite a bit as well as several of your other videos. You have for sure earned yourself a subscriber.
Correction if I may. 5:37 depicts the Fe atoms being replaced by Carbon, that's what happens in substitutional alloys. Steel is a interstitial alloy, the carbon atoms to not replace Fe atoms, instead they reside in the space between the Fe atoms. This is VERY important since the formation of martensite depends on the position of those C atoms to change the crystal structure of steel into BCT(body centered tetragonal)
Just found your page tonight I find it interesting so far. I’m a dual ticket Red Seal Ironworker and Welder and I’ve performed tensile tests both in school and at work. What you covered is very informative but you could have added more about quenching and tempering and how much tensile strength it can add. How it increases brittleness and ductility. I had a weld test on mild steel with 7018 SMAW welding electrode(rated for 70000 psi per square inch) heated red hot and quenched immediately. It sheared at 138,000 psi on the tensile test which I found very interesting.
Really interesting video!!! It is really awesome how this topic can be so simple to explain in a video of less than 7 minute instead when you are at university class normally takes 1.5 hours
😭😭😭😭😭😭😭😭 TY..TYSM! U r an ultra pro legend! God bless u! Why don't u tutor our teachers as well..I don't get a single word in his lecture! I feel blessed to have u as my tutor...TYSM!
Thank you for your job , and I'm wondering If I could take some images from this video to put it in my thesis , if you don't mind cane you send me the resources to put it in the reference Thank you again
At around 2:30, i hear wood and composites as an isotropic material. I somehow remember them to be orthotropic. Correct me if i am wrong. Nice videos: this one and others on this channel. I sometime stream them on TV as well. Thanks for putting such info in concise form. :)
Great video. Wish it were a bit longer. I especially wanted to see a comparison of various materials, including graphene, which has the highest Young's modulus as far as we know.
@The Efficient Engineer You're quite welcome. It seems like I'm an earlycomer to your channel, meaning I'll probably get to talk to you one and one and my feedback will actually matter. Just the way I like it :)
Good video that I can recommend to my students. But be careful: in your stress-strain curve, you have greatly overestimated the elastic strain (it's just 0.1-0.5% for most steels) as compared to the plastic strains. Also, while many engineering materials indeed follow Hooke's law, this is by no means generic behaviour. Many plastics, foams, and biological matter are very different :-)
4:14 Hey nice, dislocations! We need to know quite a bit about them for our geodynamics/microtectonics M.Sc. class, so I know how much more detailed all that can get. Sometimes a less stiff material can be still desired, considering (brittle) failure, right? I mean if that bridge goes from "oh, here it works to "oh, here it collapsed" in an instant, when that would be pretty bad. Also one must keep SLS and ULS in mind. There's one thing I didn't quite understand yet though. Most of the time you're talking about elastic and plastic deformation. What's with brittle deformation? Or is brittle "deformation" simply plastic deformation after the strain was too high? Will have to keep watching some youtube videos about brittle failure, as well as rheology models considering not only strain but also strain rate. I'm very grateful for your videos and visualizations!
Every topic is very well explained and helps us visualise, which is really important. Hats off to @The Efficient Engineer. But it would be very much appreciated if music is not used.
Great aninations and best teaching method....but the number of lectures are not enough to fulfill our courses..Hope that it get benifits to students in near future🥰
keep up the great work. Looks like you're channel is very new but your presentation and video making skills are already on par or better than quite a lot of educational content here on RUclips. I'm going to pass this on to my material science professors as they would be great for freshman engineering students.
At 5:10 why elastic deformation is GPa and ultimate tensile is MPa... When you extend an material in order of GPa for sure you go over MPa ... I miss something?
Ultimate strength is in MPA and Young's modulus in GPA because Young's modulus is theoretical and material would break before it reaches that point . Ultimate strength is the value where a material will fail
Awesome video! Btw, just a question. So assuming that stiffness in polymeric material is caused by the intermolecular forces. So the stress-strain curve for polymeric materials flatter in higher stresses cause the molecules are farther apart and the intermolecular forces are weaker and less stress is required to pull the molecules apart. Is that right?
Hello The Efficient Engineer! Thank you for your videos! They are great! I have one question. Why did you show on graphic on 2:38 that wood (pependicular to grain) is stiffer than wood (parallel to grain). I think it must be contrary because if load direction is parallel to grain than grains are tensed by all their length. But if load is pependicular to grains, so only part of grain and the space between grains are strained. Isn't the second case lesss stiff than the first one?
The rule of thumb that we used, for a safety factor, was 1/2 the yield stress. Though the value can be moved, we used this rule of thumb for almost every application.
I have a question: If two materals have the same Young's modulus value, but different yield strengths, will the material with a higher yield strength be called more elastic than the one with a lower yield strength? Or is only the Young's modulus a measure of elasticity?
Sir my doubt really got cleared. Thank you, sir. Sir, it would be better if you decrease the background music just a bit. yours faithfully Hriday Sahoo, India
So good an explanation it was..... believe me your subscribers are gonna increase with the speed same as the speed of light......good luck.... and I'm a subscriber too......=)
On the note of bridges during the end, isn’t yield strength of the material also of importance when wanting to avoid deflection and/or an overall elastic behavior? Of course, a rubber bridge isn’t as beneficial and sturdy as a steel bridge, but wouldn’t using high yield strength steel would also cause problems with deflection?
You did say that the higher the young's modulus of the material, the higher its stiffness but smaller elastic deformation. Mild-carbon steel has a higher E and smaller yield strength which is the opposite of the high-carbon steel. Does this mean, use mild steel in structural design? Thanks in advance for your reply.
Yes. If you know the applied force (compressive or tensile testing), the cross-sectional area and the strain, you can calculate the Young's modulus. Hooke's law is the key word. In the beginning of this video he mentioned shear modulus and bulk modulus. For isotropic materials all of these moduli (Young's, shear, bulk) are related via Poisson's ratio. I think it would be a nice video topic (also maybe how it works in orthotropic materials). He did mention shear modulus in the video "Understanding Torsion", though.
Great video! Thanks for creating all of these, they're great. At 2:27, I'm not sure if it was your accent or not but it sounded like you said isotropic rather than anisotropic?
I think he said "for anisotropic materials", but it sounded like for an isotropic materials. If he had said it the latter way, materials wouldn't have been plural.
Thanks a Lot for the Useful info, I Have a Question Please, in Car Plates Industry when we use the 1050 Aluminum Alloy, what Temper you suggest to be Used and what Mechanical Properties are the best to avoid Plastic deformation when applying the Plate Numbers Please. Thanks
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i have a question. I understand everything about Young's Modulus but, when they say a material has for example 210000 N/mm^2 , what do they mean? that it can handle 210000N/mm^2 in the elastic region? and then it goes to the plastic?
Young's modulus, yield strength (the stress at which a material goes plastic) and ultimate strength (the stress at which a material fractures) all have the same units. So it doesn't make sense to say "a material has 210000 N/mm^2", without specifying which parameter we are talking about. 210 GPa is a typical Young's modulus value for steel, so it is likely that in this case the 210000 N/mm^2 is Young's modulus.
@@TheEfficientEngineer and practically this means? that this kind of material can take up to 210000 N / mm^2 and then breaks?
No - it means that the slope of this material's stress-strain curve in the elastic region is equal to 210000 N/mm^2. So for example for an applied stress of 210 MPa, we would get a strain of 0.1%.
@@TheEfficientEngineer Doesn't that also mean that we need 2.1 MN of force to change the materials area by 1 mm^2 ?
@@whitelight32 no, it means that you need 210 GPa stress in material to deform it by 100%, of course it will fail because Young modulus is only appropriate (linear) in elastic range of the material. Simply saying, Young modulus is the number that helps you transform stresses to strains and vice versa but only in the elastic range of the material, for concrete it is 0,20% for compression, for reinforcing steel it is up to ~0.24% in tension
I get amazed at the wealth of information available to us now. It's fascinating how physics, one of the broadest subjects, is so widely accessible and easier to understand if explained by independent creators rather than by mainstream school teachers. Amazing video, btw!
Wikipedia is my book… I find myself having a deep spiritual thought next thing you know I’m clicking on all the blue words looking at the facts of words like sound, it really is amazing
Very useful and simple refresher. I had forgotten these stuff from my college days. I was doing some project with my driveway to eliminate lateral stress on a retaining wall thereby extending its life. I was stuck at a point. I could get the vertical stress figured out but horizontal is what mattered. This video refresher cleared everything and I am at completion of my project. Thank you for the educational videos.
This is a clear and comprehensible explanation.
The sounds in this video are sooo pleasing and captions are perfectly timed.
It is evident that you have really put an effort into making everything great. Thank you :)
This is a really great straight forward video. As a Metallurgist, this was a really good introduction. You explained it way better than my professors did.
I don't wanna be that guy that tells you why your video is wrong. But around 5:30, you show that carbon replaces the iron atoms in your model. In reality, carbon goes in between the iron atoms in the interstitial space. This is hopefully a video that you could do in the future talking about until cells and Crystal structures.
Keep up the good work!
Thank you for your kind comments Jon. You are of course correct about the interstitial nature of steel - my mistake. Hopefully the animation still illustrates the point without being too misleading. A video on unit cells would be really interesting - thanks for the idea!
@pyropulse As an engineer with quite some work experience i must say the following:
The stuff with the atoms is nice and everything but it should have been left out of a beginners introduction video entirely.
The only thing that has to stick in the head of an efficient engineer is that E is a material constant that represents the slope of sigma and epsilon and is different for different materials.
It is also commonly used in combinations like EI and EA. For the advanced theoretical engineer the atom part is important of course ;)
@@a1mforthetop I don't think so, I am a high school student and I get way more intuition if I understand how things work at the atomic level and then use the non-descriptive formulae.
@@nahfid2003 I agree! Atomic-Level-Explanations in Mechanics are the best!
interstitial space means?
This channel is the yardstick for engineering education
Bro the background music in disturbing the concentration. Please upload it with a smooth and lighter music like in your stress strain demonstration video. Thanks
It feels sad that you have very less subscribers. But I must say the way you explain concepts is awesomeeeee..... Looking for many more concepts from you ....
Ya your right , sir your videos are really good , l like them a lot , we can understand easily and gain good practical knowledge .
Hello by now you must have graduated
These series of videos NEVER GET OLD!! thanks!
Everything is great about this video, the explanation is top-notch supported by equally great animations and designs. This is the first video I am seeing on your channel. Looking forward to watching other videos and understanding my concepts better.
I wish I had these videos before solids and egineering experinentation courses. Incredibly well done. Ill be sure to lead other people your way when they are introduced to these concepts.
MAN! People like you deserve more subscribers!!
Keep up the good work👍
Awesome. I am a doctoral student, and found your videos amazing. Super easy to understand, but extremely effective. Many thanks.
Amazing explanation, that significance you mentioned is all the reason why this video deserves a like.
presented all aspects of youngs modulas with great clearity and graphics 👌👌👌
Channel is under rated ...i expected millions of subscribers ❤
Thank you so much bro I got an engineering final today this helped quite a bit as well as several of your other videos. You have for sure earned yourself a subscriber.
Awesome, good luck! :)
Correction if I may. 5:37 depicts the Fe atoms being replaced by Carbon, that's what happens in substitutional alloys. Steel is a interstitial alloy, the carbon atoms to not replace Fe atoms, instead they reside in the space between the Fe atoms. This is VERY important since the formation of martensite depends on the position of those C atoms to change the crystal structure of steel into BCT(body centered tetragonal)
Great, but i guess he wanted to keep the atomic level details minimum...so the beginners don't get confused, but the overall idea is correct
Fantastic gem of a channel here.
Just found your page tonight I find it interesting so far. I’m a dual ticket Red Seal Ironworker and Welder and I’ve performed tensile tests both in school and at work. What you covered is very informative but you could have added more about quenching and tempering and how much tensile strength it can add. How it increases brittleness and ductility. I had a weld test on mild steel with 7018 SMAW welding electrode(rated for 70000 psi per square inch) heated red hot and quenched immediately. It sheared at 138,000 psi on the tensile test which I found very interesting.
I meant lowered ductility, sorry it’s 1am
Really interesting video!!!
It is really awesome how this topic can be so simple to explain in a video of less than 7 minute instead when you are at university class normally takes 1.5 hours
the kind of youtube channel i was searching. thanks it has helped me in my physics course👍👍👍 u r the best
Keep up the good work of explaining these material properties in such an interesting and understandable way.
😭😭😭😭😭😭😭😭 TY..TYSM! U r an ultra pro legend! God bless u! Why don't u tutor our teachers as well..I don't get a single word in his lecture! I feel blessed to have u as my tutor...TYSM!
Now I will not forget anything about youngs modulus 👏👏
I googled what my vise grip tool was made of and ended up with a bachelor's in engineering lmao
inspiration comes in many foms!
Thank you for your job , and I'm wondering If I could take some images from this video to put it in my thesis , if you don't mind cane you send me the resources to put it in the reference
Thank you again
Probably best if you send me an email to hello@efficientengineer.com with specifics.
Thank you for the wholesome technical explanation ,it makes comprehension easier in Mechanical Engineering studies
A short & comprehensive video which well explains the basics. Thanks!
very informative with simplicity
Amazingly beautiful way of elaboration.my whole study of Youngs Modulus at one side and this at other side. Really great work👌. Keep it up
Thanks for the beautiful videos. Subscribed. But please consider not having the background music . It is quite distracting for a serious subject.
hey, continue the videos. it helps me a lot. thank you!!!
I have Materials test tmrw thanks for the help
Plzz upload such videos more in the future so we will build our cocepts in better and efficient way. Thanx.
Thx man, i have exam tomorrow, you helped me a lot ❤
The best presentation ever made
Thanks
I am from India your video is very efficient for me thanx a lot
It is soo detailed!!
Thank you upload more civil engineering related videos..
At around 2:30, i hear wood and composites as an isotropic material. I somehow remember them to be orthotropic. Correct me if i am wrong.
Nice videos: this one and others on this channel. I sometime stream them on TV as well.
Thanks for putting such info in concise form. :)
Great video. Wish it were a bit longer. I especially wanted to see a comparison of various materials, including graphene, which has the highest Young's modulus as far as we know.
Thanks Feynstein! Graphene would have been a good one to discuss. I'll try and mention it in a future video.
@The Efficient Engineer You're quite welcome. It seems like I'm an earlycomer to your channel, meaning I'll probably get to talk to you one and one and my feedback will actually matter. Just the way I like it :)
5:57 If i understand correctly...
In bending load. It is strain that increases stress which results failure of material.
Fantastic explanation. Short and on point!
Your videos are great. They help me so much. You should feel really proud of all the value u provide for people, at no cost to them!
Very good explanation of material properties, hope we can see more video like this. thanks a lot~~
Fantastic explanation!
Waiting to watch more videos on Civil Engineering!!
Great explanation in each and every video .feeling very happy to listern every video...expecting even more videos like this ..
Great going hope to have more vedio s in future
Good video that I can recommend to my students. But be careful: in your stress-strain curve, you have greatly overestimated the elastic strain (it's just 0.1-0.5% for most steels) as compared to the plastic strains. Also, while many engineering materials indeed follow Hooke's law, this is by no means generic behaviour. Many plastics, foams, and biological matter are very different :-)
Thanks for the fact checking =)
Love the videos so far, excited to see where this goes.
4:14 Hey nice, dislocations! We need to know quite a bit about them for our geodynamics/microtectonics M.Sc. class, so I know how much more detailed all that can get. Sometimes a less stiff material can be still desired, considering (brittle) failure, right? I mean if that bridge goes from "oh, here it works to "oh, here it collapsed" in an instant, when that would be pretty bad. Also one must keep SLS and ULS in mind.
There's one thing I didn't quite understand yet though. Most of the time you're talking about elastic and plastic deformation. What's with brittle deformation? Or is brittle "deformation" simply plastic deformation after the strain was too high?
Will have to keep watching some youtube videos about brittle failure, as well as rheology models considering not only strain but also strain rate.
I'm very grateful for your videos and visualizations!
Every topic is very well explained and helps us visualise, which is really important. Hats off to @The Efficient Engineer. But it would be very much appreciated if music is not used.
Your slides are so good. The background, presentation,.....😃
Thank you!!! Glad I found your channel, I have a design principle module at uni
excellent!! very illustrative and to the point. Thanks
Great aninations and best teaching method....but the number of lectures are not enough to fulfill our courses..Hope that it get benifits to students in near future🥰
Thanks a lot, for your very very good explanation of Youngs Modulus!
keep up the great work. Looks like you're channel is very new but your presentation and video making skills are already on par or better than quite a lot of educational content here on RUclips. I'm going to pass this on to my material science professors as they would be great for freshman engineering students.
Thank you, much appreciated!
At 5:10 why elastic deformation is GPa and ultimate tensile is MPa... When you extend an material in order of GPa for sure you go over MPa ... I miss something?
Ultimate strength is in MPA and Young's modulus in GPA because Young's modulus is theoretical and material would break before it reaches that point . Ultimate strength is the value where a material will fail
Wow, you sound more cheerful on this video! :-D As usual, great lessons...Thank you.
These videos are great, thank you!!
Awesome video! Btw, just a question. So assuming that stiffness in polymeric material is caused by the intermolecular forces. So the stress-strain curve for polymeric materials flatter in higher stresses cause the molecules are farther apart and the intermolecular forces are weaker and less stress is required to pull the molecules apart. Is that right?
theres no need for the sad music bro im trying to learn here im gonna cry
Hello The Efficient Engineer!
Thank you for your videos! They are great!
I have one question. Why did you show on graphic on 2:38 that wood (pependicular to grain) is stiffer than wood (parallel to grain). I think it must be contrary because if load direction is parallel to grain than grains are tensed by all their length. But if load is pependicular to grains, so only part of grain and the space between grains are strained. Isn't the second case lesss stiff than the first one?
The rule of thumb that we used, for a safety factor, was 1/2 the yield stress. Though the value can be moved, we used this rule of thumb for almost every application.
Excellent. Greatings from Colombia!
wonderful presentation
I have a question:
If two materals have the same Young's modulus value, but different yield strengths, will the material with a higher yield strength be called more elastic than the one with a lower yield strength? Or is only the Young's modulus a measure of elasticity?
Sir my doubt really got cleared. Thank you, sir. Sir, it would be better if you decrease the background music just a bit.
yours faithfully
Hriday Sahoo, India
Please post more videos. Thank you for easily explanation
In 2:41 you said E perpendicular to grain is higher than E parallel to grain. can you explain how and why?
Amazing content keep it up. love the effort to quality in the videos
Beautiful video, straight to the point and easy to understand. Subbed :)
So good an explanation it was..... believe me your subscribers are gonna increase with the speed same as the speed of light......good luck.... and I'm a subscriber too......=)
Very precise and informative
Very well explained sir. Thank you.
On the note of bridges during the end, isn’t yield strength of the material also of importance when wanting to avoid deflection and/or an overall elastic behavior? Of course, a rubber bridge isn’t as beneficial and sturdy as a steel bridge, but wouldn’t using high yield strength steel would also cause problems with deflection?
Great video, I think it would be good to add that bridge should be stiff but not brittle, because it certainly will bend to some extent
You did say that the higher the young's modulus of the material, the higher its stiffness but smaller elastic deformation. Mild-carbon steel has a higher E and smaller yield strength which is the opposite of the high-carbon steel. Does this mean, use mild steel in structural design? Thanks in advance for your reply.
So in the elastic state, does the material always return to the same length after being released before entering the plastic state?
Awesome explanation. Thanks
Great Sir!!! Kudos!!! Please post more videos
2:33 how?
We say modulus of elasticity is a material property than how is it changing on type of applied load(parallel or perpendicular to grain) ???
The reason is that wood is an anisotropic material, and so its material properties are different in different directions.
@@TheEfficientEngineer 👍
I don't get one thing, at 5:14 what ksi means in Young's modulus? Sir, can u reply pls...
This channel is amazing. Keep making videos!!!!
great animation and delivery method.. which software you used for making animation?
Thanks Hammad. I use Blender.
Well explained Sir.
i just discovered you awesome channel ! i cant find the shear/bulk modulus thank you !
Superb content. Keep going!
Hi dear Eng...I have a question..
I want to know with what software do you make these amazing videos ?
Thanks in advance.
very nice, but a question: can i discover the young's modulus with other test, insted tensile test? like compresion, or shear? thacnk you!!!
Yes. If you know the applied force (compressive or tensile testing), the cross-sectional area and the strain, you can calculate the Young's modulus. Hooke's law is the key word. In the beginning of this video he mentioned shear modulus and bulk modulus. For isotropic materials all of these moduli (Young's, shear, bulk) are related via Poisson's ratio. I think it would be a nice video topic (also maybe how it works in orthotropic materials). He did mention shear modulus in the video "Understanding Torsion", though.
Wonderful Lectures ! Thanks.
Thank you for your information and knowledge to us
I learned alot here. Thanks man!
Great video! Thanks for creating all of these, they're great. At 2:27, I'm not sure if it was your accent or not but it sounded like you said isotropic rather than anisotropic?
I think he said "for anisotropic materials", but it sounded like for an isotropic materials. If he had said it the latter way, materials wouldn't have been plural.
Very informative!!
Please create a video on iron carbon diagram
And heat treatment
Thanks
Thanks a Lot for the Useful info, I Have a Question Please, in Car Plates Industry when we use the 1050 Aluminum Alloy, what Temper you suggest to be Used and what Mechanical Properties are the best to avoid Plastic deformation when applying the Plate Numbers Please. Thanks
excellent work
why put the independent variable on the y-axis? what kind of perversion is that? also though thank you this was very helpful once i oriented myself
watching these to study for the MCAT. You should make "Efficient Doctor" videos haha
You will become engineer of human body don't worry. 😁👍