Concept and Definition of Radius of Gyration – Moment of Inertia – Strength of Materials


Hello Friends here in this video we will see what is meant by Radius of Gyration the next definition Radius of gyration is defined as that distance from a given axis up to a point where the entire area is assumed to be concentrated so here I have written the definition of radius of gyration that it is defined as that distance from a given axis up to a point where the entire area is assumed to be concentrated to understand this in a better manner we require a diagram suppose we have an arbitrary area which is called as total area capital a now within this total area if we have small areas like I am assuming here three areas a1 a2 and a3 now when I see their distances a1 a2 and a3 so I will mark their distances the distance of a 1 with respect to x-axis this will be y1 distance of a 2 distance of a 3 y 3 so here we have three individual areas I am assuming that there are three areas like this we would be having n number of areas in the total area capital e so a1 is at distance y 1 a2 is at y 2 and a 3 is at y 3 now if for this example I am considering that the entire area is in the form of strip and the distance of this strip with respect to x-axis this is K so now here if the total area is capital a and if I am taking the moment of this area about x axis well right down there for moment of area about x axis is given by I xx is equal to the moment is area into distance so I am taking the moment of area area into distance now again taking the moment of area about x axis now if I am taking the moment second time it becomes I xx is equal to a into that distance will become distance square so I xx is equal to a K square so from this I will get K is equal to root of I xx upon capital a so this I will keep this as equation number one and I get say that therefore K is equal to radius of gyration about x axis so here as I have written in the definition that the radius of gyration is defined as the distance as that distance from a given axis that is x axis here up to a point where the entire area is assumed to be concentrated so here I am assuming the entire radius concentrated at this point and previously the area was distributed throughout so the area common area denoted by capital a it is at a distance of K so this K is nothing but it is called as radius of gyration so here I have written the formula it is root of I xx upon area next similarly I can say that moment of area about y-axis is given by I YY is equal to area into K and similarly for that I will say that therefore again taking the moment of area about Y axis for that also I need to have a diagram where I can explain it so here again I am assuming a body of irregular shape which has total area capital a inside this we have three different areas now I will say that this is area 1 area 2 and area 3 they are distances with respect to y-axis the first distance is of area 1 that is here I have this is of area 2 so X 2 for area 1 it is in the oven I’ll denote it as area 1 so here I have X 1 this is ADR 2 so X 2 and here I have X 3 now similarly I can assume that this total area is in the form of a strip and that total area with respect to y-axis its distance we will call that as K so now when I’m again taking the moment of area about the y-axis by taking distance X that will become Y y is equal to a into it was K so it becomes K square so now from this I can say that therefore K is equal to root of I by Y upon area so previously in equation number 1 I had got the radius of gyration about x-axis now I will give this as equation number ii and where k is equal to radius of gyration about y axis and it’s unit since it is radius its unit will be either in terms of mm it can be in terms of centimeter or it can be in terms of meter so you’re in this video we have seen the definition and concept behind radius of gyration

70 Replies to “Concept and Definition of Radius of Gyration – Moment of Inertia – Strength of Materials”

  1. Many of them have been asking you ! why are you taking moment two times ? It will be good if you can clear our doubts

  2. you took the moment of area twice ,
    1)y Shud u take it twice?
    2) and how does taking t d second time makes Ak into Ak^2?

  3. sir …u r really teaching nice..but I request u at same time please tell the physical significance of those concepts…which is helpful to us understand better…

  4. One of the most stupid teacher… Who don't know the concept behind any topic… He has cram the whole maths of derivations without making students understand where it comes from

  5. sir mujhe batai ye ki total area a1,a2,a3 ka total area( A) to dusre drowing me k ka total area (A)kaise ky aaya sir

  6. When u take moment of area for first time it should be Mxx= Ak n moment of moment of area i.e second moment of area is Ixx=Ak^2.
    First clear ur concepts before making the videos.

  7. I got to know about this channel by watching this vedio that they will teach very butty fied concepts by them without any specific notation or specific name
    ex. moment of inertia and moment of area.

  8. Ekeeda dada zindabad. We are from ekeeda army sir. Newly formed in Hyderabad. We all are students who passed by seeing your videos. Jai ekeeda army

  9. The y is squared because he is taking the force on A times y. The Force on A is kyA. So kyA times y gives moment of inertia about x axis.

  10. making sure that I will never watch his videos again , he didn't feel any need to explain why we have to take moment of area twice, when lots of people asking why we have to do this , he just replied we have to be a member of his website to solve this doubt, are students joke to you? @Ekeeda ????

  11. one thing I should tell here is that moment of inertia and second moment of area are two different things. for areas that are geometrically important and whose mass is not as that much important in comparison to their geometry we take 2nd M.o.A. while for solid bodies (volumes) we take moment of inertia which is a measure of the resistance of that body to angular acceleration (much similar to that the mass is a measure of resistance to linear acceleration).
    Now, the second moment of area is purely geometrical, hence it will not include density or volume in its equation. It is simply distance x distance x area. Much logical to understand like Force x distance is moment of force is similar to area x distance x distance.
    The mass moment of inertia can be determined through radius of gyration which is simply the mass x R.oG^2.
    Mass moment of inertia has units kgm2 while second moment of area has units m^4. Mass moment of inertia can be converted to 2nd moment of area like this:
    Im = int(r^2) dm ; int==> itegral
    Im =int(r^2 rho dV) = int(r^2 rho l )dA ===> l = length
    Im = int(r^2 rho l ) dA = rho l (I_a ) ==> I _a =2nd moment of area

  12. Samjhana acha rahaga defination to bahur acha acha mil jata h per samaj nahi ata h or ap bahi bs nite da rahe h samjhaye plz kabke note se kaya hoga or drawings se. Dono book me likha hua …

  13. Hello Friends,

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  14. Kya chutiya banaya he bhaisahab….
    Ye bookish knowledge definition, formula, steps to hame books me mil jate he… Hame concepts chahiye bhai

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