Thursday, 13 June 2013

Elongation of a bar due to its Own weight

Analysis of a hanging beam:

A BAR HANGING



Let AB is the rod hanging from a ceiling from the end A.
                     Then let, W= Unit weight of the bar,
                                    L= length of bar,
                                   A=Area of cross section,
                                    E= Young's modulus for the bar material

Then elongation of the bar is given by delta ( l )
Formula of Elongation of a body due to its self weight.


 


                 
The Derivation part is clearly explained in the video!

46 comments:

  1. I believe the equation is wrong. I doesn't include the area.
    It should be deltaL = W*L / (2AE)

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    1. This comment has been removed by the author.

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    2. W = w*L
      w = ρ*g
      Elongation = WL/2E = wL^2/2E

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    3. Elongation= WL/2AE= wALL/2AE=wL^2/2E

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    4. It's right because here unit weight is taken and it is equal to weight/volume= wl/A

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    5. Unit weight = w/(A*L) so to use it in place of wight A and L are multiplied to have only wight

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    6. Good and I have got a clear idea

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  2. in text book elongation= (wl*l)/2e is given

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  3. No, it's actually delta L=WL/(2AE)

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  4. The answer is wl/2AE..
    Since we get after integration wl*l/2E,
    we know that Area*l=volume
    so specific weight=m*g/v
    which imples W/v
    on substituting w=W/v
    w*l=W/A
    so elongation =Wl/2AE

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  5. There are two formula
    1. If we consider Specific weight of the bar (w in terms of kg/m3), then delta L= wl^2/2E
    2. If we consider weight of the bar (W in terms of kg), then
    delta L= WL/2AE

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  6. How its derive !?
    Can any budy help ..

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  7. How its derive !?
    Can any budy help ..

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  8. This comment has been removed by the author.

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  10. Derivation of expression for change in length due to self weight on a uniformly tapering section?

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  11. If you clearly observe the equation viz.,wl^2/2E where w= unit density, The elongation is clearly proportional to l^2 and independent of Area, So Uniformly tapered bar and Prismatic bar of same length would have same elongation, What ever the size and shape the bar may be. So, no separate derivation is required for uniformly tapered bars. I Hope you are clear, else just ping once again. I'll make a video on it and clearly explain the concept.

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  12. there is little bit confusion to take specific weight w and specific density gama. n how both are equal

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  13. b chall simply get it that the weight will act at the half of it so just put L/2 at the place of L and you will get the same formula .......... jhanddu baam
    simple bhi bol diya kar kabhi

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  14. Could anyone help me tackle this problem....A copper wire of 2mm diameter ND 35m long is hanging freely from a tower.what will be it's elongation due to its own weight? (take specific weight of cupper : 89.2kN/m³,modulus of elasticity =90*10³N/mm²)

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    1. Isnt it same problem. You can find W by rho*A*l. Rho is in Kilo newton so multiply by thousand. It wont be in kg but in Newtom

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  15. Why is Center of mass concept not used for max length at which wire breaks due to its weight.

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  16. If u have not knowledge than not posting wrong thing in blog,okk,∆=wL/2AE or YL^2/2E,, because self weight (w)=unit weight*volume=Y*AL, now put these values nd get

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  17. If the radius of wire is streched by a load is double , then its modulus of elasticity will be how much ??? Plz Ans Me

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  18. Kya bakwas ho Raha h yaha par koi kaam dham nhi h kya

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  19. Tensile strength of a material is force over cross sectional area. Doubling the cross sectional area of the bar doubles its weight, but also doubles its strength, so it is correct to say the self supporting length of a bar is independent if its cross sectional area.
    Consider two identical suspended bars, each indepently supporting their own maximum length. Bringing them alongside each other does not change anything.

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    1. Unit weight and length are the only factors influencing the deformation in case of self weight. Unlike in the case of external load where elongation is dependent of area. Hence, you can confidently what ever the area of bar, if of same materials, elongation due to self weight is same.

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  20. Explained very well, thank you so much

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