Analysis of a hanging beam:
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!
I believe the equation is wrong. I doesn't include the area.
ReplyDeleteIt should be deltaL = W*L / (2AE)
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DeleteW = w*L
Deletew = ρ*g
Elongation = WL/2E = wL^2/2E
Elongation= WL/2AE= wALL/2AE=wL^2/2E
DeleteIt's right because here unit weight is taken and it is equal to weight/volume= wl/A
DeleteUnit weight = w/(A*L) so to use it in place of wight A and L are multiplied to have only wight
DeleteGood and I have got a clear idea
Deletein text book elongation= (wl*l)/2e is given
ReplyDeleteHere it's specific weight (wt/vol)
DeleteAre you mayank attri?
DeleteNo, it's actually delta L=WL/(2AE)
ReplyDeletei agree with uh
Deletei agree with uh
DeletedeltaL=WL/2E is correct
ReplyDeletewhere W in weight density
DeleteDelta L = WL/2EA is correct solution
DeleteThe answer is wl/2AE..
ReplyDeleteSince 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
There are two formula
ReplyDelete1. 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
Best answer
DeleteBest answer
DeleteIts crct ans.....tnq
DeleteThank uh so much
DeleteBut there is also apply the gravitational force .what about it
DeleteWeight is nothing but the product of mass and gravitational force..
DeleteThank u... Best answer
ReplyDeleteHow its derive !?
ReplyDeleteCan any budy help ..
How its derive !?
ReplyDeleteCan any budy help ..
Video containing the derivation is uploaded
DeleteThis comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteDerivation of expression for change in length due to self weight on a uniformly tapering section?
ReplyDeleteIf 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.
ReplyDeletethere is little bit confusion to take specific weight w and specific density gama. n how both are equal
ReplyDeleteb 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
ReplyDeletesimple bhi bol diya kar kabhi
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)
ReplyDeleteIsnt 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
DeleteWhy is Center of mass concept not used for max length at which wire breaks due to its weight.
ReplyDeleteIf 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
ReplyDeleteIf the radius of wire is streched by a load is double , then its modulus of elasticity will be how much ??? Plz Ans Me
ReplyDeleteNo change in E value.
DeleteKya bakwas ho Raha h yaha par koi kaam dham nhi h kya
ReplyDeleteTensile 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.
ReplyDeleteConsider two identical suspended bars, each indepently supporting their own maximum length. Bringing them alongside each other does not change anything.
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.
DeleteExplained very well, thank you so much
ReplyDeleteBhot bekar hai ye
ReplyDeleteKoi website pe na aao
ReplyDelete