Civil Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 1 (Q.No. 6)
6.
The ratio of elongations of a conical bar due to its own weight and that of a prismatic bar of the same length, is
Discussion:
18 comments Page 2 of 2.
Navjeet singh Nit patna said:
8 years ago
Because for prismatic bar =YL^2/2E.
and for conical bar =YL^2/6E.
So that ratio =YL^2/6E*2E/YL^2=1/3.
and for conical bar =YL^2/6E.
So that ratio =YL^2/6E*2E/YL^2=1/3.
Sourabh said:
8 years ago
@Durgesh.
Weight of conical bar is 1/3πrrh unit.
Weight of prismatic bar πrrh.
Weight of conical bar is 1/3πrrh unit.
Weight of prismatic bar πrrh.
Durgesh said:
8 years ago
If length and weight of both prismatic and conical same. Then the ratio of their elongation due to their own weight will be?
Please give me the answer.
Please give me the answer.
Baloch said:
9 years ago
Elongation of the prismatic bar due to its own weight = w l ^ 2 /2E .
Elongation of the conical bar due to its own weight = w l ^ 2 /6E.
wl^2/2E ÷ wl^2 / 6E,
wl^2/2E x 6E / wl^2,
(wl^2 and E canceled)
2/6 = 1/3.
Elongation of the conical bar due to its own weight = w l ^ 2 /6E.
wl^2/2E ÷ wl^2 / 6E,
wl^2/2E x 6E / wl^2,
(wl^2 and E canceled)
2/6 = 1/3.
Deepal Maheshwari said:
9 years ago
Elongation = PL/AE.
Now the weight of a bar of the conical shape is 1/3φr2h assuming both bars of the same material so neglecting density weight = volume.
And, the weight of the prismatic bar is φr2h.
So the weight of the conical bar is 1/3 to the prismatic bar.
Elongation in conical bar = PL/3AE.
Elongation in a prismatic bar = PL/AE .
Here, Ratio will be 1:3.
Now the weight of a bar of the conical shape is 1/3φr2h assuming both bars of the same material so neglecting density weight = volume.
And, the weight of the prismatic bar is φr2h.
So the weight of the conical bar is 1/3 to the prismatic bar.
Elongation in conical bar = PL/3AE.
Elongation in a prismatic bar = PL/AE .
Here, Ratio will be 1:3.
Munish said:
9 years ago
Deflection due to self weight = wl/2AE.
Deflection of 2nd beam = Wl/2AE + WL/AE.
Equate and Ratio is 1:3.
Deflection of 2nd beam = Wl/2AE + WL/AE.
Equate and Ratio is 1:3.
Munish said:
9 years ago
The solution for both beams when prismatic one carry additional load w with weight w.
Mujru said:
9 years ago
Γ * length. Squre/2 E.
Γ = unit weight of material.
E = young modulus.
But here bar said to be conical so the 1/3 multiple the 1st equation.
So the final equation is;.
Γ * length squre/6E.
So the answer is 1/3.
Γ = unit weight of material.
E = young modulus.
But here bar said to be conical so the 1/3 multiple the 1st equation.
So the final equation is;.
Γ * length squre/6E.
So the answer is 1/3.
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