Civil Engineering - Strength of Materials - Discussion

Discussion Forum : Strength of Materials - Section 1 (Q.No. 3)
3.
The ratio of strengths of solid to hollow shafts, both having outside diameter D and hollow having inside diameter D/2, in torsion, is
1/4
1/2
1/16
15/16
3/8
Answer: Option
Explanation:
No answer description is available. Let's discuss.
Discussion:
42 comments Page 1 of 5.

Maggie said:   1 decade ago
The strength of a solid shaft in torsion is given by,

T(solid shaft) = (pi/16)*(max stres)*(D^3).

T(hollow shaft) = (pi/16)*(max stres)*(D^4-d^4)/D.

On solving we get 15/16.

Avinash said:   1 decade ago
max stress = Tymax/Ip; where Ip = polar moment of inertia.

ymax = D/2.

max stress(solid) = 16T/piD^3.

max stress(hollow) = 32T(D/2)/pi(D^4-d^4).

Replacing d = D/2.

The ratio we get is 15/16.

Pradhyumna said:   1 decade ago
Polar modulus is a measure of strength of a shaft in a torsion.

So, simply calculate the ratios of polar modulus of solid to hollow shafts.

Polar modulus = Polar moment of inertia/Radius of shaft.

Pawan said:   1 decade ago
But ratio obtained 16/15 how?

Murli meena said:   1 decade ago
Dia of solid shaft = D.
DIA OF HOLLOW SHAFT = d/2.

The ratio of solid shaft = 16.
The ratio of hollow shaft = 15.

Total tension in shafts = 15/16.

Anil said:   1 decade ago
The maximum stress due to torsion in solid shaft is 16T/d3.

The maximum stress due to torsion in solid shaft is 16x16T/15d3.

Therefore ratio maximum stress of solid shaft to hollow shaft is simply: 15/16.

Torsional Equation:

T/J = s/R = G0/l.

Virendra said:   1 decade ago
Ratio will be 16/15.

Simply if equal outer diameter then solid shaft will be more strong. But if material are same then hollow shaft will be more strong.

Raj said:   1 decade ago
As @Pradhyumna said earlier that polar moment of inertia(J) decide the strength of the member.

J for solid section = D^4 and for Hallow section = inner D^4-outer D^4.

i.e D^4-(D/2)^4 = 15/16D^4. So the ratio is 15/16.

Bharat said:   1 decade ago
Zp(solid)/Zp(hollow) = (pi*D^3/16)/(pi*(D^4-(D/2)^4)/16D) = 16/15.

Parna sengupta said:   1 decade ago
For a hollow shaft whose external diameter is d and internal diameter is d/2, then what will be the polar modulus?


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