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
Discussion:
42 comments Page 3 of 5.
Gangadhar said:
8 years ago
Simply says (1-(1^4÷2÷4)=15÷16.
Akshay said:
8 years ago
I also get Answer is 16/15.
UMESH said:
1 decade ago
Shaft is said to be more strong if it resist moment and tmax is not the parameter to be used for it.
Tmax is used to compared material property and here we are calculating section strength, so maximum moment of resistant should be compared and answer for it will be 16/15.
Tmax is used to compared material property and here we are calculating section strength, so maximum moment of resistant should be compared and answer for it will be 16/15.
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.
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.
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.
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.
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.
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.
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.
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