Question
Download Solution PDFThe ratio of strengths of solid to hollow shafts, both having outside diameter D and hollow shaft having inside diameter D / 2, in torsion, is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Let the strength of the solid and hollow shaft is TS and TH
where τper = permissible shear strength, k = Ratio of inner diameter (din) to outer diameter (Do) i.e.
The ratio of the strength of the hollow shaft to that of the solid shaft when the outer diameter of both the shafts are the same provided RPM, Material and length are the same is given by
Here the outer diameter of both the shaft is the same
Do = D, din =
∴ k =
Alternate Method
This problem can also be solved by using
Where strength can be correlated with M (MOMENT RESISTED BY THE SECTION)
Putting the above values in M/I = σ/y
We get M = (I/Y) × σ (Assuming both are having same stress), we can say that strength depends on I/Y only
Putting the value of I and Y from the above equation, we get
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