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`        why is hollow shaft better than solid shaft?please explain with mathematical proof`
7 years ago

105 Points
```										Dear punita,
We dont need mathematical proof for this just a simple common sense is enough.The hollow shafts can withstnad the same stress as that of solid shafts.In torsion the stress profile is a  linear relationship with diameter.So the outermost surface or the outermost material of the shaft is the place where maximum stress is acting in torsion.To reduce the cost, the manufacturers prefer the hollow shaft rather than the solid shaft.so hollow shaft is better than solid shaft in terms of the cost.A solid shaft in bending or tensile  or compressive forces will always  be significantly stronger for the same  material,dimensions and loading.
All the best.
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```
7 years ago
SUBRAT KUMAR PANDA
18 Points
```										Twisting moment or torque depends upon the distance from neutral axis to the outer most fibre in mm.
So taking same weight f material the above dimension of a hollow shaft will be greater than a solid shaft.
Now the torque produced in hollow shaft will  be greater than the solid shaft.

So hollow shaft is more preferable.
```
3 years ago
KAPIL MANDAL
132 Points
```										Thank you sir for this answer. Thank you very much.
```
2 years ago
SANJAY MOHAN BHATNAGAR
19 Points
```										Prabbaly, and probably only as i am not sure about it, the total kinetic energy of a rotatin body is (1/2)Iw2, where I is moment of inertia of that body. The hollow shaft has double the moment of inertia (MR2) than that of solid shaft (MR2/2), which means a hollow sharft transmits more energy to the wheel.Sanjay Mohan Bhatnagar
```
2 years ago
Kundan
11 Points
```										It can be shown that torque required to produce unit twist in a solid shaft of radius r length L and made of material of modulus of rigidity G is given by ___ torque =πGr^4/2l also torque` is required to produce unit twist in a hollow shaft of length L internal and external Reddy R1 and R2 respectively and of material of modulus of rigidity G is given by ____ πG(r2)^2-(r1)^2/2l and now if we do torque`/torque  it will give some positive value which is greater than 1 and it will show that hollow shaft is stronger then a solid shaft made of same equal material
```
3 months ago
Togaru Lavanith
11 Points
```										All the answers here said most of it in terms of solid mechanics theory of pure bending of beams. Since you used the term `shaft` meaning we`re talking about torsion, I`ll just add a layman explanation regarding that:Since the mass is constant, A hollow shaft is necessarily a result of reallocation of material from axis to periphery. This results in decrease of slenderness of the shaft and hence, it`s torsional rigidity increases. Explanation:The strength of a shaft implies the maximum torque it can transmit. It depends on Torsional rigidity of the shaft since it renders the stiffness to the shaft. Torsional rigidity is defined as the torque required to produce a twist of one radian per unit length of the shaft. and by torsional formula:T/(θ/L)=GJ=Torsional rigidity.So, Stiffness and hence strength is proportional to J which is:by maths, less for solid shaft andby intuition, less for most slender of the two (solid shaft).
```
one month ago
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