# A 2m long solid shaft has a diameter of 10cm. It is made of stainless steel with a maximum shear stress of 184MPa. a) Calculate the maximum torque that can be transmitted through the...

A 2m long solid shaft has a diameter of 10cm. It is made of stainless steel with a maximum shear stress of 184MPa.

a) Calculate the maximum torque that can be transmitted through the shaft.(8 marks)

b) If the material of the shaft was replaced with titanium and the shaft transmits the same torque what would be the diameter of the shaft. (6 marks)

Maximum shear stress for titanium = 550MPa

Density of Stainless steel = 7700 kg/m3

Density of Titanium = 4430 kg/m3

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### 1 Answer

a) You need to remember the formula of maximum moments in circular shafts:

`T_(max) = sigma_(max)*(I_p)/r`

`` `T_(max)` denotes the maxium twisting moment

`sigma_(max)` denotes the maximum shear stress

`sigma_(max) = 184 MPa`

```I_p ` denotes the polar moment of inertia of cross section

Hence, the maximum moments in circular solid shaft is

`T_(max) = (pi/16)*sigma_(max)*D^3`

`` `T_(max) = (pi/16)*184*100^3`

`` `T_(max) = 3611*10^4 Nmm`

b) You need to remember the formula of the diameter of a solid shaft:

`D = 1.72*root(3)(T_(max)/sigma_(max))`

The maximum shear strss for titanium is: `sigma_(max) =` 550MPa

`D =1.72*root(3)((3611*10^4)/550) `

`D~~ 69.38` mm

**Hence, the maximum torque that can be transmitted through the solid steel shaft is of `3611*10^4 ` Nmm and the diameter of the shaft if the shaft transmits the same torque and the material of the shaft was replaced with titanium is `D~~ 69.38` mm.**