Mechanics assignment (please check if my answers are correct)

1. The problem statement, all variables and given/known data
As an engineer you are tasked to design a 2m long shaft which is to be manufactured either as a solid circular bar or circular tube. The shaft is required to transmit a torque of 1000Nm without exceeding the allowable strength of the material.
Address the following:
a) Material Selection and mechanical properties of material
b) Factor of safety used in the design
c) Required diameter of the solid shaft
d) Required outer diameter if the thickness of the tube is specified as one-eighth of the outer diameter
e) Angle of twist for the hollow shaft
After the shaft is manufactured, you are informed by the client that the shaft is subjected to an additional thrust force of 5000N:
f) Buckling load of the shaft
g) Provide a revised factor of safety to the client supported with appropriate calculations

2. Relevant equations
where τ is the shear stress
where Pcr is the buckling load

3. The attempt at a solution
a) I chose A36 steel
b) I chose standard factor safety 4
c) Diameter of the solid shaft=52mm
d) Outer Diameter of the hollow shaft=59mm
e) Angle of twist for the hollow shaft=0.0319 rad or 1.83 degrees
f) Buckling load for the hollow shaft=200.65kN
g) I wasn’t able to find an answer for this sum. Hoping for some help to complete this question

I hope someone checks my answers to see if they are correct and if they are not, please tell my where I have gone wrong.

Thank you
(Sorry for my bad English)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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