Answer to Question #124168 in Mechanical Engineering for Nikitha Dharana

Question #124168

The playground roundabout, shown below, has a central shaft attached to the ground with a bearing at the top that supports the roundabout. As part of a preliminary design, you have been asked to check the effect of an impact resulting from the top bearing suddenly seizing.

Use the following data:

Mass of roundabout 150 kg and radius of gyration 1.2 m

Mass of people (6 at 55 kg each) = 330 kg and radius of gyration 1.5 m

Speed of rotation 0.8 turns/sec

The central shaft extends 1.2 m from the ground and is made from a steel tube, 120 mm outside diameter and 5 mm

thick. The modulus of rigidity G = 80 GPa and the elastic modulus E = 200 GPa.


a) Determine the maximum angular displacement of the shaft due to the impact.

b) Determine the maximum shear stress in the shaft due to the impact


1
Expert's answer
2020-06-29T08:28:28-0400

As here figure is missing so i m asuming my own condition and solving it

length of shaft= 1.2 m , outside diameter= mm, 115 mm,Modulus of rigidity= G=80 GPa, Modulus of elasticity=E=200 GPa,

Mass of round about = 150 kg, and radius of gyration 1.2 m

Mass of people (6 at 55 kg)=330 kg and radius of gyration=1.5 m

and speed of rotation =0.8 turns/sec

(a) For maximum angular of the shaft due to impacts

, here J= polar moment of inertia



(b)

And for the shear stress calculation






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