107 514
Assignments Done
100%
Successfully Done
In September 2023

# 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 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
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="d_o=120" mm, "d_i=" 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

"\\frac{T}{J}= \\frac{G \\theta}{l}" , here J= polar moment of inertia

"I= M_1(K_1^2) + M_2(K_2^2)"

"I= 150(1.2^2) + 330(1.5^2)"

"I= 958.5,T= 958.5 \\times 0.8 = 766.8"

"\\frac{766.8\\times1000}{(\\frac{\\pi}{32})(120^4 - 115^4)}=\\frac{80 \\times 1000 \\times \\theta}{1200}"

"\\theta= 0.0036"

(b)

And for the shear stress calculation

"\\frac{\\tau}{R}= \\frac{G\\theta}{l}"

"\\frac{\\tau}{60}= \\frac{80\\times 1000\\times 0.0036}{1200}"

"\\tau = 14.4 MPa"

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!