How Do I Calculate the Diameter of a Shaft in a Torsion Problem?

[markles]

Hello I recently got handed this problem and I had a fair idea on how to go about it or so I thought! My only problem is I do not know how to find d? I would be grateful if someone could show me how to find d and show me the equation used

Thank you

Homework Statement

A steel shaft 3m long is transmitting 1MW at 240rev/min. The working conditions to
be satisfied by the shaft are:

(a) that the shaft must not twist more than 0.02radian on a length of 10 diameters;

(b) that the working stress must not exceed 60MN/m2.

If the modulus of rigidity of the steel 80GN/m2 what is

(i). the diameter of the shaft required;

(ii). the actual working stress;

(iii). the angle of twist of the 3m length?

Homework Equations

T/J=Gxtheta/L=t/R
T=power/W
rads=degrees x pi/180

The Attempt at a Solution

(1x10⁶) /(240/2pi/60)= T = 39.793KN

J= pi x d⁴/32
diameter=d
T= Torque
G =mod of rigidity
J= polar second moment of area?
R= radius

d=?


G=80x10⁹

G x theta (0.02) = 1.6x10⁹/10d

what is the diameter? and how would i go about finding it?

thanks

 

[jbsteele]

To find the diameter, you need to use the equation T/J = Gθ/L. Rearrange the equation to solve for d: d = (T/Gθ)*(L/J) d = (39.793*10^3N / (80*10^9N/m2 * 0.02rad)) * (3m / (π * r^4/32)) d = 0.44 m

 

[kerimek]

Hello, finding the diameter (d) in this problem involves using the equation T/J=Gxtheta/L, where T is the torque, J is the polar second moment of area, G is the modulus of rigidity, theta is the angle of twist, and L is the length of the shaft.

To find the diameter, we need to first find the polar second moment of area (J). This can be found using the equation J= pi x d^4/32, where d is the diameter of the shaft.

Next, we can substitute the given values into the equation T/J=Gxtheta/L and solve for d. This will give us the required diameter of the shaft.

To find the actual working stress, we can use the equation T/J=Gxtheta/L and solve for T. Then, we can use the equation T=power/W to find the actual working stress.

To find the angle of twist of the 3m length, we can use the equation T/J=Gxtheta/L and solve for theta. Then, we can convert the angle from radians to degrees using the equation rads=degrees x pi/180.

I hope this helps and provides some guidance for finding d in this problem. Good luck!