Understanding Area Moment of Inertia for Shaft Design

[Saladsamurai]

Okay, maybe I am retarded, but i am having trouble with this.

i need to find the equivalent spring constant K of a shaft with radius=r, length=l, and modulus of rigidity=G

I know that K=GJ/l

Question 1) Is J in this case the AREA moment of inertia? I think it is.

Question 2) Why can't I find online a formula for the J of a shaft?

I know the cross section is simply a circle and it is rotating about
a point passing through its center and perpendicular to the plane of the circle

I do not have a mechanics book with me (at work). Can anyone help me out here?

Thanks!

 

[PhanthomJay]

Okay, maybe I am retarded, but i am having trouble with this.

i need to find the equivalent spring constant K of a shaft with radius=r, length=l, and modulus of rigidity=G

I know that K=GJ/l

Question 1) Is J in this case the AREA moment of inertia? I think it is.

J is the Area Polar moment of inertia (axis thru center along the longitudinal axis, perpendicular to circle cross section); J = I_x +I_y

Question 2) Why can't I find online a formula for the J of a shaft?

You didn't Google hard enough. J = (pi)d^4/32 for a solid circular shaft.

 

[Saladsamurai]

Thanks PJ. My book is silly. For vibrations it uses J as the mass moment of inertia whereas the usual convention is I and J is area so I was all inds of confused.