Mastering the V and M Diagram: A Comprehensive Guide for Success

[hansthegerman]

I should know how to do this because I know I've learned it a year ago. This is just a refresher homework assignment and for the life of me I can't remember how to do this. In the attachments, I'm including the problem, the questions, as well as my attempts, which are likely, very wrong. Any help would be greatly appreciated.

 

[SteamKing]

Since the beam is built-in on the left end, there should be a non-zero bending moment there. Your moment diagram shows the moment at the left end is zero.

 

[hansthegerman]

So should my M diagram look more like:

and how do I figure out the moment of inertia without a mass?

 

[SteamKing]

The bending stress of a beam is inversely proportional to the second moment of area of the cross section of the beam. Although it is usually referred to as the moment of inertia, it is not the same as the mass moment of inertia of a body.

 

[hansthegerman]

So mass has nothing to do with I. Would the I in this case be I=(Pi*r^4)/4? If so my stress is close to the answer. I get 82,760 when the answer is 84,670. What about Tau? Where Tau=V*Q/Ib. Or would I use a different formula to find Tau since this is a Cylinder?

 

[SteamKing]

The answer you got for stress is only due to bending. If you look closely at the diagram, you will see a separate axial load applied at the right (free) end. This load also produces a contribution to sigma-x.

Similarly, the shearing stress due to the transverse loading of the beam must also be combined with the shearing stress due to the torque applied at the free end of the beam.

 

[hansthegerman]

OH! That makes complete sense. Okay so now for Tau, the two formulas I'm looking at are Tau=(VQ/IT) but now what is Q and I? and for the Torsion portion to add to the first tau, would I do Tau=(TR)/J, so R is radius, t is torque=15,000, what is J?

Thanks a bunch BTW, You're helping out in a huge way.

 

[SteamKing]

I is the same quantity that was used in calculating the bending stress, the moment of inertia of the cross sectional area of the beam. Q is the first moment of cross sectional area of the beam. Its calculation is described in the following link:
http://www.optics.arizona.edu/optomech/references/OPTI_222/OPTI_222_W10.pdf

J is another section constant, called the polar moment of inertia.

This is a link to another handy reference:

http://www.eng.uah.edu/~wallace/mae466/DOC/bas_str.pdf