Cantilever Beams - Do you have to make the cut at the 'free end'?

[chrissimpson]

Hi there

Just a quick question; when I'm calculating moments in a cantilever beam (in my case a quarter circular one), is there any reason (apart from my own ineptitude) why I shouldn't be able to make the cut and FBD starting from the fixed end?

I get different answers when I make the cut at one end compared to the other.

Thanks very much for your help!

Chris

 

[256bits]

Isn't your free body diagram of the canliver itself:
a force on the free end, which you know, and a force on the fixed end ( where the cut is) along with a moment, both of which which you do not know.

 

[xandro101]

It doesn't matter where you cut along the beam you should get the same answer. Make sure you use a consistent sign convention.

 

[xandro101]

I mean it doesn't matter you do your analysis from the left cut section or the right. Just use a consistent convention for shear force and bending moment at the two sides of the cut.

 

[chrissimpson]

Hi! Thanks for the help!

I've attached some of the working that I've completed - I seem to have come up with the right answer but would really appreciate it if someone could have a quick look over the working/diagram for me.

When completing the analysis I presume I'm right putting the forces and moment around the cut end in opposite directions for the two cases (i.e. when considering the left and then right sides of the cut)?

Am I correct in putting a reaction moment about the fixed end of the beam? Is this analogous to the reaction forces? Is this moment considered to be fixed (and therefore only taken into account) at the fixed end of the beam?

Thanks again for your time and help!

Chris

 

[xandro101]

I saw your working I think your problem arose from the way you refrenced the angle §. If the in the first analysis the angle is § to the vertical then in the second it should be (90-§) to the horizontal.

 

[Studiot]

Some clarification of your diagrams would be useful.

You appear to be applying axial forces as well as transverse forces to your cantilever?

Your cantilever also appears to be vertical?

 

[xandro101]

Some clarification of your diagrams would be useful.

You appear to be applying axial forces as well as transverse forces to your cantilever?

Your cantilever also appears to be vertical?

studiot. Note that the cantilever is bent into a a quadrant of radius R. And also that is possible for such a bent beam to be load horizontally and vertically.

 

[Studiot]

Note that the cantilever is bent into a a quadrant of radius R.

Thank you for this comment. Yes I thought the element appeared well bent. To well to allow the assumptions of simple beam theory I would have said.

 

[chrissimpson]

Sorry for any confusion.

The beam is quarter circular, with a vertical load V and horizontal load H applied at the free end of the beam (the V and R noted at the base are reaction forces - I guess I should have called them Rv and Rh?)

I've noted and accounted for the differences in the angle datum by calculating the moment at theta=pi/2 in the first example and theta=0 in the second (for consistency I should really use the same reference point!). These both gave a moment of HR+VR and refer to the moment at the base of the beam.

Does my working seem reasonable and logical? I managed to get myself in a bit of a twist about all of this and just want to make sure that I've finally got to the correct answer (on both sides of the cut).

Thanks again!

Chris