2 span beam with 2 points loads. Statically indeterminate?

[Mech King]

Hey guys,

I'm just pondering a beam problem fir a structure that I'm analysing. It appears statically indeterminate to me? The beam is bolted to a support at locations A,B & C. There are two point loads between span B-C.

There are no symmetrical distances or support locations etc.

Initially, I just ignored span A-B, as I assumed that the load would not transfer to the far left hand end at A, because it is rigidly fixed at B & C? Is this incorrect?

Now I am thinking that I do need to consider the left hand span AB.

I thought that I could assume "A" does not support the beam, then calculate the deflection of the beam at the left hand side in the unsupported region and then calculate what the restoring force would need to be to prevent such deflection, therefore calculating reaction A, and then take moments to calculate reactions B and C?

Or is there a better approach? I'm really getting a bit stuck here and would appreciate any guidance!

Many thanks

 

[TaxOnFear]

Mech King,

I'm sure I read something in a book about a similar system. It was a long time ago, but if my memory serves me right, it mentioned something about a "3 moment system". I'm sorry I can't help you more.

 

[TaxOnFear]

Correction - "Theorem of three moments". Read this:

http://en.wikipedia.org/wiki/Theorem_of_three_moments#Three_Moment_Equation

 

[SteamKing]

It comes down to whether the connections at A, B, and C will allow the beam to rotate with respect to the longitudinal axis of the beam. You say they are bolted connections, but do you have any further details? If rotation can occur, you have a classic continuous beam. If the bolted connections do not allow rotation, then each span can be analyzed individually, assuming full fixed connections at A, B, and C.

 

[Mech King]

Tax on Fear and steam king, thanks a lot for your input! Both methods make sense to me and I agree.

The supports at at A B and C consist of a block welded to each side of the support/beam and bolted to a column, which I will consider to be rigid.

I guess the beam won't rotate at its supports because it is built in at each support. I was unsure if I could just look at the section BC in isolation, but thanks Steam King for the direction! Also, thanks for the references Tax on Fear; I can use this for a similar problem I have :D.
Very much appreciated guys!

Thanks

 

[timthereaper]

You mentioned that A, B, and C are bolted to a support and are rigidly fixed, but the picture shows pinned connections. If they really are rigidly fixed, you have a statically indeterminate problem because statics won't give you all the equations you need to solve for all the unknowns. You really only have the Y-direction equation and the moment equations at A, B, and C to work with, and your unknowns are the 3 vertical reactions and the 3 moments at each of the rigid supports.

Even just looking at BC, it's statically indeterminate if they're rigid connections. You'll have to use mechanics of materials equations to solve for the reaction moments.