Somewhere between pinned and fixed...?

[djw2k3]

Hi all,

We have a basic "simply" supported beam, if you can imagine a beam 5000mm long with supports at (b) 3000m and (c) 5000mm - the load is applied at (a) 0mm - ie a "simply" supported cantilever.

The thing is the supports are not strictly simple but are not fully rigid. The support at (b)will prevent some rotation but not all. As in most cases in the real world I would normally disregard this and approximate the beam is simply supported for worst case for reactions etc.

The issue is I need to get some quite accurate values for the reactions at thr 5000mm support - we are running a little close to allowable loads.

I have a feeling this may not be that easy, any suggestions?

Thanks in advance

Dave

 

[TheTick]

Sounds like you need to treat your supports as additional members.

If the support at (b) prevents some but not all rotation, perhaps it can be modeled as a damped torsion spring.

 

[prex]

If you can correctly model the behaviour of the partially fixed support, then you can determine the rotational flexibility of the support and easily determine the corresponding reactions.
If your beam is supported by some vertical members (a kind of frame) then that rotational flexibility will be determined by the flexural stiffness of the vertical members.
Otherwise if you have a common type of support (a flange bolted to a stiff structure), then I don't see how you could estimate a safe value for the flexibility. In my opinion you should choose one of three options:
- design the supports as (fully) fixed and calculate the reactions accordingly
- treat the supports as pinned
- design a special type of support for a specified flexibility (it will include some kind of spring element)

prex

http://www.xcalcs.com

Online tools for structural design

 

[Iskit4iam]

I understand how the fixation affects the stress in the beam. How does it affect the reaction forces? I can't figure out (remember) how fixation affects FBD.

 

[djw2k3]

Hi Iskit4iam,

Beam: a__________b___________c

If b and c are the supports, load is applied at a.

If b was a fully fixed/rigid support then then it will take all the reactions (moment + shear) of load at a,

The FBD could be simplified to a very simple cantilever: a___________b

Hence no reaction at c,

djw

 

[Iskit4iam]

Thanks, DJW

The light comes on!

 

[jetmaker]

Check out page 39 of Flabel's book, "Practical Stress Analysis for Design Engineers". There he covers partial degrees of restraints for beam sturctures. It is not a detailed mathemathical analysis... rather a descriptive overview of the problem and how to go about solving it.

Regards,

jetmaker