simple question

[40818]

Hi, i have a simple question that i'm mulling over.

If you imagine a simple flat rectangular beam built from quad elements, with 2 supports and an overhang. A "downwards" load is applied at the overhang edge, kinda like the badly drawn drawing below. The supports are just single nodes in line with each other.

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The supports take all translational dof, and 2 rotational dof. The FE results give a "up" vertical reaction at the 1st support and also a rotational reaction at the node. The second support's reactions are downwards and also has a rotation.
Now when you come to stress the support area, would you take the nodal moment alone for a simple bending stress calc, or would you superimpose the nodal rotation(moment) onto a typical simply supported bending moment hand calc, so you end up with steps in the BM diagram.

Any thoughts (hopefully i have made the question clear)

 

[rb1957]

simple statics tells you the reactions (ok, it's doubly redundant, but unit load method, some paper, a pen, and some coffee gets you the moments without FEA; tho' maybe you were just testing the FE?).

if the supports are reacting moments then there are steps in the BM curve ... the moment increases linearly from the load and at the reaction steps (down i guessing), and starts to slope down (cause the reaction is bigger than the applied load).

 

[EdR]

There is no jump (step??) in the moment diagram at the supports....It is linear (down) from the load to the first support and then is linear (up) to zero from the first to the second support.......Use only the moment from the moment diagram (which should also be the moment reported by the code at the support)

Ed.R.

 

[rb1957]

Edr, you're right if the supports were pinned, but he has fixed supports (so the moment reacted at the support is a step on the BM diagram).

 

[EdR]

rb1957:


OK....Yep I assumed the 2 rotational reaction directions were torsional and about a vertical axis (on the drawing).....thus giving a pinned support...

Ed.R.

p.s. even after rereading the definition I didn't get that the reactions were fixed supports....but then ......

 

[corus]

If it is fixed supports then surely the problem is that of a cantilever with the support and beam redundant to the far right? If not then all that the supports see are the reaction forces and no bending moments on the supports as the beam is pinned. There is a bending moment in the beam at the left support of course, but not in the support itself.

corus

 

[rb1957]

the fully fixed supports react moment

 

[patswfc]

Agree with corus, if supports are fully fixed then the moment and shear at the first support will be taken by that support. Its a cantilever. The remainder of the frame is redundant.

You will only get the situataion you describe when the first support is not fully fixed.

 

[rb1957]

if both supports are fully fixed, then the structure is doubly redundant. unit load method clearly shows that both redundancies have affect and so both need to be taken into account.

consider only the left support is fixed. then, without doing the calcs, i expect that there will be a slope at the RH end. fixing this end removes this slope and changes the moment reaction at the LH support, since moment at the RH support affects the slope of the beam at the LH support. note, i'm talking my way thru the solution of the redundant problem, where you release the redundancies, hence the slope of the beam at the supports is non-zero (untill you add the redundant moments).

 

[40818]

Sorry about delay in responding, been busy.

My post was on an evening late after work running things through my mind, and knew i would get to the answer in the morning. It was to test the FE to see if a simple model would behave as i would expect for larger modelling purposes.
The actualities of the beam supports were that they would be fully fixed in essence. Though modelled by a quad mesh. If modelled by bars then all the FE comes out at the first support, but by modelling with quads then the load distributes to both supports. The majority of the forces/moment are taken by the first support.
The test was carried out to prove that it is an error to just take the SPC rotations as the bending moment at the support, as it isn't the true bending moment.