Basic question ofa Fixed BEam 1

[idly123]

I have a fixed beam subjected to concentrated loads to be modelled. whats the effect if i have the following changes made to this fixed beam.
1) provide an internal hinge at midspan
2) provide a hinge or a roller at midspan
3) provide a roller with a torsional spring at mid span.
will formulation get affected. how do i go about modelling the same.
regards
raj Raj
Structural Engr.

 

[vonlueke]

DrRaj: Formulation of element stiffness matrix will be modified within the software for each beam end release; and structure stiffness matrix rows and columns are probably removed within the software for each fixed dof at constraints.

Assuming x axis is the longitudinal axis of your beam, beam is horizontal, z is vertical direction, left-hand end of your beam is A, right-hand end is D, and loads are applied in z direction, the modeling you are inquiring about is as follows.

(1) To create an internal hinge, create a node at midspan. Let's call this point B. Delete your original beam element and create two elements instead, one from A to B, and the second one from B to D. Now release rotational dof about y axis (dof 5, also called RY) on one of your two beam elements at midspan. You have now modeled an internal hinge.

(2) To model the midspan hinge, place a constraint at B having x translation (dof 1, also called TX) free (released), and having RY free. To create the roller, now delete the beam end release you created in item 1, above.

(3) To model midspan roller and torsional spring, create two midspan nodes an "infinitesimal" distance apart. Let's call them points B and C. Delete the previous beam elements, and create three beam elements (from A to B, B to C, and C to D). Release RY on beam BC at end B. Place a constraint at B having dofs TX and RY free; this is your midspan roller. Zoom in and create a torsional spring element connecting B to C. Good luck.

 

[idly123]

hi vonlueke,

thanks for that response, i really understood the modelling aspect of that.
well talking aboutthe change in stiffness of the system from stage I to three..what kind of a change can we expect . or can we have any physical meaning or insight in to thi sproblem first by releasing a rotational DOf then by either making a hinge etc....what would happen to beam stifnness.
thanks for ur earlier response
regards
raj Raj

 

[vonlueke]

In general, as released dofs increase, stiffness of your system decreases. The stiffest beam is the one with fewest released dofs.

 

[trilinga]

DrRaj

You have stated that you know the modelling aspects of the three situations mentioned by you. I hope you also know which one to choose for a specific case so that the model represents the actual structural behaviour.

the first case of providing an internal hinge will impose the condition that the moment in the beam at that point is zero.

The second case is representing a continuou beam with a pin support at the midspan. This will mean that there will be moments in the beam on either side of the pin support but their algebraic sum will be zero. In other words this condition yields moment on the beam at the hinge location but the moment is transferred from one segment to the other segment without transferring any moment to the pin support. The hinge acts as a fulcrum.

I do not know when you will require the third case of modelling.

Does this cover your query?

 

[idly123]

yes , that was a better comprehension.thanks for those responses
regds
raj
Raj