Pinned-clapped frame analysis.

mmartin

Good morning to everyone:

I enclose you a simple model to depict how to model a pinned-clapped 5meters frame using MECWAY internal solver and constraints equations.

About the file attached:

• The analysis was done using MC13.0+internal solver(this lets you use constraints equations of the kind A*dof+B*dof+...=D.
  
• CCX imposes D=0.0 which will not let me raise the end release node).
  
• The model was done using the internal drawing engine (typing coordinates and remeshing).
  

MANUEL

P.D. Thanks to Victor for his help for suggesting modelling the end-release using constraint equations.

Victor

I'm confused about the purpose of the constraint equations and springs. Does putting the Z displacement directly on the end node of the beam lose something important?

mmartin

Good morning Victor:
I enclose you a scheme(brief summary) of the model of the partially release end frame.
I need the MPC to transfer displacements from end of the frame which is a theoretical zero-length joint until the rest of the 3d frame. With this 3d model of the ends of the frame I can simulate elastic unions(pinned, partially clamped, ...)
MANUEL

disla

Hi mmartin,

This is how I would normally simulate Pinned and Clamped beam connection as a whole.
The effect is clearly seen on the main beam deformation.

Keep i mind that for the main beam, stresses can be underestimated when using beam elements. Manual says:

-"Stress in element coordinates are evaluated at each of 4 predefined points in
the cross-section and one user-defined . These stress values are calculated only from the normal force and bending moments. They do not incorporate shear stress caused by torsion or shear forces"-

Regards

mmartin

Good morning DISLA:

Thank you very much for your comments and your contributions.

You are absolutely right, the beam element used in MC engines only considers axial and flexural stiffness. Besides, I also wanted to include rotational springs into the MC model but I couldn’t. But it does not matter.

The main purpose of my prototype was to model a partially rigid connections in beams. Incomplete in this case due to the lack of rotational springs.

So, after that, and for educational reasons, I coded a python script to solve the K_e(stiffness matrix of a beam) for 3d partially rigid beams(translational and rotational degrees of freedom) and it worked.

I assembled it all using LAGRANGE MULTIPLIERS, static condensation and finally the python function returns me the local stiffness matrix of the beam considering semi rigid ends. I attach you the declaration of the function. You will notice that I included a "k_infinite_displacement" and "k_infinite_giration" parameters to set "infinite value" in order to force MPC(Multi point constrains).

After solving the k_e matrix, I went ahead with the mass(M) and consistent(C) matrices. Actually in testing but seems to work.

def calculate_ke_local_Condense(l:float, E:float,nu:float,
Ax:float,Asy:float,Asz:float,
Ixx:float, Iyy:float,Izz:float,
dAlfa:float,
dY_ShearCenter_from_C:float, dZ_ShearCenter_from_C:float,
iNumPieces:int,
k_1_dx:float,k_1_dy:float,k_1_dz:float,k_1_gx:float,k_1_gy:float,k_1_gz:float,
k_2_dx:float,k_2_dy:float,k_2_dz:float,k_2_gx:float,k_2_gy:float,k_2_gz:float,
k_infinite_displacement:float=1e10, k_infinite_giration:float=1e10,
bK_g:bool=True,bM_e:bool=True,bC_e:bool=True,alfa_R:float=1.0,beta_R:float=1.0)->np.array:



MANUEL

disla

Looks really advanced. That's a complete new level for me. as I do not have programming skills.
Let us know if you get some progress.
Your name is MANUEL. ¿Are you Spanish? ¿Are you student?
Regards

mmartin

Good afternoon DISLA:

My name is MANUEL MARTÍN, spanish architect specialiced in structure calculation.
(I am not a student, I'd wish I could be one, but not).

I will let you know about the progress in my library!!!

Regards

MANUEL