Finding equilibrium position

Andrea

Hi!
Sometimes I have to evaluate the load inclination (see figure) and if it's acceptable without changing primary suspension slings (from the hook to the spreader beam).
Analitically is not complicated if secondary suspension are vertical (as in the figure) but if they are inclinated inward or outward and beam mass are taken into account is not simple
So I ask what type of analisisys is better for finding equilibrium position and where could be appropriare to apply friction and damping
I started with a simple model where the beam is composed by 2D elements and the load with 3D brick elements. Also slings are considered ad 2D elements (beam elements) because we are sure that there will be no compression
Thanks in advance

Mishal

For a similar setup in the past I have just used nonlinear static analysis, but I would not model the slings/cables to the apex since this generally allowed for better convergence since each sling can move individually... The only problem is that your slings will not meet in the center point any longer if you have large rotations.

Andrea

We are speaking about 3/4° inclination of the spreader beam negleting the beam mass.
For greater inclination is necessary to change the length of the primary suspension
I started from the attached model (is like a simple pendulum) where I know what is the equilibrium position
Note: I noticed that increasing the elastic modulus of the beam the solution converge more slowly

Sergio

Guess that you will need to add some damping or friction to the system, otherwise will be balancing constantly.

Attached two runs, the second is wit Raleigh damping, alpha =0 and beta = 1s

As I understand with damping the system will finish in the equilibrium position.

Andrea

I tried to apply Rayleigh damping but not to the rigidity (beta coefficient). I tried with some value of alfa (proportional to the mass) and for this first test I found the equilibrium position with good agreement with the theoretical (sling mass = 0 - CoM of the beam vertical respect the the suspension point)
Seocond step is to build a model with the load and for this case solution doesn't converge. I will attach another test
Solution seems to be right....the problem was related to the slings (beam elements) rotations

disla

I would solve this without dynamics if the lifting manoubers is done “slowly”.
I guess your nonlinear static attempts could be failing because of rigid body motions.(It has happened to me).

Some hints:

1-I’m considering an only compression support for the base to capture the real lifting process.
2-I’m using only tension nonlinear springs for the slings.
3-If I were only interested in the final slope, I would consider spreader beam can only fail in the connection area with the slings or buckling. (truss). Slings can’t transfer bending moment.
4-Operators typically attach a rope to control the whole system under horizontal rotation.
5-The piece is considered suspended when reaction force on the last point in contact with the base is zero.

Sergio

@disla, what kind of step have you made then? Lineal Static?

Mishal

I assume disla's solution would need to be nonlinear, the linear solver would not be able to find a balance point unless it is stabilized by some sort of springs

disla

Nonlinear quasi static step.
Compression only and nonlinear only tension springs require nonlinearity.
Quasistatic because I'm lifting the system linearly. Why?. Because only 3-legged tables do not limp. Better to check the lifting process when one corner is on the ground. I'm sure the slings are all in tension once suspended but it's not so clear to me how they split the load during the lifting maneuver.

Andrea

For 2D (plane zy in the simulation) I found an acceptable solution. In the attached model node 28 (CoM) is vertical respect the suspension point. At the end of simulation the node displacement on y direction is very closed to the initial y-coordinate of the node. Other check regard the y coordinates of extreme nodes of the secondary suspension: they have the same y-displacement.

Sergio

@Andrea, looks like the beta coefficient helps to achive the stabilization faster than the alpha coefficient. But @disla static method also is very interesting.

In my understanding the dynamic option simulates the act of releasing the load and letting it hang without touching the ground (and damping coeffcients doesn´t matter as we look for the stabilized position), while the static option simulates lifting the load from the ground. I'm going to try to simulate some of my skids to see the feasibility in real life models with both options.