Statics problem?

[psychedomination]

Hi there,

I need some help accurately calculating the compression forces in the members Cy and Cx shown in the attached image. I know how to calculate the compression in 2D triangles but not sure what to do when the object becomes 3D (includes the z axis). If it helps the cables attached to the frame are inclined at 45 degree angles to the vertex (z axis).

I calculated an estimate of the compression forces to use in my design, however I am looking to learn a more accurate calculation methodology for this current project along with all future projects.

Any help will be appreciated.

- Psyche

 

[Trenno]

Look at the forces at the nodes of the truss. They will have three components (Fx, Fy & Fz).

Then use methods of joints to solve the truss system. Find the force in one of the diagonals and then you can find the force in each of the horizontal members.

Results should look something like this...

 

[BUGGAR]

If the thing is doubly symmetric and concentric with gravity, you can just divide the load by 4 and look at one cable in 2d (cable in plane of view) with that load.

 

[psychedomination]

@Trenno Thank you, I didn't think to use method of joints but it is an intuitive approach. The numbers you have are very close to the estimate forces I originally calculated. The calculations I did were : For Cy = (215/4)*Cos68 and for Cx = (215/4)*Sin68.

@BUGGAR Thank your the advice, I actually used that method originally in the estimate calculation, I just wasn't sure if that was the correct way to go about it. However, I got very similar results to Trenno so must be correct.

 

[desertfox]

Hi psychedomination

http://files.engineering.com/getfil...sc=212727627.4.1455194918815&__hsfp=587786906

Try this I solved a problem very similar to yours.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[psychedomination]

@desertfox Thank you, I will take a look at your calcs and apply your methodology to my problem to see if I get similar results to my original calculations.

 

[Tmoose]

After the nominal solution is complete, I'd consider the possibility the real situation is likely statically indeterminate.

 

[Denial]

Tmoose's comment is highly relevant. If one of the four cables is slightly over-length it will carry zero load, and therefore (because of the symmetries involved) so will the cable diagonally opposite the over-length one. Thus the load will be carried by only two cables.

The upside to this is that your problem is now only two-dimensional rather than three-dimensional .

 

[rb1957]

simply components of load ...
diagonal = sqrt(6.1^2+2.5^2) = 6.6m
height = diagonal/2 = 3.3m
length of cable = sqrt(3.05^2+1.25^2+3.3^2) = sqrt(2)*3.3 = 4.66m

vertical reaction = 215kN/4 = 53.75 kN
load in cable = 4.66/3.3*53.75 = sqrt(2)*53.75 = 76kN
load in long side = 3.05/4.66*76 = 3.05*53.75/3.3 = 49.74kN



another day in paradise, or is paradise one day closer ?

 

[racookpe1978]

In lifting large loads (multi-ton) from that type of rig, the riggers use 4x chainfalls to each side just so they CAN adjust each leg to equal tensions BEFORE taking a heavy strain on the single big hook at the center.

 

[andriver]

I work with heavy lifts (1,200 tons was my largest yet).

As stated above by Denial, it is possible for only two slings to be engaged (although it would likely be three to "balance" the load).

As stated by racookpe1978, you could eliminate this concern with chainfalls but at my company we refuse to use chainfalls because we consider them mechanical and prone to failure. For high risk heavy lifts, we would either size the rigging lengths, or add shackles to make up the extra lengths. It can be iterative depending on how accurate your COG was determined.

Or you could just size it so that two of the slings can take the entire load. Offshore lifts would be sized so that 75% of the entire load could be handle by one sling.

 

[Denial]

Since the OP's stated concern is the forces in "Cx" and "Cy", it is worth pointing out that once the cable tensions become unequal (for whatever reason), that rectangular frame in the XY plane will have to carry bending moments as well as axial forces.

 

[NS4U]

Tmoose is correct. This problem is statically indeterminate by 2 degrees. It is obvious that you can 'cut' two of those cables and still have a load path (which will be acompanied by excessive rotation). Therefore, your internal forces depend on relative stiffness and initial tightness of all the cables.

 

[BUGGAR]

What if the frame has no torsional rigidity?