Resulting forces in the Z axis. 1

[Bert2]

Please can someone help me in the solution for calculating the resulting force in the Z axis. attached is the situation (rigging diagram) specifiaclly the top slings are in question. the end elevation shows them to have an angle 65-69deg.interior angle and in the side elevation 72-74deg. interior angle. Basically what is the resulting force acting on the top slings given the two angles their at?

Using a force off 75Te for the object itself.

thanks.

 

[chicopee]

These are easy to figure out but I am wondering why would someone in the Mechanical forum would ask this type of high school problem? I would be willing to give you answers only if I am convince that these are not school problems. My answers would be in general terms. So, in what direction is the Z axis.

 

[rb1957]

i think the OP means that the slings are inclined in both directions, ie not in the X-Y or Y-Z planes.

I agree the question is PDB (PrettyDamnBasic) ...
let the load in the sling = P
[do all the slings have the same load ?]
calc components of P in the 3 axes (yes?)
sum the (presumably)Z components to equal the applied load
solve of P,
and it's components.

 

[ione]

I can't believe it's not a student enquiry

 

[vpl]

I'm pretty sure he's not a student, based on his other posts and replies. More probably, this wasn't his specialty area and he's forgotten.

Patricia Lougheed

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Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[rb1957]

loking at it a 2nd time, it's more complicated than i originally thought, 'cause each dim'n is different (ie each sling will have a different load).

you've got 4 unknowns (the load in each sling) and 6 equations of equilibrium, so it does solve. it is possible that the solution may be impractical, if one of the slings is required to carry a -ve load.

an important practical point, the CG of the load needs to be on the line of action of the lift.

 

[Bert2]

@ rb1957 yes inclined in both planes.

i understand the basics but am i making this problem harded than it is? i guess i am ....

 

[vpl]

Somebody posted this link in another forum. As always, it's a "use at your own risk":

http://www.maximumreach.com/software.htm

Patricia Lougheed

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Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[Bert2]

@ rb1957 correct each sling has a different length and the CoG is not centered about the rigging... only to the lift itself.

i dont understand how one sling may carry a -ve load?

 

[potteryshard]

In practice, with the load c/g not centered under the lifting attachments, you will not be able to rig in this fashion to obtain a completely level load; it would require 8 slings of precisely measured and different lengths.

Because riggers carry sets of matched length slings, the load will go off level to get the c/g under the line of action. The riggers will often insert some shackles in the slings on the high side to roughly even out the load.

If the load has to be maintained level, the riggers will likely use a different, and more adjustable rigging.

 

[Twoballcane]

I can not open files due to company protocal, but have you done a FBD?

Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[Twoballcane]

You can even use the cut and sum method to figure out the loads in each strap...

Tobalcane
"If you avoid failure, you also avoid success."
“Luck is where preparation meets opportunity”

 

[rb1957]

i think there's a problem with the angles, 74deg and 72deg don't balance in Fx. 74deg requires the 72deg to be 72.5deg.

it was a bigger difference when i started, got smaller as i worked on it some more

i (now) think the problem is redundant (the lower portion has 4 unknowns and only three equations). You can still solve this with other methods (i like the unit force method, but there are probably other methods better suited to this problem).

the slings can't carry -ve load, that's what i meant by "impractical solution" ... the math will quite happily put a -ve load on a sling, but you can't in real life.

 

[rb1957]

yeah, this is a redundant problem. thinking (a little) about it, maybe an easy way to solve it is to remove each of the slings in turn, solving the remaining three (easy to do, don't worry if any sling loads are -ve), then combining the 4 different solutions (sum/4); but now -ve sling loads is a problem.

 

[rb1957]

yeah, that approach gave me reasonable numbers pretty quick. now you know the Z component at each corner, the upper sling loads can by found easily-ish.

btw, your other angles are a little off ... add a decimal place or two.

 

[zekeman]

I don't understand


















Unless I am missing something this problem looks trivially simple. So please correct me if my simple analysis doesn't stack up.

First, look at the bottom set of straps. You can easily draw a vector diagram from the left side view forcing the the vertical resultant to 1/2 the load. The length of the vector would be in true length.

Now for the upper region, you can do the same, but the vectors are not not shown in true form so they would have to be rotated to get the answer.

If I can do it graphically, it can be done analytically, easily.

 

[rb1957]

yeah, i originally though the slings were inclined to the weight, and set up a s/sheet along those lines. then i noticed the bttm slings have no Y component (inclined in the X-Z plane. this relates Px1 and Px4, and Px2 and Px3 [figure out why ... hint, sum Mz)

therefore Pz1 is relatd to Pz4, and Pz3 to Pz2 [geometry]. then sum moments in the elevation plane and the end elevation, and it should be statically determinate.

 

[zekeman]

"yeah, this is a redundant problem. thinking (a little) about it, maybe an easy way to solve it is to remove each of the slings in turn, solving the remaining three (easy to do, don't worry if any sling loads are -ve), then combining the 4 different solutions (sum/4); but now -ve sling loads is a problem."

While this approach may be mathematically correct, it doesn't square with the physics. Of the 3 tri-vectors,I find that only one has 3 tensions and therefore it is the ONLY solution compatible with the physics and the mathematics.

When I look at the 3 equations with 4 unknowns,I call one unknown 0 and solve for the others. If you do this 4 times each with a different choice, you will get only one answer that squares with the physics, namely three positive (tensions) values. I submit that that is the answer.

As for the lower support, the problem is mathematically tenable, since there are enough equations to match the unknowns.

 

[rb1957]

all i meant was it is possible for the math to give an impractical answer ... i didn't say it did.

having said that i noticed that one of trhe zero cases gave a negative load, but this is ok 'cause when you avaerage the different cases all the sling loads are positive.

Having said that, the lower portion solves easily, and this provided the Fz (& Fx) reactions for the upper portion, so all you need is the Fy component, again this solves easily.

 

[zekeman]

"having said that i noticed that one of trhe zero cases gave a negative load, but this is ok 'cause when you avaerage the different cases all the sling loads are positive."

That's my point. It is NOT ok. You have no license to average since it will give meaningless answers.

Any 4x3 linear set can have an arbitrary "solution set" by assigning an arbitrarily value to one unknown.
Does that make the answer correct?