Solving Tension Problem: Force & Moment Balances

[M.D.G]

I’m pretty stumped by this, maybe I am just making a stupid mistake but if somebody could clarify it would be much appreciated.

The system I am looking at is something like the one below, with 4 straps of each side. Their locations relative to the center of gravity along the lateral direction is not symmetric but back to front they are symmetric. Each strap has a lateral, longitudinal and vertical component. I need to determine the tension in each of the straps when resisting an acceleration of 3g in the longitudinal direction.


The problem I am have is I only have 2 equations,

A force balance, i.e. T₁ + T₂ + T₃ + T₄ = mass*3*g

And a moment blance, i.e. T₁*y₁+T₂*y₂ = T₃*y₃ + T₄*y₄

Where T₁ … T₄ are the tensions in the longitudinal direction, and y₁ .. y₄ are the distances from the CG along the lateral axis.

Am I missing something?

Edit: To clarify I drew a bird's eye view of the problem. The black arrows represent tie down lines, the red arrow represent a force acting through the center of mass due to an acceleration of 3g's

 

[Studiot]

I think your system is not statically determinate so you will not have enough equations.

However you haven't yet exhausted the possibilities since you haven't taken connection reactions into account.

It is not clear whether there are four straps passing over the box and forces are transferred by friction or whether there are eight straps anchored along the top edges of the box. Either way there are plenty of connection reactions to add to your list.

It is also not clear why ( and how ) you are claiming forces at right angles to the straps, which you are modelling as strings that cannot support such forces.

 

[M.D.G]

Sorry the bird's eye view is a bit misleading, the straps are at an angle to the vertical, longitudinal and lateral axes, but in the bird's eye view I just showed the longitudinal component for simplicity. The straps are anchored on the edges.

So I would need to solve this be determining the deflections in the straps, aka I need the Young's Modulus of the straps?

 

[Studiot]

Yes, statically indeterminate menas that you cannot solve this by considering reactions and geometry alone.
You have to introduce the materials properties of the straps as well.

 

[M.D.G]

Okay so I was working on something else for awhile but I have been reassigned to this. I guess my main problem is determining boundary conditions. I scanned a copy of a problem I made up which essentially incompasses the part of the problem above which I am having difficulties with. I have done statically indeterminate beam problems before in school, however they have always been simply supported or cantilevered. I can't figure out any boundary conditions to work with, since there aren't any deflection or slope restriction at a, b, c, d or e. Any help or suggestions would be much appreciated.

 

[M.D.G]

Bump. Sorry to resurrect this thread but I really could use some help, does anyone know of any sample problems similar to this one? I have tried searching PF fairly extensively as well as the web. Any help is much appreciated

 

[Studiot]

There are no solved problems similar to this as it is statically indeterminate.

You need the material properties of the straps to make progress, even if you are modelling the block as a rigid body.

 

[M.D.G]

There are no solved problems similar to this as it is statically indeterminate.

You need the material properties of the straps to make progress, even if you are modelling the block as a rigid body.

Sorry I didn't make that clear in my previous problem with the beam and four vertical straps, assume I know Young's Modulus for the straps, take them as nylon with E = 4 GPa. I am still fairly stumped by the boundary conditions where each of the straps connects to the block. If I make the assumption that the block is a rigid body, does this mean I can assume that the deflection in each of the straps is equal?

 

[Studiot]

You also need to make some assumptions about the distribution of the contact forces between the block and its bed.
It is not sufficient to model this as a single upward force, acting through the block's CofG, and equal to its weight. At the very least you have an upward reaction distributed in 2 dimensions over the contact surface.

 

[M.D.G]

You also need to make some assumptions about the distribution of the contact forces between the block and its bed.
It is not sufficient to model this as a single upward force, acting through the block's CofG, and equal to its weight. At the very least you have an upward reaction distributed in 2 dimensions over the contact surface.

I came across this problem,

http://www.rsip.lsu.edu/csmlab/courses/1undergr/ce3400/lectures/lect_09/sld026.htm

and if I proceed in a similar manner I can determine the forces in each of the straps. Is there a fundamental assumption which is wrong when applying the above solution to my problem?

 

[M.D.G]

I have a slightly different question but it is along the same lines. Assuming you have only 4 tie downs such as shown below, how do they come up with the solution below? I have tried playing around with it but I have only 3 equations and 4 unknows, the equations are

\SigmaF_z: T_1v + T_2v + T_3v + T_4v = Mass * G

\SigmaM_x: T_1vS₁ + T_3vS₃ = T_2vS₂ + T_4vS₄

\SigmaM_y: T_1vL₁ + T_2vL₂ = T_3vL₃ + T_4vL₄

I assume it has to due with some symmetry condition i.e. that S₁ = S₃, S₂ = S₄, L₁ = L₃ and L₂ = L₄ , but I can't seem to get the algebra right, any tips?

 

[M.D.G]

Bump, I could really use some help on my last post, this is really holding me up at work and I have been trying to make sense of those equations for awhile, anyone have any tips?