Statics 3

[Caspers6011]

I'm hoping someone can help me out with the following question

A shipping container has a force applied to the side of it. If a nonrigid chain is tied from the top of the container to an anchor in the ground, how much tension much the chain be able to withstand in order to prevent the container from moving.

Weight (W)= 1702 kg
Force (F)= 47423 N
Angle of T = 20 degrees
Coefficient of Friction=0.3

The box has dimensions of 2.436m x 2.436m

 

[GregLocock]

And your attempted solution is?

Cheers

Greg Locock


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[NRP99]

Use equilibrium equations sumFx=0, sumFy=0 and sumFz=0, Moment about x = 0, Moment about y = 0 and Moment about z = 0 and write down the equations in terms of chain tension T. Solve these linear equations to get the answer.

 

[GregLocock]

In a more general sense what are the possible failure modes (I count 2, based on a quick look)? Do you need to draw different diagrams for each one, or can you set the equations up so that they are the same for both cases?


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[BAretired]

Weight is given as 1702 kg which is mass. Weight should be expressed in units of force. I agree with GregLocock; there are two potential failure modes, namely sliding and overturning. We are not about to spoon feed the answer to you. Get off the pot and provide some evidence of having thought about the problem.

BA

 

[phamENG]

While I agree that there would be two failure modes, this strikes me as a freshman statics problem, and therefore unlikely to consider multiple failure modes. Just finding the equilibrium condition is probably all that's needed.

You do have to solve it as a system of equations, though, since the normal force is a function of the weight and the tension in the chain, and the tension in the chain is a function of the force and the friction and the friction is a function of the normal force. The greater the force, the greater the tension in the chain. The greater the tension in the chain, the greater the normal force, the greater the normal force the higher the friction force, the higher the friction force, the lower the force in the chain, and oscillate there until you reach equilibrium.

Don't look for the mathematical solution first. Try to understand the physical relationships qualitatively, and the math will follow. This is just algebra once you understand how a box tips over (or, more precisely, how it doesn't tip over...or slide).

 

[Daemon1]

Hi, I tried to do it but probably made a blunder. Could you guys please show the solution to this

 

[BAretired]

I am attaching my calculations below. I am a little reluctant to do so because the OP is getting a free ride with absolutely no effort on his part. But Daemon1 deserves a response, so here is mine.

Edit: A third failure mode should be considered, namely rotation about the chain anchor point.
Mapplied = F*a/2 = 23.7a
Mresist = W*a/2 + F[sub]f[/sub]*a = a(16.7/2 + 24.16) = 32.51a
Mresist/Mapplied = 1.37 (marginal if friction was overestimated)

BA

 

[dik]

That's great... now that that's cleared up, I can go design a building. Tipping action was neat... I'd never thought about it until engineering classes... then, for a few weeks afterwards, whenever I came across an object that could tip, I checked out the location of the horizontal force to see if it worked... I was pleasantly surprised. Thanks, guys... a neat topic.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Do you feel any better?

-Dik

 

[BAretired]

A third mode of failure was suggested as a possibility in my last post. If the friction coefficient, μ = 0.3 can be relied upon, failure by sliding is imminent (not much safety factor). If the container or its foundation were to be greased, perhaps as a prank, failure would be by overturning in a counter clockwise direction and the tension in the chain would be roughly doubled. Relying on friction has some risk.

BA

 

[Daemon1]

Thank you very much for your responses. I am reviewing your solutions right now and learning

 

[BAretired]

You are welcome Daemon1. The attachment point of the chain in this problem may test one's understanding of statics, but a hinge at Point D (bottom left of the container) would be a more logical support point which would avoid dependency on frictional resistance to secure the container.

BA