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Design a hinge pin for a folding clothes line Part 2

In this video you will specify the wall anchors that secure the washing line to the wall.
In part two, we’ll consider the pull-out force on the top wall anchor. For this we’ll need a different FBD. This time we’re only interested in the forces in the wall anchors. We’re not interested in the pin forces at A, B, and C. What we’ll need is an FBD of the entire washing line assembly in its two-dimensional form. That will include the side frame, the loads, a strut, and the wall plate. Remember, the pin forces at A, B, and C are now internal to the system and should not appear. This is most important. Pause the video, and try it.
Here’s the answer. We’ll assume that the wall plate contacts the wall only where the wall anchors are. We’ll check that this is a conservative assumption later. Even with this simplification, we have four unknowns. And, again, we only have three equations. What can we do? This situation is statically indeterminate. You can’t solve it using statics alone. The problem is the wall plate. It constrains the vertical movement of the wall anchors so that we can’t easily tell what the two vertical forces are. Luckily, although we can’t find the individual vertical forces, we can find the horizontal forces. And these are the pull-out forces we need.
Can you see how to get an equation with just the force in the top wall anchor as an unknown? I’ll give you a few seconds to think about it.
The answer is to eliminate the vertical forces, take moments about a point on the wall. But what point? To eliminate the lower horizontal force, take moments about the bottom wall anchor. Do you see how this works? It’s our zero moment arm trick again. You might think that when the frame is loaded, the compressive forces at the bottom of the wall plate might push at the bottom of the wall plate itself. We’ll assume instead that they act at the bottom wall anchor. It’s a conservative approximation. Can you see why? Be careful when you decide on the moment arm that you include the distance of the pins to the wall. It’s a small distance, but you’d want to get it right.
Once we’ve got the force in the top wall anchor, we can get the force in the bottom wall anchor by horizontal equilibrium. But what about the vertical forces? Although we can’t find the individual vertical forces on the wall anchors, we can find their combined effect from vertical equilibrium. That’s the way you go about the task. Or rather, that is a way you can go about the task. There are other ways. You just need to find one of the better ones. Now have a go yourself at implementing this analysis and put the numbers in. The screen should give you all the information you need. Why not pause the video and try it?
Here are the answers.
Now we’ve got the forces, we’ll choose a wall anchor. First we’ll select a top wall anchor. That’s D. From the table, a size 8 millimetre wall anchor looks suitable. The clotheslines that I have looked at seem to specify about 10 millimetres, which would allow higher loads and give a greater margin on the quality of the hole in the wall. Although the calculated force on the bottom anchor– that’s E– is the same as the one at D, the pull-out force is quite different. Can you see why? It’s because the force at the bottom pushes directly on the wall. In fact, there’s no pull-out at all. But we’ll make it the same size as the one at D for convenience.
Then there’s just one size of wall anchor in the box, and the installer won’t be confused. The shear load– that’s the vertical load at the wall– is complicated by the wall plate. But the combined load is much less than the capacity of even one anchor, so it looks fine. Someone will have to decide if the wall is stable enough. You don’t want it to pull over, but that’s not our job. That’s the wall anchor dealt with. In fact, you’ve completed this task. We hope that this comprehensive exercise has made you think. Post any final thoughts you have, and move on to the next step.

In this video you will specify the wall anchors that secure the washing line to the wall. The process is similar to part 1, but it requires a different FBD.

Even if you just follow the process and don’t do all the calculation, make sure you understand the new FBD and how the external forces in the diagrams of part 1 become internal forces in the diagram in part 2. Only external forces appear on an FBD.

If you just listen to the video without doing the calculations it will take about 6 minutes.

If you are stuck (or even if you aren’t) you might like to look at the worked solution that is available from the Downloads section.

Talking points

  • Share your thoughts on how internal forces on one FBD can become external forces on another.
  • The instructions for our folding washing line will include a warning about hanging off it. But, should our design be capable of saving people from themselves?
  • Can you think of other ways that the connection to the wall could fail?
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Through Engineers' Eyes: Engineering Mechanics by Experiment, Analysis and Design

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