3.14

## UNSW Sydney

Skip to 0 minutes and 10 secondsThis washing line folds down against the wall when it's not in use to save space. A new one is being designed bigger and stronger. We'll design some of the connections. You'll find the specification in the download section. This design activity comes in two parts. In the first part, you will find the pin connection at C. In the second part, you'll find the wall anchors that secure the assembly to the wall at the D and E. In both cases, we'll use two dimensional static equilibrium. It's a powerful item in the engineering mechanics toolkit. And in this task, you'll see why. If this is new to you, maybe watch this video straight through first to get the general idea.

Skip to 0 minutes and 58 secondsAnd then watch it again in detail. This engineering drawing of the new design is in third angle projection. So you need to rotate your head 90 degrees to the right to see the side view in its normal position. Dimensions are in millimeters. Here is the side view again showing the pin that you will specify. Here is the drawing of the wall plate showing the holes for the wall anchors and the lugs for the pins from the frame and struts. We will be using a bolt for the pin. In engineer speak, a bolt has a plain shank-- that's an unthreaded section-- and is generally used with a nut.

Skip to 1 minute and 43 secondsOn the other hand, if the thread goes all the way to the head, it's a set screw or machine screw which is generally used in a threaded hole to clamp two items together. What load should we design for? Here is one possible set. To find the weight of the frame, you need to know the material. We chose steel rectangular hollow section. We found the weights of the struts and the wall plates like this, too. The weight of wet washing was less clear. This estimate is for a washing machine load of eight kilograms dry but soaked with rain. The child hanging off a corner comes from life experience. We'll warn against it. But it might still happen.

Skip to 2 minutes and 31 secondsAnd we'll aim to make the frame strong enough to take it. You could explore the uncertainty in assessing loads in the discussion. Now the washing line is obviously three dimensional. So how can we use our two dimensional analysis? Well, we can use symmetry to find the loads on each side frame from the self weight and the weight of the washing, half each. Then we can add a child on the end assuming that a child hanging off the corner is the worst case. These loads are supported by a single wall plate. How to turn 3D into 2D would be a good topic for discussion.

Skip to 3 minutes and 12 secondsNow that we've sorted out the loads and how to apply 2D, we can start using engineering statics to find the forces we'll need. To find the pin force at C, you will need to reveal it with an FBD. We'll start with an FBD of the frame. Pause the video and sketch what you think it should look like.

Skip to 3 minutes and 43 secondsHere's the answer. A is represented as a pin joint with two components. C is a pin joint to another two components. The other arrows are known loads. Notice that we don't include the strut. We must remove it to reveal the force at C. But we've got four unknowns and only three equilibrium equations. We need another one. We'll try an FBD of the strut. Pause the video and see if you can sketch it.

Skip to 4 minutes and 29 secondsHere it is. Notice that by Newton's third law, the forces at C are equal and opposite to the ones on the FBD of the frame. The method won't work if you don't get this right. How does this help? Well, if we take sum of the moments about A on the frame, we will get an equation with only one unknown. That’s Cy - the vertical force at C. We often get an unknown force in a single equation like this. If you choose a moment axis that coincides with a force, the moment arm is zero which eliminates the moment of that force. OK.

Skip to 5 minutes and 8 secondsIf we now move to the strut and take moments about B, we'll eliminate the forces at B from our equation. And we will get an equation with only Cx as an unknown. Remember, we just found Cy. Now we can combine our two components to find the total force on the pin at C. That's the pin at C on the side frame. Now have a go yourself at implementing this analysis and put the numbers in. This screen should give you all the information you need for the pin force. Why not pause the video and try it?

Skip to 6 minutes and 3 secondsFinally, we'll select a component for the pin. Normally you'd need to consider the various ways the pin joint could fail. We'll just consider one. We'll consider shear. These two diagrams are cross sections through a pinned joint. The load causes the pin to be chopped through in two places. Because of this, it's called double shear. The maximum permissible load on the pin depends on the maximum allowable shear stress in the material. Shear stress is shear load over area. Units are Pascals, which is Newtons per square meter. Or kilo-Pascals or mega-Pascals. We'll need to decide on the material strength and a factor of safety.

Skip to 6 minutes and 53 secondsThe table lists the capacities of a range of bolts that we could use for the pin. We have included a factor of safety in our permitted stress. So we don't need to include it again. With this material, it looks like a four millimetre pin would do it. It seems small to me. But the pin that locates a similar strut in a typical rotary clothesline is about this. What do you think about using common sense in engineering design? For example, if something just doesn't seem right. This could be an interesting discussion point. You could try other options for the pin. You might choose a lower strength material but have a pin of a greater diameter.

Skip to 7 minutes and 36 secondsAnd shear is just one possible failure mode. You would need to check for other ways it could fail, something else to explore with your fellow learners. To finish this task, post your ideas on the discussion.

# Design a hinge pin for a folding clothes line Part 1

Here you will design a hinge pin and wall anchors for a folding washing line.

It might help if you download the design specification in the Downloads section below in case you want to refer to it as you go.

This design task has been split into two parts.

The video for part 1 (this step) sets the scene and leads you through the process for designing the hinge pin. As you go, you can do calculations yourself if you like. They involve Free-Body Diagrams and equilibrium in two dimensions. In the end you will select an item from a list.

From this you will get the basic idea of how to use rotational equilibrium to solve a problem in two dimensional forces on a rigid object.

If you just watch the video it will take about 8 minutes. If you do the calculations it will take longer; how much longer depends on so many factors, but allow a total of 30 minutes.

The video for part 2 (the next step) leads you through the process for designing the wall anchors. You will see how different FBDs can reveal different forces - forces that are external on one diagram can become internal forces on another.

If you are running out of time when you have completed part 1, you could just review the video for part 2 to get the overall idea. But this is an important topic and it would be good to study it in detail if you can.

### Talking points

• Did you see the great importance of the extra equilibrium equation we got from considering twist?
• Can you think of other ways the pin joint could fail?