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>> These are iron structures.

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And the consequences of industrialized iron is that it's lighter than structures of stone,

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which now we have the portent for major failure.

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At first, engineers didn't really understand this idea of how to design

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with iron, how to make those connections.

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And this concept of buckling and stability in members,

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was something new that was being studied by those engineers.

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So, unfortunately, sometimes we did see failures happen with these bridges.

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And one of them was a bridge in Scotland called the Firth of Tay.

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This bridge collapsed in 1879, killing all aboard the rail line.

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There were 2 great barriers to Scotland's east coast travel.

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They were the Firth of Forth and Firth of Tay,

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both stormy estuaries on the east coast of Scotland.

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After the Firth of Tay Bridge collapsed, the next time the Scots had to build a bridge

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over a stormy estuary, they wanted to make sure it wouldn't fail.

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And so, they built the Firth of Forth Bridge, designed by Benjamin Baker.

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And we see how massive this structure is and it's still standing today, spanning 1,710 feet.

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This was the longest spanning bridge in the world and it's also a railroad bridge.

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So, it was a great achievement by the engineer, Benjamin Baker.

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To give you a sense of scale, as to how large the members of this bridge are,

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if you zoom in close to the supports, we see containers.

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We can see the relative size of those containers to the members of the bridge.

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It is a massive structure.

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This close up image also gives you a sense

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of the different perspectives one can get from a bridge.

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So, close up, the Firth of Forth looks like a massive bridge full of clutter.

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Whereas from far away, the bridge looks much lighter

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and you don't get that sense of heaviness.

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Now let's look at this bridge and dissect it from a scientific point of view.

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The form for this bridge is called a horizontal cantilever.

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And to simplify the analysis, I'm only going to look at one span of the Firth of Forth.

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The cantilever arm spans from the support towards the center.

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And the back span is called the anchor arm.

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It anchors that center support towards the anchors at the end.

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And in the center, we have what we call a suspended span.

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We could think of this as essentially 2 seesaws.

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So, we've all been kids playing on seesaws and the seesaw has, let's say a center support,

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representing in this bridge, that center tower.

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If we suspend a weight between these two seesaws,

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we know that it's not going to be stable.

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The seesaw will tend to rotate and it will no longer be horizontal.

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To make those seesaws horizontal again, we know that the tips of them have to be pulled down.

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And that is what those anchors do.

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So, we can think of this Firth of Forth bridge as essentially 2 seesaws

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with a suspended rate between them.

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Let's define the reaction at the anchor, that downwards reaction, as Ra.

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And let's define the suspended weight, a downwards reaction, W. So,

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will the reaction at the seesaw support be up or will it be down?

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We need equilibrium.

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The sum of the forces in the vertical direction have to equal zero.

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Therefore, the reaction at the seesaw supports must be up.

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Let's define this seesaw reaction Rs.

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Since the arms of the seesaw, meaning the size of the seesaw to the right and to the left

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of the support are of equal length, Rs of S, must equal W. Meaning,

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the seesaw support must equal that weight that's suspended.

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In that case, what is the magnitude of the reaction at the anchor Ra, in terms of W?

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Do you think that the reaction at the anchor Ra, is equal to W, W over 2, 2W or 2/3W?

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We can solve it in 1 of 2 ways.

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The algebraic solution tells us that the forces in the upwards direction,

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equals the forces in a downwards direction.

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So, 2W is going up.

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And W plus 2Ra is going down.

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And solving that, we get Ra, equals W over 2.

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Another way to look at it is to divide that system into 2 seesaws.

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So that weight W, half of it is going to 1 seesaw

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and the other half is going to the other seesaw.

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So that you know that if you're friend weighs W over 2, you must also weigh W

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over 2, to keep that seesaw horizontal.

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This double seesaw example is exactly how the Firth of Forth Bridge acts.

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So, we have the suspended weight in the center W. And then we have the supports

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at those center towers, so to speak, is going up W. And then it's anchored down W over 2.

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Now that we understand the reactions, let's look at the internal forces in the arms

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of the cantilever and anchor arm.

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In this lecture, we're not going to try to solve for the magnitude

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of the stresses or forces in those arms.

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But we're going to try to define is it intention or is it in compression?

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Benjamin Baker did a physical demonstration to illustrate

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to the public how the Firth of Forth Bridge acts.

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So, he had 2 men sit on a chair.

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And they were holding another man in the center, who was the suspended weight.

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And then they had some bricks anchoring down.

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They acted like the anchors pulling down.

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Just like in that seesaw example I just gave you.

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So, do you think that those men's arms are in tension or in compression?

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And those wood pieces that they're holding between their fingers and the seat,

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are those wood pieces in tension or compression?

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We did a similar example to this in my classroom,

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where I asked my students the same question.

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This is an easy experiment to do on your own and to build.

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So, do you think that these students’ arms are in tension or in compression?

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After the experiment, I asked them, were your arms being stretched or compressed?

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And they knew for sure that their arms were being stretched.

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And that means that their arms were in tension.

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Meaning, that the upper cord of this cantilever is in tension.

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And the bottom pieces of wood, the reason we used wood and not rope,

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is that that wood is in compression.

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If we had used rope instead of wood, the experiment wouldn't have worked.

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So, the answer is the top cord of these horizontal cantilevers are in tension.

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And the bottom cords of these horizontal cantilevers are in compression.

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So, in this lecture, we looked at some big metal bridges for railroads.

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We looked at the Britannia Bridge, made of iron.

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The Saltash Bridge, also made of iron and the Firth of Forth Bridge,

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which was actually made of steel.

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What I didn't have time to talk about is the Eads Bridge in Saint Louis, which is also made

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of steel and the Garabit Bridge designed by Eiffel.

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Eiffel is famous for his tower, but Eiffel is also a famous bridge designer.

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And the Garabit is probably one of his most famous.

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Next time, we cross the Atlantic and come to America,

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where we're going to see John Roebling is designing some magnificent bridges

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for railroads as well.

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I hope you'll join us.