Are you trying to teach your kids some engineering concepts using bridges or cranes?
Would you like to include torque, center of gravity, applied trig, and force vectors?
THE BRIDGE/CRANE KIT consists of 3 cable stayed bridge sections, a working crane and a through truss bridge–enough structures to keep the whole class busy.
the kit contains over 800 pieces.
And with the 50-60 wooden beams, all the hardware, line, windlasses, etc.-almost 800 pieces- your kids could invent and build almost anything.
The students at FMES designed a self propelled vehicle using all the members (parts) from a different structure.
The load (3 bricks) hangs from a line (string)- the line goes over a pulley wheel and then goes down and wraps around the axle of the windlass. As the load descends, it pulls on the line, which causes the axle and the wheels to turn. So until the load hits the ground, the wheels will turn and propel the “truck”
Here’s another brilliant design by one of the kids. We reconfigured the basic cable stayed bridge into a lift bridge.
The line holding up the deck was connected to a windlass so we could raise the bridge deck.
Sam wondered if he could use that single windlass to raise both decks.
POP SICKLE STICK BRIDGES
I’ve always thought the pop sickle stick bridge curriculum was somewhat lacking.
Having spoken with a number of kids who took part in these contests-it seemed the kids didn’t really learn how trusses worked-which members were in Tension and which were in Compression. And after the bridges were tested to destruction, what did the kids have to take home? A pile of broken sticks.
So I re-configured my basic cable stayed bridge.
For the cable (string) that supports the deck I used 3/32″ steel cable- it won’t stretch and break. BUT, the for last 10″ or so I used thin fibers from a length of manila rope-these fibers will break under a heavy load.
Sure with a heavy enough load the fibers( and therefore the entire cable ) will fail, but what other factors could make the cable fail?
What is the total load- how many bricks? Is the load concentrated at a point on the deck or is it evenly spaced along the length of the deck? And obviously the angle the line makes with the horizontal is the most important factor.
Let’s first concentrate on the angle of the cable that supports the load.
So when the cable makes a lower angle with the horizontal, there’s a lot more Tension in the cable and it could break.
The 2×4 weighs 6#s but when we attach a scale to 1 end and lift vertically- the scale reads only 3#.
That’s because the floor is supporting half the weight.
Next we change the angle to 30 degrees. How much Tension is in the line now? We know it’s 6lbs. of muscle (Tension) but how could we compute it if we didn’t have the scale?
We can diagram the forces using a triangle.
The height of the triangle is 3 (remember it took 3#s of muscle originally to lift the end of the 2×4 vertically at 90 degrees).
The hypotenuse or the TENSION- (that’s what we want to find) -is the amount of muscle (tension ) needed to lift the 2×4 at 30 degrees.
Do you remember your trig functions?
SINE is opposite over hypotenuse Which in this instance is 3/ hyp.
and the sine of 30 deg is .5
sine 30= 3/hyp and substituting in we get
.5= 3/hyp and now for a little algebra
.5 hyp. = 3
hyp.= 3/.5 hyp.=6 which agrees with the reading on the scale
Did you notice that instead of using inches or feet or miles, we’re using pounds of force?
So it took 3#s of force to lift the deck @ 90deg. but 6#s @ 30deg. And you thought you’d never find a use for trig.
Now if we know the angle of the cable and the weight of the load and the deck, we can find the Tension in the cable.
But first we have to know how to find the angle.
Remember tangent? the ratio of the opposite side over the adjacent side.
The base of the triangle- that’s the adjacent side (adjacent means next to) is 40″. That’s the length of the deck from where it pivots on the metal-all thread, to the end.
The height or the opposite side (opposite the angle theta) is measured from the deck to the top of the tower. That’s 30″
since Tan= Height/Base that gives us 30″/40″ or .75
Now look up .75 in the tangent table
That shows just over 37 degrees
I always tell my students to use trig tables instead of simply
punching in the numbers in their calculators. That way they’ll see how the angles change as tan changes.
EXERCISES-
So here’s an example of the kind of exercise you can do with your students.
The 3 bricks simulate a uniformly distributed load on the deck.
Remember the 2×4 from above. Since the wood in the 2×4 is equally dense throughout, then when 1 end is sitting on the floor or resting on the pivot (the metal bar)
that means half the weight is supported by the floor (or the metal bar) and the other half is supported by the cable
.Similarly, since the bricks are equally spaced along the deck, we can say that the combined weight of the deck and load are uniformly distributed.
The deck weighs 3# and the 3 bricks (4.7#s per) weigh 14.1#s for a total of 17.1 #s Now since 1 end of the deck is supported by the length of all-thread (the metal rod), that means that if we tried to lift the opposite end of the deck by pulling up (at 90 deg) , we’d only need half or 8.55 pounds of force. The other 8.55 pounds is being supported by the all-thread.
So to find the Tension in the cable we use the same triangle we used with the 2×4.
new triangle
What if the load is NOT evenly spaced along the deck?
Say all 3 bricks are piled up at the end.
Now we have to use the torque formulas. What’s TORQUE?—the force that causes rotation. What’s rotating?
If the cable wasn’t holding up the far end of the deck, then when a load is put on the deck, the deck would pivot about the far end and ROTATE clockwise
SKETCH
Also if there wasn’t any load on the deck but the cable was still pulling up on the deck, it would rotate Counter-clockwise.
However since the deck stays level and is not moving (until the cable breaks ) in other IT’S words it’s STATIC
These static equations are what we can use to find the Tension in the cable.
The weight (force) of the bricks causes the deck to rotate- and we measure that torque by multiplying the weight (8.55#s) by the distance from the pivot point (fulcum)
Engineering students learn these formulas- it’s called STATICS.
When you’re using these cable stays bridges in this manner, you’ll need a team of 4 kids for each bridge.
2 kids to place the load and check the tension on the crossed lines ( to make sure they’re taut and the tower stays upright and secure)
Another kid to check the reading on the scale and document it
And then 1 kid to act as foreman-make sure the lines are un-obstructed and oversee the whole exercise.
You have lots of variables.—
-what is the angle of the cable?
how much is the load
how is the load positioned along the deck
Document all the above variables.
Next using the same set of variables, change the cable angle to ___ or _____.
Document your results.
Next replace the 1/4″ dowel with a 5/16″ dowel and repeat the exercise. If the holes in the tower aren’t big enough for the larger dowel, then either drill out the holes, or if that’s not possible see if your kids can come up with a solution.
The girls in my class can up with a simple yet elegant solution.
they placed the 5/16″ dowel outside the tower right next to where the 1/4″ dowel was before. then they hung 2 lines from the all thread at the top of the tower
VIDEO
nEXT SET OF EXERCISES /set ups- don’t use the short length of strands-use the 3/16″ cable for the entire length. this way
tangent-how to compute the angle of the cable.
sketch of the rt triangle superimposed over the bridge.
The Height of the trian gle is measured from the deck to shere the cable