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Hi in my engineering class we are currently making bridges and our group decided to make a parabolic bridge that will hopefully support 600 newtons (point load).

the rules are that the bridge must span 0.4 meters (40 cm) and can be held together by bolts and made out of popsicle sticks.

currently, we have an equation of the parabola which is y=-a(x+20)(x-20) but a, in this case, is a mystery to us.

my question is what value of (a) makes the parabola the strongest.

thank you so much and please help

user34877
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  • aren't you supposed to arrive at the value of a experimentally? – jsotola Sep 09 '21 at 03:04
  • @jsotola really is there no equations to help solve it – user34877 Sep 09 '21 at 03:05
  • How did you obtain this equation? I would have expected $y=a(x−h)^2+k$ (assuming the x is cm and the origin of x is at one edge of the beam, and h, k are the coordinates of the vertex in cm. – NMech Sep 09 '21 at 06:30
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    Have a look at bridges / aqueducts in use around the world - then look at the dimensions. Look at your situation and guess 3 or 4 values for a. Test and see... As this is a class assignment / project you should put the work in. We had similar projects and it is what you try that helps you learn, posting a q and being given a solution does not help you. – Solar Mike Sep 09 '21 at 07:00

2 Answers2

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You shall list the criteria in selecting the most strong curving bridge, and show your work on how you guys come up with this equation.

IMO, a semi-ellipse (vertical arch) will be a better choice, and the load is transferred as thrusts that are resisted by the vertical reactions at the supports without requiring horizontal resistances. However, the span will be short though.

r13
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This is to help you to find the equation of a parabola.

enter image description here

In order to create a parabola, we need to set a few points on it to define the curve (see graph below), and to set up the equation. For example, let's say h = 10, b = 20, and the form of the equation is $y = f(x) = -ax^2 + C$ (a & C are constants).

  • Solving the constant "C":

At the apex, $(x,y) = (0,10), y = f(0) = -a(0)^2 + C = 10$, so $C = 10.$

  • Solving the constant "a":

At the left end point, $(x,y) = (-20,0), y = f(-20) = -a(-20)^2 + 10 = 0$, solving, $a = 0.025$.

So the equation of this parabola is $y = -0.025x^2 + 10$, or $y = \dfrac{x^2}{40}+10$. As noted before, the higher the curve, the more efficient in load-carrying capacity. However, for the bridge deck, you need to take into account the driveability too.

r13
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