Arch Bridge?

Question

We have to build an arch bridge for a geometry class, with abutments, voussoirs, and a keystone.

http://www.makingthemodernworld.org.uk/learning_modules/maths/02.TU.03/illustrations/02.IL.24.gif

How big should the measurments of each part be? How many voussoirs should there be?

Would it work if we had 10 voussoirs total? The measurments of each voussoir as:

3 in and 4 in (nonparallel sides)
3 in and 3 in (parallel sides)
75 degrees (bottom base angles)
105 degrees (top base angles)

If that works, what should the keystone measures be? And the abutments?

Thanks so much!

Answer 1

The dimensions that you propose for the voussoirs would not fit together. If you extend the nonparallel sides of your voussior to form an isosceles triangle, the vertex angle would be 30 degrees. 180 divided by 30 is 6. So only six pieces would make up 180 degree arch. See the pic:

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=archbridge.jpg

If you want eleven pieces to fit together, you have 180/11 = 16.363 degrees.
You could round that off to 16 degrees and make the keystone take up 20 degrees to compensate for the rounding off.
That's 16x10 + 20 = 180 degrees around the center of the arch.
The angles would be:
voussoir:
bottom base 82 degrees
top base 98 degrees
keystone:
bottom base 80 degrees
top base 100 degrees
The linear dimensions don't work out to exact inches or fractions. You should experiment with life size sketches on graph paper before cutting your stock.
It will give you an appreciation ancient Romans' knowledge of geometry, having built arch bridges and viaducts out of hard rock that stand to this day while our steel bridges need to be repaired after 40 years.

Answer 2

via fact you're at your laptop already, you may look this up for your self. purely enter the three bridge varieties on your browser, and you gets dozens of solutions. the belief of homework is to allow you to overview. you somewhat are not learning if somebody else does the paintings for you. Sorry.