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

Are you building a Roman arch? Actually Roman's did not invent it but made a great us of it. OK let's get to the problem. Let the keystone be +/-10 deg or 20 deg total and 5 degrees for a footer... That leaves 75 degrees for 1/4 arch . The voussoirs are 75/5 0r nice 15 degrees each [10 voussoirs total works well]


Let R1 be internal radius and R2 the external radius

the ratio of (R2-R1)/R1 in your case is 1:4

Then the facade's face of each voussoir is a difference in sectors of R2 and R1.

so your
3 in and 4 in (nonparallel sides) would depend on R2 and R1

The parallel sides are okay.

Keystone is a sector of 20 degrees

and abutments just heavy enough to prevent footers from sliding.

Answer 2

Mackinaw Bridge-michigan Embasdoor-Michigan/Canada Golden Gate Bridge-California