Newby arch question

[ImSniffy]

I'm building an arch foot bridge over a small creek using large concrete blocks, but I've decided to reduce the elevation by using an ellipse. My question is regarding the calculation of the segment angles. In a normal arch the span is divided into sections and each block is shaped into a isosceles trapezoid. The side angles are derived by taking the 180deg arc and dividing it into the desired number of segment sections and bisecting these points through the focal point of the radius. The isosceles trapezoid causes a wedging action with its neighbor giving compressive strength...but you probably aready knew that

How do I do this with an ellipse? Where is the best height of the center point for the angles to start from for wedging to occure?

 

[BAretired]

Why use an ellipse? Maybe you should use a parabola as that is the shape of the bending moment diagram for a uniform load. Or better still, use a circular arc so that you get constant angles on each and every block.

BA

 

[paddingtongreen]

Instead of an ellipse, approximate it with two circular curves, a long radius for the middle, a short radius for the ends. The centers of the short radii have to sit on radii from the long radius. Then cut into the widths you want with radii from the appropriate centers. The advantage is that only two shaped are required although a half width, but greater depth, in the middle for a keystone looks good.

Look at the "Five Center Method" at this site:

http://www.uwgb.edu/dutchs/MATHALGO/Ellipses.HTM

It's a leftover from my draughting years.

Show us your result.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[paddingtongreen]

Ooops, I just realized that is a three radius solution, three different blocks, or four if you have a keystone. The technique I used was for a 2:1 ellipse. I'm not sure that I can remember it.

Sorry about that.

As BA says, you can go back to a circular arc. With abutments that can resist horizontal force, you don't need the full half circle.

http://www.terragalleria.com/pictures-subjects/stone-bridges/picture.stone-bridges.yose46647.html

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[IDS]

As BA says, you can go back to a circular arc. With abutments that can resist horizontal force, you don't need the full half circle.

A flat arch is going to have horizontal forces at the abutments no matter whether it is elliptical or circular.

The circular segment is probably better for stability because the transition from a tangential force to a vertical force takes place in the abutment, rather than in the arch.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/