1. Arches

2. Closed Spandrel Masonry Arches
Sprandrel
Retaining
Wall
Arch

3. Traditional Arch Bridge Construction
Spandrel Retaining Walls

4. Traditional Arch Bridge Construction
Filled with dirt, up to road level

5. Traditional Arch Bridge Construction
Spandrel Walls
Arch
Filled with dirt, up to road level

6. Traditional Arch Problem
The funicular shape for dead load is a parabola

7. Traditional Arch Problem
The funicular shape for dead load is a parabola
When a point load is applied (say, a horse), it is no longer funicular. Bending moment is present. Masonry cannot take tension. It might collapse.

8. Traditional Arch Solution
Use A LOT OF DIRT

9. Traditional Arch Solution
Use A LOT OF DIRT
Huge dead loads pre-compress the masonry so much that the tension from the bending action of a Horse Load will never overcome the compression

10. Traditional Arch Solution
Use A LOT OF DIRT
Huge dead loads pre-compress the masonry so much that the tension from the bending action of a Horse Load will never overcome the compression
Irony: more dead load strengthens a traditional masonry arch.

11. Puzzle
This arch is indeterminate, yet you can solve it. Why?

12. Puzzle This arch is indeterminate, yet you can solve it. Why?
It is funicular. M=0, everywhere. So…

13. You can place pins wherever you want them, to facilitate analysis.
Puzzle
This arch is indeterminate, yet you can solve it. Why?
It is funicular. M=0, everywhere. So…
You can place pins wherever you want them, to facilitate analysis.

14. You can place pins wherever you want them, to facilitate analysis.
Puzzle
This arch is indeterminate, yet you can solve it. Why?
It is funicular. M=0, everywhere. So…
You can place pins wherever you want them, to facilitate analysis.