# Sovereignty Module: Span the River

## Complete Clay Brick Arch Bridge Construction: From Foundation to Crossing

Arch bridges are among the most durable structures ever built. This campaign covers arch geometry, centering (formwork), brick laying, abutment construction, and load testing.

### Chapter 1: Arch Types

| Type | Shape | Span | Strength | Difficulty | Historical Use |
|---|---|---|---|---|---|
| Semicircular | Half circle | Up to 30 feet | Very high | Moderate | Roman |
| Segmental | Less than half circle | Up to 50 feet | High | Moderate | Medieval+ |
| Pointed (Gothic) | Two arcs meeting at point | Up to 40 feet | Very high | High | Gothic |
| Flat (jack arch) | Nearly flat | Up to 6 feet | Moderate | Low | Lintels, windows |
| Elliptical | Ellipse shape | Up to 60 feet | High | Very high | Renaissance+ |
| Corbelled | Stacked offset courses | Up to 15 feet | Moderate | Low | Ancient |

### Chapter 2: Arch Geometry

Semicircular arch: 1) The arch is a half circle. 2) Span = diameter of the circle. 3) Rise = radius = half the span. 4) Example: 10-foot span = 5-foot rise. 5) All forces are directed downward and outward to the abutments. 6) The arch is in pure compression (no tension). 7) Bricks and mortar are strong in compression. 8) This is why arches can span great distances with simple materials.

| Span | Rise (semicircular) | Abutment Width | Brick Count (est.) | Mortar (est.) |
|---|---|---|---|---|
| 6 feet | 3 feet | 2 feet | 200-300 | 2 cubic feet |
| 10 feet | 5 feet | 3 feet | 500-700 | 5 cubic feet |
| 15 feet | 7.5 feet | 4 feet | 1000-1500 | 10 cubic feet |
| 20 feet | 10 feet | 5 feet | 2000-3000 | 20 cubic feet |

### Chapter 3: Centering (Formwork)

Centering construction: 1) Centering is a temporary wooden frame that supports the arch during construction. 2) Build two curved ribs from lumber (cut to arch curve). 3) Space ribs at bridge width apart. 4) Connect ribs with cross braces. 5) Cover top with planks or plywood (smooth surface for bricks). 6) Support centering on posts (adjustable height). 7) Centering must be strong enough to support all bricks and mortar until the arch is complete. 8) The arch cannot support itself until the keystone (top center brick) is placed. 9) After keystone is set and mortar cures, centering is removed (struck). 10) The arch then supports itself through compression.

| Component | Material | Purpose |
|---|---|---|
| Curved ribs (2+) | 2x10 or 2x12 lumber, cut to curve | Define arch shape |
| Cross braces | 2x4 lumber | Connect ribs, maintain width |
| Deck planks | 1x6 lumber or plywood | Smooth surface for brick laying |
| Support posts | 4x4 or 6x6 lumber | Hold centering at correct height |
| Wedges | Hardwood | Adjustable height, easy removal |

### Chapter 4: Brick Laying

Arch brick laying: 1) Start from both abutments simultaneously. 2) Lay bricks on centering, working upward from both sides. 3) Mortar joints: 1/4-3/8 inch (thinner at intrados, thicker at extrados). 4) Joints are wedge-shaped (wider on outside, narrower on inside). 5) Each brick is angled to point toward the center of the arch. 6) Use a string or trammel from the center point to check alignment. 7) Work both sides evenly (keep weight balanced on centering). 8) Place keystone last (top center brick). 9) Keystone locks the arch. 10) Allow mortar to cure 7-14 days before removing centering.

| Step | Action | Critical Factor |
|---|---|---|
| Foundation | Build abutments on solid ground | Must resist outward thrust |
| Centering | Build and install formwork | Must be accurate and strong |
| Spring line | First course on abutments | Level, aligned, solid |
| Voussoirs | Lay bricks from both sides upward | Wedge-shaped joints, centered |
| Keystone | Place final center brick | Locks the arch |
| Cure | Wait 7-14 days | Mortar must reach strength |
| Strike | Remove centering carefully | Arch now self-supporting |
| Spandrel | Fill above arch to road level | Rubble fill, then paving |

### Chapter 5: Abutments and Load

| Abutment Specification | Small Bridge (6 ft) | Medium Bridge (15 ft) | Large Bridge (20 ft) |
|---|---|---|---|
| Width | 2 feet | 4 feet | 5 feet |
| Depth (into ground) | 2 feet | 3 feet | 4 feet |
| Height | 3 feet | 7.5 feet | 10 feet |
| Material | Stone or brick | Stone or brick | Stone or brick |
| Foundation | Compacted gravel | Concrete or stone | Concrete or stone |

### Reference Card

1. The arch works in compression (every brick in an arch is being squeezed by its neighbors; bricks and mortar are extremely strong in compression, which is why arches can span great distances). 2. The keystone locks the arch (the arch cannot support itself until the keystone (top center brick) is placed; until then, the centering carries all the weight). 3. Abutments must resist outward thrust (the arch pushes outward at its base; the abutments must be massive enough to resist this thrust or the arch will collapse outward). 4. Build from both sides equally (laying bricks from only one side creates unbalanced weight on the centering; always work both sides evenly to keep the load balanced). 5. Wedge-shaped joints are essential (the joints between arch bricks must be wider on the outside and narrower on the inside; this wedge shape is what makes the arch curve). 6. Allow mortar to cure before striking centering (removing the centering before the mortar has reached full strength will cause the arch to collapse; wait 7-14 days minimum). 7. The centering must be accurate (the shape of the centering determines the shape of the arch; an inaccurate centering produces a misshapen arch that may not carry loads properly). 8. Arch bridges last millennia (Roman arch bridges built 2,000 years ago still carry traffic today; a properly built arch bridge is one of the most durable structures humans can create).