Arch Construction

Part of Structural Engineering

Building curved masonry arches that carry loads in pure compression, spanning openings without steel or timber reinforcement.

Why This Matters

The arch is one of humanity’s greatest structural inventions. A properly built masonry arch carries loads through pure compression — pushing forces only, no tension — which plays perfectly to the strengths of stone, brick, and concrete. These materials are extremely strong in compression (resist crushing) but weak in tension (resist pulling). A flat stone lintel over a doorway must carry loads in bending, which creates tension on the bottom face and often cracks. The arch eliminates this problem by redirecting all loads into compression.

With arch construction you can span openings far wider than any available timber or stone lintel, using only masonry units and mortar. Roman aqueducts used arches spanning 20+ meters built from cut stone without mortar. Medieval cathedrals used pointed arches to span 40-meter naves. These structures survive two thousand years. For a rebuilding civilization with access to brick or cut stone but not structural steel or long timber beams, the arch is the primary spanning technology.

Understanding arch geometry and construction lets you build doorways, windows, tunnels, bridges, and roofs that will outlast any framed structure.

How an Arch Works

Force flow: A load on the arch (from a wall above, from soil, from vehicles crossing) creates compressive forces that travel diagonally through the arch material down to the supports (the springings). At each voussoir (arch stone), the compressive force is redirected to push on the neighboring voussoirs.

The thrust line: The path of the compressive force through the arch is called the thrust line. For an arch to be stable, the thrust line must stay within the middle third of the arch thickness at every cross-section. If it approaches the outer edge, that edge cracks in tension; if it leaves the arch material entirely, the arch collapses.

The problem of outward thrust: Because arches push their load outward and downward at the springings, they exert a horizontal thrust on whatever supports them. A single arch must be supported by massive piers or abutments that can resist this thrust. Where multiple arches stand in a row (like a bridge or arcade), adjacent arches provide mutual horizontal support.

Arch Types and Their Geometry

Semicircular arch: Half a circle. Rise equals half the span. A very strong, classic form. Generates the highest horizontal thrust of common arch shapes.

• Use where you have thick, strong piers
• Simple to set out: one compass point at the center of the opening

Segmental arch: Less than a semicircle. Lower rise, greater horizontal thrust. Common over wide openings where a full semicircle would be too tall.

Pointed (Gothic) arch: Two circular arcs meeting at a point at the top. Adjustable geometry — the arch can be steep or shallow by changing the radii. Pointed arches generate less horizontal thrust than round arches at the same span, which is why Gothic cathedrals could have thinner piers.

Setting out a pointed arch:

1. Mark the span on the ground
2. Choose two centers (they may be at the springing points, or inward, or outward depending on the desired profile)
3. Strike an arc from each center that meets at the crown
4. The shape between these arcs is the intrados (inner face)

Parabolic arch: The ideal shape for a uniformly distributed load. Generated by hanging a chain (which takes the exact inverse form — a catenary). For building structures, the parabola is a close approximation. Best used for bridge arches.

Making the Centering (Formwork)

The temporary support that holds the arch in position during construction is called the centering. This is the most critical element in arch construction — an arch cannot be built without it because the arch is unstable until the keystone is set.

Centering construction:

1. Cut curved ribs from timber to the exact intrados profile of the arch
2. Space ribs at 12–24 inches apart across the arch width
3. Nail lathe strips across the ribs to form a solid curved surface for voussoirs to rest on
4. Support the centering on simple posts that can be knocked away (struck) when the arch is complete and mortar has cured

Centering height adjustment: The centering should be slightly lower than the final arch soffit to allow for springback when it is struck. The arch compresses slightly as load is applied and mortar cures — typically 1/500 of the span.

Striking the centering: Remove the centering only after the mortar has fully cured (at least 7 days in warm weather, 14 days in cold). Strike (remove) the centering by knocking the support wedges — the centering drops away smoothly. Do not pry or force.

Building with Voussoirs (Arch Stones)

Voussoir shape: Each arch stone is trapezoidal — wider on the outer (extrados) face, narrower on the inner (intrados) face. The faces (joints) are radial — pointing toward the arch center. This ensures the compressive forces are transmitted squarely through each voussoir.

Sizing voussoirs: The depth (radial thickness) of voussoirs should be roughly 1/12 to 1/15 of the span for normal arch bridges. Width (across the span) is determined by available stone or brick.

Cutting voussoirs:

1. Make a template from thin board showing the trapezoidal profile of each stone
2. Mark both joint angles on the template using a bevel set to the correct angle (calculated from span, rise, and number of voussoirs)
3. Cut each stone to match the template using a chisel and mallet
4. Check the joint faces with a straightedge — they must be flat and square to the template angle

Brick arches: Bricks are not cut to voussoir shape — they are rectangular. Instead, the mortar joints are tapered (wider at the extrados, narrower at the intrados) to create the curved profile. This works well for arches up to 3 feet span. Larger brick arches use multiple rings of brickwork.

Laying the Arch

Procedure:

1. Set the centering in place, level and secure
2. Mark the centerline and springing points on the centering
3. Start from both springings simultaneously and work toward the crown
4. Place each voussoir on the centering with mortar between joints
5. The keystone (center stone at the crown) is the last stone placed
6. If the keystone is too tight, do not force it — trim voussoirs slightly on both sides to create room
7. If the keystone fits too loosely, add a thin shimming piece

Joint thickness: For cut stone, joints should be as thin as possible — 1/16 to 1/8 inch. For rough stone, 1/4 to 3/8 inch. Thick mortar joints are weaker than thin ones and more prone to squeezing out under load.

Checking alignment: Use a string stretched from center to center of the arch (the radius line) to check that each voussoir face is properly oriented. Each joint should be perpendicular to the local tangent of the arch intrados.

Mortar selection: Use lime mortar for historic compatibility and flexibility, or portland cement mortar for strength. Lime mortar allows slight movement without cracking and is easier to repair. Portland cement mortar is stronger but more brittle. For arches in wet conditions (bridges, culverts), portland cement mortar is preferable.

Abutments and Piers

Sizing abutments: The abutment must be large and heavy enough to resist the horizontal thrust from the arch. Minimum abutment width approximately 1/3 of the arch span for a semicircular arch. More for a flat segmental arch (higher thrust).

Foundation requirements: Arches transmit large concentrated loads to their foundations. The foundation soil must be capable of bearing these concentrated loads without settlement (see Soil Bearing Capacity article). Unequal settlement of arch foundations is the most common cause of arch failure — one support moves and the thrust line shifts to cause cracking.

Fill over arch spandrels: The triangular spaces between the arch extrados and the deck level (the spandrels) are usually filled with compacted granular material — rubble stone, gravel, or compacted earth. This fill distributes traffic loads across the arch and provides the road or floor surface. Well-compacted fill also contributes its own weight as a stabilizing factor.