Structural Engineering
Why This Matters
Every building that collapses was built by someone who did not understand structural engineering. Every building that stands for centuries was built by someone who did. The difference is not luck — it is knowledge of how forces travel through materials, where structures are strong, and where they are weak. A single misplaced load-bearing wall, an undersized beam, or a foundation on unstable soil can turn a shelter into a deathtrap. This article gives you the principles that Roman, Gothic, and Renaissance builders used to create structures that have stood for a thousand years — and you can apply them with nothing more than wood, stone, and mortar.
What You Need
For understanding and planning:
- String or cord for plumb lines
- A straight stick and water-filled tube for leveling
- Charcoal or chalk for marking
- A known weight (like a bucket of water — 10 liters = 10 kg) for testing
For stone construction:
- Cut or gathered stone blocks
- Lime mortar (see Lime & Cement)
- Chisels and hammers for stone dressing
- Wooden formwork for arches (called “centering”)
For timber construction:
- Seasoned hardwood beams and planks
- Saw, chisel, mallet, drill, drawknife
- Wooden pegs (trunnels) or iron nails/bolts
- Rope for raising frames
For foundations:
- Shovels and picks for excavation
- Gravel or crushed stone for drainage
- Large flat stones for footings
- Lime concrete (lime, sand, gravel mixed — see Lime & Cement)
The Four Fundamental Forces in Structures
Every structure on Earth deals with exactly four types of internal force. Understanding these is the foundation of all structural design.
1. Compression
Compression squeezes material together. A column standing under a load is in compression. Stone and concrete are extremely strong in compression — a block of granite can support over 100 MPa (roughly 10,000 tonnes per square meter). This is why stone columns and walls can be enormous and carry immense loads.
How to recognize compression: The material is being pushed together from both ends. Columns, walls, arches, and foundations are primarily compression elements.
Failure mode: Compression failure in stone causes crushing or explosive splitting. In wood, the fibers buckle and the piece kinks sideways (called “buckling”). Tall, thin columns buckle before they crush — this is why columns must be thick relative to their height.
Rule of thumb for wooden columns: The height should not exceed 12 times the smallest cross-section dimension. A 15 cm x 15 cm post should not be taller than about 180 cm without bracing. For stone columns, the ratio can be 8-10:1.
2. Tension
Tension pulls material apart. A rope holding a weight is in tension. A chain, a cable, and the bottom chord of a truss are tension members.
How to recognize tension: The material is being stretched. If you cut the member, the two ends would spring apart.
Material behavior in tension:
- Rope and cable: Excellent in tension, useless in compression
- Wood: Moderate in tension along the grain (about 10-15 MPa for most hardwoods), very weak across the grain
- Wrought iron/steel: Excellent in tension (200+ MPa)
- Stone and concrete: Extremely weak in tension (only 2-5 MPa) — this is their critical weakness
Failure mode: Tension members snap, tear, or pull apart at their weakest point. In wood, this is usually a knot, a bolt hole, or a point where the grain runs at an angle.
3. Shear
Shear force acts like scissors — two forces pushing in opposite directions on either side of a point. A beam supported at both ends with a load in the middle has maximum shear at the supports, where the upward support force and the downward load meet.
How to recognize shear: The material is being pushed in two different directions at adjacent points. A nail holding a shelf bracket to a wall is in shear — the shelf pulls the nail downward while the wall pushes it upward.
Material behavior in shear:
- Wood: Weak in shear along the grain (wood splits easily along the grain). A beam is most likely to fail in shear near the supports, where the grain can split horizontally.
- Stone: Moderate in shear, but mortar joints are weak in shear — this is why stone walls fail in earthquakes (horizontal shear force).
Rule of thumb: For a wooden beam, the beam depth at the support should be at least 1/8 of the span length. A beam spanning 4 meters should be at least 50 cm deep.
4. Bending (Combined Compression and Tension)
When a beam bends under load, the top is compressed and the bottom is stretched (in tension). The middle is relatively unstressed. This is why an I-shaped beam is efficient — material is concentrated at the top and bottom (where the stresses are highest) and removed from the middle (where it is not needed).
The key insight: Because the bottom of a bending beam is in tension, and stone is weak in tension, stone beams crack on the bottom face and fail. This is why stone lintels over windows and doors must be short or very thick. It is also why arches were invented — to keep everything in compression.
Load Paths: How Forces Travel
A load path is the route that force takes from where it is applied to the ground. Every load must have a continuous path to the ground, or the structure fails.
Example load path for a two-story building:
- Snow on the roof pushes down on the rafters
- Rafters push down on the top wall plate
- Top wall plate pushes down on the second-floor walls
- Second-floor walls push down on the second-floor joists
- Joists push down on the first-floor walls
- First-floor walls push down on the foundation
- Foundation pushes down on the soil
If any link in this chain is missing — for example, if a second-floor wall does not sit directly above a first-floor wall — the force has nowhere to go and the structure deforms, cracks, or collapses.
The Golden Rule of Load Paths
Vertical loads should travel as directly as possible to the ground.
When you must offset a load (move it sideways from one level to the next), you create bending forces, which are much harder to handle than direct compression. Minimize offsets. Stack walls directly on top of each other. Place columns directly over foundations.
Lateral Loads (Wind and Earthquake)
Wind pushes sideways on walls. Earthquakes shake the entire structure horizontally. These lateral forces must also have a path to the ground.
How to handle lateral forces:
- Diagonal bracing: Add diagonal members to rectangular frames. A rectangle is not rigid — it can be pushed into a parallelogram and collapse. A single diagonal brace turns it into two triangles, which are rigid.
- Shear walls: A solid wall (stone, masonry, or plywood-sheathed timber) resists lateral force across its length. Every building needs shear walls in both directions (north-south and east-west).
- Buttresses: Thick external supports that resist the outward thrust of arches and roofs (see Buttresses section below).
Rule of thumb: A building should have shear walls or diagonal bracing totaling at least 25% of the wall length in each direction. A 10-meter-long building needs at least 2.5 meters of bracing or shear wall on each side in the long direction, and the same proportion in the short direction.
Foundations
Every structure is only as strong as its foundation. A perfect building on a bad foundation will crack, tilt, and eventually collapse.
Soil Types and Bearing Capacity
| Soil Type | Bearing Capacity (approximate) | Suitability |
|---|---|---|
| Solid rock | 100+ tonnes/m2 | Excellent — build directly on it |
| Dense gravel | 5-10 tonnes/m2 | Very good |
| Compact sand | 3-5 tonnes/m2 | Good |
| Stiff clay | 2-4 tonnes/m2 | Adequate, but beware of moisture changes |
| Soft clay | 0.5-1 tonnes/m2 | Poor — must be improved or bypassed |
| Peat/organic soil | Less than 0.5 tonnes/m2 | Unacceptable — remove or pile through it |
| Fill (recently placed) | Variable, unreliable | Remove and build on natural soil below |
Testing your soil: Dig a test pit at least 1 meter deep. Look at what you find:
- Gravel and sand: feels gritty, does not stick together when wet
- Clay: smooth, sticky when wet, cracks when dry
- Organic soil: dark, spongy, smells earthy, may contain roots
Building a Strip Foundation
The most common foundation type for small to medium buildings. A continuous strip of stone or concrete under each wall.
Step 1 — Dig a trench below the frost line. In temperate climates, this means 60-100 cm deep. In cold climates, 120-180 cm. If the foundation is above the frost line, winter freezing will heave the soil upward, cracking walls and floors. If you do not know the frost depth, dig until the soil temperature feels consistently cool (not frozen) even in the coldest month.
Step 2 — The trench should be wider than the wall it supports. A rule of thumb: the foundation width should be at least twice the wall thickness. A 30 cm stone wall needs a 60 cm wide foundation.
Step 3 — Lay 10-15 cm of gravel or crushed stone at the bottom of the trench. This provides drainage and distributes the load. Compact it by tamping with a heavy log or post.
Step 4 — Lay large, flat stones in the trench, filling gaps with smaller stones and lime mortar. Build up to ground level in courses, making each course roughly level. Alternatively, pour lime concrete (1 part lime, 2 parts sand, 4 parts gravel) into the trench and let it cure for at least 7 days.
Step 5 — Above ground level, continue the foundation up to 15-30 cm above the surrounding soil. This “plinth” keeps the wall base away from splashing rain and ground moisture, which would wick up into the wall and cause damage.
Arches: Turning Tension into Compression
The arch is one of the greatest inventions in structural engineering. It transforms a bending problem (which creates tension) into a pure compression problem (which stone handles beautifully).
How Arches Work
An arch is a curved structure that spans an opening. When loaded, the curve channels all forces along its length as compression. The key requirement: the arch needs something strong at each end to push against — these are called abutments. The arch pushes outward at its base, and the abutments must resist this thrust.
Critical rule: An arch never pulls — it only pushes. If the abutments move apart even slightly, the arch collapses. This is why arches need massive abutments or buttresses.
Building a Semicircular Stone Arch
Step 1 — Build the two vertical piers (abutments) on either side of the opening, up to the level where the arch will begin (called the “springing point”). These piers must be at least as wide as the arch is deep, and preferably wider. Heavy masonry, large stones, or solid rock abutments are essential.
Step 2 — Build temporary wooden centering — a semicircular wooden frame that supports the arch stones during construction. This is a critical component and must be strong enough to hold all the arch stones before the keystone locks them in place.
To build centering: Cut two semicircular shapes from thick planks (or build them up from segments). Connect them with cross-boards to form a 3D semicircular cradle. Support this centering on temporary posts that can be lowered or removed later (wedges under the posts allow gradual lowering).
Step 3 — Select or cut wedge-shaped arch stones (called voussoirs). Each stone should be wider on the outer face than the inner face, so they lock together when assembled in a curve. The angle of the wedge depends on how many stones span the arch — for a semicircular arch with 15 voussoirs, each stone spans 180/15 = 12 degrees.
Step 4 — Lay the voussoirs on the centering, starting from both sides simultaneously and working toward the top center. Apply lime mortar between each stone. The stones should fit tightly, with the mortar filling only minor gaps.
Step 5 — The last stone placed at the very top center is the keystone. It locks the entire arch together. Tap it firmly into place. Once the keystone is set, the arch is self-supporting.
Step 6 — Wait at least 3-7 days for the mortar to set before removing the centering. Lower the centering slowly and evenly by knocking out the wedges under the support posts. If any stones shift during lowering, stop — the mortar needs more curing time.
Step 7 — Above the arch, fill the triangular spaces (called spandrels) with rubble stone and mortar, then continue building the wall above.
Arch Span Limits
| Material | Maximum Practical Span (semicircular) |
|---|---|
| Dry-stacked stone | 2-3 meters |
| Mortared stone | 5-10 meters |
| Mortared brick | 8-15 meters |
| Reinforced concrete (lime-based) | 10-20 meters |
Tip
A pointed arch (like a Gothic arch) exerts less outward thrust than a semicircular arch for the same span. This allows thinner walls and larger openings. To build one, use two arcs centered offset from the middle of the span rather than one arc centered directly below the keystone.
Trusses: Spanning Large Distances with Wood
A truss is a framework of triangles that spans an opening. Because triangles are inherently rigid shapes (unlike rectangles), a truss can be lightweight yet extremely strong. Trusses are how you span 6, 10, or even 20 meters with timber.
How Trusses Work
Every member in a truss is in either pure tension or pure compression — never bending. This is incredibly efficient because you use material only where force exists, and the force type in each member is simple.
The basic principle: Triangles cannot change shape without changing the length of a side. Rectangles can deform into parallelograms (this is why they collapse). By building entirely from triangles, a truss remains rigid under load.
Building a King Post Truss
The simplest roof truss, suitable for spans up to about 8 meters.
Components:
- Bottom chord (tie beam): A horizontal beam spanning the full width. This member is in tension — it prevents the rafters from pushing the walls apart.
- Two rafters (top chords): Angled members running from each end of the tie beam to the peak. These are in compression.
- King post: A vertical member hanging from the peak down to the center of the tie beam. It is in tension — it holds up the center of the tie beam to prevent it from sagging.
Step 1 — Select timber for the tie beam. For an 8-meter span, use a beam at least 20 cm x 25 cm in cross-section. Hardwood is strongly preferred. The tie beam is in tension, and a knot or weakness can cause it to snap, dropping the entire roof.
Step 2 — Cut two rafters at the desired roof pitch. A pitch of 30-45 degrees works well for most climates. Steeper pitches shed snow better; shallower pitches use less material. The rafter cross-section can be smaller than the tie beam — 15 cm x 20 cm is adequate for most spans up to 8 meters.
Step 3 — Join the two rafters at the peak with a mortise-and-tenon joint, a half-lap joint, or a bolted connection. This joint is in compression — it is being pushed together, so it does not need to resist pulling apart.
Step 4 — Join each rafter to the tie beam at the bottom. This joint is critical — it must resist the outward thrust of the rafter. Use a birdsmouth cut (a notch in the rafter that hooks over the tie beam) combined with a bolted connection or a metal strap.
Step 5 — Cut the king post to length (from the peak to the center of the tie beam). Attach it at the top to the rafter joint and at the bottom to the tie beam. Use iron straps or bolted connections. Remember: the king post is in tension — it hangs from the peak and holds up the tie beam. A simple notch-and-peg joint is not sufficient; it needs a positive connection that resists pulling apart.
Step 6 — Optional: Add diagonal struts from the king post to the midpoints of each rafter. These prevent the rafters from buckling under load and increase the truss’s capacity. These struts are in compression.
Building a Queen Post Truss
For spans over 8 meters (up to about 14 meters), replace the single king post with two queen posts, creating a wider, flatter truss with more triangles.
Step 1 — Same as king post truss, but place two vertical posts about 1/3 of the span from each end instead of one post in the center.
Step 2 — Add a horizontal straining beam between the tops of the two queen posts. This keeps them from leaning inward.
Step 3 — Add diagonal struts from the base of each queen post to the rafter above, creating additional triangles for stability.
Span Limits for Timber Trusses
| Truss Type | Practical Span Limit |
|---|---|
| Simple rafter pair (no truss) | 4-5 meters |
| King post truss | 6-8 meters |
| Queen post truss | 8-14 meters |
| Compound truss (multiple bays) | 14-20+ meters |
Columns and Buckling
A column is a vertical compression member. Columns fail by buckling — bending sideways under load — long before the material itself crushes.
The Buckling Rule
A column’s resistance to buckling depends on:
- Length — longer columns buckle more easily (buckling strength decreases with the square of the length)
- Cross-section size — thicker columns resist buckling better
- Material stiffness — stiffer materials (steel > hardwood > softwood) resist buckling better
- End conditions — a column fixed at both ends buckles at about 4 times the load of a column pinned at both ends
Practical Column Sizing for Wood
Use this table for rough sizing of wooden posts and columns:
| Column Height | Minimum Cross-Section (softwood) | Minimum Cross-Section (hardwood) |
|---|---|---|
| 2 meters | 12 cm x 12 cm | 10 cm x 10 cm |
| 3 meters | 15 cm x 15 cm | 12 cm x 12 cm |
| 4 meters | 20 cm x 20 cm | 15 cm x 15 cm |
| 5 meters | 25 cm x 25 cm | 20 cm x 20 cm |
These assume moderate loads (supporting a single-story roof, roughly 2-5 tonnes per column). For heavy loads, multi-story buildings, or columns with lateral forces, increase the cross-section by at least 50%.
Bracing Columns
A column braced at mid-height can carry approximately 4 times the load of an unbraced column of the same size. This is why cross-bracing in timber frames is so important — it is not just for lateral loads, it also dramatically increases column capacity.
Buttresses
A buttress is a mass of material (stone, masonry, or earth) built against a wall to resist outward thrust. Buttresses are essential for:
- Walls supporting arched roofs (the arch pushes the wall tops outward)
- Tall, thin walls subject to wind loads
- Retaining walls holding back earth
Sizing a Buttress
A buttress works by adding weight to resist the horizontal thrust. The heavier the buttress, the more thrust it can handle.
Rule of thumb: A buttress should project from the wall by at least 1/3 the wall height and be at least 1/3 as wide as the spacing between buttresses. For a 6-meter-tall wall with buttresses every 4 meters, each buttress should project at least 2 meters from the wall and be at least 1.3 meters wide.
Flying buttress (advanced): A half-arch that transmits the thrust from a high wall (above the aisle roof) down to a detached pier. This is the technology that enabled Gothic cathedrals — enormous stone buildings with walls that are mostly glass. You probably do not need flying buttresses, but the principle is worth understanding: you can resist thrust at a distance by building an arch from the wall to an external support.
How Buildings Fail
Understanding failure modes helps you prevent them.
| Failure Mode | Cause | Warning Signs | Prevention |
|---|---|---|---|
| Foundation settlement | Soil is too soft, uneven, or waterlogged | Cracks in walls (widening at top), doors/windows that no longer close properly | Proper soil assessment, adequate foundation width, drainage |
| Wall buckling | Walls too thin for their height, lateral forces | Walls visibly bowing outward, mortar cracking in vertical lines | Proper wall thickness (height:thickness ratio max 12:1), buttresses or bracing |
| Beam failure (bending) | Beam undersized, span too long, overloaded | Visible sagging, cracking on bottom face, creaking sounds | Adequate beam depth (1/8 to 1/12 of span), avoid large knots |
| Connection failure | Joints not strong enough for the forces | Joints opening up, members shifting, nails pulling out | Proper joinery (mortise-and-tenon, pegged, bolted), metal straps at critical joints |
| Roof thrust | Rafters push walls apart (no tie beam or truss) | Tops of walls spreading apart, roof ridge sagging | Use proper trusses with tie beams; add collar ties or king posts |
| Overturning | Wind or lateral force tips the structure | Leaning, cracking at the base on one side | Adequate weight and foundation width, diagonal bracing |
Common Mistakes
| Mistake | Why It’s Dangerous | What to Do Instead |
|---|---|---|
| Building on fill or organic soil without removal | Fill settles unevenly over time, cracking the entire structure above | Excavate to natural, undisturbed soil before building foundations |
| No frost protection for foundations | Frost heave lifts and cracks foundations every winter | Dig below the frost line (60-180 cm depending on climate) |
| Removing a wall without checking if it is load-bearing | Removing a load-bearing wall drops the structure above it | Trace the load path from roof to ground before removing any wall |
| Rafters without tie beams or trusses | Rafters push wall tops outward — walls slowly splay and roof sags | Always use full trusses or tie beams to contain rafter thrust |
| Using unseasoned wood for structural members | Green wood shrinks, joints open, and the structure loosens | Season timber for at least 6-12 months, or use green only in configurations that tighten as the wood dries |
| Ignoring lateral bracing | Buildings survive gravity loads but collapse in the first strong wind or earthquake | Add diagonal braces or shear walls in both plan directions |
| Mortar joints too thick in stone arches | Thick mortar is weak and compresses unevenly — the arch deforms and fails | Keep mortar joints as thin as possible (5-10 mm); dress stones for tight fit |
| Not building temporary centering strong enough for arches | Centering collapses during construction, dropping heavy voussoirs | Build centering to carry the full weight of all arch stones plus construction loads |
What’s Next
With structural engineering principles understood, you can advance to:
- Bridges — apply arch, truss, and foundation principles to span rivers and ravines
- Steam Engine — structural engineering of pressure vessels, boilers, and engine frames
- Water Systems — design aqueducts, cisterns, and pipeline supports
- Permanent Shelter — revisit your existing buildings and strengthen them with the knowledge from this article
Quick Reference Card
Structural Engineering — At a Glance
The four forces: Compression (squeezing), Tension (stretching), Shear (sliding), Bending (combination)
Material strengths (relative):
Material Compression Tension Best Used For Stone/concrete Excellent Very poor Walls, columns, arches, foundations Wood (along grain) Good Moderate Beams, trusses, frames Wrought iron/steel Good Excellent Ties, straps, tension members, nails Rope/cable None Good Tension members, suspension elements Key rules of thumb:
- Foundation width: at least 2x wall thickness
- Foundation depth: below frost line (60-180 cm)
- Beam depth: 1/8 to 1/12 of span length
- Column height-to-width ratio: max 12:1
- Wall height-to-thickness ratio: max 12:1 (less with wind or lateral loads)
- Shear wall/bracing: at least 25% of wall length in each direction
Truss span limits:
- King post: up to 8 m
- Queen post: up to 14 m
- Compound: 14-20+ m
When in doubt: Make it heavier. In a world without engineering calculators, a generous safety margin (build to 3x the expected load) is cheap insurance.