Heat — how far things grow, and what happens when you don't let them

Chapters 2 through 4 treated every material as if it stayed one size. It doesn't. Heat makes everything grow, and a firebox, a foundry, or just a summer afternoon on a steel roof makes a difference you can measure with a ruler. This is the one chapter in the guide where the numbers are about movement, not strength, and the Snawfus Hearth (a heater built from brick, with a cast iron cook surface at the top tier) is the build that makes it matter.

The rule: a fixed fraction per degree

A material grows by a fixed fraction of its length for every degree it warms: change in length = α × length × temperature change. The Greek letter α (alpha) is the coefficient of linear thermal expansion, and it is a tiny number, usually written in millionths per degree. Carbon steel is about 6.5 millionths per °F, meaning each inch of steel grows 0.0000065 inch for every degree. Tiny per degree, but over a long piece and a big temperature swing it adds up.

The coefficients, with where they come from

• Carbon steel: 10.8 to 12.5 millionths per °C, which is 6.0 to 6.9 per °F (Engineering Toolbox table of linear expansion coefficients)
• Cast iron: 10.4 to 11 per °C, or 5.8 to 6.1 per °F (same table)
• Aluminum alloys: 21 to 24 per °C, or 11.7 to 13.3 per °F. Copper: 16 to 16.7 per °C, or 8.9 to 9.3 per °F (same table)
• Concrete: 4.1 to 7.3 per °F (the Federal Highway Administration's table), and the stone in the mix sets most of it: granite and limestone aggregate run low, sandstone and quartzite run high
• Brick masonry: 4.7 to 9.0 per °C, or 2.6 to 5.0 per °F (Engineering Toolbox)
• Geopolymer: only one measurement turned up, about 8 per °C (4.4 per °F) for a fly ash and slag paving mix, which the authors found lower than their portland cement concrete. Your mix is not that mix, so the calculator carries 4.4 up to concrete's 7.3 until you measure your own

Two honest limits. Every number above is a published range, not a measurement of your material, so the calculator shows a low and a high answer instead of picking one. And these are room-temperature values that usually creep upward as a material gets hotter, so for a firebox they are a first estimate of the size of the problem, not a design number.

Worked example 1: how far does it move?

A 10-foot (120 in) steel member in a hearth or foundry, heated from 70°F to 370°F, a 300°F rise. At the midpoint of the range, 6.5 millionths per °F: 0.0000065 × 120 × 300 = 0.234 in. Across the whole published range it is 0.22 to 0.25 in, about a quarter inch. A 24-inch cast iron cook plate heated 400°F, at about 6.0 per °F, grows 0.0000060 × 24 × 400 = 0.058 in, close to 1/16 in. Small, but enough to bind a tight fit and crack mortar.

Worked example 2: stop it moving and the stress shows up

If the piece cannot grow, because it is locked tight between masonry or bolted rigid at both ends, it pushes instead. The stress in a fully locked-in piece is σ = E × α × ΔT. For steel, E is 29,000,000 psi, so E × α = 29,000,000 × 0.0000065 = about 188 psi for every degree. Heat it 100°F and that is 18,850 psi of squeeze, more than half of A36 steel's 36,000 psi yield strength (Callister Chapter 1), before it carries a single pound of real load. It reaches yield at 36,000 ÷ 188.5 = about 190°F of temperature rise (179 to 207°F across the range). This is a worst case, since nothing is perfectly rigid, but it is why a steel part bridging two masonry masses should slide or sit in a slot, never be fixed solid at both ends.

Worked example 3: brick can't take the squeeze either

Run the same math on geopolymer, using Chapter 4's modulus estimates (about 2.8 to 3.6 million psi) and the 4.4 to 7.3 range: E × α comes to roughly 12 to 26 psi per degree. A locked-in brick heated 100°F is being squeezed by about 1,200 to 2,600 psi. Chapter 2's working compressive stress is 975 psi (3,900 ÷ 4), so that is already over the working limit, though well under the 3,900 psi it would take to crush it. The honest reading is not that the brick fails at 100°F, it is that a masonry mass heated and held rigid is carrying real stress you never designed for, which is why masonry gets movement joints.

Why rebar in brick works at all

Chapter 4 said a composite only works if its two materials stay bonded. Heat is the other half of that. Steel at about 6.5 per °F and geopolymer at 4.4 to 7.3 per °F are close, so when the wall warms they grow nearly together and the grout bond is not being peeled apart. For a 10-foot wall heated 200°F the steel and the brick differ by at most about 0.06 in, and could even come out the other way round. If the two materials had coefficients twice apart, the same swing would try to shear the bond. That closeness is a lucky property of steel and masonry, not a guarantee, so a different reinforcement (a plastic or aluminum insert, say) would need this check again.

Heat that isn't even

Everything above assumed the whole piece is one temperature. A firebox is not: the hot face grows while the back stays cool. The hot side trying to grow against the cool side puts the cool side into tension, and Chapter 3's standing rule says to never rely on a ceramic's tension. That is the usual way hot masonry cracks. Keep any strong heat gradient away from load-bearing sections, and treat a crack in a firebox lining as expected wear, not a structural alarm, as long as it is not carrying the load.

Rule of thumb carried forward

From the numbers above, not from a code: give steel and cast iron that bridge masonry roughly 1/4 inch of room per 10 feet for every 300°F of expected rise, in a slotted or sliding connection rather than a rigid one. The heater specialist the Snawfus build card calls for at the larger tiers handles the real detailing (expansion gaps, clearances). This chapter gives you the size of the numbers to ask about.

Open items for a later pass

• Real temperatures: how hot the firebox shell, the cook surface and the flue steel actually get on a normal burn. A thermometer reading from a real burn replaces every guess here; the calculator takes any number.
• Your own geopolymer coefficient: nothing published matches your mix, and it feeds both the low-end and high-end answers. A heated-bar test with a dial indicator would pin it down.
• Temperature dependence and thermal shock (a sudden cold hit on a hot brittle piece) are not covered here.