Thermal expansion of metals: movement allowances

At a glance

One round figure per family, to the nearest 0.5 of the values read, is used for the arithmetic. Free movement only: a fixing that restrains the metal changes the picture. Sources: SCI (steel), Euro Inox (stainless), stockholders' data sheets (the rest). The product standards were not read. Zinc is left out because the figures we met conflict.

The sum, and the numbers that go into it

Movement in mm = coefficient × length in metres × temperature change in kelvin ÷ 1000. A step of one kelvin is the same size as one degree Celsius. For a 3 m brass strip warmed by 20 K: 20.5 × 3 × 20 ÷ 1000 = 1.23 mm. That is free movement, what the metal would do if nothing held it.

The temperature change is yours to set. It runs from the coldest to the warmest the metal will reach in service, and the metal's own temperature counts, not the air's. The 20 K and 40 K in the tables are illustrations. A heated interior swings less than an unheated one, and sun on a dark surface or a heat source beside the metal swings more. For external or structural metal, the engineer sets the range. We found no source that gives one, so none is quoted.

Where the coefficients come from. Carbon steel is from the Steel Construction Institute's web guidance. Stainless is from the Euro Inox tables, which take their physical properties from EN 10088-1 (2005). Copper, bronze, brass and aluminium are from stockholders' published data sheets, because the product standards were not available to us. Three things to know:

• Ranges differ, and the value rises with the range. One stockholder gives copper as 16.8 for 20 to 100 °C, 17.3 to 200 and 17.7 to 300; Euro Inox gives 304 as 16.5 to 200 °C and 17.5 to 400. So a figure quoted to 200 or 300 °C is, if anything, a little high for a swing near room temperature. That errs on the safe side, and it is our reading of those rows.
• Stainless grades differ. At 20 to 200 °C Euro Inox gives 16.5 for 304 and 316, 13.5 for the duplex grades 2205 and 2304, and 10.0 for ferritic 430. The ferritic grade moves slightly less than carbon steel; the austenitic grades move about 40 per cent more.
• Aluminium alloys sit close together: 23.1 to 23.8 across seven alloys in one stockholder's sheets, and 23.6 and 24.2 for 20 to 100 °C in a second stockholder's note. Brass and bronze data sheets were checked against a second stockholder: brass 20.4 and 21, bronze 18 and 18.2.

The grid gives the free movement in millimetres. Read across for the run, then add the fitting tolerance.

Worked examples

Each of these is the sum above. The numbers are re-checked by a separate script, and the temperature changes are illustrations.

• A 3 m brass strip, 20 K. 20.5 × 3 × 20 ÷ 1000 = 1.23 mm. Fixed at one end, the free end moves 1.23 mm. Fixed in the middle, each end moves half of it, about 0.6 mm.
• A 6 m stainless bar capping, 40 K. 16.5 × 6 × 40 ÷ 1000 = 3.96 mm. Roughly 4 mm is more than a hairline gap, so a capping this long needs a drawn joint, not a closed one.
• A 3 m aluminium panel, 30 K. 23.5 × 3 × 30 ÷ 1000 = 2.1 mm.
• The same aluminium rail on a 3 m steel frame, 30 K. The two move by different amounts, so the difference is what the fixings must take up: (23.5 − 12) × 3 × 30 ÷ 1000 = about 1.0 mm. Fix one end and slot the other.
• A 300 mm brass strip across a 300 mm oak panel. The brass moves 0.12 mm in a 20 K swing. The oak, by the Wood Handbook arithmetic below, moves 5.75 mm across the grain when the humidity goes from 35 to 65 per cent. That is about 47 times as much.

Metal beside timber: it is humidity, not temperature

The USDA Forest Products Laboratory's Wood Handbook gives the thermal expansion of oven-dry wood along the grain as about 3.1 to 4.5 millionths per kelvin for any species tested. Across the grain it is five to more than ten times that and rises with density. By the handbook's equations, for oven-dry white oak with a specific gravity on oven-dry volume of about 0.72 (our working from its Tables 5-3a and 4-3), the figures are about 41.6 tangentially and 33.1 radially. That is more than any metal in the table, but it is the wrong number to use: timber in a room is not oven-dry, and moisture moves it far more. The handbook says that at usual moisture levels, wood that is heated tends to shrink on net as it dries, and that even along the grain, moisture changes outweigh thermal expansion unless the wood is very dry.

The handbook's method for moisture is size × coefficient × change in moisture content (its Equation 13-3). For white oak the coefficients are 0.00376 per point across a plain-sawn width and 0.00194 across a quarter-sawn one (Table 13-5). At about 21 °C, 35 per cent relative humidity settles at 6.9 per cent moisture content and 65 per cent at 12.0 (Table 4-2): a change of 5.1 points. A 300 mm plain-sawn panel therefore moves 5.75 mm. Its thermal movement in a 20 K swing, oven-dry, would be about 0.25 mm, a small part of that. Along the grain, the handbook says shrinkage from green to oven-dry is generally between 0.1 and 0.2 per cent, which is small. The same arithmetic is on our timber movement sheet, for American white oak. European oak was not read.

• The direction decides. A strip along the grain sees little from either material. A strip across the grain meets a timber that moves millimetres and a metal that hardly moves, so the strip cannot be held rigidly along its length without something giving. That is our reading of the numbers, not a tested result.
• Humidity is the design input. Say the relative humidity range you assume for the room, and the moisture content of the timber at fixing. See the joinery sheets for how to write both.
• Floors are the same problem. For brass strips in timber floors see floor transitions and movement joints and underfloor heating under wood and stone.

Detailing a run so that it can move

Only one source we read describes a built example: a Euro Inox case study of a bank's stainless cladding, where sheets 1 mm and 1.5 mm thick are fixed at one end only to allow for thermal expansion along their length. The rest of this section is general practice and arithmetic, and the partner workshop sets the sizes.

• One fixed point per run, everything else free. Hold the run rigidly in one place and let every other fixing slide. A fixed point in the middle halves the movement at each end, which is why the drawing puts it there. A run held rigidly at both ends has nowhere to go; the force falls on the fixings, the background or the metal. Buckling, noise and loosened fixings are the usual signs (our reading; no source we read measures them).
• Slots, washers and gaps. Slotted or oversize holes, longer further from the fixed point, with a washer set so that the metal can slide. A gap at each end and wherever the material changes, covered by a trim that can slide, never filled with a rigid fixing or adhesive. Where a sealant is used, its own data sheet gives how much movement it can take; none was read here.
• Size the gap from the sum. The calculated movement plus the fitting tolerance, for the temperature at which the work is fixed. Record that temperature on site.
• Two metals fixed together move by different amounts: the difference is what the fixings take up. Keep them apart electrically too; see galvanic corrosion and dissimilar metals.
• Thin, wide sheet shows restraint as ripples. See the oil-canning drawing on the sheet metal thickness sheet.

Metal runs over [1.5] m long, and metal fixed to timber, stone or another metal, are to be detailed for free thermal and moisture movement, calculated from the coefficient for [alloy], the run length and a temperature range of [__ K] stated on the drawing. No run is to be held rigidly at both ends. One fixed point per run at [ ]; other fixings slotted or oversize with washers set to slide; end gaps [ ] mm minimum.

For each run over [1.5] m the fabricator is to show on the shop drawings the coefficient used with its source and temperature range, the temperature range assumed, the fixed point and the end gaps. [The engineer approves external and structural runs.] The temperature at fixing is to be recorded.

Metal inlay strips longer than [100] mm and running across the grain are to be [fixed at one point only], with clearance of [ ] mm at each end and in the groove, and are not to be glued rigidly along their length unless approved by sample. Assumed room humidity [ ] to [ ]% RH; timber moisture content at fixing [ ]%.

Where metals of different expansion are fixed together, the shop drawing is to show how the difference in movement is taken up and how galvanic contact is avoided.

Standards and sources

• Steel Construction Institute and BCSA, steelconstruction.info, Steel material properties: carbon steel.
• Euro Inox, Stainless Steel: Tables of Technical Properties (2nd ed. 2007) and Stainless Steel Facades (Vol. 2, 2002): stainless coefficients; one-end fixing case study.
• USDA Forest Products Laboratory, Wood Handbook, FPL-GTR-282 (2021): p. 4-17; Eq. 13-3; Tables 4-2, 4-3, 13-5.
• Stockholders' published data sheets: brass, bronze, copper, aluminium: not the product standards.

Questions we are asked

How much does a 3 m run of metal grow?

For a 20 K swing, about 0.72 mm for carbon steel, 0.99 mm for 304 or 316 stainless, 1.02 mm for copper, 1.23 mm for brass and 1.41 mm for aluminium. Double the swing and the movement doubles, as does the length. The coefficients are from the sources on this page; the swing is yours to set.

Which coefficient should I use?

Use the figure for the alloy you have, and say where it came from and for what temperature range. The values rise a little with the range, so a figure to 200 or 300 °C is slightly high for a room-temperature swing. The page uses one round figure per family, to the nearest 0.5 of the values read. The product standards were not read, so ask the partner for the figure they work to.

What temperature range should I assume?

That is a project decision, and we found no source that sets one. A heated interior swings less than an unheated one, and sun on a dark surface or a nearby heat source swings more. For external or structural metal, ask the engineer. Write the range on the drawing so that the fabricator calculates from the same number.

Will a brass inlay crack timber?

It can if it is held rigidly across the grain. By the Wood Handbook arithmetic for white oak, a 300 mm plain-sawn panel moves about 5.8 mm across the grain between 35 and 65 per cent humidity, while a 300 mm brass strip moves about 0.1 mm in a 20 K swing. Run strips along the grain where you can, keep cross-grain strips short, and ask the partner how they fix them.

Do stainless panels and cladding need expansion joints?

They need a way to move. A Euro Inox case study fixes 1 mm and 1.5 mm stainless sheets at one end only so that they can expand along their length. How a given panel is fixed, and how big its joints are, depends on its size, fixings and exposure, so it is for the partner and, outside, the engineer.

Why do long metal runs sometimes click or buckle?

A run held at both ends cannot grow, so the force goes into the fixings, the background or the metal itself. That is our reading rather than a measured result. The cure is the one in the drawing: one fixed point, slotted fixings and a gap at each end, sized from the sum on this page.