Free movement, and how much it actually is
An unrestrained element changes length in proportion to its length, its temperature change and a coefficient belonging to the material. That is the whole of the free case, and the numbers are larger than intuition allows.
A six-metre aluminium curtain wall mullion, over a sixty-degree swing from a winter night to a summer day on a south elevation, moves about **8.6 mm**. The same mullion in steel moves about 4.3 mm, because steel's coefficient is roughly half aluminium's. Concrete and clay masonry sit lower again, near steel — which is the lucky accident that makes reinforced concrete possible at all.
The coefficients differing between materials is the design problem. A facade is an assembly of materials with different coefficients fixed to each other, exposed to the same weather, and every interface between two of them is a place where the difference has to go somewhere.
- ΔL
- change in length, if nothing restrains it
- α
- coefficient of linear thermal expansion, a property of the material
- L
- the length free to move between fixed points
- ΔT
- temperature range the element will actually see — surface, not air
Restrained, the stress does not depend on length at all
Restrain the element completely and it does not move; instead it develops stress. Substitute the free strain into Hooke's law and the LENGTH CANCELS. The stress in a fully restrained member is its elastic modulus times its coefficient times the temperature change, and a short member develops exactly as much as a long one.
Put concrete's numbers in and the consequence is unavoidable. A modulus around thirty gigapascals, a coefficient around ten per million per degree, and a thirty-degree drop give roughly **9 MPa** of tension — against a tensile strength of perhaps three. Restrained concrete subjected to an ordinary seasonal swing does not have a margin; it cracks.
This is the single most useful idea on the page, because it reframes what a control joint is for. A control joint does not prevent cracking — the arithmetic above says cracking is already decided. It provides a plane of weakness so the crack that is going to happen happens in a straight line, in a place chosen by a designer, where it can be sealed and where it does not look like a defect.
- σ
- stress developed, tension on cooling and compression on heating
- E
- elastic modulus of the material
- α, ΔT
- as above; note that L has cancelled out entirely
Moisture moves things too, and in opposite directions
Thermal movement reverses; moisture movement frequently does not, and on masonry the two most common materials move the OPPOSITE WAY.
A fired clay brick leaves the kiln bone dry and slowly takes up moisture from the air for years afterwards, expanding irreversibly as it does. A concrete block leaves the works wet and dries out, shrinking irreversibly as it does. Build a cavity wall with a clay outer leaf and a block inner leaf — which is the commonest wall in several countries — and the two leaves are moving apart along their length, permanently, at the same time.
The two are jointed by different rules because of it. Concrete masonry shrinks against the restraint of its base, so its control joints are spaced by the lesser of a length and a multiple of the wall's height. Clay brick grows along its whole length, so its movement joints are spaced by a length alone: the Brick Industry Association gives no more than 25 ft (7.6 m) on brickwork without openings and 20 ft (6.1 m) where there are several, and UK practice about 10 to 12 m (33 to 39 ft), never more than 15 m (49 ft) under PD 6697. Growing brick pushes on a corner, so the first joint sits close to it: within half the spacing in the UK rule, and in the US rule near enough that its distance and the first joint's distance on the other wall add up to no more than one spacing. Counted along one straight run, that makes each end that turns a corner worth half a bay: the run lengthened by half the spacing per corner end is divided into equal bays no longer than the spacing, and the joints are the bays less one, because neither end of a run carries a joint of its own.
That is why a cavity tie has to allow differential movement in the plane of the wall, why the two leaves get their own joints in different places, and why a rigidly bonded return between them cracks. It also explains a detail that looks like superstition: brickwork should not be laid straight off a fresh pallet on a wet day, because a brick that arrives saturated will shrink as it dries before it starts its long expansion.
Timber's version is directional rather than temporal. It moves very little along the grain and a great deal across it — by an order of magnitude — so a stack of joists and plates in a floor build-up shrinks in height while the studs beside it barely change. Over several storeys that differential is enough to distort a facade fixed to both.
The joint's width is set by the sealant, not by the movement
Knowing the movement is only half of sizing a joint. A sealant has a MOVEMENT CAPABILITY — the proportion of its own width it can stretch and compress repeatedly without failing — and the joint has to be wide enough that the movement is within that proportion.
So the width is the movement divided by the capability, not the movement itself. A sealant rated at plus or minus a quarter of its width needs a joint around four times the one-way movement it must absorb. Halving a joint's width to make it look better doubles the strain on the sealant, and sealant failures are overwhelmingly strain failures rather than adhesion ones.
Two further rules come with it. The sealant's DEPTH must be controlled relative to its width — usually about half, set by a backer rod — because a deep plug of sealant is stiffer and tears; and the sealant must bond to two faces only, never three, or the joint cannot open without pulling the sealant off its own backing. Both are why a backer rod is not optional packing.
- W
- designed joint width, at the mean temperature the joint is installed at
- ΔL
- movement the joint must take, from the free-movement formula above
- μ
- the sealant's rated movement capability, as a fraction of joint width
Where it fails: the temperature that was used, and the joint that was filled
The temperature range that matters is the material's SURFACE temperature, not the air's. A dark cladding panel in summer sun runs far above ambient, and a metal roof more so; using a weather-station range for a surface that is absorbing solar radiation understates the movement substantially.
The installation temperature matters as much as the range. A joint set to its design width on a hot afternoon is at its narrowest, and has its entire remaining capacity in extension; the same joint set on a cold morning is at its widest and will be asked to close by the full range. Detailing normally states a setting gap AT a stated temperature for exactly this reason, and the calculators here that ask for today's temperature are asking so they can tell you the right gap now rather than the gap at some mean nobody is standing in.
And the commonest failure of all needs no arithmetic: a movement joint that has been filled. Mortar squeezed into a masonry control joint, a screed run through a floor joint, a rigid trim fixed across an expansion gap — each converts a designed plane of weakness back into restraint, and the crack then appears somewhere nobody chose. A joint that cannot move is not a joint; it is a line drawn on a wall.
The alternative: let it move, or reinforce it to crack finely
There are two honest strategies and jointing is only one of them. The first is to ACCOMMODATE: slip planes under a slab, sliding connections at a mullion stack, clips that let a standing-seam panel run, ties that permit differential movement across a cavity. Movement is allowed and nothing is stressed.
The second is to RESTRAIN AND DISTRIBUTE: accept that the element will crack, and put in enough well-distributed reinforcement that the cracking arrives as many fine cracks rather than a few wide ones. This is how continuously reinforced pavements and many water-retaining structures work, and it deliberately abandons joints — because a joint is also a maintenance item and a leak path.
Which is right is a design decision about durability, appearance and what the element has to keep out. What is not available is the third option that gets built by accident: restrain it, do not reinforce it, and leave the joints out. That produces the same total movement arriving at one unplanned location.
Calculators that use this method
Basis
- ASTM C1472, Standard Guide for Calculating Movement and Other Effects When Establishing Sealant Joint Width. The joint-width-from-movement-capability method used above.
- ASTM C1193, Standard Guide for Use of Joint Sealants — joint geometry, the width-to-depth ratio, and the three-sided adhesion prohibition.
- ASTM C920, Standard Specification for Elastomeric Joint Sealants, which is where a sealant's movement class comes from.
- BS 5628 / Eurocode 6 and the Brick Industry Association Technical Notes on movement: irreversible moisture expansion of fired clay against drying shrinkage of concrete masonry, and the joint spacings that follow.
- ACI 224R, Control of Cracking in Concrete Structures, and ACI 302.1R for slab jointing. The restrained-stress argument and the distributed-reinforcement alternative.
- National Design Specification for Wood Construction (NDS) and the Wood Handbook (USDA FPL) for shrinkage across and along the grain, and the storey-by-storey differential it produces.
- Manufacturers' published coefficients of thermal expansion. These are material properties rather than trade rules of thumb, and the site's calculators take them as inputs rather than assuming them.
