Point Thermal Bridge Coefficient (Chi-value)

What is the point thermal bridge coefficient, chi, and what does it measure?

The point thermal bridge coefficient, χ (chi), measures the extra heat flow through one isolated spot where a conductive element crosses the building envelope. Typical examples are a dowel holding ETICS insulation to the masonry, a steel bracket carrying a balcony, and an anchor for a canopy or railing. The planar U-value calculation misses this flow, so it is a specific kind of thermal bridge.

The coefficient is the point counterpart of the linear thermal bridge coefficient, ψ (psi), which applies per metre of a continuous junction. A wall-roof junction gets a ψ value, and a single fixing gets a χ value. A detail with both needs both.

Why is chi expressed in W/K and not in W/(m·K)?

A point has no length, so χ is heat loss per point for each kelvin of temperature difference between inside and outside, in W/K. That unit makes the values additive. The extra heat loss from a set of fixings is the sum of their individual coefficients, added to the building's overall heat loss coefficient. The risk lies in the count, because a point left out of the sum is missing from the result.

Where do point thermal bridges occur on a Slovak house?

Point bridges are common on facades, balconies, canopies and railings. The facade case is the most frequent: the kontaktný zatepľovací systém (KZS), the Slovak name for ETICS, is anchored with dowels across the whole wall, so the count is high.

Location	What crosses the insulation	Why it matters	Usual approach
Facade boards (ETICS)	Dowel through each board into the masonry	Identical points repeated across the wall	Recessed dowel with an insulation cap
Balcony bracket	Steel bracket through the wall insulation	Structural load and a local heat path	Thermal-break connection or calculated χ
Canopy anchor	Steel anchor fixed through the wall	Few points, often at exposed entrances	Calculate each anchor
Railing post	Post base fixed through slab or wall	Exposed on balconies and terraces	Thermally separated base, recessed fixing
Heavy facade item	Bracket for outdoor units, shutters or signage	Often added late, so the count is missed	Fix points at design stage and count them

Why do small chi values add up across hundreds of dowels?

A single dowel adds very little heat loss, and its χ value is small. A facade carries many identical fixings, and each one repeats the same heat path. The total grows in proportion to the count, so a small value per point becomes a large figure across an elevation. Doubling the dowels doubles their share of the loss.

The count comes from the anchoring pattern, which the wind loads on the boards dictate, plus extra fixings at corners, edges and openings. Both belong in the energy calculation. A common mistake is to calculate with a generic count and then change the pattern on site.

How do recessed dowels with insulation caps reduce the effect?

The usual fix is to set the dowel head below the insulation surface, in a small pocket, and close the pocket with an insulation plug called a cap, which the render and reinforcement then cover. A proud head sits under thin render and forms a conductive spot on the outer surface. A recessed head is buried in insulation, which stays continuous over it.

The cap does not remove the fixing. The dowel still crosses the insulation and still has a χ value. The benefit is at the surface around the head, and it has to be shown by comparing the recessed detail with the proud-head case.

Dowel choice matters too. A steel nail or pin conducts heat far better than a plastic shaft, so where the load requires steel, the thermal effect must be calculated and the detail improved around it. On site, a different dowel depth or a missing cap changes the real value, so the as-built detail should match the calculated one.

How is chi determined, and how is it used in the energy calculation?

There are three common routes to a χ value, and they differ in accuracy and coverage.

Route	What it gives	Where it is used	Limits
Detailed 2D or 3D simulation to EN ISO 10211	Calculated χ for the exact detail	Certification-level and unusual details	Needs skill and an accurate model
Published value from the anchor maker or a test	Value for one product in a stated setup	Early design and product selection	Valid only for the stated configuration
Routine U-value with fastener correction, EN ISO 6946	Averaged addition to the planar U-value	Everyday facade U-value work	Averages over the area, no local point

Calculated values are summed into the building's heat loss coefficient for the energy balance. Published values apply only where the stated configuration matches the building. Applying a value from one configuration to another is the most common error in point bridge work.

How is the point coefficient different from the linear coefficient in practice?

The difference is what the designer counts. A linear coefficient needs the length of a junction, and a point coefficient needs the number of points. Replacing a continuous balcony slab with individual brackets moves the detail from ψ to χ, and the total can fall or rise, so the change must be calculated.

In the model, a junction is a line of constant section, while each fixing is one local point. A linear value used for a row of brackets, or a point value used for a continuous edge, gives a plausible but wrong result.

Can a small chi value be ignored?

Not when the count is large. One common misconception is that a low value per point means the point does not matter. Another is that a recessed dowel removes the bridge, when it only reduces the surface effect. A third is that point bridges occur only on balconies, when they also occur on facades, canopies, railings and heavy fixings. Every fixing belongs on the design list, with its type, count and location, so the calculation and the site work from the same numbers.