Thermal resistance and U-values
U-value with a timber-bridged layer (ISO 6946 combined method)
- where
- total resistance through the insulation (m²K/W)
- internal surface resistance (m²K/W)
- resistance of all other layers (m²K/W)
- depth of the bridged layer (mm)
- insulation conductivity (W/mK)
- external surface resistance (m²K/W)
- total resistance through the timber (m²K/W)
- timber conductivity (W/mK)
- upper limit of total resistance (m²K/W)
- timber fraction (%)
- lower limit of total resistance (m²K/W)
- total resistance, combined method (m²K/W)
- U-value (W/m²K)
- maximum relative error (%)
Explain this equation
Works out the U-value of a construction where insulation sits between timber studs, rafters or joists, using the BS EN ISO 6946 combined method.
Timber conducts heat about three or four times better than mineral wool, so it forms a thermal bridge. The upper limit R′_T imagines separate parallel paths, one through insulation and one through timber, each the full build-up, combined by area fraction. The lower limit R″_T instead averages λ across the bridged layer as if heat could spread sideways freely. The truth lies between them, so the method takes the mean. The difference gives an estimate of the error.
Parallel paths average their U-values (conductances); layers in series add resistances. The two limits use each idea in turn.
Sense check: 140 mm studs at 15% timber with λ 0.035 insulation give about 0.29 W/m²K, noticeably worse than the 0.22 you would get if the whole layer were insulation.
Watch out: if the upper limit is more than 1.5 times the lower (usually with metal bridging) the method is not valid and a numerical model is needed.
Works out the U-value when insulation sits between studs, rafters or joists, using the BS EN ISO 6946 combined method (average of the upper and lower limits).
Enter your values to see the result.
Good to know
The upper limit treats the insulated and timber sections as parallel paths through the whole element; the lower limit blends the timber and insulation into one equivalent layer. The standard U-value is the reciprocal of their average. BR 443 timber fractions: work them out as stud width / centres plus allowances for noggings and plates, for example 35 mm joists at 600 mm centres give 0.068 and 50 mm at 400 mm give 0.135; timber-frame walls are commonly 15%. Softwood λ is 0.13 W/mK. Put everything outside the bridged layer (plasterboard, sheathing, continuous insulation, masonry) into Ro.
Common mistake
Using the insulation-only U-value for a stud wall or rafter roof. At 15% timber the bridging can raise the U-value by 15–25%, which often turns a pass into a fail.
Limits
One bridged layer with two materials. Not valid where the upper/lower ratio exceeds 1.5 (metal studs or fixings through the whole build-up): use BS EN ISO 10211 software. Fixings and air-gap corrections are separate (see the Annex F calculator).
Sources
- BS EN ISO 6946:2017 Building components and building elements – Thermal resistance and thermal transmittance – Calculation methods (surface resistances; combined method; Annex F corrections for air voids and mechanical fasteners)
- ISO 6946:2017 catalogue entry and preview (iTeh Standards)
- BetterBuilding documentation: Total R-value calculations to ISO 6946:2017 (restates Annex F: ΔUf = α λf Af nf / d0 × (R1/RT,h)², α = 0.8, recessed α = 0.8 d1/d0; ΔUg = ΔU″ (R1/RT,h)²; corrections only if over 3%; combined method valid while upper/lower ≤ 1.5)
- BRE BR 443 (3rd edition, 2019) Conventions for U-value calculations (Rsi 0.13 / 0.10 / 0.17 and Rse 0.04 m²K/W; air-gap levels 0 / 0.01 / 0.04; timber fractions; ground λ clay 1.5, sand/gravel 2.0, rock 3.5 W/mK; ignore corrections under 3%)
- BS EN ISO 10456 Hygrothermal properties – tabulated design values (as reproduced in the SEAI DEAP guide: gypsum plaster 1200 kg/m³ 0.43; plasterboard 0.25; cement–sand render 1.00; brick outer leaf 0.77 W/mK; softwood 0.13 W/mK as used by BR 443)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS EN ISO 6946, BS 5250, PAS 2035, Building Regulations Part L and manufacturers’ data. Whole-house retrofit needs a qualified retrofit assessor and coordinator.