Standard U-valuesThis Digest provides information which enables U-values for wallsand roofs to be calculated on the basis of standard assumptions, inaccordance with the CIBSE Guide, Section 3, Thermal propertiesof building structures.

The calculation of heat losses from ground floors is described inIP3/90 and from dwellings in general in Digest 190.

Technical enquiries to:Building Research EstablishmentGarston, Watford, WD2 7JRTelex 923220 Fax 0923 664010

Digest 108Revised 1991

CI/SfB (M3)

The thermal transmittance or U-value of a wall, roofor floor of a building is a measure of its ability toconduct heat out of the building; the greater the U-value, the greater the heat loss through thestructure. The total heat loss through the buildingfabric is found by multiplying U-values and areas ofthe externally exposed parts of the building, andmultiplying the result by the temperature differencebetween inside and outside.

U-values can be obtained by a variety of methods: bymeasurement, by adjustment of measured values, or bycalculation from thermal resistance of componentparts. These different methods of assessment will, ingeneral, yield slightly different results. In fact, the U-value of a structure does vary to some extent fromone situation to another; among other things itdepends on the moisture content of the componentmaterials, the wind speed and the internal conditions.The results obtained by measurement depend onconditions during tests and may differ from oneanother as well as from calculated values. Although allthese methods give values that are accurate enough forheat loss calculation, a standard method of assessmentis needed for comparing different constructions on acommon basis or for meeting a stated figure specifiedby a client or by regulations.

BASIS OF THE STANDARD U-VALUESStandard U-values are calculated from the resistancesof the component parts, which in turn are based onstandard assumptions about moisture contents of mat-erials, rates of heat transfer to surfaces by radiationand convection, and airflow rates in ventilatedairspaces. The effects of any heat bridging through thestructure also have to be taken into account in astandard manner. The standard assumptions are, as faras possible, typical of practical conditions althoughthey cannot be expected to agree in every case asconditions vary between one situation and another.

EXPLANATION OF TERMS USED

Thermal conductivity (λ) is a measure of amaterial's ability to transmit heat; it is expressed asheat flow in watts per square metre of surface areafor a temperature difference of 1K per metrethickness and may be expressed as : Wm

m2K

but thickness over area m cancels to 1 and the m2 m

expression is normally given as W / (mK).

Thermal resistivity (1/λ) is also a property of amaterial, independent of thickness. It is thereciprocal of conductivity: (mK) / W.

When the thickness of a material is known, itsactual thermal resistance (R) can be calculated bydividing its thickness in metres by its thermalconductivity. The resistance is expressed in (m2K) / W.

Thermal transmittance (U) is a property of anelement of a structure comprised of giventhicknesses of material and is a measure of itsability to transmit heat under steady flowconditions. It is defined as the quantity of heat thatwill flow through unit area, in unit time, per unitdifference of temperature between inside andoutside environment. It is calculated as thereciprocal of the sum of the resistances of eachlayer of the construction and the resistances of theinner and outer surfaces and of any air space orcavity. It is given in W / (m2K).

CALCULATION OF U-VALUESTo summarise so far: a property of any material is itsthermal conductivity (λ); the reciprocal of this isresistivity (1/λ). For material of known thickness, theresistance (R) can be calculated (thickness / con-ductivity) and from the resistances of the various layerscomprising a construction and the resistances ofcavities, and of inner and outer surfaces, the U-valuecan be calculated.

For a simple structure without heat bridging, thethermal transmittance coefficient U is expressed as:

U = 1/(Rsi + Rso + Rcav + R1 + R2......)

where Rsi = internal surface resistance (see Table 1)Rso = external surface resistance (see Table 2)Rcav = resistance of any cavity within the

building element (see Tables 3 and 4)R1,R2 = resistance of slabs of material

Resistance of cavities (Rcav) The thermal resistance ofairspaces, such as cavities in hollow wall constructions,depends mainly on the following factors:

•Thickness of the airspace (its dimension through thethickness of the wall) — resistance increases with thethickness up to a maximum at about 20 mm.

•Surface emissivity — commonly-used buildingmaterials have a high emissivity and radiationaccounts for about two-thirds of the heat transferthrough an airspace with high emissivity surfaces.Lining the airspace with low emissivity material, suchas aluminium foil, increases the thermal resistance byreducing radiation.

•Direction of heat flow — a horizontal airspace offershigher resistance to downward than to upward heatflow, because downward convection is small.

• Ventilation — airspace ventilation provides anadditional heat flow path but, because air movementin such conditions is very variable, estimates for thisare necessarily approximate. Ventilation may beeither deliberate (ventilated cavity walls) orfortuitous (sheeted constructions with gaps betweensheets).

Standard values for various airspaces, unventilated andventilated, are given in Tables 3 and 4. The smallamount of ventilation required to avoid condensationin roof spaces does not significantly affect the airspaceresistance and, where this is the only ventilationprovided, data for unventilated airspace should beused. Similarly, the data in Table 3 are applicable tothe airspace in a cavity wall that is ventilated only tonormal standards.

Materials As explained previously, the resistance (R)of a material is equal to its thickness divided by itsthermal conductivity λ . Values of λ for insulatingmaterials can be obtained from the CIBSE Guide.These materials are intended for use in dry situationsand their thermal conductivity in air-dry conditions isappropriate.

For the materials commonly used for masonry walling— brick, lightweight concrete, dense concretes — thereis a relationship between bulk dry density and thermalconductivity, but the effect of moisture must also beconsidered. Table 5 sets out for a range of dry densitiessome average thermal conductivities at moisturecontents appropriate to solid brickwork and concrete,protected from rain and exposed to rain as, forexample, in the inner and outer leaves respectively ofcavity walling.

If available, however, measured λ-values should beused for calculating standard U-values. The testsshould have been made on specimens at fairly lowmoisture content and should be adjusted, using Table 6, to the standard moisture content appropriateto the conditions of use, as indicated by the columnheadings of Table 5.

Building Heat flowelement direction (m2K)/W

Walls Horizontal 0.12

Ceilings or roofs,flat or pitched Upward 0.10Floors

Ceilings and floors Downward 0.14

Building Heat flowelement direction (m2K)/W

Wall Horizontal 0.06

Roof Upwards 0.04

Floor (exposed Downwards 0.04on underside)

Width Surface Thermal resistanceemissivity (m2K)/W

Heat flow directionHorizontal or upwards Downwards

5 mm high 0.10 0.10low 0.18 0.18

20 mm or more high 0.18 0.22low 0.35 1.06

High emissivity planes andcorrugated sheets in contact 0.09 0.11

In general, the surfaces of most building materials have high emissivities;reflective foils or polished metals have low emissivities.

Table 1 Internal surface resistance Rsi

Table 2 External surface resistance Rso

Table 3 Standard thermal resistance of unventilatedairspaces

HEAT BRIDGINGA metal or other high conductivity member bridging astructure increases the heat loss. In simple cases, thethermal resistance can be found by calculatingseparately the thermal transmittance of the differentportions of the construction and combining them inproportion to their relative areas.

Multi-webbed bridges occur in components such asslotted blocks and perforated bricks. For these,calculation should be by three-dimensional analysis orby the combined method in the CIBSE Guide.

Thermalresistance*

(Airspace thickness, 20 mm minimum) (m2K)/W

Airspace between asbestos-cement or blackpainted metal cladding with unsealed joints,and high emissivity lining 0.16

As above, with low emissivity surface facingairspace 0.30

Loft space between flat ceiling and unsealedasbestos-cement or black metal claddingpitched roof 0.14

As above, with aluminium cladding instead ofblack metal, or with low emissivity uppersurface on ceiling 0.25

Loft space between flat ceiling and unsealedtiled pitched roof 0.11

Loft space between flat ceiling and pitchedroof lined with felt or building paper 0.18

Airspace between tiles and roofing felt orbuilding paper on pitched roof 0.12

Airspace behind tiles on tile-hung wall 0.12

Bulk Thermal conductivity W/(mK)dry

density Brickwork Concrete Brickworkprotected protected or concrete

from from exposed tokg/m3 rain: 1%* rain 3%* rain: 5%*

400 0.12 0.15 0.16600 0.15 0.19 0.20800 0.19 0.23 0.26

1000 0.24 0.30 0.331200 0.31 0.38 0.421400 0.42 0.51 0.571600 0.54 0.66 0.73

1800 0.71 0.87 0.962000 0.92 1.13 1.242200 1.18 1.45 1.602400 1.49 1.83 2.00

Moisture content 1 3 5 10 15 20 25(% by volume)

Moisture factor 1.3 1.6 1.75 2.1 2.35 2.55 2.75

Material Condition Bulk(if known) density λ

kg/m3 W/(mK)Asbestos-cement sheet C 1600 0.40Asbestos insulating board C 750 0.12Asphalt, roofing dry 1600-2325 0.43-1.15Brickwork see Table 5Concrete see Table 5Cork granules, raw dry 115 0.052Corkboard 145 0.042Fibre insulating board C 260 0.050Hardboard: medium 600 0.08

standard 900 0.13Metals:aluminium alloy, typical 2800 160copper, commercial 8900 200steel, carbon 7800 50

Mineral fibre (glass or rock)mat or quilt dry 1220 0.04semi-rigid felted mat dry 130 0.036loose, felted slab or mat dry 180 0.042

Perlite, loose granules dry 65 0.042plaster C 600 0.19

Plasterboard, gypsum 950 0.16perlite 800 0.18

Plaster, gypsum 1280 0.46lightweight 400-960 0.079-0.30sand/cement C 1570 0.53

Plastics, cellularexpanded polystyrene dry 15 0.037

dry 25 0.034polyurethane foam (aged) dry 30 0.026pvc flooring dry 0.40

Plastics, solidepoxy glass fibre dry 1500 0.23polystyrene dry 1050 0.17

Stone see Table 5Timber, across grainsoftwood C 0.13hardwood 0.15plywood C 530 0.14

Vermiculite loose granules 100 0.065Wood chipboard C 800 0.15Woodwool slab C 500 0.085

C 600 0.093

C conditioned to constant weight at 20˚C and 65% rh

Table 4 Standard thermal resistance of ventilated airspaces

*including internal boundary surface

Table 6 Moisture factors, for use with Table 5

Table 5 Thermal conductivity of masonry materials

*Moisture content expressed as a percentage by volume

Table 7 Thermal conductivities ( λ) of some buildingmaterials

NotesSome of the figures in this table are representative values to be usedin the absence of precise information. Materials commonly used asthin membranes are not included. The contribution to overallinsulation made by a membrane is due largely to the forming ofadditional airspaces, the resistance of the actual material being toolow to be significant.The thermal resistance of roofing tiles and slates should be neglectedbecause of the airflow through the units; the resistance of thisportion of the structure is allowed for in the values for ventilatedairspaces given in Table 4.

EXAMPLE 2Calculate the effect of filling with polyurethanefoam the cavity in Example 3.

U-value of the original construction 0.94 W/(m2K)

(1) 1/0.94 = 1.06

(2) Deduct Rcav 0.18= 0.88

(3) Add Rfill 0.050 = 1.920.026

= 2.80

(4) U = 1/2.80 = 0.36 W/(m2K)

THE CALCULATION OF U-VALUESTable 7 sets out the thermal conductivities (from the CIBSE Guide) of a rangeof building materials and, in conjunction with Tables 1-6, enables U-values tobe calculated for a wide range of constructions.

EXAMPLE 1Find the U-value of an unplastered 'one-brick' solidwall, built of bricks of 1700 kg/m3 density.

From Table 1: Rsi = 0.12 (m2K)/WFrom Table 2: Rso = 0.06 (m2K)/W

Rbrick = thickness in metres = 0.215λ -value 0.84

= 0.26

U = 1 = 1 = 2.3 W/(m2K)0.12 + 0.06 + 0.26 0.44

EXAMPLE 3Calculate U-value of wall shown.

U = 1Rsi + Rso + Rcav + R1 + R2 + R3

From Table 1: Rsi = 0.12 (m2K)/WFrom Table 2: Rso = 0.06From Table 3: Rcav = 0.18From Table 5:(outer leaf) R1 = 0.10 = 0.12

0.84

(inner leaf) R2 = 0.10 = 0.530.19

From Table 7:(plaster) R3 = 0.01 = 0.05

0.19

1.06

U = 1 = 0.94 W/(m2K)1.06

The CIBSE Guide lists standard U-values for aselection of external wall and roof constructions.These constructions, or any others for which a U-value is already known, may be varied and theeffect of the variation calculated by the followingprocedures:1 Find the reciprocal to the U-value

(= total resistance of the construction).2 Deduct from this the resistance of any layers that

are to be omitted.3 Add the resistance of any layers that are to be

added.4 Find the reciprocal of the new total resistance

(= the U-value).

Printed in the UK and published by Building Research Establishment. Crown copyright 1991Price Group 3. Also available by subscription. Current prices from:BRE Bookshop, Building Research Establishment, Garston, Watford, WD2 7JR (Tel: 0923 664444).Full details of all recent issues of BRE publications are given in BRE News sent free to subscribers.

ISBN 0 85125 285 0

FURTHER READINGIP 3/90 The U-value of ground floors: application to Building RegulationsDigest 190 Heat losses from dwellings

Digest 108Revised 1991

CI/SfB (M3)

108 108 108 108 108 108 108

108 108 108 108 108

1 2 3 4 5 6 7 8 9 10

11 12

1 2 3 4 5 6 7 8

9 10 11 12

Technical enquiries to:Building Research EstablishmentGarston, Watford, WD2 7JRTelex 923220 Fax 0923 664010

Printed in the UK and published by Building Research Establishment. Crown copyright 1991Price Group 3. Also available by subscription. Current prices from:BRE Bookshop, Building Research Establishment, Garston, Watford, WD2 7JR (Tel: 0923 664444).Full details of all recent issues of BRE publications are given in BRE News sent free to subscribers.

ISBN 0 85125 285 0