Both smaller wooden houses and larger brick buildings have traditionally been
constructed with timber floors. Timber tier of beams is still dominating as construction type in wooden houses. In larger buildings, however, it has become common to use floors of concrete or steel.
The design of tier of beams constructions have changed over the last century. The modified constructions make use of more slender beams, and decreased centre distance between the beams. While the most common dimension of the beams was approximately 100 mm × 150 mm (4" × 6") in the first part of this century, 48 mm × 198 mm and even more slender beams are common today. The use of pugging of clay, kiselguhr or sawdust ended when mineral wool was introduced as thermal insulation material. This transition to mineral wool in the floors also made it unnecessary to construct double floors.
Calculations of effective U-values of the floors
The thermal resistance of basement and ground is taken into account in the calculations of effective U-values of the floors of the stereotypes of houses. These effective U-values, which are denoted Ueff in the following, are calculated from indoor air in the dwelling to outdoor air. All stereotypes of houses are presumed having unheated basements, except for the stereotype of house defined for one-family houses constructed between 1971 and 1980. This stereotype is presumed to be a basement house with dwelling area in the basement. The effective U-values of the floors are calculated differently for houses with unheated basements and the basement house. A thermal conductivity of 1.5 W/mK in the ground is used in the calculations.
Houses with unheated basements
The principal heat loss of unheated basements is illustrated in Figure 3.6. The
temperature (Tc) in the unheated basement is calculated to estimate the effective U-value of the floor (Ueff), from indoor air (Ti) to outdoor air (Te). The basement temperature (Tc) is solved from the equation of the heat balance of the unheated basement.
The heat loss from the unheated basement to the heated dwelling in the storey above is denoted qf :
qf = kf · (Tc - Ti ) = Af · Uf · (Tc - Ti ) (Equation 3.2)
where Af is the floor area, and Uf is the U-value of the floor between dwelling and basement. The surface resistance is presumed to be 0.13 m2K/W on both sides of the floor.
The heat loss from the unheated basement to outdoor air through the basement walls above ground level, is denoted qw:
qw = kw · (Tc - Te ) = Aw · Uw · (Tc - Te ) (Equation 3.3)
where Aw is the wall area, and Uw is the U-value of the walls abound ground level. The infiltration heat loss from the unheated basement to outdoor air is denoted qi:
qi = ki · (Tc - Te ) = Vcellar · ni · (Tc - Te ) (Equation 3.4)
where Vcellar is the volume of the unheated basement and ni is the rate of air exchange. The heat loss through the basement floor to the ground is denoted qg:
qg = kg · (Tc - Te ) (Equation 3.5)
where the heat loss factor, kg, includes the thermal resistance of both the basement floor construction and the walls below ground level. The heat loss factor kg is calculated using "CELLAR", which is a PC-program developed by C. E. Hagentoft (Hagentoft, 1988). The heat balance of the unheated basement can be expressed as:
qf + qw + qi + qg = 0 (Equation 3.6) kf · (Tc - Ti ) + (kw + ki + kg) · (Tc - Te ) = 0 (Equation 3.7) Tc = T k T k k k k k k k i f e w i g f w i g · + · ( + + ) ( + + + ) (Equation 3.8)
By setting Ti = 1 and Te = 0, Tc can be determined from:
Tc = k
k k k k
f
f w i g
( + + + ) (Equation 3.9)
Tc can then be used to find the effective U-value of the floors of the heated dwelling. The heat loss through the floor can be expressed both as the heat loss from the heated
dwelling to the outdoor air:
qf = Ueff · Af · (Ti - Te ) (Equation 3.10)
and as the heat loss from the heated dwelling to the unheated basement:
qf = kf · (Ti - Tc ) = Af · Uf · (Ti - Tc ) (Equation 3.11)
The effective U-value of the floors, from indoor air (Ti = 1) to outdoor air (Te = 0), is then calculated by combining Equation 3.10 and Equation 3.11:
Ueff = U A T T A T T f f i c f i e · · ( - ) · ( - ) = Uf · (Ti - Tc ) (Equation 3.12)
The basement floors are presumed to be 1.75 meter below ground level, and the rate of air exchange from basement to outdoor air is presumed to be 0.2 h-1. Table 3.28 shows
the effective U-values of the floors calculated for the stereotypes of houses having unheated basements.
Table 3.28. Calculated effective U-values of floors in houses with unheated basements.
Stereotype of house
Effective U-value
Assumed floor and basement construction. (The U-values stated for the floors include surface resistances of 0.04 m2K/W and 0.13 m2K/W.)
W/m2K
One-family houses
Before 1956 0.69 Floor with pugging of clay, kiselguhr etc., U-value = 1.0 W/m2K (1). Unheated and uninsulated basement with concrete walls.
Improved 0.34 100 mm mineral wool or cellulose fibre as additional insulation in floor, U- value = 0.40 W/m2K (1).
1956 to 1970 0.27 Floor of 200 mm tier of beams with 100 mm mineral wool, presumed U- value = 0.35 W/m2K. Unheated and uninsulated basement with LECA walls.
Improved 0.17 The whole cavity in floor filled with mineral wool or cellulose fibre, presumed U-value = 0.20 W/m2K (1).
1981 to 1990 0.15 Floor with 200 mm mineral wool, U-value = 0.20 W/m2K (2). Unheated basement. LECA walls with 50 mm mineral wool. Basement floor with 100 mm mineral wool.
Divided small houses
Before 1956 0.66 Floor with pugging of clay, kiselguhr etc., U-value = 1.0 W/m2K (1). Unheated and uninsulated basement with concrete walls.
Improved 0.33 100 mm mineral wool or cellulose fibre as additional insulation in floor, U- value = 0.40 W/m2K (1).
1956 to 1970 0.26 Floor of 200 mm tier of beams with 100 mm mineral wool, presumed U- value = 0.35 W/m2K. Unheated and uninsulated basement with LECA walls.
Improved 0.17 The whole cavity in floor filled with mineral wool or cellulose fibre, presumed U-value = 0.20 W/m2K (1).
1971 to 1980 0.20 Floor of 200 mm tier of beams with 150 mm mineral wool, U-value = 0.26 W/m2K (2). Unheated and uninsulated basement with LECA walls. 1981 to 1990 0.15 Floor with 200 mm mineral wool, U-value = 0.20 W/m2K (2). Unheated
basement. LECA walls with 50 mm mineral wool. Basement floor with 100 mm mineral wool.
Large houses
Before 1956 0.47 Floor with pugging of clay, kiselguhr etc., U-value = 1.0 W/m2K (1). Unheated and uninsulated basement with brick walls.
Improved 0.28 100 mm mineral wool or cellulose fibre as additional insulation in floor, U- value = 0.40 W/m2K (1).
1956 to 1970 0.38 Concrete floor with sleepers and 50 mm mineral wool, U-value = 0.63 W/m2K (2). Unheated basement. Concrete walls with 75 mm wood wool cement.
1971 to 1980 0.24 Concrete floor with sleepers and 100 mm mineral wool U-value = 0.37 W/m2K (2). Unheated basement. Concrete walls with 150 mm LECA. Basement floor with 50 mm mineral wool.
1981 to 1990 0.17 Concrete floor with 120 mm floating insulation U-value = 0.28 W/m2K (2). Unheated basement. Concrete walls with 100 mm mineral wool. Basement floor with 100 mm mineral wool.
(1) NBI 722.506, 1991 (2) NBI G471.010, 1987
Basement house
The basement in the stereotype of house defined for one-family houses constructed between 1971 and 1980 contains both heated and unheated space. The heated part, which is assumed to represent 50% of the basement area, is included as a part of the dwelling area. Figure 3.7 shows the principal heat loss of the unheated part of the basement of basement houses.
The principal heat loss is the same as for houses with unheated basements. However, the heated part of basement houses also has a heat loss through the inside wall to the
unheated part of the basement. In addition, the infiltration heat loss between the heated and unheated parts of the basement may be taken into account. The total heat loss from the unheated basement to the dwelling can be expressed as:
qf_tot = qf + qw_indoor + qi_indoor (Equation 3.13)
where
qf is the heat loss through the floor to the heated dwelling in the storey above,
qw_indoor is the heat loss through the inside wall to the heated part of the basement, qi_indoor is the infiltration heat loss to the heated part of the basement. Equation 3.13 can be rearranged to give:
qf_tot = kf_tot · (Tc - Ti ) = (kf + kw_indoor + ki_indoor ) · (Tc - Ti ) (Equation 3.14)
The heat balance of the unheated part of the basement can be calculated similarly as for the houses having unheated basements:
qf_tot + qw + qi + qg = 0 (Equation 3.15) kf_tot · (Tc - Ti ) + (kw + ki + kg ) · (Tc - Te ) = 0 (Equation 3.16) Tc = T k T k k k k k k k i f tot e w i g f tot w i g · + · ( + + ) ( + + + ) _ _ (Equation 3.17)
By setting Ti = 1 and Te = 0, Tc can be determined from:
Tc = k k k k k f tot f tot w i g _ _ ( + + + ) (Equation 3.18)
The heat loss through the floor can be expressed both as the heat loss from the heated dwelling to the outdoor air:
qf_tot = Ueff · Af · (Ti - Te ) (Equation 3.19)
and as the heat loss from the heated dwelling to the unheated basement:
qf_tot = kf_tot · (Ti - Tc ) (Equation 3.20)
The effective U-value of the floor in the dwelling, from indoor air (Ti = 1) to outdoor air (Te = 0), may then be calculated from:
Ueff = k T T A T T f tot i c f i e _ · ( - ) · ( - ) = k T T A f tot i c f _ · ( - ) (Equation 3.21)
In addition, the heat loss through the floors of the heated parts of the basement must be taken into account in the calculations of the total energy consumption of basement houses. The U-value of the floors in the heated part of the basement is calculated from:
Ueff_heated = k T T A g i e f · ( - ) = k A g f (Equation 3.22)
When kg is calculated in the PC-program "CELLAR", the floor in the heated part of the basement is assumed to be 0.4 meter below ground level. The thermal heat loss taken into account in the calculation of the U-value of the floor in the heated part of the basement thus includes the heat loss through the lower 0.4 meters of the outer walls as shown in Figure 3.8.
The rate of air exchange is assumed to be 0.2 h-1 for both the air exchange between the unheated part of the basement and outdoor, and between the unheated part and the heated part of the basement. Table 3.29 shows the calculated effective U-values of the floors in the basement house.
Figure 3.8. Basement house. Heat loss to the ground of the heated part of the basement.
Table 3.29. Calculated effective U-values of floors in the basement house.
One-family house constructed between 1971 and 1980
Part of the basement
Effective U-value
Assumed floor and basement construction
W/m2K
Unheated part 0.36 Floor of 200 mm tier of beams with 150 mm mineral wool, U-value = 0.26 W/m2K (NBI G471.010, 1987). Unheated and uninsulated basement with LECA walls. Heat loss from heated part of the basement through the inner wall to the unheated part of the basement is included in the U-value. Heated part 0.36 Basement floor of 100 mm concrete, 50 mm thermal insulation and 250
mm gravel. Basement floor is 0.4 m below ground level. The U-value includes the heat loss through the lower 0.4 meters of the outer walls. The outer walls are presumed constructed of 250 mm LECA-blocks with 50 mm mineral wool as thermal insulation.