MIT Sloan Garage THERM modeling
12-7-2006
Marc Rosenbaum
A portion of the building/garage interface was modeled in the LBNL software called THERM, a two dimensional thermal analysis program. The area
modeled is based on detail 1/A5.01 in the Schematic Design drawing set. It consists of the radiant floor slab supported at the building edge by a 60
inch plate girder, which in turn supports the garage roof under earth as the garage extends beyond the building face. The exterior building wall above
the floor slab is not shown.
The grey elements in the section above are concrete (the steel decking is omitted as it is not necessary for the modeling). The blue element is the steel
girder – the section is two inches thick. The beige elements are polyurethane foam insulation, at R-6 per inch. The dark green elements are one inch
of gypsum, to form an enclosure around the WF beam, and the light green is air space. The brown element is earth.
Each element has a thermal conductivity. Boundary conditions are set around the assembly in order to calculate heat flow. All boundaries exposed to
outdoor air were set at 30°F, including the garage interior. The floor boundary is set at 80°F, to represent a heated floor slab. Boundaries at the left
and right edges of the assembly are not real – the structure keeps going – and so those boundaries are adiabatic, which is a five syllable word that
means without heat flow. Given these boundary conditions, each case is analyzed for its heat flow, and the output includes a color representation of
the temperatures across the assembly, as well as a U value for the assembly based on the projected horizontal area of the building floor slab.
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Case 1 – No insulation
Without insulation, the calculated U = 0.8791 BTU/ft2-hr-°F. With heat at the floor surface, this does not result in a cold floor, but it does require a
lot of energy. The annual energy going out each ft2 of floor area over this ten foot perimeter segment would be close to one gallon of fuel oil, or
slightly over a therm of natural gas. This is not good.
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Case 2 – Insulation on the vertical foundation wall and under the slab
Adding three inches of foam insulation (R-18) to the underside of the slab and the exterior of the vertical foundation wall drops the U value to 0.1798
BTU/ft2-hr-°F, or about a five-fold reduction over the uninsulated case. This is about R-5.5, still not great. The interior side and bottom of the beam
are uninsulated.
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Case 3 – Add insulation to the vertical wall of the beam enclosure
Adding three inches of foam to the interior (garage) side of the beam enclosure drops the U to 0.1330 BTU/ft2-hr-°F, a 26% reduction.
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Case 4 – Bumping the underslab foam to four inches
Additional insulation beneath the building floor slab doesn’t improve performance much (7%) over the same approach with three inches (Case 3). U
value drops from 0.1330 to 0.1234 BTU/ft2-hr-°F.
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Case 5 – Add insulation to the underside of the garage roof
Adding three inches of foam to the underside of the garage roof drops the U value further to 0.0980 BTU/ft2-hr-°F, or about R-10. The steel is now
fairly well isolated thermally. This is a 26% reduction in heat loss coefficient from Case 3.
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Case 6 – Cutting the garage roof foam back to just beneath the steel girder
The U value goes up to 0.1074 BTU/ft2-hr-°F from 0.0980 BTU/ft2-hr-°F, about a 10% increase.
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Case 7 – Add insulation to the top of the garage roof slab with full insulation of the underside as well
Adding three inches of foam to the top of the garage roof slab makes a rather marginal improvement (4%), as the U drops to 0.0944 BTU/ft2-hr-°F.
The earth over the concrete is about three feet deep and provides some insulation, so the insulation beneath the earth isn’t doing much.
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Case 8 – Foam directly on the steel girder
This case is very similar to cases 5 and 6, with a U value roughly in the middle of the two – 0.1015 BTU/ft2-hr-°F. It is not important to encase the
steel directly in insulation (although this may prove easier to build.)
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Case 9 – Change insulation to four inches
Bumping the insulation from three to four inches drops the U value to 0.0819, about a 20% drop. The nominal R value here is about 24, and the
effective R value is about 12. This is not as bad as it may appear; the effective R value is computed based on the ten foot length of floor, and the heat
loss area is roughly doubled at the edge by the beam depth. So the effective R will be roughly halved in this condition.
Conclusions:
- Insulation of the floor slab and adjacent area is important for energy efficiency reasons, especially as the floor is heated.
- Not heating the floor – putting heat into the space with convectors/radiators above the slab – will reduce heat loss as the driving temperature
differential will be less. I assumed an 80F floor surface temperature, which implies a higher temperature in the body of the floor around the tubing.
- The insulation should go beneath the steel beam, not just on the side. How far along the garage ceiling the insulation extends is not optimized here,
but there are diminishing returns as the insulation extends further along the ceiling. In the last two cases the insulation extends two feet beyond the
edge of the steel girder, perhaps another two feet would be worthwhile.
- Encasing the beam directly isn’t worth much from a thermal point of view. However, the further the insulation plane is from the beam, the higher
the chance of cold air getting in behind the insulation and bypassing it.
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