What's that sticking out of the envelope?

Just to follow on from the excitement of my last post on thermal bridges, here is a practical application.

A couple of places on the north side present challenges to the insulation performance of the building envelope. The first problem is the external structure of the steps and the roof over the front door. I'd hoped this could be kept as a separate structure to the house, just as the balcony over the southern terrace is, so that it would not affect the building envelope. However, it seemed to be very difficult for the architect to reconcile structural demands. For example, in the case of an earthquake two separate structures would move independently and damage where the roof connects to the wall. Also, with no beams protruding from the main structure, pillars would have had to come out of the foundation right next to the house, which would have been difficult.

Anyway, the result is six beams sticking out through the thermal envelope, some 120 x 180 mm, some 120 x 240. 

Using Therm again, and starting with the pillar in the middle of the wall, we can estimate how much extra heat is being lost by this disturbance in the insulation-wall continuum. I looked at three cases. First, what would happen if the beam just reached the outside wall? Second, how about if it stuck out for 500mm? Next, what if it stuck out for a metre?

There was virtually no difference between the 500mm protrusion and the one-metre protrusion (Ufactor 0.169874 versus 0.169972 W/m²K, around 15% extra heat loss for a unit area) so we probably don't need to worry about what exactly is happening to the beam after the first two or three hundred millimetres. Interestingly, the beam that just stopped at the outside wall did much worse (0.179 W/m²K, around 20% worse). I looked at 200 and 300 mm protrusions, and it looks like the ideal length for a protruding beam is somewhere between these two lengths. When I say the ideal length, obviously it's ideal not to have anything puncturing the thermal envelope.

The moral of this little tale so far, although of no use in our case, is that if you have insulation on the outside of the structure, and if you need to have wood sticking as far as the wall, it's better to have it stick out than flush with the wall, but much better to not have it stick out at all. 

The colours in these pictures show thermal flux, white representing a high heat flow and black representing a low heat flow. So you can see that heat is leaking through the corners where the beam protrudes, but is leaking through the surface where it is flush. Practically, to the extent that we should be worried about this thermal bridge, there is a chance that on a hot and humid day in summer, these corners may have a much lower temperature than the ambient, and attract condensation. This is going to be outside in summer rather than inside in winter, and the outside is designed to stand up to rain. Also, it will be most critical when the temperature has just risen, and in these situations the humidity usually drops.

This kind of thermal bridge is called a punctual thermal bridge, where punctual refers to a puncture in space, rather than it's usual temporal meaning. It may in fact have the opposite meaning to that of "on time"--if you have a puncutal thermal bridge in your structure, it's probably too late!

For punctual thermal bridges, rather than considering heat loss per unit length, in W/mK, we need to consider the heat loss for each beam sticking out, in W/K. There are six of them, so once we have a number, we need to multiply by six.

  

While simple calculations only take into account one-dimensional heat flow (ie what the material is and how thick it is) Therm can simulate two-dimensional heat flows. In fact, and of course, the heat is in a three dimensional world, or in fact a four dimensional world as it's not a steady state, but temperatures are changing all the time. To use the two-dimensional models from Therm to estimate the three-dimensional situation of a beam sticking out of the wall, we can look at two slices of the wall, one vertical, which will include the pillar running up and down the whole wall, and the other horizontal, which will have a few centimetres of pillar in the middle, but the rest of the middle layer will be insulation.

As well as the situation above with a wooden beam sticking out from a perfect wall, as we'd see if we made a horizontal slice through the wall, we should consider this situation, where the middle layer of the wall is wood. For a unit metre of wall, with a metre of beam 240 mm wide sticking out, the U value for a section with the above situation is 0.170 W/m²K, compared with the ideal 0.145 W/m²K. If we look at a 240 mm square section beam, this will represent a difference of 0.006 Watts per Kelvin for the puncture. This amounts to 0.43 KWh lost per year, per beam. If we look at the more severe situation, as if the whole of the the middle layer were wood, the U value (again for 240 mm wide beam sticking one metre out) is 0.215 W/²K; corresponding to a difference of 0.017 W/K, again assuming a square section 240 x 240 mm. The real answer is likely between the two, around 0.011 W/K. Actually, the beams are smaller, so this is a mean estimate. A 120 x 240 mm beam looks closer to 0.006 W/K. There are six of them, so over the year, with 70,000 heating degrees, this comes to a significant 4.8 kWh per annum. We should still be within the passive house limit of 15 kWh/m²a (kilowatt hours per square metre of floor space per year).

It would have been better to work harder to keep this structure outside the envelope, although this may have had structural problems, stuck further out of the house and been more expensive. It could have been a lot worse. Wood is a relatively bad conductor (under 0.2 W/mK). Had it been concrete (around 1 W/mK) or steel (around 40 W/mK) it would have been much worse.

More info, and coincidentally the same example as in my last post here on wikipedia and more here here from the Passive House institute who have pioneered work on thermal bridges.