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Introduction Now that we have briefly introduced the common wall types, we will now go into the materials that make them up in more detail. Let us begin with the outer skin and work our way into the building. You have already seen the main components listed in the wall sections. Starting with siding, there are several material sources and shapes available. Among them, wood, metal, and plastic are the most common. The most common shapes are bevel and tapered lap siding. V-joint and shiplap are two other shapes that seal better against wind and water intrusion between subsequent boards when applied. They don't dry as quickly owing to the tighter joint geometry. In wood, you typically see rot-resistant woods such as cedar, cypress, or redwood used. White pine, yellow pine, fir, spruce, and other products can be purchased, many of them pressure-treated to make them more resistant to damage from exposure to moisture. Paint and stain, like sealant, are temporary and need reapplication to be effective in preventing moisture from entering wood. In order to minimize warping or twisting, pre-paint the wood on all sides prior to installation. Treat all cut ends before installing the next piece. Seal and paint holes from fasteners, if exposed, and then apply another coat of finish product. Plastic has become much more popular lately because of improved chemistry and cost comparison. Vinyl siding is available in various colors and faux wood grains that seldom need painting. They are close-cell plastics and , as such, are more resistant to water penetration, dirt, and organic materials. This also makes them easier to clean. We have seen some vinyl products come loose during hurricanes, so it's important to make certain that they are fastened according to manufacturer's recommendations for the code-required wind speed in the locale. Aluminum siding is not as common as a horizontally lapped product but has great strength-to-weight properties. Sheet goods and boards are also installed as exterior finish materials. Texture 1-11 and 6-11 plywoods were common on low-cost projects in the late 1960s and 1970s. Those numbers identified the spacings on scored lines in the sheathing. Cedar and pressure-treated pine were common. Joints often were closed with sealant and painted or covered with thin batten strips. Board and batten applications were common in rural areas where trees were plentiful and affordable. In board and batten installations, 1 by 12s were nailed to horizontal wood stripping, leaving a narrow gap between boards. Battens, in the range of 1 by 3s, were applied to cover the gaps. Reverse board and batten siding is just the opposite, with the boards exposed when finished. As you may know, none of these are low-maintenance, long-term solutions to keep out wind and rain by themselves. They work nicely in conjunction with other products, if the desired look is rustic. Cementitious coatings, such as stucco or portland cement plaster, as it's sometimes called, are very common finish materials. Although they are similar, we will not include synthetic plaster products in this category, such as are used in exterior insulation and finish systems (EIFS). Basically, cementitious coatings are spray- or trowel-applied coatings that consist of various sand and cement products that have water added on site and dry to a hard finish. They can have integral colors or just take on the color of the sand and cement. Our favorite among them is white stucco (see ill. 58), which is made from clean white beach sand, white portland cement, and lime, which is also white. This creates a very workable mixture that never needs painting. The amount of lime affects how hygroscopic the finished product is. Lime effectively reduces the ease by which water moves through the cured stucco. Depending on how well it's installed, the climate, the chemistry of rainwater, the amount of plant material and other staining agents that come in contact with it, roof drainage and overhangs, etc., white stucco can last up to 50 years without any maintenance other than cleaning every 5 to 10 years and possibly light bleaching with a dilute chlorine and water solution (1 part chlorine in 10 parts water). Ill. 58 -- 15-year old White Stucco residence, Ill. 59 Image of hardie siding, replicating wood. In the middle of the twentieth century it was common to see siding materials that contained asbestos because it was so durable and resisted the elements. Late in the century, a new kind of thin panel was introduced that had the same kind of weather resistance but was less hazardous to health. Cementitious planks and panels can be used in much the same way as wood, aluminum, or asbestos. You see them used commonly in horizontal lap siding to replicate wood siding (see ill. 59). Column build-outs and suspended ceilings are other common applications of the fiber-reinforced cement boards. They can be cut, nailed, and painted much like wood. Some are available in wood grain. They are also used as facings in exterior wall diaphragm systems with foam cores. They are dimensionally stable, but they are not nearly as hygroscopic as formed-in-place concrete, CMU, or wood. Stucco typically is installed over CMU walls or over frame construction when combined with sheathings, membranes, and lath. As a rule, the minimum thickness of stucco ranges between 7/8 and 1” (2 and 2.5 centimeters) and requires three coats to build up properly to the required thickness. The first coat is referred to as the brown coat. It is applied as a general leveling coat. This also serves to fill voids in the CMU or irregularities in the lath. After it's dry, a second coat is applied to further prepare for the finish coat. This second layer is referred to as a scratch coat because it's deeply scratched with a tool before the mix sets up (see ill. 60). These scratches aid in the mechanical adhesion of the finish coat(s). Depending on the desired texture, the next one or two coats are applied using different techniques with a steel trowel. Smooth textures typically are referred to as sand finish, the easiest to paint and keep clean. There is a multitude of expressive ways to give character to the final coat. The rougher the final texture, the easier it's for dirt and insects to take root, and the harder it's to keep clean. The rougher, thicker textured coats also trap more air at the surface, slightly improving thermal performance. Ill. 60 Scratch coat. We recommend applying stucco over expanded metal lath. The lath acts as reinforcement in every direction, reducing cracking over time and improving the bond to a substrate. In the drainage wall, we use stucco over an air and water barrier to reduce the amount of moisture that enters the wall material. Remember, the less water entering the wall, the lower will be the likelihood of mold and mildew growth period. Several techniques are used to limit cracking in stucco, but the most important is to prevent the moisture in the mix from leaving the stucco and going into the block or concrete substrate. This can be achieved by pre-wetting the substrate. Do not re-temper the stucco or make it too wet in an attempt to prevent the moisture from leaving-wet the wall. Paper-backed lath helps here. In many building codes, membranes are required to be used behind stucco on frame walls. In EIFS systems, the synthetic plaster coating is most often relied on to minimize water and vapor penetration of the surface. The foam beneath does allow hygroscopic action from molecule to molecule over time. The use of reinforcing fiber glass mesh makes the foam less susceptible to damage from light contact. It does little to reduce moisture transmission. We have not shown EIFS details as one of our illustrated wall types, but you can anticipate excellent performance of the rain screen version of EIFS, one with cavity drainage behind the foam and an effective air and moisture barrier in front of that. We would not hesitate to use an EIFS based system in the right application. It should prove to be a cost-effective system where barrier-type systems can be used, such as in areas with low amounts of annual rainfall, say, in the range of 10 to 15” (0.4 meter) per year. The structural system can serve as a finish material by itself depending on the product. Concrete or CMU walls, for example, have been used as the exposed finish material since their inception. Architecturally, exposed natural concrete can be a very attractive finish. There are several civic structures in most big cities that rely on the aesthetic of exposed concrete as part of the intended effect. This works well in modern, classic, and brutalist forms, as well as in certain organic expressions, such as the Miami Public Library (see ill. 61). Here, rough-sawn form boards were planned to be part of the finished image of the place. From the moment the forms were stripped, the addition from the late 1970s blended in with the timeless look of the original edifice constructed in the 1960s. The biggest negative of exposed concrete is that in wet climates the concrete is always wet. You can deal with this. It requires additional dehumidification by the building HVAC system and careful selection of wall materials behind the wall. The biggest drawback is the dew point issue and where to put insulation in hot, humid climates. Good design would use concrete outside the air cavity, then the air and moisture barrier on the interior side of the cavity, and then wall insulation. Since condensation in a hot, humid climate is likely to occur at the MRB, that plane would need to have planned drainage to the outside. Setting the drainage plane of the cavity and MRB up so that it drains any condensation down and away past the lowest-level slab is critical. In this scenario, you dry toward the outside from the moisture barrier, as you have been taught. In addition, from the MRB inward, you need to permit drying toward the interior wall finishes for removal by the building HVAC system. No problems. In cold climates, the insulation would be installed on the warm (inside) face of the concrete. The MRB would be at the inside face of the insulation. Condensation would form on the MRB and would need to be dried toward the inside by the building HVAC system. In order to minimize the amount (volume) of the condensation, the building humidity set point should stay as low as practical and healthy for the occupants, say, in the 30 percent RH range. Ill. 61 Miami Public Library, Glass and glazing Some of our favorite skin materials are glass and stone. The physical proper ties of glass now can be modified to achieve things never before possible in construction. Spans, reflectivity, insulation, colors, refractance, thicknesses, joints, and other factors that used to limit applications are no longer obstacles. We can do anything. Our only limits are our imagination and our pocketbooks. Glass now can be engineered to fit the needs of your project. Manufacturers offer a range of colors and thermal performance, a variety of support and joint systems, and many thicknesses. Many of the standard insulating glass projects are based on two layers of 1/4-inch-thick glass with an evacuated void in between. These range in U values from 0.5 to less than 0.29. The lower the U values the better the insulating R values. Some of the better glass has very low ultraviolet (UV) transmittance values, some as low as 1 percent. These can have very low shading coefficients as well. For cold climates, UV values can be more than 85 percent transmittance, and solar heat gain coefficients can be in the 90 percent range. By fine-tuning the insulating and heat gain coefficients you can reduce energy consumption as well as potential condensation in the inside face of glazed systems. Ill. 62 Exterior, Kendall Physics Laboratory in Cambridge, Mass. Projects pushing the limits on glass We want to share with you two outstanding examples of what can be done- in fact, has been done recently-in glass. The first is the Kendall Physics Laboratory in Cambridge, Massachusetts, by Steven Ehrlich, AIA. This project, completed in 2003 uses European terra cotta panels and channel glass (see ill. 62) in an exciting interplay of overlapping planes and cubic mass seen from the outside and from within the space (see ill. 63). A design paradigm was developed to reflect the new technologies emblematic of the biotech world and also to relate to the existing architectural fabric of Cambridge. A kinetic interplay is achieved through planar massing of contemporary materials from Europe. Terra cotta was chosen for its harmonious fit with the traditional brick architecture of the city and its lighter, softer qualities in mass. The material's warm earthiness, in counterpoint to the translucent, fluid quality of the channel glass, forms a composition of Modrianesque syncopation between weight and weightlessness. The project boasts North America's first large-scale panelization of an energy-efficient terra cotta rain screen wall system that covers 40,000 square feet of the exterior in panels of up to 12 feet, 6” by 40 feet in size and 10,800 pounds in weight. The surface patterning of the terra cotta rain screen subtly alludes to the nature of the research taking place within the building. Four textures of the extruded terra cotta tiles represent the four sequencing gels of DNA molecules: adenine, thymine, guanine, and cytosine. This pattern, in taut extruded clay, changes character as the light changes at different times of the day, (see ill. 64). Providing additional variations in light, shade, and shadow are the structural braces that function to support the large overhanging roof plane, above (see ill.65). The second reference project pushing the limits in glazing is the new Beijing Poly Plaza by S.O.M. in China. This project also was designed using a large glass panel system in a contextual manner, as expressed in the study sketch shown in ill. 66. Each facade was planned in response to sun angles and adjacent building forces. As seen from the inside (see ill. 67), this huge expanse of glass provides a unique connection between inside and outside, creating an image statement of clean lines and dynamic expression. This is believed to be the world's largest glazed panel system at more than 100 by 150 feet (30 by 42 meters). Ill. 63 Interior image of Kendall Physics Research Lab. Ill. 64 Variety of exterior finishes represent the physics inside. Ill. 65 Rain screen glazing system and braces. Ill. 66 Plans and Solar study, Poly Plaza. Sunset Atrium; Main Atrium; Secondary Atrium to Provide Direct Daylight to Invigorate Space; Oriented to Provide View of Existing Headquarters and Street Intersection Ill. 67 Interior image of space created, as seen from Walkway. Ill. 68 Exterior of Façade China Poly, a major state-owned company with influence in many market sectors, wanted to create a new landmark headquarters complex that, through its quality and mix of public and commercial uses, would establish a grand civic presence in Beijing, It provides functional and symbolic access for its citizens. The new 100,000 square meter headquarters is located opposite to the existing headquarters building on a prominent intersection along the Second Ring Road, Northeast of the Forbidden City. With its program of office space, retail, restaurants, and the Poly Museum, the new headquarters reflects the project's public mission. The Poly Museum houses one of the most important collections of bronze and Buddhist antiquities in the country. The building's simple monolithic triangular form is based upon an L-shaped office plan enclosed by an expansive, glass cable-net wall. The bars of office space align with the surrounding development while the large atrium looks outward to the intersection and the existing China Poly building beyond, (see ill. 4.68). The design takes full advantage of the natural day-lighting, with the Northeast facing atrium, which is one of the largest cable-net enclosures in the world. This is roughly four times the size of Time Warner Center's cable-net wall in New York City. The use of the cable-net system maximizes the transparency of the glazed wall system (see Ill. 4.67) as compared to a truss or column and beam structural system. Due to seismic considerations, a V-cable system was engineered to allow the main cable to accommodate movement that might result from an event with a specially designed rocker mechanism. The counter-weighted rocker responds to movement caused by wind or earthquakes, giving more or less slack to compensate for movement of the glazed panel. The Museum is the counter-weight, attached to the other end of the cable. The suspended lantern's delicate and luminous qualities call attention to the Poly Museum framed within the main atrium. Public circulation areas and custom-designed lighting occupy the space between the interior and exterior, adding to the play of light, shade and shadow. Through innovation in technology and engineering, a unique architecture capturing the prominence of this stalwart company is created. The rainscreen aspect of the project is almost overshadowed by the prominence, however it will function well as a thermal and water separator to protect people and places inside. Now back to more common applications and solutions. Table 4 Air infiltration barriers Number | Product | Thickness | Air leakage rate, cfm/sf | Tensile strength | Tear resistance 1 Dupont Tyvek 1 mil. 0.04 2 Grace Perm-a-Barrier VP 2 ply 0.04 3 Johns Manville ProWrap 0.017 4 Closed Cell Spray Polyurethane foam 1.5” 0.001 5 Polyethylene sheet 6 mil. 0.0015 Membranes Behind the skin system, whether glass, stone, stucco, or wood, both the drainage system and the rain screen system rely on additional components that form a second line of defense. Rather than count on the coat of paint to stop air and moisture at the surface of the wall, you have additional parts and pieces to perform specific tasks. In the quest to stop liquid water, we recommend the use of a continuous membrane. Membranes come in two main types-air and water. Air barriers are intended to stop or retard the flow of air through them. We refer to them as air infiltration barriers (AIBs). Water molecules can be carried through some AIBs in the form of vapor. The gaseous water molecules of water vapor can move in an airstream through microscopic openings in the AIB. To stop water molecules, both liquid and vaporous (gas), you can use one or more of a very broad family of products referred to as moisture reduction barriers (MRBs). For a chart listing air leakage rates for commonly used air infiltration barrier materials, see Table 4. The number, placement, and performance of these membranes will be of paramount importance for the performance of the building envelope over time. Building codes should be consulted as a minimum criterion for stopping water. Engineered and computer-calculated performance models are only as good as the information being input into them. Designers need to weigh all available data, consider their experience with previous projects, think about the client groups, liability issues, and initial and long-term costs, and make the right decisions. The minimal perm rating of the appropriate membrane for a project can be determined based on the amount of rainfall and the duration of anticipated rain events. The greater the intensity and longer the duration of rain events, the lower is the perm rating selected; therefore, the less water will pass through it. Another consideration must be the type of use for the building and how important is it to you to minimize water intrusion. Is it going to be a laboratory or a hospital? High-end condos on the beach might require a moisture barrier (lower than 1 perm). There is a debate going on as to breathable versus non breathable wall systems in moist, humid climates. It is not as simple as choosing one over another. Many factors contribute to the choice, and initial cost never should be the only factor. Another consideration is the finish going over it. If the surface is metal panels, the only exposure to moisture is that which might get between the panels. For the wet rout and return panels, the risk is minimal. Sealant at the face of each metal panel reduces exposure to and pressures from surface rain. A higher perm rating might be acceptable. For a rain screen system in stucco on block, you might use the best membrane (lowest perm) that you can find. More important than matching the MRB to the budget is matching it to the climate and rainfall data. Other considerations may include the mechanical equipment, insulation, overhangs, available work force, and maintenance. Air infiltration barriers AIBs can take many forms. A coat of paint or a sheet of plywood can be considered a barrier to air. An air barrier function is to resist the movement of air through a material, thereby stopping air pressure. Depending on the system chosen, the AIB must fit the physical requirements of the application. In hot, humid climates, for a rain screen system you are talking about a sheet of thin material that gets fastened to the skin. A 1-mil-thick visqueen sheet stops air movement quite well but has very little resistance to tearing if it's stretched tight. Therefore, it does not meet the physical requirements. For an AIB to work, it must be extended continuously from floor to roof. This means stretching over corners, where puncture resistance is important. Reinforced AIBs, such as Typar, effectively reduce punctures owing to the fabric fibers in their makeup. The roof needs an AIB sealed to the wall membrane. For a crawl-space first floor, the AIB must extend under the floor area and be sealed to the walls, including penetrations. The slab on grade condition can be detailed with a 2-inch over lap of material taped or otherwise sealed to the concrete below the finish floor. For the AIB to perform to its fullest potential, the fastener penetrations should be sealed as well. Several means for sealing the fasteners are used, including special nails with an oversized washer that closes off the penetration. This is more important in coastal zones with high wind speeds and in cold, wet climates where snow can build up against exterior walls. Any voids in cold climates can allow water vapor penetration, which can freeze. This freezing action causes water to expand, further enlarging the voids. The main purpose of an AIB is to help create an airtight seal around the exterior. By controlling leakage, you can efficiently control humidity, temperature, and creature comfort. Drafts can be especially troubling in cold climates. The doors, windows, and other components that interrupt the AIB need to be considered as parts of the AIB system. Louvers through the envelope need to be ducted tight to the building air-conditioning system or they become points of admission for air. Attic vents, soffit vents, and similar openings should be closed to the indoor environment. The intersection between the AIB and other components must be an airtight seal as well. Tapes are available from most manufacturers to seal between the AIB membrane and other materials such as metal. Depending on the design, you may choose an AIB that allows vapor dif fusion through it. This can help drying in some conditions. An AIB, if used, should be at least four times as vapor permeable as the vapor barrier. Roof membranes that serve as continuous AIBs are being used more commonly in hot and cold climates. Self-adhesive membranes (SAMs), which were developed specifically for roof underlayment, such as W. R. Grace Ice and Water Shield, are also being used in wall installations as air and vapor barriers. The self-sealing aspect of SAM products makes them desirable. Moisture-reduction barriers In Florida, especially near the coast, many designers try to create barriers to water and vapor transmission. They rely on continuous and well-sealed membranes with low perm ratings. The goal is to limit the number of grains of water that enter the envelope to the lowest total. One approach is to try to seal the envelope and pressurize it from the inside with the building air-conditioning system. Therefore, you must strive to seal from the lowest point of the pressurized envelope to the highest and around all four sides. Other designers choose to use permeable wall systems that permit moisture through the wall system, just in some limited designed quantities. One rule we can agree on for all climates is that the permeability should increase as you move away from the MRB. There should be only one low-permeable material in the wall section, and materials should increase by a factor of 4 to 10 in both directions from there. For a table showing perm ratings of stated products refer to ill. 113. There is no one way that works well for all building materials; however, you can group all MRBs into two major headings-sheet or liquid-applied membranes. It is obvious what the apparent differences are-their physical states are different. Sheet membranes are solid when applied, and liquid-applied membranes need to cure before they become solids. Sheet products are made in factories with con trolled environments, and thus they have very consistent thickness and com position. Their quality-control practices are quite good. Sheet membrane's perm ratings are achieved in the field consistently and can be relied on regardless of the installer. There may, of course, be differences in the joints, cuts, and seams from individual to individual, but the sheets themselves are quite dependable. For these reasons, sheet membranes typically are preferred over liquid-applied membranes in hot and humid climates. Liquid-applied membranes in warm climates are mostly used on horizontal surfaces where they can flow to fill difficult to reach areas, and are seldom exposed to the direct heat of the sun to avoid creep. Some sheet membrane materials you may be familiar with are tar paper and visqueen. Liquid-applied MRBs you might know include paint, sealers, and bituminous and rubber coatings. These typically are applied with roller, brush, trowel, or sprayer. Liquid products need to be applied over the right kind of material in a uniform thickness in order to have a consistent perm rating. There are many advantages to liquid-applied products, including their ability to flow into voids, corners, and tight spaces. Since they are applied in a continuous coat, there are no laps and cuts to worry about. Each MRB has different benefit versus-cost considerations, so designers and specifiers must fit the product with the client's needs and budget. Over the years, manufacturers have continued to improve their product lines to meet the ever-growing need for moisture-control products. SAMs were developed in the 1990s in response to the need for easier application of membranes over large vertical surfaces. A very small crew can install SAMs without having to fasten them as they go and at the same time avoid sagging. For applications over nonporous materials, manufacturers recommend using their own specially formulated primers. These primers significantly increase adhesion to almost any material, including lapped edges of SAM to itself. Penetrations from fasteners seal themselves. Imagine how many nails, screws, and staples get installed in a building facade. Assume that there are about 4,800 per wall. If you multiply 4,800 times an average tear or rip of 1/8 square inch, you would have a total opening size of 600 square” or just under 5 square feet (1.8 square meters) per wall. This is especially meaningful near window or door openings, where you frequently get a concentration of fasteners and where so many of the leaks originate in buildings. The self-adhesive and self-sealing qualities of SAMs (also referred to commonly as "peel and stick") provide the construction industry with a whole new solution set for tightening up the envelope. Just like everything else, though, it must be done right. In order to take advantage of the adhesive properties, the surface below must be dry and clean. If it's dusty or porous, prime it first to remove loose particles. Then, after every application of SAM, it's very helpful to use a special roller created by the manufacturer to apply pressure evenly in an attempt to force out bubbles and complete the adhesion process. It is not enough just to smooth the SAM with your hand and walk away because it looks good enough. To take full advantage of the inherent properties, use the roller at every joint and over strategic portions of the entire surface, (see ill. 69). This will minimize sagging over time. At least one manufacturer now offers pre-primed glass fiber impregnated sheathing. This will prevent you from having to prime sheathings, but needs to be protected from dirt and dust to maximize adhesion to the SAM. Ill. 69 Tool for applying SAM. Improvements in the SAM family have been well received. SAMs now have such refinements as foil facing bonded to them. The foil-faced SAM can be used when you expect it to be exposed to UV radiation or for aesthetic purposes. Aluminum faced SAM can be used in the corners of sill pans to be more dimensionally stable and resist puncture better. Another good place for foil-faced SAM is where sealant will be in contact with the SAM. To continue on with the theme of the right way to apply SAM at windows, please review the next two photographs beginning with ill. 70 showing the right way to install SAM stripping at a window opening. We begin with this example of a fin-type aluminum window. Note the plywood sheathing around the perimeter to accept screw fasteners along all four sides. Ideally, these screws also penetrate the metal framing, however that's not necessary if jamb or head and sills are fastened through the extrusions. Ill. 71 SAM window wrap, step 2. As work progresses, pieces of SAM are applied over the primed surfaces, being careful to extend past the edge of wood sheathing onto the fiber reinforced gypsum sheathing a minimum of 4” (10 cm), (see ill. 71). Make sure sharp edges and fasteners are smooth and will not tear through the membrane. Take your tool, and work out all voids and bubbles in the applied membrane. Ill. 70 SAM window wrap, step 1. For best protection, install head flashing and strip it in with another layer of SAM. Now you are ready for application of air barriers, and finish materials, in many cases leaving space for a sealant joint around the frame. Due to the fin-type window flanges we have a redundant air and water barrier system that will perform well for decades to come, even without sealant. Depending on the wall type, climate, budget, and client (again), you may choose to use the MRB as an AIB as well. Several recent articles mention their acceptance of the use of an MRB on only a portion of the envelope. The articles go on to discuss the fact that the total volume of water in the building is a function of both the surface area of membrane and the perm rating. What they fail to discuss is that anyplace the membrane is not installed, you have created a concentration of water molecules, not to mention vapor-driven dynamics resulting from the pressure gradients along the border. Once in the walls, that moisture will be able to move to locations where the conditions may be ripe for condensation. If you are going to limit your SAM applications, we recommend you use it at windows, doors, and all other locations with concentrations in the fasteners or in proximity to grade. In cold climates, where your concern is snow piled up against a wall, this may make some sense to some of you. The approach would keep the moisture in that location from moving through the wall, but it still doesn't make sense to me. In cold climates, you place the MRB on the inside of the insulation, so that scenario won't work well. Perhaps in mixed climates in the winter time it would make more sense, but in either cold or hot, humid climates, we recommend that the MRB be extended to every part of the envelope. For this reason, in temperate, humid climates with fewer than 20” (0.5 meter) of average annual rainfall, with a good HVAC system and good insulation, it may be acceptable to use a partial MRB to save a few dollars on initial cost (if you have to). We are just not proponents of doing anything halfway. If you're going to use an MRB, use it everywhere. This is, in our opinion, just as important as insulating the complete envelope. |
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