From a thermal efficiency standpoint, substandard roofing envelope insulation is a major factor contributing to heat loss in residential and commercial buildings. Another important aspect of the challenges associated with planning and building roofing envelopes is the presence of skylights. In typical situations, roofs can generate a heat loss of almost 30% [1] from the total heat of a residence, whereas the presence of skylights pushes that figure to 35%-45% [2] more than a corresponding surface window laterally positioned on a building façade. The phenomenon is attributable to the existence of convection currents, which play a key role in the thermodynamic behavior of the air present in enclosed building spaces. For this reason, skylights are sometimes anecdotally called sky warmers.

Based on customer preferences, roofs with skylights have secured market prevalence in recent years, which transforms them into a significant problem for HVAC engineers of today. The frequency of skylight installation on buildings has increased because they are a widely used method for improving surface utility of residential buildings and psychological comfort of inhabitants. Due to modern consumers, skylights are no longer a mere occasional nuisance in construction works and require special precautions in the planning and installation phases to prevent heating, cooling, and humidity issues during the exploitation period. Furthermore, skylights are sometimes the sole source of natural light in industrial settings, such as warehouses with large footprint and no interior courtyards.

At the same time, there is a great variety of roof types which allow architects and structural engineers to select the optimal envelope for a given construction. However, each of these roof types encounters its own associated planning, material, and structural challenges. One of the most widely known issues involving structural and integrity calculations is beam deflection observed in large, unsupported sections of envelope, or in cases of positive and negative (uplift) structural loads. Several landmark formulae are briefly presented and discussed here.

1.1.                      Scope and Objectives

The purpose of this whitepaper is to provide a comprehensive – albeit not exhaustive – overview of the specificities associated with roof envelope planning, construction and maintenance. The major themes in this area are touched, while some minute details are left unexplored and can be used as a source for future papers. The discussion in section 2 is structured around several roof types and the associated planning challenges. From a resistance and load calculation perspective, the paper presents considerations regarding flat roofs and metal roofs. Known to deflect and fail due to light steel structures, flat roofs can be approached with numerical methods which correctly predict the envelope behavior from stages previous to construction. Metal roofs assembled from modular components have been tested for strength and resistance to dynamical and static direct loads. The testing of modular metal roofs and seams has been achieved by dynamical and static water penetration tests. The specimens have been subjected to uniform structural load test. The results are presented in subsection 2.6. Furthermore, experimental testing was executed for rafter to ceiling, roof to wall, and toe-nailed connections and joints. The empirical results are shown in the same subsection.

From a construction material perspective, natural materials such as wooden tiles and slate can be used to achieve different architectural visual aspects and different roof lifetimes. Another aspect of roof construction material is the increased albedo and the microclimate their presence can cause inside dense urban areas. This propensity can be countered by the implementation of cool roofs and photovoltaic roofs, the secondary category having many other advantages beyond environmental temperature control. The second chapter of the paper is centered on construction planning and material considerations regarding these roof types. In the same section, a brief portion is dedicated to a few aspects regarding workforce safety and accident prevention. In section 3, opto-photometric tests results of skylights are presented, along with other considerations involved in planning. The results of three testing situations on skylights are discussed in the same sections, along with the theoretical considerations necessary during the planning phase. Domed skylights are treated separately from flat skylights.

2.    Roof Scenarios and Common Planning Considerations

Various roof scenarios are considered here from multiple perspectives. Structural considerations are discussed in this section, such as flat roof structural integrity problems due to water ponding. Planning considerations presented here regard the urban microclimates that can be controlled by a certain amount through cool and photovoltaic roof implementation and subsequent albedo reduction in the area. From a roofing material standpoint, high durability slate roofs have been abandoned in the last century throughout North America, resulting in a decreased body of knowledge about surface integrity and wind load calculations. This problem is addressed here by means of presenting British standard BS 5534.

2.1.          Flat Roof Strength Shortage Failure Modes

Large flat or extremely low slope roofs are encountered on public buildings, warehouses, shopping areas, and factories. The light structures presently used for such spaces are sensitive to long lived loads cause by precipitations. The ponding causes a vicious circle of incremental increases in deflection in a non-linear manner. Various national building codes address this problem in different ways, such as requiring a slope, however in practice the structures can still fail due to extremely adverse weather. Another possible cause is the incorrect placement and design of emergency drains.

The structural integrity of flat roofs is primarily affected by stationary loads causing incremental stress for prolonged periods of time [3]. An example of such stress is rain water ponding. This type of stress can lead to roof failure by two distinct action mechanisms, strength failure and stability. The first failure mechanism is known to structural engineers as a nonlinear problem modeled by means of the equation Royal Roofing Blog for a uniform surface load q. The applicability of this approach encompasses sloped and horizontal roofs, envelopes showing initial camber and deflection from long term loads, and roofs with primary and secondary members including profiled steel sheets.In the case of stability problems generated by ponding, a verification of the ultimate capacity is necessary and presented here. The purpose of this estimation is to serve designers, while being based on a previous paper for structural engineers. The features of this estimation are briefly discussed, while providing points of interest for code developers and structural engineers.

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Fig. 1. Steel sheeting; primary and secondary members

For simplification, a regular rectangular shaped roof is considered. The structure of the envelope with sheeting and primary and secondary members is shown in the next figure. The notation represents steel sheeting span by lsh, primary member span by lp, and secondary member span by ls. Unless otherwise stated, the working assumption is that the secondary members, on which the secondary sheeting relies, are directly supported by primary members. Due to their limited stiffness, normally all the components in roofs show deflection. For simplification, perfectly stiff roof parts are considered, with the secondary member representing a beam supported directly by rigid supports, the beam being horizontal and showing no deformation. Unless otherwise stated, the subscript s will be eliminated from the discussion but remains implicit.

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Fig. 2. From left to right. Initial state; actual deflection; idealized deflection due to loading

The length of secondary members is denoted by l, and the separating distance by a. The assumption is that the regular drain system is clogged and the emergency drainage is present at the roof edges. In this scenario, equilibrium stable states are assumed to exist for a liquid level denoted by d above the structure, as depicted at the left of the following figure. The liquid depth is the initial condition before any bending occurs.

The deflection distance is denoted by Royal Roofing Blog-5 and the shape contains liquid. The beam load is now composed of two contributions, one with homogeneous distribution on the span d, and one which can vary over the span Royal Roofing Blog-6. The next part assumes substitution of the varying contribution by a constant which is statistically equivalent, with liquid depth δ. Taking into consideration a sinusoidal shaped deflection and a given liquid weight Royal Roofing Blog-7 results in a configuration of half-sine bending with a maximum Royal Roofing Blog-8. The moment of the distributed load is Royal Roofing Blog-9. Setting the momenta as equal gives us Royal Roofing Blog-10. The applicability of the 0.8 factor spans beyond simply supported members and holds true for other various support conditions.

Since the shape is the same for initial and additional liquid weight, the weightless piston and spring model can be introduced. Parameter d includes the liquid height above emergency drain that is necessary to ensure evacuation. The average displacement δ was just discussed. When the piston force is above a certain level, the friction elements will start slipping, consequently the setup reaching its superior strength limit.

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Fig. 3. Without and with water piston model of a roof component

Two useful values can be calculated in this situation, W and D, where W is the weight of a liquid with height of 1 meter above the piston (in kN/m), and D is the rigidity of the spring (also in kN/m). Subsequently the load/resistance relation can be written as:

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where the first equation represents the liquid load and the second represent the roof ability to withstand a certain distributed load.

W can be calculated immediately by plugging the value of the area al of the roof section assigned to the individual roof component:

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A derivation for D can be found in [3]. The formula is:

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where El represents member flexural rigidity.

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Fig. 4. Visual representation of the relation between the loads

The weight load equations find a representation in F w space in the figure above. The parallel lines can only meet if deviated such that D > W, otherwise they meet an infinity. Therefore a dimensionless parameter n can be introduced to represent the stiffness, n = D/W. Equilibrium states only exist for n strictly larger than 1. The intersection at the left of the figure represents one such equilibrium state. The following formulae can be derived, where the multiplicative factor of d is applied to the initial liquid load before ponding:

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Liquid accumulation is checked starting from a span l, spacing distance a, rigidity El, and liquid height d. The next step is to compute n, then the multiplicative factor in the equation above, resulting in a liquid column w by multiplication of the above equation with d. The liquid load can be found, and subsequently the bending moment M can be calculated as:

 

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The value obtained here must be added to the permanent bending moment. Regarding the calculation of n, derivations show it can be alternatively treated as:

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The critical points of Elcr are dependent on the specific liquid weight and the situational geometry. The literature typically assumes a sinusoid shape of the bending, which results in a factor of 4p instead of 96, however the two values are close up to 1.5%. At the same time, both values depend on the assumption that was made, and the situation leading to 96 is more general.

A complete treatment of deflection and camber, calculations for a variety of member end conditions, and composed roof geometries can be found in [3].

2.2.          Low Albedo and Photovoltaic Roofs Simulations

Cool roofs, and pavements and asphalt surfaces, reflect more solar energy back into space compared to the ground that they replace. In recent research [4] results suggest that the solar reflectance for averaging roof material is approximately 0.2, and in comparison cool roof has a solar reflectance of 0.5-0.6. Cool roofs have been found to provide electrical energy savings in theoretical [5] and in field [6,7] research. Consequently because of this well-established effect, policy has been adopted in the United States and the European Union [5][6] to reduce energy usage by installing cool roofs. Cool roof material has been researched for decreasing the urban heat island effect, for decreasing the level of ozone (O3) in the atmosphere [11], and on its effect on radiative forcing in the Earth climate system [11][12][13]. There has been extensive research on the importance of surface albedo in the urban heat island effect, such as atmospheric cooling as a result of the installation of greenhouses [14] which have a high albedo. Another study [15] found that there is up to a 2 oC temperature decrease in maximum temperature in urban cities in California, and these results are corroborated with research studies in different cities [16][17]. Similarly at 2 oC temperature decrease in maximum temperatures in Atlanta was found [18]. However for studies in other cities, for example in Houston, Texas, an increased albedo did not produce a decrease in temperature [19]. For theoretical simulations run by [10][17][18][19] over a period of up to four days with 4 km resolution, showed the impact of factors such as urban topography and vegetation. It is possible that these simulations do not show feedback effects that become significant over longer periods of time and larger geographical areas.

Using the radiative transfer equations a study [11] found that if roof and pavement albedos are increased to 0.25 and 0.15, then average global radiative forcing can be decreased by 0.044. In another study [12] the urban reflectance was increased by 0.1, to simulate roofing and pavements with high higher albedos, and modeled an increase of 0.5 W/m2 in reflected radiation over worldwide land regions. In this study the researchers used a simplifying assumption where the land was not coupled to the circulation, so feedback effects were ignored. In other research [13] the urban land and atmospheric circulation were coupled to model cool roof replacement worldwide. Their results showed that urban heat island temperatures were decreased by 0.4 oC when albedo was set to 0.9. Feedback was again not modeled used to lower resolution modeling.

An important recent study [20] looked at the effects of urban albedo, localized feedback with the atmosphere over monthly to seasonal periods, and an extrapolation to continent-wide effects. The researchers also investigated changes in desert climates due to decreases in albedo caused by photovoltaic arrays. In the former urban albedo study, a localized atmospheric model was used with a coupled land-atmosphere system and a land area equivalent to the United States with a resolution of 25 km. Another interesting study [21] made a comparison, using simple equations, between a decrease in radiative forcing due to photovoltaic power plants and an increase in radiative forcing due to the lower albedo of the photovoltaic cells directly. The researchers found that the difference between these two counteracting effects was that the photovoltaic power plants were a factor of thirty times more important.

In the recent study [20] the researchers used a coupled land-atmosphere model, to investigate the effects of lower albedo in the California desert due to a terawatt capacity photovoltaic power plant (PVPP). The PVPP would be designed to decrease a billion tones of annual CO2 emissions [21]. There was an investigation into the localized and larger region effects on the atmosphere and radiative forcing.

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Fig.5. Right: A twelve year difference for control minus cool surface models, at 2100 UTC, 2m air temperature in Kelvin. Hatched parts are two standard deviation confidence intervals difference from zero. Left: The continental region.

The other goal of the study was to investigate localized climate effects from the installation of cool roofs and pavements. For the ten largest cities in California the average temperature decrease after midday were 0.22 ? 0.13 oC in the summertime and 0.18 ? 0.02 oC in the wintertime under the cool surface model. The value uncertainty in the given temperatures are calculated using standard deviation. Urban areas generally did not a show large increase in temperatures after midday under the cool surface model. The coupled land-atmosphere model allowed the investigation of feedback effects in the atmosphere. These effects included the temperature and radiative forcing due to increased urban albedo in the summer months, and these effects increased or decreased depending on the area. When these feedback effects were investigated it was found that there was a larger decrease in temperature and radiative forcing with the cool surface model in contrast to studies done previously. The carbon offset due to raising the urban albedo was 3.3 ? 0.5 billion tons of CO2 which is equal to 175 ? 33 kg/m2 of unit roof surface, with a two stand deviation confidence interval. The PVPP gave a localized temperature rise of 0.4 oC. In contrast to the cool surface model, the PVPP did not come with changes to radiation emission over a state-wide land area. The PVPP did show high annual volatility over state-wide regions which dominated localized effects.

2.3.          Cedar Wood Tile Roofs Installation

North American architects typically specify in building instructions shingles and shakes originating from three species, commonly included in the building code requirements: yellow cedar, redwood, and western red cedar.To meet these standards, wooden tiles must follow certain quality specifications. Prior to acquisition, the material needs to be checked for adherence to the local standards. Along with products installation and maintenance, quality standards secure roof lifetimes of up to 30 years [22].

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Table 1. From left to right: Yellow cedar, western red cedar, and redwood roof tile description and grading. Northern white cedar roof tile description and grading.

The product selection is based on the product grading, listed in decreasing order of quality in the above table. In most cases, the product lifetime is directly proportional to the quality of the initial acquisition. Heartwood tiles and preferred to sapwood tiles, due to their longer service time and resistance to decay. Vertical (edge) grain tiles are superior to flat grain, since product stability ensures a smaller chance of warping and splitting. For similar warping and bending considerations, narrow but thick tiles are better suited than wide and thin ones. Some local building codes may require fireproofing and preservative treatments, which are recommendable for implementation even in cases when the building codes do not require them specifically, for obvious reasons. Different manufacturing procedures imply further benefits. Wood tiles that have been produced by splitting expose fewer sectioned wood cells to weathering and reduce water permeability as opposed to sawn tiles.

The standard commercial size for shakes is 18×24? (or 457mm x 610mm), with different sizes available on order. They come in three varieties according to manufacturing procedures: hand-split (split face, sawn back), tarper-split (both sides have been split), or tarper-sawn (both sides have been sawn), with all types available in 2 different grades (Premium and No. 1). The grading benchmark is based on flaws, proportion of heartwood to sapwood, and grain angle (see table). Premium and No.1 shakes are treated with fireproofing solutions or flame retardants.

Shingles are thinner than shakes but still graded according to the same benchmarking principles, into 4 grades: No.1,2,3, and 4. No.1 must be manufactured entirely from heartwood, vertical grain only, and completely free from imperfections showing as knots.Flat grain, imperfections, and sapwood are expected to show in lower grade shingles. Only No.1 graded shingles are treated against fire. The thickness parameter describing shingles is a number describing the butt-end thickness for a specified number of tiles. A 18? x 5/2 ?? description means that for every 5 tiles the total thickness is at least 2 ??.

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Fig. 6. Installation of 2-ply shakes with interlaid felt, with spaced sheathing

The installation of wood tiles is typically executed over a substrate of solid deck or spaced sheathing. In humid climate, rain screen systems or spaced sheathing have been preferred, whereas dry climate sees mostly solid sheathing with wood tiles directly applied on top. Regions with intense winds carrying snow require shakes to be installed with plywood solid decks. During installation, the grain angle, relative humidity, tile width, and spacing must be taken into consideration to allow for seasonal variations without damage to the roof surface integrity. Vertical grain tiles absorb less water and swell less than 50% compared to flat grain tiles, whereas wide tiles require more expansion space than the narrow ones. Typically tiles installed in ideal conditions, such as environmental moisture at about 12%, are in equilibrium with the ambient from a humidity perspective. In this case, shakes have to be installed between 3/8? and 5/8? apart (or 10 to 16 mm). In the same conditions, shingles require a spacing of 1/4 to 3/8 (or 6 to 10 mm). In low moisture content, the extra space should be proportionally enlarged, while in high humidity the spacing should be slightly decreased.

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Fig. 7. Installation of shingles with spaced sheathing

Spaced sheathing. A traditionally used method, it implies the tiles to be attached to boards (1×4? and 1?x6?) which are attached horizontally across the rafters of the envelope. Better performance is seen when this system is used together with a ventilated attic. Shingles and shakes need to follow different installation steps. In 2-ply installations, shakes have to be interlaid with asphalt bearing felt, to prevent infiltration of precipitations carried by wind. In 3-ply installation, tarper-sawn shakes can be installed without felt, whereas split shakes require a layer of felt. A complete discussion regarding the installation of shakes can be found in [23]. Shingles require a 3-ply installation without felt interlaying, which leads to rot felting due to slow drying.

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Fig. 8. Shakes with rain screen on solid deck

Solid deck underlayment. Wooden tiles can be installed over solid decks by means of direct application, rain screen, or strips with horizontal attachment by nails. The deck sheathing is commonly realized by plywood in recent years; typically at least 3/4? (or 19mm) thickness should suffice for proper nail anchorage or thicker, even if local regulations permit less thick plywood. Thinner plywood raises the likeliness of failure after shorter service lifetimes. The best methods however are the horizontal nail strips and rain screens due to improved ventilation. All wooden tiles require anti-aging treatment prior to installation in highly humid climates.

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Fig. 9. Shingles with rain screen on solid deck

Rain screen over solid deck. The method allows for better water insulation by creating a second barrier, and for better ventilation. The rafters support a layer of sheathing, after which vertical spacers are attached to the solid sheathing. They support a layer of horizontal nailing strips on which the tiles are fixed. The tiles must be attached by stainless steel or galvanized screws long enough to pass through the spacers and be partially inserted into the rafters. For slopes smaller than 3:12 for shingles and 4:12 for shakes, the method requires a membrane, such as interlaid felt, over the decking. Felt can be used with shakes but other types of membrane have to be identified for shingles, using the local building codes.

Direct application and horizontal nail strips. These less complicated attachment techniques are briefly described in [22].

2.4.          Slate Roofs Revival Considerations

Although declining in market adoption since the start of the 20th century, slate roofs are long lived solutions that are presently making a comeback triggered by the necessity to reinstall and repair existing roofs. Adaptable and permeable to air, roofing slate is also a long lived product. However, new methods and standards have to be found, along with a revisiting of past methods.

Slate is a metamorphic, micro crystalline rock composed of quarts, micas, and chlorite, and obtained from shale. The roofing variety is a naturally dense and fireproof material with high durability and low permeability to water. After weather exposure, some types of slate will harden. From an architectural perspective, the variety of slate types allows for diverse finished aspects. Through its presence as a roofing solution on historical monuments, slate proved to be able to survive weathering for times longer than one millennium.

The roofing option has been present in Europe and America throughout the 19th century, sustained by a skilled labor pool with the ability to install and maintain slate roofs however the demand started sinking in American, with a 90% drop over the past century, as reported by the Bureau of Mines. This tendency is due to the preference for lower cost alternatives that slowly replaced exceptionally durable but more expensive materials. At this point, only 2% of the American re-roofing market is represented by slate along with only 3.5% from the new roof installation market. Europe, on the other hand, still prefers this material, France singlehandedly being responsible for a slate consumption 9 times larger than that of North American, with a comparative population of only 18% of the number of people on the North American continent. As a consequence of the decline in use, the American standards have not been recently updated, while the skilled labor necessary for installation and maintenance is virtually non-existent.

The British standards such as BS 5534 require specific wind resistance for slate roofs, and the benchmark is based on air permeability and air flow through the discrete elements composing tile and slate roofs. The distribution of air flow loads is different between tile assemblies and monolithic roof structures. In 1991, the design and testing method has been brought to North America through the Redland Report [24]. The approach assumes a zero sum of forces about an axis and is modeled as an equation of motion on a rigid surface. The negative (uplift) pressure is equivalent to an upward pointing vector at the wind facing edge rather than a constantly distributed pressure for the entire area. For the unit area, the air current load q acts on discrete roof elements on an area calculated as the cover width b, a leading edge length c, multiplied by the step height t between courses, resulting in an equation modeling the force as Royal Roofing Blog Photo-15.

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Fig. 10. Exemplification of equation of motion on discrete rigid slate roofs

This analysis allows designers to treat the problem of wind resistance by usage of vector force and establish the moment of resistance necessary for attachment, while at the same time analyzing negative pressure on clips and fasteners.

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Fig. 11. Clip and track fasteners

The main reason for slate roof failure is typically given by slate tile perforation and attachment. For this reason, automation in perforation techniques improves the durability and lifetime of the finished roof. Air circulation can be improved by clip and track attachment fixtures.

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Fig. 12. Installation of spaced sheet

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Fig. 13. Problems caused by improper nailing and comparison to proper attachment

2.5.          Workforce Safety Considerations

The 21st century saw fatalities in the construction field decreasing by 33% in the first decade however it is to be noted that this occurred simultaneously with a drop in the number of hires in construction accounting for 18.7%. Between 2000 and 2006, the employment increased by 13.3% and fatalities increased by 7.4%. In the next four years, employment saw a decrease of 28.3%, while fatalities dropped by 37.5% [25][26]. Starting with 1992, three major work accident categories were marked by decreasing trends, namely homicides, highway accidents, and accidents dealing with being struck by an object. Falls followed an opposite trend and raised from 600 to 635.

In 2010, the total private sector fatalities were 4,206, and 18.4% of these originated in construction works. Construction was the number one sector for 15 private sectors to account for fatalities, and number four from a perspective of rates of fatal injuries. In the same year, falls represented the cause of death for 14% of the cases. Out of this number, 18% of the falls involved roofs, and 57 of those deceased were identified as roofers by occupation. Among roofers, there are 32.4 fatalities for 100,000 workers, making roofing 9 times as dangerous as the private industry average, and 3.3 times as dangerous as other occupations from within the construction sector.

Recently a study was made regarding the circumstances leading to fatalities in construction of residential roofing envelopes [27] at a request originating from OSHA. For this purpose, 112 cases were investigated regarding the conditions surrounding each fatal event. The cases occurred between 2005 and 2010. A number of options for protection have been presented and are believed to reduce the number of fatalities if implemented at construction sites.

For low-sloped roofs (<4/12 slope) the recommendations are: a) a rope of wire bearing signaling patches of brightly colored material should be positioned 6 ft. (or 1.8m) from the edge at a height of ~36.5? (0.8m); b) construction sites should ensure the presence of a skilled safety monitor with no other duties.

For roofs with higher slopes (>4/12) the recommendations are: a) slide guards positioned parallel to the roof edge and secured with brackets , for heights no larger than 25 ft. (or 7.6m) and slopes <8/12; b) mandatory harness systems used to stop falls and secured to the roof.

The causes of fatal accidents are outlined based on an industry snapshot extracted from the cases that have been studied. These causes can be characterized as follows:

a)      Dangerous activity environment for construction operations. Over 60% of the cases that have been documented were related to slopes larger than or equal to 3/12. The slope was greater than 8/12 for 20% of the documented cases.

b)      Grave injury and fatalities are ensured by fall on distances larger than 15 ft. (or 4.6m). This was the case in 75% of the situations.

c)       For half of all fatalities, the employees were not skilled and undertrained. In fact, a percentage as large as 10% of the workers involved in fatal accidents had a total experience in the environment of less than four weeks.

d)      The population of workers in the study has a large Hispanic element, approaching 37% comparative to a Hispanic presence of 25% in the overall construction industry.

2.6.          Experimental Testing of Roofing Envelopes

Experimental results of a variety of tests are presented in this section. The first battery of tests regards an experimental verification of the metal sheet roof panes commercially available at present. Static and dynamical loads testing have been executed, as well as deflection and uniform structural load tests. These tests have been required and supported by the Sheet Metal and Air Conditioning Contractors’ National Association, Texas.

2.6.1.      Metal Roof Testing Under Static and Dynamical Conditions

Successfully installed throughout the last hundred years and covering hundreds of thousands of square meters, metal roofs with batten and double lock standing seams are now found in prefabricated, ready for installation modular arrays. The SMACNA Architectural Sheet Metal Manual discusses several roof geometries which require laboratory experimental testing after roof assembly from component parts, to ensure the adherence of the prefabricated parts to the standards of the Sheet Metal and Air Conditioning Contractors’ National Association.

For this purpose, specimens constructed according to the Manual have been tested at CCLC (the Construction Consulting Laboratories in Carrollton) in Texas. For internal construct validity and ethical considerations, all the phases of testing have been supervised by a committee composed of members of SMACNA. The aim of the tests was to evaluate the performance of the specimens in conditions that are more severe than those encountered in typical settings or needed in the industry.

The evaluation was made on 1 ?? batten and 1? double lock standing seams. Both unsealed flat lock and soldered form were applied to transverse seams. Despite lack of guidelines for controlling air leaks in the SMACNA manual, initial air infiltration and exfiltration tests were attempted. However, due to technical issues related to the chamber calibration, the results have been deemed unreliable and subsequently discarded. A notable exception is the observation that fascia edge behavior shows increased air leaks as compared to surface seams.

The specimens have been target to static water pressure and penetration empirical conditions. Curtain walls are typically subjected to similar experiments and the battery of tests in this case has been chosen based on severity and destructive potential. The next stage was conducted by means of a turboprop engine generating dynamic lateral air current loads, whereas a constant water stream was left to cover

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Fig. 14. Specimen configuration details.

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Fig. 15. Specimen configuration. Ridge, eave and rake.

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Fig. 16. Cross-sectional details.

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Fig. 17. Transverse joint, ridge, gable, eave.

the other side of the test specimens, to evaluate the potential air flow through the joints. The third text was executed by means of vertical structural loads in both directions orthogonal to the ground, by lifting and pushing onto the specimen surface. The pressure was created in incremental manner to evaluate the roof geometries and check whether they can stand pressure above the UL90 standard requirements. A complete discussion can be found in [28].

The tests were ran on specimens 6?x19?5? and roof pitch 4/12, with a seam height of 1? double lock standing and 1 ? batten, and pan width of 20.75? at the center and 15.25 at the rakes. Fasteners have been chosen as standard 2? cleats, and fixed with two shank nails each. The specimens have been tested with various underlayment substrates: 2 overlapping 30 lbs. felt; APA-rated plywood with number 12 fasteners; 3.5? laminated iso-cyanurate insulation with number 12 fasteners; 1.5? steel deck previously attached to the structure by welding.

2.6.1.1.             Metal Roof Testing Results

Results of static water penetration test. The current test has been chosen based on close resemblance to the ASTM E331-86 used for curtain walls and has been performed as a vacuum chamber test equivalent to 2? hydraulic head with a constant flow (10.4 psf), for a duration of 15 minutes. The test simulates severe storm with rapid wind direction change and high lateral loads in bursts. Slight infiltration has been observed at the rake and eave joints with the test chamber, infiltration which is attributable to the fascia joint bearing imperfect connections. No infiltration has been observed on the surface of the metal roof. Testing has been visually supervised from inside the chamber.

Results of dynamic water penetration test. The rapidly changing loads and total water exposure in this test is similar to rainstorm effects on metal roofs. The current test has been chosen based on close resemblance to the Standard 501.1-83 used for curtain walls. 5 gpm/sq. ft. water lateral load has been simultaneously applied with an 82.5 mph average air current load produced by a turboprop engine situated 20? away from the roof eaves. The dynamic load testing has been ongoing for 15 minutes and visually supervised from inside the chamber. Infiltrations have been noted again at the joint and are due to improper connections. Deformation or other types of damage have not occurred.

Results of deflection and uniform structural load tests. The roof systems have been put to test by both positive and negative loads (uplift), the latter having been performed by vacuum ducts and pumps installed at the top of the pressure chamber. The applied pressure was released after 10 seconds and was of 20, 40, 60, and 90psf respectively for each load interval. The stainless and galvanized steel, the copper batten, and the aluminum seams have been put to a negative load of 150psf, whereas another run of 190psf has been applied separately to the copper and stainless steel with the purpose of causing structural failure. This did not occur prior to reaching the upper capacity threshold of the pressurization machine. Close visual inspection revealed that no structural damage, joint damage, or permanent deformation have occurred in the roofing systems put to the test. Deflection measurements at the center and seam of the modules showed non-permanent deformations during test of 3/4? deflection at pressures above 125psf.

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Table 2. Maximum test loads

2.6.2.      Testing of Framing Joints in Conventional Residential Roofs

Together with the U.S. Department of Housing and Urban Development, the National Association of Home Builders performed a series of tests to assess structural performance of roofing envelopes used in residential buildings. The goals were: to test the rigidity of ceiling to rafter connections or heel joints built with pneumatic and hand driven nails; to test the shear in roof to wall joints with a shear direction pointing downward; assess the limits of the methodology derived from yield theory for connection capacity predictions. For this purpose, an equation for load displacement in yield mode has been formulated for a single-shear joint bearing symmetric bolts. Validation was made by means of comparison with other experimental results. The contributions of this formulation have two sources for the resistance Pjoint:

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where:

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2.6.2.1.             Testing Rafter to Ceiling Joints

The tested connection is depicted in the images below.

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Fig. 18. Benchmark setup

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Table 3. Specimen configuration

The test was done on a roof consisting of two parallel trusses, totaling 4 rafter to ceiling connections, thus creating a single multi-heel joint system. Trusses were framed by 2 rafters 2×8? in size, and a ceiling joist 2?x6?. The testing has been achieved by compression load by UTM with a constant displacement rate of 0.2/min applied at the ridge joint. The test specimen was suspended on top plates to replicate rafter bearing on wooden walls.

2.6.2.2.             Test Results Rafter to Ceiling Joints

The curves for load deformation are shown below for tests of heel joint connections of pairs of joist systems. Assuming equally distributed load between sides of each specimen, and a load tension equal between ceiling and heel, the calculation was based on the following formula:

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The value of the parameter T was further used in the load analysis and plotting. The figures show heel joint load deformation curves for double sided specimens, where the total deformation of a specimen is assumed to average over the individual camber of each rafter.

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Fig. 19. From left to right: Configuration 1. Configuration 2.

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Fig. 20. From left to right: Configuration 3. Configuration 4

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Fig. 21. Configuration 5

The performance of the configurations put to test is summarized in the table below. The failure modes of nails have been identified by splitting the specimen joint and visually inspecting the failure.

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Fig. 22. Classification of failure modes

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Table 4. Test results

The next table shows the predicted and observed lateral load resistance for a slip limit state at 5% nail diameter offset.The table comprises the calculated yield and measured failure modes.

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Table 5. 5% nail diameter offset slip, comparison of predicted and observed values

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Fig. 23. Nail diameter offset load 5%

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Table 6. Predicted and measured ultimate loads

2.6.2.3.             Testing Roof to Wall Connections

Tests for roof to wall connecting joints have been conducted. The tables show testing configurations, whereas the figure demonstrates the experimental setup. Three systems were built and each was tested twice. The test specimens were roof geometries of dimension 12ft x 20ft, with 11 MPC trusses of 12 ft. each. The construction was placed on a reaction wall on one side and on a 20ft. long braced wall on the other. The 20 ft. long wall has been used in all the 6 tests, having a bearing capacity larger than the tested joints.

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Table 7. Test configurations

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Table 8. Configuration details

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Fig. 24. Test setup

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Fig. 25. Attachment of loading strap

A steel strap facilitated the transmission of load to the roof geometry from a hydraulic actuator, where it was attached by a clevis. The strap was screwed in place on the roof panel in-between trusses. The actuator was installed with a pinned connection on a reaction frame to avoid transmission of moments between the cylinder and the specimen. The measurement of load was achieved by means of a 100,000 lbs. electronic load cell connected between the actuator and strap. The relative deformation between the braced wall and the specimen diaphragm was measured by two LVDT placed at the ends of the roof specimen.

2.6.2.4.             Test Results Roof to Wall Connections

With similar peak loads between 3x8d nails and 2x16d (3,030 lbs. vs 3,115 lbs.) pneumatic nails for each connection but high difference between the loads applied in each test repetition (2,387 lbs. and 3,843 lbs.), the two nail types cannot be decisively declared equivalent. The variation is assumed to pertain to the workmanship practices used during assembly. The lateral resistance was approximately magnified x2 by the presence of hurricane clips, even though they are crafter to resist uplift. The 9 hurricane clips and 4 toe nail trusses performed superiorly to the 9 hurricane clips and 22 toe nail trusses, indicating unsuitability of toe nails for lateral loads.

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Table 9. Test results

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Fig. 26.Specimens 1 and 2 behavior and failure modes

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Fig. 27. Specimens 1 and 2 behavior and failure modes

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Fig. 28. Specimens 5 and 6 behavior and failure modes

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Fig. 29. Specimens 3 and 4 behavior and failure modes. Shorter 8d common nails withdrew from the top plate.

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Table 10. Comparison between yield predictions and empirical observations

2.6.2.5.             Testing Toe-Nailed Joints

A battery of tests investigated toe nailed connection. The next table shows two joints pertaining to geometries 1 and 2 from the previous tests being investigated.

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Table 11

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Fig. 30. Test setup

A test platform was built for the test specimens in the universal test machine. A vertical downward force acted to displace the side member at a constant rate of 2? per minute. Deflectometers measured the side and center relative displacements for 10 configurations.

2.6.2.6.             Test Results Toe-Nailed Joints

Two geometries of roof to wall joints have been tested correspondingly to the configurations 1 and 2 shown in Table 9. The following figures show individual displacement curves, and the next table shows a summary of the results.

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Fig. 31. Load-slip relation, from left to right: configuration 1 and configuration 2

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Table 12. Test results

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Fig. 32. Toe nailed connection behavior

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Table 13. Predicted and observed ultimate loads

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Table 14. Comparative analysis between connection types

3.    Skylights

A building that is expertly designed to admit solar daylight improves the quality of lighting in internal open spaces, it has been shown to increase the productivity of company employees [30], and it saves expenditures on electrical energy for lighting artificial luminaires. It has been documented that more than 60% of the floor space in commercial buildings is situated on the first floor or the top floor of the building, with direct access to day lighting. Given these factors, skylights, apertures, or other natural luminaires are an intelligent resource to utilize for corporations.

Artificial electrical luminaires have ample published documentation and testing results in comparison to skylights. Extensive research is required into the performance photometrics of skylights in order to inform standards for building design. There is not enough information at present to accurately model the beneficial impact that skylights have.

This shortfall of information prompted the California Energy Commission to launch the Public Interest Energy Research (PIER) program [31] which funded on-site photometric and goniometric testing. The results and conclusions from testing in diffuse-light overcast conditions, and clear sky conditions, on a total of twenty-two skylight geometries, produced a database of information for architects, lighting designers, researchers, and software developers to effectively utilize.

A recent paper summarizes the standards and practices that the PIER program data influences concerning designers and developers [32]. This includes making revisions to the light measurement (LM) standards. It includes providing essential information to software developers to improve the modelling precision of skylights in lighting software, from photometric data in Illuminating Engineering Society of North America (IESNA) documentation. It further includes changing standards for electrical circuit layout in buildings for electrical luminaires, so that these standards can inform more efficient luminaire placement for lighting internal open spaces to accommodate for skylight luminaires. This improved efficiency reduces electrical energy expenditures on lighting and the lighting quality.

The conclusions of this paper state that single-story commercial buildings can lower their costs on electrical energy if skylights are efficiently incorporated into the building design and utilized in a complementary way with electrical luminaires. Reducing energy consumption is of chief importance to companies and corporations. The IESNA is in a position to update its testing protocol and photometric information in its LM standards for the benefit of designers, developers and companies. Public daylit zone standards will need to be re-evaluated if there are growing trends for skylight installation and incorporation into new building designs. Lighting designers will have access to much needed information for considering skylights in their combined luminaire design of buildings. In addition, as software developers use this data to improve simulations, light designers will be able to design more effectively with simulations which are capable of modelling the angle of the sun and diffuse light. These software do not currently feature realistic lighting conditions from skylights as luminaires.

Each year in the United States 686 million sq. ft. of commercial floor space is constructed. Of this new floor space approximately 46% is single-story, and together with floor space on the top floor of new buildings, sums to 62% of floor space that can benefit from skylights. A significant percentage of single-story commercial constructions are located in the suburbs. Some institutions have estimated that electrical lighting energy can be lowered by 50-70% [33], and another lower-bound estimation states that reductions of one third can be made for electrical lighting energy in daylit zones. The figure for the amount of energy used per year in the United States, for newly constructed commercial building, for electrical lighting is 4.6 × 109 kWh. From this figure an estimation can be made: If half of new commercial floor space is adequately lighted by skylights over the next decade, then the cumulative reduction would be 4.7 × 109 kWh. The reasons that commercial buildings can largely benefit from skylights as opposed to residential buildings, is that commercial buildings use lighting in daylight hours, the density of luminaires to floor space is high, and that these buildings are robust against the total heat transfer or U factor. The PIER program involved measurements of solar heat gains (SHG) and heat dissipation during night hours through a skylight.

3.1.          Comparing skylights and artificial luminaires

In this section, a comparison between skylights and electrical luminaires is considered. In order to make a fair comparison a skylight has to be considered with its light well, which often spans some distance from the internal ceiling to the skylight. The light well influences the optical and thermal properties of a skylight, however more significantly the optical properties. Skylights and luminaires have the same function insofar as they provide lighting, have definable intensity distributions, and have efficiency limitations on their separation distance. The key difference between these luminaires is their optical properties. The intensity and intensity distribution of skylights depends on the solar angle, which changes at a continuous rate throughout the day, and year, where the changes are more gradual but nonetheless significant. Fig. 32 shows the intensity distributions for the same skylight at high and low solar angles. The intensity distributions can be seen to be very different in the two cases and exhibit complex variation. Overcast weather conditions will substantially affect the light that is admitted by a skylight with respect to intensity, intensity distribution, and optical spectrum.

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Fig. 32. Differences between high and low solar angles in intensity transmittance

table of skylights and light wells.png

Table 15. Measurement results

From these comparisons conclusions can be drawn. In order to effectively characterize the photometric properties, a large range of solar angles and weather conditions must be considered. Normalization of intensity measurements is required due to these variations by calculating candelas divided by lumens. In addition the properties of the light well will need to be taken into account, such as the shape and geometry, and the reflectivity of the light well surface.

It was necessary to choose an encompassing set of commercial skylights and light wells, with differing shapes, geometries and sizes, so as to make the measurements as generalized as possible. The set of skylights and light wells were intentionally designed to complement electrical luminaires and reduce energy expenditures. Given these considerations it was appropriate not to include architectural skylights with elaborate design features. Above is Table 15 of the twenty-two skylights that were measured.

setup.png

Fig. 33.

The square aperture size of the twenty-two skylights was 4 ft. × 4 ft. and a total area of 16 sq. ft. This size was appropriate because the skylights had to be able to fit into a thermal chamber for U-factor testing, while being the largest size that is comparable to typical 4 ft. × 8 ft. commercial skylights. These were purchasable skylights from a sample of manufacturers. Skylights with the largest availability are plastic domed skylights and because of this a range of different light wells were measured. The light wells differed by depth, optical properties of the surfaces, and the diffuser. Flat glass glazing was also tested because performance is simple to simulate and the effects of a diffuser is easy to measure. Optimal light transmission and light diffusion present a trade-off in skylight design which is notable in the case where a lack of diffusion can result in a drop in interior light levels in locations between skylights. Diffusion can be implemented either through a physical diffuser or with glazing diffusion in the use of semi-transparent plastic.

This trade-off between diffusion properties and light transmission was considered by testing plastic glazed skylights with different glass color tinting, fully transparent plastic that uses refraction effects to realize diffusion, and fiberglass which contains fibers that serve to diffuse transmitted light. Calculations for light transmission in light wells with diffusion are simple and measuring light wells with different depths provides a means to verify simple calculations.

In the study methodology [34][35] far field photometric measurements are made which means that the luminaire is assumed to be a point source. As the far field approximation is used the photometric sensors were required to be at least a fivefold distance from the largest dimension of the skylight [36] which is the diagonal of a 4 ft. × 4 ft. aperture equal to 5.6 ft. Therefore using the fivefold rule the minimum required sensor distance was 28 ft. This gives the desired height of the thermal test chamber which was effectively attained in a piecewise manner. The maximum height that could be achieved was 17 ft, so 2 ft. × 2 ft. sections were tested as a scaled down version, and the data was accumulated to give the expected data from a 4 ft. × 4 ft. aperture, which can be seen in Fig. 33. What can also be seen in Fig. 33 is the mirror system that was used to further reduce the spatial dimensions of the setup. It can be seen that a goniometer was used to collect light from a total of ten incident angles determined from the vertical axis. These ten angles were equally spaced by 10?. These implementations provide a compact setup for ease of experimentation and for reductions in expenditure.

Interior skylight intensities were measured and exterior total incident flux per unit area (illuminance) in a horizontal direction was measured. Effective visible light luminous flux incident, in units of lm (lumens), on the skylight surface are determined by multiplying horizontal illuminance with the protruding cross-sectional area of the skylight glazing. From these measurements normalization can be ensured and is given in units of cd/Mlm (candelas / megalumens) of exterior sky light. To ensure that the goniometer readings are done correctly, background horizontal illuminance is recorded. All plastic glazings were tested independently with a BYK-Gardner haze-gard for transmission and haze.

A PIER report [38] contains test results of individual skylight glazings, and skylights with: light wells, and diffusion, as part of the glazing or with a separate diffuser. The effective visible transmission (EVT) was defined as the ratio of incident light to transmitted light and is given in units of lm (lumens). Measurements were made in two standard ways, one being a matrix grid of light meters beneath the skylight light well that measured the illuminance, and the other being a goniophotometer which was situated in a central position beneath the light well which measured intensity in cd in an equally spaced positions of horizontal and vertical angles. The first setup is more appropriate because it does not assume far field conditions and use the fivefold rule. So this setup is appropriate and reliable for measuring collimated light from skylights with or without a diffuser.

EVT was detected for a range of skylights having different glazings, glazing geometry, light well geometry and light well surfaces, namely white paint and metal. White paint serves as a diffuser and metal is a specular reflector. These results will influence energy budgeting simulations and optical simulations. The most significant result was that EVT was notably affected by glazing light transmission and the geometry of the skylight and light well. This effect is substantial for solar angles of approximately 30? which is important in the United States as it is representative.

Flat skylights with a glazing surface parallel to the ground have low EVT for solar angles below 30? as compared to orthogonal angles around 90?. This study found that domed skylights have a light transmission that is approximately constant for all solar angles, due to the protrusion and nonzero cross-section that the domed glazing presents.

The National Fenestration Rating Council (NFRC) standards only apply to skylights with flat glazing and without glazing diffusion. Energy budgeting simulations model skylights as flat and do not take domed glazing into account, even though flat skylights make up a small fraction of the market for commercial premises. The authors suggest that the NFRC consider a testing standard for domed or arbitrarily shaped skylights, and use simulation software such as NRC Canada?s SkyVision which can model the optical performance of domed or protruding skylights. Indeed the authors have approached the NFRC directly.

Skylights are used to replace electrical luminaires but as a suitable source of internal space lighting they should be used with diffusers or diffuse glazing so as to minimise unwanted glare. When the haze of a glazing is measured to be higher than 90% it is a good diffuser. Software developers use this rule in the specification of skylights used to replace electrical luminaires.

The main conclusion of the PIER report was that EVT of domed or arbitrary non-flat skylights behaves significantly different to flat skylights. This means that three-dimensional geometry skylights require an updated scheme for the adequate performance of energy budgeting and optical simulations.

Models of EVT against solar angle can be fit to this measured data. Horizontal domed skylights with equivalent glazing and transmission properties to horizontal flat skylights allowed for approximately 10% less in electrical energy expenditure as a result of replacing electrical luminaires. A solar angle of 30? is representative of the solar angles across the United States for most of the year and accordingly the market ratings for skylights and diffuse light wells should respect with this fact. At present ratings are stated in accordance to a solar angle of 90? which is unrepresentative for the US. It was found that EVT measurement data is important for skylight energy budgeting in US climates such as California. In addition EVT measurements used to rate skylights is more reliable than photometric measurements because EVT does not make far field assumptions that lead to errors for diffuse skylights. SkyVision used by NRC Canada is a far superior simulation software to what is used in the US, primarily because of its ability to accurately model light transmission in non-flat skylights. The data shows that ASTM D1003 haze testing clearly differentiates between diffuse and clear glazing. Skylight EVT decreases with increasing light well depth. Light wells with specularly reflecting surfaces are better at light transmission than diffuse surface light wells. The IESNA Handbook predictions were verified for the light transmission of light wells with diffuse surfaces and that the transmission does not strongly depend on solar angle.

The recommendations from the PIER report are the following. EVT testing should be standardized in NFRC and ASTM. EVT testing takes into account arbitrary skylight geometry and diffusion. This testing is accurate for building models that accurately predict skylight light transmission at relevant solar angles. A limitation to the EVT testing conducted here is that SHG had to be measured at the same time, which influences the results of both measurements. Future EVT testing should use more detectors at a larger range of sample points. The NFRC should upgrade their modeling software to superior software such as SkyVision or similar that can manage three-dimensional skylight geometries. For non-diffuse glazing skylights with specular reflecting light wells, the light transmission is sensitive to the solar angle and therefore the incident angle on the glazing. Energy budgeting software needs to include models for diffuse white surface and specular reflecting light wells for transmission efficiency. The threshold for diffuse glazing should be with a ASTM D1003 haze measurement of 90%, which is currently implemented in the 2013 California Building Energy Efficiency Standards. Additional research is required to update the ASTM D1003 for diffusion measurements, because it is currently limited to haze measurements for glazings less than 30%. Another measurement for glazing haze that could be investigated is the intensity per Mlm. The IESNA Handbook needs to be updated for specularly reflecting light wells of various geometries. Skylights and sky wells will over time degrade from UV damage and a build-up of particulate matter. The energy budgeting and optical properties of skylight degradation and degradation types needs to be researched.

3.2.          Domed Skylights

Domed skylights are becoming a new feature in the design of buildings for their aesthetic appeal and for replacing artificial luminaires with natural sky lighting. Large domed skylights that service large spaces such as a building atrium, lobby, or sporting arena, create the effect of a naturally lit, outdoor space. In replacing artificial luminaires with domed skylights, an individual or company can make financial savings on energy costs for electrical lighting and temperature control [39-42]. In terms of temperature control there is a drawback as domed skylights will raise the costs of room cooling under certain conditions. For these reasons there is a need for extensive investigations into physical theory and direct experimentation on the optical properties and energy budget of domed skylights. There is an evident trade-off between using domed skylights to light an interior space and consequent temperature control requirements.

A domed skylight has different optical properties and energy budget to a flat or planar skylight due to large and evident geometrical differences. Extensive research has been carried out with planar skylights to ascertain trade-off optimality with effective lighting and temperature control costs. In contrast there are many less theoretical models and experimental data on the domed skylight design. An exemplary example however considered a theoretical optical model that accounted for transmission, reflection and absorption of solar, and diffuse light, for a domed skylight with multiple glazing. An exemplary example of experimentation with a large, installed pyramid-shaped skylight [43] included internal and external measurements. This study however failed to achieve congruence with predicted and experiment results. Experimentation has been performed in controlled laboratory conditions with scale models of domed skylights but the results of their illuminance, the total incident flux on a surface per unit area, have not been corroborated with field experimentation with installed skylights [44]. A range of programs for simulating the optical properties and energy budget, : ASHRAE [45], VISION [46], and WINDOW [47], utilize simplified planar and slanted surface dome geometries [48][49]. The IESNA Handbook [50] specifies calculations for skylight transmittance of solar lighting for both a single and double glazed domes but these calculations have not been satisfactorily compared with field experimentation.

A more recent research study with the aim of developing an efficient theoretical model for the optical properties and energy budgeting of domed skylights was conducted with promising results [51]. In this theoretical work for domed skylights, a fully transparent, single glazed skylight was modeled and based on the transmission by beam tracking and diffuse light sources. The geometry of the dome is simulated with a planar skylight that has the same optical and thermal properties as a domed skylight, which makes it a feasible approach for existing programs.

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Fig. 34.

Domed skylights were found to have lower transmission from direct sunlight and lower solar heat gain (SHG) when the sun is at higher angles in the proximity of the zenith, in a range of hours around midday but comparatively at angles very close to the zenith and close to the horizon, the transmission and solar heat gain were much higher than the planar skylight. For the extreme case of domed skylights with a full hemisphere of protrusion, these observations are more significant. For diffuse light, as what would obtain in overcast weather conditions, modeled domed skylights have marginally less transmission and SHG than the planar design, and full hemisphere domes have 14% and 7% less than planar skylights for transmission and SHG, respectively. In simulated conditions of direct solar light and diffuse light it was found that domed skylights have large SHG than the typical planar design, with full hemisphere domes having the larger SHG on an annual average. Summer solar angles saw the hemisphere design with 3-9% larger SHG than the planar design over the latitude range 0-55?. As expected, winter angles of the sun produce large SHG, as well as countries residing at higher latitudes, because of the equivalent range of angles. For countries residing in tropical latitudes 0-24?, in the northern hemisphere, SHG of the hemisphere design exceed the planar design by 19%. For a range of other latitudes: 24-35? and 35-55?, the SHG for hemisphere domes reaches 33% and 232%, respectively. Clearly the latter latitude range exhibits a very large SHG. The research also concludes that domed skylights are more appropriate for particular latitudes and climate to compensate for heat loss.

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Fig. 35. Dome and incident angle

Another recent theoretical work on the optical properties of domed skylights [52] provides an analytical model using ray tracing methods that can manage transparent and semi-transparent glazing. Models were constructed for sky lighting conditions considered with overcast, and clear sky standards as defined by the International Commission on Illumination (CIE) and partly cloudy skies as defined by the Illuminating Engineering Society (IES), and a model for realistic and dynamical sky light conditions. These models were in excellent agreement for semi-transparent glazing, and good agreement for transparent glazing. The model for dynamical sky light conditions predicted an optical transmission for the transparent glaze by 14% in contrast to the standard conditions model based on aforementioned CIE and IES definitions.

4.    References

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Performance of Windows, Skylights, and Clerestories?. Report NBSIR 83-2726. U.S. Department of Commerce
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