All Natural

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What the subtractive process requires, more than anything else, is a firm understanding of necessity. Knowledge of universal human needs and the archetypal forms that satisfy them is a prerequisite for the practice of good design. This knowledge is available to anyone willing to pay attention.

A vernacular architect who has come across a photo of a Kirghizian yurt and encountered a Japanese unitized bathroom and a termite mound while traveling does not set out to build a yurt with a unitized bathroom and termite inspired air conditioning just to show what he has learned. He retains the forms for a time when necessity demands their use.

Vernacular architects do not strive to produce novel designs for novelty’s sake. Necessity must be allowed to dictate form. The architect’s primary job is to get out of its way. It might seem that such a process would produce a monotonously limited variety of structures, but, in fact, there is infinite varia­tion within the discipline. Vernacular architecture is as diverse as the climates and cultures that produce it. The buildings in a particular region may all look similar as they have all resulted from the same set of socionatural conditions, but within these boundaries, there is also plenty of room for variance. With the big problems of design already resolved by the common sense of their predecessors, vernacular architects are left free to focus on the specifics of the project at hand. Instead of reinventing the wheel, they are left to fine-tune the spokes.

Reactions Between Oxidizers and Reducers (Electron Exchange)

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Many chemical reactions imply the transfer of electrons from one chemical species to another. These reactions are called redox reactions and they are usually rather slow. In soil and water, redox reactions involve hydrogen ions and are thus greatly pH dependent. The most important redox reactions involve oxygen, carbon, nitro­gen, sulphur, manganese and iron. In polluted soils, arsenic and mercury can also participate.

The redox potential, and changes thereof, play a crucial role in the behaviour of metals in soils. For instance, iron oxides are formed at high redox potentials. Iron oxides and hydroxides are capable of adsorbing heavy metals onto their surfaces, which will greatly reduce the mobility of the heavy metals. When the redox potential is lowered, the iron oxides dissolve and the adsorbed heavy metals are released and will be available for leaching further down the soil profile. Many redox reactions in nature are speeded up by certain bacteria, however. The bacteria utilise the energy released from redox reactions (Berggren Kleja et al., 2006).

Reactions Between Acids and Bases (Proton Exchange)

The amount of protons (H+) in solution greatly influences most chemical reactions. Proton transfer reactions are usually very fast. According to the Brensted definition, protons are provided by an acid and captured by a base. To each acid Ac there is a corresponding base Ba:

Aci Bai + H+

The acid and the corresponding base constitute an acid/base couple (Ac1 /Ba1).

In most natural waters, the pH lies within the range from 5 to 8. All the sub­stances dissolved into water (gases, mineral and organic compounds) contribute to the acid-base equilibrium of water. All components of the carbonate system make a major contribution to the acid neutralizing capacity (called alkalinity) of the water and to its base neutralizing capacity (acidity). The buffering capacity of water (the ability of the water to maintain its pH despite any addition of H+ or OH-) is also largely determined by the carbonate system. However, dissolved silicates, ammonia, organic bases, sulphides and phosphates also contribute to the alkalinity. In like manner, non-carbonic acids, polyvalent metal ions and organic acids contribute to the acidity.

Rainwater often contains strong acids originating in atmospheric pollutants (dis­solution of gases leading to HCl, HNO3, H2SO4). Acid rain may increase the heavy – metal solubility in soils. The pH effect of strong acids on soil and water will depend on the buffering capacity of the soil or water, however. Oxidation reactions lead to a decrease in pH whereas reduction tends to increase the pH.

Critical Flow Depth

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When the depth of flow is plotted against the specific energy, the specific energy diagram may be obtained and the critical depth found as illustrated in Fig. 5.5. The critical depth is defined as that depth where the specific energy is minimum. The flow velocity at the

Critical Flow DepthCritical Flow DepthШШїші

HTDKAUlic graoe LINE

channel bottom

DATUM LINE

FIGURE 5.4 Flow characteristics for uniform open-channel flow. (From F. S. Merritt, ed., Standard Handbook for Civil Engineers, McGraw-Hill, 2004, with permission)

Supercritical

range

(critical

depth)

Подпись:(Specific energy)

FIGURE 5.5 Specific energy diagram. (From Highway Design Manual, California Department of Transportation, with permission)

critical depth is called the critical velocity. The channel slope that causes the critical depth and critical velocity is termed the critical slope. If the depth is greater than the critical depth, the flow is said to be subcritical and the velocity head reduces. Where the depth is less than the critical depth, the flow is said to be supercritical and the velocity head increases. For any particular energy level, except where the depth is critical, there are two corresponding depths that may occur. However, the depth may not alternate between these two values without a change in the channel configuration or slope.

Although the critical depth gives the greatest discharge, flow that causes the depth to be close to critical should be avoided, and thus the critical slope should be avoided. Flows near the critical depth may be turbulent. Inspection of the specific energy diagram reveals that where the depth is close to the critical depth, it takes little energy to change the flow from subcritical to supercritical or the reverse. If the flow does change from subcritical to supercritical, a hydraulic jump will occur. If placing the depth of flow near critical is unavoidable, it is advisable to assume the least favorable type of flow for design purposes. The critical depth may be determined from the following relationship:

Подпись: (5.14)TT = 62 T g

where A = cross-sectional flow area, ft2 (m2)

T = top width of channel flow, ft (m)

Q = discharge, ft3/s (m3/s) g = acceleration of gravity, 32.2 ft/s2 (9.8 m/s2)

Подпись: V c Подпись: (5.15)
Critical Flow Depth

For a channel with vertical walls, the velocity corresponding to the critical depth is given by

where Vc = critical velocity, ft/s (m/s). Also, for a channel with vertical walls, the flow area at a point of critical depth dc is

Подпись: (5.16)A = T(dc)

Critical Flow Depth Подпись: TTY/3 gT2 ) Подпись: (5.17)

Substitution in Eq. (5.14) leads to

It can be seen from this relationship that for a given flow, as the width of the channel changes the critical depth also changes. Such locations should be investigated for a hydraulic jump.

Points of control are locations where the depth of flow may be easily determined. The critical depth is one point of control and may be found in several typical loca­tions. As discussed above, one of these locations may be where there is a change in the channel section. Other typical locations are where the slope changes abruptly from flat (subcritical) to steep (supercritical), at the crest of an overflow dam or weir, and at the outlet of a culvert on a subcritical slope discharging into a basin or wide channel.

The Froude number (Fr) may also be used in determining whether the channel is under supercritical, critical, or subcritical flow:

Подпись: (5.18)V

(gdh)1/2

where d. = A/T. If Fr < 1.0, the channel flow is subcritical; if Fr = 1.0, the channel flow is critical; and if Fr > 1.0, the channel flow is supercritical.

Water surface profiles for the gradually varying flow condition may be determined by either the direct step method or the standard step method. The former method is applicable only to straight prismatic channel sections with gradually varying areas of flow. The standard step method may be used in nonprismatic channel sections and channel alignments that are not straight. Where the flow is subcritical, the analysis for determination of the water profile begins at the control point and proceeds upstream. Where the flow is supercritical, the opposite is true. (See V. T. Chow, Open-Channel Hydraulics, McGraw-Hill, 1959; and F. S. Merritt, ed., Standard Handbook for Civil Engineers, McGraw-Hill, 1996.)

Example: Critical Depth and Critical Velocity. A channel has a width of 10 ft (3 m)

and vertical sides. Determine the critical flow depth and critical velocity for a flow of 1000 ft3/s (28 m3/s).

U. S. Customary units:

From Eq. (5.17), dc = (Q2/gT 2)1/3 = [(1000)2/32.2(10)2]1/3 = 6.77 ft.

From Eq. (5.16), A = T(dc) = 10(6.77) = 67.7 ft2.

From Eq. (5.15), the critical velocity is Vc = (gA/T )1/2 = (32.2 X 67.7/10)1/2 = 14.8 ft/s. SI units:

From Eq. (5.17), dc = [(28)2/9.8(3)2]1/3 = 2.07 m.

From Eq. (5.16), A° = 3(2.07) = 6.21 m2.

From Eq. (5.15), Vc = (9.8 X 6.21/3)1/2 = 4.5 m/s.

Exchange Reactions

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Exchange reactions take place between two reactants, usually meaning that both are in the liquid phase (although some surface complexation reactions may involve an exchange reaction, too). They include electron exchanges (reactions between ox­idizers and reducers), proton exchanges (reactions between acids and bases) and
“particle”[13] exchanges (formation of complexes from ions or molecules) (Stumm & Morgan 1996).

On its way from the road surface downwards, the infiltrating seepage (carry­ing chemicals accumulated during rainfall and runoff) will encounter and interact with varying redox-potential and acidity conditions in the various layers of the road construction and soil layers beneath. The resulting more or less steady conditions will govern the equilibria of chemical reactions. More or less oxidizing or reduc­ing road/soil materials will, through dissolution, create more or less oxidizing or reducing conditions. This will influence the toxicity of some chemicals (chromium for example). In like manner, road/soil materials will influence the acidity/alkalinity of the medium and its buffering capacity. Under special conditions, e. g. where very alkaline man-made road materials are present, percolating water can reach very high pH levels followed by more neutral conditions in subsequent layers. In this way, the buffer capacity of the road/soil materials can mitigate the influence of an acid or base spillage, should it occur.

Extra joists and headouts

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Extra joists are needed under parallel walls (walls that aren’t perpendicular to the floor joists) to carry the added weight that gets transferred down through these walls. Move the extra joists away from the center of each
parallel wall about 3 in. to allow room for pipes and conduit to be run up into the walls from below (see the draw­ing above).

Sometimes joists must be cut to allow room for a stairway, access to an attic, a place to install a skylight, or even for a heater vent in a wall or a tub trap in a bathroom. Carpenters call these open­ings headouts (see the drawing on p. 98). Regular 2x joists (not I-joists) can be cut as long as they are sup­ported by a header joist and fastened to parallel joists. Here are some basic rules for headouts:

• If more than one joist is cut, double the header joist and side joists.

• Support cut joists temporarily by nail­ing a flat 2x across their tops.

• Nail 16ds through the header joists into the cutoff joists.

• Support both header and cutoff joists with metal joist hangers at intersecting points.

• Extra joists and headouts
Nail double joists together with 16ds at 1 б in. o. c.

• Keep all wood at least 1 in from heat­ing vents.

• A common mistake made by carpen­ters framing a headout is to forget to leave room for the header joists. If, for example, a 6-ft.-long floor opening is needed, cut it б ft б in. This leaves room for a double header joist at each end.

SHEATHING THE FLOOR

Once floor framing is complete, it’s time to cover it with sheathing. Although it’s easier to install rough plumbing and heating ductwork now, this can be done after the subfloor has been laid. After the sheathing is nailed in place, you’ll have a level platform, perfect for build­ing a house or for having a dance!

Normally floors are sheathed with 4×8 sheets of 5/s-in. or 3/4-in. tongue-and – groove (T&G) plywood or OSB. The sheathing should be exterior grade so that it won’t come unglued when exposed to moisture. While square- edged sheathing can be used, codes often require it to be supported by edge blocking between joists. The edges of T&G sheathing are self-supporting and don’t require blocking.

Floor sheathing is bulky and awkward and in windy conditions can act like the sail of a windsurfer. So be mindful when handling it. Also, T&G plywood should be handled with care so you don’t wind up with damaged edges, which can make it hard to fit two sheets together. When I carry sheathing, I grasp it with one hand underneath and one on top

Подпись: Construction adhesive helps secure sheathing tight to the joists and reduce floor squeaks. Place a У4-ІП. bead on each joist. (Photo by Roe A. Osborn.) Подпись: After each row of sheathing has been installed, mark the joist location on top at the leading edge so you will know where to drive the nails. (Photo by Roe A. Osborn.)

for balance, allowing much of the weight to rest against my upper body.

Or I get a helper.

Sheathing is installed so that the 8-ft. edges are perpendicular to the floor joists. Before laying any sheathing down, though, first measure in 481Л in. from each end and snap a chalkline across the joists between these two marks. This line acts as a control, or reference, line for the first row of sheathing, and the extra 1/4 in. allows for any slight variation in the rim-joist alignment. With the first row of sheathing straight, the rest of the job will be easier.

Fastening down the sheathing

It’s a good idea to lay down a bead of construction adhesive on each joist before installing the sheathing. The adhesive secures the sheathing tight to the floor joists and helps prevent or reduce floor squeaks, which happen when joists dry out and shrink away from the subfloor. Apply а Ул-т. bead to each joist over a section large enough to lay down a 4×8 piece of sheathing (see the top photo at right).

Lay the first sheet with the grooved edge right along the control line with each end hitting along the center of a joist. If the plywood edge doesn’t fall on a joist, snap a chalkline and cut the sheet to length so that it breaks on the center of the joist. Set the circular saw to the proper depth (% in.) and make the cut. Don’t leave the cutoffs under the floor, or you’ll give termites an easy meal.

Tack down the sheet to the joists with one 8d nail near each corner. On large floors, nail off the sheets after you have laid four or five; otherwise, the adhesive could set up (especially in hot weather). Be careful not to drive nails within 6 in. of the leading edge, because you’ll need

Floor joists

Extra joists and headouts

 

a little flexibility here to make it easier to mate the groove of the first row with the tongue of the next

After placing a row of sheathing, mark the location of every joist with a pencil or keel on the leading edge of the sheathing (see the bottom photo on p. 99). This will make it easy to find the joists when you start nailing all the sheets down.

If you live in a wet climate, leave about Vs in. between the ends and edges of the sheets to allow for expansion. This gap can be gauged by eye or by using an 8d nail as a spacer.

Don’t install sheets so that four corners meet at the same point. Instead, stagger the plywood joints, as a bricklayer would do when building a chimney, to add strength to the floor (see the drawing above). Begin the second row with a 4-ft. by 4-ft. sheet, and install it adjacent to the 8-ft. sheet in the first row. Then complete the row with 8-ft. sheets.

Sometimes a little extra persuasion is needed to unite T&G plywood. One way to do this is for one person to stand on the sheet, holding it flat and snug against the previous row of sheathing. The second person places a scrap 2x against the edge (to protect the edge

SIZING WATER HEATERS

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S

izing water heaters is not a complicated process. It is, however, an im­portant part of most plumbing jobs. Local code requirements call for minimum standards. The minimum facility requirements can be found in any major codebook or local code enforcement office. Since plumbing codes are regional, you will have to check your local code for exact requirements. But, the math that I’m about to show you will work in any location. Some of the numbers might be different, depending on code requirements, but the mathematical procedure will be the same.

When you figure the size of a water heater, remember that the codes of­fer suggestions and regulations for minimum requirements. The fact that a 40- gallon water heater will pass code may not mean that it is the best size heater for a given job. Use some common sense when sizing water heaters. Skimp­ing on heater size can prove to be frus­trating for your customers,- no one enjoys running out of hot water.

Подпись: A mistake that some plumbing contractors make is installing water heaters that meet minimum code requirements. This is legal, but it may not make for happy customers. Few people enjoy taking cold showers. With dishwashers running, clothes washers running and large families, the size of a water heater can become very important. If you can get by with a 40-gallon water heater, go with a 52-gallon water heater. Upgrade the size of water heaters to meet your customer needs to avoid complaints down the road.There are three types of water heaters that we will discuss. Oil-fired wa­ter heaters are the least common of the three. Depending upon where you work, you might find that gas-fired water heaters or electric water heaters are the most prevalent in your region. Overall, electric water heaters are more prolific than gas-fired heaters. Regardless of which type of water heaters you will be working with, you will find the following sizing information helpful.

129

ELEMENTS OF SIZING

Подпись: ✓ fast code fact Most codes require electric water heaters to have a disconnect box near the appliance and a number 10 electrical wire. In years past, a number 12 wire was acceptable, but this is rarely the case these days. Check your local code for electrical requirements and don’t replace or install a water heater that is not in compliance with current code requirements. Elements of sizing are something that you must understand, so let’s discuss what they are. The first element is the number of bathrooms in a home or building. When we move to the sizing charts in this chapter, you will see three different formats. This is due to the number of bathrooms. An additional element is the number of bedrooms found in a home. The number of bed­rooms is very important. Of course, the storage size of a water heater is a key element. Other elements are the recovery rate, the draw, and the input in either British thermal units per hour (Btuh) or kilowatts (KW). i have prepared some sizing tables for you to use that will make your sizing efforts very easy. Let’s look at each table and do a few simple sizing examples to make sure you understand how to use the charts effectively.

The water delivery system of Pergamon: the first large forced main

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Lysimachus, who had received Thrace in the partition of Alexander the Great’s empire, imprudently left part of his war spoils in the custody of Philetairos, in the Asia Minor citadel of Pergamon. This citadel occupied a rocky spire that overlooked the plain from 300 m above it, and about 30 km from the sea. After the secession of Philetairos, in 282 BC, Pergamon rapidly became the capital of a kingdom, then an intellectual center that sought to rival Alexandria with a great Library (some 200,000 rolls of papyrus) and a School of original thought.

The provision of a supply of water to these citadels perched on hills always posed a problem in Antiquity. Initially, cisterns were built to store rainwater. Later, tunnels (or sinnors) were often dug to ensure access, especially during sieges, to underground cis­terns fed by springs located on the flanks of the hills; this was the solution adopted at Mycenae, and at Jersusalem.

The water delivery system of Pergamon: the first large forced main

Figure 5.8 The Hellenistic aqueduct of Mandradag for water delivery to Pergamon (after Garbrecht, 1983)

Having become a powerful city, Pergamon needed water, and this need was met with an unprecedented hydraulic installation. The project was founded on the understanding of the hydraulic concept of a siphon and the experience of the first Hellenistic applica­tions, as well as on the mastery of the metallurgy of lead. This project is known to us through site studies carried out by a German team between 1968 and 1972.[178] Its con­struction was probably carried out during the reign of King Eumene II (197 – 159 BC). This water delivery system comprises two parts (Figure 5.8). The upstream portion brings water from the Mandradag spring (captured at an altitude of 1,230 m) as well as from other springs, some as far away as 25 km as the crow flies, to a reservoir located 3 km from the city across from the citadel, at an altitude of 376 m (i. e. about 26 m higher
than the citadel). This original project includes parallel buried pipelines (three of them downstream of the Kemerdere spring) assembled from about 200,000 connected clay sections (Figure 5.9). These sections are from 50 to 70 cm long, with interior diameters from 16 to 19 cm, and wall thicknesses of about 4 cm. The watertight joints between the sections are built up from a mixture of sand, mud, and clay, including certain organic matter such as petroleum or greases.[179] The parallel pipelines follow the slope of the land along a total length of more than 40 km. They do not flow under pressure, and thus in principle belong to the family of water delivery systems developed earlier in Greece (see the end of Chapter 4) – but on a larger scale.

The water delivery system of Pergamon: the first large forced mainFigure 5.9 The three clay pipelines of the Mandradag aqueduct (photo of G. Garbrecht).

It is the second section of the pipeline that, although much shorter, is of revolution­ary conception (Figure 5.10). It conveys water from the reservoir that we just described, at an altitude of 376 m, down to the citadel at 350 m, in a straight-line distance of only 3 km. But this section crosses a valley whose lowest elevation is only 175 m, i. e. near­ly 200 m below the reservoir. The inverse siphon comprises a pressure conduit made of lead, with an outside diameter that appears to have been 30 cm, the inside diameter
appearing to be the order of 20 cm.[180] The conduit is not buried, but rests on above­ground stone supports. No visible traces remain of the forced main itself (the metal, hav­ing considerable value, was ultimately recovered for other uses). But the conduit’s sup­port blocks, with their 30-cm holes, have been recovered, along with massive anchor blocks on the two high points of the profile, to withstand static and hydrodynamic forces. Traces of lead have been found on the ground along the course of the conduit. The lon­gitudinal profile of the pipeline (Figure 5.10) is in the form of a W, unlike the earlier U- shaped Hellenistic siphons. It seems that the designers of the facility, concerned with the effects of hydrostatic pressure corresponding to 200 m of elevation difference, sought to limit the length of pipe sections subject to the greatest pressure. They appeared to have done so by intentionally routing the conduit over intermediate high points within the depression. At these intermediate high points, there is a risk of the formation of air pock­ets that can endanger a pipe system in several respects. Air release vents were very like­ly installed at these locations.

The water delivery system of Pergamon: the first large forced main

Figure 5.10. Longitudinal profile and routing of the inverted siphon of Pergamon: the first large forced main (Hodge, 1995).

The discharge in this system has been estimated to be 45 l/s (i. e. nearly 3,900 m3 per day). Later, urbanization spreads to the low areas situated at the foot of the hill. New aqueducts will be built, in particular during the period of Roman domination, to supply these low areas. But none of these aqueducts can rival the audacity of the Mandradag pipeline, the only one to provide water to the summit of the Acropolis. No subsequent Roman aqueduct will ever approach the bold technical audacity of this forced main.

Energy Equation

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The energy equation is based on the principle that energy must be conserved; that is, the energy at any one cross-section on a stream is equivalent to the energy at any other section plus any intervening energy losses. This relationship, a form of the Bernoulli equation, may be used wherever there is a change in the size, shape, or slope of the channel and is useful in determining the depth of flow.

Подпись: FIGURE 5.3 Nomograph for solution of Manning equation. (From Highway Design Manual, California Department of Transportation, with permission)
Energy Equation

/ V2 І V2

z1 + d1 + у j = z2 + d2 + у ^Lg j + hL (5.13)

where zn = distance above some datum, ft (m) dn = depth of flow, ft (m)

Vn = flow velocity, ft/s (m/s) g = acceleration of gravity, 32.2 ft/s2 (9.8 m/s2) hL = head loss between the two sections, ft (m)

TABLE 5.6 Values of the Roughness Coefficient n for Use in the Manning’s Equation

Min

Avg

Max

A. Open-channel flow in closed conduits

1. Corrugated-metal storm drain

0.021

0.024

0.030

2. Cement-mortar surface

0.011

0.013

0.015

3. Concrete (unfinished)

a. Steel form

0.012

0.013

0.014

b. Smooth wood form

0.012

0.014

0.016

c. Rough wood form

0.015

0.017

0.020

B. Lined channels

1. Metal

a. Smooth steel (unpainted)

0.011

0.012

0.014

b. Corrugated

0.021

0.025

0.030

2. Wood

a. Planed, untreated

0.010

0.012

0.014

3. Concrete

a. Float finish

0.013

0.015

0.016

b. Gunite, good section

0.016

0.019

0.023

c. Gunite, wavy section

0.018

0.022

0.025

4. Masonry

a. Cemented rubble

0.017

0.025

0.030

b. Dry rubble

0.023

0.032

0.035

5. Asphalt

a. Smooth

0.013

0.013

b. Rough

0.016

0.016

C. Unlined channels

1. Excavated earth, straight and uniform

a. Clean, after weathering

0.018

0.022

0.025

b. With short grass, few weeds

0.022

0.027

0.033

c. Dense weeds, high as flow depth

0.050

0.080

0.120

d. Dense brush, high stage

0.080

0.100

0.140

2. Dredged earth

a. No vegetation

0.025

0.028

0.033

b. Light brush on banks

0.035

0.050

0.060

3. Rock cuts

a. Smooth and uniform

0.025

0.035

0.040

b. Jagged and irregular

0.035

0.040

0.050

Source: From F. S. Merritt, ed., Standard Handbook for

Civil Engineers,

McGraw-Hill,

2004, with permission.

Subscripts 1 and 2 refer to two sections along the flow line as depicted in Fig. 5.4. The velocity head is given by V2/2g and the specific energy is defined as d + V2/2g. The plots in Fig. 5.4 illustrate the head at points along the length of the channel. The line drawn through points of static head is known as the hydraulic grade line, and the line drawn through points of total head is known as the energy grade line. The head loss between sections includes losses due to flow friction along the channel and losses due to turbulence at junctions and bends.

Plumb and brace the trusses

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When bracing trusses, take time to read and follow the directions from the engineering com­pany. These, along with local building codes, must be followed to guarantee that the house will have a strong and stable roof. Most simple gable-truss roofs are easy to brace.

After four to six trusses have been installed, plumb the gable-end truss and begin bracing the roof. Use a level to plumb the end truss, then install a diagonal 2×4 sway brace from the double top (cap) plate of the exterior wall (where the gable-end truss is installed) to an inboard truss (see the photo on p. 124). The brace should extend at a 45-degree angle from the top plate and be nailed to the top chord (or rafter) or the webbing of an inboard truss.

Plumb and brace the trussesПодпись: ATTACHING TRUSS CLIPSPlumb and brace the trussesПодпись:If the gable-end rafter is plumb, the rafters tied to it at 24 in. o. c. should also be plumb.

When all of the trusses have been installed, nail in a sway brace at the other end of the roof. On longer roofs, use additional diagonal sway braces near the center of the house to further strengthen the roof. These are important braces. In a high wind, they will help keep your roof intact.

The next step is to stabilize the joist chords by nailing a long board (a 1x or 2x will do) on top of each joist chord near the center of the span. You can move this bracing to one side or the other if you need to accommodate an opening for attic access, storage space, or room for a heat­ing unit. Frequently a forced air heating unit will be set in this area. Nail this long brace to each chord with two 8d (for 1x stock) or 16d (for 2x stock) nails (see the bottom photo on the facing page). Additional 2×4 braces are often nailed at 45-degree angles across the underside of the raf­ter chords or webbing from the plate line to the ridge (see the top photo on the facing page). Nail these braces into each chord with two 16d nails. This provides lateral stability to the entire roof.

Other Methods

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Various methods of testing for an increase in the softening point are used in many countries. For example, in Germany, two methods are applied: the R&B method and Wilhelmi’s method. According to an U. S. review of fillers (Harris and Stuart, 1995), in Germany an acceptable range of AR&B of 10-20°C has been adopted for the R&B method, with components selected at the filler-binder content ratio (F:B) equal to 65:35, % (v/v). Mortars with AR&B greater than 20°C are too stiff and are not accepted. Similarly, mortars with AR&B less than 10°C are not accepted due to their excessive plasticity.

Another interesting test applied in Germany is the determination of a stiffen­ing factor (in Germany Stabilisierungindex) (Schellenberger, 2002). It is an F:B for which the mortar AR&B increase is equal to + 20.0°C. It is necessary to make a series of filler-binder mixtures with different F:B ratios (e. g., 1:1, 1.5:1, and 2:1) and then determine a AR&B increase compared with the pure binder R&B. As a result, we obtain a graph showing the increase versus the F:B ratio; this can be interpreted as the relationship of the stiffening power of a given filler. When studying the results of stiffening factor tests, it is taken as a general rule in Germany that the results should be higher than approximately 1.9. The lower the stiffening factor, the stronger the stiffening impact of that filler on an asphalt mix.

Basically, the results of the tests lead to the conclusion that research on the increase in a softening point does not always reveal all the negative properties of a filler (e. g., swelling). Nevertheless, their merits lie in the ease with which the softening point can be measured through the R&B method.