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Load and Resistance Factor Design America's Modern Wood Engineering Method

A Step-by-Step Guide to Modern Timber Frame Engineering Patrick Gauthier

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Timber Frame Engineering in Load and Resistance Factor Design Published by TFE Publishing Company 710-900 Howe Street Vancouver, BC V6Z 2M4 www.tfepub.ca All rights reserved Copyright © 2014, 2015 by Patrick Gauthier Cover design by Patrick Gauthier Every effort has been made to ensure that all information, equations and solutions in this book are accurate. The author welcomes all comments and suggestions, including errors and/or omissions concerning this book. iStockphoto LP for images used under license. BigStockPhoto. com for images used under license ISBN 978-0-9812967-1-5 While every effort has been made to ensure the accuracy of all information presented in this book, neither the author nor TFE Publishing shall be responsible for the manner in which the information is used, nor for any interpretations thereof.

CONTENTS Section 1 - Properties of Wood 1.1. basic wood information 1.2. wood properties 1.3. effects of moisture 1.4. equilibrium moisture content 1.5. effects of shrinkage 1.6. ideal air drying practices 1.7. other wood characteristics 1.8. effects of shrinkage in buildings 1.9. calculating wood shrinkage 1.10. conclusion

Section 2 - Load & Resistance Factor Design 2.1. load & resistance factor design 2.2. safety limit states 2.3. serviceability limit states

Section 3 - Loads and Forces 3.1. loads compression tension horizontal shear bending 3.2. type of loads dead loads

3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9.

live loads snow loads wind loads assigning values to loads designing for loads tributary area live load reduction roof live loads and snow loads wind loads outward thrust

Section 4 - Design Values 4.1. design values previous testing methods in-grade testing lumber grading species groups in-grade testing results duration of load size effects design values modification factors 4.2. design values conclusion

Section 5 - Design Value Tables 5.1. introduction DV-1 wood species specific gravity DV-2 wood species average weight DV-3 weights of materials

DV-4 standard lumber sizes DV-5 lumber sectional properties DV-6 dimension lumber / built-up beams DV-7 beam and stringers, post and timber DV-8 resistance factor DV-9 time effect factor DV-10 repetitive member factor DV-11 wet service factor DV-12 size factor: dimension lumber DV-13 size factor: larger timbers DV-14 incising factor DV-15 flat use factor: dimension lumber DV-16 format conversion factor DV-17 metric / imperial conversion table DV-18 lumber sectional properties: metric version

Section 6 - Beam Design 6.1. beam design bending horizontal shear horizontal shear with notching deflection bearing on supports 6.2. concentrated loads 6.3. cantilever loading 6.4. lateral stability 6.5. plank decking 6.6. beam design conclusion 6.7. mathematical review

Section 6A - Workshop Beam Design floor joists sill beams roof purlins middle principal rafter outer principal rafters notes

Section 7 - Column Design 7.1. column design 7.2. design of wood posts 7.3. slenderness ratio 7.4. compression 7.5. compression and bending 7.6. built-up columns 7.7. stud walls 7.8. selection tables 7.9. net area 7.10. design examples 7.11. conclusion

Section 7A - Workshop Column Design middle column

Section 8 - Joinery 8.1. traditional joinery mortise and tenon stub mortise and tenon blind mortise and tenon through mortise and tenon housed mortise and tenon through mortise and tenon with diminished haunch through mortise with extended tenon brace mortise and tenon open mortise and tenon rafter seats step-lapped rafter seat housed bird mouth rafter seat floor joists splice joints 8.2. joint connections strength stiffness ductility failure modes peg diameter peg spacing 8.3. all-wood joint connections 8.4. mortise and tenon design equation 8.5. mortise and tenon design equation in LRFD 8.6. peg spacing detailing

8.7. splines 8.8. joinery conclusion

Section 9 - Timber Frame Design roof purlins principal rafter cross-beam column joinery

Section 10 - References & Resources 10.1. references 10.2. resources

How to Use this e-book This e-book has been specifically formatted to be viewed on an iPad, iPad Mini or any other e-reader in the market today than can open PDF documents. The contents of this e-book are best viewed with the e-reader in a vertical position. Every effort has been made to place the various images and drawings in the same flow of the discussion taking place so the reader could avoid flipping between pages to see the referenced image or drawing. Therefore, the best way to achieve a nice continuous flow was to design this e-book with the e-reader in a vertical position in mind. I also purposely avoided using academic jargon, and instead focused on presentable, clear and concise prose that maximizes the readers enjoyment of the subject at hand. The contents of this book is not intended to be an authority on how to build a timber frame structure, nor a guide on timber frame joinery. Rather, its intent is to present an environmentally sustainable approach to heavy timber construction by providing the means in which to choose the most efficient size timber member(s) for the given design situation.

I believe in mixing styles of wood construction. Everyone will agree that large, exposed timbers are beautiful to see. At the same time, there’s not much point in using big timbers if they are going to be hidden from view, such as within a wall. So I’ve emphasized the use of stud walls. Not only are stud walls easy to construct and install, but they are cheap, strong, versatile and are typically fashioned from inexpensive, low-grade wood from fast growing trees such as spruce and pine. Moreover, using wood from fast growing trees lessens the overall environmental footprint that goes into constructing a timber frame structure. Besides the environmental angle, I wanted to include information that respects the amazing material known as wood. For example, Section 1 is totally dedicated to wood characteristics, and these properties are emphasized throughout the rest of the book, especially how wood shrinks and swells. Regarding measurements, it has become a fairly common practice to incorporate the metric system along side imperial measurements. So I’ve mixed the two styles where convenient, but imperial units are always referenced first.

Introduction My goals in writing a book on timber frame engineering were two-fold: to provide the most modern available wood engineering equations related to timber frame design, and to present realistic three-dimensional visuals specific to the timber frame member(s) being designed. In my years of research and design of timber frame structures, I found that a fundamental ingredient was missing from every journal and book that I consulted. None of them provided three-dimensional visuals to help me understand the problems and calculations that are essential to solving timber frame engineering equations. I have undertaken to resolve that shortcoming by providing complete 3D visuals of the structural members. In addition, I have provided step-by-step guidelines for each phase of the design process. This book is intended for anyone who is interested in wood engineering. Students intending to pursue a career in timber frame design, as well as those with an advanced understanding of the subject, will benefit from the information contained here. The concepts covered range from wood properties to the most up-to-date engineering formulae, including the engineering behind all-wood joinery.

The equations presented are based on the latest version of the National Design Specification for Wood Construction. The building codes used are based on the most recent edition of the International Building Code. Design codes for timber engineering have changed little since 2006. The 2006 design codes were put together from a vast culmination of data relating to wood strength that resulted in quite an evolution of wood engineering understanding. Therefore, the codes and design procedures shown in this book will remain relevant probably for generations to come. The wood design philosophy used in this book is known as Load and Resistance Factor Design. A background of this method is explained in detail in the Load and Resistance Factor Design section. Most of all, this book presents a realistic look at the most common post and beam structural design equations and their corresponding solutions. You will not find another book with this amount of mathematical detail specific to timber frame design, combined with precision 3D pictorials and dimensioning. Trust me I’ve looked. Two timber frame designs are presented in this book, each quite similar to each other. Step-by-step equations based on their respective structural make-up are presented,

including all-wood joinery using wood pegs. The designs were developed to represent a varied assortment of timber frame post and beam design possibilities. Once you grasp the concepts on how to solve for these beams and columns, you will be able to design any structure you can imagine. The following lists what is not included in this book: • No glue laminated (glulam), engineered wood products, laminated veneer lumber (LVL), or parallel strand lumber (PSL) design equations of any kind. • No roof truss designs. • No metal fastener design equations. • No plywood or oriented strand-board (OSB) design equations. In other words, this book is entirely focused on solid sawn post and beam members and how they are joined together. Once you have mastered these, you will find it relatively simple to branch out to other aspects of timber frame design, especially using glulam members. PG May 31, 2014

The illustration below shows most of the timber frame structural components used in this book: 1. Floor Joists 2. Sill Beams 3. Posts / Columns (both mean the same thing) 4. Knee Brace 5. Principal Rafters w/ Cross-Beam 6. Principal Rafters w/ Stud Wall 7. Principal Rafters w/ Ceiling Joist 8. Principal Rafters w/ Hammerhead Truss 9. Roof Purlins

Might I suggest bookmarking the next few pages. Listed below are all the abbreviations and symbols used in this book. The three bolded ones are used very often. AF&PE American Forest and Paper Association ASCE American Society of Civil Engineers ASD Allowable Stress Design ASTM American Society for Testing and Materials CSA Canadian Standards Association DOL Duration of Load EMC Equilibrium Moisture Content IBC International Building Code

ICC International Code Council LRFD Load and Resistance Factor Design NLGA National Lumber Grades Authority (Canada) NDS National Design Specifications WWPA Western Wood Products Association Ф Ф b Фc Фs Фt Фv λ A Af Ag An At b Ce CF

Resistance Factor Resistance Factor, Bending Resistance Factor, Compression Resistance Factor, Stability Resistance Factor, Tension Resistance Factor, Shear Time Effect Factor Area Fastener Area Gross Area Net Area Tributary Area Width Exposure Factor Size Factor

Cfu Flat Use Factor CG Connectors in a Row Factor Ci Incising Factor CL Beam Stability Factor CM Wet Service Factor Cp Column Stability Factor Cr Repetitive Member Factor Cs Slope Factor Ct Temperature Factor d Depth dn Net Depth D Dead Load D Diameter E Earthquake Load E Modulus of Elasticity E’ Adjusted Modulus of Elasticity Emin Modulus of Elasticity for Stability E’min Adjusted Modulus of Elasticity for Stability ft Feet Fb Design Value for Bending F’b Adjusted Design Value for Bending F’bx Adjusted Design Value for Bending: x-axis FbEn Euler Buckling Formula for Bending Fc Design Value for Compression Parallel to the Grain F’c Adjusted Design Value for Compression Parallel to the Grain F’cb Adjusted Design Value for Compression Parallel to the Grain: y-axis

F’cd Adjusted Design Value for Compression Parallel to the Grain: x-axis Fc┴ Design Value for Compression Perpendicular to the Grain F’c┴ Adjusted Design Value for Compression Perpendicular to the Grain FcE Euler Buckling Formula for Columns Ft Design Value for Tension F’t Adjusted Design Value for Tension Fv Design Value for Shear F’v Adjusted Design Value for Shear Fvy Shear Yield Stress G Gust Factor G Specific Gravity Gpeg Specific Gravity Peg Gbase Specific Gravity Base Material kPa Kilo Pascals kN/m Kilo Newton per Metre Ke Effective Length Factor Kf Reduction Capacity Factor KF Format Conversion Factor KLL Live Load Element Factor Kzt Topographical Factor I Importance Factor I Moment of Inertia Jf Factored Load, Joints Jr Factored Resistance, Joints lbs Pounds

lbs/ft Pounds per Foot lb Effective Length: y-axis ld Effective Length: x-axis le Effective Unbraced Length lu Unbraced Length L Live Load L Length Lb Bearing Length Lo Specified Unreduced Floor Live Load Lr Roof Live Load Mf Factored Load, Bending Mr Factored Resistance, Bending o.c. On Centre P Total Load pf Flat Roof Snow Load pg Ground Snow Load Pf Factored Load, Compression Pr Factored Resistance, Compression ps Sloped Roof Snow Load ps Design Wind Pressure ps30 Simplified Design Wind Pressure pcf Pounds per Cubic Foot psf Pounds per Square Foot psi Pounds per Square Inch Qf Factored Load, Bearing Qr Factored Resistance, Bearing R Rain Load R1 Reduction for Tributary Area

R2 RB R C S S Tf Trn V Vf V r W wf

Reduction for Roof Slope Slenderness Ratio for Bending Slenderness Ratio for Column Design Snow Load Section Modulus Factored Load, Tension Factored Resistance, Tension Basic Wind Speed Factored Load, Shear Factored Resistance, Shear Wind Load Total Factored Load

1. Properties of Wood 1.1 Basic Wood Information Wood is generally divided into two broad categories: • •

Hardwoods Softwoods

Hardwoods come from slow growing deciduous trees, otherwise known as trees that shed their leaves in winter. Ash, Birch, Cherry, Poplar, Black Walnut, Maple, Red Oak and White Oak are common hardwood trees. Softwoods come from faster growing, cone bearing trees known as conifers or evergreens. Douglas Fir, Hemlock, Eastern White Pine, Southern Yellow Pine and Spruce are common softwood trees. Two kinds of wood exist in all trees: • •

Sapwood Heartwood

Sapwood is the wood located closest to the bark of the tree, and serves to carry sap to the leaves. Softwoods tend to contain relatively greater amounts of sapwood than hardwood trees. The sapwood of a tree is best suited

to fashion lumber such as planks, siding, studs and other building components that are subject to little or no stress. Also, lumber members made from sapwood are more susceptible to decay than heartwood. Heartwood is the wood located closest to the centre of the tree, and is generally quite dense. The heartwood of a tree is best suited for structural members, such as beams, posts and other larger members in timber frame construction. Figure 1.1 illustrates where wood structural members would be cut within a typical log. Figure 1.1 Sapwood and Heartwood

1.2 Wood Properties Wood is a naturally occurring material, therefore subject to the natural conditions of the environment in which trees live and grow. Such conditions produce variability in wood properties such as rate of growth, growing conditions, species and moisture content. The most important property of wood to understand is its hygroscopicity, which is the ability, or tendency of a substance to absorb moisture. Being aware of such tendencies is very important for timber frame design. When wood is cut and transformed into building materials, the moisture content of the wood continues to be lost from the wood or gained into the wood, depending on the environmental conditions to which the wood is exposed. Moisture affects wood in two ways: • Change in moisture content causes dimensional change due to shrinkage (loss of moisture) and swelling (gaining of moisture); • Excessive moisture leads to deterioration and decay of the wood.

1.3 Effects of Moisture Moisture affects wood weight, shrinkage and strength. The moisture content of wood is the actual weight of the water in the wood, expressed as a percentage of the weight of the wood. The heartwood of a freshly sawn lumber can contain anywhere from 30 to 100% moisture content. Sapwood content is usually much higher, from 100 to 200%. The wood-fibre saturation point occurs when the moisture content of the fibre is approximately 28%. The strength of the wood-fibre increases as the moisture content decreases because the cell material of the fibre stiffens as it dries. However, the strength properties are not affected to the same degree throughout the entire area of the wood. The extent to which dimensional change occurs depends upon the species and the orientation of the wood fibres. Figure 1.2 illustrates the typical stages of wood cell drying after a tree is felled.

Figure 1.2 Wood Fibre Cells Moisture Content

When wood dries from its green state, negligible or even zero shrinkage occurs until the moisture content falls below the fibre saturation level. Green lumber is freshly felled wood that is not dried or seasoned. At the saturation level, all moisture within fibre cells have been released, leaving only the walls of the cells saturated with moisture. As the cell walls continue to release moisture (continually falling below 28%) the wood does not shrink equally in each direction due to the cellular structure of wood. As wood dries, three types of shrinkage can occur: • Longitudinal • Radial • Tangential Longitudinal This type of shrinkage is a very small concern. For wood dried to 15 percent moisture content, shrinkage ranges from .05 to .12 percent. A twenty foot timber might shrink 1/4”. However, if a timber is excessively crossgrained, is not centre-cut, has large knots, contains juvenile wood (first 5 to 20 annual growth rings), or if the wood has been subject to unusual compression stresses during its growth, then other shrinkages come into play, and combined shrinkages can be considerable.

Radial Radial shrinkage affects the thickness of the annual rings. In a centre-cut timber, this tends to reduce the overall dimensions of the cross-section. Tangential This one is where shrinkage occurs on the length of the circumference of the annual rings. In a centre-cut timber, large cracks will develop parallel to the length. The crack is widest at the surface and tapers to nothing at the heart, which tends to distort the cross-section of the piece. Of the three types of shrinkage, tangential is the most significant. Figures 1.3 and 1.4 show the three types of shrinkage that occur in wood as it dries. The shrinkage rates graph shown is a good source of information for wood design purposes.

Figure 1.3 Shrinkage Characteristics

Figure 1.4 Shrinkage Rates

Table 1.1 is a very useful reference in order to determine the extent to which the most common woods used in timber framing will shrink from green state to roughly 19% moisture content. Tangential shrinkage applies to the width of the flat-grain face. Radial shrinkage applies to the width of the edge-grain face. To calculate expected shrinkage, determine the average equilibrium moisture content of wood for end use conditions. Table 1.1 Shrinkage Rates Species Western Red Cedar D-Fir Coast D-Fir Interior Western Hemlock Western Larch Eastern White Pine Red Pine Western White Pine Eastern Spruce Engelmann Spruce

Shrinkage Direction Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential Radial Tangential

% of Shrinkage from Green State to: 19% 0.9 1.8 1.8 2.8 1.4 2.5 1.5 2.9 1.7 3.3 0.8 2.2 1.4 2.6 1.5 2.7 1.5 2.5 1.4 2.6

15% 1.2 2.5 2.4 3.8 1.9 3.4 2.1 3.9 2.2 4.6 1.0 3.0 1.9 3.6 2.0 3.7 2.0 3.6 1.9 3.6

12% 1.4 3.0 2.9 4.6 2.3 4.1 2.5 4.7 2.7 5.5 1.3 3.7 2.3 4.3 2.5 4.4 2.4 4.4 2.3 4.3

6% 1.9 4.0 3.8 6.1 3.0 5.5 3.4 6.2 3.6 7.3 1.7 4.9 3.0 5.8 3.3 5.9 3.2 5.8 3.0 5.7

1.4 Equilibrium Moisture Content (EMC) Once wood has been seasoned, it adjusts slowly to changing humidity levels. The slow adjustment is an important factor because wood can serve in very high relative humidity without reaching an EMC that will initiate decay (moisture content beyond 19%). Wood is considered to be in dry service condition when the EMC over a year is 15% or less and does not exceed 19%. As Table 1.2 indicates, the average indoor EMC for most of the continental US is 8% or less. Therefore, dry service conditions always apply to wood when used indoors, with the exception of where wood may be used around swimming pools. Table 1.2 Equilibrium Moisture Content (EMC) Average EMC%

Location Most US Areas Dry Southwestern Areas Damp, Warm Coastal Areas

Indoors

8

Outdoors

12

Indoors

6

Outdoors

9

Indoors

11

Outdoors

12

1.5 Effects of Shrinkage Warping may occur as a result of uneven shrinking during drying. However, warping can be remedied to some extent by restraining the wood while it dries. Checking occurs when lumber is rapidly dried, causing cracks along the growth rings. The surface dries quickly, while the core retains a higher moisture content for some time. Consequently, the surface attempts to shrink but is restrained by the core. Such restraint causes tensile stresses at the surface, which if large enough, can pull the fibres apart, thus creating a check. Splits are through checks that generally occur at the end of wood members, where moisture is lost most rapidly (outside faces at both ends). Midway through the member, however, the wood still contains relatively high moisture content. Again, such differences cause tensile stresses at the end of the member. A split occurs when the stress exceeds the strength of the wood. Figure 1.5 illustrates checks and splits at the wood surface. Sawn timbers are susceptible to checking and splitting since they are always dressed green (S-Grn). In addition, due to their large size, the core dries slowly and the tensile stresses at the surface and at the ends can be significant.

Minor checks at the surface areas very rarely have any effect on the overall strength of the member. Deep checks, however, are significant if they occur at a point of high shear stress. The severity of splitting and checking can be reduced by controlling the rate at which wood dries. Most shrinkage problems arise when wood is subject to fast drying. If a freshly cut piece of timber is exposed to the sun, the exposed surface will dry much quicker than the rest of the timber, causing uneven shrinkage at that surface. The fibres will separate, damaging the wood. The wood should also be kept away from artificial heat sources. Figure 1.5 Checked / Split Wood

Tensile stress cracks at the surface because of restrained shrinkage.

1.6 Ideal Air Drying Practices As a rule of thumb, air drying takes about one year for every 25 mm (1”) of thickness. However, economic realities more often than not prohibit ideal drying conditions, so other practices are generally used. Coating the ends of the sawn members with sealer or lacquer will serve to retard the moisture loss, which is greatest at the ends and makes for more equal drying throughout the timber. Winter is the best time for timbering because the wood contains less sap. The members can be stacked and stored, then covered outdoors in a shaded location for approximately 16 months or longer for more seasoned drying. It is best to do the necessary carpentry work to the timbers as soon as possible after they’re cut because the reduced cross-section will allow more even drying through the member. The timbers should be protected from the sun, rain and ground moisture, but open to air flow. Based on the above, a realistic time frame for timber frame construction can be as follows: • one winter to cut the members, do the carpentry work and then stack them • stored for drying for the spring, summer, fall and one additional winter

From start to finish, the structure can be built in about 16 months. In a heated house, air is warm and dry. Thus, during the first winter in a timber framed house it is very common to hear the timbers cracking. During this time, it is a good idea to create moisture inside the house either by boiling water or by using a humidifier. 1.7 Other Wood Characteristics Knots Knots are virtually unavoidable. They form where the branch meets the trunk. Small, tight knots are preferable, and timbers with many large knots should be avoided. Knots play a vital role in the determination of overall wood strength for a given species. Later sections provide more detail on the significance of knots. Figure 1.6 Knots in Wood

Spiral Grain Where trees are subject to windy conditions, or have more branches on one side than the other, they may grow with spiral grain. A moderate amount of spiral grain is acceptable, but excessive spiralling tends to distort and twist a timber as it dries. Cross Grain Where a crooked log is sawn into a straight timber the grain will seem to wander off the edge. Ideally, the grain should run straight through the timber. Like spiral grain, it can twist and distort a timber as it dries. If wood is excessively cross-grained, huge chunks of a timber may split off under stress. Such timbers can be used in low stress locations and only for short members. Shakes Where a tree is subject to severe weather conditions such as those on a mountain ridge, shakes may be found. A shake is a gap or separation between the growth rings of successive years. Shakes weaken timbers and large chunks of wood may actually fall off when working with it.

Wane Waning occurs when a log cannot be cut completely square, and the edge of the cut timber is still rounded in parts. Although sometimes considered a defect, a waney timber does not pose serious structural problems. For aesthetic reasons, though, wanes on exposed timbers should be avoided. Figures 1.7 to 1.9 illustrate the various wood characteristics mentioned above.

Figure 1.7 Sprial Grain

Figure 1.8 Cross Grain

Figure 1.9 Waning & Shakes

1.8 Effects of Shrinkage in Buildings When exposed to outdoor air, wood dries to the fibre saturation level at a fairly rapid rate. The wood then dries at a decreasing rate until it’s in equilibrium with the surrounding air. The rate of drying slows as the outdoor temperature drops. As seen in Table 1.2, the EMC for wood stored outdoors under cover does not exceed 13% anywhere in the US. As outlined earlier, the time required for lumber to dry is a significant design factor. If lumber is installed in a heated building before the equilibrium level is reached, more shrinkage will occur, thereby increasing the risk of related problems. The International Building Code (IBC) specifies that the moisture content of lumber must not exceed 19% at the time of installation for a heated building. A frame can be erected, however, and left exposed to the outside air until the 19% is reached. An additional design factor is the part of the tree from which the lumber was sawn. Sapwood lumber has a much higher moisture content than heartwood, and should be allowed more drying time.

Plywood, a virtual necessity in any timber or wood framed building, has shrinkage characteristics similar to that of lumber in the longitudinal direction. Plywood is very stable, due to its much higher modulus of elasticity (covered in the Beam Design section) with the grain (parallel) rather than across the grain (perpendicular). Because of this stability, a common construction practice is to alternate the directions of the sheets as they are laid and nailed over floor joists, thus minimizing joist movement. The stabilizing effect of different grain directions also applies to oriented strand-board, popularly known as OSB. Also, the manufacturing process for plywood and OSB results in a final moisture content of roughly 4%, which is quite a bit lower than the final average indoor moisture content. In areas of potential high moisture content, such as an outside wall and roof areas, a gap of 1/16” must be left between the sheets to account for the ongoing swelling and shrinkage. 1.9 Calculating Wood Shrinkage Although wood shrinkage can be calculated, as will be illustrated below, economic realities often supersede all other concerns. Nevertheless, for the designer, predicting potential shrinkage is a powerful tool in ensuring quality design. The shrinkage of a wood member can be estimated using the following equation:

S = D x (M x c) where S = shrinkage (in) D = actual dressed dimension (in) (depth) M = percent of moisture change below the fibre saturation point c = shrinkage coefficient Shrinkage coefficients for both radial and tangential directions have been determined for individual species (see Table 1.1). To calculate the shrinkage coefficient for both types of shrinkage, we can assume 0.002 per 1% change in moisture content. Example 1.1 The IBC stipulates a maximum 19% moisture content at installation prior to enclosure. However, the beams in the design are green lumber and are assumed to have roughly 28% moisture content. The joists are seasoned lumber and are assumed to contain 19% moisture content. The location of the building is on the West Coast, which shall be classified as a warm coastal area. As specified in Table 1.2, the average indoor EMC for wood frames in this area is 11%, so the final indoor EMC value used for this example will be 11%.

Figure 1.10 illustrates the design when taking shrinkage into consideration. The goal of the designer is to determine the potential shrinkage of the beams and joists in order to design the depth of the joist pockets accordingly. Proper pocket depth will allow the beams to shrink so as to obtain a flush surface for the floor above. The actual pocket depth is not being determined in this example. Determination of actual depth is covered within the Beam Design section under notching. The goal is to ascertain how much more or less the pocket should be cut in order to obtain the tightest fit possible while in service. Figure 1.10 Accounting for Shrinkage

With the determination of both the initial moisture content of the beams (IMC=28%), the final expected indoor moisture content (FMC=11%) and the shrinkage coefficient (0.002), the following can be ascertained (longitudinal shrinkage is not considered): Step 1: Beams M = IMC - FMC c = 0.002 M x c = (28 - 11) x 0.002 = .034 Beams: (assumed size) 6x12 Beam Depth: 11 1/2” D S S S

= 11.5” = D x (M x c) = 11.5” x .034 = 0.39” = 3/8”

The overall in-service shrinkage for the beams at 28% moisture content prior to enclosure for this design can be expected to be about 3/8”. Step 2: Joists M = IMC - FMC (IMC assumed to be 19%) c = 0.002 M x c = (19 - 11) x 0.002 = .016

Joist Size: 4x8 Joist Depth: 7 1/4” D S S S

= 7.25” = D x (M x c) = 7.25 x .016 = 0.12” = 1/8”

Subtracting the beam overall shrinkage with the expected joist shrinkage yields: 3/8” - 1/8” = 1/4”. Therefore, the joist pocket should be designed 1/4” greater than the calculated depth. 1.10 Properties of Wood Conclusion One of the basic considerations in timber frame design is the effects of wood shrinkage in the radial and tangential directions. Inadequate drying practices can cause undesirable effects such as checking and splitting, thereby weakening the strength and structural soundness of the wood. The seasoning of main structural members to 19% moisture content or less prior to enclosure installation will ensure minimal in-service shrinkage while the members reach the indoor EMC. However, as shown in Example 1.1, the overall shrinkage even when using green lumber is not that significant in terms of a floor beam system.

Nevertheless, a timber frame designer should stipulate shrinkage as part of a quality design process. It is critically important to take the potential shrinkage of a structural member such as a beam into account when that beam is to be joined to a post by, for example, a mortise and tenon connection. The joint connection is probably the second most important design consideration next to the structural capacity of the member itself. For a structure to remain rigid and strong, the joinery must fit as snugly as possible to maintain the integrity of the frame. The designer must thereby stipulate the exact size of the mortise and tenon cuts considering the shrinkage that will occur as the member reaches the indoor EMC. If not, the joint will loosen to a greater extent over time.

2. Load & Resistance Factor Design 2.1 Load and Resistance Factor Design The purpose of this section is to present as much information as possible about this new wood design method known as load and resistance factor design (LRFD). Although LRFD is a recently introduced method for the design of wood structures in the US, it is widely used for the design of concrete and steel structures. In the United States, the wood design method that still predominates today is known as allowable stress design (ASD). ASD is likely to remain the preferred method for the foreseeable future because of the rather large undertaking of fully converting to a LRFD methodology. Many questions have been raised as to why LRFD should be adopted at all, since the ASD method has been used successfully for many years. Case studies comparing designs by LRFD vs ASD indicate a 15% reduction in cross-section for column design when using LRFD, due primarily to load factoring combinations specific to LRFD. Additional calculations indicate as much as 30% smaller cross-section for structural members subject to multiple loads such as snow, wind and live roof load. 1

Moreover, some particular load combinations might result in a 50% increase in structural resistance capacity compared to ASD calculations. Of course, some combinations may result in less required cross-section when using ASD, but for the majority of cases, LRFD methodology will produce a net reduction of wood volume compared to ASD. 1

Showalter et al. 1998 ASCE Annual International Meeting

Smaller size members reduce costs and more critically, the environmental impact of wood harvesting and processing, thus securing the long-term economic viability of such an important resource, especially for the US housing market. Also, LRFD is a more reliable method because it is based on rational statistical probabilities. ASD relies on older methods of material testing, which will be demonstrated in the Design Values section as being inadequate for the realities of wood construction. Before proceeding into more detail about LRFD, there are two US publications in which the designer must become quite familiar with to fully grasp the scope of required knowledge for structural timber design. • National Design Specification for Wood Construction • International Building Code

National Design Specification for Wood Construction (NDS) The NDS is published by the American Wood Council (AWC), which is an organization within the American Forest and Paper Association (AF&PE). The NDS for wood construction concerns itself with presenting the latest structural design recommendations by the wood industry, along with design values for various species groupings of structural lumber. The NDS publishes the design values as a supplement to its formal design section, named NDS Supplement: Design Values for Wood Construction. The designer must become familiar with the supplement because of the importance of using and understanding the design values. A portion of the supplement is reproduced in this book, along with all the required information in using it properly. The NDS publishes an additional supplement named NDS Supplement: Special Design Provisions for Wind and Seismic. This supplement was introduced in 2005 due to the unique requirements related to wind and seismic resistant design. The formal design section of the NDS along with the two supplements comprise the core, but not all, of what is required for timber frame engineering design using the

LRFD format. The NDS also publishes another supplement called ASD/LRFD Manual for Engineered Wood Construction, but for the purposes of this book it is not required because the contents throughout the remaining sections are LRFD specific, and much more detailed than what you will find in that manual. International Building Code (IBC) The IBC is published by the International Codes Council (ICC), and the main concern of the publication is assigning values to loads and forces. For example, the IBC will state the maximum permissible live load for a floor or roof. In addition, it contains information on calculating for snow loads and forces induced by wind loads. This type of information is not contained within the NDS, or in any of its supplements. The first edition of the IBC was published in 2000 and is generally updated on 3-year cycles. Most regions of the US have adopted all or part of the IBC at either the state or local level. As a result, it can be used as a sole reference in determining the correct values for the above mentioned loads and forces. With the information contained in both the NDS and IBC, the timber frame designer has all the required values to use in LRFD. Note that much of the relevant information in these two publications pertaining to timber design is reproduced in this book.

What exactly is load and resistance factor design? It is a design method that expresses the limits to which a structural member can sustain a load in a given load situation. In other words, determining the limits a member can withstand under a particular state of load. In this design method, two broad limit states can be identified for structures: 1. Safety, or ultimate limit state 2. Serviceability limit state 1. Safety Limit States Safety limit states correspond to the maximum loadcarrying capacity. The load-carrying capacities include: • Loss of equilibrium of the whole or of a part of the structure considered as a rigid body. In other words, overturning or uplifting. • Loss of load-bearing capacity of members due to the exceeding of material strength, buckling, fracture, fatigue, fire or deformation. • Overall instability of the structure. For example, the P-Delta effect (covered in the Column Design section), ponding instability (water ponds on roofs) or wind effects. •

Very large deformation: Impact, for example.

Furthermore, the factored resistance is not less than the effect of the factored loads, considering all applicable loads and load combinations. Factored is simply defined as the summary of applicable loads or resistances. In other words, the design criterion to be satisfied becomes: Factored Resistance ≥ Factored Load Effect Safety limit states usually fall within fairly narrow limits. A structural member must not be designed below the minimum strength requirements, but neither must it be so much stronger than required. Therefore, emphasis is placed on the maximum load capacity of an individual member coming closest to, but still less than the total factored load. The LRFD equation for safety limit states thus evolves into: ФR ≥ Total Load Combinations x Time Effect Factor In analyzing the left side of the equation, the Ф is the resistance factor. Resistance factor values are derived through statistical analysis so that the actual specified strengths of lumber contain a high degree of reliability. The analyses are based on test results conducted on many thousands of full dimension size lumber specimens (more detailed information is presented in the Design Values section).

The tests conducted were for bending (flexure), compression and tension forces. Ultimately, the factor takes into account variability of material properties and dimensions, workmanship, type of failure and uncertainty in the prediction of resistance. The results of the analysis led to the values used for the resistance factor, Ф. The resistance factor values are shown in Table 2.1. Table 2.1 Resistance Factor Property

Fc and Fc┴ Bending Fb Tension Ft Shear Fv Stability (modulus of elasticity) Emin

Compression

Ф Value

Symbols

Фc Фb Фt Фv Фs

0.90 0.85 0.80 0.75 0.85

The R is the calculated resistance of a member or connection based on the specified material properties. The letter R is actually never used. Typically, a letter signifying the type of stress being solved is used with an r subscript. For example, to solve for bending moment, M, at the safety limit state, the factored bending moment resistance, Mr , must be greater or equal to the factored bending load, Mf . Mr must now be solved based on the appropriate resis-

tance factor (in this case 0.85 because the force is bending) and other applicable adjustments and values. Mr = Фb x (section modulus)(adjustment factors) Mr = 0.85 x (section modulus)(adjustment factors) Other factored resistances to particular forces are solved in a similar manner, but with different values and/ or other applicable adjustments to use for the force being solved. Exact values and adjustment factors are explained in subsequent sections. The total load combinations on the right side of the equation is the effect of the factored loads for each applicable load in a given situation, and it is expressed in the same units as the factored resistance. Load combinations are important concepts in LRFD, and all of them are shown in Table 2.2.

Table 2.2 LRFD Load Combinations Case

Load Combination

1

1.4D

2

1.2D + 1.6L + 0.5(Lr or S or R)

3

1.2D + 1.6(Lr or S or R) + (*0.5L or 0.5W)

4

1.2D + 1.0W + *0.5L + 0.5(Lr or S or R)

5

1.2D + 1.0E + *0.5L + 1.6H + 0.2S

6

0.9D + 1.0W + 1.6H

7

0.9D + 1.0E + 1.6H

D = Dead Load L = Live Load: *0.5 applies to typical residential loads Lr = Roof Live Load S = Snow Load R = Rain Load W = Wind Load E = Earthquake Load **H = Load Due to Lateral Earth or Water Pressures **Please note that the IBC does include H in all LRFD combinations except for the first (1.4D). Only combinations 2, 3 and 4 apply to this book. H is not shown in those combinations because it would cause unnecessary confusion. F (load due to fluids) also forms part of some of the combinations, but it does not pertain to the contents of this book so it is omitted for clarity.

An additional criterion assigned to the LRFD load combinations is the time effect factor, λ, which is the same concept, but significantly different from, the more familiarly known load duration factor. Wood has the unique property that it can support higher stresses if the loads are applied for a short period of time. The time effect factor adjusts the nominal resistance based on the given LRFD load combination. This factor ensures that consistent reliability is achieved for various load duration effects. Table 2.3 provides the time effect factor assignment to the appropriate load combination. Table 2.3 Time Effect Factor Load Combination 1.4D 1.2D + 1.6L + 0.5(Lr or S or R)

Time Effect Factor, λ 0.6 *0.7 or 0.8 or 1.25

1.2D + 1.6(Lr or S or R) + (0.5L or 0.5W)

0.8

1.2D + 1.0W + 0.5L + 0.5(Lr or S or R)

1.0

1.2D + 1.0E + 0.5L + 1.6H + 0.2S

1.0

0.9D + 1.0W + 1.6H

1.0

0.9D + 1.0E + 1.6H

1.0

*0.7 when L is from storage *0.8 when L is from occupancy *1.25 when L is from impact

The role of the time effect factor is to consider lumber’s load resistance capabilities under long-term loading conditions, short-term loading conditions and extreme shortterm loading conditions. The 0.7 and 0.8 values are generally applied to load combinations dominated by sustained live loads such as S, R, Lr or L. A standard time effect of 1.0 is assigned when short-term loading conditions dictate the design, such as W or E. The 1.25 increase to load resistance capacity considers extreme short-term loading conditions such as sudden impact. For determining the applicable load combination, consideration must be given to the load source(s) and which, or combination thereof, will produce the greatest amount of load. The following examples will demonstrate possible load combination scenarios. Example 2.1 Floor Joists Supporting a Typical Floor in a Residence Load Combination

Time Effect Factor, λ

1.2D + 1.6L

0.8

The + 0.5(Lr or S or R) portion from load combination 2 is excluded because there are no roof, snow or rain loads to consider.

Example 2.2 Roof Joists for a Typical Residence Load Combination

Time Effect Factor, λ

1.2D + 1.6(Lr or S or R) + (0.5L or 0.5W)

0.8

1.2D + 1.0W + 0.5L + 0.5(Lr or S or R)

1.0

A roof load would be subject to dead, wind and rain loads for certain. In southern areas of the US such as Arizona, there would be no need to consider snow loads. In this case, deciding on either Lr or R depends on the greater source of load. If it is determined that Lr is greater than R, then the load combination becomes: 1.2D + 1.6(Lr) + 0.5W

λ = 0.8

However, if the residence is to be built in Denver, then snow load would be a factor. If snow turned out to be the greatest source of load, then the combination becomes: 1.2D + 1.6(S) + 0.5W

λ = 0.8

Perhaps the house will be constructed in both a high wind and snow location, such as in some areas of Montana. If wind turned out to be the greatest source of load, and snow the second greatest source, then the combination becomes: 1.2D + 1.0(W) + 0.5(S)

λ = 1.0

No live load would be considered for that last combination because the snow load would supersede it. However, for multiple load source situations such as this, it might become necessary to solve two separate combinations to determine which one produces a greater net load. For example, if the loads were determined as follows: D = 13 psf, Lr = 12 psf, S = 8 psf, W = 17.5 psf then two combinations are possible, and whichever produces the greater load is used. 1.2D + 1.6(Lr or S or R) + (0.5L or 0.5W) 1.2(13) + 1.6(12) + 0.5(17.5) = 43.6 psf 1.2D + 1.0W + 0.5L + 0.5(Lr or S or R) 1.2(13) + 17.5 + 0.5(12) = 39.1 psf How to go about solving for particular loads such as wind and snow is covered in later sections.

2. Serviceability Limit States Serviceability limit states are more subjective and there is more latitude for interpretation. Serviceability limit states are considered in the design process to ensure that structural performance is satisfactory when the specified loads are applied under day-to-day conditions. Vibration and deflection of members and slippage in a joint are examples of occurrences that may not cause collapse, but might cause unsightly deficiencies. Other examples may include, but are not limited to: • Excessive deflection or rotation that affects the use of the structure, the appearance of structural or nonstructural components, or the operation of equipment. • Excessive local damage (cracking or splitting, local yielding, slip of connections) that affects the use, durability, or appearance of the structure. • Excessive vibration that affects the comfort of the occupants or the operation of equipment. It becomes apparent that the above criteria could mean different things to different people. However, the IBC provides better clarification towards minimum steps required for serviceability.

For wood design, the deflection of a member is included as part of the design process, and it is a measure of how much a member, or system of members, will actually bend while in-service. Excessive deflections of, say, an upper level floor system might cause cracking and a distinctly visible displacement of the finished ceiling material attached to the bottom of the floor system. To account for these in-service possibilities, the IBC requires that deflection be calculated as part of the design process. More detailed information about deflection is covered in the Beam Design section, along with the IBC deflection stipulations.

Conclusion The information presented in this section explains the requirements of using the load and resistance factor design approach in wood engineering. The designer is first introduced to the two publications required to obtain the necessary design and load values: the National Design Specification for Wood Construction and the International Building Code. Design considerations using the LRFD format falls into two categories: Safety Limit States and Serviceability Limit States. Safety limit states deals specifically with applied loads and corresponding resistance factors. Serviceability limit states presents more interpretational latitude that essentially revolves around the deflection of a member or system of members. The concept of the resistance factor, Ф, is a unique LRFD specification derived from the statistical analysis of specified strengths of lumber, thus providing a high degree of reliability for lumber strength design values. Design in LRFD format begins with the determination of load combinations for the given design situation. As shown from the examples, the designer must consider all possible load sources before deciding on the most appropriate combination to use.

The next section describes the type of loads acting on structural members along with the forces involved with the accompanying loads. It also covers how values for loads are obtained and applied to LRFD. Please note that the calculation of earthquake loads requires a speciality that is beyond the scope of this book. Therefore, earthquake loads will not be included as a load criterion in this book.