TIMBER FRAME ENGINEERING

Transcription

1 TIMBER FRAME ENGINEERING Canadian Timber Frame Engineering in Limit States Design Canada s Timber Engineering & Wood Design Method wood properties loads and forces beam & column design engineering behind timber joinery with wooden pegs two detailed timber frame designs included hundreds of 3D illustrations P a t r i c k G a u t h i e r

2 Timber Frame Engineering in Limit States Design Published by TFE Publishing Company Howe Street Vancouver, BC V6Z 2M4 All rights reserved Copyright 2014, 2015 by Patrick Gauthier Cover design by Patrick Gauthier Edited by Sandra McKenzie Photos by Patrick Gauthier and Derek Johnson Grateful acknowledgement is made to the Canadian Standards Association (CSA) for permission to reproduce material from CSA Standard CAN/CSA , Engineering Design in Wood, which is copyrighted by Canadian Standards Association, 5060 Spectrum Way, Suite 100, Mississauga, ON, Canada, L4W 5N6. While use of this material has been authorized, the CSA shall be neither responsible for the manner in which the information is presented, nor for any interpretations thereof. 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. Feel free to him at

3 Library and Archives Canada Cataloguing in Publication Gauthier, Patrick, Timber frame engineering in limit states design / Patrick Gauthier Canadian ed. Includes bibliographical references and index. ISBN Building, Wooden. 2. Wooden-frame buildings. I. Title. TA666.G C

4 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 properties of wood conclusion Section 2 - Limit States Design 2.1. limit states design 2.2. ultimate 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

5 live loads snow loads wind loads 3.3. assigning values to loads 3.4. designing for loads 3.5. tributary area 3.6. live load reduction 3.7. roof live loads and snow loads 3.8. wind loads 3.9. outward thrust Section 4 - Design Values 4.1. design values previous testing methods in-grade testing lumber grading canada s 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

6 DV-4 standard lumber sizes DV-5 lumber sectional properties DV-6 structural light framing DV-7 light framing grades DV-8 beam and stringer grades DV-9 post and timber grades DV-10 built-up beams DV-11 load duration factor DV-12 system factor DV-13 size factor DV-14 service condition factor DV-15 treatment factor DV-16 metric conversion table Section 6 - Beam Design 6.1. beam design bending horizontal shear horizontal shear with notching deflection bearing area 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

7 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 design examples conclusion Section 7A - Workshop Column Design middle design Section 8 - Joinery 8.1. traditional joinery mortise and tenon stub mortise and tenon

8 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 limit states design 8.6. peg spacing detailing 8.7. splines 8.8. joinery conclusion

9 Section 9 - Timber Frame Design roof purlins principal rafter cross-beam column joinery Section 10 - References & Resources references resources

10 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 e-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.

11 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, Canada uses the metric system, but as with most people involved in the construction trade, I am more comfortable using imperial measurements. So I ve mixed the two styles, with an emphases on metric units, but always referencing the equivalent imperial unit in brackets.

12 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, and include wood joinery.

13 The equations presented are based on codes and specifications of the National Building Codes of Canada, British Columbia Building Codes and wood design codes published through the Canadian Wood Council. Design codes for timber engineering have changed little since 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. Canada s timber design philosophy is known as Limit States Design to wood engineering, which is explained in detail in Section 2 of this book. The building codes used are specific to the province of British Columbia. 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,

14 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

15 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

16 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. ASCE American Society of Civil Engineers ASD Allowable Stress Design ASTM American Society for Testing and Materials BCBC British Columbia Building Code CSA Canadian Standards Association DOL Duration of Load EMC Equilibrium Moisture Content NBCC National Building Code of Canada NLGA National Lumber Grades Authority

17 Ф Resistance Factor A Area A f Fastener Area A g Gross Area A n Net Area b Width C a Accumulation Factor C b Roof Snow Load Factor C B Slenderness Ratio: Beams C c Slenderness Ratio: Columns C e Exposure Factor C g Gust Effect Factor C p External Pressure Coefficient C s Slope Factor C w Wind Exposure Factor d Depth d n Notch Depth D Dead Load D Diameter e Required Bearing Length E Earthquake Load E Modulus of Elasticity E 05 Modulus of Elasticity for Compression Members ft Feet f b Design Value for Bending F b Design Value for Bending After Modifications F ben Euler Buckling Formula for Bending f c Design Value for Compression Parallel to Grain

18 F c Design Value for Compression Parallel to the Grain After Modifications F ce Euler Buckling Formula for Columns f cp Design Value for Compression Perpendicular to the Grain F cp Design Value for Compression Perpendicular to the Grain After Modifications F r Factored Resistance for Notching f t Notch Shear Force Resistance F t Notch Shear Force Resistance After Modifications f t Design Value for Tension F t Design Value for Tension After Modifications f v Design Value for Shear F v Design Value for Shear After Modifications F vy Shear Yield Stress G Specific Gravity G peg Specific Gravity Peg G base Specific Gravity Base Material I Importance Factor I Moment of Inertia I s Importance Factor, Snow I w Importance Factor, Wind J f Factored Load, Joints Connectors in a Row Factor J G

19 J r Factored Resistance, Joints kpa Kilo Pascals kn/m Kilo Newton per Metre K B Length of Bearing Factor K c Slenderness Factor K D Load Duration Factor K e Effective Length Factor K H System Factor K L Beam Stability Factor K N Notch Factor K S Service Condition Factor K Sb Service Condition Factor: Bending K Scp Service Condition Factor: Compression Perpendicular K SE Service Condition Factor: Modulus of Elasticity K St Service Condition Factor: Tension K Sv Service Condition Factor: Shear Treatment Factor K T K Z Size Factor K Zb Size Factor: Bending K Zc Size Factor: Compression K Zcp Size Factor: Bearing K Zt Size Factor: Tension K Zv Size Factor: Shear lbs Pounds lbs/ft Pounds per Foot

20 l b l d l e l u L L L b M f Effective Length About the y-axis Effective Length About the x-axis Effective Unbraced Length Unbraced Length Live Load Length Bearing Length Factored Load, Bending M f Factored Bending Moment Due to Lateral Loading Only M r Factored Resistance, Bending MPa Mega Pascals N Number of Connectors o.c. On Centre p Specified External Pressure P Total Load P f Factored Load, Compression P r Factored Resistance, Compression pcf Pounds per Cubic Foot psf Pounds per Square Foot psi Pounds per Square Inch q Reference Velocity Pressure Q f Factored Load, Bearing Q r Factored Resistance, Bearing R Rain Load s Spacing of Connectors

21 S Snow Load S Section Modulus S r Associated Rain Load S s Ground Snow Load t Thickness of Thinnest Member T f Factored Load, Tension T rn Factored Resistance, Tension V f Factored Load, Shear V r Factored Resistance, Shear W Wind Load Total Factored Load w f

22 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

23 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

24 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.

25 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

26 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 six metre timber (20 ) might shrink 6mm (1/4 ). However, if a timber is excessively cross-grained, 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.

27 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.

28 Figure 1.3 Shrinkage Characteristics Figure 1.4 Shrinkage Rates

29 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 Shrinkage % of Shrinkage from Green State to: Direction 19% 15% 12% 6% Western Red Cedar Radial Tangential D-Fir Coast Radial Tangential D-Fir Interior Radial Tangential Western Hemlock Radial Tangential Western Larch Radial Tangential Eastern White Pine Radial Tangential Red Pine Radial Tangential Western White Pine Radial Tangential Eastern Spruce Radial Tangential Engelmann Spruce Radial Tangential

30 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 in all of Canada rarely exceeds 11%. 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) West Coast Prairies Location Central Canada East Coast Average EMC% Winter EMC% Summer EMC% Indoors 10 to Outdoors 15 to Indoors 6 to Outdoors 11 to Indoors 7 to Outdoors 13 to Indoors 8 to Outdoors 14 to

31 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.

32 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.

33 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. 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 would be: 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

34 In a heated house, air is warm and dry, so 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

35 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.

36 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

37 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 in summer does not exceed 13% anywhere in Canada. 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 National Building Code of Canada, most provincial building codes and US codes specify 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.

38 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. 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 2mm (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:

39 S = D x (M x c) where S = shrinkage (mm) D = actual dressed dimension (mm) (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 per 1% change in moisture content. Example 1.1 The NBCC 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. As specified in Table 1.2, the average indoor EMC for wood frames on the West Coast is 10 to 11%, so the final indoor EMC value used for this example will be 10%.

40 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

41 With the determination of both the initial moisture content of the beams (IMC=28%), the final expected indoor moisture content (FMC=10%) and the shrinkage coefficient (0.002), the following can be ascertained (longitudinal shrinkage is not considered): Step 1: Beams M = IMC - FMC c = M x c = (28-10) x =.036 Beams: (assumed size) 140x292mm (6x12) Beam Depth: 292mm (11 1/2 ) D = 292mm S = D x (M x c) S = 292mm x.036 S = 10.5mm (0.41 ) The overall in-service shrinkage for the beams at 28% moisture content prior to enclosure for this design can be expected to be about 10mm (3/8 ). Step 2: Joists M = IMC - FMC (IMC assumed to be 19%) c = M x c = (19-10) x =.018

42 Joist Size: 89x184mm (4x8) Joist Depth: 184mm (7 1/4 ) D = 184mm S = D x (M x c) S = 184mm x.018 S = 3.3mm (0.13 = 1/8 ) Subtracting the beam overall shrinkage with the expected joist shrinkage yields: 10mm - 3.3mm = 6.7mm (1/4 ). Therefore, the joist pocket should be designed 6.7mm greater than the calculated depth 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

43 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.

44 2. Limit States Design 2.1 Limit States Design In Canada, limit states design (LSD) has replaced the method known as working stress design (WSD). In fact, the use of WSD is no longer permitted for wood structural design. Although LSD was introduced as a method to wood design relatively recently, it is widely used for the design of concrete and steel structures. 1 Case studies comparing designs conducted through a limit states approach versus a working or allowable stress approach indicate a 15% reduction in cross-section for column design when using a limit states approach, due primarily to load factoring combinations. 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. Moreover, some particular load combinations might result in a 50% increase in structural resistance capacity compared to working stress calculations. Of course, some combinations may result in less required cross-section when using a working stress approach, but for the majority of cases, a limit states methodology will produce a net reduction of required wood volume for the design situation. 1 Showalter et al ASCE Annual International Meeting

45 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. Also, LSD is a more reliable method because it is based on rational statistical probabilities. Working stress design relied upon older methods of material testing, which will be demonstrated in the Design Values section as being inadequate for the realities of wood construction. In Canada, the National Building Code of Canada (NBCC) is the governing publication that provides standards for the design of many various construction materials, which of course includes wood. The NBCC is published by the Research Council of Canada. The NBCC derives its published standards through the work of the Canadian Standards Association (CSA). Chartered in 1919, the CSA is a not-for-profit, nonstatutory and voluntary membership association engaged in the development of standards and certification activities. CSA standard 086.1, Engineering Design in Wood (Limit States Design) was prepared by the CSA Technical Committee on Engineering Design in Wood (CSA standard 086 was the WSD wood design method).

46 The committee consists of professional engineers with balanced representation from producers of wood products, consulting engineers, universities, government and other interested parties. CSA standard was written under the jurisdiction of the CSA Standards Steering Committee on Structures (Design), which was then subsequently approved as National Standards of Canada by the Research Council of Canada. The standards set out minimum requirements for the structural design and appraisal of timber buildings and other structures of normal proportions. The design values for structural wood members stipulated by the CSA are contained within Tables DV-6 to DV-10 in the Design Value Tables section. It is to be noted that the CSA, along with the NBCC, have no inherent legal status but they both do acquire legal status by reference in provincial legislation (i.e. the British Columbia Building Code) that regulates building construction. What exactly is limit states 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.

47 The CSA special publication S : Guidelines for the Development of Limit States Design states: A structure, or part of a structure, is considered unfit for use or to have failed when it, or any part thereof, exceeds a particular state, called limit state, beyond which its performance or use is impaired. The limit states are classified into two categories: 1) Ultimate Limit State Ultimate limit states are those concerning safety and correspond to the maximum load-carrying 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 (see Column Design section for an explanation), ponding instability (water ponds on roofs) or wind effects. Very large deformation: Impact, for example.

48 2) Serviceability Limit State Serviceability limit states are those that restrict the normal use and occupancy or affect durability, and include: 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. In analyzing CSA special publication S , it becomes apparent that it is the responsibility of the structural designer to determine all of the limit states that apply to the structure being designed. Furthermore, that for each limit state, 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:

49 Factored Resistance Factored Load Effect Ultimate Limit States Ultimate 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, the emphasis is on the maximum load capacity of an individual member or connection coming closest to, but still less than the total factored load. The LSD equation for ultimate limit states is: ФR Total Load Combinations x Importance Factor In analyzing the left side of the equation, the Ф is the resistance factor. Resistance factor values are derived by the CSA 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. Detailed information on the significance of the test results are presented in the Design Values section. The tests conducted were for bending, 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.

50 The results of the analysis led to the values used for the resistance factor, Ф. The values are: Bending, Shear and Tension: Ф = 0.90 Compression Parallel to the Grain: Ф = 0.80 Compression Perpendicular to the Grain: Ф = 0.80 Plywood: Ф = 0.95 The R is the calculated resistance of a member or connection based on the specified material properties. The letter R is always replaced by another letter with an r subscript. The new letter signifies the particular load situation. For example, to solve for bending moment (M) at the ultimate limit state, the factored bending moment resistance, M r, must be greater or equal to the factored bending load, M f. M r replaces the R in the equation and must now be solved based on the appropriate resistance factor (in this case 0.90 because the force is bending) and other applicable adjustments and values. M r = Ф x (section modulus)(modification factors) M r = 0.90 x (section modulus)(modification factors)

51 Other factored resistances to particular forces are solved in a similar manner, but with different values and/ or other modifications to use for the particular force being solved. Exact values and modification 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. Design in LSD format begins with a determination of the design loads. The loads acting on the member(s) are either a single total dead load or a combination of loads. Load combinations are very important concepts in limit states design. Combinations for ultimate limit states are shown in Table 2.1. Table 2.1 Load Combinations for Ultimate Limit States Case Principal Loads Companion Loads 1 1.4D - 2 (1.25D or 0.9D) + 1.5L 0.5S or 0.4W 3 (1.25D or 0.9D) + 1.5S 0.5L or 0.4W 4 (1.25D or 0.9D) + 1.4W 0.5L or 0.5S 5 1.0D + 1.0E 0.5L or 0.25S

52 D L S W E = Dead Load = Live Load = Snow Load = Wind Load = Earthquake Load In Table 2.1, the principal loads are the loads acting on the member(s). The... or 0.9D refers to situations where the dead load is counteracting the other loads within the particular combination. Note that 0.9D is never used throughout the timber frame calculations presented in this book. The companion loads are used in situations where three loads are acting. For example, should the loads acting on a structure be coming from dead, live and snow as in Case 2, the snow load is reduced by 50% (0.5S). In Case 2, the snow load would be the companion load only when the total live load is greater than the total snow load. Conversely, in Case 3 the snow load would be greater than the live load thus allowing a 50% live load reduction (0.5L). The reductions take into consideration the unlikely occurrence of all three loads acting at their very maximum at any given time. And finally, the importance factor, I, is assigned for snow (S) and wind (W) loads. Earthquake loads are also

53 assigned an importance factor, but they will not be covered for the purposes of timber framing. The importance factor pertains to categories for buildings based on their intended use and occupancy. Table 2.2 presents values to use for the importance factor for ultimate limit states. Table 2.2 Ultimate Limit States Importance Factors Category I s, I w Low 0.8 Normal 1.0 High 1.15 Post Disaster pertains to structures such as a barn, where it can be shown that collapse is not likely to cause injury or other serious consequences is for normal importance which is a typical residence pertains to buildings to be used as post-disaster shelters such as schools and community centres pertains to structures that are essential to provide services in the event of a disaster, such as a hospital.

54 For typical one or two storey timber frames, we can assume that at ultimate limit states the importance factor will always be 1.0 so it need not ever be considered. Note that 1.0 is also the earthquake importance factor for the normal building category. The importance factor at serviceability limit states, however, does contain different values for both snow and wind loads that must be considered in the design process. 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. The loads acquired to determine serviceability limit states are the same as that for ultimate limit states except for the differences in load combinations and importance factors. Table 2.3 presents the load combinations for serviceability limit states.

55 Table 2.3 Load Combinations for Serviceability Limit States Case Principal Loads Companion Loads 1 1.0D D + 1.0L 0.5S or 0.4W 3 1.0D + 1.0S 0.5L or 0.4W 4 1.0D + 1.0W 0.5L or 0.5S And the importance factors to assign for loads at serviceability limit states are presented in Table 2.4. Table 2.4 Serviceability Limit States Importance Factors Category I s I w Low Normal High Post Disaster As will be shown throughout the timber frame designs presented in this book, the serviceability limit states are calculated only for the expected deflection of a structural member. And again, the importance factor, I, is assigned for snow (S) and wind (W) loads only.

56 Conclusion The information presented in this section explains all that is required in order to use the limit states design approach for wood engineering. The tables presented for both ultimate limit states and serviceability limit states are essential in determining the total factored load for a given design situation. 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 limit states design.