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Reliability based design of light gauge timber connectors Kazemi, Masoud Reza 1994

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RELIABILITY BASED DESIGN OF LIGHT GAUGE TIMBER CONNECTORSbyMASOUD REZA KAZEMIB. A. Sc., The University of British Columbia, 1992A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Civil EngineeringWe accept this thesis as conformingto the required standardTHE UNiVERSITY OF BRITISH COLUMBIAAugust 1994© Masoud Reza Kazemi, 1994In presenting this thesis in partial fulfillment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission forextensive copying of this thesis for scholarly purposes may be granted by the headof my department or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.•(Signature)________________________________Departmentof CivicThe University ofBritish ColumbiaVancouver, CanadaDatelAbstractJoist hangers are one of the most common types of mechanical connectorsused in today’s wood construction industry. Yet, testing agencies and design codesdo not have a proper testing procedure and design guidelines to predict thecapacity of these connectors. The exisiting design guidelines are not compatiblewith the current Limit States Design Code in Canada.Various issues related to the existing joist hanger test procedures werestudied to identify the important criteria for possible adaptation to currentCanadian design standards, while maintaining the link between testing rules andcommon construction practice. A list of recommendations and notes were made toact as guidelines for future modification or subsequent revision of these standards.As the main focus of this study, an analytical model which predicts theserviceability and ultimate resistances of light gauge joist hangers was developed,based on a wide-ranging series of experimental results. This was achieved byadapting analytical procedures to reflect observed failure modes in tested joisthanger assemblies, and ultimately through calibration against experimental testresults. This model is suitable for load capacity calculations or for reliabilitystudies of light gauge structural timber connectors.11Table of Contents NAbstract iiTable of Contents iiiList of Tables viiList of Figures viiiAcknowledgmentsSpecial Notice xiCHAPTER 1.0 Literature Study 11.0 Introduction 11.1 Material Properties ofWood 21.1.1 Basic Composition ofWood 21.1.2 Compression Perpendicular to Grain 31.1.3 The ASTM Test Method for Bearing 51.1.4. Madsen’s Proposed Testing Method 61.2. Tension Perpendicular to Grain and Longitudinal Shear Effects 71.3. Cold Formed Sections 101.3.1 Mechanics and Effects of Cold Forming 101.3.2 Codified Approach in Design of Cold Formed Sections 121.4 Load-Slip Characteristics ofNailed Connections 131.4.1 Moisture Effects 171.5 Limit States and Reliability Based Design 171.6 Joist Hanger Investigations 22111CHAPTER 2.0 Joist Hanger Testing Procedure 252.1 Introduction 252.2 Codified Approach 262.3 Loading Conditions and Test Methods 272.4 Testing Apparatus 282.5 Data Acquisition 292.6 Joist Hanger Variables and Sampling 302.7 Vertical Resistance Test Specimens 322.8 Vertical Resistance Test Procedure 372.9 Allowable Design Loads 412.10 Inclined and/or Skewed Joist Hangers 422.11 Uplift Resistance of Joist Hangers 44CHAPTER 3.0 Experimental Program and Results 463.1 Introduction 463.2 Component Testing 473.2.1 Joist Seat Component Testing 483.2.2 Joist Side Nails Component Testing 513.2.3 Header Face Nail Component Testing 553.2.4 Header Top Flange Component Testing 583.3 Material Property Tests 603.3.1 Compression Perpendicular to Grain Tests 603.3.2 Joist Hanger Coupon Tests 623.4 Horizontal Hanger Assembly Tests 633.5 Inclined or Variable Slope Hanger Tests 65ivCHAPTER 4.0 Development of Analytical Model.674.1 Introduction 674.2 Load Path of Joist Hanger Systems 684.3 Joist Seat Model 684.3.1 Serviceability Model 694.3.2 Ultimate Strength Model 744.4 Joist Stirrup Nail Behaviour 774.4.1 Serviceability Model 774.4.2 Ultimate Strength Model 814.5 Header Nail Behaviour 844.5.1 Serviceability Model 844.5.2 Ultimate Strength Model 854.6 Header Top Flange Model 874.6.1 Serviceability Model 874.6.2 Ultimate Strength Model 884.7 Model Verification 914.7.1 Reliability Analysis 94CHAPTER 5.0 Conclusions and Recommendations 955.1 Joist Hanger Test Procedure 965.1.1 Inclined Joist Hangers 975.2 Joist Hanger Analytical Model 975.3 Final Thoughts 98Bibliography 100VAppendix A Additional Literature 1081.0 Plate Buckling 109Al. 1 Elastic Plate Buckling 109Al .2 Inelastic Plate Buckling 111Al.3 Post Buckling behaviour of Plates 1122.0 Other Related Topics 114A2. 1 Multiple Fastener Connections 115A2.2 Load Duration Effects 1163.0 System Reliability 118A3.1 Introduction 119Appendix B Summary ofModel Formulae 122B.1 Introduction 123B.2 Joist Seat Serviceability Model 123B.3 Joist Seat Ultimate Model 124B.4 Joist Stirrup Nail Serviceability Model 124B. 5 Joist Stirrup Nail Ultimate Model 124B.6 Header Nail Serviceability Model 125B.7 Header Nail Ultimate Model 125B.8 Top Flange Serviceability Model 126B.9 Top Flange Ultimate Model 126viII List of Tables UTable 3.1 - Standard ASTM compression perpendicular to grain test results 62Table 3.2 - Hanger coupon test results 63Table 3.3 - Summary of horizontal hanger assembly test results 64Table 3.4 - Summary of inclined hanger assembly test results 66viiList of FiguresFigure 1.1 - Typical structural components in a joist hanger connection 1Figure 1.2 - Idealized model of timber under bearing stresses 4Figure 1.3 - Standard ASTM compression perpendicular to grain specimen 5Figure 1.4 - Madsen’s proposed compression perp. specimen 6Figure 1.5 - Mathematical interpretation of Reliability Index 21Figure 2.1 - Typical loading conditions and test setups ofjoist hangers 27Figure 2.2 - Typical components used in a joist hanger test 37Figure 2.3 - Pre-load and seating location on load-displacement curve 38Figure 2.4 - Load transfer mechanism of a joist under transverse loading 40Figure 2.5 - Flow chart outlining the existing hanger capacity determination 41Figure 2.6 - An example of inclined and/or skewed testing apparatus 44Figure 3.1 - Schematic of seat component testing specimens 49Figure 3.2 - Schematic ofjoist nail component testing specimens 52Figure 3.3 - Schematic of header nail component testing specimens 56Figure 3.4 - Schematic of top flange component testing specimens 59Figure 3.5 - Standard ASTM compression perp. specimen 61Figure 4.1 - Load path model of a typical joist hanger system 68Figure 4.2 - Seat linear elastic model 71Figure 4.3 - Seat linear elastic deflected shapes 73-74Figure 4.4 - A close-up ofjoist hanger seat under applied load 76Figure 4.5 - Elastic model of a laterally loaded single fastener 79Figure 4.6 - Structural model of steel plate and wood connected by nails 80Figure 4.7 - Connection failure modes for two-member joints with one nail 83Figure 4.8 - Elastic model of a top flange single fastener 88vii’List ofFiguresFigure 4.9 - Free Body Diagram of a typical top flange 90Figure Al. 1 - Plate Buckling 106ixAcknowledgments UThe author wishes to express his sincere appreciation to his advisor, Dr.Helmut G.L. Prion, for his advice and guidance in the course of this researchproject. Drs. Ricardo 0. Foschi and Robert G. Sexsmith are also thanked fortheir advice during this study. Sincere thanks go to Mr. Alan loon of theNational Research Council, without whose involvement and contribution thisproject was not possible. Mr. George Shahnazarian of MGA Connectors Ltd. isgreatly thanked for his advice and financial support throughout this study.The author wishes to categorically thank all those who contributed incompleting this research project.xSpecial Notice NThis publication was prepared to outline the format for a structural andreliability analysis of light gauge joist hangers. Although the includedexperimental results in general represent the behaviour of light gauge joist hangercomponents, all the model formulae are based on basic structural mechanics andare therefore tentative or hypothetical. None of the provisions of this proposal, ormodel formulae, should be used for actual design purposes.This thesis is a partial report of a professional Partnership Projectconducted in collaboration with MGA Connectors Ltd. of Maple Ridge, BritishColumbia. Due to the proprietary nature of the majority of test results, as per prioragreement, only conceptual aspects of the study are included in this thesis. For acomplete report, the reader is referred to MGA Connectors Ltd.xiChapter 1 Literature Study U1.0 IntroductionIn light timber framing construction, the floor or roof gravity loads arecarried by horizontal or inclined joists or beams to the adjacent girders or headers.Joists are usually dimension lumber nominally 2 inches by 10 to 12 inches, whileheaders may be manufactured sections such as Parallel Strand Lumber (PSL) orLaminated Veneer Lumber (LVL) and I-joists. Joist hangers are commonlyutilized to transfer the joist reaction load to the main members. For the sake ofsimplicity the joist or beam hanger is referred to, hereinafter, as ajoist hanger andthe adjacent girder or multi-ply beam as a header. Figure 1.1 is a schematicpresentation of these structural components.Headerm Joist HangerFigure 1.1 - Typical structural components in a joist hanger connection.Due to the proprietary nature of this product, available literature on theperformance and behaviour of light gauge joist or beam hangers is scarce. Theliterature invariably concentrates only on the various components and materialsthat affect the behaviour ofjoist hangers as used in timber construction.1CHAPTER 1 Literature Study1.1 Material Properties of WoodLight gauge joist hangers are commonly used in light timber framingconstruction. Since wood is the primary material in this type of construction, itshould be examined for its mechanical properties, as well as its composition. In atypical connection, basic material properties that are required to be investigatedare:• perpendicular to grain compression strength ofjoist and header,• perpendicular to grain tension and shear strength ofjoist and header,• bending, buckling and tensile behaviour of cold formed steel sheetswhich are used to manufacture joist hangers, and• bending, shear and pull-out of nails in a typical joist hanger.1.1.1 Basic Composition of WoodThe structure of wood consists of large numbers of tubular cells or fibers ofsquarish cross section bound together with ligrnn. The variations of tree shapesand sizes are of significance, since the cell formations and orientations have adirect impact on the density of the timber. Due to the fact that the cell tubes aremade of essentially the same material, the large density variation of wood iscaused by various thicknesses of the cell walls. As a consequence, most of themechanical properties of different wood species are approximately proportional totheir densities. For instance, in general, a timber twice as dense will be twice asstrong and so on (Gordon, 1976). It is interesting to note that it is this simple factthat governs the basic design and structural principal of modern manufacturedwood products.To best visualize the wood mitrix, it is convenient to model the individualwood cells as drinking straws and the piece of wood as a bundle of straws held2CHAPTER 1 Literature Studytogether by a weak rubber glue representing the lignin in which the cells areembedded (Madsen, Hooley and Hall, 1982). Throughout this report, the tube orstraw analogy will be used to explain the behaviour and properties of wood in atypical timber joist hanger connection.1.1.2 Compression Perpendicular to GrainCompression perpendicular to grain stresses, in the form of bearing stresses,are inevitably present in most timber structures. Relatively high bearing stressesusually occur in timber connections, and are an important consideration in thedesign of effective connections. These stresses can be encountered in trussstructures, beam to column connections, concrete form work structures and, mostimportantly, in structural joist hangers. To clearly understand this behaviour is ofsignificant importance in the design of timber connections.As Madsen (1992) points out, it should be noted that catastrophic failuresare rarely caused by compression perpendicular to grain stresses; it is more likelythat serviceability conditions will be the governing design criterion for the designof bearing surfaces. In testing full sized specimens, Madsen observed thatcompression perpendicular to grain stresses can, however, cause prematurestructural failures when combined with relatively high tension stresses parallel tograin. This combined state of stresses and associated failures do indeed occur injoists during testing of light gauge joist hangers; this phenomenon will beexamined at a later point in this report.In reality most bearing situations are much more complex and the pureperpendicular to grain compression failure very seldom applies. Madsen et a?.(1982) and Madsen (1992) investigated and explained the failure modes and stress3CHAPTER 1 Literature Studydistributions under a steel plate. lii a typical case of a bearing plate over a column,the load is earned by two different mechanisms (Figure 1.2). The first mechanismis the uniform resistance of wood along the length of the bearing plate, which canbe visualized as a cluster of small springs. Under the applied load, the plate tendsto crush or sink into the wood with uniform deformation in the springs. As adirect result of this plate deformation into the wood, a second mechanism isactivated which is the shear at the corner where the bearing plate enters the wood.Depending on circumstances, this shear resistance significantly contributes to theload carrying capacity of the wood.Typical Timber Beam Idealized ModelLi i— Bearing Plate 4 —--—- Uniformly Distributed SpringsColumn ConcentratedFigure 1.2 - Idealized model of timber under bearing stresses.It should also be noted that the magnitude of the shear resistance is highlydependent on the deformation or indentation of the wood and is independent of theplate length, whereas the load carrying capacity of the springs is directlyproportional to the length of the bearing plate (Madsen, 1992). A similarcompression perpendicular to grain stress distribution is generated in the wood of atypical joist hanger seat under gravity loading conditions.4CHAPTER 1 Literature Study1.1.3 The ASTM Test Method for BearingThe current test method for bearing or compression perpendicular to grainis governed by the testing standard ASTM D245 (1988). This method requiresclear wood specimens to be 2” x 2” x 6” long (or 50 x 50 x 150 mm), with rigidsupport at the base, being loaded at the center of the specimen via a 2” X 2” x 1”thick (50 x 50 x 25mm) steel plate (Figure 1.3).2’x2x6’LONG p pWOOD SPECIMRIGID FOUNDATION OF TESTING MACHINEFigure 1.3 - Standard ASTM compression perpendicular to grain specimen.By carrying out a standard ASTM bearing test, it is possible to obtain aload-deflection curve and consequently the proportional limit and modulus ofelasticity, E±. As Madsen (1992) points out, allowable stresses and Ei values, withdue consideration given to wet and dry service conditions as well as load durationand safety, were determined from these tests and were the basis for compressionperpendicular to grain properties stated in the code. In addition, depending on thebearing length or bolt diameter, proper modification factors had to be applied tothe code values. These modification factors significantly increased as bearinglength or bolt diameter decreased.Since no explanation is provided for this substantial increase in allowablestresses, Madsen, based on early work by Hall (1980) and Madsen et al. (1982),claims that it is undoubtedly due to the two load carrying mechanisms: uniformly5CHAPTER 1 Literature Studydistributed resistance of the compressed wood and the concentrated shear force atthe edges.The load-deflection curves generally exhibit a soft initial response,therefore the determination of the equivalent crushing strength (point A on curvein Figure 1.4) requires a certain amount of judgment to produce consistent results.This initial settlement is an inherent property of wood when subjected tocompression perpendicular to grain. It can be accounted for by applying a preload or by shifting the origin of the load-deflection curve by the observed amountof settling (see Figure 1.4).1.1.4. Madsen’s Proposed Testing MethodTo avoid unnecessary complications in the detenrnnation of theproportional limit due to initial curvature, and to maintain consistency in loadingplate dimensions, Madsen (1992) recommended that a specimen 2” x 4” x 6” long(38 x 89 x 150 mm) be utilized to establish compression perpendicular to grainstresses to coincide with the Tn-Grade testing philosophy. Figure 1.4 demonstratesthis proposed method.2x4’x6LONG STEELPLATEWOOD SPECIMEN/A E1 // /— — — — — / /—*0.002,4--RIGID FOUNDATION OF TESTING MACHINE ._-‘Figure 1.4 - Madsen’s proposed compression perpendicular to grain specimen.6CHAPTER 1 Literature StudyMadsen further recommended the crushing strength of an individualspecimen be evaluated as the 0.2 percent offset value obtained from the load-deflection curve (Figure 1.4). It should also be noted that this proposed methodgoverns the general material properties of wood specimens under compressionperpendicular to grain loading. The standard ASTM procedure, however, isappropriate for those particular cases that simulate compression perpendicular tograin loading under or over plates that only cover a portion of the structuralmember.To better understand the behaviour of wood under bearing stresses, Hall(1980), through finite element analysis in both elastic and inelastic deformationranges, concluded that wood under a bearing plate is analogous to a beam ondeformable foundation. He also investigated the infinite stress concentrationphenomenon under a sharp plate corner. He recommended that rounded cornerswould remove this singularity, but would still leave a large stress near the edge.Madsen et al. (1982) confirmed this early work by Hall, and proposed a limitstates design method for bearing stresses in wood.1.2. Tension Perpendicular to Grain and Longitudinal ShearEffectsWhile wood performs poorly under tension perpendicular to grain and shearstresses, these stresses are very common in timber structures and in particulartimber connections. As mentioned earlier, wood’s fundamental structure consistsof tubular cells with the ligrnn (or bonding material) being the weak link.Consequently, among the strength properties of wood, tension perpendicular tograin (or transverse tensile strength) and longitudinal shear are by and large theweakest. Unfortunately, tension perpendicular to grain commonly occurs in most7CHAPTER 1 Literature Studytimber comiections, mostly in the form of splitting around fasteners. In joisthangers, for example, they are induced by shrinkage and/or load effects. Thelongitudinal shear strength of wood is only slightly higher than the tensionperpendicular to grain strength. In joist hanger connections this is seldom agoverning parameter, however.Foschi and Barrett (1976), through finite element analysis, investigated thestrength of Douglas-fir wood beams under longitudinal shear. By assuming thatshear failure in wood, at 12 percent moisture content, may be considered as brittle,Foschi and Barrett used Weibull’s theory of brittle fracture to further studyconditions under which failure may develop. By considering a volume V of woodunder a distribution of shear stresses v, the Weibull fracture mechanics model inthe form of:[1] F = 1— exp{—---f(V0)kdv}mwas used to compute the probability of failure of the volume V when the stressesare known. m, k, and v are material constants, V is a reference volume, andcorresponds to the minimum strength of the material.Foschi and Barrett (1976) verified that the Weibull model [1] provides arational explanation of size effects in shear, as well as the difference in strengthvalues between small shear block and beam tests. Model [1], more importantly,allows the calculation of ultimate short-term shear strength values for verydifferent structural components. This conclusion undoubtedly relates to the studyof possible shear problems in the vicinity of a typical joist hanger connection.8CHAPTER 1 Literature StudyBy recognizing the differences in failure criteria associated with the shearfracture of cracked and uncracked members, Barrett and Foschi (1977) proposed arational procedure for predicting the shear capacity of dimension lumber. For thecase of uncracked beams with a uniformly distributed load w (lb./in), the shearstrength cjear at a given survival probability level S = 0.5 was given to be:[2] Vciear= (VIa)llkwhere ‘a = o 0548{1 — exp [—0.0013( L /d)2M’]}; V=bdL, width times depth timesspan, beam volume (in.3); z-= shear strength of a unifornily stressed unit volume ata survival probability level S = 0.5, in psi; and k = parameter related to thevariability in shear strength. In the case of beams with end cracks, through theconcepts of linear elastic fracture mechanics, the loads corresponding to the onsetof rapid crack growth were studied. The stress intensity factor K11 at the tip of atypical crack was given to be:[3] K11 = /H(L/d,a/L)where r= 3aL / 4bd is the nominal shear stress, a the crack length, and H afunction of the non dimensional ratios L/d and a/L. It should be noted that,according to linear elastic fracture mechanics, at the onset of the crack growth, K11equals the critical value of the stress intensity factor.Consequently, for different grades of dimension lumber, the authorsconcluded that shear strength values given by ASTM D245 were too conservative9CHAPTER 1 Literature Studyand thus allowable stresses could be increased. In addition, end splits longer thanthose assigned to the different grades, for the uniformly distributed loads beingused in development of span tables, could be tolerated.1.3. Cold Formed SectionsTimber connectors such as joist hangers and nail plates are examples ofefficient usage of thin steel sheeting, which is typically galvanized for corrosionprotection. It is thus useful to briefly look into the characteristics of thin metalsheeting and how it affects the behaviour of joist hanger connections. By coldforming a virgin steel sheet, a significant increase in strength is observed in theregions of high strain (i.e. the corners), accompanied by a reduction in ductility.From a stability point of view, bends and other deformations such asembossments, can enhance the buckling resistance to the extent that yielding andfracture become the critical failure mechanisms. Furthermore, the bendingstiffness of a steel sheet is increased significantly by changing the geometrythrough strategically placed deformations. This increase of strength and stiffnessenables the design of efficient and light sections, resulting in inexpensive and easyto handle building components. Light gauge joist hangers, being manufacturedfrom light gauge steel sheets through the cold forming process, should be studiedfor bending, tensile and stability effects. Furthermore, the available theoretical,empirical, and existing code procedures, as they relate to cold formed steel sheets,should be briefly reviewed.1.3.1 Mechanics and Effects of Cold FormingIn general, the effects of cold forming can be examined by considering theprocess of cold stretching. The main effects of cold stretching are an increase in10ChAPTER 1 Literature Studyproportional limit, yield stress, ultimate strength and a decrease in ductility. Thedegree of these effects varies with:• the direction of stretching with respect to the direction of loading(parallel or perpendicular),• the type of loading (i.e. tension or compression),• the type of steel,• the amount of aging after cold forming, and• the ratio of yield to ultimate strength of the virgin steel.The significant increase of the yield point locally in sheet corners is one ofthe main advantages of cold forming. This changes the shape of the member’sstress-strain diagram from one with a sharp yield point to one with gradualyielding.The mechanics of the cold forming process plays an important role. Ametal sheet bent to a sharp radius undergoes high straining beyond yield andexperiences significant strain hardening over a small area. The same metal sheetbent to a larger radius has a smaller increase in the yield point, spread over a largerarea. It has been observed that the bending stress is approximately inverselyproportional to the bend radius, while the affected area is directly proportional tothe bend radius. Therefore, the product is approximately constant. It has alsobeen found that the raise in yield point is practically proportional to the bendangle, the thickness of the sheet, and the difference between ultimate and yieldstrength. From a practical point of view, it has been shown that this increase inyield strength can be accounted for by replacing the yield point with the ultimate11CHAPTER 1 Literature Studystrength over a length of five times the thickness for each 90° bend (Schuster,1974).It should be noted that research has mainly predicted the behaviour of lightgauge steel element under pure cold stretching, as opposed to cold forming due toflexural action. Although results from simple stretching are not directlyapplicable, most of them have some related result applicable to cold forming bymeans of bending.Because the material properties are not uniform or isotropic throughout thecross section, it becomes a relatively complicated problem to analyze and designcold formed sections.t32 Codified Approach in Design of Cold Formed SectionsBoth the Canadian code, CAN/CSA-S136-M89, and the US code (AISI,1983) are based on empirical approaches for design and analysis of cold formedsteel sections. However, there exists a fundamental difference between theCanadian and the US. codes: the Canadian code employs a consistent Limit StatesDesign approach, whereas the US. code employs a Working Stress Designapproach. It should be noted that both approaches will, on average, yield thesame safety limits and results, when they are adopted for design of cold formedsections.The problems associated with thin-walled structures arise primarily fromthe phenomenon of instability. Instability is a property of structures in theirextremes of geometry, such as long slender columns, thin flat plates and thincylindrical shells. Therefore, the extremes of geometric forms are of significant12CHAPTER 1 Literature Studyimportance to the structural designer. Thus, some portions of the code which dealwith stability limitations, particularly with respect to both flexural andcompression members, are discussed here.Buckling problems are generally divided into two separate categories:elastic and inelastic buckling. Elastic buckling problems, are relatively straightforward to analyze and literature is readily available on these types of problems.Elastic stability considerations are of significant importance for slender memberswhere the critical stresses are significantly below the material yield stress. It isinteresting to note that in most practical cases, structures are usually in an elasticstate, as opposed to collapse (or ultimate load) conditions.On the other hand, inelastic buckling problems pose greater analyticaldifficulties and literature is usually vague on these types of problems. Inelasticforms of buckling often occur in the non-slender structural members, such ascolumns and plates in the intermediate ranges of slenderness (or thimiess). Mostpractical cases are of this type.A short review of elastic and inelastic plate buckling is presented inAppendix Al.I A Load-Slip Characteristics of Nailed ConnectionsNails are the preferred choice of connector for joist hangers and the load-slip (or load-deflection) characteristics of nails are critical in many instances,especially where lower grade species of timber are used. It should be noted thatthere is an abundant source of literature on this topic, both for nails and other13CHAPTER 1 Literature Studysimilar single or group fasteners, such as Glulam rivets, Griplam nails, bolts,dowels, lag screws, or nailed truss plates.Initial analytical investigations to predict the load-slip response of nailedtimber joints were carried-out by Kuenzi (1955), Noren (1961), and Wilkinson(1971 and 1972) and others, all of whom assumed the nailed joint to behave as abeam (the nail shank) on an elastic foundation (the wood under the shank).Although this beam on elastic foundation assumption closely predicted the initialstiffness (or spring constant) of various nailed connection configurations, it failedto anticipate the true non-linear, elasto-plastic response of the noted connections.This non-linear response is generally due to bearing failure of wood under the nailshank and yielding of the nail in bending. Consequently, to properly model thisbehaviour and to determine the ultimate load of the nailed connection, an elastoplastic and non-linear model, as opposed to the linear-elastic model, is required.Having realized the true non-linear behaviour of nailed connections, Foschi(1974) utilized finite element approximations to study the load-slip behaviour ofnailed connections. Foschi proposed a foundation load-slip or load-deformationrelationship of the form:-kw[4] p=(p0+p1w)(1—e°)where w nail embedment or penetration into wood, and p0, p1, k are theparameters obtained by fitting to the experimental data for any particularconfiguration of the connection.14CHAPTER 1 Literature StudyUsing the principle of virtual work, a functional V was derived for thedeformation of the nail, or any other similar fastener, at a particular load level. Bydividing the nail length into beam elements, and prescribing cubic polynomials asdisplacement fields for these elements, the functional was approximated to bestationary, which corresponded to the equilibrium condition of the nail under theapplied load. Foschi’s theoretical predictions agreed well with experimentalresults.Foschi and Bonac (1977) extended the elasto-plastic analysis introduced byFoschi (1974) to the general case of wood-to-wood and wood-to-plywood jointsnailed with standard conimon nails. Initial connection stiffnesses were comparedto values obtained by Wilkinson’s method, and the ultimate loads were comparedwith those derived by Larsen’s procedure (Foschi and Bonac, 1977), with theassumption of ideal frictionless interface between connected members. Thus,contrary to the linear elastic analysis proposed by earlier researchers, Fosehi andBonac recommended that a complete load-slip curve be used to provideinformation on initial stiffness, ductility, and residual deformations after unloadingof a particular connection. The authors recommended that the noted procedurecould be utilized to study other types of nailed, bolted, or dowel connections intimber construction.Malhotra and Thomas (1982) investigated the effect of interface frictionneglected by Foschi and Bonac (1977) by carrying out a series of joint tests withvarying interface gap size, including the case with no gap between the connectedmembers. In their predictions, the authors assumed a constant clamping forcebetween the joined members throughout the loading history. By showing goodagreement between the theoretical model and experimental results, the authors15CHAPTER 1 Literature Studyconcluded that the inclusion of interface friction effects considerably enhances theinitial theoretical model first introduced by Foschi (1974) and later by Foschi andBonac (1977).To further modify the original model by Foschi (1974), Hunt and Bryant(1990) included the effects of nail head size, shape, and the direction of loadingwith respect to the wood grain, as well as rotational resistance of the nail beingoffered by the nail head. Similar to other studies, the authors showed goodagreement between the theoretical predictions and the experimental results.Erki (1991), based on earlier work by Erki (1988), used the beam-on-foundation approach, initially proposed by Foschi (1974), to devise a generalmethod for short-term response prediction of single fasteners. By considering thekey characteristics of fastener behaviour, such as penetration length, withdrawaleffects due to lateral loads, as opposed to looking at individual fasteners, thebehaviour of a particular fastener was described. The model takes into accountwithdrawal effects due to lateral loads, axial forces in the fastener, crushing orembedment behaviour of the joint members along the fastener shank, fastener headrotation, shear interface characteristics and yielding of the fastener in bending.The model furthennore considers the fastener to be in single or double shear withwood or steel side members.More importantly, Erki (1991) recommended that the predicted onedimensional finite element beam-on-foundation model can be used to include thevariability in wood and fastener properties, as well as its incorporation into largenumber of computer simulations to predict the fifth percentile of the joint16CHAPTER 1 Literature Studyresistance populations, which in turn would be used in a limit states or reliabilitybased design approach of fastened timber connections.1.4.1 Moisture EffectsIt is widely known that variation in moisture content due to temperaturechange and environmental conditions greatly influences the structural behaviour oftimber elements and connections. For instance, increase of moisture leads to theswelling of the material, while decrease in moisture content leads to shrinkage ofthe timber material, causing parallel to grain splits and cracks. With this in mind,timber connections should be designed such that cracks are minimized between therestraints created by fasteners as nails in a typical connection. Breyer (1980)recommends that for cases where restraint occurs, the cross grain distance betweenthe restraining elements or fasteners should be established so that the totalshrinkage between these points is minimized. This type of wood cracking undercyclic changes of moisture often occurs in timber connections where joist hangersare utilized. Numerous experimental aspects of moisture effects on wood’smechanical and strength properties are explained by Madsen (1992).Additional topics related to wood and connection behaviour are presentedin Appendix A2.1.5 Limit States and Reliability Based DesignIn the past, structural engineers relied upon factors of safety in the design ofstructural members and connections. Although the use of common safety factorsprovided some assurance of safety in a particular design situation, it did not,among other factors, provide a consistent level of structural reliability in the17CHAPTER 1 Literature Studydesign. The basic concept is straightforward: factor of safety of some quantity issimply the ratio of the allowable value, called Capacity (C), to the calculatedvalue, called Demand (D), and is generally expressed as:[5] FOS=-DThe widely used Working Stress Design method (WSD) uses allowable andcalculated stresses from applied loads in a particular structural member, andensures that equation [5] is greater than a predetermined value of the safety factor,FOS. In the past, and to some extent even at present, subjective judgment byengineers was used to select a proper factor of safety in design. Invariably, thisapproach did not explicitly take into consideration the variability in loads andmaterial strength.Principles of probability theory, in the form of reliability analysis haverecently been utilized to minimize the high variability in safety that is inherent inthe simple Working Stress Design method. The concept of reliability based designhas now been adopted by most industrialized countries in the form of Limit StatesDesign (LSD) or Load and Resistant Factor Design (LRFD). Ongoing research isbeing conducted to determine accurate load and resistance factors. Recentliterature (Hasofer, Lind, 1974; Allen, 1975; Foschi, 1978; Sexsmith, Fox, 1978;Sexsmith, 1979; Whitman, 1984; Foschi, Folz, Yao, 1989 and 1993; etc.), isbriefly reviewed here.In general, a structural design problem involves the interaction of severalrandom variables which include the geometric and material properties of the18CHAPTER 1 Literature Studystructure, and can be mathematically formulated as a vector of basic randomvariables, in the form of:[6] X={X1,X23...,X}The limiting state and performance of the structure, in terms of X, may then bedescribed by aperformancefunction in the form of:[7] G{X}={X1,23...,X}To differentiate between Capacity and Demand random variables, as its the usualcase in structural design, equation [7] can be re-written as:[8] G=C-DTherefore, failure of structure is imminent when G <0 (i.e. demand is greater thancapacity), and conversely, survival of the structure is indicated by G >0. Then,the boundary between failure and survival, G =0, can be considered as a limitstate surface between all the variables involved in the performance function [7].From a structural design point of view, a limit states is defined by various states ofcollapse and unserviceability that are to be avoided (Allen, 1974). Ultimate limitstates relate to the safety and integrity of the structure, and relate to the loadcarrying capacity of the entire structure or part of it. Material fracture, structuralinstability and excessive crushing are some typical cases that are encountered instructural design. On the other hand, serviceability limit states correspond to thosecases that relate to the level of comfort in a structure under specified loads.Common examples are floor vibration, excessive floor deflection and cracking.19CHAPTER 1 Literature StudyIn general, an entity’s reliability, by definition, is the probability that it willremain fully functional throughout its design life span. For a structural entity,reliability can be viewed as the complement of the probability of failure, P, whichis given by the multiple integral:[9] F1=ff3(X,2..., )dXd. dXwhere the failure domain, , is expressed as G{X} 0, and the integrand isthe joint probability density function of the intervening variables. Alternatively,equation [9] may be simply expressed in terms of the vector of basic randomvariables X:[10] F=G{X}<OOn the other hand, the reliability or probability of survival is the volume integralover the safe region:[11] i= $ixcixG{X}>OSince a high number of random variables define a typical structuralproblem, the joint probability density function of all involved variables is difficultto model, and if indeed the function exists, then the closed form solution of thegoverning integral [10] or [11] becomes very complicated. Aside fromapproximate Monte Carlo simulation techniques, a commonly used approach tothis reliability evaluation procedure is to work with the so called reliability index,,B, which is based on approximate FORM (First Order Reliability Method) and20ChAPTER 1 Literature StudySORM (Second Order Reliability Method) procedures. Thus, the probability offailure, Pf, may be estimated by the standard normal (or Gaussian) probabilitydistribution function, O:[12] Pf=(I)(,8)It should be noted that if all participating variables are normally distributedwith known model parameters and the performance function [7] is linear, then theprobability of failure [12] can be determined exactly. However, to generalize theanalysis, by knowing the mean, X, and standard deviation, of each involvedvariable in the equation[7], and introducing reduced variates = x — /cr, forI = 1,2,3,...,n , the reliability index, fi, as depicted in Figure 1.5 for the simple caseof two variables, can be established as the minimum distance from the origin to thelimit states surface. The intersection point between this minimum distance and thelimit states surface may be called the design point, , and can be found throughFORMJSORM techniques (Foschi et a!. 1989).(FORM)Iafle.ran9eG<O (Failure Zone)G=O RM)(Limit States. Urfae(SSurface) 13 QuadratIG>O (Safe Zone)’ NFigure 1.5- Mathematical interpretation ofReliability Index.As shown in Figure 1.5, FORM approximates the limit condition by fittinga tangent plane to the limit states surface at the design point, while SORM utilizes21CHAPTER 1 Literature Studyprobability of failure, Pf, it is required that the related variables be non-correlated.Since most structural problems involve correlated variables, a propertransformation is required to acquire uncorellated variables and consequentlyestimate P (Der Kiureghian and Liu 1986).A computer program RELAN (RELiability ANalysis) was developed byFoschi, Folz, Yao (1989) to carry out the above analysis and calculations.RELAN includes the Rackwitz-Fisseler algorithm for non-normal variables andtransformation of correlated variables by Der Kiureghian and Liu (1986). Sincethe work of this thesis is focused on the reliability aspects of joist hangers, thisprogram is considered to be of use to compute and establish reliability indices forvarious joist hanger components.A brief introduction to system reliability is presented in Appendix A3.1.6 Joist Hanger InvestigationsBerkoh (1990) conducted a reliability study of structural joist hangers toinvestigate the strength and serviceability performance of joist hangers. Byexamining the behaviour of individual components in a typical joist hanger, astreated by existing design standards (e.g. CAN3-086. 1-M84), various limit statesequations were formulated and calibrated to the experimental results. For a jointwith multiple nails, for example, an expression is proposed (Thomas andMalhotra, 1985) to calculate the effective number of nails in a row, t’, as[13]22CHAPTER 1 Literature Studywhere = joint slip; A, B parameters; N = number of nails in a joint, and CN =modification factor. Of particular importance was the evaluation of CN factor forexperimental results of metal-timber joints with 1,2,3,4 and 5 nails connected in arow parallel to the external load but perpendicular to the grain direction. Thesemodification factors were calibrated such that the empirical model [13] closelyrepresented the true load slip behaviour of the tested specimens, with respect to thenumber of nails.Moreover, to ensure the design performance of light gauge structural joisthangers, Berkoh proposed a sampling plan which included safety and decisiontheory concepts. This sampling plan was based on the assumed samplingcharacteristics such as Rejection Quality Level and probabilities of Type I and IIerrors. As a result, operation characteristic curves were recommended formanufacturer’s general use.Significant conclusions from Berkoh’s study are:• modification factors, CN, could be developed to account for the effect ofthe number of nails in a row of a joint on the overall joint stiffness(Expression [13]).• the loss of stiffness of the joist hanger connection stemming from theend rotation effects due to bending action ofjoist under gravity loading,• the proposed sampling plan for joist hangers validates the plan proposedby the ICBO Evaluation Services Inc.23CHAPTER 1 Literature StudyAlthough Berkoh’s work utilizes reliability based concepts to study aparticular type ofjoist hanger and species, it does not provide a general limit statesdesign framework for these structural connectors. A model which incorporatesvarious joist and/or header species; joist hanger material thicknesses, fastenertypes, as well as the significant contribution of top flanges, combined withfasteners and/or embossings needs to be formulated to properly predict thereliability of these common timber connectors. To develop such a thorough modelis the focus of this thesis.24Chapter 2 Joist Hanger Testing Procedure2.1 IntroductionTo properly understand the behaviour of joist hangers in timberconstruction, it is imperative to follow a testing procedure that clearly reflects thehanger in use. This sometimes requires examining and perhaps adapting theexisting joist hanger testing procedures. On the other hand, it is also importantthat nationally approved methods be used to ascertain standardized design valuesfor all similar products. The testing code must also be in compliance with currentdesign codes. Presently, this is not the case as the codes (ICBO, ASTM) producedesign values that are used with the allowable stress (ASD) or working designcodes. In Canada, timber design is currently covered by a reliability based code(CAN/CSA-086. l-M89) which makes the testing and design codes incompatiblewith each other. From this point alone, it is clear that a revision of the presenttesting codes is of imminent importance. Not only changes to the testingprocedures, but also the derivation of design values need to be re-evaluated,especially since different criteria prevail when considering serviceability orultimate limit state conditions. The testing procedures, as outlined in theAmerican Society for Testing and Materials D1761 (ASTM, 1988) and theInternational Council of Building Officials (ICBO, 1966), are generally referred toin the discussion of appropriate testing methods and related issues. Initially,comments are in reference to hangers connecting horizontal members only(hereinafter called horizontal hangers), followed by some notes on hangersconnecting inclined and/or skewed members (hereinafter called inclined and/orskewed connectors).25CHAPTER 2 Joist Hanger Testing ProcedureA joist is defined as the primary load carrying member composed of singleor multiple plies of lumber with least dimension of 38 mm (nominal 2 inches).The joist is carried by a joist hanger which is defined as a metal device, usuallymanufactured from light gauge sheet steel through the cold forming process and/orwelded from steel plates, used to transfer loads from a horizontal or inclined beamor girder to other horizontal members in building construction. lii addition togravity loads (dead and live loads), joist hangers must provide adequate lateralrigidity for the entire joist. Although the use of blocking or bracing along thelength of the joist might prevent torsional loads on the joist hanger, this is notalways the case and the hanger must be adequate to provide torsional resistance forresisting any applied or secondary torsional moments. The latter may arise due toconstruction misalignments or from lateral torsional buckling of the joist.2.2 Codified ApproachTo comply with the limit states philosophy of Canadian design codes, it isimportant that a testing procedure identify the serviceability limit and ultimateresistance of a joist hanger. In most design codes, for example, compliance withultimate limit states are mandatory, while only guidelines with respect toserviceability conditions are given. It is equally important, however, that theprocedure provide design values for use with the working stress design method,which is still the current code in the USA. One major difference is that, in thelatter, specified loads are used regardless of the design condition. These arecompared with safe design loads that may be governed by slip criteria or a failure.It would be advisable, of course, to devise a testing method which is independentof governing code conditions, but this may not be practical, given the fundamental26CHAPTER 2 Joist Hanger Testing Proceduredifference in code philosophies. In some cases, this may be possible by usingvariables describing limiting conditions observed in the test.2.3 Loading Conditions and Test MethodsThe different loading conditions and the pertinent testing method for eachare discussed in this section. For most loading conditions, the same test setup canbe used, sometimes a special arrangement is required (see Figure 2.1).Load LoadHeader(a) gravity (b) upliftHeader Joist)(c) torsion (d) gravity and inclined joistFigure 2.1 - Typical loading conditions and test setups of joist hangers.The vertical load capacity test is performed by applying a point load at thecenter of a horizontally aligned specimen, made of a joist, supported by joist27ChAPTER 2 Joist Hanger Testing Procedurehangers on both ends which are attached to two horizontal headers. The verticaldisplacement of the joist at the hanger locations is measured relative to the header.Of specific interest are the loads at a certain “service deflection” (usually 1/8 inchor 3 mm) and at ultimate. If the load is applied downward and normal to the baseof the joist hanger, the hanger capacity is classified as downward verticalresistance (or capacity) for dead and live load conditions. The dead load isdefined as the self weight of the horizontal joist member or any other permanentload on the joist, and live load as the effects from occupancy, snow, wind etc.If load is applied upward and normal to the base of the hanger, then thehanger capacity is classified as upward vertical (or uplift) resistance. This isusually the case for wind load conditions only.The torsion test is performed by subjecting the joist to a torsional momentby a suitable testing apparatus and machine, while clamping down the twoheaders. The top and bottom lateral displacements of the joist with respect to theheaders are measured to calculate the angular displacement and moment-rotationcharacteristics.In the following section the vertical resistance of joist hangers is discussedin detail; topics such as torsion and uplift require future studies.2.4 Testing ApparatusAs mentioned earlier, In accordance with the governing testing standards(ASTM and ICBO), a proper testing machine is to be utilized to provide a constantspecified rate of loading for both the vertical and torsional resistance tests. Figure28CHAPTER 2 Joist Hanger Testing Procedure2.1 illustrates possible test setups for various joist hanger loading conditions. Forall cases shown in Figure 2.1, headers should be braced or clamped, to preventrotation and movement of headers during testing. For torsion tests, for instance,headers should remain completely clamped such that upward and downwardmovement of headers are restrained, and for test specimens under gravity loads,bracing can be used to prevent rotation of headers.Load application for various loading conditions and test setups are depictedin Figure 2.1. For all test setups, load (gravity or moment) should be applieddirectly in the centroid of the joist specimen, to induce equal distribution of load inhangers. Note that, for torsion test setups, suitable load mechanisms should beutilized to accurately produce the applied moment.2.5 Data AcquisitionTo obtain load-deformation or load-rotation curves, a minimum of twodeformation gauges or transducers are required for the vertical resistance test, anda minimum of four for the torsional resistance test. lii the case of the verticalresistance test, transducers are to be placed on top of the joist, directly above thecentroid of hanger’s seat. For the torsional resistance test, transducers are placedhorizontally at the top and bottom of the joist, at the hanger locations, to measurethe relative rotation of the joist with respect to the headers. These gauges may bemechanical dial gauges or electronic transducers controlled by a computerized dataacquisition system. It is important to note that manual recording may result in anon-uniform data acquisition, thus contributing to experimental errors. Anautomatic data acquisition system will assure that no important data are lost, whensudden failures or slips occurs.29CHAPTER 2 Joist Hanger Testing Procedure2.6 Joist Hanger Variables and SamplingNumerous controlled parameters, such as header and/or joist material andsize, nail type and spacing, and random variables, such as joist hanger thicknessand material properties, fabrication techniques and moisture content variations,influence the behaviour of joist hangers. To determine the design load, theminimum load (governed by either the slip criterion or ultimate) obtained from aseries of three tests should be used to establish joist hanger serviceability andultimate loads. As indicated in ASTM D1761, if the ultimate load of any one ofthe tests conducted in a series of three deviates more than 20 percent from theaverage value, an additional series of three tests is to be carried-out, in which casethe average of these six tests may be used to evaluate the ultimate resistance ofjoist hanger. The outlying data point is to be included. However, based onexperimental studies and numerous test results, a limit of 15 percent variance fromthe average may seem reasonable. Note that this will affect the reliability of thehangers and a possible reduction of safety factor may be appropriate. Furtherreliability studies are recommended in order to clearly specify an appropriatevariance.Since joist hanger performance is affected by a number of controlledparameters and random variables, test results involving either dimension lumber,glue-laminated wood, Laminated Veneer Lumber, Parallel Strand Lumber, Timber-Strand, or any other manufactured product may be applied to all of these woodtypes provided that results of a specific joist and/or header type is only applied to atest with similar joist hanger configuration but having higher species grade thanthat of the tested joist and/or header species. For instance, resistance of aparticular hanger in a test involving Spruce-Pine-Fir header and/or joist may beassigned to a similar hanger using Douglas-Fir header and/or joist. Although this30CI{APTER 2 Joist Hanger Testing Procedureleads to conservative design values, it may reduce the number of tests required bythe manufacturer in specifying this product, hence, significantly reducing the costof testing.In the case of fastener variations, test results, in general, may be applied tohangers with stronger nails, i.e. nails with higher diameters and lengths, with dueconsiderations given to spacing and number of nails in a nail group. For caseswith a lower quantity of nails, the serviceability and ultimate resistances may beapplied to tests having similar specimens but stronger nail capacities. Due to theinherent presence of splits or checks in timber members, however, a limit shouldbe imposed on the allowable nail size, quantity and spacing, to minimize splittingor checking in test specimens.Since joist hanger tests should reflect the worst possible scenario within thespecified installation rules, any structural disturbance, such as reinforcement ofjoist and/or header material is not permitted. For instance, by reinforcing I-joistsunder the loading point, the possibility of joist failure via lateral torsional bucklingis greatly reduced. For manufactured products, that are very sensitive to parametervariations, tests should be conducted for each joist hanger configuration and joistsize and/or header material. Knowing that I-joists have a totally different crosssection than sawn lumber joists, the joist behaviour during a standard test could bequite different, since stability problems, such as lateral torsional buckling, is ausual failure mode associated with tests involving simply supported beams andconcentrated loads. Therefore, in the case of I-joist hangers, it is highlyrecommended that each joist hanger configuration be tested for all different joistand/or header material. It should be noted that stiffeners should be used in thecase of I-joist hangers, since these stiffeners increase connection lateral support31CHAPTER 2 Joist Hanger Testing Procedureand provide proper contact area for joist nails. An additional remedy may be theuse of a relatively long loading plate over the I-joist to prevent early failure of thejoist. This is discussed later in this chapter.When considering the case of manufactured wood products, prior to testingthe specimens should be protected from drastic fluctuations in environmentalconditions, such as moisture and/or temperature, since they significantly contributeto expansion (swelling) or shrinkage. This ensures unifonnity in the properties ofthe manufactured products and splits and checks are reduced in the material.2.7 Vertical Resistance Test SpecimensA test specimen for the vertical resistance test should consist of a joistconnected horizontally by two identical joist hangers to two similar headers. Incontrast to ASTM or ICBO procedures, two dial gauges, or preferably electronictransducers, should be placed on top ofjoist hangers directly above the centroid ofhanger seats. By measuring the relative displacement between top of header andtop ofjoist, the compression displacement of the header is excluded.To determine the vertical shear resistance of joist hangers, it is important toselect a joist and header length which precludes any form of premature memberfailure under the applied load. Failure of the joist under bending stress or lateraltorsional buckling are typical examples of such premature failures. A joist lengthof[1] L0=3OO+2d [mm]or = 12 + 2d [inches]32CHAPTER 2 Joist Hanger Testing Procedurewhere d is the joist depth, is recommended to be used which takes into account thejoist depth, which in turn will determine the type of hanger used. Note thatexpression [1] takes into account the type ofjoist hanger to be tested; for instance,heavy gauge and light gauge hangers are normally utilized to connect large andsmall beams which, for testing purposes, in turn, warrant adequate joist lengths.Another often observed failure is header splitting due to its insufficientlength. Wood splitting, often initiated during installation, typically propagatesoutwards from the connector location, which greatly reduces the effective nailresistance. This often results in premature wood failure, distorting the results ofthe joist hanger. To avoid such secondary failures, a minimum length should bespecified for the header. Based on experimental studies at MGA Connectors Ltd.and University of British Columbia, a header length of[2] LHeader 600 mm nor less than 500 +Wj0 [mm]where Wj01 is width of the joist, seems reasonable. Moreover, this ensures thattests involving multi-ply or layered joists have suitable proportions, to develop thefull capacity ofjoist hangers.To eliminate the effect of friction between joist and header a gap of 1/8inch (3 mm) is recommended. Placement of any foreign objects, such as Teflon,or any low friction material similar to that, between joist ends and headers tomaintain this space during loading is not recommended, since this is not commonin structural framing and construction.33CHAPTER 2 Joist Hanger Testing ProcedureDepending on joist hanger test specimen size and capacity, blocking orbracing may be utilized to prevent rotation or outward movement of the headers.Bracing may be in two forms: (a) a simple cross (X) bracing system, connectingthe top of one header to the bottom of the other, or (b) spacer brackets consistingof two horizontal members, such as pipes or dimension lumber, connected to theends of headers via a proper connection or fastening system. This will reducesecondary effects, such as nail pull-out, buckling and distortions of the hangerresulting from header rotation.To simulate realistic construction practice and allow proper seasoning ofthe wood components, it is recommended that the assembled test specimens bestored for at least 7 days prior to testing. In the experimental studies, it wasobserved that as joist or header wood shrinks, a series of splits and checks formaround the fasteners, which affect the behaviour and resistance of joist hangersduring testing. This moisture variation has a compounding effect with too shortheaders and/or joists, which may result in premature failure of wood specimens.The seasoning period is especially important for those tests that involve natural ornon-manufactured wood species, since sawn lumber typically has a highermoisture content than manufactured products. Salinas (Berkoh 1992), byconducting an experimental study on nailed joints, observed a reduction in jointstrength after some initial period of their assembly. Beyond 14 days, theadditional reduction in joint strength was minimal. He suggested a minimum oftwo weeks as the seasoning period.Apart from the abovementioned seasoning requirements, the moisturecontent variation is an important issue related to the duration of load. This, ofcourse, is not covered in the standard joist hanger tests and warrants an34CHAPTER 2 Joist Hanger Testing Procedureindependent experimental and theoretical study. A few remarks can be made,however, as to the behaviour of wood under moisture variations.Experimental studies at MGA Connectors Ltd. and University of BritishColumbia, as well as those from Madsen (1992), revealed that as the moisturecontent increases in sawn lumber specimens, such as Spruce-Pine-Fir andDouglas-Fir, the stiffliess and strength of connectors decrease considerably. Inparticular, being a softer species, Spruce-Pine-Fir, for example, yields a lowerstrength than Douglas-Fir. Failure modes such as wood crushing, nail lateralfailure and pull-out illustrated this reduction in connector resistance. Since joisthanger capacities often depend on nail resistance, this inevitably is an importantissue to be considered. ICBO acceptance criteria indicate a moisture content rangeof 17 to 25 percent, whereas ASTM requires a limit of 11 to 19 percent. Althoughan upper limit of 19 percent is often cited (e.g. Canadian Wood Council, 1991) tobe the maximum permissible moisture content of dry lumber, it is recommendedthat, for the purpose of joist hanger testing, this upper limit be increased to 22percent and the lower limit be decreased to 10 percent. Any specimen having amoisture content higher than 22 percent should not be tested since a specimen withmoisture content higher than 25 percent is well within the fiber saturation point(typically between 25 to 30 percent), which has significant impact on strengthproperties of the wood. On the other hand, the lower limit of 10 percent seems tobe reasonable, since most wood species have approximately 12 percent moisturecontent under normal room temperature.With the foregoing discussion in mind, note that most timber design codes,including CAN\CSA-086. 1 -M89, require a service condition factor for the designof timber members or connections to account for moisture effects during buildingconstruction. Based on this fact alone, a service condition factor can likewise be35CHAPTER 2 Joist Hanger Testing Procedureapplied to joist hanger capacities. Attention should also be given to the loadingconditions of timber structures. During construction, timber material can beassumed to be wet, regardless of summer or winter season conditions, whereas,durmg the occupancy of structure, timber members typically are dry, sincecladdings and moisture protective sheathings greatly reduce the passage ofmoisture into the structure. The latter possibly rationalizes the lower moisturecontent limits required by ASTM in comparison to those specified by ICBO.In light of the abovementioned moisture effects on connectors and lumber,it is clear that the seasoning period eliminates, to a large extent, the uncertaintiesresulting from moisture fluctuations. The target limit of 10 to 22 percent isgenerally achieved, while at the same time splitting and checking is allowed tooccur around the fasteners and wood specimen, which is representative of the trueapplication ofjoist hangers.Special consideration should be given to joist specimens composed ofseveral layers or plies, as well as manufactured wood products. It is imperativethat, in the case ofmulti-layer joist, the moisture content of each ply fall within thespecified range of 10 to 22 percent. Furthermore, a mean moisture content of alllayers should be recorded as the moisture content of the test specimen. For thecase of manufactured wood products, it is recommended that moisture contents bemeasured by means of electronic moisture meters or the traditional oven dryingprocedure. With the exception of glue-laminated products, no adjustment shouldbe made to the electronic moisture measurement for the adhesive materials, sincethey are an integral part of the wood product. Adhesives may, however, influencemoisture meter readings as measured by electronic moisture content meters, whichin turn may require special calibration.36CHAPTER 2 Joist Hanger Testing Procedure2.8 Vertical Resistance Test ProcedureThe design values for joist hangers are governed by either a predetermineddisplacement or the ultimate load capacity. It is thus important to clearly definehow these quantities are measured, especially the load at the displacement limit(also called the slip load). Especially for low density wood species, crushing playsa dominant role in the total displacement and positioning of transducers can have asignificant effect on the results. From a practical point of view, the relativedisplacement between the top surfaces of the header and joist are of interest, andshould be the measured quantity. Based on experimental studies at MGAConnectors Ltd., to measure the relative displacement between header and joist,electronic transducers or dial gauges should be attached to headers, directly abovethe centroid of the joist hanger seat (see Figure 2.2); this is contrary to the currentASTM!ICBO requirements which prescribe a transducer location underneath thejoist hanger. If for reasons, such as joist wood splitting and subsequent upwardmovement, placement of transducers at the top do not record proper displacements,then transducers may be placed directly beneath the centroid of the joist hangerTransducerJoistHeaderJoist HangerFigure 2.2 - Typical components used in a joist hanger test.Note the transducer location.37CHAPTER 2 Joist Hanger Testing Procedureseat. In principal, transducers should be placed at locations which yield the properrelative displacements of joist and header, based on the expected behaviour of thetested specimen, and test type.Splitting of the joist close to the top often results in incorrect (sometimesnegative) displacement readings. This is not of major concern, since such failureusually occur at load levels much higher than the slip load, beyond which only theultimate load is of importance. For severe cases of wood end splitting and uplift,removal of dial gauges or electronic transducers is recommended to preventdamage to the measuring devices.Since the slip load can be unrealistically low due to initial settlement andalignment, it is suggested that an initial pre-load be applied to seat the testassembly. To avoid premature nonlinear behaviour, this pre-load should remainwithin the elastic range (see Figure 2.3). Based on experimental studies at MGAConnectors Ltd., for most cases, a pre-load of 10 percent of the estimated ultimateload is adequate. This, of course, varies with the connector type and expectedLoad// —astic stiffnesspre-load - -— — LJII..iI!JI II 4seatingFigure 2.3 - A typical pre-load and seating location on joisthanger load-displacement curve.38CHAPTER 2 Joist Hanger Testing Procedureultimate load. Alternatively, the equivalent displacement can also be derived fromthe load-deflection curve, by redefining the intersection of the elastic curve and thezero load base line, as the origin of the displacement axes (see Figure 2.3).The length of the loading plate (Figure 2.4), based on experimental studiesat MGA Connectors Ltd., was shown to have a significant influence on the failuremode and load, especially where joist failures are dominant. To allow a realisticend rotation (due to moment) of the joist, testing standards typically limit theloading plate to a maximum of Lj0jt /3. this study, this was foundunrealistically restrictive and is suggested that the range be extended to[31_____T Lj0I i3LLoad1ngPlafThis would more realistically reflect load conditions in practice where bending orshear failure of the joists seldom governs the hanger capacity. For this reason,tests involving I-joist hangers, longer loading plates should be permitted. By usinga longer loading plate, stability effects, such as lateral torsional buckling can bereduced, if not eliminated, thus preventing premature failure of the specimen.The load transfer mechanism within the joist can be modelled as shown inFigure 2.4. It is clear that the loading plate length plays an important role indetermining the angle of the compression strut, C, as well as the accompanyingtension force, T. Such a load transfer model may be adopted in structural analysisof elements involved in a typical joist hanger. The analysis is further discussed inchapter 4.39CHAPTER 2 Joist Hanger Testing ProcedurePartial Uniform Loading under the loading plateq)L!3 U3Figure 2.4- Load transfer mechanism of a short joist under partial transverseloading. Note that T=tension & C=compression.The constant rate of loading, as specified by the current testing standards(0.10 and 0.03 inches per minute, as per ASTMJICBO, respectively), based onexperimental studies at MGA Connectors Ltd., was found to be very restrictive,since it largely determines the required time to obtain the hanger’s ultimatecapacity. It was found that a rate of loading of 0.05 inches per minute wasreasonable, from an efficiency point if view, while at the same time notcompromising the integrity of the test results. Minor variations, due to testingequipment tolerances etc., do occur but were found to have minimal effects on theoverall behaviour of hangers. It is known that the strength of wood is loading ratedependent and significantly higher rates of loading should be avoided.On the other hand, the behaviour of a particular testing assembly may begoverned by a given minimum testing time. This time constraint ensures anapproximate and consistent time frame for tests involving light and heavy gaugejoist hangers. Examples such as testing assemblies composed of heavy gauge joisthangers and manufactured wood products clearly illustrate the relevance of timeconstraint to the joist testing as a whole. Consequently, based on the time-constraint criteria, the rate of loading may be increased to reach a reasonable andfeasible test duration.40CHAPTER 2 Joist Hanger Testing Procedure2.9 Allowable Design LoadsThe ASTM/ICBO standards state that the capacity of a particular joisthanger assembly must be determined by following the sequence shown in Figure2.5 whereP1 = Ultimate capacity of each of 3 tests (i = 1, 2, 3);Pat. = Average ultimate capacity; andP = Load at 1/8” slip.C Do 3 ASTM/ICBO TestsDoes average Pult. deviate more than NOi,2percent from any P1?YESDo 3 more ASTMIICBO Testsr It( pAllowable = mm Avg. ( pAllowable = mm 3 ) mm()Ave.J (JnnFigure 2.5 - Flow chart outlining the existing procedure in establishing joist hangercapacities.As illustrated in the flow chart, serviceability and ultimate loads should berecorded and proper safety factors should be applied to the ultimate resistances.The standards also require that, based on existing timber design codes (e.g.41CHAPTER 2 Joist Hanger Testing ProcedureCAN/CSA-086. l-M89), the capacity of relevant components in the joist hangerassembly should be calculated.Based on the latter regulation, it is considered that there is not a properdesign procedure for establishing joist hanger capacities, thus warranting a properdesign model. To develop such a model is the primary focus of this thesis.2.10 Inclined andlor Skewed Joist HangersVariable angle and skewed joist hangers are widely used in residentialconstruction, for example to connect rafters in pitched roofs. The currentASTM!ICBO standards do not clearly prescribe a procedure for inclined and/orskewed joist hangers. This deficiency may possibly cause inconsistency inanalysis of these structural connectors. Furthermore, as it stands, manufacturersare free to deviate from current standards based on their own discretion.Therefore, it is very important, at this stage, to discuss the significance of variableangle or inclined joist hangers. So far, the definitions and requirements mentionedabove only apply to horizontal joist configurations and do not include similarconsiderations for variable angle joist hangers.Based on recent experimental studies of inclined joist hangers at theDepartment of Civil Engineering, University of British Columbia, the followingrecommendations can be made:• The joist lengths should be shorter than those stated by ASTM!ICBOstandards. By having shorter lengths, the applied load is transferredmore directly into the connectors, thus preventing any premature42CHAPTER 2 Joist Hanger Testing Procedurefailures, due to excessive bending or lateral torsional buckling of thejoist.• The results should not be affected by a variation or tolerances of the testsetup. Among other variables, for instance, the loading rate should notvary from test to test. Hence, consistency in overall behaviour of testspecimens and results should be observed.• To avoid wood splitting in inclined test specimen, for relativedisplacement measurements, transducers should be placed either directlyabove the header, as is the case for heavy lumber and manufacturedwood products, or, directly below the hanger seat, as is the case for lightlumber and natural wood species.• Other effects, such as the influence of end fixity under various loadingconditions, should be considered.• The testing apparatus should be adaptable to accommodate joist andheader dimensions resulting from angles as low as 15 degrees, and ashigh as 45 or 50 degrees.• The load is best applied downwards via a loading block, adequatelyfastened to the joist, to ensure proper vertical load application withoutslip along the joist.43CHAPTER 2 Joist Hanger Testing ProcedureIt should be noted that the use of an improper procedure for inclined and/orskewed joist hanger tests often results in a lower resistance of the connector,which is not in the best interest of manufacturers.Other observations and notes regarding horizontal joist hangers, in theforegoing section, can equally be applied to inclined and/or skewed joist hangers.A suggested test setup is depicted in Figure 2.3; necessary modification can bemade to this configuration, depending on material and component types involvedin the study.2.11 Uplift Resistance of Joist HangersAs mentioned in section 2.3, uplift forces often occur in a structure, mostlydue to wind effects. It is therefore reasonable to briefly study the resistance ofstructural connectors subjected to upward loading.Figure 2.6 - An example ofmclined and/or skewed testing apparatus.44CHAPTER 2 Joist Hanger Testing ProcedureBased on the observed behaviour of joist hangers under gravity loading, itcan be said that two joist hanger components contribute in resisting uplift forces:first, by the pull-out resistance of fasteners connecting the top flanges, and second,by the lateral shear resistance of fastener groups connecting the joist hanger to thejoist, and the joist hanger to the header. To establish the true resistance of thecomponents contributing to uplift resistance, a suitable experimental setup is to bedevised.45Chapter 3 Experimental Program and Results fi3.1 IntroductionAs mentioned earlier, the objective of this study was to develop ananalytical model for the capacity of light gauge joist hangers, which takes intoconsideration the behaviour of all individual elements of the connection. For thepurpose of verification of the model, the following individual experimental studieswere conducted to provide the relevant data:• To establish the contribution from the different components that makeup a hanger connection, joist hanger component tests were conducted.The variables considered were the joist seat and side nails, header facenails, and header top flange. Each of these in turn were investigated forvarious fasteners, material thicknesses and wood species.• Since the wood properties play an important role, especially forserviceability considerations, compression perpendicular to grain testsof joist specimens were conducted, based on ASTM D245 testingstandards.• Tensile coupon tests of the joist hanger virgin galvanized sheet steelwere conducted according to ASTM E8 standard.• To verify the contribution of individual components, standard joisthanger tests were conducted at University of British Columbia on thetotal hanger assembly, using a specific horizontal hanger, model46CHAPTER 3 Experimental Program andResulzUJH21O, manufactured by MGA Connectors Ltd. of Maple Ridge,British Columbia, Canada.To establish the effect of inclined slopes on the capacity of joisthangers, a series of tests were conducted at University of BritishColumbia on total hanger assemblies of the inclined (or variable slope)hanger, model VS 1.5, manufactured by MGA Connectors Ltd. of MapleRidge, British Columbia, Canada.Additional data, such as nail yield strength values, and nail-woodinteraction properties were obtained from the available literature.3.2 Component TestingTo understand the behaviour of joist hangers under load, a study wasinitiated to investigate the individual contribution of each component involved inthe load resisting mechanism. For comparison purposes, the general form anddimensions of these component test specimens were based on generic types ofhangers, i.e. they did not necessarily resemble a particular type of hanger. Thefollowing section describes in detail the tests done on joist hanger seats with andwithout side nails, as well as header face nails and header top flange.All specimens were fabricated and tested according to the ASTMDl 761f1CB0 standards, using an automated custom-made hydraulic testingmachine, located at the research and development facility of MGA ConnectorsLtd. of Maple Ridge, BC. The tests were performed under displacement control,while maintaining a near constant cross head motion of 0.03 5 inches per minute,47CHAPTER 3 Experimental Program andResultswith ±50 percent tolerance. For each test type in the component testing program,a series of three experiments were conducted, while load and deflectionmeasurements were recorded continually with a computer controlled dataacquisition system. Special attention was given to the so called serviceability loadwhich is defined as the load when the relative displacement between joist andheader reaches 3.175 mm (or 1/8 inch). Furthennore, the ultimate load at whichthe specimen ceases to carry any additional load was recorded. As required byASTM/ICBO standards an additional series of three tests was conducted when theultimate load of a specimen varied with more than 20 percent with respect to theaverage of the series of three tests. In that case, the average of all six tests wasused to calculate the vertical resistance of the joist hanger assembly.3.2.1 Joist Seat Component TestingTo establish the vertical resistance contribution of the joist hanger seatsalone, special hanger specimens were fabricated and tested as shown in Figure 3.1.Note that some dimensions, such as seat width and depth, hanger thickness, etc.were varied in the different tests.The hanger specimens were connected to channel steel headers by fourM20 (3/4” diameter) bolts and 12 mm (1/2”) thick steel plate brackets. This was toprevent the rotation and vertical deformation of headers which could affect the seattest results. The joists under study were made from 38 x 235 mm (2 x 10 nominal)Spruce-Pine-Fir and 38 x 286 mm (2 x 12 nominal) Douglas-Fir dimensionlumber, with up to 4 plies nailed together side by side, requiring seat widths of 38to 152 mm. The hanger material thicknesses as tested were 18, 16, and 14 gauge(1.22, 1.52 and 1.9 mm) respectively. The seat length and hanger depth were keptconstant at 76 mm (3 inches) and 200 mm (8 inches) respectively.48steel headersCHAPTER 3 Experimental Program andResultsFigure 3.1 - Schematic of hanger & joist specimens in the component testingprogram. AU units are in Immi.The moisture content of all specimens was measured with the DelnihorstInstrument Company, model RC-1C moisture detector and recorded prior to each436843200Typical 20 mm BoltIVariable Width Joist & Hanger Specimens38 634side flange__0ISEAT—Variable Thickness Hanger MaterialII112,\steel plate mm gapjoist49CHAPTER 3 Experimental Program andResultstest. Although the moisture content of test specimens was intended to be between10 and 22 percent through proper storage of lumber stocks, some specimenscontained moisture as high as 25 percent which is approximately the fibersaturation point.Results of the seat tests indicate a general increase in capacity with anincrease in hanger material thickness increase from 18 gauge to 14 gauge, althoughsome overlap is evident. This is also the case for increase in number of plies inmulti-ply joists, as well as the use of wood from a stronger species. In some casesthe reverse is true, however, which can be ascribed to the variability in sourcematerial and moisture content.Failure modes varied between test types. For multi-ply joists, and thinhanger material, failure was governed first through outward buckling of sideflanges, followed by yielding of the bottom portion of the side flanges (or stirrups)until rupture occurred. Tears typically initiated from the corner of the side flangeand face portion of the specimen and propagated throughout the stirrups, resultingin a sudden failure of the test assembly. For tests with single ply joists and thickerhanger material, imtial buckling of the side flanges was typically followed byfailure of the joist which seemed to be the result of an interaction of shear andcrushing stresses. Wood splitting of the joist adjacent to the loading plate wasevident throughout this part of the study, although it usually occurred after theultimate load was reached.Although it is expected, in general, that the serviceability and ultimateresistances increase as the number of joist plies increase, some decrease inresistance is evident for 4-ply joist specimens. From a statistical point of view, the50CHAPTER 3 Experimental Program andResultshigh variability in test results is considered to be due to the inherent variability inwood material.3.2.2 Joist Side Nails Component TestingThis test series was designed to obtain information about the contñbution ofthe side nails in a joist stirrup. Due to the difficulty of having hangers with onlyside flanges, specimens, similar to the previous series were fabricated with theprovision of having up to 10 nails per side (see Figure 3.2). Apart from the sidenails, this test series was similar to the seat component tests. It was assumed thatthe dfference between serviceability and ultimate capacities as determined in theseat tests, and the seat plus joist nail tests would reflect the resistance of the joistside nails.To understand the influence of all the significant parameters, tests wereconducted for various combinations of material thickness, nail type and quantity,and joist species. To reduce the required number of tests, some combinations wereleft out and the results were interpolated (or extrapolated) based on a general trendin the experimental results.Although the moisture content of all specimens should have been in the 10to 22 percent range, similar to the previous series, some recorded values were ashigh as 24 to 25 percent. The effect of moisture content and variations thereofwere found to be of great importance for nailed connections, since test assembliesthat were fabricated a few days prior to testing, and subsequently stored in dryconditions, often exbibited joist shrinkage and wood splitting around fasteners. Tohave a consistent set of results, it was desirable to fabricate all test51CHAPTER 3 Experimental Program and ResultsVariable nail holes to accommodatedifferent nail diameters, with fabricationtolerance of 1.5 mm.12.5 l412.5 12.5w0 0c:.1229292929250 o15250Figure 32 - A side view of basic nail configuration and dimensions of specimens used incomponent testing. AU units are in (mini.7652ChAPTER 3 Experimental Program andResultsassemblies at least few days prior testing. Due to problems in fabrication, lumberprocurement, and testing delays, this was not always possible and consistencymight have been compromised, which is a factor contributing to overallexperimental variability.In general, it can be said that the joist nails reinforced the stirrups, whichincreased with the number of nails. For the 14 gauge hanger with 2-lOd x 3” nailand Spruce-Pine-Fir joist material, however, the ultimate strength of seat plus nailspecimen was lower than that of the seat by itself Although it might appearunreasonable, the variability of the materials can be larger than the benefit of theadded nails, making this apparent reversal in trend a likely phenomenon within therange of expected values. In general, it was found, however, that as the quantity offasteners increased, the reinforcement contribution decreased significantly,although the normalized strength of the nails, being the total contribution of a nailgroup divided by the number of fasteners, fluctuated considerably from case tocase. These results will be reflected in the development of a rational model,discussed at a later stage of this report.The failure modes varied with the number and type of fasteners, as well ashanger material and joist species, although some seat failure modes, similar tothose of the previous series, were observed. When two fasteners (one per side)were utilized as side joist reinforcement, both the serviceability and ultimatevertical resistance of the test assembly increased considerably; failure occurredafter the nails suffered high lateral and pull-out deformations. This was followedby stirrup yielding and final rupture, for thin hanger material, or yielding of sideflanges followed by joist wood shear failure and excessive wood crushing at seat53CHAPTER 3 Experimental Program andResultslocations, for thicker hanger material. Wood crushing and splitting occurred morefrequently for softer species of Spruce-Pine-Fir than Douglas-Fir, in general.In the case of hanger assemblies with 10 fasteners, more load than the lattercase, in total, was carried by the side nails, for both the 18 gauge and 14 gaugehanger material. For thin hanger material, nail deformation was commonthroughout, combined with stirrup yielding, inducing a material rupture whichinitiated from the corner between the stirrup and header flange, propagatingthrough the stirrups, leading to eventual rupture. This rupture was more commonfor test assemblies with Douglas-Fir joists. For thicker hanger material,considerable nail yielding occurred accompanied by more extensive woodcrushing and splitting. Random nail shear-off was also observed.For the test assemblies with 20 fasteners, the majority of the load wascarried by the nails. For test configurations with Spruce-Pine-Fir joists and 18gauge hanger material, failure was mainly through excessive crush and splitting ofwood at the top of the joist, combined with high deformations at connectorlocations, with random cases of stirrup rupture through the side joist nail patterns.Stability problems, in the form of lateral instability of the top portion of the joist,were also encountered in single ply joists. This was common for Spruce-Pine-Firjoists, although a few cases were observed with Douglas-Fir joists.Furthermore, when 14 gauge hanger material was used with Douglas-Firjoists, wood crushing at the top portion of the joist underneath the loading platewas evident with relatively smaller deformations at the connector locations. Thedominating failure mode for this case was sequential shearing of nailsaccompanied by a sudden drop of load. For some tests, nail shearing was initiated54CHAPTER 3 Experimental Program andResultsat the bottom or top nails, sometimes fasteners sheared off at random naillocations.Concluding from the foregoing discussion, test assemblies with 10 nails ormore seem to reach ultimate loads close to optimal levels, since failures wereobserved in both the hangers and joists.3.2.3 Header Face Nail Component TestingTo establish the behaviour of header face nails, specimens as shown inFigure 3.3 were fabricated and tested. Similar to the previous series of joist nailcomponent tests, assemblies with 2, 10, and 20 fasteners were studied, usingSpruce-Pine-Fir and Douglas-Fir joists and 18 and 14 gauge hanger material. Toavoid the influence of nail types, only two types of nails were used: 1 Od x 3.0 inchand 16d x 2.5 inch common nails.Since wooden joists often influence failure modes or fail themselves, forthis series a steel box joist was used in the test assembly to transfer load to theconnectors. The generic hanger specimens, as illustrated in Figure 3.5, werefastened to timber headers with nails. Testing thus focused on the behaviour ofheader nails under lateral and/or pull-out forces. Note that the steel joist wassimply resting on the hanger specimens and that it was not fastened to the hangersby any means.The moisture content of all the header specimens was measured prior toeach individual tests and can be, in general, grouped into two ranges. For the 18gauge category tests the moisture content ranged from approximately 12 to 17percent; for the 14 gauge category tests in the moisture content was mostly55CHAPTER 3 Experimental Program andResultsdriM- 10 12 12 1014I’14 k k I10282828282828Figure 3.3 - Basic dimensions of specimens used in the component testing.All units are in mimi.between 21 and 25 percent, although out of range moisture contents in bothcategories were observed. It was felt that the moisture content variation did have asignificant impact on the overall behaviour of the test specimens, in particular forcases involving Spruce-Pine-Fir headers. For these tests, it was noted that, atrelatively low load levels, with increasing moisture content, the wood matrix1056CHAPTER 3 Experimental Program andResultsseemed softer and thus underwent visibly larger deformations, under both lateraland pull-out actions.The header nail resistance increased significantly as the hanger materialthickness increased from 18 gauge to 14 gauge for both Spruce-Pine-Fir andDouglas-Fir headers. Ultimate load capacities seemed to be highly dependent onthe length of the fasteners and less on the diameter, indicating a high dependencyon withdrawal resistance. This was confirmed by observations that fastenerslocated on top portion of the nail pattern underwent significant withdrawal,induced by the rotation of the headers. The variation in results can be attributed towood strength variability which, in turn, influences the failure modes andbehaviour of fasteners under study.Since the applied load was eccentrically applied to the centroid of thehanger nail pattern (or nail group), failure modes were more or less consistent forthis test series, exhibiting a combination of pull-out (top nails) and lateral shear(bottom nails). Note that, for all test specimens, buckling of the side flangesproceeded deformations of the header flange and nails.For assemblies with 2 nails, initial lateral deformations were observedfollowed by complete nail pull-out at ultimate load. For specimens with 10 nails,more deformation of the header flange was observed with some pull-out atultimate load levels. Finally, for 20 nails, at ultimate load levels, those fastenerslocated at the top portion of the nail group experienced pull-out, while those in thebottom portion showed no withdrawal but experienced shearing off of some or allof the nails, especially for thicker hanger material.57CHAPTER 3 Experimental Program and ResultsIt was interesting to note that initially, loads were canied by a mechanismin which all header nails seemed to carry more or less equal lateral loads, while themechanism at ultimate load consisted of the top nails carrying tensile loads, andthe bottom nails contributing mainly through lateral shear resistance. The degreeof these effects varied with the number of fasteners involved.3.2.4 Header Top Flange Component TestingAs last part of the component testing program, hanger specimens as shownin Figure 3.4, were fabricated and tested to study the vertical load resistingcontribution of top flanges in joist hangers. The basic behaviour of top flangeswith one and two embossments combined with a varying number of nails werestudied. In line with the other parts of the testing program, header wood species ofSpruce-Pine-Fir and Douglas-Fir, and common nails lOd x 3.0 and 16d x 2.5 wereutilized. In addition, hanger material thicknesses of 18 and 14 gauge were used,along with embossments of 1.53 mm (0.06 inches) depth and 10.7 mm (0.421inches) width (standard practice at MGA Connectors Ltd.).The moisture content of all specimens, measured prior to each test, waswithin the 12 to 14 percent range. As learned from previous tests involvingfasteners under lateral and pull-out actions, it was important to keep test specimensat relatively low moisture contents (less than 20 percent), since top flange nailsexperienced these actions.Experimental results indicate a minimal contribution in both ultimate andserviceability resistances of hanger specimens, for the case when no nails and noembossments were used. In general, both serviceability and ultimate loadsincreased as the hanger material thickness increased from 18 gauge to 14 gauge,58CHAPTER 3 Experimental Program andResultsI Line of action of the1 53 applied load, P I 17 20 13typical embossment”\j—_ ii : :15—:1212T 0 - 10+0:38j : 4052Figure 3.4 - Dimensions of top flange specimens used in component testing. Thenail holes and embossments are symmetric per specimen. All units arein Lminl.and header species changed from Spruce-Pine-Fir to Douglas-Fir. This behaviourwas also evident when the number of top flange nails was increased from 2 to 4per hanger specimen. Most importantly, nail diameters did not have an influenceon ultimate load capacities, whereas nail penetration lengths contributed greatly toultimate loads. The nail penetration length had a negligible effect on serviceabilityloads, in general, for all cases.59CHAPTER 3 Experimental Program andResultsFailure of top flange specimens occuffed mainly through nail lateral andpull-out actions. For hangers with 18 gauge plate thickness, however, materialrupture was observed, combined with header wood crushing under the top flangecorner. For test specimens with no nails and no embossments, failure wasencountered at low load levels through combined vertical and out-warddisplacement of the top flanges. Wood crushing under the top flange was evidentfor all cases involving fasteners, with high plastic deformations at the corners ofheaders.3.3 Material Property TestsTo properly understand and model the behaviour of joist hangers, it isimportant to establish material properties of all the relevant components in atypical joist hanger test assembly. The crushing strength of wood and the tensileyield strength of the hanger sheet material were experimentally determined at theStructures Laboratory, University of British Columbia. Nail yield strength andbending strength were retrieved from available literature (e.g. Berkoh 1990).3.3.1 Compression Perpendicular to Grain TestsThe performance of the joist and header in a typical joist hangerconfiguration depends largely on the compression perpendicular properties of thewood. The proportional limit and modulus of elasticity of Spruce-Pine-Fir andDouglas-Fir species, under compression perpendicular to grain loads wasdetermined using the procedure as specified in the ASTM D245 standard (1988).The required material properties were obtained from load-displacement curves (seeFigure 3.5).60CHAPTER 3 Experimental Program and Results2” x 2” x 6” LONGWOOD SPECIMEN-O.OO3/4--Figure 3.5 - Standard ASTM compression perpendicular to gram specimen.It should be noted, however, that the ASTM specimens do not simulate thetrue behaviour of joist specimens at joist hanger seat locations. The actualcondition is one of confined compression perpendicular to grain, whichsignificantly increases the material properties of joist elements to carry loadshigher than those indicated by the ASTM procedure.Due to the difficulty of simulating the actual conditions of joist hangerseats experimentally, it was decided that material properties be determined withthe standard ASTM specimens. The results could later, for analysis and designpurposes, be calibrated for this confinement effect.2” WIDERIGID FOUNDATION OF TESTING MACHINE61CHAPTER 3 Experimental Program andResultsTo clearly represent the material properties of the component testingspecimens, the compression perpendicular to grain specimens were cut from joistsinimediately after completion of each test. Moisture contents of all ASTMspecimens were measured prior to testing. These were all in the range of 11 to 14percent.A population of 90 Spruce-Pine-Fir and 119 Douglas-Fir specimens weretested and relevant material properties, such as fifth percentile and average valuesof proportional limits and moduli of elasticity, were determined. A summary ispresented in Table 3.1.Note that MOE values in Table 3.1 are somewhat lower than those in theliterature. This can be partially due to prior distortions existing in ASTMspecimens extracted from joist specimens after each component test.Mean Value Design Value Standard COV Mm.(50th %) (5th %) Deviation ValueMax.Value3878.9742811.68SPF-MOE 152 78 56 0.398 44SPF - Fcp 5.47 3.56 1.37 0.25 1 3.21D.Fir-MOE 212 107 71 0.336 73D.Fir - Fcp 6.72 3.77 1.71 0.255 3.63Table 3.1. Standard ASTM compression perpendicular to gram test results.All units are in [MPa]MOE = Modulus of Elasticity & Fcp = Compression perpendicular to grainproportional limit. COV Coefficient of Variation3.3.2 Joist Hanger Coupon TestsCoupon specimens of virgin sheet steel, representing joist hangerspecimens, were prepared and tested, as per ASTM E8 (1988), to establish theyield and ultimate strength properties. In this part of the study, 9 specimens were62ChAPTER 3 Experimental Program andResultsprepared and tested; 3 specimens for each of the 18, 16 and 14 gauge hangermaterial thickness. Table 3.2 presents a summary of coupon test results.Test Serial No. Material Gauge Yield Stress (MPa) ULtimate Stress (MPa)1 18 314 3562 18 325 3593 18 324 3614 16 290 3565 16 295 3556 16 289 3537 14 279 3578 14 279 3649 14 281 368Ivlinimum Values 279 353Average Values 297 359Table 3.2. Hanger coupon test results.Note that average sheet thicknesses were measured to be 18 gauge = 1.27 mm; 16gauge = 1.5 mm; and 14 gauge 2.22 mm.Due to the fact that the sample population of coupon tests was not large, aminimum value of 280 MPa as yield strength and 350 MPa as ultimate strength ofjoist hanger material sheets was for the design and analysis of joist hangercomponents. The modulus of elasticity was assumed to be 200,000 MPa, althoughsome fluctuation was observed from the data.3.4 Horizontal Hanger Assembly TestsTo properly model the behaviour of total joist hanger assemblies, for designpurposes and reliability analysis, it is important to establish statistical parameters,such as mean, standard deviation and coefficient of variation for bothserviceability and ultimate resistances. For that purpose, an experimental study onutility joist hangers, model UJ}1210 manufactured by MGA Connectors Ltd. ofMaple Ridge, British Columbia, was undertaken at the University of BritishColumbia’s Structures Laboratory. Two test series, comprising of 15 tests each for63CHAPTER 3 Experimental Program andResultsSpruce-Pine-Fir and Douglas-Fir, were performed. As for the component tests, thevertical load of the joist hanger test assemblies at 3.175 mm (1/8”) displacementand at ultimate were recorded.A computer program was subsequently utilized to determine the best fitcumulative distribution curves to the test results. It was concluded that a 2parameter Weibull distribution best represented both the serviceability andultimate resistances of the joist hangers. Other findings, in regards to test anddesign procedures resulting from this particular study were discussed in chaptertwo of this report.Serviceability Load [kN] Ultimate Load [kN]Specimen SPF D.FIR SPF D.FIRNumber1 14.38 19.80 26.70 31.602 13.50 19.60 30.90 38.203 13.30 19.38 29.80 35.804 15.63 14.95 26.60 32.705 20.68 19.10 30.40 30.606 15.13 15.75 28.80 30.307 15.85 15.40 27.70 31.608 12.75 16.55 30.40 37.609 12.28 14.25 28.60 31.7010 12.53 15.20 29.90 37.3011 14.88 19.90 27.70 36.1012 15.23 20.20 28.40 34.3013 16.20 14.50 31.80 38.4014 12.78 13.80 30.40 33.9015 15.15 15.20 27.90 28.50Average Values 14.68 16.91 29.07 33.91Standard Dev. 2.11 2.42 1.58 3.19Coeff. of Var. 0.14 0.14 0.05 0.09Table 3.3. Summary of horizontal hanger assembly test results.Note that serviceability values are measured with transducers locatedat the top of the joist.64CHAPTER 3 Experimental Program andResultsFor Douglas-Fir specimens, the general modes of failure consisted of woodsplitting at the joist and yielding of the hanger seats combined with some joist nailpull-out; for Spruce-Pine-Fir specimens, excessive joist nail pull-out wascommonly observed followed by rupture of joist hanger material. A thoroughexplanation of issues, such as moisture effects, hanger yield patterns, experimentalsetup and results, can be found in a report prepared by Jeffery et al., Departmentof Civil Engineering, University of British Columbia (1994). A summary ofresults is shown in Table Inclined or Variable Slope Hanger TestsAs final part of the overall experimental study of joist hangers, anexperimental program was conducted to study inclined joist hangers. Variablesloped joist hangers, model VS1.5 manufactured by MGA Connectors Ltd. ofMaple Ridge, British Columbia were tested at University of British Columbia’sStructures Laboratory. Overall, 18 tests were conducted, using three different joistslopes of 15, 30 and 45 degrees (3 tests per joist slope), utilizing Spruce-Pine-Firand Douglas-Fir species for the joists and headers. To accommodate the testingapparatus and reduce material costs, the joist and header lengths were reducedfrom 30 to 24 inches and from 14 to 12 inches respectively. It is believed thatthese changes did not affect the test results.The major conclusion of this study was that a variation in joist inclinationhad no considerable effect on the downward vertical resistance of joist hangerassemblies. Detailed experimental results, such as those relating to test proceduresand proper element joist and or header sizes are discussed in chapter two of thisreport. A detailed report on this study was prepared by Caley et al., Department65C}{APTER 3 Experimental Program andResultsof Civil Engineering, University of British Columbia (1994). A swnmary ofresults is shown in Table 3.4.Joist Slope Test Serviceability Load [kNI Ultimate Load [kNI[Degrees] Serial SPF D.FIR SPF D.FIR15 1 8.9 11.2 19.84 27.5515 2 11.2 11.1 19.16 24.1915 3 9.3 11.6 18.98 27.65Average 9.8 11.3 19.33 26.4630 1 8.2 9.0 19.51 21.4830 2 9.9 13.7 17.72 23.4830 3 8.4 9.8 21.13 24.62Average 8.8 10.8 19.45 23.1945 1 7.7 9.6 19.26 26.5145 2 8.0 9.2 18.90 25.3545 3 8.0 10.1 19.89 24.89Average 7.9 9.6 19.35 25.58Table 3.4. Summary of inclined hanger assembly test results.Note that serviceability values are measured with transducers located at top of thejoist.66Chapter 4 Development ofAnalytical Model U4.1 IntroductionIn compliance with the initial objectives of this study, an analytical modelto predict the serviceability and ultimate load resistance of light gauge joisthangers is presented in this chapter. The behaviour of the individual components,namely joist hanger seat, stirrup nails, header face nails, and header top flange, ismodelled, based on rational mechanics principles. The model is furthermorecalibrated against experimental results as presented in the previous chapter.To be in line with the existing Limit States Design codes in Canada andother countries, this rational model may subsequently be implemented in areliability study of light gauge timber connectors. Safety or reliability indices canbe determined for each component of a typical joist hanger from which thereliability of the connector assembly can be determined. The detailed procedurefor evaluation of safety indices is explained in the literature study, in chapter 1 ofthis report.In developing a rational analytical model, the serviceability resistance isbased on elastic principles, and the ultimate strength is based on observedbehaviour at failure. For instance, in the case of ultimate load predictions, thefailure modes dictate the formulation of the overall model ofjoist seats.67CHAPTER 4 Development ofAnalyticalModel4.2 Load Path of Joist Hanger SystemsFigure 4.1 is a graphical illustration representing the resistance of joist andheader assembly by dividing the joist hanger into two main components: firstly thejoist components, which include resistance of side nails yielding, wood crushing inthe seat and stirrup rupture through yielding; and secondly the header componentswhich include the top flange and header face nails. In the case of face-mounthangers the top flange component in Figure 4.1 is eliminated, and for the top-mount hangers the top flange component is included.XYV\AXY Y%AAXVV\A‘TopF!ange Header‘3FaceNail = min{‘Vai1Shear___________________NailBendingSeat = min{Shirrup1e1d1SeatWood jr pAPPliedhangerFigure 4.1 - Load path model of a typical joist hanger system.4.3 Joist Seat ModelThe downward vertical resistance of a typical joist hanger seat involves twointegral elements: firstly, the behaviour of joist material (wood) at the seatinterface; and secondly, by the hanger material (cold-formed steel) at both seat andadjacent stirrup locations. This was confirmed by failure modes involved in the‘SideNails68CHAPTER 4 Development ofAnalyticalModelcorresponding tests. From tests on total hanger assemblies, it was found that theseat was a critical element in the serviceability and ultimate capacity of thehangers.It is important to note that the behaviour of wood under any type of loadingis usually non-linear; this was widely observed during the experimental portion ofthis study. In general, the hanger seat initially maintained perfect contact with thejoist, and, as the load was increased, a gradual separation was observed.4.3.1 Serviceability ModelTo simulate the behaviour at serviceability load levels, the joist hanger seatassembly was modelled as an elastic beam on an elastic foundation; the beambeing the hanger seat, and the joist being the elastic foundation. Although theresponse of joist hangers is slightly non-linear, even at low loads, it is consideredacceptable to assume linear elastic behaviour for service load conditions. Thetheory of beams on elastic foundations (Hetenyi, 1974) is reviewed briefly here.By considering an infinitesimal element of the elastic beam, thefundamental differential equation for the deflection curve of a beam supported onan elastic foundation, under a variable distributed load, can be derived as[1] EI—--ky+qwhere El is the beam flexural stiffness (N.nim2); q is the distributed loadin’g(N/mm); and k is the foundation modulus (N/mm2). At any point of the beam, areaction force, p (N/mm) develops in the foundation, which is linearly proportional69CHAPTER 4 Development ofAnalyticalModelto the deflection of the beam y (mm) at that point: p = icy. It is assumed that thesupporting medium, or elastic foundation, is able to carry both compressive andtensile loads.The solution of the differential equation [1] depends on the type of loadingand the boundary conditions of the problem. A collection of standard solutions,for various boundary conditions and loads is available in the literature (e.g.Hetenyi, 1974).Applying this to the joist hanger seat problem (Figure 4.2), as a downwardload is applied on the joist, the stirrup flanges experience tensile stresses anddownward displacements. A model, as shown in Figure 4.2 (i) is used to simulatethe elastic behaviour of the hanger under service loads. For the purpose ofassessing the serviceability criterion, the following assumptions are made:• The permissible downward vertical displacement of the joist withrespect to the header is taken as 3.175 mm (1/8 inch).• All the materials remain linearly elastic.Based on the foregoing assumptions, the principle of superposition was applied,and the structural systems, presented in Figures 4.2 (ii) and (iii), weresuperimposed to produce a model of the joist hanger seat (Figure 4.2 (i)). Because70CHAPTER 4 Development ofAnalytcalModelA close-up of a typical/joist hanger seatFigure 4.2 - Ranger seat linear elastic model (beam on elastic foundation).PAKçp,.j,igCE !eat1—12F2‘cpringI Elseat p +Ksprb,g-H1t(i) Beam on elastic foundation model ofhanger seat. A solution can be obtainedby superposition of cases (ii) & (iii)shown below.(ii) Primary System (free ends).(iii) Secondary System (fixity moment applied).M0ç Elsea, JM71CHAPTER 4 Development ofAnalyticalModelthe joist prevents the stirrups from displacing inwards, the seat can be assumed tobe effectively fixed at the corners. A zero slope condition is thus imposed byapplying an end moment, M0, that is calibrated to this boundary condition. Thesolution for system (ii) is given (Hetenyi, 1974) in the form of— P2 cosh(2x) cos(2(l — x)) + cosh(2(l — x)) cos(2.x)[2] Yfree— k sinh(21) + sin(21)where1k[3] 2=4!‘J4E1which is a factor representing the ratio of the flexural rigidity of the beam, El,versus the elasticity of the supporting foundation, k. The factor 2, which has asignificant influence on the shape of the elastic line, is called the characteristic ofthe system, and, since its dimension is [lengthj1,the term ) is usually referredto as the characteristic length.The solution for system (iii) is given (Hetenyi, 1974) assinh(Ax) cos(2(l — x))—— 2M0 1 — cosh(Ax) sin(2(l — x))[4] ‘— k siiih(21) + sin(%l) + sirih(2(l — x)) eos(Ax)— cosh(2(/ — x)) sin(Ax)In this particular case, M0 is the compatibility moment, determined by equatingthe sum of the end slopes of the beam in (ii) and (iii) to zero:72CHAPTER 4 Development ofAnalyticalModelM= P( sinh(2l) — sin(21)[51 ° 42 cosh(21) — cos(21)The deflected shape of the joist hanger seat is influenced by thecharacteristic factor of the system, 2, the applied load, F, and the beam length, 1.For a constant value of P, El, and 1, the foundation modulus, k, was considered tobe the only factor with significant influence on the deflected shape atserviceability loads. Thus, foundation moduli in expressions [2] and [4] werecalibrated to the measured serviceability loads, for each test configuration.Foundation moduli decrease as the width of the joist hanger seat increases;variation is also evident for wood species of Spruce-Pine-Fir and Douglas-Fir, aswell as joist hanger material thickness. A typical load-displacement curve, for aparticular case, is shown in Figure 4.3 (a). Figure 4.3 (b) shows the effect ofchanging stiffness ratios.Concentrated End Forces —— Concentrated End Moments ‘ Resultant/Width of SeatFigure 4.3 (a) - Deflected shape of hanger seat on elastic foundation (14 gauge hanger,-ply Douglas-Fir joist).73CHAPTER 4 Development ofAnalyticalModelConcentrated End Forces Concentrated End Moments ‘ ResultantWidth of SeatFigure 4.3 (b) - Deflected shape of hanger seat on elastic foundation ( for soft foundation orthick hanger material).The model will, in general, be too stiff since tension develops in the centrewhere ‘lift-off’ or seperation occurs between joist and hanger. Since tensioncannot occur across a gap in reality, some inaccuracy will result. For such joists,the foundation stiffliess, k, should be adjusted upwards to reflect the lower systemstiffness of a real joist plus hanger.4.3.2 Ultimate Strength ModelThe ultimate strength model is derived from the failure modes as observedin the joist hanger seat experimental study. Two general failure modes occurred:firstly, by net section rupture of hanger stirrups for tests with thin hanger material,stiff joist material and relatively wide seats; and secondly, by excessive crushingand splitting of the wood at the joist/hanger seat interface, for tests with thickhanger material, soft joist species, and relatively narrow seats. The ultimatestrength model was therefore formulated as the minimum resistance of either the74CHAPTER 4 Development ofAnalyticalModelsteel stirrup, or the bearing capacity of the joist, and can be mathematicallypresented as:([6] Pseat=ruflp —F AI bearing — P cnish bearingwhereF, = yield strength of steel (N/mm2);“crush = wood perpendicular to grain, or bearing strength (N/mm2);= Bseat. tstirp= cross sectional area of only one hanger stirrup (nim2);Abearing Bjj Wse = hanger seat bearing area (rim2);Bseat and Wseat are hanger seat bearing depth and width respectively (mm);thickness of the hanger stirrup (mm);a and fi are empirical amplification factors for wood and steel materialsrespectively.Expression [6] gave results which agreed relatively well with theexperimental results; with due consideration given to a and j adjustment factors.Since, at failure, the true material strength of either steel or wood material is notknown, a and j factors were respectively applied to the yield strength of steel, F,,and the bearing strength of the wood species, Fh , to account for this effect.Note that1earing in expression [6] is based on the assumption that the joistseat stress distribution is uniform. This assumption is reasonable, since, during thestatic load history, there is a relatively high stress concentration at the inner side ofthe joist seat interface, due to presence of a concentrated shear. This edge effect isvery similar to that explained by Madsen (1992), in regards to ASTM compression75CHAPTER 4 Development ofAnalyticalModelperpendicular to grain loading plates, which already has been discussed in chapter1 of this report. Perhaps a better distribution would be a curve or triangular stressdistribution. For simplicity, however, a uniform distribution was adapted in [6](see Figure 4.4), with calibration factors to take these secondary effects intoconsideration.Furthermore, similar stress distribution anomalies were encountered in thedevelopment of the serviceability model [2] and [4], in which a uniform stressdistribution was also assumed.4rHeaderdistribution distributionFigure 4.4 - A close-up of joist hanger seat under applied load. Note the bearing stressdistribution experienced by the joist at the seat interface.The percentage difference between experimental and model resultsmoderately fluctuates for each case, with lowest difference of 0.35 percent andhighest of 17.8 percent. This variation is considered acceptable, since model [6]76CHAPTER 4 Development ofAnalyticalModelseemed to yield results, for each individual test setup, close to those obtained fromthe experimental program. In addition, with the 20 percent variation inexperimental results, similar variation in model results (preferably belowexperimental values) can be considered acceptable.44 Joist Stirrup Nail BehaviourThe lateral load resistance of nails connecting steel sheets to woodmembers was the predominant feature in assessing the resistance of the nailed sidestirrups. Rational models to determine serviceability and ultimate load capacitiesare presented in the following sections.It is important to note that experimental revealed that the joist hangerstirrups, during the static load history, had a beneficial effect on the crushingstrength of the joist in the seat. In compression perpendicular tests of wood blockswithout adjacent supports, such as standard ASTM blocks, it was observed thatwood material moved outwards under the applied load which is prevented by thestirrups. This beneficial load resisting contribution was taken into account in thedevelopment of serviceability and ultimate strength formulae, explained in thefollowing sections.4.4.1 Serviceability ModelSimilar to the seat model, the concept of beams on elastic foundations wasapplied to establish a nail serviceability model. The nail was treated as an elasticbeam and the surrounding wood material as an elastic foundation. Only lateralload resistance was considered, since withdrawal is believed to be a phenomenonassociated with advanced yielding and crushing. A single nail was first modelled77CHAPTER 4 Development ofAnalyticalModeland calibrated to experimental results before fastener group ratios were determinedfor connectors with multiple nails.Various fastener types were considered under the experimental part of joiststirrup nail tests. To gain understanding of the fastener group effect, two fastenertypes (lOd x 1.5 and lOd x 3) were tested, in groups of 2, 10 and 20 nails perhanger of one particular fastener. The remaining tests were done with only 10fasteners per connector (16d x 2.5” and 20d x 2.5”). To be consistent with otherresults, the serviceability resistances of the remainder of the incomplete test seriescould be estimated via extrapolation of experimental results of the former nailtypes.The fastener head fixity was considered an important factor in theserviceability resistance of sheared nailed connections. Because of fabrication andinstallation tolerances in nailed plates, the fastener heads were modelled as pinned.One could argue, however, that the fastener head behaves as fixed during theassumed linear elastic response of the hanger and the assumption of pinnedfastener heads would be conservative. The true condition is believed to beinbetween and can only be represented properly by a very complex model.The load-displacement relationship, under serviceability conditions, for asingle fastener as shown in Figure 4.5, is given as (Hetenyi, 1974)— P2 sinh(21) cos(21) cosh(2(l — x)) — sin(%l) cosh(Ax) cos(2(l — x))[71— k sinh2(21) — sin2 (21)78CHAPTER 4 Development ofAnalyticalModelwhere the variables are as before. The deflection at the fastener head (when x 0)is then— P2 sinh(21) cosh(2l) — sin(%l) cos(%l)[8] YTip— k sinh2(2!) — sin2 (2?)Relationships [7] was then calibrated, by varying the foundation modulus, k, to theexperimental results. Since a variety of fastener types were under study,foundation factors were determined for each individual nail type._BFigure 4.5 - Elastic beam on elastic foundation model for a single fastener.To determine the load distribution for hangers with multiple fasteners, ananalytical study was undertaken. Structural models, such as in Figure 4.6, wereanalyzed to study the contribution of each fastener to the total lateral load. Theone dimensional model, Figure 4.6 (a), simulated nails as springs and the hangerstirrup as a steel beam, while the wood was considered rigid.79CHAPTER 4 Development ofAnalyticalModelcE.1ng ‘cp,hg ‘pebg ‘cpringL, EAsteei L, L, EAsieci L, EAsieei(a) Rigid WoodPin SupportP L, EAVOOd L, EAOOd L, EA,Od L, EACOd1Kig c K51,,,,, prñg Kp,:j,g i:::I Kp.j,g PL, EA51 L, EAçj,1 L, EAcieei L, EAsteei(b) Flexible WoodFigure 4.6 - Structural models of steel plate & wood connected by nails (or springs) underlateral load P.A linear elastic analysis with the computer program PSA (Department ofCivil Engineering, University of British Columbia, 1991) revealed that the nailslocated nearest to the load application point carry the highest proportion of theload, while the nails towards the centre carry lower loads. These proportionsvaried with the relative stiffliess of the springs and beams. For the limiting casewhen the beams or side plates had infinite stiffhess, equal distribution of lateralload was observed.In a more sophisticated model, Figure 4.6(b), the stirrup, as before, istreated as a one-dimensional beam with steel properties, the joist as a one-dimensional beam with wood properties, and the nails as elastic springs, as before.soCHAPTER 4 Development ofAnalyticalModelThe serviceability resistance of the hanger assemblies with n fasteners canthen be formulated as the sum of all single nail capacities multiplied by a nailgroup factor,[9] N=n = N=1where N=1 is the lateral strength of a single fastener, and a3is called the nailgroup factor for joist nails. The group factors were derived from experimentalresults.44.2 Ultimate Strength ModelThroughout this study, the lateral load resistance of nails, at ultimate levels,is based on the plastic theory, originally proposed by K.W. Johansen (Ehibeck,Larsen, 1993) and is briefly reviewed below. The basic assumption is that thedowel (or nail) acts as an elastic-perfectly plastic beam on a stiff-plastic-foundation. Although this assumption seems to result in unconservative or unsaferesults, beneficial influences, such as the axial withdrawal resistance of fastenersand surface friction effects are neglected and do, to some extent, offset thelimitations.The assumption of a stiff-plastic foundation results in two types of basicbehaviour: firstly, the nail or dowel remains straight and is forced through one ofthe members or both, with either a transitional or combined transitional/rotationalmovement; and secondly, one or two plastic hinges develop in the nail. Note that,in the latter case, the nail remains straight outside the infinitesimal yield zones.81CHAPTER 4 Development ofAnalyticalModelBy considering only these two yield modes, various fastener failure modes can bemodelled with theoretical formulae for each case (Ehlbeck & Larsen, 1993).In the joist hanger problem, the sides of a joist hanger stirrup can be treatedas a single steel-to-timber shear connection and the lateral capacity, for aconnection with single fastener, can be determined as(a) 3F D110P1=min (b) FWLfPDf(-J—1)(c) J2FWDfMYfwhere Df = diameter of the fastener;L1 fastener penetration length;F = wood embedding strength, which is the average crushingstrength of wood under the dowel; and= steel plate yield strength;Mf = yield moment of the beam or fastener.The capacities (a), (b) and (c) correspond to the failure modes shown in Figure4.7. Note that expression [10] was derived for cases with thin steel sheets wherethe head of the nail is modelled to be pinned. For relatively thick plates, where thenails or dowels fit tightly, a plastic hinge may occur close to the surface, for whichcase a different expression is used. Expression (a) relates to bearing failure (byyielding) of the steel sheet at the fastener location, and conforms to the steeldesign code CAN\CSA-S16.1-M89.82CHAPTER 4 Development ofAnalyticalModel+1Member F One plastic hinge locatedin the wood member.Steel Memberj‘LI(a) (b) (C)Figure 4.7 - Connection failure modes for two-member joints with one nail (J)inned head).The most important parameters in [10] are the yield moment, Mf, and theembedding strength, F. For fasteners made of mild steel with a yield strength ofF, the theoretical yield moment is defined asDf3[11] MyfZ.Fyf(6)1’yfThe embedding strength, F, is not a material property, but rather a systemparameter depending on the nail diameter, stirrup thickness, and wood species.Ultimately, it relates to the confinement phenomenon of the wood, which dependson a rather complex stress distribution in the vicinity of the dowel, underconcurrent presence of compression perpendicular to grain stresses (Ehibeck &Larsen, 1993).83CHAPTER 4 Development ofAnalyticalMock!By calibrating expressions [10] and [11] to experimental results,embedment strength values, for each type of fastener, were determined. Becauseof experimental difficulties and some inconsistency in the results, some outlyingfastener ultimate load values were neglected in the calculations.The high variability in embedment strength, F, was derived fromexperimental results and is considered to be due to the 20 percent variability inthese results.4.5 Header Nail BehaviourThe load resistance of the joist hanger component attached to the headerface was considered in this part of the study. The model formulation is similar tothat of the fasteners connecting the hanger stirrups to the joist, as discussed in theprevious section of this chapter. Hence, details regarding formulae, presented inthe following sections, can be obtained from the foregoing section.4.5.1 Serviceability ModelAs before, the beam on elastic foundation concept was utilized to obtain thelateral nail resistance at the serviceability load corresponding to a 1/8 inch (3.175mm) downward vertical displacement. Again, group effect ratios were determined,to match the fastener resistance of a single nail to cases with multiple nails.To limit the number of variables in the tests, only lOd x 3 and 16d x 2.5nails, combined with 18 and 14 gauge hanger material, and Spruce-Pine-Fir andDouglas-Fir species, were considered in this part of the study. A complete set ofhanger assemblies with 2, 10 and 20 nails were tested, to avoid errors associatedwith extrapolation or interpolation of experimental results.84CHAPTER 4 Development ofAnalytical ModelAs before, the elastic load-displacement relationship of a single fastener canbe presented as— P2 sinh(21) cos(21) cosh(2(l — x)) — sin(21) cosh(A.x) cos(2(l — x))[7] Y— k sinh2(2!) — sin2(2!)For each nail type, calibration of the foundation modulus was performed by usingheader nail experimental results.The serviceability lateral load resistance of test assemblies with multiplefasteners was determined to be similar to that ofmodel [9] and can be re-stated as[12] 1N=n = aj N=lwhere all terms are already explained in section 4.4.1, except here, aj is the nailgroup factor for header nails. From the experimental results, the group factor wascalculated for every series of tests.4.5.2 Ultimate Strength ModelAs in section 4.4.2, Johansen’s yield theory was utilized to establish theultimate capacity of the laterally loaded connection. For the case where sheetmetal is fastened to the timber header, the ultimate shear capacity is expressed,similar to equation [10], for header connector assemblies as3F Df tplate[13]]—min FWLfPDf(-J—1)J2FWDJ Mf85CHAPTER 4 Development ofAnalyticalModelwhere all the variables in [13] are as per section 4.4.2. Again, to be conservative,and more or less follow observed nail failure modes, the chosen model [13]simulates a pinned nail head condition.Observed failure modes indicated that, depending on the number offasteners, the top portion of the header nail group experienced withdrawal as wellas lateral shear while the bottom part experience a compression between thehanger and header, and shear deformation in the nails. Therefore, to develop amore realistic model for the nails, the interaction of lateral and pull-out action onthe nails should be considered. A general interaction formular if r if[14]S11+ I L 0L Faxial] [Ppuzzoutjhas been suggested (Ehibeck & Larsen, 1993), where S and P are fastener load andresistance, respectively. A value ofj=1 has been prescribed as suitable for casesinvolving smooth nails. The above formulae and expressions for fastener pull-outare readily available in the literature.Experimental results strongly suggested that withdrawal of the nails did notadversely affect the lateral resistance. It is thus proposed that a simpler model beused for the ultimate lateral capacity ofmultiple fastener connections:[15] ‘N—n 1N=1where N1 is the lateral capacity of a single fastener. From tests, it is suggestedthat equation [15] be used for connections with up to 20 nails. This is based on86CHAPTER 4 Development ofAnalyticalModelaverage normalized capacities of all cases, including test assemblies with 2, 10 and20 nails, in the experimental study.4.6 Header Top Flange ModelAs last part of this study, the joist hanger top flanges were considered.Because of minimal bending strength of the sheet metal, it was found that topflanges without nails were of no practical use. The case without nails is thus notconsidered in the modelling process.4.6.1 Serviceability ModelThe top flange was assumed to behave as an elastic beam on an elasticfoundation (the header). It was modeled as a semi-infinite elastic beam havingboundary conditions of non-zero slope and displacement at the nail location, and anon-zero slope, with a concentrated force, at the other end (see Figure 4.8 (a)). Tosimplifr the analytical procedure, the nail force was neglected. By applying theseboundary and load conditions to the general solution of the fundamentaldifferential equation [1], a load displacement relationship, in the form of2P21[16]= kexp(—Ax) cos(2x)where all related parameters are noted as before, was obtained. A typical plot ofthis deflected shape is shown in Fig 4.8 (b).87CHAPTER 4 Development ofAnalyticalModelIx> ç..nail locationtopflange locationFigure 4.8 (a) - Elastic beani on elastic foundation model for the joist hanger top flange.0.50I ::72025-3.50Distance Along the Top Flange (mm)Figure 4.8 (b) - A typical deflected shape of the top flange.The foundation modulus, k, is here the only unknown quantity which wasobtained from results.4.6.2 Ultimate Strength ModelTo establish an ultimate load model for light gauge joist hanger top flanges,the failure modes and material behaviour during testing were studied. As88CHAPTER 4 Development ofAnalyticalModeldiscussed in chapter 3, at ultimate load levels, a nailed top flange experiencesrelatively high stress concentration at the top corner of the header. The contactstresses decrease rapidly with distance along the top flange and diminish to zero atthe free end of the top flange. At the corner, crushing of the wood results in arounded profile and at ultimate, it can be assumed that a circular shape evolveswith near constant contact pressure and friction. This is presented in form of afree body diagram (Figure 4.9), which takes into consideration the followingassumptions and factors:• All forces are to occur at ultimate load levels;• The top flange deflected shape is similar to a quarter of a circle;• The header material has passed the proportional limit, and has a crushresistance,‘1crush;• The ffiction force between the top flange material (steel) and the headermaterial (wood) is a function of header crush load;• The top flange nail resistance, na,j, has a fixed magnitude, and variabledirection, inclined at an angle 9 from the top of the header;• The top flange load, ], has a downward vertical direction.Integration of stresses in the model of Figure 4.9 results in the ultimate loadformulationI____.[17] F1f a n1P11cosO — smOj89CHAPTER 4 Development ofAnalyticalModelwhere P,11 = Capacity of a particular top flange fastener type, obtainedfrom the header experimental results of correspondingfastener type;= Top flange calibration factor;fl = Number of fasteners in top flange;e = Top flange nail angle of inclination; and= Top flange interface friction coefficient.itTop flange deflected shape • 2F110, :/ \ zait9o IFigure 4.9 - Free Body Diagram of a typical top flange.Expression [17] is essentially some ratio multiplied by nail capacity of thetop flange, assuming that the friction coefficient and angle of inclination are givenfor a particular case. This formula, furthermore, is only one of few possibleexpressions obtained from the noted free body diagram. For the cases studied, an90CHAPTER 4 Development ofAnalyticalModelinclination angle 0 = 45 degrees was assumed, and formula [17] was calibrated tothe experimental data. As determined experimentally, a coefficient of friction of0.55 for Spruce-Pine-Fir, and 0.585 for Douglas-Fir were utilized in calculation oftop flange ultimate capacities. Note that is independent of the crushingstrength of the wood, although the radius will change to result in an equilibriumstate.4.7 Model VerificationHaving developed an analytical model to predict the serviceability andultimate resistances of individual components in light gauge joist hangers, it isappropriate at this stage to verify results obtained from the model against thoseobtained from complete hanger assembly tests. As mentioned earlier, anexperimental study on utility joist hangers, model UJH21O manufactured by MGAConnectors Ltd. of Maple Ridge, British Columbia, was undertaken at theUniversity of British Columbia’s Structures Laboratory. The face-mount joisthanger was modelled as a series of springs (Figure 4.10) with each springrepresenting individual components in the joist hanger.The ultimate resistance of the UJ}{210 face-mount hanger was evaluated,by considering the spring system shown in Figure 4.10, to be the minimumresistance ofjoist or header components. Due to a faulty joist stirrup nail location,stirrup rupture was the predominant failure mode of total hanger assembly tests,thus indicating that stirrup capacity governs the ultimate resistance of the UJH21Oface-mount joist hangers (Table 3.3). The ultimate resistance of hanger stirrupswas calculated to be 17.5 kN, which deviated by 20 and 3 percent from theSpruce-Pine-Fir and Douglas-Fir ultimate resistances of face-mount hanger91CHAPTER 4 Development ofAnalyticalModelassembly respectively (14.5 kN and 16.95 kN). The ultimate resistance of sidejoist nails were neglected in the foregoing, due to the proximity ofjoist nails to theedge ofjoists and presence of significantly large cracks and beThe serviceability resistance of the face-mount joist hanger was determined[18] ‘ervice = ksystem servicewhere Aservice is the prescribed serviceability deflection limit of 1/8 inch (3 mm),and ksystem is the equivalent joist hanger system stiffness which, by consideringthe spring system shown in Figure 4.10, can be evaluated asHeaderFaceNai1‘3Stirrup‘SeatSideNailsAppliedhangerFigure 4.10 - Structural model of face-mount joist hangers.92CHAPTER 4 Development ofAnalyticalModel1[19] ksystem= 1 1+ *kHeader k + kO15Nailwhere kHeade,. and kJoistNail are header and joist side nail component stiffnessesrespectively, and can be calculated by the application of equation [8]. Thecombined seat and stirrup stiffness, k, in expression [19] is1[20] 1 1+keatwhere and keat are stirrup and seat component stiffriesses respectively,and can be calculated by the application of equations [2] and [4]. The stirrupstiffness can generally be considered much higher than that of the wood or nailcomponents and is neglected in the calculations. By applying the experimentalresults from component tests, the equivalent system stiffness of the UJH21O face-mount joist hanger was calculated from [19] and inserted into [18] to obtain theserviceability load, Psei.vice. The serviceability load calculated from the foregoingprocedure was 4.7 kN and 4.72 kN for Spruce-Pine-Fir and Douglas-Fir woodspecies respectively which deviated by 46 and 68 percent from those obtainedfrom the total UJH21O hanger assembly test results (7.3 kN and 8.4 kN),respectively. Although a significantly high deviation is observed in the results, itis believed that expressions [18] through [20] could be applied in establishingserviceability resistances of light gauge joist hangers, since, among other factors,the component tests in the foregoing calculations do not match those particularcomponents present in the UJH21O face-mount joist hangers.93CHAPTER 4 Development ofAnalyticalModel4.7.1 Reliability AnalysisA computer program RELAN (Foschi et al., 1989) was utilized to assessthe reliability of the UJH21O total joist hanger assemblies. By using the averageserviceability values and corresponding standard deviations from Table 3.3, andassuming a mean standardized live load of 1.0 kN with standard deviation of 0.25(Foschi et al., 1989), a design value of 4.38 kN was obtained for a target safetyindex, /3, of 2.0. A normal distribution was assumed in the foregoing process,although a 2-parameter Weibull distribution was earlier established to bestrepresent the UJH21O joist hanger serviceability and ultimate resistances. Theobtained design value of 4.38 kN was subsequently utilized in ultimate loadresistance calculations, where, for a mean dead load value of 1.0 kN and standarddeviation of 0.05 with standardized live load, a safety index of 2.6 was obtained.For a target safety index of 3.0, a design ultimate load of 6.6 kN was obtained.The preceding reliability analysis reveals that for this particular type ofjoisthanger, the serviceability load is the governing criterion for the design of lightgauge joist hangers, if the minimum of ultimate or serviceability loads concept isadapted. This is confirmed by the serviceability model (Figure 4.10) withexperimental component results as input, If serviceability and ultimate resistancesare separated to represent individual limit states, however, the former analysiscould also be applied in establishing design values for serviceability or ultimatelimit states.94Chapter 5 Conclusions and Recommendations UA relatively extensive experimental program was undertaken at MGAConnectors’ testing facility and the University of British Columbia’s StructuresLaboratory to• Understand the general behaviour of light gauge joist hangers;• Investigate the contribution of the various load resisting elements inlight gauge joist hangers under gravity loading;• Propose modifications to the existing testing standards by the AmericanSociety for Testing and Materials (ASTM D1761, 1988) and theInternational Council of Building Officials (ICBO, 1966), for joisthangers;• Develop an analytical model for the load carrying capacity of lightgauge joist hangers under serviceability and ultimate limit states; and• Study the behaviour of inclined light gauge joist hanger assemblies;• Conduct a limited series of test with larger population size to find atypical statistical distribution for horizontal hangers.On the basis of a rational design model for joist hanger elements, aprocedure is proposed to establish reliability or safety indices of joist hangers incompliance with the Canadian Standard Association regulations (CAN\CSA-M89-086.1).Some of the major issues are discussed hereinafter.95CHAPTER 5 Conclusions andRecommendations5.1 Joist Hanger Test ProcedureVarious issues related to the existing joist hanger test procedures (ASTMand ICBO) were studied, to identify the important criteria for possible adaptationto current design standards, while maintaining the link between testing rules andcommon construction practice. A list of recommendations and notes were made toact as guideline for future modification or subsequent revision of these standards.This was also done in light of the current development of a Canadian Standard inthis regard. Some of these are briefly summarized below.It is recommended that a 7 days conditioning period under indoor climaticconditions be imposed on the total test assembly prior to testing. This willeliminate drastic variations in moisture effects, reducing wood splitting aroundfasteners. Splitting of the header or joist can also be reduced significantly byassuring an adequate member length. For too short members splitting is ofteninduced during fabrication and worsens when drying of the wood takes place.To assure realistic serviceability conditions and eliminate initial settlingeffects, it was found that the application of a pre-load to the hanger test assembly,prior to the actual test proved to be sufficient. A pre-load of about 10 percent ofthe ultimate load is suggested. By doing so, resistance variability induced byhanger specimen and test assembly tolerances have been greatly reduced at theservice load level.Other issues that were dealt with are the loading plate dimensions and theireffect on the load carrying mechanism in a joist, as well as the impact of theloading rate on the joist hanger capacity. In the modeling stage, a load path modelfor light gauge joist hangers was recommended, which could be implemented in a96CHAPTER 5 Conclusions andRecommendationsprocedure establishing joist hanger capacities. It can also be applied in reliabilityanalyses ofjoist hangers.5.1.1 Inclined Joist HangersSince the current ASTMJICBO joist hanger test standards do not explicitlyspecify a procedure for inclined joist hangers, an experimental study of inclinedjoist hangers was undertaken to establish the impact of variations in joist slope onthe hanger behaviour. The most important observation was that a consistentfailure pattern in joist hanger specimens, joist and header material, was observedfor a particular joist species, regardless ofjoist angle.Other effects, such as the influence of end fixity on the performance ofjoisthangers under possible lateral loading conditions, (e.g. seismic) was brieflystudied. Further study is suggested. In addition, the uplift resistance of lightgauge joist hangers was suggested to be determined from pull-out and shearresistance of fasteners in a typical joist hanger.5.2 Joist Hanger Analytical ModelAs the main focus of this study, an analytical model was developed whichpredicts the serviceability and ultimate resistances of light gauge joist hangers,based on experimental results. This was achieved through analytical procedures,by observing failure modes in tested joist hanger assemblies, and ultimatelythrough calibration against experimental test results. This model is suitable forsubsequent reliability studies of light gauge structural timber connectors.97CHAPTER 5 Conclusions andRecommendationsThe serviceability model of the hanger elements, such as joist seat, joiststirrup nails, header face nails and header top flange, was primarily based on theconcept of elastic beams on elastic foundations. The hanger steel material wassimulated as an elastic beam, while the wood material was treated as an elasticfoundation. The ultimate strength model, on the other hand, was based on theproportional limit (or crush load) of the wood, and the yield strength of the steelmaterial. The ultimate strength of the steel components was largely derived fromobserved failure patterns, while fastener capacities were based on Johansen’s yieldtheory. The proportional limit of the wood, under compression perpendicular tograin stresses, was determined using ASTM experimental procedures.The serviceability resistance of large nail groups could not readily bepredicted from elastic theory and several nail group factors were introduced, basedon test results. These values depend on the fastener type and wood properties.The resistance expressions are similar to those presented in most design codes,where nail group factors are used to simplify calculations.A summary of model formulae is presented in Appendix B.5.3 Final ThoughtsThe relatively simple mechanical timber connector, commonly known asjoist hanger, is indeed a highly complex structure, contrary to the general belief inthe structural engineering community. Although most designers consider it to bealmost a trivial component in a timber structure (usually residential) which istypically over-designed, manufacturers of joist hangers are competing in a tightmarket and need efficient and reliable means to improve their product. Interaction98CHAPTER 5 Conclusions andRecommendationsof fastener types, quantities and locations, with variations in hanger geometry,wood species, and material properties of steel sheathing are factors contributing tothe complexity in analysis and design of these structural connectors. Furthermore,with the rapid development of manufactured wood products, such as Parallelstrand lumber, Laminated Veneer Lumber and I-joists, a demand for specializedconnectors arises. Often appearance and other architectural demands are of majorconcern. Whereas past design codes, based on allowable stress design, prescribeddesign values reflecting the minimum of the strength and slip requirements,modem reliability based codes differentiate between serviceability and ultimateresistances. The hanger manufacturing industry will have to follow suit andfurnish hanger design values that reflect these two design conditions. It would bebeneficial if manufacturers and code agencies would cooperate to propose generic,rational design methods and establish a rigorous testing standard. It is important toopen up the process and allow designers to understand the behaviour of thesestructural connectors, which is vital to assume the proper use of each individualconnector type for every construction application. More importantly, designers,who are active in structural timber design, should be constantly aware of ongoingdevelopments in this field, by having continual contacts with manufacturers andcode agencies.99Bibliography H1. Aalami, B., Williams, D.G. Thin plate designfor transverse loading,CONSTRADO Monograph Series, Crosby Lockwood Staples, London,1975.2. Aalami, B., Williams, D.G. Thin plate designfor in-plane loading,CONSTRADO Monograph Series, Crosby Lockwood Staples, London,1979.3. Allen, D. B., Limit States Design—A Probabilistic Study, CanadianJournal of Civil Engineering, Vol. 2, 1975, pp. 3 6-49.4. American lion and Steel Institute, Cold-formed steel design manual,1983 edition.5. American Society for Testing and Materials, Standard TestMethodsforMechanical Fasteners in Wood, Designation Dl 761, Philadelphia, PA,1988.6. American Society for Testing and Materials, Standard TestMethodsforCompression Perpendicular to Grain Tests, Designation D245,Philadelphia, PA, 1988.100Bibliography7. American Society for Testing and Materials, Standard TestMethodsforTensile Coupon Tests, Designation E8, Philadelphia, PA, 1988.8. Ang, A. H-S, Tang, W. H. Probability Concepts in Engineering PlanningandDesign: Volume II: Decision, Risk, and Reliability, John Wiley andSons, New York, 1984.9. Arnie, Peter. Design Conceptsfor Nailed and Screwed Joints,International Workshop on Wood Connectors. Forest Products Society,Madison, Wisconsin, 1993.10. Barrett, J. D., Foschi, R. 0., Fox, S. P. Perpendicular-to-Grain StrengthofDouglas-Fir, Canadian Journal of Civil Engineering, Vol. 2, 1975, pp.50-57.11. Barrett, J. D., Fosehi, R. 0. Shear strength ofunformly loadeddimension lumber, Canadian Journal of Civil Engineering, Vol. 4, 1977,pp. 86-95.12. Berkoh, F. 0. Assessing the Reliability ofJoist Hangers in ConnectionsofWood-Floor Systems, M. Eng. thesis, Carelton University, Ottawa,Ontario, 1990.13. Breyer, D. E. Design ofWood Structures, McGraw-Hill Book Company,1980.101Bibliography14. Caley et. al. Testing andAnalysis ofInclined Joist Hangers,Undergraduate Course Project, Department of Civil Engineering,University of British Columbia, Vancouver, BC, 1994.15. Canadian Standards Association, Coldformed steel structural members,CAN’CSA-S136-M89.16. Ehibeck, J., Larsen, H. J., Eurocode 5—Design ofTimber Structures:Joints, International Workshop on Wood Connectors. Forest ProductsSociety, Madison, Wisconsin, 1993.17. Erki, M. A. Modelling the load-slip behaviour oftimberjoints withmechanicalfasteners, Canadian Journal of Civil Engineering, Vol. 18,1991, pp. 607-61618. Foschi, R. 0. A discussion on the application ofthe safety index conceptto wood structures, Canadian Journal of Civil Engineering, Vol. 6, 1979,pp. 51-58.19. Foschi, R. 0. Load-Slip Characteristics ofNails, Wood Science, Vol. 7,No. 1, 1974, pp. 69-74.20. Foschi, R. 0., Barrett, J. D., Longitudinal shear strength ofDouglas-fir,Canadian Journal of Civil Engineering, Vol. 3, 198, 1976, pp. 198-208.21. Foschi, R. 0., Bonac, T., Load-Slip Characteristicsfor Connections WithCommon Nails, Wood Science, Vol. 9, No. 3, 1977, pp. 118-128.102Bibliography22. Foschi, R. 0., Folz, B. R., Yao, F. Z. Reliability BasedDesign ofWoodStructures, Structural Research Series, Report No. 34, Department of CivilEngineering, University of British Columbia, Vancouver, 1989.23. Foschi, R. 0., Folz, B. R., Yao, F. Z. Reliability BasedDesign ofWoodStructures: background to CSA-086. 1-M89, Canadian Journal of CivilEngineering, Vol. 20, 1993, pp. 349-357.24. Foschi, R. 0., Longworth, J., Analysis andDesign ofGriplam NailedConnections, Journal of the Structural Division, ASCE, Vol. 101, No.ST12, December 1975.25. Foschi, R. 0., Yao, F. Z., Reliability analysis ofwood I-joists, CanadianJournal of Civil Engineering, Vol. 20, 1993, pp. 564-573.26. Galambos, Theodore V., Guide to stability design criteriafor metalstructures, fourth edition, John Wiley & Sons, New York, 1988.27. Gordon, J. E. The New Science ofStrongMaterials or Why You Don’tFall Through the Floor, Penguin Books Ltd., Middlesex, England, 1976.28. Hall, C. P. Behaviour ofcompression perpendicular to grain loading inwood, M.A.Sc. thesis, University of British Columbia, Vancouver, B.C.1980.103Bibliography29. Hasofer, A. M., Lind, N. C. An Exact and Invariant Second—MomentCode Format, ASCE Journal ofEngineering Mechanics Division, 100(E’ll), 1974, pp. 111-121.30. Hetenyi, M. Beams on Elastic Foundation, University ofMichigan Press,Ann Arbor, 1974.31. International Conference of Building Officials Evaluation Service Inc.Acceptance Criteriafor Joist Hangers and Similar Devices, Whittier,California, 1966.32. Jaeger, L. G. Elementamy theory ofelastic plates, Pergamon press, NewYork, 1964.33. Jeffery Lance et. al. Testing andAnalysis of Utility Joist Hangers,Undergraduate Course Project, Department of Civil Engineering,University of British Columbia, Vancouver, BC, 1994.34. Karacabeyli, E., Foschi, R. 0. Glulam rivet connections under eccentricloading, Canadian Journal of Civil Engineering, Vol. 14, 1987, pp. 621-630.35. Lapin, L. L. Probability and Statisticsfor Modern Engineering, PWS-KENT Publishing Company, Boston, 1990.104Bibliography36. Madsen, Borg, Hooley, R. F., Hall, C. P. A design methodfor bearingstresses in wood, Canadian Journal of Civil Engineering, Vol. 9, 1982,pp. 338-349.37. Madsen, Borg. Structural Behaviour ofTimber, Timber EngineeringLtd., North Vancouver, British Columbia, 1992.38. Madsen, B., Sexsmith, R. Recent Developments in Timber Engineering,Canadian Society for Civil Engineering, 1982-83 National Lecture Tour.39. McLain, T. B., Mechanical Fastening ofStructural WoodMembers—Design andResearch Status, Workshop of Structural Wood Research,Ivlilwaukee, Wisconsin, October 1983.40. National Research Council of Canada, Supplement to the NationalBuilding Code ofCanada 1985, Associate Committee on the NationalBuilding Code, NRCC, Ottawa, Canada.41. Noren, B. Nailed Joints—Their Strength and Rigidity under Short-Termand Long-Term Loading, Report 22, The National Swedish Institute forBuilding Research, Stockholm, Sweden, 196842. Rackwitz, R., Fiesseler, B., Structural Reliability Under CombinedRandom Load Sequences, Computers and Structures, Vol. 9, PergamonPress Ltd., Great Britain, 1978.105Bibliography43. Sexsmith, R. G. Proposed Limit States Design Formatfor WoodStructures, Forintek Canada Corp. Technical Report No. 7, Vancouver,B.C., 1979.44. Sexsmith, R. G., Fox, S. P. Limit States Design Conceptsfor TimberEngineering, Forest Product Journal, 28(5), 1978, pp. 49-54.45. Schuster, R.M., editor, Design in coldformed steel, Solid Mechanicsdivision, University ofWaterloo Press, Waterloo, Ontario, 1974.46. Stalnaker, J. J., Harris, B. C. Structural Design in Wood, Van NostrandReinhold , New York, 1989.47. Tall, Lambert, editor, Structural steel design, second edition, John Wiley& Sons, New York, 1974.48. Thomas, B., Malhotra, S. K. Behaviour of Timber Joints with MultipleNails, Journal of Structural Division, ASCE, Vol. 111, No. 5, May 1985,pp. 991-973.49. Whitman, R. V. Evaluating Calculated Risk in GeotechnicalEngineering, ASCE Journal of Geotechmical Engineering, Vol. 110, No. 2,1984., pp. 145-188.50. Wilkinson, T. L. Theoretical Lateral Resistance ofNailed Joints, Journalof Structural Division, ASCE, Vol. 97, No. ST5, 1971,pp.1381-98.106Bibliography51. Wilkinson, T. L. Analysis ofNailed Joints with Dissimilar Members,Journal of Structural Division, ASCE, Vol. 98, No. ST9, 1971, pp.2005-2013.52. Yao, F. Z., Foschi, R. 0. Duration ofLoad in Wood: Canadian resultsand implementation in reliability-based design, Canadian Journal of CivilEngineering, Vol. 20, 1993, pp. 358-365.53. Yener, M., Pekoz, T., PartialMoment Redistribution in Cold-FormedSteel, Journal of Structural Division, ASCE, Vol. 111, No. 6, June 1985,pp.1187-1203.107SdI-IC 00CtC)‘-I.APPENDIX Al Plate BucklingA1.1 Elastic Plate BucklingFor a perfectly flat elastic plate, the partial differential equation whichforms the basis of the linear elastic buckling analysis can be written as:[1] +2+ = 12(1— ô2w+2N +N2W}2 Et x 2 “ ox Y 2in which N ,N,,N, are the in-plane forces, per unit length, acting on the edges ofthe plate element; w = lateral deflection of plate; t = plate thickness; and E and vare, respectively, modulus of elasticity and Poisson ratio. Obviously, the solutiondepends on the boundary conditions and loading conditions. For instance, takingthe case of uni-directional compressive loading (i.e. N = = O;N = —ot)Equation [1] may be reduced to:[2]Et2 2For simplicity, if simple support conditions are assumed all around a rectangularplate (Figure Al.1 .a), it can be shown that the characteristic solution for this caseis:nzx[3] W=WmnSffl Sm—a bwhere m=l,2,3 ;n=l,2,3 j—1,jSubstitution of this equation into equation [2] yields the smallest characteristicstress or critical buckling stress as109APPENDIX Al Plate Buckling4— kn2E t2l2(1-bwhere k is called the buckling coefficient which is a number depending on theend fixity or boundary conditions. k for this particular case (i.e. simple support)is:[5] k =(__)2a nibIt is apparent that the lowest critical stress occurs in a simply supported plate whenthe buckle pattern has a half sine wave form across the width, b, of the plate.aFINAL RUPTUREa(a) (b) /b (c)INELASTICa %%çLASTIC(d)Figure Al .1 - Plate Buckling.Figure Al. l.b illustrates the relationship between k and the aspect ratio(a/b) for different integer values of m. For each curve, the minimum value of k(= 4) corresponds to the aspect ratio for which square half waves form. The lowerenvelope of these overlapping m curves is to be used in conjunction with equation[4] to calculate the critical stress of a given plate. For long, simply supported110APPENDIX Al Plate Bucklingplates under end compression, k approaches a value of 4 and buckling alwaystakes place in square half-waves of width b.Similar analytical steps are necessary to solve for different loadingconditions and other edge support conditions. However, the final result forcharacteristic stress always takes the form of equation [4] with the k factor beingentirely dependent upon the particular load and edge conditions underconsideration.A1.2 Inelastic Plate BucklingUnlike slender plates, stocky plates may buckle at stress levels whichexceed the proportional limit (or yield limit) of the plate material. This occurswhen the b/t ratio lies in the so called intermediate range. The theory of inelasticplate stability relaxes the assumption of a linear stress-strain relationship andintroduces certain laws of plasticity. Instead of using one or the other theory toarrive at an inelastic buckling stress, the effects of exceeding the proportional limitare usually implemented into a single plasticity reductionfactor, i, defined as:[6]er(ELASTIC)which is used in conjunction with equation [4] in the form:[71 — i1k,z2E t2L i cr 12(1—This relatively simple expression unifies the results for both elastic (i = 1) andinelastic (i <1) buckling cases. The different boundary conditions and the aspect111APPENDIX Al Plate Bucklingratio (a/b) affect mainly the buckling coefficient k, with only little effect on theplasticity reduction factor,.A1.3 Post Buckling behaviour of PlatesDuring the post buckling process of thin flat plates, lateral deflections growrapidly under continued loading and soon they exceed values in the order ofmagnitude of the plate thickness. When this occurs, lateral deflections can nolonger be considered small as was assumed in the linear equilibrium equation [1],resulting in only bending stresses to dominate.During post buckling, both bending and stretching of the middle surface ofthe plate occurs and it is therefore necessary to add additional terms in the analysisto account for the membrane action. The middle surface tensile stressesperpendicular to the primary compressive stresses have the beneficial effect ofstiffening the plate against further lateral deflection. Therefore, the plate can carryin-plane compressive loads considerably in excess of the linear buckling load (e.g.approximately 35% for long, simply supported plates). This behaviour is bestillustrated in Figure Al. i.e.In addition, as in the case of columns, small initial geometricalimperfections in plates cause additional deflections to develop from the start ofloading and these grow rapidly as the critical load is approached. Figure Al. i.eshows a typical load-deflection curve for an imperfect plate, which is the usualcase in most structures. It should be noted that the beneficial effects of in-planestretching restraints are retained in the presence of imperfections.112APPENDIX Al Plate BucklingThe post-buckling strength of thin plates depends largely on the possibilityof this “secondary” load carrying mechanism to develop which, in turn, is mainly afactor of the boundary conditions and/or restraints. In plate girders, for example,typified by the truss action that is developed through the tension field (ormembrane) action of a thin web supported by the flanges and transverse stiffenersthat act as compression struts. In light gauge timber connectors this post-bucklingstrength is achieved in a similar way by providing edge lips or embossings or“compression struts.”Post-buckling analysis for inelastic plates is complex and few results areavailable in that respect. However, there is general consensus by researchers thatvery little additional load can be carried after inelastic buckling has occurred. Atypical plot of the relationship between the plate geometry (b/t) and the criticalstresses in the inelastic and elastic regions is illustrated by Figure Al. 1. d. To theright of the “divider” line, significant post-buckling strength can be utilized, whileto the left, crcr more or less represents the collapse condition.113I-.C CD IAPPENDLX A2 Other Related TopicsA2.1 Multiple Fastener ConnectionsSince installation of joist hangers typically requires a large number offasteners, in the form of nail groups or clusters, it is perhaps necessary to look atthe group effect of multiple fastener connections. Among others, Foschi andLongworth (1975), through energy principles, studied the wood and nail failuremodes in Glulam Rivet connections and proposed a rational design procedure.The allowable load for the nail yielding mode was proposed to be as:[1]NRNC(P*)3.36where NR = the number of rows of rivets; NC = the number of rivets per row; andP* the maximum load carrying capacity for a single rivet in this failure mode. Inthe case of a wood shearfailure mode, the allowable load was given to be:[2] ‘sa= VLaASKj33Yhin which the allowable stress in shear, rLq = 24.5+ 720.0 / (psi) and theparameter fi is related to the geometry of the connection. For obvious reasons, theallowable load of the connection is the minimum of the two values given by [1]and [2]. As recommended by the authors, the noted analysis was general in natureand could be extended to other types of connectors used in timber structures.To generalize the analysis, Karacabeyli and Foscbi(1987) investigated thebehaviour of Glulam rivet connections under eccentric loading. Weibull’s theoryof brittle fracture, as well as finite element analysis of the stress distribution in thewood around the rivets were applied to study the wood failure around the rivet115APPENDIX A2 Other Related Topicscluster. Analysis of rivet yielding in bending with simultaneous bearing failure ofthe wood under the rivet’s shank was based on the previous work by Foschi andLongworth (1975). In addition to good agreement between experimental resultsand theoretical predictions, the authors demonstrated that the load-carryingcapacity of wood failure cannot be calculated in closed form. Conversely, theload-carrying capacity of rivet in yielding was calculated in closed form.A2.2 Load Duration EffectsTo understand the behaviour of timber connections during the life of astructure is of significant importance in the overall design of timber structures.Yao and Fosehi (1993), based on earlier work by Yao (1987) and Foschi, Folz andYao (1989), carried out experimental and theoretical studies to investigate theduration of load effects in wood structures. By defining a time dependent damagestate variable as a, the so called Canadian damage accumulation model wasdevised to be in the form of[3] a[v(t)— jvlb +c[r(t)— cT0T3]”ain which parameters a, b, c, n, and o- are assumed to be constants for a givenmember, but vary randomly and independently across members; ; is the standardshort term strength of the member, measured in a ramp test of short duration; o isthe model parameter which is termed the threshold stress ratio. The product odefines a threshold that must be exceeded for damage to accumulate. For instance,when Q) — ; <0 there will be no damage accumulation.116APPENDIX A2 Other Related TopicsThe differential equation [3] can further be evaluated, through approximateintegration techniques, to yield the damage, a, at any time T, for any load history,rQ). Based on earlier research by Foschi et al. (1989), the authors alsoinvestigated the relationship between duration of load effects and modificationfactor, KD , as used in the Canadian limit states design code for wood structures,CSA-086. l-M89. The relationship between the performance factor, q5, andreliability index, ,8, for two cases was studied: (i) when the duration of load effectsare ignored and only short-term strength is considered; and (ii) when duration ofload effects are taken into account, was studied. To maintain the same targetreliability index for the two applications, the authors, through computer simulationof model [3], estimated and recommended reliability indices at the end of theservice life of a particular structural member. However, the influence of creep,load duration, moisture and temperature service conditions were not explored anddiscussed, due to the lack of available test results.117s.c a Cl) C12 IAPPENDIX A3 System ReliabiliiyA3.1 IntroductionA substantial application of reliability analysis is to closely estimate thereliability of a system based on reliability of its individual components. Thesystem reliability is in essence a problem involving various failure modes. Forinstance, failure of a particular component or a group of components in a systemrelate to distinct failure modes of the system. For a structural system that iscomposed of various components, shch as a joist hanger, the reliability of a singlecomponent may be expressed as the probability that the single component isurvives beyond a certain load Q*(limit states load), during the structures usefullife, or[1] R(Q) = Th(Qeomponenti> Q*)The system reliability is then a function of the reliabilities of its components:[2] Rgygtem (Q) = f{R1(Q),R2(Q),R3... ,R(Q))When Q* is limited to a certain magnitude, then a closed form solution to thesystem reliability [2] may be obtained. However, as its the case with structuralproblems, Q* is usually unknown, which in turn necessitates approximatetechniques to predict the system reliability.A typical joist hanger can be considered, for example. If a shear failureoccurs in one or few nails, failure of the joist hanger may not be imminent; that is,the joist hanger may still be able to function under the applied load. In theforegoing case, the system behaves as a redundant or parallel system. However, ifa more catastrophic failure occurrs, such as rupture of the joist hanger seat under119APPENDIX A3 System Reliabilitythe applied load, then failure of the connection is imminent. Thus the system maybe classified as a weakest link or series system. A joist hanger may therefore beviewed as a system having parallel and series characteristics. It should be notedthat failure of one connection in a floor does not necessarily indicate the failure ofthe entire floor system. The general system reliability analysis is thoroughlyoutlined in Aug and Tang (1984), and can be reviewed briefly.In light of the fact that n failure modes and thus n failure functionsmathematically define a structural problem, the system probability of failure maybe re-expressed as the volume integral [18] in chapter 1:[3]= f . . . J (X1,..., X, )dX1,... ,dXwhere a failure event defines the integration domain and is the complement of theevent that none of the n potential failure modes occur:[4] =1— (E1 rE2ri... mE)As mentioned earlier, closed form integration of [3] is tedious and generallydifficult. Thus, via approximate methods, lower and upper bounds of theprobability of failure are established to study the reliability of a structural system.By considering two positively correlated events E and E, the uni-modal or firstorder bounds for the probability of failure F1is expressed as[5] nlaxPfPf1—fl(1—Pf)120APPENDIX A3 System ReliabilityThe urn-modal bounds on P [5], or conversely on 1,, may be refined by takinginto account the correlation between pairs of failure modes; thus, requiring theprobability ofjoint events. This is usually called bi-modal or second order boundsand may be written, for n potential failure modes, in the form[6] Pf +max[{Ff -P(E1E)};O]F -nmxP(E1E)Since joint probabilities P(EIEJ) are required when failure modes are correlated,as its the general case in structural problems, then evaluation of [6] still remains tobe a difficult task Various cases and examples of system reliability are presentedin Mg and Tang (1984).121I I IAPPENDIX B Summaiy ofModel FormulaeB.1 IntroductionThe followings are a summary of model formulae. Note that there are nailquantity and type restrictions on some of the component models. For a thoroughexplanation of the model, the reader is urged to refer to chapter 4 of this report.B2 Joist Seat Serviceability ModelTotal joist seat displacement: Ysystem = Yfree +Primary system (free ends):— P2 cosh(2x) cos(2(l — x)) + cosh(2(l — x)) cos(2x)Yfree— k sinh(21) + sin(21)System characteristic: 2 = 41J4J where EI= flexural rigidity of the beam,k = supporting elastic foundation,x = distance along the beam,1 beam (seat) length,P = applied axial load in joist stirrups.Secondary system (fixity moment applied):‘sinh(Ax) cos(2(l — x))—— 2M0 1 — cosh(Ax) sin(2(l — x))— k sinh(21) + sin(21) + sinh(2(l — x)) cos(Ax)—cosh(2(l — x)) sin(Ax)whereM0 = fixity (compatibility) moment:MP( sinh(21)—sin(21)° 4% cosh(21) — cos(21)123APPENDIX B Summaiy ofModel FormulaeB.3 Joist Seat Ultimate ModelI = a. F,, .2. 4Joist seat ultimate load: Se = rmn— ‘F Abearing — P crush bearingwhere P, = yield strength of steel (N/mm2);“crush = wood perpendicular to grain, or bearing strength (N/mm2);= Bseat. cross sectional area of only one hanger stirrup (mm2);Abearing = Bseat ‘seat = hanger seat bearing area (mm2);Bseat and Wseat are hanger seat bearing depth and width respectively (mm);t1,0=thickness of the hanger stirrup (mm);a and ,6 are empirical amplification factors for wood and steel materialsrespectively.B.4 Joist Stirrup Nail Serviceability ModelP2 sinh(2l) cosh(21) — sin(%l) cos(21)Tip dispalcement for a single nail: YTIP = ShIh2(2?) — sin2 (2?)Serviceabilty resistance of n fasteners: Nn = awhere N1 is the lateral strength of a single fastener, and a3is called the nailgroup factor for joist nails.B.5 Joist Stirrup Nail Ultimate ModelLateral load capacity of single joist hanger stirrup nail:(a)]=min (b) FWLfPD1(41i—1)(c) /2FWDfMYf124APPENDIX B Summaiy ofModel Formulaewhere Df diameter of the fastener;L fastener penetration length;F = wood embedding strength, which is the average crushingstrength of wood under the dowel; andF,, = steel plate yield strength;D13Mf = yield moment of the beam or fastener: Mf = Z. Ff =6)1,j;Ff fastener yield strength.B.6 Header Nail Serviceability ModelSimilar to the joist nail model:— P2 sinh(21) cosh(21) — sin(21) cos(21)YTip— k sinh2(2?) — sin2 (21)where all variables are as per section B.3.B.7 Header Nail Ultimate Model3 F, Df tplateJ.=min FLD(Ji-1)Similar to the Joist nail model: fl W f/2FD1Mfwhere all variables are as per section B.4.Ultimate resistance of n fasteners: • N=1 Where N1 is the ultimatestrength of a single fastener.125APPENDIX B Summaty ofModel FormulaeB.8 Top Flange Serviceability Model2P2Load-displacement relationship: ‘= k(exp(—Ax) cos(Ax))where all related parameters are noted as before.B.9 Top Flange Ultimate ModelI 1+/IFf = a1 tf PnaIiCOS6 — sin8j‘itt’where = Capacity of a particular top flange fastener type, obtainedfrom the header experimental results of correspondingfastener type;= Top flange calibration factor;flt,e = Number of fasteners in top flange;9 = Top flange nail angle of inclination; and,Uf = Top flange interface friction coefficient.126


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