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New constructions of glulam beams in Canada Mohadevan, Nahulesalingam 2007

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NEW CONSTRUCTIONS OF GLULAM BEAMS IN CANADA by NAHTJLESALINGAM MOHADEVAN B.Sc.Eng., The University of Peradeniya, 2000 M.Phil., The University of Preadeniya, 2003 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF A P P L I E D S C I E N C E in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Forestry) T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A July 2007 © Nahulesalingam Mohadevan, 2007 ABSTRACT A n optimized 24f glulam beam lay-up has been investigated with a series of laboratory testing and computer modeling. The basic ideas of these assessments are to increase the efficient use of timber resource in the glulam construction with integration of reliability based procedures to characterize the specified strengths for the glulam beams. During this study, existing grade specifications in the Canadian Standards have been refined. Five new Douglas fir lamina grades ( T l , Cc , B , C and D) and their tensile strength data have been established. Finite element glulam analysis program U L A G has been used for the primary beam modeling and analysis. N e w routines to account for the laminating effects on the beam strength and to evaluate the shear capacity of the glulam beams have been incorporated in the U L A G program. The shear stress output from the finite element analysis has been integrated to consider weakest link stress volume effect for the shear capacity assessment. Subsequently 24f glulam beams have been successfully simulated using the refined U L A G program. A similar analysis based on A S T M D3737 has been carried out using the U S - G A P program based on a detailed knot survey on the new lamina grades. The model has been calibrated by full scale test results. The model predictions and the corresponding assessments have been further validated by a second set of full scale glulam bending and shear tests. Glulam beams 305 mm and 610 mm deep, have been tested to assess the flexural strength. Three sets of glulam beams, 305 mm and 457 mm deep have been tested at short span to depth ratios to determine the shear capacity. Excellence prediction accuracy by U L A G has been confirmed. i i Table of Contents Page Number Abstract i i Table of Contents i i i List of Tables v i List of Figures • ' - i x Acknowledgements x i 1. Introduction 1.1 General Background. 1 1.2 Aims and Objectives 3 1.3 Research Plan ..3 1.4 Scope of the Testing 4 1.5 Organization of the Thesis 6 1.5.1 Unit Used 7 2. (.lulam : State of the Art 2.1 Introduction :\ 8 2.2 Glulam Models 9 2.2.1 G L U L A M 9 2.2.2 G A P 9 2.2.3 U L A G 10 2.3 Glulam Flexural Strength 12 2.4 Glulam Shear Strength 12 2.4.1 Shear Strength Models 13 2.5 Tensile Strength of Lamina 14 2.5.1 Laminating Effects 14 2.6 Laminating Grades 15 2.7 Knot Survey... . . 15 i i i 3. Development of New Lamina Grades 3.1 Introduction -16 3.2 Development Procedure 17 4. Lamina Strength Assessment 4.1 Introduction 27 4.2 Modulus of Elasticity 28 4.3 Tensile Strength Tests I - Lamina 29 4.4 Tensile Strength Tests II- Finger Joint 33 4.4.1 M L E Assessments 33 4.4.2 Finger Joint Test Results 35 4.5 Moisture Content •.••••4? " ! 4.6 Knot Survey... 40 4.6.1 Knot Survey: Procedure 41 4.6.2 Knot Size Calculation 42 4.6.3 Results 43 5. Glulam Beam Modeling 5.1 Introduction -46 5.2 U L A G Upgrading 47 5.3 U L A G Analysis 47 5.3.1 Performance of the Lamina Grades 49 5.3.2 Tension Laminating Factors 50 5.3.3 Bending Simulations 51 5.4 U L A G Calibration Tests - Flexure 52 5.4.1 M O E Values 56 5.4.2 U L A G Calibration - Bending 58 5.5 U L A G Shear 59 5.5.1 Numerical Modeling 59 iv 5.5.2 Shear Simulations 61 5.6 Shear Tests .. . . . . . . . . .62 5.6.1 M O E Values , 65 5.6.2 Shear Failure Characteristics 65 5.6.3 Shear Calibration 65 5.7 G A P Assessments 66 5.8 Determination of Specified Strength .69 6. Glulam Model Verifications 6.1 Introduction 71 6.2 Bending Tests 72 6.2.1 M O E Values 76 6.3 Shear Tests 77 6.4 U L A G Verification ......82 6.4.1 Influence of Finger Joints 83 6.5 Size Effects in Bending , 84 6.6 Flexural Strength and Stiffness Compatibilities 87 6.7 Reliability Analysis 89 7. Concluding Remarks 7.1 Summary • 92 7.2 Conclusions • 93 7.3 Justifications 95 7.4 Suggestions for Future Research ; 95 Bibliography 97 L I S T O F T A B L E S Page Number Table 3.1 Key grading factors considered for the resource assessment-Trial 1 18 Table 3.2 M O E values of the first three batches of material 19 Table 3.3 Grade outturn corresponds to Trial 1 20 Table 3.4 Key grading factors considered for the resource assessment-Trial II 21 ; fable 3.5 Grade outturn corresponds to Trial II 23 Table 3.6 Grade outturn corresponds to Trial III 26 Table 4.1 Summary statistics of M O E test results 29 Table 4.2 Summary statistics of the tensile strength test results at 2.44 m gauge length... 30 Table 4.3 Details of the finger joint failures 35 Table 4.4 Details of the finger joint strength values predicted by M L E program 35 Table 4.5 Specific gravity of the new Douglas fir lamina grades measured at the test moisture content 40 Table 4.6 Details of the lamina samples used for the knot survey. 41 Table 4.7 Knot survey summary, details of the knot distribution corresponding to knot size 43 Table 4.8 Knot survey results: Values corresponding to 300 m length of laminae 45 Table 5.1 Details of the beam lay-ups used for the initial U L A G simulations 49 Table 5.2 Summary of the preliminary U L A G simulation (bending, 3 r d point loading).... 50 Table 5.3 Trial sets of laminating grades proposed for the new lamina grades 51 Table 5.4 Beam Lay-ups selected for U L A G calibration (beam ID A 8 U ) 52 Table 5.5 U L A G strength predictions for the trial beams 52 Table 5.6 Details of the bending test configuration 53 Table 5.7 Summary of the bending test results. 54 Table 5.8 Key failures observed in 0. 30 m deep beams 55 Table 5.9 Summary of the M O E values of the 0.30 m deep bending beams. 57 Table 5.10 Comparison between bending test results and U L A G prediction - specified strength 58 v i Table 5.11 Comparison between bending test results and U L A G prediction - M O E 58 Table 5.12 Clear wood Douglas fir shear strength (Lam et al. 1997) of a standard shear block 61 Table 5.13 Shear calibration beam lay-up 62 Table 5.14 Results of the initial shear simulations 62 Table 5.15 Shear test configuration 63 Table 5.16 Summary of the shear test results 64 Table 5.17 Details of the M L E simulated shear capacity (based on laboratory test results) 64 Table 5.18 Shear strength parameters based on the experimental data 64 Table 5.19 Predicted clear wood shear strength values corresponding to Douglas fir D grade laminae 66 Table 5.20 Predicted shear capacity of the glulam beams 66 Table 5.21 Glulam lay-ups used for the G A P assessments 67 Table 5.22 Details of the specified strength values corresponding to the G A P predicted allowable strengths 68 Table 5.23 Comparison between the U L A G and G A P predicted specified strength values69 Table 6.1 Details of the bending test configuration 72 Table 6.2 Beam lay-ups selected for bending tests (beam ID A 5 U ) 73 Table 6.3 Summary of the bending test results 74 Table 6.4 Key failures observed in 0.61 m deep beams 75 Table 6.5 Summary of the M O E values of the 0.61 m deep bending beams 76 Table 6.6 Shear test configuration 77 Table 6.7 Summary of the shear test results : 78 Table 6.8 Details of the M L E simulated shear capacity (based on laboratory test results) 78 Table 6.9 Shear strength parameters based on the experimental data 78 Table 6.10 Comparison between bending test results and U L A G prediction - specified strength 82 Table 6.11 Comparison between bending test results and U L A G predicted M O E 82 Table 6.12 Comparison between shear test results and model prediction. 82 v i i Table 6.13 Comparison between the capacities of glulam beams constructed with different length of lamina stocks 83 Table 6.14 Beam lay-ups used for the volume effect analysis 84 Table 6.15 Summary of the size effect analysis 85 Table 6.16 Glulam beam lay-ups used for the special investigation ...87 Table 6.17 Key strength parameters of the grades T l and B 88 Table 6.18 Results of the special investigation 88 Table 6.19 Summary of the reliability analysis 90 v i i i L I S T O F F I G U R E S Page Number Figure 1.1 Research plan 4 Figure 3.1 Tensile strength distribution of T l grade (Batch 5) 25 Figure 4.1 Tensile strength distributions of the new lamina grades.; 31 Figure 4.2 Images of some of the T l grade material failed at low strength level 32 Figure 4.3 Tensile strength distribution of the T l grade 38 mm X 140 mm Douglas fir fingerjoints .36 Figure 4.4 Tensile strength distribution of the B grade 38 mm X 140 mm Douglas fir fingerjoints ...36 Figure 4.5 Tensile strength distribution of the C grade 38 mm X 140 mm Douglas fir fingerjoints 37 Figure 4.6 Tensile strength distribution of the D grade 38 mm X 140 mm Douglas fir fingerjoints 37 Figure 4.7 Some of the typical finger joint and lamina failures 39 Figure 4.8 Illustration of the pitch center of a knot in a cross section of a lamina 42 Figure 4.9 Knot size distributions 44 Figure 4.10 Knot size distributions at the upper tail..~: 44 Figure 5.1 Typical third point loading configuration used for the bending test 53 Figure 5.2 Test setup for the 0.30 m deep beam. 54 Figure 5.3 Comparison between the U L A G predicted strength distribution and the laboratory test results for 0.30 m deep glulam beams 55 Figure 5.4 Bending failure of a 0.30 m deep glulam beam 56 Figure 5.5 Cable - yoke system used to measure the relative displacement at the middle of the beam 57 Figure 5.6 Configuration of the typical shear testing arrangement 63 Figure 5.7 End section of a failed shear beam (This beam is 0.30 m deep and tested at 2.13 m test span) 65 Figure 6.1 Typical third point loading configuration used for the bending test 72 Figure 6.2 Test setup for the 0.61 m deep glulam bending beam 73 Figure 6.3 Comparison between the U L A G predicted strength distribution and the ix laboratory test results for 0.61 m deep glulam beams. 74 Figure 6.4 Bending failure o f a 0.61 m deep glulam beam 75 Figure 6.5 Bending failure of a 0.61 m deep glulam beam 76 Figure 6.6 Configuration of the typical shear testing arrangement 77 Figure 6.7 Visual comparison of 0.30 m and 0.46 deep shear beams at 6 span to depth ratio 79 Figure 6.8 Shear Failure images form a high speed video 80 Figure 6.9 Load vs. Stroke curve for a 0.46 m deep glulam shear test 81 Figure 6.10 Variation of log(MOR) with log(V) for the glulam beam cases considered in the volume effect analysis 85 Figure 6.11 Comparison of the variation of log(MOR) with log(V) with different size effect factors (V in units of m 3 and M O R in units of MPa) 86 x Acknowledgements I wish to express my sincere appreciation to my supervisor Prof. Frank Lam for his invaluable guidance and support during this research. His comments, suggestions and criticisms strengthened my confidence in formulating and finalizing this thesis. I also acknowledge him for the financial support provided to me during this period. M y sincere thanks to Prof. Ricardo Foschi, emeritus professor for his expertise assistance during the research especially for his guidance in the U L A G modeling. I also like to extent my thanks to Prof. David Barrett and Dr. Bryan Russell Folz for their support extended during the study. The continuous assistances and coordination of Mr . Kent Fargey and M r . Travis V a n de Vliert throughout this research is greatly acknowledged. I am also grateful to Dr. Borjen Y e h for his technical assistance, feedback and support during the research. I also would like to extent my sincere thanks to M r . Bob Myronuk, M r . George Lee, M r . Larry Tong and other technical staff members attached to the Wood Mechanics Laboratory for their supports during the laboratory testing. The assistances and funding from the industrial partners, especially Western Archrib-Structural Wood Systems and the Natural Resources Canada Value to Wood Program is greatly acknowledged. xi Chapter 1 INTRODUCTION 1.1 GENERAL BACKGROUND Glue laminated timber (Glulam) is a type of engineered wood product that has improved performance and attributes compared to solid sawn members leading to very efficient use of the timber resource. In North America the minimum requirements for the manufacturing of Glued laminated timber (Glulam) beams are specified in C S A 0122 M 8 9 (Canada) and A N S I / A I T C AI90.1 (US). C S A 0122 M 8 9 uses visual grading and modulus of elasticity ( M O E ) assessment to build different grades of glulam while A N S I additionally requires the knot distribution of the material to be considered. C A N / C S A 0122 M 8 9 specifies four grades of lam-stock B - F , B , C and D . B - F is the highest grade designated for the extreme tension zones of 20f and 24f beams. For this grade, knots or other similar defects exceeding 10 mm and local slope of grain steeper than 1:16 shall not be permitted within 13 mm of the edge of the outer tension face lamination after finishing. D is the weakest grade, generally placed at the mid zone of the beam. The laminating boards of this grade are allowed to have knot sizes up to 50% of the board width. The current Canadian specifications generally deal with pre-established lamina grades and specify whether the given beam lay-up is admissible. The U S procedures require tedious knot assessments to qualify the material grade. It is recognized that there is a need for more efficient beam design procedures which wi l l increase the performance of the glulam beams as well as improving the efficient use of timber resource. 1 One of the key-issue from the glulam manufacturers' point of view is the availability of supply o f the high grade material needed for the extreme tension zone of the 24f beams. Here the interest is to investigate the possibility to modify some of the knot size restrictions at the extreme tension zone of the 24f beams in order to match the strength requirements to the knot size characteristics of the lamina resource for the tension lamina-grades. In the past there were many studies targeting various aspects of glulam beam design and construction were reported. In Canada the glulam analysis computer model U L A G , Ultimate Load Analysis of the Glulam, was developed by Folz and Foschi (1992). In the United States G A P , Glulam Analysis Program, developed based on A S T M D3737 is recognized as the tool to configure new lay-up and construction o f glulam beams. U L A G is a stochastic finite element program developed at the University of British Columbia. The program can simulate virtual construction of glulam beams/columns and progressive loading until collapse to investigate the bending capacities and failure behaviors of the glulam. Therefore, the program has high potential to be use in exploring the structural performance of glulam with new lay-ups and/or new lamina grades. A t this point the idea o f the current research is to develop new lamina grades to construct more efficient 24f glulam lay-ups as wel l as verify/fine-tune U L A G predictions. The information w i l l subsequently be used to develop reliability based specified strengths for implementation in Canadian Codes. 2 1.2 AIMS AND OBJECTIVES The current research focused on three main aims as given below : • Develop new Douglas-fir laminae lay-ups for the construction o f glulam beams. • Verify/fine-tune/upgrade/validate U L A G performances. • Analyze the strength characteristics and failure behavior of full scale-24f glulam beams. These developments w i l l enhance the glulam design and analysis and facilitate the Glulam-Industry/researcher to achieve the following objectives in the long run, • Expand the use of glued-laminated beams (glulam) by establishing reliability-based procedures to qualify/optimize new construction (grades/species/lay-up) o f glulam in the Canadian Codes. • Develop the associated test data for predicting the performance (bending strength and stiffness) of high performance glulam beams in engineering applications. 1.3 R E S E A R C H P L A N The research plan has three phases namely : Development (Phase I), Assessment (Phase II) and Verification (Phase III). Phase I deals with the initial literature survey, grade development process, and assessment of the lamina strength properties required for the beam modeling. Phase II focused on the glulam beam modeling/analysis using U L A G and G A P to assess the performance o f new grades and the calibration o f the U L A G model. This analysis w i l l facilitate the design of target 24f glulam beams for the verification tests as well . The final verification tests and the subsequent assessments were carried out during Phase III. A detailed flow of the research plan is given in Figure 1.1. 3 Figure 1.1 Research plan Phase I Development I Literature Rev iew Knot Survey Industry Input Initial A s s e s s m e n t of the Laminae G r a d e and Strength Character is t ics Tens i le Strength Test ing Phase Ii Assessment Phase III Verification 1 Mode l A s s e s s m e n t Us ing G A P G lu lam Mode l ing and Cal ibrat ion Veri f icat ion & Final iz ing of the Mode l ( Construct ion and Test ing of Ful l S c a l e G lu lam B e a m s ) 1.4 SCOPE OF THE TESTING The current research requires a series of laboratory testing. The scopes o f these tests are given below. (I) Grade Development and Knot Survey (38 mm x 140 mm lamina) 4.88 m long lamina ~ 500 boards 2.44 m long lamina ~ 200 boards These assessments were focused on developing a database for five new lamina grades. 4 (II) Tension Testing (38 mm x 140 mm lamina) Four tension lamina grades T l , B , C and D were considered for the tension testing. These tests were carried out in three groups corresponding to 4.88 m and 2.44 m long laminae and finger joints. 4.88 m long lamina - four grades @ 100 boards/grade 2.44 m long lamina - four grades @ 100 boards/grade Finger joint - four grades @ 100 boards/grade (III) Full Scale Beam Testing Glulam bending tests : 3rd point loading test. Two sets of tests were carried out; 0.30 m deep beams were tested during U L A G calibration process and 0.61 m deep beams were tested during the verification phase. Each of these sets consisted of twenty four beams. 0.30 m deep 24f glulam beams tested at 21 span to depth ratio 0.61 m deep 24f glulam beams tested at 18 span to depth ratio Glulam shear tests: four point loading test. Three sets of beams were tested during the glulam shear assessments; two sets o f 0.30 m deep beams were tested during the U L A G calibration process and one 0.46 m deep beam was tested during the verification phase. Each of these sets consist twenty four beams. 0.30 m deep 24f glulam beams tested at 6 span to depth ratio 0.30 m deep 24f glulam beams tested at 7 span to depth ratio 0.46 m deep 24f glulam beams tested at 6 span to depth ratio 5 1.5 ORGANIZATION OF THE THESIS Chapter one of this thesis provides general background of the study and discusses the key aims and objectives of the research. This chapter also provides details o f the scope o f the laboratory testing, the research plan and the organization of the thesis. Chapter two describes the glulam beam strength characteristics and the computer models. It details the general lamina strength characteristics, glulam design parameters and discusses on the glulam beam modeling. Chapter three focuses on the grade development for the new lamina grades. This chapter describes the step by step assessments procedures carried out during the grade development process. Chapter four details the lamina strength assessment procedures. This chapter mainly presents the tensile strength test results of the laminae and finger joints. A n illustration of the M a x i m u m Likelihood Evaluation ( M L E ) procedures used for finger joint strength assessments and the details o f knot survey are also discussed in this chapter. Chapter five provides the information about the U L A G upgrading and the details of the subsequent U L A G analyses of full scale glulam bending and shear calibration tests. The details of the G A P assessments are given at the latter part of this chapter. This chapter also describes the glulam shear volume effect analysis and the reliability based normalization procedures carried out to obtain specified strengths of the glulam beams. Chapter six gives the details of the glulam verification tests. The information about the full scale glulam bending and shear tests is described at the initial part o f this chapter. Size effect assessment and reliability analysis corresponding to 0.30 m and 0.61 m deep glulam beams tested are given in the latter part o f this chapter. 6 Chapter seven presents the summary of the research carried out, key outcomes, concluding remarks and the recommendations for the future study. 1.5.1 U N I T U S E D The beam dimensions were originally measured in imperial unit as practiced in the industry. However for computation/numerical analysis purposes the SI units were adopted during the analysis/assessments. Therefore the SI units have been used as the primary unit throughout this dissertation and in some instances beam dimensions were given in both imperial and SI unit systems for convenience. 7 Chapter 2 Glulam : State of the Art 2.1 INTRODUCTION In North America, glulam beams are produced with lay-up and laminae specifications based on the Canadian standard - C A N / C S A - 0 1 2 2 - M 8 9 and American standard A S T M D3737. These standards provide guidelines for the assessment/qualification of the lamina grades and the beam lay-ups. In Canada, 20f E and 24f E are commonly manufactured glulam grades. Generally these beams were constructed to yield a modulus of elasticity ( M O E ) of 12,400 M P a (1.8 mil l ion psi). In addition there are many glulam beam analysis models available to evaluate different beam lay-ups and lamina properties. One of the initial works was the computer model G L U L A M developed by Foschi and Barrett (1980). Glulam Analysis Program ( G A P ) is another glulam design tool developed based on A S T M D 3737. Folz and Foschi (1997) developed a computer model U L A G to predict the capacity and failure behavior o f the glulam beams. This model is considered to be one o f the most versatile tools to analyze the glulam beam failure behavior. Douglas fir, southern pine and hem fir are the main species used in North American glulam construction. Initially the lumber is sawn into a standard 38 mm thick lamina and graded. The graded boards are then end joined using finger joint and gluing techniques according to standard specifications. One of the major advantages of using finger joined boards is that the length of the beam w i l l not be limited by the length of the lamina boards. In this way, the finger jointing is a vital part of the glulam beam. 8 Furthermore, the glulam technique makes it possible to use material from small trees to construct very large beams. However, this finger jointing process can reduce the net strength of the laminae and thereby may control the overall strength of the glulam beam. 2.2 GLULAM MODELS 2.2.1 GLULAM Foschi and Barrett (1980) developed a finite element m o d e l - G L U L A M to predict the statistics of the strength o f glulam beam. This model uses the M O E , tensile strength, compression strength and the knot distribution to simulate a number of gulam beams. The model basically considers 154 mm wide lamina boards. Based on model simulation, each element w i l l be assigned a net strength a c and a modulus of elasticity Ec . Then the finite element model can be used to perform beam loading/failure simulations. The beam failure is determined by the brittle fracture of the weakest element. The model was originally calibrated and verified using a trial and error fit based on tensile strength test results. The model was not calibrated to assess the influence of fingerjoints. 2.2.2 GAP This is an analytical program based on A S T M D 3737. The program mainly utilizes the data from full scale laminae tests, knot distribution, and slope of grain information corresponding to the laminating grades to predict the beam strength. The allowable properties for a structural glued laminated timber lay-up is specified as the products of stress index values, stress modification factors and adjustment factors for end use condition ( A S T M D3737). Here the stress index values are 9 species dependent and established based on laboratory testing. The bending stress index values for the visually graded and E-rated lumber are given in A S T M D 3737. The adjustment factors for the end use condition are given in the Section 9 of the above standard. The stress modification factors are determined based on the knot distribution and the corresponding M O E values. 2.2.3 U L A G U L A G (Ultimate Load Analysis of Glulam) is a one dimensional linear stochastic finite element program. The main advantages of this program are that it has the capacity to simulate a virtual construction of glulam beams and analyze the progressive loading until collapse. This program can be used to investigate the beams bending and shear strength capacities and critical failure behaviors. It doesn't require any knot data as input. The key strength parameters required for the assessment are the tensile strength test data of the lamina and finger joint and the corresponding M O E values. These data were inputted to the program as text data files and processed using an auxiliary program U L A G D A T 1 which generates the primary data file U L A G D A T l . d a t with the summary statistics of the strength data corresponding to the material grades considered. The lamina length details of the material grades used for the beam construction were stored in a secondary data file U L A G D A T 2 . d a t using another auxiliary program U L A G D A T 2 . Based on these data the U L A G program simulates the virtual construction of glulam beams. The key processes followed during the beam simulation are given below. 10 1. Randomly pick the laminating boards from the lamina stock o f various length groups representing the actual material supply for the beam production. 2. Place the boards in sequence at corresponding beam layers to form the beam and determine the finger joint locations. 3. Formulate the finite element mesh and determine the nodal locations. 4. Assign random- M O E values to each piece of lamina in the beam corresponding to the material grade considered. 5. Provide beam's support and loading conditions. 6. Assign the stochastic flexural strength to each segment of the lamina between the nodes corresponding to the material grade considered. 7. Derive a finite element solution for the problem. 8. Assess the axial deformations along the beam axis. 9. Evaluate the non linear normal and shear strain distribution at each of the nodal sections across the beam. 10. Determine axial stresses. 11. During beam loading simulation identify the preliminary lamina failure within the beam based on the exceeding of the axial stress over the lamina strength assessed at each of the lamina segments between the nodes. 12. Replace the stiffness and strength of the failed lamina segment with null values and repeat steps 7 to 12 until collapse of the beam. 13. Record the failure load, deflection failure type and other details of interest. 14. Repeat the steps 1 to 13 until getting the required sample size to obtain the statistics of the beam capacities and failure data. 11 2.3 GLULAM FLEXURAL STRENGTH Tensile strengths of lamina and finger joints and the M O E of the laminating boards are the key factors to determine the strength/capacity of the beam. These factors are species dependent and controlled by the grade of the lamina. Generally the capacity of the beams is given in terms of the specified strength. The typical glulam specified strength ranges from 25 M P a to 35 M P a . This is about 20% higher than the flexural capacity of the corresponding solid sawn timber beams. Timusk (1997) reported results of two sets o f 30 spruce-pine-fir (SPF) glulam beam tests and four sets of SPF C and B grade lamina and finger joint tension tests. These testing were carried out as part of the U L A G calibration/verification program. The beams, 0.30 m and 0.46 m in depth, were built with 38 mm nominal thickness lamination. They were tested with a four point loading setup at a 16 span to depth ratio. The 0.30 m beams had eight C grade laminae and the 0.46 m deep beam had two B grade tension lamination and ten C grade lamination. Average M O R values of these two sets are 35.5 M P a and 38.3 M P a , respectively. A high correlation between the tensile strength o f the extreme lamina and the flexural strength of the beam was observed. Different patterns of failure were reported for the beam tests. However, initial failure behavior was not identified due to the sudden collapsing nature of the failures. 2.4 GLULAM SHEAR STRENGTH Y e h and Will iamson (2001) studied the shear strength of full size glulam beams using four point test method. The beams had a span of 3.05 m with a span to depth ratio of approximately 6.7. The test consists of five sets of beams, two for Douglas fir, two for 12 southern pine and one for SPF. The Maximum Likelihood Evaluation procedure was used to analyze the censored data. A n overall 70% of shear failures with mean shear strength values of 4.5 M P a , 5.5 M P a and 4.5 M P a were reported for Douglas fir, southern pine and SPF, respectively. The resultant coefficients of variation ( C O V ) values are 7.5%, 9% and 12%, respectively. The corresponding characteristics strength values are about 30% lower than the A S T M small block shear test results. Although, this is a significant reduction, the results demonstrated that significantly higher (35%-60%) allowable shear strength can be justified. 2.4.1 S H E A R S T R E N G T H M O D E L S Foschi and Barrett (1976) developed a technique to determine the longitudinal shear strength of wood beams based on the Weibull 's theory of brittle fracture. The method relates the survival probability of the two wood volumes under different loading conditions and predicts the critical loads for one volume based on the failure load of the other one. A sequence to predict the longitudinal shear strength based on the A S T M block shear test was established. L a m et al. (1997) investigated the shear strength of Canadian soft wood structural lumber based on a series of laboratory tests and numerical modeling. A two span five point test procedure with span to depth ratios of 6 and 5 were used for the laboratory assessments and a finite element assessment incorporating the Weibull weakest link theory was used for the numerical predictions. A very good model performance with a maximum 6% error was demonstrated. 13 2.5 TENSILE STRENGTH OF LAMINA Timusk (1997) reported tensile strength values of 38 mm x 140 mm spruce-pine-fir C and B grade laminae and fingerjoints. Average tensile strengths of C and B grade laminae tested at 3.66 m gauge length, are 24.0 M P a and 33.0 M P a , respectively. Corresponding C O V are 25% and 18%. Average tensile strength values of the finger joined C and B grade boards are 26.5 M P a ( C O V = 23%) and 33.7 M P a ( C O V = 20%), respectively. The finger joined boards had a gauge length of 1.22 m and only boards failed at the fingerjoints were used for the assessment. Marx and Evans (1988) reported the tensile strength of laminating grades of 38 m m x 140 m m Douglas-fir and southern pine lumber. The highest Douglas fir grade L I had an average tensile strength value of 34.3 M P a and the corresponding southern pine N o . I D grade had 34.5 M P a . The overall coefficient of variation and the mean modulus o f elasticity for these grades are 30% and 14,800 M P a , respectively. 2.5.1 L A M I N A T I N G E F F E C T S Falk and Col l ing (1994) investigated the laminating effects in the European and North American glulam beams. Influence of three key factors: 1) effect of test procedures, 2) reinforcement of defects, and 3) dispersion of low-strength lumber on the bending strength was discussed. Overall laminating factor ranges of 1.06 to 1.59 for European glulam and 0.95 to 2.51 for North American glulam were reported. 14 2.6 LAMINATING GRADES C A N / C S A -0122-M89 specifies four laminating grades B - F , B , C and D for the construction of glulam beams. B - F is the highest grade designated for the extreme tension zones of 20f and 24f beams. Here the 20f and 24f beams have allowable bending strength of 13.8 M P a and 16.5 M P a , respectively. For this grade, knots or other similar defects exceeding 10 mm and local slope of grain steeper than 1:16 shall not be permitted within 13 mm of the edge of the outer tension face lamination after finishing. D is the weakest grade, generally placed at the mid zone of the beam. The laminating boards of this grade are allowed to have knot sizes up to 50% of the board width. 2.7 KNOT SURVEY A S T M D 3737 provides guidelines to establish the knot frequency distribution in the laminating grades. This data w i l l be used to establish the beam lay-ups and the allowable properties for the structural glue laminated timber. A sample consisting of a minimum of 100 pieces or 300 m of lumber randomly chosen from a representative group is required to assess each of the grades considered. A set of nine types of knots and their measurement procedures are outlined in A S T M D 3737. A l l the knots greater than 6 mm of equivalent cylindrical cross-section need to be measured. Finally the statistical parameters of the knot data can be used to guide the building o f new glulam beams with new lay-ups. 15 Chapter 3 Development of New Lamina Grades 3.1 INTRODUCTION The initial guidelines for the new lamina grades were proposed by M r . Kent Fargey (Western Archrib - Structural Wood Systems). This consists of the specifications for a set of seven laminating grades T l , T2, Cc , B , C, Dc, and D . Here T l and T2 are tension lamina grades and Cc and Dc are compression lamina grades. Each o f these grades is intended to match different levels of stresses developed across the glulam beam. In beam applications under positive moment, generally, the lamina grades corresponding to the bottom layers w i l l be subjected to the maximum tensile stress, the top layers are expected to bear high compressive stresses, and the middle layers w i l l be subjected to a lower level of axial stresses. Douglas fir 38 mm x 140 mm laminae were used for all the grade assessment and verifications. Lamina samples were randomly selected from the mills and delivered to U B C as batches. The first four batches of material were used for the primary grade development process and verification. These batches consist of one hundred and eighty nine 2.44 m long boards and five hundred and nine 4.88 m long boards. The development process consists of a series of grading analysis and testing. Grading was conducted by the combination of E rating and visual grading as specified in the new guidelines. Initially the grade yield and the grade distribution across the samples were analyzed. Then the guidelines were modified to improve the grade yield. After confirming that sufficient grade outturn for the potential lamina grades, the samples were 16 tested in tension to assess the strength distribution. In October 2005, a results review was carried out by experts from the industry and U B C . This visit was focused on fine-tuning the guidelines to improve the grade properties. Subsequently an additional edge distortion restriction was proposed for the T l grade material to improve the lower tail o f the strength distribution. The finalized grade set was inspected and verified by M r . A l l an Rosek, Executive Director, National Lumber Grades Authorities ( N L G A ) . 3.2 DEVELOPMENT PROCEDURE Initially three batches o f material were graded according to the proposed specifications aiming to identify the resource distribution; therefore, some of the very minor grading criteria were not followed. The key grading factors considered for the resource assessment are given in Table 3.1 and the resource distribution obtained is given in Tables 3.2 and 3.3. 17 Table 3.1 Key grading factors considered for the resource assessment-Trial I (Assessment date: July 7, 2004, Material: 38 mm x 140 mm Douglas fir laminae) Parameter T1 T2 B C c C Dc D MOE ( m i n ) , GPa 13.1 13.1 13.1 13.1 11.0 11.0 -MOE ( a v e r a g e ) , GPa 15.4 15.4 15.4 15.4 12.0 12.0 -Knot size, mm 35 35 35 55 55 70 70 Edge knot, mm 23 35 - - - - -Slope of grain (all 4 sides) 1:16 1:16 1:16 1:12 1:12 1:08 1:08 Pith (maximum allowed)1 1/8 of cross section Clear wood, % 67 60 Spacing between strength reducing characteristics (SRC), mm 600 600 Knot spacing near finger joint2 20 20 Notes: 1. Pieces containing wide growth rings or lightweight pith associated wood at the end of the piece occupying over l / 8 t h o f the cross-section shall be excluded. 2. A n y knot over 10 mm in diameter shall not occur within 2 knot diameters (0) of any finger joint. 18 Table 3.2 MOE values of the first three batches of material MOE range, GPa Number of boards Total length, m Less than Greater than or equal to Batch 1 Batch 2 Batch 3 - 15.2 55 3 4 168 15.2 14.5 15 9 11 134 14.5 13.8 11 6 10 105 13.8 13.1 21 14 13 183 13.1 12.4 19 20 26 271 12.4 11.7 20 32 23 317 11.7 11.0 14 32 25 312 11.0 - 34 73 48 673 Total 189 189 160 2,163 19 Table 3.3 Grade outturn corresponding to Trial I MOE G range, Pa Number of boards E j£ Grade yield, m Less than Greater than or eaual to Grade Batch 1 Batch 2 Batch 3 Total lengl T1 T2 B Cc C Dc D 11.0 D 34 72 48 668 668 11.7 11.0 C 13 32 25 310 310 Dc 1 0 0 2 2 D 0 0 0 0 0 12.4 11.7 C 20 32 23 317 317 Dc 0 0 D 0 0 13.1 12.4 C 18 20 26 268 268 Dc 1 0 0 2 2 D 0 0 T1 8 0 4 39 39 T2 1 4 4 41 41 13.8 13.1 B 5 0 1 17 17 Cc 7 10 4 85 85 Dc 0 0 D 0 0 T1 7 2 1 32 32 T2 1 1 1 12 12 14.5 13.8 B 1 2 2 22 22 Cc 2 2 6 44 44 Dc 0 0 D 0 0 T1 10 7 4 78 78 T2 1 1 2 17 17 15.2 14.5 B 1 0 2 12 12 Cc 3 1 3 27 27 Dc 0 0 D 0 0 T1 39 1 3 115 115 T2 0 0 0 0 0 15.2 - B 8 0 0 20 20 Cc 6 2 1 29 29 Dc 0 0 D 1 0 0 2 2 R* 1 Total Length, m 189 189 160 2158 263 71 71 185 895 5 675 R* - rejected board which did not confirmed with the specifications. 20 The grade outturn from trial-I shows a fairly low yield for the T2, B and Dc grades. Wi th subsequent discussions between industry experts and U B C team, it was decided to drop Grade D c from the grade set. Based on this outcome, the initial grade proposal was modified to further mobilize the material resource across the grades considered. Mainly the M O E values of B grades and C c grades were lowered to 12.4 GPa in order to re-distribute some high quality boards from the C grade group to the B and Cc grade groups. Some o f the key grading factors of the modified guidelines are given in Table 3.4 and the corresponding grade outturn is given in Table 3.5. Table 3.4 Key grading factors considered for the resource assessment-Trial II (Assessment date: March 1 s t 2005, Mater ia l : 38 mm x 140 mm Douglas fir laminae) Parameter T1 T2 B C c C D MOE ( m i n ) , GPa 13.1 13.1 12.4 12.4 11.0 -MOE ( a v e r age), GPa 15.4 15.4 12.0 -Knot size 1, mm 35 35 35 55 55 70 Edge knot, mm 23 35 - - - -Slope of grain (all 4 sides) 1:16 1:16 1:16 1:12 1:12 1:08 Pith (maximum allowed)2 1/8 of cross section Clear wood, % 67 60 SRC spacing, mm 600 600 Knot spacing near finger joint 3 20 2<P 21 Notes: 1. For T l and T2 all knots within 200 mm length is summed. For al l other grades, including B , C and D , knots are summed according to the criteria set out in clauses 4.2.1.7 and 4.2.1.8 of the modified grading specifications as given below: Clause 4.2.1.7 Knots shall be measured between lines enclosing the knot and parallel to the edges of the wide faces. If two or more knots are in line, ie, partially or completely enclosed by the same parallel lines and separated lengthwise by less than 200 mm, the effective width of the knots shall be the distance between two parallel lines which enclose the knots. Clause 4.2.1.8 When two or more knots appear in the same cross section of a piece (Opposite each other on a face or edge), the sum of their sizes shall not exceed the maximum permitted knot size. 2. Pieces containing wide growth rings or lightweight pith associated wood at the end of the piece occupying over l / 8 t h o f the cross-section shall be excluded. 3. A n y knot over 10 mm in diameter shall not occur within 2 knot diameters (ct>) of any finger joint. 22 Table 3.5 Grade outturn corresponding to T r i a l II MOE G range, Pa a> Number of boards jth, m Grade yield, m Less than Greater than or equal Grac Batch 1 Batch 2 Batch 3 Batch 4 Total lenc T1 T2 B Cc C D R 11.0 -D 33 72 46 81 1051 1051 R 0 0 12.4 11.0 C 30 63 48 42 819 819 D 1 1 0 0 7 7 R 3 0 1 0 12 12 13.1 12.4 B 12 18 21 16 297 297 Cc 0 0 0 0 0 0 C 3 2 6 3 61 61 D 1 0 0 0 2 2 R 1 0 0 0 2 2 13.8 13.1 T1 10 7 6 6 117 117 T2 1 0 1 0 7 7 B 3 0 3 0 22 22 Cc 6 7 3 0 63 63 C 0 0 0 0 0 0 D 1 0 0 0 2 2 R 1 0 0 1 7 7 13.8 T1 52 16 10 10 302 302 T2 3 0 1 0 12 12 B 6 1 9 0 63 63 C 2 0 0 0 5 5 Cc 7 2 5 1 56 56 D 2 0 0 0 5 5 R 11 0 0 0 27 27 Total length, m 189 189 160 160 2943 419 20 383 119 885 1068 49 23 The laminae graded with the above guidelines were inspected and verified by M r . A l l an Rosek (Executive Director, N L G A ) Again the resource distribution was assessed and very low yield for grade T2 observed. A t this point tensile strength tests on the new grades were carried out to assess the strength characteristics of the new grades. It was observed that some of the weakest T l grade boards which failed with lower load (~ 25 MPa) were caused by a combination of edge knot and local slope of grain deviation. Therefore, following changes were further proposed to improve the strength values at the lower tail o f the distribution. 1. Clear wood (board with no edge distortion, no edge defect such as knot, knot hole, local slope of grain deviation etc.): Each lamina shall have at least 2/3 (67%) clear wood free o f strength reducing characteristics with a slope of grain no steeper than 1:16. 2. Clear Wood (boards with edge distortion) : A n y cross section (200 mm) which has any edge defect (knot, knot hole, local slope of grain deviation, etc. ) shall have at least 75% clear wood free of strength-reducing characteristics with a slope of grain no steeper than 1:16. The typical change in the strength distribution due to the changes in the grade specifications are illustrated in Figure 3.1. It is clear that changes to the grade have minimal impact on the overall tensile strength distribution eventhough some o f the lower strength pieces are eliminated by the new grading rules. 24 Figure 3.1 Tensile strength distribution of Tl grade (Batch 5) ro - O O 1.0 0.9 0.8 0.7 0.6 0.5 g> 0.4 ro E =5 o 0.3 0.2 0.1 0.0 TENSILE STRENGTH DISTRIBUTION (Batch 5, Grade T1, 38 x 140 mm Douglas fir lamina) ®® ® < Tensile Strengt > Tensile Strengt h Destribution According to Trial i Destribution According to Trial 1 i C II a ® / jg_ f f J 7 sr ? 10 20 30 40 50 Tensile Strength, MPa 60 70 During the subsequent re-grading and assessments following observations were made: 1. The bending T l grade has acceptable strength distribution. 2. The material resource has been fairly distributed between the grades T l , Cc, B, C andD. 3. The grade T2 has a very small (a total of 20 m length) yield. Based on these outcomes the grade T2 was dropped from the grade set. The finalized grade set consists of five potential grades : T l , Cc, B, C and D. The details of the final grade yield for these grades are given in Table 3.6. 25 Table 3.6 Grade outturn corresponding to T r i a l III Grade Number of boards Total Batch 1 Batch 2 Batch 3 Batch 4 Total length, m T1 62 23 16 16 117 419 B 25 19 35 16 95 403 Cc 13 9 8 1 31 119 C 35 65 54 45 199 885 D 38 73 46 81 238 1,068 Rejected (R) 16 0 1 1 18 49 Total 189 189 160 160 698 2,943 26 Chapter 4 Lamina Strength Assessment 4.1 INTRODUCTION The strength of laminae plays a major role in determining the load carrying capacity of glulam beams. Here the strengths of interest are the tensile strength and M O E of the laminae which are considered to be critical in common beam loading conditions. The magnitudes of these parameters are mainly controlled by the lamina grade specifications. Therefore, it is a necessity to determine these parameters each time when the grade specifications changes. The M O E of the boards can be determined using non-destructive test methods. Destructive tensile strength test is the only accurate means to measure the lamina tensile strength. Tensile strength tests were carried out in this study to determine the strengths of the laminae and the fingerjoints. A s mentioned in Chapter 2, strength of the laminating boards, strength of the fingerjoints and the distribution of the fingerjoints determine the overall strength of the laminae. The distribution of the finger joints is controlled by the length of the glulam beam and the length distribution of the laminae used for its construction. These factors have been taken in to account during the beam modeling process. Shear capacity is another important parameter considered in the glulam beam design. Here the main concern is the shear strength of the D grade material which is generally placed at the middle shear core of the beam. A S T M small clear block shear test and the short span beam bending tests are the two standard test methods available to 27 assess the shear strength of the core material. On the other hand, it is recognized that the capacity of a beam in shear is influenced by its stressed volume. Therefore, A S T M small clear shear block tests are considered to be not appropriate to determine generalized shear strength of the laminae (Foschi and Barrett 1976, Lam et al. 1997). Therefore, the use of a numerical model is needed to assess the shear capacity of the glulam beam. Verification/fine-tuning of the model can be performed using full scale shear beam testing. The details of these assessments are discussed in Chapters 5 and 6. Compressive strength of the laminae is another important factor in glulam beam design. However, this is not considered to be critical within the scope of the current study and is ignored in the modelling and analysis. A S T M D3737 specifies the glulam design procedures based on the knot distribution of the laminating boards to determine the allowable properties of the structural glued laminated timber. A s part of the study a detailed knot survey was carried out to assess the performance of the new lamina grades based on A S T M D3737. 4.2 MODULUS OF ELASTICITY The M O E of the boards was measured during the grade development process using the Metriguard Model 340 E-Computer system. Summary statistics of the M O E test results are given in Table 4.1. 28 Table 4.1 Summary statistics of the M O E test results Grade T1 C c B C D Mean, M P a 15,226 14,155 13,683 11,774 9,992 Standard deviat ion (SD), M P a 1,753 941 1,224 664 1,684 C O V , % 12 7 9 6 17 Total number of boards tested 184 44 223 201 138 4.3 TENSILE S T R E N G T H TESTS I - LAMINA Approximately 750 lamina specimens of the four tension laminating grades, T l , B , C and D were tested in tension parallel to grain. A Metriguard tension testing machine with full resistant grips and a capacity of about 450 k N was used for the testing. The tests were carried out at two gauge lengths 3.66 m and 1.22 m with a 0.61 m grip length at each end. For each grade the speed of loading was adjusted to maintain an average failure time of 10 minutes. The mean tensile strength values corresponding to the T l grade tested at 3.66 m and 1.22 m gauge length are 42.9 M P a and 52.6 M P a , respectively. Based on this values a length effect factor k of 5.4 was established for the material tested. The relationship between the strength values and the corresponding material volume (Lam 2000) used in the assessment of k factor is given in equation 4.1. 29 In the equation 4.1 x and V corresponds to the tensile strength and the volume of the material, respectively. The subscripts 1 and 2 refer to the samples corresponding to the two different volumes considered. Then all the lamina strength values were size adjusted to a 2.44 m gauge length in order to establish a unique set of reference strength data. This database was used as input for the U L A G analysis. The summary statistics of the lamina tensile strength test are given in Table 4.2 and the corresponding tensile strength distributions are given in Figure 4.1. Table 4.2 Summary statistics of the tensile strength test results at 2.44 m gauge length Grade T1 B C D Mean, M P a 49.8 34.8 29.4 24.0 S D , M P a 12.2 8.0 9.4 6.5 C O V , % 24 23 32 27 Total number of boards 184 223 201 138 30 Figure 4.1 Tensile strength distributions of the new lamina grades Variation of Tensile Strength (38 mm x 140 mm Douglas fir lamina, at 3.66 m gauge length) 0 10 20 30 40 50 60 70 Tensile Strength, MPa Images of some o f the T l grade material failed at low strength level is given in Figure 4.2 31 Figure 4.2 Images of some of the T l grade material failed at low strength level 3 2 4.4 TENSILE S T R E N G T H TESTS II - FINGER JOINT Approximately four hundred finger joined lamina specimens of the four grades, T l , B , C and D were tested in tension to determine the finger joint strength. Here the gauge length and the grip lengths were kept at 0.66 m and 1.22 m, respectively. Again the speed of loading was kept to achieve a time to failure of approximately 10 minutes. A s expected, both lamina and finger joint failures were observed during the tests. This resulted in two set of strength data: one corresponding to the finger joint failure cases and the other corresponding to the lamina failure cases where the finger joint strength is higher than that of the failure load of the specimen. This issue of mixed failure modes was sorted out using the Maximum Likelihood Evaluation ( M L E ) theory to isolate the strength of fingerjoints from a censored database. A computer program based on this theory was developed to carry out the assessments. 4.4.1 M L E A S S E S S M E N T S A s mentioned earlier the M L E assessments were performed to establish the un censored data for the finger joint strength. This procedure w i l l be later used for the assessment o f glulam beam shear capacity as well . The theoretical formulation of this program is discussed below: Consider two continuous random variables x, s and the corresponding statistical parameters 0. X j - primary data Sj - suspended data 0i - statistical parameters. 33 Then the likelihood functions L i and L 2 corresponding to the primary and suspended data can be written as, L\ (primary) = J J / ( * , 10,) L2 (suspended) = ]J [(1 - F(s, 10,)] (4.2) (4.3) where f(x/ 0) and F(s/0) are probability density function and cumulative distribution function, respectively. N o w for the likelihood of obtaining primary and secondary data, the total likelihood function can be written as, Z = Z , Z 2 For a 2p-Weibull distribution, the probability density functionf(x/ 0) and cumulative distribution function F(s/0) can be written as fallows. f(x,/0) = -m kfx >* F(sl/0) = l-e Then the logarithmic likelihood function can be written as, (4.4) (4.5) l n ( l ) = 5> 1=1 k-\ N ( Y \ Xj_ Xj_ Kmy (=1 V 7 W , (4.6) The maximum likelihood estimators of 0j were obtained by maximizing ln(L). The parameters m and k corresponding to the maximum value of equation 4.6 have been obtained by a trial and er ror-MLE program written in F O R T R A N . 34 4.4.2 F I N G E R J O I N T T E S T R E S U L T S The summary statistics of the finger joint test results are given in Tables 4.3 and 4.4. The distribution of the finger joint strength with a comparison of test specimen's strength is given in Figures 4.3 to 4.6. Table 4.3 Details of the finger joint failures Grade T1 B C D Total number of specimen tested 126 100 104 100 Number of finger joint failures 110 67 46 31 Table 4.4 Details of the finger joint strength values predicted by M L E program Grade T1 B C D 2P Weibull strength parameters m, MPa 45.1 43.8 35.5 30.7 k 5.4 5.6 6.1 5.3 Mean, MPa 41.59 40.48 32.96 28.28 COV, % 21 21 19 22 35 F i g u r e 4.3 T e n s i l e s t reng th d i s t r i b u t i o n o f the T l g r a d e 38 m m x 140 m m D o u g l a s f i r f i nge r jo in ts 1.0 • 0.8 1 0.6 o cu I 0.4 E 5 0.2 0.0 15 25 ° T1 grade- FJ and lamina (gauge length 0.66 m) tested * T1 grade - FJ failure cases (gauge length 0.66 m) tested A T1 grade - FJ strength predicted (MLE) 35 45 55 Tensile Strength, MPa 6 5 F i g u r e 4.4 T e n s i l e s t reng th d i s t r i b u t i o n o f the B g r a d e 38 m m x 140 m m D o u g l a s f i r f i nge r j o in t s 1.0 0.8 -Q O a> > IS 0.4 E 0.2 0.0 I '~: r ; | If & i w — -n t ,6 — I i jn i f • / J / -4— • B-FJ&Lamina (Gauae Lfinoth n Rfi / Tested A B -FJ predicted (MLE) J T *AT^ A —53 / A 1 A = 1 1 1 I 1 1 1 | i 1 T 15 25 35 45 Tensile Strength, MPa 55 65 36 Figure 4.5 Tensile strength distribution of the C grade 38 mm x 140 mm Douglas fir finger joints Figure 4.6 Tensile strength distribution of the D grade 38 mm x 140 mm Douglas fir finger joints E 0.0 4 ......... p.. ...... ft J -- J f £ _ *— IT r f ... : IT - p i — • u-f-J&Lamma(Gauge Length 0.66 m) Tested — a D-FJ predicted (MLE) / — ? I -z IF — <** • 4* _ ill 111 15 25 35 45 55 65 Tensile Strength, MPa 37 A s expected, in T l grade's case, the lamina strength is much higher than that of the finger joint's. In B grade's case, both strength values come closer and in C grade's and D grade's cases, the finger joint's strength is higher than that of the lamina. Some of the typical finger joint failure images observed during the laboratory testing is shown in Figure 4.7. 38 Figure 4.7 Some of the typical finger joint and lamina failures 4.5 MOISTURE CONTENT Prior to the tensile strength test, all the boards were subjected to moisture content assessment to confirm the acceptable moisture content level of less than 15%. Moisture measurements were taken at three random locations using a moisture meter. A t this stage weight and the dimensions of the specimens were measured to determine the specific gravity of the specimens kept at room temperature. The specific gravity values corresponding to the lamina grades are given in Table 4.5. Table 4.5 Specific gravity of the new Douglas fir lamina grades measured at test moisture content Lamina grade T1 Cc B C D Mean 0.58 0.56 0.55 0.52 0.50 SD 0.05 0.04 0.04 0.04 0.03 4.6 KNOT SURVEY The knots present in a wood member are one of the key factors that influence the strength of the member. The size of the knot is measured in terms of the diameter of an equivalent cylinder placed at that section. The size of a knot varies from a tiny pin hole to a size occupying up to 70-80% of the cross-section of the wood. Generally the knots are in conical shape originating from the pith of the wood. 40 As discussed earlier ASTM D 3737 provides guidelines for knot measurement and the use of knot data to determine the allowable properties of the glue laminated timber beams. Glulam beam analysis using the GAP program and the knot data were carried out by Dr. Borjen Yeh (APA). In general the GAP program results indicated a satisfactory performance of the proposed grades. 4.6.1 KNOT SURVEY: PROCEDURE ASTM D3737 requires physical measurements (mapping) of all the knots in individual pieces of lumber. A set of nine types of knots and their measurement procedures are outlined in this standard. Based on the standards, all knots greater than 6 mm of equivalent cylindrical cross-section were measured. A sample consisting of a minimum of 100 pieces or 300 m of lumber randomly chosen from a representative group was considered for the assessment of each grade. The details of the lamina samples used for the knot survey assessments are given in Table 4.6. Table 4.6 Details of the lamina samples used for the knot survey Lamina grade T1 B Cc C D Total Total length of lamina, m 419 383 119 885 1,068 2,875 The types of the knots were determined based on the location and the shape of the knot. The measurements of the Types 7 and 8 knots were associated with the location of the pith center (Figure 4.8). Most of the cases, it was inside the lamina and its location 41 was determined based on the locations /exposures of the pith outcrops. Therefore, generally the values corresponding to the parameters PI and P2 were estimated based on judgments. Figure 4.8 Illustration of the pith center of a knot in a cross section of a lamina A s the standard requires, the scope of the knot survey was to measure all the knots greater than 6 mm. The dimensions of Types 1 and 2 knots were measured quickly; whereas Types 3 and 6 knots took little bit more time to determine some of the dimensions. Therefore, in order to ensure that all the knots greater than 6 mm were measured and expedite the knot survey process, most of the knots having an exposure larger than 6 mm across the lamina were measured with reasonable judgment. 4.6.2 KNOT SIZE CALCULATION The knot size corresponds to the diameter of the cylindrical section equivalent to the area displaced by the knot. Each of the considered nine basic knot types needs different sets of formulation to calculate their knot sizes. Furthermore within a knot type group, this formulation was slightly different based on the knot's orientation with the reference side of the board. Calculating large number of knot-sizes using simple Knot outcrop Section of the volume 'displaced by the knot Pith center of the board 42 manual/measures was practically impossible. Therefore a spread sheet program was developed to track the knot orientation from the knot data and automatically calculate the knot sizes. 4.6.3 R E S U L T S Table 4.7 shows the typical distribution of the knot sizes with the lamina grades T l , B , Cc , C and D and Figures 4.9 and 4.10 show the corresponding knot size distributions. The values given in Table 4.8 were normalized corresponding to a lamina length o f 300 m per grade for comparison purposes. Table 4.7 Knot survey summary, details of the knot distribution corresponding to knot size Number of knots Lamina grades T l B Cc C D Knot size, K*, cm K < 6 292 267 456 603 0.6 < K < 1.5 569 826 152 1788 2720 1.5<K<2.5 100 223 81 692 995 2.5<K<3.5 13 37 13 103 153 3.5 <K 12 31 42 Maximum knot recorded, cm 7.4 *The knot sizes correspond to a single knot and the knot size values were calculated using a spreadsheet program. 43 Figure 4.9 K n o t size distributions Figure 4.10 K n o t size distributions at the upper tail Variation of Knot Sizes 38 mm by 140 mm Douglas fir lamina Knot Size, cm Table 4.8 Knot survey results: Values corresponding to 300 m length of laminae Lamina grade Number of knots T l B Cc C D Knot size, K, cm 0.6 < K < 1.5 407 647 382 606 764 1.5 < K < 2.5 72 175 203 235 279 2.5<K<3.5 9 29 33 35 43 3.5 <K 0 0 30 11 12 Total 488 851 648 886 1098 45 Chapter 5 G l u l a m B e a m M o d e l i n g a n d C a l i b r a t i o n 5.1 INTRODUTION The beam modeling process deals with two main aspects: fine tuning and validating the U L A G program for glulam strength assessments to confirm code requirements and to assess the performance o f the new lamina grades. First U L A G program itself needs some modifications to make it compatible with the current windows X P versions. Subsequently some additional routines and procedures were introduced into the program to incorporate the shear strength assessments and to account for the laminating factors during the beam simulations as well . Initially a series o f trial U L A G simulations were carried out to study the beam strength characteristics corresponding to different beam lay-ups. This information was used to assess the performance of the new lamina grades and to select the trial laminating factors which were used in subsequent U L A G simulations. Parallel to the U L A G analysis, a set of G A P analysis was carried out by Dr. Borjen Y e h ( A P A ) to confirm the model requirements according to A S T M . Based on these findings beam dimensions and lay-ups for the calibration tests were determined. Three beam cases, one for bending and two for shear were chosen for the calibration tests. The beams were manufactured in a glulam plant and the testing was carried out at U B C . 46 5.2 ULAG UPGRADING The U L A G was originally composed using Lahey F O R T R A N , one of the F O R T R A N compilers commonly used during mid 1980's. The program needs a re-compiling using one of the latest versions of the F O R T R A N compiler in order to make it compatible with the current Windows X P platforms. The re-compiling was carried out using the Digital Visual Fortran software. During the re-compiling process some of the old commands were replaced with the equivalent ones compatible with the Digital Visual Fortran (1988). 5.3 ULAG ANALYSIS The basic input material for the U L A G analysis were the tensile strength and the M O E test databases of the lamina and finger joints and the length distribution of the lamina. Here the tensile strength and the M O E are provided as a companion data set, based on which the program determines M O E for the boards and the corresponding tensile strength during the beam simulation. The finger joint strength database was developed based on the M L E assessment. The M L E finger joint strength did not have a corresponding M O E values; therefore, a series of M O E values were randomly selected from the lamina-MOE database and used as companion data. A very low correlation is expected between the finger joint strength and M O E data sets. Other material parameters of interest are the proof load levels of the lamina and finger joints, the minimum permissible M O E values to the beam lay-ups and the laminating factors. The minimum tensile strength values of the lamina and finger joints obtained from the laboratory tests were used as the proof load for each of the lamina 47 grades considered. The minimum M O E specifications for the T l , Cc , B , and C lamina grades were used as the minimum permissible M O E values in the beam lay-ups. There were no minimum values used for the D grade lamina as there was no minimum value specified for this grade. Furthermore, this is the first time laminating factors were incorporated in the U L A G assessments. A set of four laminating factors for the lamina grades T l , B , C and D were determined based on a trial and error assessment. Then the data was used in all the subsequent U L A G analysis to account for the laminating effects. During the U L A G assessments, the finite element glulam beam models were simulated with 0.05 m segments along the beam length. The models were subjected to a virtual progressive loading until collapse yielding the corresponding failure load, M O E and the failure details. For each of the beam case investigated, the beam strength statistics were determined based on a set of one thousand beam-simulation and loading data. The key U L A G assessments were carried out at three stages. Preliminary U L A G simulations were carried out after the tensile strength assessments of laminae and finger joints. The re-complied U L A G program (compatible with the Windows X P platforms) was used for this assessment. This analysis was focused on assessing the performance of the proposed lamina grades and to estimate the corresponding laminating factors. The second stage of analysis focused on determining the beam-lay-ups for the calibration tests. The upgraded U L A G program with the shear strength assessment features and the updated strength database with an additional thirty finger joint test results was used for this assessment. The third step of U L A G analysis concerned with the beam lay-ups and configurations for the glulam verification tests. The finalized U L A G program was used for this assessment. 48 5.3.1 PERFORMANCE OF THE LAMINA GRADES Initially a series o f trial U L A G assessments were carried out with different beam lay-up arrangements to investigate the performance of the proposed lamina grades. The on hand tensile strength and the M O E values of the lamina grades were used for these assessments. This is a preliminary analysis, intended on identifying the border-line issues, therefore, it didn't include the laminating effects o f the glulam lay-up. Details o f the beam lay-ups used for this assessment are given in Table 5.1. The results of the corresponding U L A G simulations carried out with 21 span to depth ratio are given in Table 5.2. Table 5.1 Details of the beam lay-ups used for the initial ULAG simulations Lamina number (from the bottom of the beam) Lay-up-ID A1 A1u A8 A8u A6 A6u A9 A9u A7 A7u 12 T1 Cc 11 B B 10 T1 Cc Cc Cc C C 9 B B C C D D 8 T1 Cc T1 Cc D D D D D D 7 B B C C D D D D D D 6 D D D D D D D D D D 5 D D D D D D D D D D 4 D D D D D D D D D D 3 D D D D D D D D C C 2 B B C C B B C C B B 1 T1 T1 T1 T1 T1 T1 T1 T1 T1 T1 49 Table 5.2 Summary of the preliminary ULAG simulation (bending, 3rd point loading) Balanced Unbalanced Beam lay-up, ID A1 A8 A6 A9 A7 A1u A8u A6u A9U A7u Beam depth, h, cm 30 30 37.5 37.5 45 30 30 37.5 37.5 45 Beam length, m 6.71 6.71 8.31 8.31 9.91 6.71 6.71 8.31 8.31 9.91 Beam test span, m 6.30 6.30 7.88 7.88 9.45 6.30 6.30 7.88 7.88 9.45 Ultimate failure load, kN Mean 92 87 106 105 119 90 86 105 101 117 SD 12 11 13 11 14 12 11 13 12 13 MOR, MPa Mean 51 48 47 46 44 50 47 46 45 43 SD 7 6 6 5 5 6 6 6 5 5 COV, % 13 13 12 10 12 13 13 12 12 11 Specified strength, Rs, MPa 35 34 35 36 34 35 33 34 33 34 The specified strength values of these trials are above the target value (30.6 MPa) for the 24f glulam beams. This indicates a satisfactory performance of the proposed lamina grades. The reliability based normalization procedures adopted for the specified strength assessments is discussed in section 5.8. 5.3.2 TENSION LAMINATING FACTORS A s discussed in Chapter 2, laminating factors play a positive role in modifying the strength of the glulam beam. However, so far laminating factors were not considered in the U L A G model. 50 During the current analysis, it was realized that the relative support from adjacent laminae tends to reduce when the level of strain increases across the beam. Considering this as a basis, a series of U L A G simulations were carried out with different combination of laminating factors ranging from 1.0 to 2.0. Based on this, a trial set of laminating factors were proposed for the new lamina grades (Table 5.3). These factors were used in subsequent U L A G analysis to determine the beam configuration and loading setup for the calibration tests. Table 5 . 3 T r i a l sets of laminating grades proposed for the new lamina grades Material grade Laminating factor T1 1.1 B 1.2 C 1.3 D 1.4 5 . 3 . 3 B E N D I N G S I M U L A T I O N S A s mentioned earlier the second stage of the U L A G analysis focused on determining the beam-lay-ups for the U L A G calibration tests. A series of glulam trial bending and shear simulations were carried out to identify the beam lay-up satisfying a 24f 1.8 E grade. Beam lay-up and dimensions of the finalized beam selected for the bending tests are given in Table 5.4 and the strength parameters predicted prior to the calibration tests are given in Table 5.5. 51 Table 5.4 Beam lay-ups selected for U L A G calibration (beam ID A 8 U ) Lamina number (from the bottom of the beam) 1 2 3 4 5 6 7 8 Lamina grades T1 C D D D D C Cc Table 5.5 U L A G strength predictions for the trial beams Lay-up ID A 8 U Beam depth, m 0.30 Test span,m 6.40 Ultimate failure load Mean, kN 88.9 COV, % 14 MOR Mean, MPa 49.0 Specified strength, MPa 34.5 5.4 U L A G CALIBRATION TESTS - F L E X U R E A set of twenty-four 0.30 m deep glulam beams manufactured according to the beam lay-up proposed based on the U L A G simulations (Tables 5.4 and 5.5) were used for the bending calibration tests. The tests were carried out with a third point loading (Figures 5.1 and 5.2, Table 5.6). The test apparatus consists of two end supports, two loading heads attached to a load evener and a machine head. The advancement of the machine head and the corresponding load is monitored and controlled by a computerized data acquisition system. The beams were tested with 21 span to depth ratio. The loading rate was kept at 52 10 mm/ min to maintain an average failure time of 10 minutes. A l l the beam tests were videotaped. Figure 5.1 Typical third point loading configuration used for the bending test Table 5.6 Details of the bending test configuration Beam set ID E Beam depth 0.30 m (1 ft) Beam width 0.130 m (5 %in.) Span to depth ratio 21 Test span 6.40 m (21 ft) Beam length 6.71 m (22 ft) Loading rate 10 mm /min 53 Figure 5.2 Test setup for the 0.30 m deep beam The summary of the bending test results is given in Table 5.7 and a comparison between the U L A G predicted strength distribution and the laboratory test results are given in Figure 5.3. Table 5.7 Summary of the bending test results Beam depth, m 0.30 M O R Mean, M P a 48.3 C O V , % 11 Speci f ied strength, M P a 34.5 54 Figure 5.3 Comparison between the U L A G predicted strength distribution and the laboratory test results for 0.30 m deep glulam beams Glulam Bending- 0.3 m deep beams 50 70 90 110 130 Failure Load, kN The details of key failures observed during the glulam bending tests are given in Table 5.8. Table 5.8 Key failures observed in 0. 30 m deep beams Failure type Number of breakdowns finger joint 8 finger joint and knot 5 finger joint and lamina 4 lamina 6 slope of grain (SOG) and knot 1 A n image of one of the bending failures case is shown in Figure 5.4. 55 Figure 5.4 Bending failure of a 0.30 m deep glulam beam 5.4.1 MOE VALUES M O E values for all the bending beams were evaluated from load-deformation curves obtained prior to the ultimate loading. A specially designed cable yoke system as shown in Figure 5.5 was used to obtain the required load-deflection data with a loading level of 25% of the U L A G predicted mean failure load. This cable system consists of a cable (Ai r craft cable, 1.58 mm diameter and maximum working load capacity o f 43 kg), pair of pulleys, a weight (4.5 kg) and a displacement-gauge connected to the data acquisition system. The pulleys were fixed on the vertical face of the beam, at the intersection of the simple support reaction line and the horizontal axis of the beam. Then the cable was fitted over the pulleys to form a loop. The constant weight was applied at the center of the lower portion of the cable to keep the upper portion of the cable taut. The slope of the lower portion of the cable was kept around 10 degrees and a load in the range between 200 N to 250 N was expected on the cable. The vertical relative displacement between the upper portion of the cable and the horizontal axis of the beam 56 was measured at the middle of the beam during loading. This value corresponds to the relative displacement of the beam at the given load level. Figure 5.5 Cable - yoke system used to measure the relative displacement at the middle of the beam Center Pulley loading Cable i ~ ® + - # - f -I Support I „ Ci reaction Constant weight The summary of the M O E value for the 0.30 m deep bending beam is given in Table 5.9. Table 5.9 Summary of the M O E values of the 0.30 m deep bending beams Parameter M O E values Mean, M P a 13,326 C O V , % 4 5 7 5.4.2 ULAG CALIBRATION (BENDING) A comparison of the specified strength and mean modulus of elasticity values based on the bending test results and the U L A G predictions made prior to the calibration tests are given in Tables 5.10 and 5.11, respectively. Table 5.10 Comparison between bending test results and ULAG prediction - specified strength Beam case Glulam specified strength Based on laboratory test results (MPa) Based on ULAG simulations (MPa) Error % 0.31 m deep beam at 21 span/depth ratio 34.5 34.5 -0.2 Table 5.11 Comparison between bending test results and ULAG prediction - MOE MOEmean Beam case Based on laboratory test results (MPa) Based on ULAG simulations (MPa) Error % 0.30 m deep beams at 21 span/depth ratio 13,326 12,484 -6.3 A very small -0.2 % error was observed for the glulam specified strength prediction. The corresponding error for the mean M O E prediction is -6.3%. These errors are within the acceptable limit. Therefore, at this stage no further modifications or fine tuning is required in either the U L A G model or the proposed laminating factor set. 58 5.5 ULAG SHEAR A s part of the U L A G upgrading process new routines were introduced in the U L A G model to incorporate additional features needed to investigate shear failures. A finite element model volume integrating scheme of Foschi & Barrett (1976) and Lam et al. (1997) was used for this assessment. This model basically predicts the failure load of a full scale beam that has a common probability of failure as a clear wood block shear specimen. 5.5.1 N U M E R I C A L M O D E L I N G The following section summarizes the numerical formulation o f the shear stress assessment procedures. The displacement field of the beam-column element is given by : U = N d (5.1) where u = [ u, cp, w ] 1 , d = [ u i , cp i , W i , Gi, U2, <p2, 62]' and N = shape function array. u and w denote, respectively the axial and transverse displacements of the beam-column axis, cp is the rotation of a transverse normal about this axis, and 6j is the variation of Wj with respect to the principal bending axial coordinate x for i = 1,2. For a given beam lay-up, the nodal displacements d; (i = 1, 2 , number of nodes) can be determined using the existing U L A G program and therefore, the displacement field U can be evaluated. N o w the transverse shear strain y (y « 1) can be given by the following equation : 59 r dw dx 1 - 4 h (5.2) where, z is the thickness coordinate and h is the height of the beam. Then the shear stress developed for a given load level can be determined based on the following equation: T = G y (5.3) The values of the shear modulus G is generally given as a ratio of M O E ( E / G ratio). The typical E / G ratio of 20 is used in the current analysis. N o w , based the weakest link theory (Foschi and Barrett, 1976) the mean shear failure load P can be written as : r = yk (5-4) where, x*o.5 - mean shear strength of a unit volume 1.64E-05 m ( 1 in. ) / - shear stress field integrated over the volume under the applied load P k - Weibul l shape parameter. r*o.5 can be determined based on the following relationship (Foschi and Barrett 1976): T * 0 J = PtlASTM (5.5) where, P, = 1.333+0.336(k-4) if4<k<8 p, = 2.678+0.251(k-8) if8<k<10 TASTMIS the A S T M block shear strength at the probability of interest. 60 5.5.2 SHEAR SIMULATIONS The main aims of the shear analysis are to determine a beam configuration which w i l l be more vulnerable to shear failure and to identify the ultimate loading level. In general the chances of getting pure shear failure can be increased by reducing the beam test span under a simple three point loading. However, there are many practical issues to account for when designing the beams for shear test. A t very short span, the ultimate failure load levels are expected to be very high. High load level may cause crushing or excessive deformation near the loading head and supports. Also it requires a higher-capacity testing facility to safely handle these extraordinary loads. Therefore, the target is to produce a significant number of shear failures with a moderate load level and determine the overall shear strength parameters using the maximum likelihood method ( M L E ) . The clear wood-shear strength parameters (Table 5.12) reported by L a m et al. (1997) was used as basis for the clear wood strength corresponding to the D grade Douglas fir material. The beam-lay-up given in Table 5.13 was used for this assessment. Table 5.12 Clear wood Douglas fir shear strength (Lam et al. 1997) of a standard block shear Parameter TASTM Mean, M P a 8.98 C O V , % 16 61 Table 5.13 Shear calibration beam lay-up (Al) Lamina number (from the bottom of the beam) 8 7 6 5 4 3 2 1 Lamina grades T1 B D D D D B T1 Initial simulations were carried out using the clear wood strength parameters given in Table 5.12. The results of these shear assessments are given in Table 5.14. Table 5.14 Results of the initial shear simulations Beam depth, m Span to depth ratio Predicted shear capacity, kN Predicted shear strength, MPa 0.30 7 345 6.21 0.30 6 433 7.79 The D grade material used in the glulam shear zone (middle core of the beam) is the weakest grade, expected to be having inferior strength parameters. Therefore, the clear wood strength corresponding to the Douglas fir D grades should be weaker than that o f given in Table 5.12. In this way the predicted strength values given in Table 5.14 can be considered as an upper bound for the shear capacity of the glulam beams considered. 5.6 SHEAR TESTS Two sets o f 0.30 m deep glulam beams were tested with two different span to depth ratios 7 and 6 for the shear calibration. Each of these sets consists of 24 beams. The details o f the test configuration used for the shear tests are given in Table 5.15 and the schematic diagram of the typical shear testing arrangement used is shown in 62 Figure 5.6. This four point loading setup is basically a modified version of the simple three point loading setup used to generate high shear stress at the middle core of the beam. In order to avoid the excessive load concentration at the loading point the center point load was split and applied symmetrically at two locations close to the center. Table 5.15 Shear test configuration Beam depth 0.30 m (1 ft) 0.30 m (1 ft) Beam width 0.129 m (5 %in.) Span to depth ratio 7 6 Test span, / 2.13 m (7') 1.83 m (6') Beam length 2.44 m (8') 2.13 m (7') Loading type Four point loading Figure 5.6 Configuration of the typical shear testing arrangement 0.30 m / - test span b = 0.46 m, the spacing between the pair of loading heads at the center P- total load on the beam 63 The summary of the shear test results is given in Table 5.16. This data was processed using the M L E technique in order to determine the uncensored statistical parameters. The M L E predicted 2p-Weibull data and the equivalent normal distribution values are given in Table 5.17 and the corresponding shear strength values are given in Table 5.18. Table 5.16 Summary of the shear test results Shear testing case Failure load Number of shear failures Total number of beams tested Mean (kN) COV (%) 0.30 m deep beams tested at 6 span to depth ratio 311 9 20 24 0.30 m deep beams tested at 7 span to depth ratio 263 10 17 24 Table 5.17 Details of the M L E simulated shear capacity (based on laboratory test results) Shear testing case Scale, m (kN) Shape, k Mean, (kN) COV (%) 0.30 m deep beams tested at 6 span to depth ratio 330 9 313 13 0.30 m deep beams tested at 7 span to depth ratio 284 16 275 8 Table 5.18 Shear strength parameters based on the experimental data Shear testing case Mean, (MPa) COV, (%) 0.30 m deep beams tested at 6 span to depth ratio 6.0 13 0.30 m deep beams tested at 7 span to depth ratio 5.3 8 64 5.6.1 M O E V A L U E S For the case of the shear beams, shear deformation is expected to be significant; therefore, M O E values were not measured during the laboratory assessments. 5.6.2 S H E A R F A I L U R E C H A R A C T E R I S T I C S The shear failures of the beams were recognized by a horizontal tearing with an outward jerking of the top portion at one of the end of the beam. Generally the splitting extends up to the mid section. Figure 5.7 shows the end section of a failed shear beam. Here the failure paths can be easily tracked by the breaks in the vertical lines drawn onto the beam surface prior to loading. Figure 5.7 E n d section of a failed shear beam (This beam was 0.30 m deep and tested at 2.13 m test span) 5.6.3 S H E A R C A L I B R A T I O N After the shear beam testing the clear wood strength parameters used in the shear-stress volume model were fine-tuned based on the test results. This was done by a series 65 of trial and error assessments using different sets of the clear wood strength parameters which are close to the values given in Table 5.12. The selected clear wood strength set which produce the minimum errors between the tested and predicted average shear loads is given in Table 5.19. This is the predicted clear wood strength values for the Douglas fir D grade material. Table 5.19 Predicted clear wood shear strength values corresponding to Douglas fir D grade laminae. Parameter TASTM Mean, MPa 9.0 COV, % 18.0 The results of this analysis with a comparison of the shear test results are given in Table 5.20. Table 5.20 Predicted shear capacity of the glulam beams Beam depth, m Span to depth ratio Simulated shear capacity, kN Simulated shear strength, MPa Tested shear strength, MPa Error, % 0.30 7 266 5.1 5.3 -3.4 0.30 6 330 6.3 6.0 5.4 5.7 GAP ASSESSMENTS A s mentioned earlier the gap assessments on the new lamina grades were carried out by Dr. Borjen Y e h ( A P A ) . The assessments were carried out based on the knot 66 distribution of the new lamina grades (section 4.6). The laminae lay-ups used for the assessments are given in Table 5.21. The program predicts the allowable strength capacities equivalent to a standard glulam beam of o.3 m (1 ft.) with 6.4 m (21 ft.) loading span. Corresponding specified strength values and some details of the adjustment carried out to derive that are given in Table 5.22. Table 5.21 Glulam lay-ups used for the GAP assessments Lamina number (from the bottom of the beam) Beam lay-up cases #1(8) #4(8) U1(10) U2(10) U1(20) U2(20) #4(20) 20 Cc Cc Cc 19 Cc Cc Cc 18 Cc C Cc 17 C C C 16 C C C 15 D D D 14 D D D 13 D D D 12 D D D 11 D D D 10 Cc Cc D D D 9 Cc C D D D 8 Cc Cc C C D D D 7 C C D D D D D 6 D D D D D D D 5 D D D D C C C 4 D D D D C C C 3 D D C C B C B 2 B C B C T1 T1 B 1 T1 T1 T1 T1 T1 T1 T1 67 Table 5.22 Details of the specified strength values corresponding to the GAP predicted allowable strengths Parameters Beam lay-up cases #1(8) #4(8) U1(10) U2(10) U1(20) U2(20) #4(20) Depth, m 0.30 0.30 0.38 0.38 0.76 0.76 0.76 Width, m 0.13 0.13 0.13 0.13 0.13 0.13 0.13 No. of laminations 8 8 10 10 20 20 20 Allowable strength predicted by GAP, MPa 18 17 18 17 18 18 18 MOR( 5%)(Standard beam, ASTM)> MPa 37 36 37 35 39 38 37 COV(MOR), (assumed same as the corresponding ULAG simulated COV values) 0.17 0.17 0.16 0.16 0.13 0.13 0.14 B (reliability based normalization procedure) 1.15 1.13 1.16 1.17 1.20 1.20 1.20 C f (tolerance limit), n=50 0.94 0.93 0.94 0.94 0.95 0.95 0.95 Duration of load 0.87 0.87 0.87 0.87 0.87 0.87 0.87 ( S | z e adjustment to 0.130 x 0.61 x 9.1 cu. meter) 1.06 1.06 1.06 1.06 1.06 1.06 1.06 Specified strength, GAP ( 0.13 x o.ei x 9.1 cu. meter). MPa 32.8 31.2 33.3 31.8 36.0 35.1 34.5 Parallel to these G A P analyses a set of U L A G simulations were carried out to assess the performance of the same lay-ups at a span to depth ratio of 15. The U L A G and G A P predicted specified strength values adjusted to the standard beam size of 0.13 x 0.61 x 9.1 cu. meter are compared in Table 5.23. 68 Table 5.23 Comparison between the U L A G and G A P predicted specified strength values Parameter Beam lay-up cases #1(8) #4(8) U1(10) U2(10) U1(20) U2(20) #4(20) Specified strength, GAP, MPa 32.8 31.2 33.3 31.8 36.0 35.1 34.5 Specified strength, ULAG, MPa 30.1 28.3 32.8 32.6 35.3 35.2 32.8 Ratio of specified strength(ULAG) to specified strength(GAP) 0.92 0.91 0.98 1.03 0.98 1.00 0.95 The G A P predicted specified strength values are above 30.6 M P a . This indicates a satisfactory performance for all the lay-ups considered. The U L A G simulated specified strength values for the 0.3 m deep beam cases #1(8) and #4(8) are below 30.6 M P a . However, #4(8) lay-up simulated at 21 span to depth ratio predicts 34.5 M P a specified strength (Table 5.5 lay-ups A 8 U and #4(8) are the same). With subsequent investigations it was observed that the U L A G simulated specified strength values tend to decrease with the reduction of the loading span of the beam. Further investigation on this issue to verify these results is recommended. 5.8 DETERMINATION OF SPECIFIED STRENGTH The Canadian standard specifies the bending, compression and horizontal shear capacities of the glulam beam in terms of the specified strength. This is a modified version of the characteristic strength (5% strength) after the accounting for the reliability factors, duration of load, data confidence and beam size. The details of the assessment of correction factors and the specified strength are discussed below. 69 The nominal strength R n can be written as Rn = BR, 0.05 Roos is the non parametric fifth percentile short term strength. B is the reliability normalization factor. B = 1.58 - 2.1 SV and V is the coefficient of variation. Data confidence factor C / i s given by, Cf = 1 -2.1V and n is the sample size. 4~n~ A = 0.87 duration of load factor (Clause 4.3.2 C S A 086-01). Size factor K z is given by Kz = 1.03(Z?Z)"°18 where b width of the widest building block used in the beam and L is the beam span. This size adjustment is used to correct the strength o f the beam considered based on the strength o f a standard beam o f 0.13 x 0.61 x 9.1 cu. meter. Based on these correction factors the specified strength (Rs) can be written as given below. ACfRn (5.6) 70 Chapter 6 G l u l a m M o d e l V e r i f i c a t i o n 6.1 INTRODUCTION Model verification tests have two main aims, verifying the U L A G prediction and qualifying the proposed lamina-lay-up for the target glulam beam grade. Two sets o f glulam beams with depths 0.61 m and 0.45 m were used for the bending and shear verification tests, respectively. Here again the beam depths were chosen based on the U L A G simulations. One o f the concerns in selecting the beam depth was to verify the model predictions at significantly different load-levels than that o f the calibration test loads. For each case, similar to the calibration tests, twenty four glulam beams manufactured in a glulam plant were used for the assessments and all the testing were carried out at U B C . In both cases the basic loading configuration was kept similar to that o f the calibration tests, the bending tests were carried out with third point loading and the shear tests were carried out with a four point loading. The span to depth ratios corresponding to the bending and shear tests were kept at 18 and 6, respectively. These setups were chosen to enhance the breaking at the target failure mode. For each of the test cases different loading rates were used to maintain an average failure time of 10 minutes. A l l the beam tests were videotaped and for bending tests and 0.46 m deep shear case high speed video taken at 1000 images per second speed was used to study and detect the failure modes. 71 6.2 BENDING TESTS The detail of the test setup and the beam lay-up used for the assessment are given in Tables 6.1 and 6.2. The bending verification beams are fairly deep beams. Therefore, four special lateral supports were provided at 1.22 m, 2.74 m, 8.53 m and 10.06 m locations to provide support against lateral instability. Figure 6.1 Typical third point loading configuration used for the bending test /=10.97 m P/2 1 / - test span P - total load on the beam P/2 1 113 ^ s 113 113 < > Table 6.1 Details of the bending test configuration Beam case F Beam depth 0.61 m (2 ft) Beam width 0.130 m (5 %in.) Span to depth ratio 18 Test span, / 10.97 m (36 ft) Beam length 11.28 m (37 ft) Loading rate 13 mm/min 72 Table 6.2 Beam lay-ups selected for bending tests (beam I D A 5 U ) Lamina grades 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Lamina number (from the bottom of the beam) T1 B C C D D D D D D D D C C B Cc Figure 6.2 Test setup for the 0.61 m deep glulam bending beam The summary of the bending test result is given in Table 6.3 and a comparison between the U L A G predicted strength distribution and the laboratory test results are given in Figure 6.3. 73 Table 6.3 Summary of the bending test results Beam depth, m 0.61 M O R Mean, M P a 41.8 C O V , % 14 Speci f ied strength, M P a 32.2 Figure 6.3 Comparison between the ULAG predicted strength distribution and the laboratory test results for 0.61 m deep glulam beams G l u l a m B e n d i n g - 0.61 m d e e p b e a m ( 3rd point l o a d i n g , 18 s p a n / d e p t h ratio) 100 120 140 160 180 200 220 Failure L o a d , kN The details of key failures observed during the glulam bending tests are given in Table 6.4. 74 Table 6.4 Key failures observed in 0.61 m deep beams Failure type Number of breakdowns finger joint 14 finger joint and lamina 1 finger joint and knot 1 knot 1 knot, SOG and lamina 1 lamina 3 lamina and finger joint 1 shake 1 SOG 1 Images of two of the bending failures are shown in Figures 6.4 and 6.5. Figure 6.4 Bending failure of a 0.61 m deep glulam beam Figure 6.5 Bending failure of a 0.61 m deep glulam beam 6.2.1 MOE VALUES M O E values for all the bending beams were evaluated from load-deformation curves obtained prior to the ultimate loading. A specially designed cable yoke system similar to the one used in the calibration test was used to track the beam deflections. The summary of the M O E values for the 0.61 m deep bending beams are given in Table 6.5. Table 6.5 Summary of the MOE values of the 0.61 m deep bending beams Parameter 0.61 m deep beams Mean, M P a 12,923 COV, % 3 76 6.3 SHEAR TESTS A s mentioned earlier twenty four 0.46 m deep shear beams at 6 span to depth ratio was used for the assessments. The details of the test configuration used for the shear tests are given in Table 6.6 and the schematic diagrams of the typical shear testing arrangements used are shown in Figure 6.6. Similar to the shear calibration tests, four point loading setup was selected to avoid the excessive load concentration at the loading point. Table 6.6 Shear test configuration Beam depth 0.45 m (1.5 ft) Beam width 0.13 m (5 %m.) Span/depth ratio 6 Beam length 3.1 m (10 ft and 2 in.) Test span, / 2.74m (ft) Loading type Four point loading Figure 6.6 Configuration of the typical shear testing arrangement / = 2.74/M 0.45 m / - test span P - total load on the beam b = 0.46 m, spacing between the pair of loading heads at the center. 77 The summary of the shear test results is given in Table 6.7. This data was processed using the M L E technique in order to determine the uncensored statistical parameters. The M L E predicted 2p-Weibull data and the equivalent normal distribution values are given in Table 6.8 and the corresponding shear strength values are given in Table 6.9. Table 6.7 Summary of the shear test results Shear testing case Failure load Number of shear failures Total number of beams tested Mean (kN) COV (%) 0.46 m deep beams tested at 6 span to depth ratio 389 10 18 24 Table 6.8 Details of the MLE simulated shear capacity (based on laboratory test results) Shear testing case Scale, m (kN) Shape, k Mean, (kN) COV <%) 0.46 m deep beams tested at 6 span to depth ratio 415 12 397 11 Table 6.9 Shear strength parameters based on the experimental data. Shear testing case Mean, (MPa) COV, (%) 0.46 m deep beams tested at 6 span to depth ratio 5.01 11 78 From the shear strength values presented in Tables 5.18 and 6.9 a consistent reduction in the shear strength with the shear volume increment was observed. This is an indication of a significant size effect in shear beams. A visual comparison of the 0.30 m and 0.46 m deep shear beams discussed above is given in Figure 6.7 Figure 6.7 V i sua l comparison of 0.30 m and 0.46 deep shear beams at 6 span to depth ratio Shearing occurred within a couple of mille second's time and is difficult to observe in real time. Therefore, a high speed video camera was used to track and to confirm the shear failure. Images from this video taken in a mille-second interval are shown in Figure 6.8. Here the failure surface can be tracked by the dislocation of the vertical grids along the length of the beam. 79 Figure 6.8 Shear failure images from a high speed video About twenty five percent of the beams broke in bending mode. In a couple of cases the failures were initiated by the tensile cracks and the ultimate failure occurred in shear. The load vs. stroke curve for a typical ultimate shear failure followed by an initial tensile crack is plotted in Figure 6.9. The sudden drop in load level after the initial failures was due to the changes in the net modulus of elasticity after the preceding break. Figure 6.9 L o a d vs. Stroke curve for a 0.46 m deep glulam shear test G L U L A M S H E A R - L O A D V S S T R O K E (0.46 m deep beams tested at 6 span todepth ratio) 6.4 ULAG VERIFICATION The verification tests demonstrate the U L A G ' s precision in predicting the flexural and shear strength capacities of the glue laminated timber beams. A comparison of the 81 bending test results and U L A G predictions for the specified strength and modulus of elasticity are given in Tables 6.10 and 6.11, respectively. A similar analysis for the shear strength is given in Table 6.12. Table 6.10 Comparison between bending test results and ULAG prediction - specified strength Beam case Glulam specified strength laboratory test results (MPa) ULAG simulations (MPa) Error % 0.61 m deep beam 18 span/depth ratio 32.2 32.7 1.6 Table 6.11 Comparison between bending test results and ULAG predicted MOE Beam case MOE laboratory test results (MPa) ULAG simulations (MPa) Error % 0.61 m deep beams at 18 span/depth ratio 12,923 12,278 -5.0 Table 6.12 Comparison between shear test results and model prediction Beam depth, m Span to depth ratio Simulated shear strength, MPa Tested shear strength, MPa Error, % 0.46 6 4.8 5.0 -2.9 From the results presented in Tables 5.10, 5.11, 5.20, 6.10, 6.11 and 6.12 a very accurate U L A G prediction with a maximum error of 1.6% observed for the glulam flexural strength and a maximum error of 5.4% observed for the glulam shear strength predictions. These errors are around -5% for the M O E assessments. 82 6.4.1 INFLUENCE OF FINGER JOINTS The number of finger joints present in the tension side of the beam lay-up is expected to have significant impact on the overall capacity of the Glulam beam. Further during the laboratory tests and U L A G simulations a significant number of finger joint failures were observed. Therefore, a U L A G assessment was carried out to investigate the influence of fingerjoints on the overall flexural capacity of the glulam beam. The beam lay-up given in Table 6.2 was used with 18 span to depth ratio and third point loading setup. The summary of the assessments are given in Table 6.13. Table 6.13 Comparison between the capacities of glulam beams constructed with different length of lamina stocks Parameters The ratio between 4.88 m and 2.44 m long boards in the samples corresponding to each of the lamina grade 75:25 (Casel) 50:50 (Case 2) 25:75 (Case 3) Beam Depth, h, cm 60.6 60.6 60.6 L/h ratio 18 18 18 Number of finger joints per 100 lamina layers* 61 92 122 Ultimate Failure Load,kN Mean 182.2 179.8 176.6 SD 23.5 22.6 21.2 MOR, MPa Mean 42.2 41.8 41.8 SD 5.4 5.8 5.8 R s , MPa 33.3 32.2 32.2 *Number offinger joints observed at the middle 3.5 m segment of the beam layer For the cases investigated it was observed that the changes in the number finger joints, for example a variation of the presence (middle 3.5 m length of the beam was considered for this observation) of number of finger joints from sixty finger joints per hundred lamina layers (case 1) to hundred and twenty fingerjoints per hundred boards 83 (case 3), has a 3% impact on the overall flexural capacity of the 0.61 m deep glulam beam simulated with 11.0m test span. 6.5 SIZE EFFECTS IN BENDING U L A G beam simulations account for the presence of two major defects within a glulam beam; the effects of knot distributions (defects) and the finger joints. Therefore, U L A G can be used directly to study the glulam-size/volume factors. A glulam size effect study was carried out for Douglas fir glulam beams. Three beams with depths of 0.30 m, 0.61 m and 0.91 m were used for the assessments. The 0.30 m deep beam lay-up A 8 U given in Table 5.4 with a span to depth ratio o f 12 was used as the primary lay-up. In order to avoid any influence of the beam configuration, the ratio of the various grades of lamina in the 0.61 m and 0.91 m was kept as similar to the 0.30 m deep beam. The details of the beam lay-ups considered for the assessments are given in Table 6.14. Table 6.14 Beam lay-ups used for the volume effect analysis Beam Lamina number (from the bottom of the beam) case 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 C c C D D D D C T1 2 C c C c C C D D D D D D D D C C T1 T1 3 C c C c C c C C C D D D D D D D D D D D D C C C T1 T1 T1 The beams were evaluated using U L A G under third point loading in a simulation study with 1000 replications. The summary of the size effect analysis is given in Table 6.15. 84 Table 6.15 Summary of the size effect analysis Depth, m Test s p a n , m Beam vo lume, V, m 3 Failure load M O R (mean), M P a Mean, kN C O V , % 0.30 3.66 0.14 164 17 48.1 0.61 7.32 0.58 314 12 45.9 0.91 10.97 1.3 441 12 43.0 The relationship between the size factor k, M O R , and beam volume V for beams having same span to depth ratio can be given by the following equation. \og{MOR) = - - l o g ( F ) + C, C is a constant (6.1) k A plot of log (V) vs. log(MOR) along with a linear trend line is shown in Figure 6.10. Figure 6.10 Variation of log(MOR) with log(V) for the glulam beam cases considered in the volume effect analysis 1.70 j ^^^^——r^.—_—j . — i —i 1 0.8 -0.6 -0.4 -0.2 0 0.2 log (V) 1.62 L -1 85 From the gradient of the line, the size-effect factor k = 21. However, the size factor used in the Canadian Standard C A N / C S A 086.1-M89 is 5.4 with the beam width and length as parameters; i.e., beam depth is not explicitly considered. Subsequently the variations of M O R values with volume were investigated with different size-effect factors (Figure 6.11). The k value provided in the standard seems too conservative for beams smaller than the standard beam size (0.13 m x 0.61 m x 9.1 m) but non-conservative with the beam larger than the standard beam size. More work is needed to experimentally confirm the k factor using large beams. Figure 6.11 Compar ison of the variat ion of l o g ( M O R ) wi th log(V) wi th different size effect factors (V in units of m 3 and M O R in units of M P a ) 1.69 -1.0 -0.8 Original data (simulated with ULAG) Size adjusted* with k=20 Size adjusted* with k=10 ©—Size adjusted* with k=5.4 -0.6 -0.4 log(V) -0.2 0.0 0.2 * Size adjusted to standard beam size of 0.13 m x 0.61 m x 9.10 m. 86 6.6 FLEXURAL STRENGTH AND STIFFNESS COMPATIBILITIES When developing new lay-up for glulam beams, it is common to place the grades with high flexural strength and M O E at the extreme tension zone of the beam to increase the beam's flexural capacity. During U L A G simulations it was observed that the combining effect of the laminae strength and stiffness plays a significant role in controlling the ultimate beam capacity. The detail o f this analysis is given below. Two beam lay-ups C I and C2 shown in Table 6.16 were considered for the analysis. The difference between these lay-ups is that the extreme tension lamina grade B in C I is replaced by a better T l grade in C2. The key strength parameters of the grades T l and B are given in Table 6.17. A t this point C I is expected to be weaker than C2. Subsequently U L A G beam simulations were performed on these lay-ups and the results are tabulated in Table 6.18 These lay-ups had average M O E values of 11,900 M P a and 12,100 M P a respectively. Table 6.16 Glulam beam lay-ups used for the special investigation Lamina number (from the bottom of the beam) Beam lay-up ID 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 C1 Cc Cc C C D D D D D D D D C C B B C2 Cc Cc c C D D D D D D D D C C B T1 87 Table 6.17 Key strength parameters of the grades Tl and B Lamina grade Tensile strength, MPa (2.44 m gauge length) Tensile strength of the fingerjoints, MPa Average, E, MPa T1 50 42 15,200 B 35 40 13,700 Table 6.18 Results of the special investigation Progressive failure (ultimate load), kN First failure loads, kN Beam lay-up ID C1 C2 C1 C2 Mean 187.1 181.3 142.1 148.9 SD 20 24 24 24 U L A G predicts higher mean ultimate failure loads for C I (187 kN) than C2 (181 kN). The first failure data shows C2 is stronger than C I . In C2 due to the higher stiffness of the T l grade compared to the B grade lamina, higher stress are expected to be developed in the T l layer in C2 compared to the B layer in the C I . Even though the T l grade laminae are stronger than the B grade laminae, the finger joint strengths for these laminae are similar. Therefore in the C2 beam ended up to be weaker than the C I beam. This finding is not unique and was previously observed in older studies. Therefore, further investigation on this is recommended. 88 6.7 RELIABILITY ANALYSIS The U L A G simulations described previously focused on analyzing the simple load carrying capacity of the glulam beams. One important concern is the reliability or the chances of failure of the beam under a general loading condition. In this way a reliability analysis was carried out to study the general performance of the beams/beam lay-ups. The assessment was carried out for the 0.30 m and 0.61 m deep glulam beams used for the calibration and verification tests. The analysis was preformed with the common reliability parameters acceptable in general situations as given below: The performance function can be written as E(D) and E(Q) are the design dead and live loads , respectively. After substituting the appropriate parameters for E (D) and E(Q) equation 6.2 can be re-written as fallows. where, L - loading span of the beam, b - width of the beam, h - height of the beam, R -bending strength; M O R (assuming a normal distribution, obtained from U L A G simulation), Q„ - nominal live load and d and q are the dead and live loads normalized with respect to their corresponding design values. G = R - (E(D) + E(Q)) (6.2) G = RJQA(dy + q) Abh2 v ; (6.3) 89 d = — = 1 + VDRn; VD =0.10, Rn = standard normal random variable here R, R n , Q n and q are random variables. Following load data and other conditions were used based on the provisions given by Foschi etal . (1989) (i) Target reliability p = 3.0 (ii) Occupancy loads (Extreme type I distribution), for offices corresponds to maxima over 30 years return period. q(mean) =0.925 and q ( C O v) =0.236 (iii) Vancouver snow load with 30 years of return period. Qn(mean) = 0.0014 M P a and Q n ( C O v ) = 0.287. Second order reliability analyses were carried out using the computer program R E L A N (Foschi and Folz 1992). A trial and error beam spacing varying from 3 m to 5 m was used to find the optimum beam spacing corresponds to the target reliability. The summary of the reliability analysis results is given in Table 6.19. Table 6.19 Summary of the reliability analysis Beam lay-up Parameters Beam spac ing , m 3.0 4.0 5.0 A8U P 4.3 3.3 2.6 Probability of failure 9.0E-04 4.0E-02 4.6E-01 A5U P 4.8 3.9 3.1 Probability of failure 9.3E-05 5.5E-03 8.9E-02 90 A s mentioned earlier the target reliability index (P) of the analysis is 3.0. Therefore, 4.0 m spacing is recommended for 0.30 m deep beams with 21 span to depth ratio and 5.0 m spacing is recommended for 0.61 m deep beams with 18 span to depth ratio. 91 Chapter 7 C o n c l u d i n g R e m a r k s 7.1 SUMMARY Canadian glulam industry has a resource optimization issue related to the supply of the high grade laminae material required for the glulam manufacturing. From the manufacturers' point of view there is a need for some modification in the current grade specifications in order to fairly match the supply and demand of the material resources, especially for the high grade material placed at the extreme tension zone. Here the main concern is to develop a new laminae grade set focusing on increasing the efficient use of lamina on construction of 24f glulam beams. In this way specifications for a set of five Douglas fir lamina grades T l , Cc , B , C and D were developed and the grade outturn was established based on subsequent grading and analysis. Initially the new lamina grade boards are subjected to knot survey in order to qualify the new lamina grades according to A S T M D3737. The data were analyzed using the computer program G A P and a satisfactory performance was reported. Samples from each of the new laminae set were E rated. Furthermore samples of laminae and finger joints of the tension lamina grades T l , B , C and D were tested in tension to establish the strength of the laminae and finger joints corresponding to the new grades. Modifications were done in the U L A G program to make it compatible to the Windows X P versions. Then a procedure to account for the laminating factor and subroutines required to perform the shear capacity assessment were developed and incorporated with U L A G . The shear assessments were performed based on the weakest link stress volume theory. The shear stress outputs from the finite element analysis was 92 integrated and compared to the strength of a small clear specimen at a common probability of interest to predict the shear capacity of the full scale glulam beam. Then a series of U L A G analysis were performed and a 0.30 m deep 24f glulam beam was successfully simulated using the refined U L A G program. A set of twenty four 0.30 m deep glulam beams were tested with 21 span to depth ratio to as part of U L A G calibration process. Very small errors between the U L A G predicted flexural capacity and test results were observed. Two sets of 0.30 m deep glulam beams were tested at short span to determine the shear capacity. This information was used to fine tune the clear wood strength parameters used in the shear capacity assessment model. Subsequently two sets of forty eight 0.61 m and 0.45 m deep glulam beams were tested in bending and shear, respectively to verify model predictions. The bending strength and M O E of the 24f glulam verification tests agreed very precisely with U L A G predictions. A s intended a sufficient number of pure shear failures were obtained to predict the shear strength capacity. The M L E method was used to predict the pure shear capacity of the beams considered. Subsequent analyses confirmed the significant of size factor in shear. 7.2 CONCLUSIONS The current study provides many results/research findings in relation to the modeling of glulam beams. Some of the key outcomes are given below : 1. A new grade set consisting five new glulam lamina grades T l , Cc , B , C and D was developed and validated for the manufacturing of the 24f glulam beams. 93 2. The accuracy of U L A G in simulating the flexural strength of glulam was demonstrated. 3. The new U L A G model also predicts the shear capacities of glulam with sufficient confidence. 4. A significant size effect in shear was verified. U L A G program predicted some initial failures at the inner D grade layers of the beam which are generally not expected to break. High speed videos taken during the beam testing also confirm some initial inner failures to some extent. This finding shows the efficiency of U L A G in assessing the performance of the glulam-lay-up combinations. A s predicted by U L A G , a very low strength glulam beam in bending was found at the lower tail o f the distribution during testing. Subsequent investigation identified it to be caused by a knot failure at the 2 n d tension (inner) layer. The procedures established from this study demonstrate a new method for glulam beam lay-up design and assessment by using U L A G to predict the flexural capacity of Glulam beams as well as using the tensile strength and the corresponding M O E values of the lamina and the tensile strength of the fingerjoints as input. Other significant outcomes of the study are the details of the material properties obtained for the Douglas fir laminating grade boards. 1. Knot survey/knot mapping information 2. Tensile strength distribution 3. Finger j oint strength distribution 4. M O E data for laminae 94 7.3 JUSTIFICATIONS The full scale shear strength tests of this kind are unique. The beam lay-up for the shear tests was made based on the U L A G predictions. During these assessments the lay-up was made targeting a significant number of shear failures as resulted. Since the data contain both bending and shear failure modes, the shear beam test results were subsequently analyzed using M L E procedures to obtain un-censored data. The model assessments and the laboratory testing were focused on flexural strength and shear strength. During the modeling and testing it was assumed that the glue bond in between the laminae is very strong. There were no significant delamination failures observed during the full scale beam testing. There were couples of minor compression deformation observed near the top layers. This again was treated as insignificant, with the justification that there was no noticeable beam failures observed related to these deformations. 7.4 SUGGESTIONS FOR FUTURE RESEARCH Even though the U L A G predictions made a significant revolution in the development of glulam lay-up, the complicated internal stresses near the supports and loading points need careful consideration. Investigations on these issues may further enhance the model predictions. Current analysis produces a strength distribution for the 38 mm x 140 mm Douglas fir laminating grades. It is recommended to expand this data- base incorporating the strength profile of other key species such as Hem fir, etc. and different member widths. 95 The compatibility issue related to the flexural strength and modulus of elasticity presented in section 6.6 is an issue of interest, especially when designing new beam construction. It is recommended to verify this by means of further full scale laboratory testing. Calibration/Verification of U L A G for the glulam tension and compression loading cases w i l l be another constructive step in upgrading U L A G for more efficient glulam design and analysis. The type of the glulam supports and connections widely differ depending on the structural applications considered. These factors may develop different types of stress interactions across the beam. It is recommended to investigate the influence of the supports and connectors on the overall capacity of the glulam beam. 96 B i b l i o g r a p h y A I T C . 2004. Standard specifications for structural glued laminated timber of softwood species. A I T C 117-2004, American Institute of Timber Construction, Centennial. A P A E W S . 2003. Glulam Product Guide. Form N o . E W Z X 4 4 0 B , Engineered Wood Sys tems-APAEWS, Tacoma, Washington. A S T M . 2006. Test methods for mechanical properties of lumber and wood-based structural material. Standard A S T M D 4761, American Society for Testing Materials, West Conshohocken, Pa. A S T M . 2006. Standard methods of static tests of timber in structural sizes. Standard A S T M D 198, American Society for Testing Materials, West Conshohocken, Pa. A S T M . 2006. Practice for Establishing allowable properties for structural glued laminated timber (Glulam). Standard A S T M D 3737, American Society for Testing Materials, West Conshohocken, Pa. Bathe, K . J . 1982. Finite element procedures in engineering analysis, Prentice-Hall Inc., Englewood Cliffs, New Jersey. 735 p. Bodig, J. and Jayne, B . A 1982. Mechanics of wood and wood composites, Van Nostrand Reinhold, Co. , New York. 712 p. Buchanan, A . H . 1984. Strength model and design methods for bending and axial load interaction in timber members. Ph.D. Thesis, The University of British Columbia, Vancouver, Canada. 298 p. Cramer, H . and Leadbetter. M . R . 1967. Stationary and related stochastic process; sample function properties and their applications. John Wiley & Sons, N e w York. 348 p. C S A . 1989. Engineering design in wood (limit states design). Standard C A N / C S A 086.1-M 8 9 , Canadian Standards Association, Rexdale, Ont. C S A . 1989. Qualification code for manufacturers of structural glued-laminated timber. Standard C A N / C S A - 0 1 7 7 - M 8 9 , Canadian Standards Association, Rexdale, Ont. C S A . 1989. Structural glued-laminated timber. Standard C A N / C S A - 0 1 2 2 - M 8 9 , Canadian Standards Association, Rexdale, Ont. Falk, R. and Coll ing, F. 1994 Glued -laminated timber: laminating effects. Proceeding of the Pacific Timber Engineering Conference, Gold Coast Australia, July. 11-15. Falk, R. and Coll ing, F. 1994 Laminating effects in glued-laminated timber beams. Journal of Structural Engineering, A S C E , 121(12): 1857-1863. Folz, B . and Foschi, R .O . 1992. Stochastic finite element analysis of laminated beams. Annual Conference of the Canadian Society for C i v i l Engineering, Quebec, May 27-29. 97 Folz, B . and Foschi, R .O. 1993. U L A G : Ultimate load analysis of glulam-user's manual. Version 1.0, Department of C i v i l Engineering, The University of British Columbia, Vancouver, Canada. 23p. Folz , B . and Foschi, R .O . 1994. Stochastic finite element analysis of progressive failure in a laminated wood beam, in: Schueller, Shinozuka, Yao (Eds.), International Conference on Structural Safety and Reliability, I C O S S A R 93, Balkema, Rotterdam, 1994. 585-592. Folz, B . R . 1997. Stochastic finite element analysis of the load-carrying capacity of laminated wood Beam-Columns. Ph.D. Thesis, The University of British Columbia, Vancouver, Canada. 163 p. Foschi, R. O. and Barrett, J .D. 1976. Longitudinal Shear in Wood Beams: a design method. Canadian Journal of C i v i l Engineering, N R C Canada, 3: 199-208. Foschi, R. O. and Barrett, J .D. 1977. Longitudinal Shear in Wood Beams: a design method. Canadian Journal of C i v i l Engineering, N R C Canada, 4: 363-369. Foschi, R. O. and Barrett, J .D. 1980. Glued-Laminated Beam Strength: A Model . Journal of the Structural Division, A S C E , 106(ST8): 1735-1754. Foschi, R. O., Folz, B . and Yoa, F. Z . 1993. R E L A N : RELiabi l i ty ANalys is -user's manual, Version 2.24. Department o f C i v i l Engineering, The University of Brit ish Columbia, Vancouver, Canada. Foschi, R. O., Folz, B . and Yao, F .Z . 1989. Reliability-based design o f wood structures. Structural Research Series, Report No . 34, Department of C i v i l Engineering, The University of British Columbia, Vancouver, Canada. Hernandez, R., Bender, D . A . , Richbur, B . A . and Kline , K . S . 1992. Probabilistic modeling of glued-laminated timber beams. Wood and Fiber Science, The Society of Wood Science and Technology, 24(3): 294-306. Heylinger, P.R. and Reddy, J .N. 1988. A higher order beam finite element for bending and vibration problems. Journal of Sound and Vibration, 126(2): 309-326. Klapp, H . and Bruninghoff, H . 2005. Shear Strength of Glued Laminated Timber. Proceedings of the International Council for Research and Innovation in building and Construction, Working Commission W18- Timber Structures. 38 t h meeting, Karlsruhe, Germany, August 2005. Koka , E . N . 1987. Laterally loaded wood compression members: Finite element and reliability analysis. M . A . S c . Thesis, The University of British Columbia, Vancouver, Canada. 120 p. Lam, F. 2000. Length effect on the tensile strength of truss chord members. Can. J. C iv . Eng. N R C Canada, 27: 481-489. Lam, F. , Yee, H . and Barrett, J.D. 1997. Shear strength of Canadian softwood structural 98 lumber. Can. J. C iv . Eng. N R C Canada, 24: 419-430. Lee, J.J., K i m , K . M . and Oh, J .K. 2005. Prediction of bending properties for structural glulam using optimized distributions of knot characteristics and laminar M O E . Journal of Wood Science, The Japan Wood Research Society, 51: 640-647 Marx, C M . and Evans, J .W. 1986. Tensile strength of A I T C 302-24 grade tension laminations. Forest Prod. J. 36(1): 13-19 Marx , C M . and Evans, J .W. 1988. Tensile strength of laminating grades of lumber. Forest Prod. J. 38(7/8): 6-14 Melchers, R . E . 1987. Structural reliability analysis and prediction. El l i s Horwood Limited, Chichester. 437 p. Moody, R. C. and Hernandez, R. 1997. Glued-laminated timber. In: Smulski, Stephen, Ed. , Engineered wood products-A guide for specifiers, designers and users. Madison, WI. Chapter 1. 1-139. Moody, R., Falk, R. and Williamson, T. 1990. Strength of glulam beams - volume effects. 1990 International Timber Engineering Conference, Tokyo, Japan. 176-182. Moody, R . C and Falk, R . H . 1989. Development of design stresses for glulam timber in the United States. Proceeding or the 2 n d Pacific Timber Engineering Conference, Auckland New Zealand, Aug . 28-31, vol . 2. 309-313 Rammer, D .R. 1997. Shear strength of solid-sawn Douglas-fir beams. Journal of Materials in C i v i l Engineering, A S C E , 9(3):130-138. Rammer, D.R. , Soltis, L . A . and Lebow, P .K . 1996. Experimental shear strength of unchecked solid-sawn Douglas-fir. Research Paper FPL-RP-553 , Madison, WI : U S . Department of Agriculture, Forest Service, Forest Products Laboratory. 33p. Steiger, R. and Kohier, J. 2005. Analysis of censored data-examples in timber engineering research. Proceedings of the International Council for Research and Innovation in building and Construction, Working Commission W18- Timber Structures. 38 t h meeting, Karlsruhe, Germany, August 2005. Timusk, P . C 1997. Experimental evaluation of the U L A G glulam beam simulation program. M.Sc . Thesis, The University of British Columbia, Vancouver, Canada. 80 P-Yeh, B . and Williamson, T .G . 2001. Evaluation of glulam shear strength using a full-size four-point test method. Proceedings of the International Council for Research and Innovation in building and Construction, Working Commission W18- Timber Structures. 34 t h meeting, Venice, Italy, August 2001. 99 

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