AN ANALYTICAL AND EXPERIMENTAL INVESTIGATION OF CONTACT AREA STRESS DISTRIBUTION AND BUCKLING STRENGTH OF LIGHT GAUGE PUNCHED METAL HEEL PLATES FDR TIMBER TRUSSES Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ISAAC SHEPPARD, JR. 1969 I I— _ lEI’I‘ L ~ B R A R Y Michigan State University 7—— THESIS This is to certify that the thesis entitled AN ANALYTICAL AND EXPERIMENTAL INVESTIGATION OF CONTACT AREA STRESS DISTRIBUTION AND BUCKLING STRENGTH OF LIGHT GAUGE PUNCHED METAL HEEL PLATES FOR TIMBER TRUSSES presented by Isaac Sheppard, Jr. has been accepted towards fulfillment of the requirements for __Ph_oR-_degree in Agr, Em. Major professor Date Nov. 202 1969 0-169 ABSTRACT AN ANALYTICAL AND EXPERIMENTAL INVESTIGATION OF CONTACT AREA STRESS DISTRIBUTION AND BUCKLING STRENGTH OF LIGHT GAUGE PUNCHED METAL HEEL PLATES FOR TIMBER TRUSSES BY Isaac Sheppard, Jr. The purpose of this investigation was to develop a simple testing procedure and make a theoretical and experi- mental study of the contact area stresses and buckling ' stresses of light gauge metal heel plates used on wood trussed rafters. A small, hand-operated hydraulic cylinder was mounted in a Specially designed jig to apply a concentrated load at the peak of 8'-O" long triangular trusses. By mounting a dial gauge on the joint, load-deflection data was obtained“ A theoretical investigation developed the theory of contact area stresses in accordance with recent work on nailed joints and other analyses that combine direct stresses vectorially with eccentric, or rotational, stresses to get critical combined stresses. Methods of computing tensile stresses in heel plates, shear streses, and bending stresses on small elements, are presented. 1 Isaac Sheppard, Jr. 2 An initial comparison of six plate sizes, shapes, and orientations revealed that contact area stresses were.not significantly different for any of the plates studied at 0.015” heel joint deflection. At ultimate load, however, those plates 2-3/4" to 3-3/4" wide, and lengths from two to three times their width were best, and were 20% to 50% stronger than the next three. These two strong joint types were morefghan twice as good as the worst group, 5"x7", placed the ”wrong way." A detailed study of surface strains using Stress-Coat brittle lacquer revealed that the shear stress in the steel is highest directly over the joint between members; that corner teeth are initially stressed quite highly; but that even at loads that cause buckling, large areas of wider plates are not stressed significantly. It was concluded that heel plates should be kept to a lesser width to better utilize contact area strength and prevent an erroneous feeling of confidence due to excessive width of the heel plates. In a first preliminary comparison of 24 matched specimens (two repetitions each): 8'-0" vs. 24'-0"; Douglas fir vs. white fir; 3"x5", 3"x8", and S"x5" heel plates; all evaluated at 0.015", 0.040", 0.080", and 0.150" heel deflection; it was found that: 1. The heel joints for 8'-0" specimens were 8% stronger than those on 24'-0" matched trusses. Isaac Sheppard, Jr. 3 2. The white fir heel joints were only 70% as strong as Douglas fir joints. 3.‘ The 3"x5" and 3”x8" plates were almost identical, on a psi basis, but both were about 20% stronger than the S”x5" plates. 4. Contact area stress was affected by several two- way interaction effects. A second preliminary comparison verified these conclu- sions, plus showing there was no significant difference between 8'-0" specimens tested on the hand-operated jig and matched 8'-0" specimens tested on a Riehle mechanical testing machine. A final analysis of variance comparison, performed with a least squares statistical routine on a Control Data Corp. 3600 computer, included the variables mentioned earlier, plus moisture content and specific gravity, along with their squares, as covariants, and was based on the load-deflection data from 56 different test specimens. This final comparison confirmed the earlier conclusions, plus finding that moisture content affects contact area stress significantly. Multiple correlation coefficients were computed that accounted for 91% of the variance and a contact area stress prediction equation was deve10ped, with predicted stress being compared with measured stress for four deflection readings on each specimen. Isaac Sheppard, Jr. 4 A comparison of the theoretical results with the experi- mental tests showed that a simple axial stress calculation of contact stress, in the P/A manner, is a better predictor of test results than the theoretical method proposed. The experimental work led to recommendations for heel joint design that are also included. AN ANALYTICAL AND EXPERIMENTAL INVESTIGATION OF CONTACT AREA STRESS DISTRIBUTION AND BUCKLING STRENGTH OF LIGHT GAUGE PUNCHED METAL HEEL PLATES FOR TIMBER TRUSSES BY 'Isaac Sheppard, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1969 ewe/4 #14170 © COpyright by ISAAC SHEPPARD, JR. 1970 ACKNOWLEDGMENTS This will express appreciation to TrusWal Systems, Inc., Troy Steel Corp., and Duratile of Ohio for their truss plates, test specimens, and testing apparatus. Many members of the Agricultural Engineering Department, my family, and others offered encouragement along the way, but special gratitude is due Dr. M. L. Esmay, my major professor; and also Dr. A. Sliker, who aided with the research. The most important help of all was from my loving wife who not only typed the manuscript, but much more importantly buoyed my spirits at crucial points. ii LI IN Che II. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES . . INTRODUCTION . . . . . . . . Chapter I. II. III. REVIEW OF LITERATURE . . . . . . . . . . PURPOSE . . . . . . . . . . . . . . . . . . THEORETICAL INVESTIGATION Types of Heel Joint Failure . . . . . . . Tensile Failure . . . . . Tooth Failure . . . . . . . Wood Failure . . . . . Buckling Failure . . . . Description of Stresses in the Heel Plate Axial Contact Area Stresses Eccentric Contact Area Stresses Shear Stress in the Steel Proposed Heel Joint Contact Stress Calculation Method Comparison of Existing Heel Joint Analysis Methods General Method TPI Method . FHA Method . . . . Proposed Method . Typical Calculations . Calculation of Tensile Stresses within the Bottom Chord Contact Area Assumptions . . . . . Notation . . . . . . . . . —Shear Stress Calculations Improvements to Calculations iii Page 10 10 10 14 14 15 15 16 16 20 20 23 23 25 25 28 33 33 35 38 Chapter Buckling and Shear Stresses in the Steel . . . Investigation of the Cause of Buckling . Discussion of Shear Stress in the Steel Calculation of Shear Stress at Critical Section Iv. EXPERIMENTAL ANALYSIS General Test Specimens Test Jigs Instrumentation . . . . . . . . Test Procedure Test Results . . . Types Of Failure of Experimental Specimens Stress- -Coat Analysis . Determination of Top Chord Axial Force Contact Stress and Shear Line Stress Comparison of Six Plate Types . . . . Initial Comparison of 8'-0" vs. 24'-0" Test Specimens Final Statistical Comparison of Matched 8' and 24' Specimens V. DISCUSSION OF RESULTS General Initial Study of Effect of Size, Shape, and Orientation on Contact Area Strength . Description . Statistical Comparison . Analysis of Results Summary . . . . . . . Comparison of Matched Specimens Description . . . . . . . . . . Comparison of 8'- 0" vs. 24'-0" Specimen Length . . Comparison of Small 8'- 0" Jig Results with Riehle Machine Results . Comparison of Douglas Fir vs. White Fir Comparison of 3"x5", 3"x8", and S"xS" Plates . . . . . . . . . . . . iv Page 39 39 42 44 47 47 47 51 58 58 67 67 75 90 94 95 99 100 100 101 101 101 101 115 115 115 116 117 124 131 Chapter Page Final (4-way) Comparison, including Moisture Content and Specific Gravity . . 132 Description . . . . . . . .,. . . . . . . 132 Data . . . . . . . . . . . . . . . . . . . 133 Results . . . . . 133 Summary of Final Analysis .of Variance Comparison . . . . . . . . . . . . . . . 133 Stress Prediction Equation . . . . . . . . . 137 General . . . . . . . . . . . . . . 137 Categories Studied . . . . . . 148 Creation of Indicator Variables for Categories . . . . . 148 Creation of Indicator Variables for . Interactions . . . . . . . . . . . . . . 149 Regression Equation . . . . . . . . . . . 150 Theoretical vs. Experimental Analysis . . . 152 General . . . . . . . . . . . . . . . . 152 Theoretical vs. Experimental Results at 0.150" Deflection . . . . . 152 Theoretical vs. Experimental Results at 0.015" Deflection . . . . . . . . . . . 153 Summary . . . . . . . . . . . . . . . . . 154 VI. CONCLUSIONS . . . . . . . . . . . . . . . . . 155 VII. RECOMMENDATIONS FOR HEEL JOINT DESIGN . . . . 159 VIII. RECOMMENDATIONS FOR FURTHER RESEARCH . . . . . 161 APPENDIX--LOAD DEFLECTION DATA . . . . . . . . . . . 162 REFERENCES . . . . . . . . . . . . . . . . . . . . . 184 Table 10. 11. 12. l3. 14. 15. LIST OF TABLES Comparison of Heel Joint Calculations Methods for 3”x5", 3"x8", and 5"x5" List of Specimens Tested . Moisture Content and Specific Gravity Calibration Data for Blackhawk Hydraulic Gauge . . . . . . . . . . . . . . . . Calibration Data for Full Scale Test Jig . Preliminary Comparison of 8' vs. 24' Speciemns Preliminary Comparison of 8' Small Jig vs. Riehle Machine . . . . . . . . . . . . . Computer Input for Comparison of Six Plate Sizes . . . . . Duncan's Multiple Range Comparison of Six Plate Sizes At 0.015" Deflection Level At 0.040" Deflection Level At 0.080" Deflection Level At 0.150" Deflection Level At Ultimate Load . 8'-0" vs. 24'-0" Specimens at Ultimate Load 8'-0" vs. 24'-0" Specimens at Four Deflection Levels Riehle Machine 8'-0" Test Specimens . White Fir vs. Douglas Fir at Ultimate Load White Fir vs. Douglas Fir at Four Deflection Lévels O O O I O O O O I -O O O .0 O O O 3"x5", 3"x8" and 5"x5" Plates Compared at Ultimate Load . . . . . . . . . . . . . . vi Page 34 48 52 64 65 97 98 110 111 112 113 114 116 117 117 131 131 Table Page 16. 3"x5", 3"x8", and 5”x5" Plates Compared at Four Deflection Levels . . . . . . . . . . . . 132' 17. Data Input for Final Analysis of Variance . . 134 18. Final (4-way) Comparison - Statistics on Transformed Variable . . . . . . . . . . . . . 138 19. Final (4-way) Comparison - AOV for Over-A11 Regression and Regression Coefficients.. . . . ' 139 20. Final (4-way) Comparison - Simple Correlatidn Doefficients . . . . . . . . . . . . . . . . . 140 21. Final (4-wya) Comparison - Measured Stress vs. Predicted Stress (224 Data Points) . . . . . . 142 22. Final (4-way) Comparison - Analysis of Variance for 4 Factors, 2 Cofactors and Interactions . 146 23. Interaction of Plate Size and Deflection . . . 147 24. Theoretical Contact Stress for 3"x5", 3"x8", and 5"x5" . . . . . . . . . . . . . . . 152 25. Comparison of Theoretical vs. Experimental Results @ 0.150" Deflection . . . . . . . . . 153 26. Comparison of Theoretical vs. Experimental Results @ 0.015" Deflection . . . . . . . . . 153 27. Load-Deflection Data for 2-7/7”x9" Plates . . 163 28. Load-Deflection Data for 3-11/16”x6-3/4" Plates 164 29. Load-Deflection Data for 5-5/16"x6-3/4" Plates 165 30. Load~Def1ection Data for 5—5/16"x4-1/2" Plates 1,to Bottom Chord . . . . . . . . . . . 166 31., Load-Deflection Data for 3-11/16”x4-1/2" Plates . . . . . . . . . 167 32. Load-Deflection Data for 5-5/16"x6-3/4" Plates I to Crack . . . . 168 33. Load-Deflection Data for 8' vs. 24' - 3"x5" - Douglas Fir . . . . . . . . . . . . . 169 34. Load-Deflection Data for 8' vs. 24' - 3”x8” F Douglas Fir . . . . . . . . . . . . . 170 vii Table Page 5"x5" - Douglas Fir . . . . . . . . . . . . . 171 3"x5" - White Fir . . . . . . . . . . . . . . 172 24'- 3"x8"-WhiteFir 173 8' Small Jig - 24' Full-Scale - 8' Riehle 8' Riehle - 8' Riehle - 8' Riehle - 8' Riehle - 35. Load-Deflection Data for 8' vs. 24' - 36. Load-Deflection Data for 8' vs. 24' - 37. Load-Deflection Data for 8' vs. 38. Load-Deflection Data for 8' vs. 24' - S"x5" - White Fir . . . . . . 39. Load-Deflection Data for 3"x5" - Douglas Fir . 40. Load-Deflection Data for 3"x5" - Douglas Fir - 41. Load-Deflection Data for 3"x5" - Douglas Fir 42. Load-Deflection Data for 3"x8”-- Douglas Fir 43. Load-Deflection Data for 5"x5" - Douglas Fir 44. Load-Deflection Data for 3"x5" - White Fir 4S. Load-Deflection Data for 3"x8" - White Fir 46. Load-Deflection Data for S"x5" - White Fir viii 8' Riehle - 174 175 176 177 178 179 180 181 182 Figure ‘0 11. 12. 13. 14. 15. 16. 17. 18. LIST OF FIGURES Tensile Failure at Heel Plate Plate Buckling along Shear Line Heel Plate Not on Member C.L. Eccentric Resisting Moment Vertical Forces Taken by Wood-to-Wood Bearing . . . . . . . . . . . . . Rotational Moment . . . Vector Addition for Combined Stress FHA Eccentricity Analysis . . . . . Typical Heel Plate Contact Stress Calculations 3-11/16"x9" Plate 3"x5" Plate . 3"x8" Plate 5"x5" Plate Typical Heel Plate for Tensile and Shear Calculations . . . . . . . . . . . Element on Shear Line Free Body Diagrams of Shear Element Eccentricity for Alternate Heel Plate Positions . . . . . . Critical Shear Stress (Buckling) Area Free Body Diagram at Shear Line 8fl-0” Test Specimen 8'-0" Test Jig . Dial Gauge Set-Up . . . . . . . . . . . ix Page 13 13 17 18 21 22 24 26 29 31 32 36 41 41 43 4s 4s S6 57 59 Figure Page 19. Sequence of Truss Assembly Photos . . . . . .4 6O 20. Small Test Jig for 8'-0" Specimens . . . . . . 61 21. Test Jig for 24'-0” Trusses . . . . . . . . . 62 22. Riehle Test Machine for 8'-0" Specimens . . . 63 23. Typical Wood and Tooth Failures (Contact Area) 68 24. Distortion of 18 Gauge Heel Plates . . . . . . 70 25. Photos of Nailed Plate Distortion . . . . . . 71 26. Initial Buckling of Specimen 26 . . .'. . . . 72 27. Progressive Buckling of Specimen 26 . . . . . 73 28. Buckling Sequence of 5-5/16”x4-1/2" Plate . . 74 29. Photos of Stress-Coat Cracks on Specimen 27 . 76 30. Progressive Buckling of Specimen 27 . . . . . 77 31. Sequence Drawing of Stress-Coat Cracks on 5-5/16"x6-3/4" Plate . . . . . . . . . . . . . 79 32. Large Scale of Initial Stress-Coat Cracks on 5-5/16"x6-3/4" Plate . . . . . . . . . . . . . 80 33. Large Scale of Later Stress-Coat Cracks on 5-5/16”x6-3/4” Plate . . . . . . . . . . . . . 81 34. Large Scale of Stress-Coat Cracks at Start of Buckling of 5-5/16"x6-3/4" Plate . . . . . 82 35. Sequence Drawing of Stress-Coat Cracks on 3-11/16"x6-3/4" Plate . . . . . . . . . . . 84 36. Large Scale of Initial Stress-Coat Cracks on 3-11/16"x6-3/4" Plate . . . . . . . . . . . 85 37. ' Large Scale of Later Stress Cracks on 3-11/16"x6-3/4” Plate . . . . . . . . . . . . 86 38. Large Scale of Stress-Coat Cracks at Failure of 3-11/16"x6-3/4" Plate . . . . . . . 87 39. Stress-Coat Cracks in Nailed Plate Specimen 44 . . . . . . . . . . . . . . . . . 89 Figure Page 40. Stress—Coat Cracks in Nailed Plate Specimen 36 . . . . . . . . . . . . . . . . . 91 41. Stress-Coat Cracks in Nailed Plate Specimen 37 . . . . . . . . . . . . . . . . . 92 42. Load-Deflection Curves for 2-7/8"x9" Plates . 102 43. Load-Deflection Curves for 3-11/16"x6-3/4" Plates . . . . . . . . . . . . . . . . . . . . 103 44. Load-Deflection Curves for 5-5/16"x6-3/4" Plates . . . . . . . . . . . . . . . . . . . . 104 45. Load-Deflection Curves fer 5-5/16"x6-3/4” Plates (Parallel to Crack) . . . . . . . . . . 105 46. Load-Deflection Curves for 5-5/16"x4—1/2" Plates (1 to Bottom Chord) . . . . . . . . . . 106 47. Load-Deflection Curves for Comparison of Six Plates . . . . . . . . . . . . . . . . . . 107 48. Load-Deflection Curves for 8' vs. 24' - 3"x5"'- Douglas Fir . . . . . . . . . . . . . 118 49. Load-Deflection Curves for 8' vs. 24' - 3"x8" - Douglas Fir . . . . . . . . . . . . . 119 50. Load-Deflection Curves for 8' vs. 24' - 5"x5" - Douglas Fir . . . . . . . . . . . . . 120 51. Load-Deflection Curves for 8' vs. 24' - 3"x5" - White Fir . . . . . . . . . . . . . . 121 52. Load-Deflection Curves for 8' vs. 24' - 3HX8" - White Fir o o o o o o o o o o o o o o 122 53. Load-Deflection Curves for 8' vs. 24' - 5"x5" - White Fir . . . . . . . . . . . . . . 123 54{ . Load-Deflection Curves for Douglas vs. White . Fir " 3"x5” " 8' o o o o o o o o o o o o o o o 125 55. Load~Def1ection Curves for Douglas vs. White Fir - 3"x8" - 8' . . . . . . . . . . . 126 56. Lead-Deflection Curves for Douglas vs. White Fir - SHXSH - 8' o o o o o o o o o o o o o o o 127 57. Lead-Deflection Curves for Douglas vs. White Fir - 3"x5" - 24' . . . . . . . . . . . . . . 128 xi Figure 58. 59. 60. Load-Deflection Curves for Douglas vs. White Fir - 3"X8" - 24' o o o o o o o o o o Load-Deflection Curves for Douglas vs. White Fir - 5"x5" - 24' . . . . . . . . . . FullrScale Tooth Layout for 3"x5", 3"x8", and 5"x5" Plates . . . . . . . . . . . . xii Page 129 130 INTRODUCTION The twenty year period, 1948-1968, has seen the use of wood trussed rafters grow from an almost infinitesimal begin- ning to a major market factor. Trussed rafters are now used on about half of all single family residential construction, as well as on a large share of agricultural, and a signifi- cant share of commercial and industrial construction. The trussed rafter has the advantages of greater strength, more uniformity, and lower cost as opposed to conventional joist- and-rafter construction. Greater spans without supports, faster construction and other benefits are provided by trussed rafters, too. Trussed rafters, commonly called "trusses," may be built with any structurally suitable joint system to attach the wood framing members. Split-rings, nail-glued plywood gussets, bolts, nails, light gauge metal gusset plates, and other connector types have been used. The light gauge metal gusset plate has essentially taken over the market now, having displaced the other joint types due to its lower cost, faster fabrication, and easier shipment of completed trusses. Many tests have been performed to insure that the truss plates have adequate tooth values or nail values and tensile strength. Other tests have been performed on completed trusses to show the over-all truss design to have adequate 1 2 strength. While both these sets of tests have shown struc- tural adequacy, there have been only minor attempts to, analyze the shear stresses, buckling stresses, and eccentric forces that affect the heel joint, where the bottom chord and top chord meet. Since this joint is subject to a more complex set of forces and stresses than any of the other truss joints, and since it requires more steel than any other joint, a more elaborate study of it seems warranted. This project is intended to answer that need. CHAPTER I REVIEW OF LITERATURE The design loads on trusses are usually specified by local building codes or nationally recognized building codes such as the "Basic Building Code" (1965), the "Uniform Building Code" (1967), the "Southern Standard Building Code" (1967), or the "National Building Code of Canada" (1966). Where no building code governs, the requirements of the Federal Housing Administration (1966), the United States of America Standards Institute, or, in the case of farm build- ings, by the American Society ongricultural Engineers (1967) may be used. Local climatological data is available for more detailed study from the Dept. of Commerce (1968). 'The lumber used in trussed rafters has been standard- ized as to grades and strength by the officialgrading associations, Western Wood Products Association (1965) for west coast woods, and the Southern Pine Inspection Bureau (1968) for southern woods. These lumber allowable stresses, plus connector values for bolts, split—rings, nails, etc., are all published in one booklet by the National Forest Products Association (1968). The properties of individual species are given in separate reports by Littleford on Deuglas fir (1967) and the Forest Products Laboratory on 3 4 western hemlock (1965) and southern pine (1966)- Strength and related properties of Canadian woods are summarized by Kennedy (1965). Probably the most important thing, the factor of safety, has been described in detail as a multi- valued characteristic by Wood (1958). The background testing for the lumber grading rules and specifications has been performed under the American Society for Testing and Materials (A.S.T.M.) Designation” D 245-67T (1967). The "strength ratio" related these tests of small, clear specimens to structural size by allowing for the reduction effect of knots, slope of grain, and other strength-reducing characteristics. The "strength ratio" is discussed by the Forest Products Laboratory in the "Wood Handbook" (1955). Non-destructive testing of lumber has been described by McKean (1962, 1963), Bolger (1962), Miller (1962), Sunley (1962), Senft (1962), and Wood (1964). This non-destructive testing, commonly called "machine grading," permits more uniform strength standards for timber based on a statistical correlation of strength with flatwise stiffness. Recent arguments of ”green" (unseasoned) vs. "dry" (moisture content of 19% or less) lumber are being resolved through a set of "green" sizes and allowable stresses that match the existing size standard, but a set of equivalent "dry" sizes with smaller dimensions to account for shrinkage. The ratio of dry to green clear wood properties has been determined u; A.S.T.M. in D-2555 (1967). These equivalent 5 ”dry" sizes were recommended by the Forest Products Laboratory (1964) on the basis of stiffness and shrinkage tests of green and dry joists. The engineered use of nails for connections in wood structural members, particularly trusses, has been exten- sively reported by Stern (1952 through 1967). Nailed joint rigidity was studied by L. L. Boyd (1959) and rotational resistance of three-membered nailed joints was reported by Perkins (1962). The use of nail-glued plywood gussets for wood trusses has been extensively investigated by Radcliffe (1954, 1956), J. S. Boyd (1955), Countryman (1954), Angleton (1960), and Suddarth (1961). A digital computer W-truss analysis pro- gram was developed by Suddarth (1964) for symmetric trusses with rigid joints (nail-glued plywood) or various combina- tions of rigid and pinned joints. I The design of light gauge metal connector plates with wood trussed rafters has been covered by the Truss Plate Institute's (T.P.I.) "Design Specifications for Light Metal Plate Connected Wood TrusSes" in various editions (1962, 1965, 1966, 1968). These metal plates of every different manufacturer have been subjected to a large number of tensile tests, following either the T.P.I. procedure or the more recent A.S.T.M. procedure Designation D 1761-68 (1968). A tensile test has been proposed by Dudley, 1966, and A.S.T.M., 1968, to help evaluate the net tensile strength of steel, in addition to the strength of the truss plate teeth. 6 Deflection and creep characteristics of trussed rafters with metal plate fasteners were reported by Sliker (1965). The effect of three different types of metal plates, as compared to nail-glued plywood, as well as variations in moisture content, was reported by Radcliffe (1964). Moisture content cycling of trussed rafter joints was reported by Wilkinson (1966). An extensive series of Canadian trussed rafter tests to develop general performance criteria was reported by Hansen (1963). The effect of member stiffness and moisture content history on the deflection behavior of trusses fastened with metal plates was reported by Kawal (1965). Suddarth (1963) reported on a detailed analytic study of W-trusses made with metal gusset plates, including the moment-rotation effect at the heel joint. This was his initial study, and reported that A workable formula for the rotational slippage- resisting moment relationship has been devised and tested for nailed joints with wood gussets by Perkins (1962). (He was referring to Perkins' conclusion that the torsion formula for the force on the extreme nail is suitable.) As yet, unpublished pilot experi- ments with short-tooth, long-tooth and nailed metal gusset plates have shown that the same fundamentals apply to the same degree. The rotation-moment formula is derived from the load-slip characteristics of a single fastener and considers the arrangement of the fasteners about their centroid. Suddarth continued his study to analyze a 26'-8" span, 3/12 slope, 2"x4" W-truss as if it had rigid joints, then as if it had pinned joints but continuous chords and assumed that actual member moments in this metal plate connected truss lie between those obtained in these two cases. 7 A second report by Suddarth (1964) also concerned the fastener stresses, particularly the moment resisting capacity of metal plate joints. He reiterated his earlier conclusion (noted in the preceding paragraph). He also described a heel plate reduction ratio, Pk/Fki, in which; Pk = unit nail, tooth, plug, or psi value of connector, Fki = extreme force on an individual fastener due to moment being transferred at the joint. Suddarth's reduction ratio for 24' trusses with short-tooth metal plates varied as follows: Top Bottom Pitch Area Area Ave. Zk/lz .906 .848 .877 4/12 1.045 .616 .732 6/12 1.113 .527 .820 These percentages of allowable heel plate connector values were later adjusted to a uniform scale and adopted by the Truss Plate Institute (T.P.I.) as a practical engineering means of heel plate design to account for loss in heel strength due to moment transfer and eccentricity. The Federal Housing Administration in its ”Trussed Rafter Criteria" (1960) has always required a heel plate analysis based on the net verticaI reaction, the distance from the intersection of member centerlines, and the polar section modulus of the heel plate. The FHA requirement is described in more detail under "Typical Calculations" and illustrated in Figure 8. 8 Misra (1966) studied the stress distribution in the punched metal plates at a straight tension joint and con- cluded that even for this type of joint the tensile stresses are not uniform. The maximum stress he calculated was 2.4 times the average, and was based on the distance from center- line of joint to tensile area being considered, much like rows of rivets at a riveted joint. He used a difference equation, as well as the principle of minimum complementary energy to predict stresses and got good agreement with experimental results. Der-chun Lee (1965) did an experimental analysis of a king-post truss with semi-rigid joints, measuring the rela- tive rotation of the top chord with respect to the bottom chord by means of the Moire Fringe effect. He assumed the rafter member is supported by a continuous elastic foundation, i.e., by equally spaced nails, which yielded analytical results reasonably close to those found experimentally. Ivan Dah-Wu Chow (1965) worked along with Der-chun Lee on the analytical work and reported that the analytic results, using the assumption of semi-rigid joints, were closer to experimental results than the assumption of rigid joints. CHAPTER II PURPOSE The purpose of this investigation was to develop a simple testing procedure and make a theoretical and experi- mental study of the contact shear stresses and the buckling stresses of light gauge metal heel plates used on wood trussed rafters. The specimens tested were fabricated with a variety of truss plate sizes from each of two manufac- turers. Three different species of lumber were used. CHAPTER III THEORETICAL INVESTIGATION The theoretical analysis of the heel joint was made by first describing the types of failure known to occur. These failure types are all caused by overstress. The next step, therefore, was an attempt to develop a rational design through prevention of premature failure by consideration of the types of overstresses that resulted in failure. Types gf_Heel Joint Failure Assuming that the metal gusset plate is sufficiently strong to be properly impaled, there are four types of failure that can occur at the heel joint: Tensile Failure Tensile failure can occur when the length of plate in tension (and consequently the number of teeth) exceed the "development length." "Development length" refers to primary tensile joints and means the length of truss plate contact area necessary on each side of the joint to balance the net steel section in tension at the critical location. The development length is similar to the minimum permis- sible anchorage for reinforcing bars in reinforced concrete 10 ALI“' 3...: ‘ ‘I'I I nrrIIIQ I’ll! III ‘4Il‘ 11 construction. Development length in that case refers to the bar length that must be used to develop the strength of the reinforéing bar. The concept has been described in detail by Ferguson (1958). When the contact area exceeds the development length, as when a longer plate is used, no extra strength is gained because the plate will fail in tension. The extra length, beyond the "development length" may add to better appearance, but can not increase the strength because the net tensile V strength limits the joint performance. This concept of development length is a means of assuring that contact area and net tensile section are both considered as possible limitations on joint strength. When riveted joints are designed in steel construction, both shear area of the rivets, as well as bearing area on the connected parts, must be checked, with the more limiting factor gov- erning design. In the case of punched metal truss plates, connecting timber tension joints, both contact area on the wood and net tensile section of steel must be considered and the design is limited by the smaller value. Development length is the minimum length required for the contact area to develop the tensile capacity. Truss plate areas shorter than the development length will be limited by their contact area stress, whereas those truss plate areas longer than the development length will be limited by net tensile capacity. Development length, then, I 12 is a convenient expression of the maximum contact length that may be used without being limited by the net tensile strength of the steel. The development length is affected by the truss plate's thickness, percentage of holes, and yield or ultimate tensile stress of the steel being used. In addition, Since the tooth, nail, or plug value of the truss plate contact area is dependent on the density, specific gravity and species of lumber, these wood properties affect development length too. Development length is a property of both the truss plate and the lumber. The same connector plate will have a longer deve10pment length in balsa wood, due to its lesser nail holding power, than in white oak. For a heel joint to fail in tension, the contact area of the plate provides more strength than the tensile cross- section. While this type of failure is much more common at true tensile joints (such as lower chord splice joints), it can be a factor in heel joints that are placed parallel to the bottom chord. The triangular contact areas on the top and bottom chord develop increasingly large tensile stresses in the small isthmus between teeth at the smallest end of the triangular area. See Figure l. Tensile failures can be prevented by providing more net section of steel, either by thicker or wider truss plates, or by reducing the percentage of holes in the truss plate surface, or by properly positioning the plate to prevent excessive tensile stresses. . “‘- l3 \\'Most likely location of tensile tears. Figure l. Tensile failure at heel plate. / \/\ i? D \__L—Note ends of plate are no longer true due to lateral diStortion. Figure 2. Plate buckling along shear line. .I 14 Tooth Failure Tooth failure refers to withdrawal of the teeth from the wood. Normally this occurs by progressive enlargement or elongation of the entrance area of the hole which the tooth makes in the wood during impalement. As this entrance area of the hole becomes more and more elongated (due to exceeding the bearing capacity of the wood) the tooth attempts to follow the slope of the hole by bending. The further the tooth bends, the more nearly it is loaded in withdrawal (as opposed to its typical shear loading). Eventually, the tooth is bent nearly 45° back from vertical and pulls out of the hole entirely. It has been found that teeth being bent back toward their original hole in the parent steel are more vulnerable, less rigid, and weaker than teeth which are being bent~ further away from their original plane (within the parent steel). However, that was outside the area of this research and was not investigated further. Wood Failure Wood failure occurs when the truss plate teeth essen- tially retain their original shape and direction, yet tear through the wood fiber. Wood failure results from the tooth exceeding the bearing capacity, and/or the shear parallel to grain capacity, of the wood. It may be counteracted by either choosing a denser species or by increasing the size of the metal plate. Wood failure and tooth failure are inter-related. 15 Buckling Failure Buckling failure occurs along the shear line (i.e., the crack between the top and bottom chords)~and is related to truss plate thickness, size and shape of holes (or more precisely, the isthmus size, shape, and thickness between holes), orientation of holes to the shear line (i.e, paral- lel to it, perpendicular, or some angle in between) and size and shape of over-all truss plate contact area. See Figure 2. Description gf_Stresses in_the Heel Plate It has already been established by Misra in a straight tensile test that the stresses in the isthmus between holes in the surface of the plate vary approximately linearly with each row of teeth from the end of the plate to the tensile joint. This verifies the commonly held belief that each tooth provides equal value. However, this is only true where it is a straight tensile joint with no eccentric effect. Further, Misra showed that the teeth, holes, and metal between holes of a thin truss plate behaved exactly the same as the theory has always been for rivets making tensile joints, as for example, relatively thick boiler plate. At a heel joint, there are both axial forces and eccentric forces, due to the type of joint. The description of these two types of forces, as they affect heel joints, follows: 16 Axial Contact Area StreSses Axial contact area stresses which result from the direct forces in the members must be contained and resisted by the joints. These so-called axial forces, then, must move toward the surface of the member in the vicinity of the truss plate. They may move considerably away from the axis of the member. It is possible to place a truss plate in such a position that it fits less than half way onto one of the members, thereby not even passing over the axis of the member. See Figure 3. Since the members are mono-planar in a metal plate connected wood truss, the heel gusset plate can not occur at the intersection of center lines because the lower chord butts into the bottom edge of the upper chord.. It is essen- tial that the direct forces in the members be taken by the metal plate at this contact line between the members. By keeping the metal plate essentially centered over the crack, half the contact area will be on the top chord and half will be on the bottom chord. Then, making the usual assumption, there will be a uniform load on the teeth due to these axial forces. Eccentric Contact Area Stresses Eccentric contact area stresses are caused by the eccentric force, or rotational moment, brought into play by the fact that the two contact areas (one on the tap chord and the other on the bottom chord) each have their own distinct centroids and that these centroids are separated by a certain distance, e. See Figure 4. 17 .4.u Menace no we: oumam.aoom .muonEoe mo mwxm uo>o mmmn we: meow .uaw0n on» Ho>o .pououcou pawn: .oumam mmsub “\II cuozu Eouuom e\V ouwam mmahh A. \\ \\.\\ .d\\\\ —I \\ .+ ulu\\\\\\ ‘ \ .m ohsmwm :owumuoq Haw: . euogu FI‘ 90H. v \ . 18 .uaosoz mewumwmom ufiuueouum .e ouamwm .H was so .meupom amazeswao: on» :ooSuon :u: ouqmpmwu on» >9 vomzmu on on mucomnm geese: wcmumwmom uwuucouum one u _ . . Tx {IAIHAAAAV . . . \\\/u I..l nm' NH acosoz \\\\\\\V wcwumflmom ownuaouom 19 To determine the magnitude of this rotational moment, both the size and direction of the forces must be known, as well as the distance between centroids of_their respective contact areas. It would first appear that the magnitude and direction of the axial forces could be used, but closer inspection shows that these are not in fact equal or opposite since the top chord is on a slope and has a larger force than does the bottom chord. a. The horizontal torsion component results from the force in the bottom chord contact area. This force must be parallel to the chord since there is no vertical component (except when the top chord is birdsmouthed to bear on the support, letting the bottom chord hang in such manner that any ceiling load must be transmitted vertically into the top chord by the connector plate). This means that the force on the top chord contact area must be equal and opposite, rather than parallel to the slope of the top chord. The vertical component of the top chord force must be transferred directly to the support from the top chord by crushing on the very small feather end of the scarf cut of the bottom chord. This is due to the tight fit between chord members at the heel joint. A tight fitting heel joint is the general rule Since it is the simplest joint to cut, easy to 20 clamp together in a jig, easy to inspect, and the wood-to-wood contact area is longer than other joints. See Figure 5. c. The rotational moment is due to the vertical dis- tance, e, between the centroids (c.g.u) of the upper chord contact area and the centroid (c.g.b) of the bottom chord. This concept is illustrated in Figure 6. Shear Stress in the Steel Shear stress exists in the steel, being a maximum directly over the crack, since the top chord area is in com- pression and the bottdm chord in tension. The heel plate must resist the entire axial force of both member, causing these shear stresses. Since the members are very large and stiff, compared to the plate, which results in the_shear stress being essentially uniform along the shear crack. Pr0posed Heel Joint Contact Stress Calculation MetHEd The direct stress, b, is found by dividing the axial force, c, by the "effective" contact area At.c.a ("effective" area means that the nails within 1/4" edge distance or 1/2" end distance, assumed too close to the crack to be useful, have not been counted). 'The eccentric moment stress, c, is found by multiplying the force under consideration by the distance, e, to the opposite force, and dividing this quantity by the polar section modulus, Zp. 21 .wzwumon vooz-ou-vooz kn :oxmu mouuom Hm0fiuno> .m enamfim 22 .unoaoa HanoMumuom .o ouamwm “mg I l ouamumflw In). II R omuo :xIb n. \J. / \\\ \X . 9‘ c. .+ \ \\\ s I. QomoU \ \ AU m} u o \ \\m\* e t \A \\\ 0+ voaammm \I \ . 853mg 28 ..x\N.Afl\ Pad _ no Aw: weasmmm oucmumwv omvo : “fl rm: . I a bk \04 23 The direct stress, b, and the eccentric moment stress, c, must be added vectorially, b ++ c = a. The resultant, a, therefore depends on the angle, A, between "b" and "c," as well as on their relative quantities. This vectorial addi- tion may be performed by the use of the Cosine Law, a2 - b2 + c2 - 2bc cos A. By noting which direction the vectors "b" and "c" point with respect to each other at each corner, the critical corner can be located so the Cosine Law solution need be applied only once, instead of at all four corners. Normally, the Critical corner will be the outer- most top chord corner, due to its having the largest angle, A, between "b" and "CV because of the effect of the top chord slepe. See Figure 7. Comparison of Existin Heel Joint AnaIySisFMet ods There are several alternate procedures for determining heel joint contact shear stress, as described below: General Method The general requirement of heel joint analysis is that the connections be designed to provide adequate capacity for the direct axial forces at the joint involved. Normally the effects of eccentricity would be neglected by most engineers not familiar withethe FHA or TPI requirements mentioned in the Review of Literature. 24 .mmouum vocwpaou new :ofiufivuw Houuo> .u ouamfim :k); u .oougu nonuo one me man we cusp n pounce wasp um weaned on on < oawam momamu omega whose mos 25 TPI Method The Truss Plate Institute requires, in their specifi- cation, TPI-68 that: To allow for moment effects at the heel joint, design the heel plate to have sufficient capacity to withstand the direct axial stress of the top and bottom chords by their respective nail, tooth, or plug groups, with the following reductions in allow- able nail, tooth, or plug load: Under 3/12 slope 85% of allowable 3/12 to less than 4/12 slope 80% of allowable 4/12 to less than 5/12 slope 75% of allowable 5/12 to and including Sk/lz slope 70% of allowable Over 53/12 slope 65% of allowable FHA Method FHA requires that the eccentric moment be found by multiplying the net reaction, Rn’ at the support, by the dis- tance, e, measured from the intersection of center-lines of the top and bottom chord to the centroid of the connector plate. Then eccentric moment stress is added vectorially to direct axial stress to determine the critical stress. See A Figure 8. Proposed Method It is proposed that the eccentric moment be computed by using the bottom chord axial tension force, T, multiplied by the vertical distance, e, between the centroid, c.g.b, of the bottom chord contact area and the centroid, c.g.u, of the upper chord contact area. This eccentric moment results in an eccentric stress that must be added vectorially to the axial stress to obtain the critical stress. 26 .mwmxamnm AHMUAHucouuo fiuuommm ~.:w m.o~ u noun o>fluuommo pea «SEA «\m-e u so A =e\n , rm. Mumuo we umoa wou< «.cw ~.mm u «can oumam mmouo :m ooeaa Hoe: Hoowase .fievm oesmfim .oofl ooo.~.u ea .mnH coo.m u H ..mna ooa.n u U \4 III— .11.\\ \ :oH\HH-m 1k 30 3,000 lbs. (top chord force) .a. H ‘< z n u u 3 000 x 1.42" + 3 000 x 4 x 0.98" I2 #055 This: 4040 + 930 = 4970 lb.in. z a Combined stress equation (FHA) P + M - 3,000# + 40409" + 930 2K' 23' 2 x k x 3 x 5 2’x 14.61n.1 2 x I4.6 8 200 + 138 + 31.8 = 369.8 psi The direct stress is 200 psi and the torsional moment adds 85% to total 370 psi. . Figure 9(b). Typical Heel Plate Contact Stress Calculations for 3"x5" Plate. 31 J‘s Try C = 4,800 lbs. (top chord force) M = 4 800 x l" + 4 800 x 4 x 1.00" M - 4,500 + 1,517 = 6,067 lb.in. Combined stress P + M a 4,300 lbs. + 4,550 1b.in. 2K 25 TxkxTxB' 2x34.16in.3 . 200 + 66.5 + 22.2 288.7 psi 1 517 2x 31.16 The direct stress is 200 psi and the torsional moment adds 44% to total 288 psi. Figure 9(c). Typical Heel Plate Contact Stress Calculations for 3"x8" Plate 32 = %E,Vb2 + d2 = 29.45 in.3 Try C = 5,000 lbs. (top chord force) SP M =-5 000 x 2.33" + 5 000 x T2 x 0.6" = 11,050 + 950 ms first Combined stress: P + M43 5 000 + 11 050 + 950 2A' 23' 2’1 klx 5 x 5 2 x 29.45 2 x 29.45 s 200 psi + 188 + 16 = 404 psi The direct stress is 200 psi but the torsional moment adds-102% to total 404 psi. Figure 9(d). Typical Heel Plate Contact Stress .Calculations for 5"x5" Plate. Proposed method: b = C = 3,160 lbs. = 119 psi Knet 2 x 13.25 1n.2 c = 3,000 lbs. x 1.25 in. = 34.7 psi 27x 54 in.3 each Cosine Law: 2 a (119)2 +-(34.7)2 - 2(119)(34.7)(-O.65) 143 psi a Shear stress: Assume the critical shear section is approximately 50% holes: S s C (it 3,160 lbs. 9" x /(4)2 + (12)2 x 0.035 in. 12 = 9,550 psi where 1d = length of plate along shear line t = thickness of plate (A comparison of these four theoretical heel joint calculation methods for 3"x5", 3"x8", and 5"x5" heel plates (See Figures 9(b), 9(c), and 9(df) yielded the results shown in Table 1. These three plate sizes were later studied experimentally, too. Calculation of Tensile Stresses within the Bottom’ChordEantact Area Assumptions It is assumed that the plate is positioned parallel to the bottom chord, with equal "effective" teeth into both 34 mam omo.HH HHS omo.nH . A.SSN SON ooo.m smxsm meN oom.e maN oao.e A.ooN ooN cow.e swxzm m~n oeo.e wen ‘ oom.e A.SEN ocN oco.m smxzm moopom fl.efi.eflv mmosom fl.cfi.aflv fiaco cu vouuo>cou «one uuogm ~.=« mmuo.c u :cnc.c x :m\n "zou non noun umozm «02 .cm 2.5.... u «cm x :03... 3» :Nnme "mag—5mm you «one onmcou uoz III. I; macaw Eouuom . H 5. goo,— N u a m Aunmv e< < e m m e mfiwez U\e N all 55500 vN mN NN HN oN ma wH mg on ma ea 37 Assume uniform shear along the.crack line; which is assumed further to have only 50% effective area (the other 50% holes). The shear per lineal inch will be 3,160 lbs. - 332 lbs./in. 9%" x 2 SIdEs x 50% (166 lbs./in. III’Gross Shear). Assume 50% net tensile area at all sections with teeth cut out. .. Assume allowable shear stress is 2/3 of allowable tension stress, and that the net shear area is 2/3 as effective, per inch, as the net tension area due to this 2/3 relationship., Tension section A-A (3 effective teeth 8 34.1 lbs. per tooth, A {(7 x 13/32") + 6/32"} x 0.036" x 50% - 0.054 in.2 net section in tension, 3/16" net shear line length. Section A9 ‘ 3 teeth x 34.1 lb./each - (78 tensile strips @ 0.0073 in.’) + 0.0045 21,730 psi Section B- 10 teeth x 34.1 1b. = 5,600 psi (6% strips x 0.0073) + (18 x 0.009) ' Section c- l6T x 34.1 lb. 8 8,240 psi (6 x 0.0073) x (23 x 0.009) 38 Section D- 21 x 34.1 = 10,000 psi (58 x 0.0073) x (3% x 0.0009) Section E- 26 x 34.1 = 12,100 psi (42 x 0.0073) + (43 x 0.009) Section F- 30 x 34.1 = 13,000 psi Section G- '34T x 34.1 = (38'x 0.0073) + (6% x 0.009) Improvements to Calculations 13,800 psi Since the "slip" is uniform along the shear line (crack between the top and bottom chord), the shear stress must also be uniform along the crack, rather than different in each section as indicated in the preceding set of compu- tations. If the shear stress is in fact uniform, then the amount of shear force at each strip may be the tooth value tensile force to determine tensile force to be carried by net tensile isthmuses between the holes. This concept subtracted from the effective section of the is used in the following calculations for the same sections used before: Shear force per strip 125 lbs./strip 332 lbs./in. (net x 3/8" strip) 39 Section A- 3 x 34.1 lb. - a x 125 1b. = 730 psi 7% strips x 0.0073 in.2 Section B- 341 1b. - 1% x 125 lb. - 3,200 psi 6% x 0.0073 in.2 Section C- 545 lb. - 2% x 128 = 5,300 psi 6 x 0.0073 Section D- 715 1b. - 6% x 125 = 6,920 psi 5% x 0.0073 Section Es 886 1b. - 4% x 125 = 9,850 psi 0.0328 Section F- 1023 lb. - 5% x 125 = 11,500 psi 0.292 Section G- 1160 lb.- 6% x 125 = 15,550 psi 0.0256 Buckling and Shear Stresses in the Steel Investigation of the Cause of Buckling A small element centered over the shear line will be in a state of pure shear. The element may come from the area 40 123 - Et’ or that vicinity, on the truss plate shown in Figure 10. Figure 11 is a blown-up view of this element. Since pure shear can exist only in one particular plane through a two-dimensional element, there also exiSt tensile and compressive stresses on other planes through the point. The maximum and minimum normal (principal) stresses occur as shown in Figures 12(b) and 12(c) on planes that bisect the angles between the planes on which the given Shearing I stresses act, and these principal stresses are equal in magnitude to the shearing stresses. The shearing stresses on these 45° (principal) planes are equal to zero. The principal stresses at a point are used to compute the shearing stress as follows; T = % (Gmax - 0min) in which a principal stress is considered to be positive if it is a tensile stress and negative if a compressive Stress. Furthermore, this maximum shearing stress occurs on each of the two planes that bisect the angles between the planes on which the maximum and minimum principal stresses occur. Compressive buckling, applying this concept to the truss plate, is caused when the compressive stresses that result from the shear exceeds the Euler formula critical level. The direction of the buckling can be determined, prior to its occurrence, from the slope of the shear line, rotating 45° to get to the maximum compressive stress. 41 Element 12-1/2-ET, subjected to pure shear along the plane of the shear line. Figure 11. Element on shear line. B Figure 12. Free-body diagrams of shear element. 42 Discussion of Shear Stress in the Steel The shear stress in the steel at the crack is uniform along the plate. If the truss plate is oriented parallel to the shear line and centered over it, the equal contact areas will provide an approximately equal number of effective teeth into each chord member. Since the "parallel to shear crack" orientation keeps the eccentricity of the two contact area centroids (see Figure 13) approximately the same as the "parallel to bottom chord" orientation, the effect of the eccentric moment will be minimized. The "parallel to crack" orientation permits a more precise determination of cross-sectional area at the shear crack than does the "parallel to bottom chord" orientation. Since the tooth hole punch-outs are located in uniform rows (in one of the types of plates investigated), in line with each other, the net steel area parallel to either the "die direction" of the plate (b, which is always equal to some multiple of 2-1/4") or the "across die direction" (h, which is equal to 2-7/8", 3-11/16", or 5-5/16”) is about 50% of surface area, at the critical section of that particular ‘plate type. For orientations of the plate other than "parallel to crack" or "perpendicular to crack," it is much more difficult to precisely compute effective net shear area, due to the unequal waythe rows of teeth cross the shear line. This can be easily seen in Figure 10, which is shown for a 4 in 12 pitch. 43 .mcvoAmoa ooeaa Hoe: oooeuoufio sou sofioasocooom .mH ousmua, E E E wom uo>o wow u mono Hoonm poz wow u «ohm Hmocm uoz ma mono Hoogm uoz NH D N 0 NH m H 0 S N 0 cfilsld \ 44 Since the net steel area exactly parallel or exactly perpendicular to the plate, measured along the critical line, is 50% (for this particular manufacturer's plates), no other plate orientation results in a shear line of less than 50%. For design purposes, it could be assumed that the net steel was 50% of the shear line length. This assumption is conservative. Calculation of Shear Stress at Critical Section The calculation of shear stress at the critical section uses the conventional formula: S5 = c = c 2(plates)Lt 50%(net) E? where C top chord compressive force (which acts parallel to the shear line) L = length of plate along shear line t = thickness of plate From Figure 9: S = 3,160 lbs. = 9,550 psi 5 9" x /(4)2 + (12)2 x 0.035" '12 For a similar plate parallel to the crack: 85 = 3,160 lbs. = 10,050 psi 9” x 0.035" This shear stress must be transferred through eleven full size steel sections, 0.375 in. x 0.035 in., and two half sections 0.1875 x 0.035 per plate. These sections are approximately 13/64 in. high (0.203 in.). See Figure 14. 45 Figure 14. Critical shear stress (buckling) area. 3 s P = 131.8 lbs. 5 A 3 x 0. $ 10,050 psi Figure 15. Free body diagram at shear line. 14). 46 Analysis of SectiOn A-B-C-D (shown hatched in Figure a. Shear force on line E-F = 3,160 lbs. = 3,160 22 thl sections + 4‘half secIIons 22 + 2 131.8 lbs. per section b. Shear stress on a full section, such as E-F = s = s = 131.8 lbs. = 10,050 psi 2 A x (This checks with the general calculations on the preceding page.) c. From Figure 15, the stress at the line C-D can be computed by assuming that C-D-E-F is a short canti- level beam, 3/8" deep, 13/128" long, 0.035" thick, with a concentrated load of 1,318 lbs. at the end. d. Section Modulus, S, at section C-D = bd2 = (0.035 in.)(.375 in.)2 = 0.00082 in.3 6 6 e. f = P1 = 131.3 lbs. x 13/128 in. = 16,300 psi UN: S‘ 0.00082 in.3 CHAPTER IV EXPERIMENTAL ANALYSIS General A variety of heel plate sizes and shapes were used to test the proposed heel joint analysis method. A small 8'-0” test specimen and corresponding jig were developed and used to permit a large number of different specimens to be tested quickly and cheaply. Each type of plate could have Several repetitions very easily to confirm results. A second set of 8'-0" specimens was built and matched to 24'-0" trusses to correlate the load-deflection data with full scale trusses. Lastly, Stress-Coat brittle lacquer was used to determine location and direction of the principal stresses. Test Specimens The initial set of test specimens were built using 20 ga. TroyTrus plates of various Sizes of the type Shown in Figure 10. The lumber was all 1500f Industrial Light Framing West Coast Hemlock. All the plates and lumber were supplied, and specimens fabricated,by Troy Steel Corp. using a press assembly similar to that shown in Figure 19. All the lumber was kiln dried, but no attempt was made to determine moisture content or specific gravity. See Table 2. 47 48 Table 2. ~List of Specimens Tested. No. Size Mfr. Lg. Pitch Species. Grade Remarks 1 3 x 10 TW 8' 4/12 Doug. 1500f Z 3 x 8 H H H "O H 18 3 3.7 x 6.7 TB " " Hem, " 4 5 x 7 TW " " Doug. " 5 S x 5 H H H H H 18 6 2.9 x 6.8 TR " 6/12 Hem. 1500f (1) ‘7 3 . 7 x 4 . 5 H H H H H 8 H H H H H H H (1) 9 ‘Zr. 9 X 9 H H I! H H 10 3.7 x 2.2 " " " " " (l) (S) 11 2 . 9 x 6 . 8 H H H H H l;_ 2.97; 2.2 " " " ” " (6) 13 5.3 x 4.5 " " 4/12 " " 14 3. 7 x 6.8 H H H H H 1 5 2 . 9 x 9 H H H H H 16 5.3 x 4.5 " " " " " (l) 17 H II M H H H H (2) 18 H H H H H H H [31 19 S . 3 x 6 . 8 H H H H H 20 2 . 9 x 9 I! H H H H 21 3 . 7 x 6 . 8 H H H H H 22 3.4 x 5.1 DU " " " " (3) 23 3 7 x 6.8 TR " ” " " 24 L: x 6 . 8 H H H H H L3; 25 3.7 x 4.5 " " " " " (2) (5) 26 5.3 x 4.5 " " ” " " (2) 2 7 5 . 3 x 6 . 8 H , H H H H 28 H H H H H H I! 29 3.7 x 6.8 " " " " " (1) 30 2 . 9 x 9 H H H H H 31 5.3 x 4.5 " " " " " (2) 32 33 3.4 x 5.1 DU " " " " 34 2.9 x 9 TR " " " " 35 3 . 7 x 6 . 8 H H I! H H 36 3.4 x 7.6 DU " " " " 37 n n n n n n n (3) 38 3 x 5 TW " " Doug. Const. 39 H H H H H H H 40 3 x 8 H H H H H 41 n n n n 'H n H 42 5 X H n n n n [7) 43 H H n n n n n (7) 44 3 x 5 II 24! H H H 45 H H H H H H H 46 3 x 8 H H H H H 47 H H H H H H 'I H H H H H 49 Table 2. (cont'd.) No Size Mfra Lg. Pitch Species Grade Remarks 49 5 x 5 TN 24' 4/12 Doug. Const. 51 3 x S " 8' " Wh.Fir. 1650f 52 H H H H H H H r—S'g X 8 n n n n n 54 H H H H H H H 55 S x 5 H H H H H 56 WT WT H N If T H 57 " " " " " Doug. Stand. 58 L H H H H H H 59 3 x S " 24' " Wh.Fir. 60 H H H H H H I! 61 3 x 8 H H H H H 62 H H H H H IT H 63 5 x 5 H H H H H 64 I! H H H H H H 65 55/16x41/2‘TR 8' " w.Hem. " (2) 66 311/16x63/4 " " " " ” 67 311/16x41A2 " " " " " 68 N If If H 1' 1! H 69 55/16x41/4" " " " " (2) 40 H H H H H H H (2) 71 H H H H H H H (2) 72 55/16x63/ " " " " " (3) 73 H H H H H H I! 74 H H H H H H II p 75 H H H H H H II (1) 76 H H H H H H 1500f (1) 77 H H H‘ H H H H (1) 78 3 x 5 TW " " Doug. 1500f 79 H H H H H H H 80 H H H H H H H 81 H H H H H H H H H H 0 H H H % n n n u2v4 n n 71 84 H H H H H H H 5 H H H H H H H 86 3 x 8 H 8' H H H (4) 87 H H H H H N H 88 H H H H H H H 89 H H H H H H H 90 S x 5 H I! H H H 91 H H H H H H H 92 H H H H H H H 93 H H H H H H H 94 3 x 8 " " ” Wh.Fir. 1500f 95 H H H H H TT VT 96 H H H H H H H 97 H H H H H 17 H 98 3 x S " " ” Doug. " Table 2. 50 (c0nt'd.) No. Mfr. Lg. Pitch Species Remarks 99 100 H H TW 8' 4/12 Doug. "O 101 102 103 Wh.Fir. H (4) 104 105 106 H H 'I 107 108 109 H H H "Lg." in Table denotes length of test specimen. "Mfr." in Table denotes manufacturer of truss plates as follows: . TW stands for TrusWal Systems TR stands for Troy Steel Corporation DU stands for Duratile. parallel to crack perpendicular to bottom chord perpendicular to bottom crack testing machine Two plates each side Three plates each side Remarks" (1) Plates (2) Plates (3) Plates (4)' Riehle (5) (6) (7) Plates not impaled properly 51 The second set of test specimens, including 24'-0” trusses, were built using truss plates of 3"x5", 3”x8", and 5”x5” of a second type, shown in Figure 39. The lumber was of Coast Region Douglas Fir for one set, both 8'-O" specimens and matched 24'-0" trusses, and white fir for a second matched set, both 8'-O” and 24'-0". Truss plates of 20 gauge steel were applied without nails, using a roller press. Moisture content and specific gravity at time of test were determined for the top and bottom chords of each test specimen and are recorded in Table 3. Test Jig For the first series of tests, a small 8'-0" long test jig with single hand-pumped hydraulic cylinder (Blackhawk Mfg. Co., Milwaukee, Wis., 53227, Model R159 Porto-Power 10 ton capacity, 6" travel, 1.688" diameter ram with Model P76 pump) was built as shown in Figure 17. The actual jig is shown in Figure 20 with a test specimen in place. For the second series of tests, a wall mounted full scale hydraulic test jig located in the Michigan Building Components plant on Decker Road, Walled Lake, Michigan, was used to test the 24'-0" trusses. It is shown in Figure 21. For the third series of tests, an old Riehle Testing Machine located in the Forestry Building, Michigan State UniVersity, was used to test 8'-0" specimens. It is shown in Figure 22. SZ . . m.amH o~.oo mw.mo : P am new H N oH Hom.o H~.oH m.wHH mm.qm am.mo : m cm . w c.mH qoe.o H~.mH m.mmH o¢.¢o ow.oa : e mm mos oqm.o so.mw. m.mmH «m~.oq oo.¢m : m mm . » m.cH qwm.o *w.aH v.5mH Ha.~m no.~o : a mm NOH m~v.o so.oH a.~vH em.mm Hm.mo = H mm m . w o.oH Nam.o Hc.mH m.mmH on.Hm mm.Ho = a Hm oHe HmH.o H¢.mH m.mmH Ho.Ho ma.~n opHas m Hm . . mam.o sm.hH m.QNH H¢.Ha mH.¢m : a me mhvm *mm 5H on.c Hm.oH m.qu om.ea mm.om z m as m m. w w.aH mmm.o “H.wH o.omH ou.om Nm.mm : e we H ~mq.o “v.5H m.mNH ~5.Ho me.~n : m we . . 55¢.o sw.aH «.mMH mm.me ma.¢a : e as mma won OH ovq.o Hm.mH ~.~mH mo.mm mm.ao : m as moo. .mm.mH Nao.o wo.~N o.HmH Hm.ww «5.50H : s cc . mmm.o «5.9H ~.mQH oc.wm. mo.Hm : m as . . omm.o *m.aH «.msH ao.ma Na.mw : a me OHHm me NH ~m¢.c *o.hH H.5mH m¢.ao Hm.mMI. = m we . . mo¢.o wm.uH e.qu wu.ao wo.ma : a we mmmq won NH ~om.o NH.mH “.mMH 0H.mw Ho.wn : m as “cm. s q.wH Hem.o wo.mH n.wHH em.¢o ”0.55 z b He cam.o wN.aH o.HmH mq.hh mm.om : m HH . . mHm.o Hm.wH m.mNH Ho.ao mo.om : H OH OHmm smv mH mmm.o m¢.mH o.NMH -wH.mw¢ oo.ow : m ow . . mma.o *w.NH o.mmH ma.am a~.wc : H mm mHHQ wmq NH eme.o wH.hH w mmH mm.mo om.ma : m owl . em .o omm.o Ha.wH o.omH mo.ao mN.ow : H mm mNOm H N mmq.o x|wo.HN m.NmH .m~.so NH.ma .mzoa H mm awv fiwv floov Hwy mug >uw>mpo acoucou zufl>muu ucoucoo .HmmHQ .uz .uz ommwoomm ogsummoz owmfioomm ousumwoz Hope: xho co>o umoh mowooam .02 .oon ommuo>< .xpfl>mpo oflwwooam dam Humanou ohsumfioz .m oanmh 53 qu.o * N.NN mam.o ”N.QN N.N©H mH.cOH Hm.mNH :. s cm Hov.o NN.NH «M.HNH samba Hm.omw+ ; m om mmm.c N.m.HN Nam.o NN.NN c.0NH wN.moH No.NNH z a mN No¢.o NN.ON N.¢NH mo.HN Nm.Nm : N am; mmv.o N N.mH °N¢.c *m.NH N.¢NH HN.oN OH.ea : N-NN Nom.o HN.NN m.NoH .NH.mN mo.NOH .mson m NN mmm.o » o.mH Noe.¢ HN.NH H.mmH oN.mo om.¢N z , N awn . omeo N¢.HN N.NOH NN.mo MN.NN z m we . mo<.o w o.mH ‘Nme.c NH.NH c.HOH H¢.¢N NH.NN : N mo . .NNm.o NN.Nm m.omH mm.mm 2...:w : m me mam.c w N.oN mom.c NN.NH N.NNH NN.mm NN.mo : N No _ NN¢.o NN.NN m.oeH mmuom» Ho.oN : m No . . eH¢.o No.NH m.moH No.ON mH.mN = a He ace o Nmm mH Nam.o Nm.ON m.HNH OH.NN Ho.NN : m H omn.o N N.HN oom.o No.0N m.omH NH.Nm mm.wo : H CO emm.o NN.NN m.HOH mm.no No.mm. z m so . . qu.o *N.NH H.ooH om.em NN.mo : H mm moqm o *mH oN HNMHDII mm.HN v.mNH om.mm mm.mN oomgz N am . . mNmuo N.ON m.oNH NH.oo Hm.mN : N mm mmHm o s 0 ON condo Hm.ON N.NNH oo.mm mN.oN z m Nm1 . . Nmm.o N.NNH om.No : N Nm «me o N N mH om¢.o NN.mH. m.mmH No.Nm mamMo .msoa m Nm . . Nme.o .N¢.NH o.NmH 0H.oo mN.HN : N om Nam o Nmm 0H mwm.o NN.mH N.mNH .HH.mN NN.mm :, m mwl . . Nmm.o wm.mH N.NNH mm.mv 0N.mm : N mm mmNm o N N NH Hoe.o Nm.oH N.mNH Nm.qm Nm.mo ooan m mm HNV Hwy Huuc Hwy HNV knuw>mhu HfiOHfiOU >HM>NFU H§®HCOU .Hfimfln— .Hz .93 owmwoonm unapmfioz omeoomm ousumwoz hope: sun co>o amok mowuomm .oz .ooam o wuo>< m.v.u:oov .m oHan 54 HNN.N N N.NH NNN.N NN.NH N.NNH NN.NN NN.NN : N NN NNN.N NN.NH H.NNH NN.NN NH.NN NNNNz N NN . . NNN.N NN.NN H.NNH NN.NN HN.NN : N NN NNN N N N HN mNN.N NN.NH N.NHH NN.MN NN.NN : N mm. . . NNN.N NN.NH N.NHH NH.HN NN.NN z. N NN NNN N N N NH NNN.N NN.NN N.NNH NN.NN HN.Nm : N NN . . NNN.N NN.NH N.NNH NN.NN HN.NN : N HN NNN N N N NH NMN.N NN.HN NNNNH NNNNN NHMNN ,: N HN . . NNN.N NN.NH N.NNH NN.NN NN.HN : N NN NNN N N N NH .MNN.N NN.NN N.NNH NN.NN NN.MN : N.NN NNN.N N N.NN NNN.N NN.NH N.NNH HN.NN NN.NN : N NN .NNN.N NN.HN N.NHH NN.HN NN.NN : N NN NNN.N N N.NN NNN.N NN.HN N.HNH NN.NN NN.NN : N NN NNN.N thmN N.NNH NN.NN HmuNN N N NN NNN.N N N.NN NNN.N NN.NH N.NNH NN.NN NN.NN : N NN NNN.N NN.HN H.NHH NN.NN NN.mN\ = N le NNN.N N N.NN NNN.N NN.NN N.NHH HN.NN HN.NN : N NN NNN.N NN.HN N.NHH NN.NN NN.NN, = N NN . . NNN.N NN.NH N.NNH NN.HN NN.HN : N NN NNN N N N NH NNN.N NN.NH N.NNH NmmmN NN.NN = N NN . . NNN.N NN.NH N.NNH .HN.NN NN.NN : N NN NNN N N N NH HNN.N NN.NH N.NNH NN.NN NN.NN : N NN . . . HNN.N NN.NH N.NNH NN.HN NH.NN : N NN NHN N N N NH NNN.N NN.NH_ N.NNH NN.NN HN.NN : N NN . . NNN.N .NN.NH N.NNH .NN.NN NN.NN : N NN NNN N N N NH NNN.N NN.NH N.NNH NN.HN NN.NN : N NN NNN.N TN N.NH NNN.N NN.NH N.NNH NN.HN NN.NNH : N HN NNN.N NH.NH H.NNH NH.NN NN.HN .NNoN N HN ANV mNV moov Amy Hwy NNN>mNo acoucou NNN>NNU acoucou HmmNn .uz .uz ,onNooam ONSNNNoz onNoomm oNSNNNoz Noam: NNQ co>o amok moNuomm .oz .uoam o mNo>< H.N.NNOUN .N NHNNN 55 . . ~mm.o NN.NN N.NNH No.Ne wo.¢m : N moa NNN N N N NH NNNNN NN.~N, N NNH NN.HN NN.NN NNNNN N NNH eom.o N N.NH mmm.o Nv.oa m.NNH om.me mo.Nm : N m _ Immm.o Nm.~H m.~mH. Nm.ve mN.mm : m moH wmm.o N m.vH Nov.o No.vH N.mmH mm.em mm.~o : N NON «mm.o Nm.mH N.Nmfi om.vm mm.~o : m nod Nmm.o N N.NH owm.o quwa m.HmH mo.om wc.mm : N OOH NNMNO Nmmma m.mvH mm.Nv ov.vm : m ooH mmm.o N N.NH HNm.o Nm.NH m.mHH om.~¢ mm.om : N moH Nwm.o No.eN m.mHH oH.HN Hw.ov : m moH ovm.o N N.MH mmm.o N¢.mH w.mvH Ne.me mo.om : N NON .MMM.o NowMN NMMmH mH.NNN NNNNNou .HNNNN .N2 .N2 onNoomm oNSNNNoz onNoonm ohzumNoz Noam: NNQ :o>o umoN moNooaw oz .ooam oMflHo>< N.e.peouv .N oHNNN 56 .coENoomm umou :o-.m .oH oNsmNm .vonapm mcwon unwoN .mHHm3 oumHDENm op MNN umou mo New: on» an onnaNmm oNsch op cam some um “Nommzm come m.¢Um wooNochoN mN chon Moon mNnN \\V NpNono Souuon No camcoav 7 N N .l E; x i /.H... . \\ I (.38 mNHNu Ii:_ :0 mN vonzum oN oN NNNoN Hum: .moNNm> :ouNm_ H mm .NochHNo vmoa oNHSNNwN: Now chNmon anomNcs .Ho>oH ovN>on op umHm S7 .NNN NNNN =N..N .NH oNsmHN smH> Nzomm zmH> :oENoomm umou NNHN NHHNNNN Nam NH NNNNHN ooNN w.wHoa./( owsmm :oNpoonoa vmoH NHQQMI/I op Mooan Hoopm owsmw oNfiomeN: meoENoomm :UNNQ ucouommww NNENom ou mnwxooan woo2;\\ .9539 oNasmeN: :.u:o MGNNUNN: usoguNz onNN 05mm may mcoam AMWumNomo use: chuom NochHNo mmoox IIIIIIIII I. Novao: HmwucoNowsnoNNu .coENoomm mo xwon um oNammon mowamnw NoszHNo oNasvaN:\ mm\fi oamcm QNHU .on:m QNHU umnNmmm voomun mN Nowcwaxu 58 'Instrumentation A Starrett dial gauge, accurate to 0.001”, was mounted at one heel joint as shown in Figure 18. It was mounted with screws on the centerline of the top chord. Its plunger was against a steel angle which was screwed symmetrically over the bottom chord center line. A hydraulic gauge on the R159 Porto-Power was used to read the pressure on the peak of the initial 8'-0” specimen. The gauge had marks for every 400 psi and was read to 200 psi accuracy. This gauge was calibrated on the Instron machine at the Forestry Building, Michigan State University, and the calibration data is given in Table 4, page 64. A hydraulic gauge on the wall-mounted full scale test jig was installed in the hydraulic line at the peak of the 24'-0" trusses as shown in Figure 21. It was marked in 25 psi increments and read in 10 psi increments. This gauge was also calibrated on the Michigan State University Forestry Department Instron machine. The calibration data is given in Table 5, page 65. The Riehle testing machine used for the last series of 8'-0" specimens is mechanically operated and has a balance scale accurate to 5 1b. increments. The heel deflection was read every 200 lbs. of peak force, at the instant the balance arm hit the top. See Figure 22, page 63. Test Procedure For the initial series of 8'-0” tests, on the hand- ;pumped hydraulic test jig, the heel deflection was read 59 N¢—7— .m:-uom omomm HmNn .wH ousmNm .ocNH Noncou can mmoNum mucouxo cNono Eouuon op wozoNom ofimcm QNHUV Ho 3 voNommoE NNNNNN HHN uh0>o . \\ / \ .ocNH Nmogm ‘ :33 on: HHN mN Nomcsam ”:23 G om oamcm QNNU vNonu no» \\\\\\\\ op womEmHo NZNNMNN \\ . mN omnmm HmNn tl‘l - ll..uuonu now on msoNom oz» guNz voucsoe mN wsmw Hmwv uNoQQSm ou oawcm ANNU 60 .mouonm NHnEommm mmdNu mo mucoscom .uaoEonmEN Nouw< may .NH NNNNHN .NcoanmQEN mqfisz wNN NHnEommm mmSNN Nov ANN 61 (a) Test apparatus for 8'-0" specimens. - I. , " , C.) OI’P’q'I—‘I‘.‘,:‘y . Mum (b) Close-up of gauges. Figure 20. Small test jig for 8’-0" specimens. (a) Wall mounted hydraulic apparatus. (b) Close-up of heel, showing gauge. Figure 21. Test jig for 24'—0” trusses. 63 .mnoENuomm :o-.w Now ocwgume umou oanon .NN oNDMNm .ENm commamn wan omsmw Han chzoam 3oN> Nmom .m=-omoHu pcONm may ..\ 53 .uNoQQSN :oENooam cum :oNNNUNHmmm umoq Nov 4 J :1 . , . 2.35:3. .qu r. 7.3 u, . 64 Table 4. Calibration Data for Blackhawk Hydraulic Gauge. Instron Reading Act. Press. Press. Read. #1 #2 #3 #4 Ave. 0 0 0 0 0 0 0 37 25 85 88 83 75 82.75 58.2 50 135 132 128 125 130.00 80.6 75 185 183 180 172 180.00 102.3 100 232 232 229 221 228.50 124.8 125 282 283 280 270 278.75 147.3 150 335 332 328 322 329.25 176.9 175 400 398 397 385 395.00 200 200 446 452 448 437 446.75 218.5 225 487 497 493 482 489.75 240.5 250 537 542 541 532 538.25 264 275 592 595 591 581 589.75 286 300 638 645 642 631 639.00 312 325 693 705 698 687 696.75 335 350 745 757 747 742 747.75 356 375 794 802 797 790 795.75 379 400 845 852 850 838 846.25 400 425 887 902 897 890 894.00 422 450 937 948 946 938 942.25 450 475 1007 1017 1013 1000 1009.25 472 500 1057 missed 1063 1053 1057.67 495 525 1109 1115 1110 1105 1109.75 518 550 1153 1163 1162 1155 1158.25 540 575 1202 1215 1212 1208 1209.25 562 600 1255 1263 1260 1262 1260.00 Blackhawk Porto-Power hand operated hydraulic pump Model R159 Serial #A21233 Area: 2.2365 sq. in. Oil capacity: 13.419 cu. in. 6" travel 1.688" diameter cylinder 8950 psi maximum pressure @ 103 1b. handle pressure 5. 65 Calibration Data for Full Scale Test Jig. Instron Reading Hyd. ress. #1 #2 #3 #4 #5 0 0 0 0 0 0 500 510 575 575 535 560 1000 975 1065 1050 1040 1035 1500 1485 1540 1540 1505 1530 2000 1910 2025 2055 2000 1985 2500 2440 2520 2530 '2500 2490 2496 3000 2935 2970 2960 9240 2910 2943 3500 3410 3450 3430 3425 3400 3423 4000 2910 4065 3960 3920 3915 3956 4500 4455 4290 4405 4410 4390 5000 4900 5000 4950 4900 4938 66 approximately every 400 lbs. of peak pressure. This gave a minimum of five readings and a maximum of ten, depending on specimen type. It was necessary to use both hands to take the deflection data, which necessitated releasing the hydrau- lic pump handle. This in turn allowed a slight relaxation in the pressure, reducing the measured deflection. As a result, it was believed that the load-deflection data from these initial 8"0" specimens indicated too much stiffness. To counteract this possibility, later tests were performed on the Riehle testing machine. Duration of tests varied from five to ten minutes for these tests and all tests were performed indoors at 600 to 650 F, on this hand jigN The second set of tests, performed on the 24'-0" full- scale wall mounted hydraulic jig, took twenty to twenty-five minutes per test. Pressure was applied 24" o.c. using a motor driven pump which maintained constant pressure.' The heel deflection gauge was allowed to stabilize before each reading, and readings were made about every 50 psi, for a minimum of six per test specimen. These tests, also inside, were performed at temperatures ranging from 650 to 85°. The third set of tests, performed on Michigan State University Forestry Department's Reihle machine, involved readings at every 200 lbs. of peak loading. The load was mechanically applied at a uniform speed of 1/16” per minute and readings were made each time the balance arm hit the top. About twenty readings were made per test specimen. 67 In all cases, the deflection gauge at the heel had to be removed when failure appeared imminent to prevent damage to the gauge. This meant that deflection data could not be taken in the neighborhood of ultimate load. Should further research by others be continued on this type of joint, the dial gauge should be mounted to read by extension rather than by compression, to eliminate the danger of damage and permit the full range of readings to be made. Test Results Types of Failure of Experimental Specimens During the testing program, all the types of failure described earlier were observed. A record of type of failure was made of most of the specimens, with the following results: a. All 3155: and 3158: in both white fir and Douglas fir, and all 2-7/8”x9”, 3-11/16”x4-1/2", and 3-11/16"x6-3/4" in western hemlock failed by the tooth withdrawal associated with the highest stresses. See Figure 23 for photographs of this type of failure.- Very little rotation was noticed in the 3"x5" and 3-11/16"x4-1/2" sizes, and no rotation was seen in the three longer sizes. This amount of rotation, or lack of it, was in accordance with the pr0posed theoretical analysis which predicts less rotation in longer plates due to their higher polar section modulus (higher resistance to eccentric forces). 68 .nmon pompnouV moNSHNmm nuoou bum woo: HmonNN .mm oNawNm .oumHm :N x :N :m x :m New A NN .NNNHN :N x :N HUN 0o ... . r) . N): T. , .3Rsn1raf. . . 1 AW, . . 2...: 69 All the 5:55: plates (which had teeth oriented in all four directions, every 900) showed considerable rotation, as well as some S-shaped distortion, prior to failure. See Figure 24 for photographs of this S-shaped distortion, though of a different, heavier gauge plate. The rotation was less pronounced but somewhat similar to that shown for the nailed plate in Figure 25. Ultimate failure of these 5"x5" plates was the result of tooth withdrawal, which always started essentially simultaneously at the upper left and lower right corners as they lifted ' out of the wood first, due to that diagonal dimension of the plate stretching as the plate became S-shaped. All the 5-5/16"x6-3/4” plates which were equally applied on top and bottom chords failed by buckling, regardless of their orientation. Those placed perpendicular to the crack (see photo sequence in- Figures 26 and 27) failed at lower loads than those placed parallel to the bottom chord (see photo sequence in Figures 29 and 30). This showed the higher shear value and greater buckling resistance when the long dimension of tooth holes is oriented approximately parallel to the crack. All the 5—5/16"x4-1/2" plates (which had teeth and holes pointed perpendicular to the bottom chord) showed both buckling and rotation, as seen in the 70 (a) Right-hand heel joint. .(Note S-shape of ends of plate.) (b) Left-hand heel joint. Figure 24. Distortion of 18 gauge heel plates. 71 (a) Original location, showing deflection gauge. .'. :. ‘ «5.33353- .. - . ', .' » (b) Deflected position. Figure 25. Photos of nailed plate distortion. 72 (b) 0.019" deflection. (c) 0.045" deflection. (d) 0.075" deflection. (Note initial buckling (Initial buckling is along shear line.) more severe.) (e) 0.088" deflection. (f) 0.162" deflection. Figure 26. Initial buckling of Specimen 26. (a) 3/16" deflection. (b) 1/4" deflection. (c) 5/16” deflection. (d) 7/16" deflection. (e) 9/16" deflection. (f) 9/16" deflection. (No rotation. All (Close-up.) buckling failure.) Figure 27. Progressive buckling of Specimen 26. (a) 1/4" deflection. (b) 3/8" deflection. (Note rotation of plate.) (Hole enlargement at upper right.) (c) 1/2" deflection. (d) 5/8" deflection. (Pulling of teeth at pencil.) (Lifting of teeth at pencil.) (6) 3/4" deflection. (f) 1" deflection. (Buckling severely.) (Holes enlarged on adjacent corners, showing rotation.) Figure 28. Buckling sequence of 5-5/16" x 4-1/2" plate. 75 photo sequence in Figure 28, prior to ultimate failure by tooth withdrawal. Close inspection of the corner teeth in Figure 28 reveals the hole enlargement, especially at the upper right behind the tooth at the pencil, and at the lower left. e. The 3"x10" plates on one of the earliest speCimens tested failed in tension, rather than by either buckling or tooth withdrawal. The tensile joint had already been studied by Misra and was only of marginal interest to this study as an additional limiting factor, rather than a part of the main study of contact area stresses and buckling strength. As.a result, it was not studied in more detail. Shorter heel plates were selected to prevent this type of failure in the main protion of the tests. Stress-Coat Analysis A Stress-Coat analysis was made of several sizes of plates, on both 8'-0” specimens and full size 24'-0" trusses. Both showed the same pattern of stress cracks. The Stress-Coat crack pattern development sequence has been photographed (Figure 29) for specimen 27, a 5-5/16”x 6-3/4" plate applied in the normal position. Since the cracks were too small to show up in the photos, red dye etchant was painted over the increasing area that had Stress- Coat cracks, for each new level of loading. By following the Sequential photos, Figures 29(a) through 29(e), the spreading Stress-Coat pattern indicates that the strains are greatest 76 .. q. ..... . - c . I .- nl'_,u {:232M2u01'...-‘.-- (a) 0.037" Deflection. (b) 0.056" Deflection (Stress-Coat cracks painted.) (c) 0.072" Deflection. (d) 0.105" Deflection. (e) 0.214" Deflection. (f) 0.401" Deflection. (Some areas still have (Entire plate painted to no stress cracks.) show buckling.) Figure 29. Photos of Stress-Coat cracks on Specimen 27. 1011. 1/2" deflect ) b ( 1011. 3/8" deflect (a) 5/8" deflection. (d) 3/4" deflection. (C) deflection. ll! f) ( 3/4" deflection. (e) ing of Specimen 27. ive buckl Progress Figure 30. 78 in the area of the shear crack, with just a few teeth at the upper right and lower left beginning to show high strains in Figure 29(d) at 0.105" deflection. Even in Figure 29(e), at 0.214" deflection, just prior to the start of buckling, the top three rows of teeth (about 1-1/4") and bottom three rows (another 1-1/4" strip of plate) still showed very few Stress- Coat cracks. This means that for a 5-5/16” wide plate, almost 2-1/2", or 50%, is not contributing its full value to joint strength. The joint apparently would have been just as strong, in terms of total top chord axial force, had a somewhat smaller heel plate been used. The entire surface of the plate has been painted in Figure 29(f) to better illustrate the buckling sequence by showing the light reflection off the ripples. A small-scale sequence of crack pattern development on a 5-5/16"x6—3/4” plate is shown in Figure 31, followed by larger scale drawings in Figures 32, 33, and 34. It should be noticed in Figure 32 that the Stress—Coat cracks between' teeth start in the vicinity of the shear crack between top 311d bottom chord members. At the same time, initial Stress- C<>at cracks also occur at the bases of teeth located in the e> <13 qc:>: wmc:3w:c:jw4c;j\w C2? €13 CZ) €13 (3:) mammwmm,w @mwa / top chord force. 6,950 lbs. (b) Large scale of later Stress-Coat cracks on 5-5/16" x 6-3/4" plate. Figure 33. No stress cracks in any of this 82 Buckling has just started all along shear line; Stress-Coat is crazing off in that area. area. \ (:9 co co (3an C:> one)» so: «mco c0 c3 co co <23 WWW. co c:> co co'co on GONG-DMD co m co co c0 co co c9 c9./ c:> C:> 4:0 «co “COME c:> 192/63 6:) 0:) Ci) '61:)...3 ”$53“ &W¢E3— 0:)“ qwcfi, '48s ”2%;9.’ czfi ‘3 $79 ccg figs-m ff)? govmgmlmi 900‘“ 6:) Co’fiaw”? "(LL/5 a» 0:9 0:9 (:0 c:> /'§:f)sgc:fif§fo «3 c0 cs co or.) c1) ‘.\....£oc:>mcmc:>c:ac=>c:> [a score-<3 c.9643 en cajcs co Q59 co m c:> c::> co 0:0 C:> N o Stress-Coat cracks in this area. 8,850 lbs. top chord force. Figure 34. Large scale of Stress-Coat cracks at start of buckling of 5-5/16” x 6-3/4" plate. 83 Close inspection of Figure 33 reveals that stresses and strains are definitely increasing rapidly along the shear line, due to these increased top chord forces. There is very little indication of new Stress-Coat cracking at the upper right and lower left corner teeth, indicating that the plate, or teeth, is slightly distorted or undergoing relaxa- tion, and tooth forces are being redistributed. Figure 34 shows very dramatically that large areas of this 5-5/16" wide plate are not stressed highly enough to cause Stress-Coat cracking, despite forces high enough to initiate buckling along the shear line between top and bottom chords. Load-deflection data showed that the initiation of buckling precluded higher loadings. Large areas of the plate just weren't very highly stressed, even at ultimate load. Figure 35 shows drawings of the Stress-Coat crack development for a 3-11/16"x6-3/4” plate applied with its centerline directly over the crack between top and bottom chords (the so—called ”parallel to crack" orientation). Figure 36(3) indicates that initial stresses at the base of the teeth are highest for teeth nearest the crack, and that one tooth at the upper right corner is also stressed about the same amount (apparently due to rotation, or attempted rotation, of the plate). Figures 36(b) and (c) show the progressive development of stress cracks at higher top chord forces, indicating the higher strains at the shear line, and one tooth base at the lower left corner. Since _ sagaeasas ammmammaw amaawaaaa mmwmflmamw amazemmmw away gnaw mamm.bmmm mama swam mumm.&mmm 84 _ » mmmammwuw mummemmma mmmaaamaw mammaaaam mummammmm mammaaaam mmmnfimmmm aaamflaama mammubmma d 4,420 lbs. (b) 3,790 lbs. (@ ,r smasaaaas mafipapaaa ammmwmaaa amendmmmm meamwmmmm memam.mwmmwm amasbeama mmmwapmmé mmmmwbmmw _ anamwmmmm .mmmmemwmm mammaawaw aaapaaaaa mammammmm manageama mmm%flmmmm ammmwmmmm aaammaaaa _ 5,690 lbs. w) 5,050 lbs. (0 p aaaaaempa a sfiwpwaw mwmhuéwmw ganuww: a mmamwwamm manage: mmc%b&mmm ammmmeama a - P magmaaaaa mammawmmm aaeeapaaa amapweaaw mampwmmmm m%m&*bwmm 35“.. wmmm amambammm mummmbmmn a 6,920 lbs. (0 6,320 lbs. (0 Top chord axial force is given below each drawing. 7,270 lbs. (9 Figure 35. Sequence drawing of Stress-Coat cracks on 3-11/16” x 6-3/4” plate. 85 BBBBBBBBB BmBBBBBBB BBBBBBBBB BBBBBBBBB ll“ ll‘ II BBBBBBBBB BBBBBBBBB BBBBBBBBB BBBBBBBBB BBBB.BMBBBB _ top chord force. 3,790 lbs. (3') :BBB .BBB BBBBBBBBB BBBBBBBBB BBBBBBBBB u.“ R BBBBBBBBB BBBBBBBBB BBBBBBBBB BBBBBBBBB BBBBBBBBB Wm» top chord force. 4,420 lbs. 0)) BBQBBBBBB BBBBBBBBB BBBBBBBBB BBBBBBBBQ .BBBBBBBBB BBBBBBBBB BBBBWBBBB BBBBBBBBB BBBBBbBBBB B top chord force. 5,050 lbs. (C) Large scale of initial Stress-Coat cracks on 3-11/16" x 6-3/4” plate. Figure 36. 86 BBBBBBBBB \\\. V «r BBBBBBBBB BBBBBBBBB BBBB.BBBB memm... Emmm BBBB BBBBB BBBBBBBBB \\\l but“ u BBBBBBBBB B Iv t0p chord force. 5,690 lbs. (8) B \S BBBBBBBBB BBBBBBBBB BBBBBBBBB BBBB.B BBB BBBBBBBBB BBBB BBBBB BBBBBBBBB W BBBBB:BB H“ mm HM BBQBBBBBQ _ top chord force. 6,320 lbs. (b) Large scale of later stress cracks on 3-11/16" x 6-3/4" plate. Figure 37. 87 This corner lifting. Holes considerably elongated. V co m cm co co co cs co cs (:0 (:9 CD cores .c:>~...c:>ms<>o (:3 CZD <:3 C:le:Dm ‘C:) (:3 09 mm , mm. .09: {.”;93>~§§~ c5»- .co fiefi-euefl— Ci) fi-ém é; ’é'ifi Ci) <20 2&9 ‘02 go a,c::> (‘30:: Cg)!» SWIICO‘Fc—O (:9 (:9 c» :0? #90 \Holes somewhat elongated. Eff: 88% 4' Dark areas are where Stress- Coat crazed off the plate. (a) 6,920 lbs. top chord force. Original location of plate had ~moved about as shown dashed. ‘~_-_-- (:3 Ci) (:3 16:) €:D ‘C:) (:3 C13 8 8 a as ,3 is =58 . 01> —a.«-’&M%W:fi , - ‘ 7~ é;$>g£:9 I l fib‘flS-WS-fiopo-m‘cpy , mooco&<:oc:o~cd"”cog .om :oEfiUon oumfia-vmafimc :« wxomuo umou-mmowum :oflumooH oumam P 71‘ I 0‘ \‘ .oq oeswflm .»Hm>auuommmc :oflpuofimme :waN.o we“ .:oNN.o .:va.° m>mm some: .uuuow euogu moo .mnH ovom w:m woomhu one: mxomuo pmou-mmouuw HHDM czoam aw eon: :w\mvBK ownm .omfim um woaaonma can .oNHm .mfifim: NH xaco pan .moHo; :w\m-m ma woman mace 91 mouom p.830 no“. & awed Hoahou pawfih nozoa ho Roma: um mxomno 30w Auo> 92 E Top chord force Plate location / This plate is 3-3/8” x 7-5/8" with 24 holes, but only 12 nails shown full size. Stress-Coat. cracks were traced and labelled at 1890 lbs. (.240" defl.) and 2520 lbs. (0.368" defl.) top chord force. Figure 41. Stress-Coat cracks in nailed plate specimen 37. 93 The total load was divided by two to get the value of the two equal reactions. All loadings were applied symmetrically. For the 24'-0" trusses, continuity was counted at the quarter panel points since the 2"x4" chords were continuous members across those joints. The peak, heel, and bottom chord splice joints were assumed as pin-connected. To aCcount for the two- span continuity of the chords, 5/8 of the t0p chord load on each side was assumed to act at the quarter point (for a two-span continuous beam on.unyielding supports) rather than 1/2 as in the case of pin- connected joints. The vertical heel panel load, then, was only 3/16 of the top chord load instead of 1/4 as for pin-connected designs. 'This analysis" resulted in the net reaction being 13/16 of top chord load, rather than 3/4 for pin-connected, increasing the calculated axial force in the top chord by about 8-1/3% over a pin-connected analysis. The 8'-0” specimens were assumed pin-connected throughout. Top chord axial forces were computed using the geometrical relationship of forces at the heel joint after the net reaction had been computed. 94 IDetermination of Contact Stress and Shear Line Stress The contact area stress was determined by dividing the 1:0p chord axial force by the area of the heel plate. The zirea.of one plate equals one-half the area of the front and Jreaar plates. This was a straight P/A stress calculation. FJC) allowance was made for end distance or edge distance and rlcane for eccentricity. The shear line stress in the steel was computed by cicividing the top chord axial force by the length of one 'tnruss plate measured along the shear line crack. To get ‘tlie stress per inch on one plate, these Values would have to 1363 divided by two, for the front and rear plates. (3cnnparison of Six Plate Types The load-deflection data for the initial series of 8'-0" 'téast specimens are given in the Appendix in Tables 27 through )312. The results of repetitive tests on six different 20 ga. I’lxites manufactured by Troy Steel Corp. were compared statistically using Duncan's New Multiple Range Test. - Duncan's Test compares all possible pairs of means to deter- nliJne whether the differences are significant. The six truss plates used for this evaluation were all ihnlpaled in kiln-dried western hemlock (tsuga Heterophylla). a. 3-11/16” x 4-1/2” - 2 specimens b. 3-11/16" x 6-3/4" - S specimens c. 2—7/8" x 9" - 5 specimens d. 5-5/16" x 4-1/2” 1 5 specimens 95 e. 5-5/16" x 6-3/4” - 3 specimens f. 5-5/16" x 6-3/4” i - 4 specimens (perp. to crack) The three 5-5/16" x 6-3/4" plates in group e were applied parallel to the crack, rather than parallel to the bottom chord (the usual position). They were applied off—center, and had only four rows of teeth (about 1.84 inches) instead of six rows (about 5.31"/2 = 2.65") as normally required- The contact area calculations were based on actual area, 1. 84" x 6.75", rather than the expected area. This group, then, had actual contact area about equal to that of the 3-11/16" x 6-3/4" plates in group b. The statistical comparison of these 8'-0” specimens, done in part on Michigan State University's CDC 3600 Computer using the ABS Stat Series, Description 13, was performed uSing the cards and data given in Table 8. The output for each of four levels of deflection (0.015", 0.040", 0.080", 0.150") and ultimate load is, given in Table 9 along with the Duncan Table of Mean Differences for each level. Initial Comparison of .8'-0"' vs. 24'-0" Test Specimens The load-deflection data for the 8'-0" and 24'-0" matched specimens are-given in Tables 33 through 38. The reSults of repetitive tests (two in each cell) were analyzed With the M.S.U. CDC 3600 Computer using ABS Stat Description 14 a Analysis of Variance with Equal Frequency in Each Cell, 111 two separate preliminary analyses as follows: a. b. 96 8'-O” vs. 24'40" specimens - See Table 6, next page. 8'-0" small jig tests vs. 8'-0" Riehle tests - See Table 7, page 98. These preliminary analyses indicated that the following :Etactors had a significant effect on strength (stress level): a. Species of lumber - Douglas fir was stronger than white fir. Size of heel plate - The 3"x5" plates were strongest, 3"x8" next, and 5"x5" weakest, in terms of contact area stress. Length of test specimen - The 8'-0" specimens were significantly stronger than the 24'-0" trusses, all other factors being equal. Species and plate size had a significant inter- action. Species and deflection level had a significant interaction. Plate size and deflection level had a significant interaction. It was also found that the repetitions (whether the Sample was No. 1 or No. 2 of a matched pair) were not signif- icant in either preliminary analysis. The level of deflec- tjAbnhad a highly significant effect on contact area stress, ‘is ‘would certainly be expected. 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This final statistical analysis llfied the M.S.U. ABS Stat Series Description 18, Analysis of ‘Chavariance and Analysis of Variance with Unequal Frequencies Permitted in the Cells (Least Squares Routine). This LS routine permitted the inclusion of moisture ccuatent and specific gravity as covariants along with the Cirtegory variables of species, length of test specimen, I>lzite size, and deflection level. It required the creation (Df' twenty "indicator variables" as described in Description 318 for all these categories and the two-way inter—actions Inelitioned previously. The transformation instructions for t11e:creation of those indicator variables are given near the bcxginning of Table 17 followed by the data cards. Two addi- tiJanal covariants were created, (a) the square of the mois- tlrre content and (b) the square of the specific gravity, as Va‘I'iables nos. 29 and 30, with the transformation sub-deck. The computer output from this analysis is reprinted, aiiter slight abridgement to reduce unnecessary material, as Table 18. Statistics on Transformed Variable. Table 19. Analysis of Variance for Over-All Regression. Table 20. Simple Correlation Coefficients. Table 21. Measured Stress vs. Predicted Stress. CHAPTER V DISCUSSION OF RESULTS General This section presents load-deflection curves of each set of plates evaluated experimentally to permit quick, convenient visual comparison of the data. These load-deflec- tion curves are grouped accordingto their purpose, and . include a small drawing of the plate size, orientation, and other pertinent data. These load-deflection curves can be compared in terms of t0p chord axial force (Graph A for each figure), contact area stress in lbs. per sq. in. (Graph B for each figure), or shear on the joint in lbs. per. lineal inch (Graph C1 for each figure). ‘The statistical analysis of the experimental results is Presented in more detail in this chapter for each comparison Studied. The raw data input, the computer statistical output, Other comparison calculations, and a discussion 0f the sig- nificance of the findings is included. A prediction equation for the contact area stress is presented, along with a table comparing the predicted contact stI‘ess with the ‘experimentally measured contact stress. Finally, the results of the theoretical and experimental al'lellyses are compared . 100 101 Initial Study of Effect of Size, Shape, and Orientation on Contact Area Strength l)escription Six different types of heel joints, using 20 ga. truss {plates manufactured by Troy Steel Corporation impaled in vvestern hemlock were compared. The plate sizes, orientation, stud load-deflection curves are shown in Figures 43 through 117. The raw data for these plates is in the Appendix, Tables 27 through 32. V Statistical Comparison V This data was prepared as the computer input given in Trajole 8, for comparison of the contact area stress at 0.015", 0..040", 0.080", 0.150", and ultimate load. The results, irlcluding Duncan's Multiple Range Comparison of Mean IDigfferences, are_given in Table 9 (a) through (e). AJlalysis of Results -An analysis of Tables 9 (a) through (e) yields the following: a. From Table 9(a), for 0.015" deflection, there are no significant differences between the plates 'tested. This is reassuring since truss plate design values are based on strength at 0.015" deflection, as well as on ultimate. Any plate size, shape, and orientation can be used at the same relative efficiency for this low level of load. 102 SI'EAR ON JOINT - TOTAL LOAD IN POUNDS . '4 l ‘e Ag I f w ,’ QR” I” / WK - l . 1 / fl” / m, 1 l A 3“” ‘“n u u I PLATE 5:25: '2 X 9 1909 Contact area. each ernbors 25.9 sq..in. moo Shear lino length,tineal inches of plate-=95" Species of lumber sWut Coast Hemlock 0pc Grade of lumber 8150!” an coo anemone“ us no Effi— , HEEL JOINT OEFLECTION U-O' ' ' (A) All 5 Speculum E a < L a“ g u a) ' . .‘ I 3 / g 2 ’ RA .- :g :5.«* I 'p/ A ,/ fi 5 j r/r// ’13P o. 4 p, a: ’1 /, P" T’s“: ;é%jp z *2- A v 2 5- " -4 5 z c O «< c: a: i :5 , -h.- I . _ - u: . 1 An All» akin x:12.u J5 p.10 our» 0613 on x>Jz » ms.m;n HEEL JOINT DEFLECTION HEEL JOINT DEFLECTION I BI I C ) Figure 42.. Load-Deflection Curves for 2:7/8"x9" Plates. E wmwmmmm m immune (“hu‘ “0 .2— M a a 3 KW.“ ““4 I hz~°3 2° ttwuzmw 103 T accuse-mama'- ooeoeoacoQQJoQ e-lep oooooemmpfiac: 1.," womgdcwcw ueopo‘mooaemam ,avfiommcamam ammo-amount: newaawww ‘ 'II II PLATE SIZE = 3‘: X 6 Contact area. each member s 2 .9 sq. in. Shear line length,lineal inches oI plate:7.12" Species of lumber -West Coast Hemlock Grade of lumber 8150M SHEAR on JOINT - TOTALLOAD m nouuos HEEL JOINT DEFLECTION P- 3'-o";———--I (A) All 5 Specimens < a I. u S . j o: n. U r ‘ B I /l" ' j" 8 2 3‘3 ' E “ “-9 ‘/ r’ i // 3 3 a / y I E 77— * 07/ a «n I m '3 ' 1 3 d5: -' s s 0/ c“ .1 6 ( I 3 “°° '5 / g z 300 -1 O . <2) 1 200‘ Le-4 a / S I u n -- ‘f” 5 a: 1' i .oooeoeoe'oeJonchxzo .ooozoeoeoepaznicicflo HEEL JOINT DEFLECTION HEEL JOINT DEFLECTION (B) I C I Figure 43. Load-Deflection Curves for 3-11/16”x6-3/4" Plates. 104 I . a PLATE 5:25: 5% x 6 Contact aree. each member: u sq. in. Shear line length,lineal inches of plateau" Species of lumber aWeet Coast Hemlock Grade oI lumber - 150M - SHEAR on JOINT - TOTAL LOAD IN POUNDS B'-0' All 3 Specimens HEEL JOINT DEFLECTION (A) \ l '5 § -~ SHEAR ON JOINT - LBS PER 50. IN. OF AREA SHEAR ON JOINT- LBS. PER LIN. IN.“ PLATE § . oeoe'oeJonuxJeao oommoe*oe.onuic.e.ao HEELJOINT DEFLECTION , HEEL JOINT DEFLECTION (B) (C) Figure 44. Load-Deflection Curves for 5-5/16"x6-3/4" Plates. SHEAR ON JOINT- TOTALLOAD IN POUNDS SHEAR ON JOINT - LBS PER 50. IN. OF AREA 105 N I PLATE SIZE 5&16 Contact area. each members tannin. Shear line length,lineal inches of platezZlZ" Species of lumber IIWeist Coast Hemlock Grade of lumber s15001,_ HEEL Jomr cOEFLECTlON .( A) . equally on the members. There were I i it SPECIAL NOTE: These plates were not positioned only 24.9 sq.in. on the bottom chord, as shown, instead of 35.8. Contact stress is based on 24.9, giving values 10.9/24.9=44% higher than expected if 35.8 were used. -‘31: car» ocrn Jo.u JI.B 1’10 HEEL JOINT DEFLEC TION ' (8) Figure 45. IHJWE 2“?” z \ SHEAR ON JOINT- LBS. PER LIN. "LOP \ ‘ mmmmoepaznxiezo HEEL JOINT DEFLECTION (C) LoadeDeflection Curves for 5-5/16"x6-3/4" Plates (Parallel to Crack). J“ A- 2- acid SHEAR ON JOINT - TOTAL LOAD IN POUNDS SHEAR on JOINT - LBS PER so. In or: AREA II I! PLATE SIZE 5% X 4 2" Contact area. each member- 23.9 ' Shear line length,lineal inches of plate: 5.6 Species of lumber sWeet Coast Hemlock Grade of lumber slSOOI . F——. you—:1 HEEL JOINT DEFLECTION All 5 Specimens (A) E I 7'" O. U ‘l as ’t z E a , /" 5 1f / .J a / o: / a m / 8 can .4 // / r a f g. z 400 2 too . / o zoo o: < u l I m mos'oeio.Iz.IaJc.ezo oomoeoeoepiznisieiao HEEL JOINT DEFLEC-TION HEEL JOINT DEFLECTION (a) (C) Figure 46. Load-Deflection Curves for 5-5/16"x4-1/2" Plates (1 to Bottom Chord). (Mn—4 uC 2. CU one “C - SHEAR ON JOINT - LBS PER 50. IN..OF AREA 107 ' I .00 .02 .04 .06’ .08 .l0 .l2 J4 .l6 .l8 .20 HEEL JOINT DEFLEC-TION Figure 47. Load-Defiectioh Curves for Comparison of Six Plates. 108 From Table 9(b), both 2-7/8"x9" and 3-11/16"x6-3/4" heel plates are significantly stronger than 5-5/16"x 6-3/4" plates applied perpendicular to the top chord, at 0.040" deflection. From Table 9(c), 2-7/8"x9", 3—11/16"x6-3/4", 5-5/16"x6-3/4” (parallel to the crack), and 5-5/16"x 4-1/2" plates perpendicular to the bottom chord are all highly significantly (at 0.01 level) stronger than the weakest ones, 5'5/16"X6r3/4" plates applied perpendicular to the crack. It might be noted that these range from 55% to 88%~stronger than the weakest ones. From Table 9(d), at 0.150” deflection, the same results as in c above, plus the fact that both 2-7/8"x9" and 3-11/16"x6-3/4" plates are signifi- cantly stronger than the 3-11/16"x4—1/2" plates. From Table 9(e), at ultimate load, all plates were significantly stronger than the 5-5/16"x6-3/4" applied perpendiCular to the crack. Also, the 2-7/8"x9" and‘3-1l/16"x6-3/4" were the strongest, and were significantly better than all the others. (The 5-5/16”x6-3/4" plates applied parallel to the top chord were not positioned uniformly over the two members, which made their results, based on the lesser contact area, appear better than normal.) 109 0FOHIP.90=MT(CTAT) 'DDUTINFoUNFfll ' ”UN. 0.44. 1000. P U TDhY QTFFL TDUSQ DLATF COMDADIQON (unto!) 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Q.’ .... . _... l _.J._... _.9. Q ..NHtVK:O .. sooood.n««. “a“.oouun c=°°c°.nroc.m .caoa.ar .o.a°o°...~n a aeae.a.s.o« =. ”-0 x =oH\~H-n ' . I . I nee.on..... o...o..o~ oeccoo....non .e.. n..m .o.°oo°~.nnn a geae...eneu dudqqqquuaaqaInIIIuIumqaNqquqllulnluluqquduqquuunv.41 . u¢.a..an.u-‘ ¢~ .g..qq4um«a .44.¢m>o. : p x a a : \duxu man azo—»<_>wa oc«ozarm ouucaon no tau wmoq mumswuH: um monwm madam xwm mo comwumnaou omnmm vanguazz m.:mu:=Q .onm vanmh Summary 115 The over-all conclusions from this series of tests and statistical comparisons of six plate sizes and orientations were that: a. b. At 0.015” deflection, any plate size may be used. At high levels of deflection (and high loads), plates ranging in width from 2-3/4" to about 4” and in length from two to three times their width are the most efficient, being about twice as strong as the nearly square plates applied in the weakest possible direction. The comparison of loadfdeflection curves is shown in Figure 47 for the average values of these six plate sizes, shapes, and orientations. 'Comparison of Matched Specimens Description Fifty-six specimens were tested to evaluate the effect of each of the following factors on contact area stress: a. b. C. Size of truss plate (3"x5", 3"x8", or 5"x5"). Length of test specimens (8'-0" or 24'-0"). Species of lumber (Douglas fir or white fir). Level of deflection (0.015”, 0.040", 0.080", 0.150"). Moisture content. Specific gravity. Location of 8'-0” tests (at home on small jig, or at M.S.U. on Forestry Dept.'s Riehle Testing.MachineJ. 116 The plate size, specimen length, species, load-deflec- tion curve, and other pertinent data for each group of specimens is given in Figures 48 through 59. The raw data is given in the Appendix, in Tables 33 through 46. Comparison of 8'-0" vs. 24'-0" Specimen Length The results of an initial comparison of 24 matched specimens was reported in "Test Results" of the chapter on "Experimental Analysis.” Load-deflection curves comparing 8'-0" specimens with full-scale 24'-0" trusses are given in Figures 48 through 53. The load-deflection curves for the 24'-0" trusses are shown with solid lines, while the 8'-0" specimens and curves are shown dashed. The 8'~0" specimens had higher values than the 24'-0" trusses for all cases except the 3"x5" plates in Douglas fir (Figure 48). However, by taking the average ultimate contact stress from the data Tables 33 through 38 in the Appendix, the comparison in Table 10 can be made: Table 10. 8'-O" vs. 24'-0" Specimens at Ultimate Load. Average Ultimate Contact Stresd Description Plate 8'/24' Size Species 8'-0" 24'-O" Ratio 3"x5" D. fir 301 322 938% g'txsu n H 317 422 75 "x5" " " 287 . 290 99 3"x‘F' Wh. fir 232 213"? 100 3"x8" " " 225 193 116i; c’5x5" " "_, 220 202 109 | 62593 5 8' average = 99% of 24' 117 This means the 8'-0” specimen average was almost identical to the 24'-0" average at ultimate load. Ultimate load data was not included in the statistical analysis. A similar comparison at the other loads is given in Table 11. Table 11. 8'-0" vs. 24'-O" Specimens at Four Deflection Levels. Deflection Comparison 0.015" 8'-0" specimen is 81% stronger than 24'- 0" 0.040" 8'-0" " " 21 % 24'- 0" 0.080" 8|_0H H H 9 % H H 24'- 0" 0.150" 8'-0"! H H 4 % H H 241-0" Ultimate 8'-0" " " l % weaker " 24'-0" Over-all 8'-0" specimen is 8 % stronger than 24'- " Comparison of Small 8'-0" Jig Results with Riehle Machine Results As a result of concern over the data from the 8'- 0" specimens tested on the small hand operated hydraulic test jig, an additional set of 24 specimens 8'-O" long was built, listed in Table 12. Table 12. Riehle Machine 8'-0" Test Specimens Group Quan. Heel Plate species 3”x5" D. fir H H H M iii?" I! H 3"x5" Wh. fir H H H II 3":3" H I! O‘U‘IhLNNI-l h-b-b-k-h-b Two samples, the first two tested, were selected from each group and matched in a Preliminary Analysis of Variance tC> compare the effect of test location. The results are ww m mmlmmmmmmwmluutm s $02306 Z. 0.20.. 4(b0h 1 5.2.0.. 20 «.(UIm (N!( “20...: .GW Iva. mm... s L250} 20 C(Ulm wwmmwmww 118 n u PLATE 5:25: 2 3 X 5 Contact area. each member: 15.0 sq. in. Shear line length,lineal inches of plate=5.27" Species of lumber IOouglss Fir Oredeot Iumber 8 Construction 850' Specimen is shown dashed to correspond with its data which is dashed in the W3. TEST no.3” 39 TEST nouns SHEAR ON JOINT - TOTAL LOAD IN POUNDS HEEL JOINT DEFLECTION (A) C l . ‘ I fl \ \ p... -- o ‘ ‘5 ‘ s \ \ I l’---- ‘ § 'é fr I 'I 0’! r s SHEAR ON JOINT - LBS PER 50. IN.OF AREA t” ' '\ SHEAR ON JOINT- LBS. PER LIN. IN.OF PLATE “NMIN'DOJOJIMKflZO mummm»nx.ns.ozo HEEL JOINTBDEFLECTION HEEL JOINT DEFLECTION " I I , (C) Figure 48. Load-Deflection Curves for 8' vs. 24' - ”3"x5" - Douglas Fir. g , U E SHEAR ON JOINT - TOTAL LOAD IN POUNDS 000 HEEL JOINT DEFLECT ION 119 (A) l ‘ U C “ l k T o l 2 l C a: ‘ ‘ ‘1 a, ‘9’ / s Q , ' 1‘ I’ .1; ‘4"-‘v l I- I, ’4’ r E I 1’ O I l ‘3 I” z . I O ,"I J C H j ( I m I 3 . .oo .02 M 5' .0. J0 .I2 14 .16 JD .20 HEEL JOINT DEFLECTION (8) Figure 49. Load-Deflection Curves for 8' vs. ‘V u PLATE SIZE : 3 x 8" Contact ores. each member: 24.0 sq. in. Shear line length,lineal inches of plate=845” Species of lumber soouglss Fir Grade oi lumber 3 Construction B'-O' Specimen is shown dashed to correspond with its data which is dashed in the l grads“ . treat: Kg TEST No.40!“ TEST No.46847 S U .14 / g» --ll-‘J-r- SHEAR ON JOINT- LBS. PER LIN. IN. OF a ».-m r- w OODZD‘DSDBflJZJOJG HEEL JOINT DEFLECTION (C) 24' - 3"x8" - Douglas Fir. 120 Ii II It sees ’ PLATE SIZE: 5 X 5 m 1' Contact area. each members 25.0 sq. in. , “ Shear line length,lineal inches of plate=5.27” woo ’ Species of lumber 8 Douglas Fir Gradept lumber I Construction lace tmo ' $0" Specimen is shown dashed to correspond with its data IN . which is dashed in the we 000 0" C5537" , 24'- d’ HEEL JOINT DEFLECTION SI'EAR W JOINT - TOTAL LOAD IN POUNDS ‘ m: “‘11“ V R:‘::‘. M, 1851 new so rasr riotous .5 S a: 3/ a: "' I r ,9 ( 8 It” 25 ,3 z - ~ 2 I” S! :l . H - t: m if g 7 . g ”""E." m I, ..I 'IV"" S I t 5 I- v', r” ' I g , x "z” ' I 9 .6” § "' t, , E I’ g I, o: f, 4 < a i s ' i U). mama'oeioizxxnzo ooozoaoaoenizinxieao HEEL JOINT DEFLECTION HEEL JOINT DEFLECTION (B) (C) Figure 50. Load-Deflection Curves for 8' vs. 24' - 5"x5" - Douglas Fir. WOZJOL Z. OSOJ JcFOh i #232. 20 C(MIW 1...!1 to «5 Gm ILL wei— r SECS 20 teflelm 121 g . n it PLATE SIZE : 3 x 5 Contact area. each member: 15.0 sq. in. Shear line length,llneal inches oi plate=5.27" Speciesot lumber "Hem -Fir" Gradepf lumber ' 1650f "Dry" I” 810' Specimen is shown dashed to correspond with its data which is dashed in the , 9mg: l Cow-3 --—- 24'-d‘& SI-EAR ON JOINT - TOTAL LOAD IN POUNDS HEEL JOINT DEFLECTION (A) TEST NO.51852 TEST NO.598 60 u cook b"q " -f’ '1 w” ,. P.” 3%,". 0 ‘\ . \ Tat? \ \ \ x ‘5 x i'" X - / if ii ‘9 \\ \‘N‘ ‘9 I SHEAR ON JOINT - LBS PER 50. IN.OF AREA SHEAR ON JOINT- LBS PER LIN IN.OF PLATE ‘: hamsrcenunxnao DOIDZDOOGDODJZMJSJBZO HEEL JOINT DEFLECTION HEEL JOINT DEFLECTION ‘ (B) (C) Figure 51. Load-Deflection Curves for 8' vs. 24' - 3"x5" - White Fir. 122 II it PLATE Size: 3 x 8 Contact area. eac’n member=24.0 sq. in. Shear line length,lineal inches of plate=8.45” Species of lumber 8"Hem-Fir" Gradepf lumber ”650! ”Dry" 850' Specimen is shown dashed to correspond with its data which is dashed in the SHEAR ON JOINT - TOTAL LOAD IN POUNDS on 136533 H INT F TI ‘ EEL JO (A)DE LEG ON TEST "NO. 53854 TEST NO.618 62 < i a .. .. < 3 8 2' g - e 1 3 3 o G g . g g 7 P’-—~""’--: a U5 ~1- 33" -""" fi;“ 7. 3 5 4.4"”. fiL/ oh 0 D." . ’v .‘z- “8":2'té'4zv'- P' 1”}/ v—‘E‘M 5 0‘ “—1.:1 2 J, .3 ’g’ A 5 4' / 2 . fl'I-f .5 vvv "I’ r I’ O ’ " (23 II, / C I I," 200‘ .‘ a: //' i g a , A . “I... I ' ' ' i 1 w I l I I l i l mumm'oemunxxzo DOMMDSDODJZJAJGJSZO HEEL JOINT DEFLECTION HEEL JOINT DEFLECTION (B) (C) Figure 52. Load Deflection Curves for 8' vs. 24' - 3"x8" - White Fir. 123 éo§o§0 m a m 52 -.- a g 7 3 .1345" r a) ’ ” a: “I r” m ’ “V’.

%J%.% Q, L ‘3 & o - - mic 23»: 9° @gé’ 0 ° 0 ° 9. 9 9 7? I I PLATE SIZE : 5"x 5" Contact area. each member: 25.0 sq. in. Shear line length,lineal inches of plate=5.27" SHEAR ON JOINT- LBS. PER LIN. IN.OF PLKI’E I I._u'-o‘—._.I DOUGLAS FIR (solid) VS WHITE FIR (dashed) ‘- 'V 5.: ID N ’é’fi /7 j 7 % \k ,’ A’ f" I,» $04 / " 1’ ” I I I I ’ / .I x’ I 4 / 1’ I I 1' I I I NDZMDSDD1>JZJ¢JSJBZO HEEL JOINT DEFLECTION (C) Load-Deflection Curves for Douglas vs. White Fir - 5"x5" - 24'. 131 A similar comparison of the other loads is given in Table 14. Table 14.- White Fir vs. Douglas Fir at Four Deflection Levels. Deflection Comparison' 0.015" White fir averages 72% of Douglas fir 0.040" I! H. H. 70% I! I H H 0 . 080" H H I! 62% H H H o . 150" H ' H H 69 % H. H H ‘ Ultimate H H H 69% H H 'H Over-all White fir averages 68% Of Douglas fir Comparison of 3"x5". 3"x8", and 5"x5" Plates 'USing the same data. the average ultimate loads, based on plate sizes are shown in Table 15. 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Deflection 0.015" 0.040" 0 080“ 0.150" § 3"x5" 101.5 172.3 223.7 261.5 E 3"x8" 73.2 155.1 229.1 280.6 33 5"x5" 76.9 140.1 194.9 233.7 All other variables and covariates are their means. held constant at 148 Categories Studied In order to describe the regression equation more detail, the data used in the analysis must be more completely explained. In punching the original cards for the Stat Description 14, Analysis of Variance, preliminary analysis for Tables 6 and 7, the following categories were used: Category Description Value A (X2) Species Doug. fir White fir #MNH 4:.me DINO-i NH NH B (x3) Length 3;:03" C (X4) Plate Size 3"x5" . H H Elli?" D (X5) Level of Defl. 0.015" - ' 0.040" 0.080" 0.150" E (X1) Repetitions Spec. #1 Spec. #2 Spec. #3 Spec. #4 By using equal number in the cells, that is, the same number of repetitions and all factors matched, the following number of data points must be used: Species (2) x Length (2) x Plate Size (3) x Deflection (4) x Repetitions (2) = 96 So 96 separate data cards must be used so that each point may be unique. Creation of Indicator Variables for Categories To use the Unequal Frequencies (Least Squares Routine) to perform an Analysis of Variance, the distinct category 149 variables described above must be converted to Indicator Variables, denoted I.V., by use of a matrix, where each I.V. may have a value of 1, 0, or -1. i .For example, if the category has just two possibilities, (such as either Douglas fir or white fir), then just one I.V. is required, as follows: Value of X9 (I.V. for Species) Douglas fir ' 1 White fir -1. Similarly, X10 (I.V. for test specimen length) = l for 8'-0" specimens and -l for 24'-0" specimens. If the category contains three possibilities, such as 3"x5", 3"x8", or 5”x5" plate sizes, two I.V.s are required in a matrix as follows: ,Plate Size X' X 11 12 3"x5" 1 0 3"x8" o 1 5"x5" -1 -1 This same type matrix may be used for the levels of deflection (4 choices in the category) by using three I.V.s; Level of Deflection X13 X14 X15 0.015" 1 0 0 0.040" 0 l 0 0.080" 0 0 1 0.150" -1 -1 -1 Creation of Indicator Variables for Interactions To accommodate interactions, such as plate size (2 I.V.s) with level of deflection (which has 3 I.V.s), 2 x 3 = 6 hew I.V.s must be created as follows: 150 I.V. for Plate Size I.V. for Level of Deflection X11. X12 X13 X21 X24 x14 x22 X25 x15 x23 X26 Each of these Level of Deflection - Plate Size interaction indicator variables will have values as shown in the matrix following: . Plate Deflection Interaction Indicator Variables Description X21 X22 X23. X24 X25 X26 3"x5" @ 0.015" defl. l 0 O 0 O 0 3"x5" @ 0.040" defl. 0 1 0 0 0 0 3"x5" @ 0.080" defl. 0 O l O 0 0 3"x8" @ 0.015" defl. 0 0 0 l 0 0 3"x8" @ 0.040" defl. 0 0 0 0 l 0 .3"x8" @ 0.080" defl. 0 0 O O O 1 It is not necessary to include the third plate size (5"x5") or the fourth level of deflection (0.150") since these are handled with the -1 values. The Indicator Variables described in this section were created by the computer by use of a transformation sub—deck. Regression Equation After creation of the appropriate indicator variables, (indicator variables must be used not only for all the main categories to be studied, but also for all the interactions which are of interest), the Least SquaresPrediction Equation for stress can be written in terms of these indicator 151 variables (along with the continuous variables used as co- variants), by using the regression coefficients given in Table 19. -Y(stress) - 112.69 - 12.43 x Moist. Cont. + 793.29 x Spec. Grav. + 25.67 x Species (Indicator Variable) + 7.85 x Length (I.V.) + 11.21 x 3"x5" Plate (I.V.) + 5.94 x 3"x8" Plate (I.V.) - 94.66 x 0.015" Defl. (I.V.) - 22.74 x 0.040" Defl. (I.V.) + 37.34 x 0.080" Defl. (I.V.) - 2.73 x 3”x5" - Fir Interaction.lndicator Variable (I.I.V.) + 9.69 x 3"x8" - Fir (I.I.V.) 9 18.90 x 0.015" - Fir (I.I.V.) - 2.02 x 0.040" Fir (I.I.V.) + 9.90 x 0.080" - Fir (I.I.V.) + 6.40 x 3"x5" - 0.015" (I.I.V.) + 5.26 x 3"x5" - 0.040“ (I.I.V.) . 3.38 x 3"x5" - 0.080" (I.I.V.) - 16.62 x 3"x8" - 0.015" (I.I.V.) - 6.67 x 3"x8" 6 0.040" (I.I.V.) + 7.25 x 3"x8" - 0.080" (I.I.V.) - 8.05 x 8' - 3"x5" (I.I.V.) + 8.51 x 8' x 3"x8" (I.I.V.) - 0.24 x (Moist. Cont.)2 - 745.43 (Spec. Grav.)2. ' The predicted stress of the particular sample can be computed by just putting in the appropriate values for moisture content, specificgravity, and a +1, 0, or -1 as required for each of the Indicator Variable (I.V.) and Interaction Indicator Variable (I.I.V.) terms. The computer has already done this for all the data used in the analysis and compares the measured stress (Y = X6) with the estimated stress, plus giving the differences (residuals, which equal measured stress minus predicted stress). See Table 21- 152 Theoretical 13. Experimental Analysis General The contact area stresses derived in the theoretical section were based, in the main, on a standard engineering analysis of eccentricity, with just two modifications; (a) teeth closest to the crack were not counted due to edge or end distance, and (b) the vertical component of top chord- axial force was neglected in the eccentricity calculations since it is believed to act directly on the support through crushing of the feather end of the bottom chord, without being transferred by the heel plate. The theoretical contact area stress, for each of the three sizes studied moSt closely in the experimental phase is given in Table 24. Table 24. Theoretical Contact Stress for 3”x5", 3"x8", and 5”x5" Plates Plate Axial Eccentric 1 Size Stress" Stress a Total Pr0portion 3"x5" 200 ++ 138 => 323 130.2% 3"x8" 200 ++ 66 = 248 100 % 5"x5" 200 ++ 188 =. 378 152.5% Theoretical vs. Experimental Results at 0.150" Deflection Comparing these results with those contained in Table 23 (using stress at 0.150” deflection as the reference level), and assuming that the 3"x8" plates are equal experi- mentally and theoretically, the percentage comparison values are in Table 25. 153 Table 25. Comparison of Theoretical vs. Experimental Results @ 0.150" Deflection. Plate ’ Size Experimental Theoretical _ Difference 3"x5" 107.3% 130.2% 21.3% 3”x8" 100.0% 100.0% - 5"x5" ‘ 121.0% 152.5% 26 % If the theoretical results are exactly right for the 3"x8" size, then they are 21:3% and 26% too conservative for the 3"x5" and 5"x5" plates, respectively. The experimental stresses for both the 3"x50 and 5"x5" plates were much closer to the simple axial stress computation (no eccentricity considered) than either the proposed method of heel plate analySis or the FHA method. When comparing experimental results at 0.150" deflection, the simple axial stress method is more accurate, especially for plates of the same width, than the more elaborate methods. Theoretical vs. Experimental Results at 0.015" Deflection. If the experimental results at 0.015" deflection (which is the design deflection) from Table 23, are compared with the theoretical values, Table 26 results: Table 26. 'Comparison of Theoretical vs. Experimental Results @ 0.015" Deflection. Plate Size Experimental Theoretical Difference 3"x5". 72.0% 130.2% 80.7% 3"x8" 100.0% ' 100.0% - 5"x5", 95.0% 152.5% . 60.5% 154 Summary This means that at the lower deflection levels, due to the considerably better performance of the 3"x5" and 5"x5" plates, the more elaborate theoretiCal methods are even worse predictOrs than at the higher deflection levels. The simple P/A contact stress calculation method was more accurate for the plate sizes tested than the proposed method of analysis. CHAPTER VI CONCLUSIONS A statistical c0mparison of average stress at ultimate load for repetitive tests of six different heel plate sizes yielded the following conclusions: 1. Plates proportioned three times as long as their breadth are stronger by about 2%, but this is not significantly stronger,than those two times their breadth. Plate lengths ranging from two to three times their breadth are from 13k% to 50% stronger (statistically significant) than those nearly square (one and one- quarter times their width). All plates applied with their long dimension paral- lel to the bottom chord are significantly stronger than those applied perpendicular to the bottom chord. A check of the Stress-Coat crack patterns on several plates indicated the following: 4. The shear stress in the steel plate is highest near the crack between the members. 155 156 The contact area remote from the crack is still flat and is not stressed to the buckling point even when the plate is destroyed at the shear crack if the plate width exceeds the "development width" for shear. Shear stresses in the steel, as well as buckling stresses, are lower in plates applied with the teeth oriented parallel to the bottom chord than in those with teeth oriented perpendicular to the bottom chord. Inspection of the photographs (confirmed by visual inspection of numerous specimens during failure) reveals: 7. The nearly square plates undergo rotation or side- ways distortion during deflection of the heel joint, showing the effect of torsional forces. Buckling resistance is higher when the entire plate area is backed up by wood than when a portion of the truss plate is over the triangular air space between members. Comparison of matched 8'-0" and 24'-0" specimens showed the following factors to be statistically significant. 9. Douglas fir had about 42% stronger heel joints than white'fir. This emphasizes the need to specify the species. 10. The length of heel plate had no effect on joint strength, for plates 3" wide. The 3"x5" plates had 3% more strength per square inch than 3"x8" heel -plates. 11. 12. 13. 14. 15. 16. 17. 157 Narrower heel plates are stronger than wider heel plates. The 5"x5" plates were only 82% as strong, on a per square inch basis, as the 3"x5" plates, which was a significant reduction. Small plates are significantly better at the lower levels of deflection (0.015" to 0.040") whereas the larger plates were better at higher levels (0.080" to 0.150"), an inter-action effect of plate size with level of deflection. Moisture content had a highly significant effect on results. The lower moisture content specimens gave better test values. There was no significant effect of specific gravity on stress values. This was an unusual finding since all connector values for mechanical fasteners are based on species groupings by specific gravity. The 8'-0" specimens tested better than the 24'-0" trusses by a significant amount which cannot be explained. The 24'-0" truss heel plates are about 92% as strong as the same plates on the 8'-0" specimen based on the statistical correlation. The small 8'-0" hand-operated test jig provides an accurate heel test not significantly different from results obtained on the Riehle test machine. .Nider truss plates are weaker, due to their buck- ling in the steel, but provide a much more uniform, 18. 19. 20. 21. 158 predictable load-deflection pattern and greater total deflection than narrower plates. This may be of benefit where a known safety factor is essential. Where two plates are used on each side of the heel joint, both should be oriented the same direction, or their design strengths adjusted in accordance with load-deflection data relating their stiffness. Average ultimate contact area stresses, figured on the straight P/A basis of gross area, were: Plate Size Doug. Fir White Fir 3x5 315 226 3x8 374 281 5x5 264 227 2-7/8x9 (Hem.) 33S 3-11/16x6-3/4 330 3-ll/l6x4-l/2 309 S-5/l6x6-3/4 290 (Unequal areas--see text) 5-5/16x4-1/Zi, 271 S-5/l6x6-3/4i, 163 Twenty gauge plates with all teeth parallel to bottom chord buckled at loads of about 575 lbs. shear per inch of plate (1150 pli on joint), and 500 pli shear if teeth were perpendicular to crack. Twenty gauge plates with teeth in four directions did not buckle at loads of 675 pli shear (1350 pli on joint), but failed by tooth withdrawal. CHAPTER VII RECOMMENDATIONS FOR HEEL JOINT DESIGN The following recommendations are based on this research: 1. Provide sufficient truss plate contact area to accom- modate the top and bottom chord axial forces, using the TPI reduction factors for slope effect. An additional reduction factor of 20% is recommended for plates over 4" wide, to account for eccentricity. 2. Twenty gauge heel plates placed parallel to the bottom chord should be kept short enough (probably not exceeding 9" in most cases) to prevent tensile failures in 'the steel. 3. Twenty gauge heel plates should be kept narrow enough (probably not over -l/2" in most cases) to prevent buckling failure in the steel. If wide plates are used, they should be designed on the basis of their buckling resistance rather than their contact area. 4: Heel plates should be proportional from two to three times as long as their breadth, whenever possible, to increase their rotational resistance to eccentric forces. 5. Tooth values and plate sizes are highly dependent on species of lumber. Care in specifying the species on the 159 160 drawings must be folloWed in the actual production of the trusses, or larger plates used if a less desirable species is substituted in the design. 6. Heel plates should be positioned with the longest possible amount of plate over the crack to resist rotation, with equal contact areas on both members. 7. Heel plates should not be positioned perpendicular to the crack if avoidable, or, if this positioning is unavoidable, appropriately reduced tooth values should be used in the design, plus checking the buckling resistance of the reduced steel shear line. 8. Large sized heel plates, when used for girder trusses, widely spaced trusses, or other trusses with high axial forces, should be checked for buckling strength and tensile strength to prevent a misplaced feeling of confidence .based on contact area size. CHAPTER VIII RECOMMENDATIONS FOR FURTHER RESEARCH Bracing (Bridging) Methods and Requirements for Flat Trusses. Load-Sharing (and Its Stress Increases) as It Applies to Trussed Rafters. Top Chord Column Buckling Resistance Provided by 2"x4" Roof Boards 24" O.C., or 3/8" Plywood Sheathing. Study Methods of Improving Stiffness of Long Span - Shallow Depth Flat Trusses. Long Term Deflection Characteristics of Flat Trusses. Suitability of Metal Plates in Making Joints in Continuous Floor Joists. 161 APPENDIX APPENDIX LOAD DEFLECTION DATA This appendix contains the tabular test data obtained experimentally. The tables are grouped as follows: Tables 27 through 32 33 through 38 39 and. 40 41 through 46 Purpose Comparison of Six Plate Sizes. Initial Comparison of Plate Size Specimen Length, Species, and Level of Deflection. Substantiating Tests for Table 33. Tests of 8' Specimens on Riehle Testing Machine to Verify Suitability of Small Hand Hydraulic Jig. 162 Pages 163-168 169-174 175-176 177-182 .mcoEouomm 03H :0 comma ommuo>< «go .mcoamoonm oounu no woman ommao>< «« . .wocosoouow on was fiasco wmoa ouwswufis oyowouocu ”unw0n umou on moonm oxoun phone now enamonao « 163 coco ooo . cmc occo.ooao moo moo o mco coo ccao cooo . coco coco . . coco coo coca Nao caa oac cao Noa omo ..oocoo oooa oooc Nco oca coo ooo coo caa oco oco ..accc moca coca coco coo moo. 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O. & § 00 & § & no W$W§WQ¥0A§§QVWQMVQVAW ,, 9%.o%.o%.o%o%ofiuvo%o REFERENCES REFERENCES AmeriCan Society for Testing and Materials. (1967). "Tentative Methods for Establishing Structural Grades A.S.T.M. Designation for Visually Graded Lumber." D 245-67T. Philadelphia, Pennsylvania. American Society for Testing and Materials. "Tentative Methods for Establishing Clear Wood Strength Values." A.S.T.M. Designation D 2555-67T. Philadelphia, Pennsylvania. American Society for Testing and Materials. (1968). "Standard Methods of Testing Metal Fasteners in Wood." A.S.T.M. Designation D 1761-68. .Philadelphia, Pennsylvania. (1967). American Society of Agricultural Engineers. "Designing Buildings to Resist Snow and Wind Loads." A.S.A.E. R288.1T. St. Joseph, Michigan. .Bolger, R. J., and C. A. Rasmussen. (1962). "Stress- O-Matic Stress Rating System." Philadelphia, Pennsylvania: American Society for Testing and Materials. Boyd, J. S., and H. Geise. (1955). "Secondary Stresses in Glued Trusses." 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