I LLINOI S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN PRODUCTION NOTE University of Illinois at Urbana-Champaign Library Large-scale Digitization Project, 2007. The Effect of Bearing Pressure on the Static Strength of Riveted Connections by William H. Munse PROFESSOR OF CIVIL ENGINEERING ENGINEERING EXPERIMENT STATION BULLETIN NO. 454 © 1959 BY THE BOARD OF TRUSTEES OF THE UNIVERSITY OF ILLINOIS 3000-7-59-68181 UNIVERSITY Of"RF LI NI ABSTRACT The effect of bearing pressure on the strength and behavior of riveted connections was studied in tensile and compression tests of 131 riveted joints. In the tensile tests the bearing ratio, the ratio of bearing stress to tensile stress, was varied from 1.28 to 3.05. In the compression tests the ratio of bearing stress to shearing stress was varied from 1.78 to 4.21. On the basis of the test results it is found that, under static tensile load- ing, the ultimate strength of riveted connections is not reduced as a result of permitting the bearing stress to equal 2.25 times the tensile stress; nor, under static compression loading, by permitting it to equal 3.0 times the rivet shear- ing stress. However, it is found also that increasing the gage to produce higher bearing intensities did not increase the ultimate strength in proportion to the attendant increase of net section. CONTENTS ABSTRACT 3 I. INTRODUCTION 9 1. Bearing Pressure in Riveted Structural Connections 9 2. Object and Scope of Investigation 10 3. Acknowledgments 10 II. DESCRIPTION OF SPECIMENS AND TEST 12 4. Description of Specimens 12 5. Properties of Materials " 13 6. Description of Equipment 14 7. Description of Tests 16 III. RESULTS OF TESTS 17 8. Results of Tensile Tests 17 (a) 49 Series 17 (b) 50 Series 19 (c) 51 Series 19 9. Strain Distribution in Plates 21 10. Fractures of Tensile Connections 26 11. Results of Compression Tests 29 IV. ANALYSIS OF TEST RESULTS 31 12. Theoretical Efficiency of Tension Connections 31 13. Effect of Bearing and Gage on Test Efficiency 32 14. Effect of Bearing on Strength of Joints in Tension 34 15. Effect of Bearing on Strength of Materials 35 16. Effect of Bearing on Strain in Members 36 17. Variation in Behavior of Joints from Two Fabricators 38 18. Effect of Geometry on Behavior of Joints 39 19. Effect of Bearing on Strength of Joints in Compression 39 V. SUMMARY OF RESULTS AND CONCLUSIONS 41 20. Summary of Results 41 21. Conclusions 42 VI. SELECTED BIBLIOGRAPHY 43 FIGURES 1. Dimensions and Details of Tensile Specimens 12 2. Dimensions and Details of Compression Specimens 13 3. 600,000 Lb. Testing Machine 14 4. Slip Gage on Tension Specimen 14 5. Slip Gages and Loading Blocks on Compression Specimens 15 6. Strain Gages Mounted on Specimen 50-5A 15 7. Patterns of Strain Gages for Various 50 Series Specimens 16 8. Stress-Slip Curves for Original 49 Series 18 9. Stress-Slip Curves for Retest 49 Series 18 10. Stress-Slip Curves for Specimens of the 50 Series 20 11. Stress-Slip Curves for Specimens of the 51 and 50-X Series 21 12. Stresscoat Patterns for Specimen 50-11A 22 13. Distribution of Longitudinal Strains, Specimen 50-6B 23 14. Stress-Strain Curves for Individual Gages, Specimen 50-6B 24 15. Transverse Distribution of Longitudinal Strains at Various Loads 25 16. Typical Fractures of the 49 Series Specimens 26 17. Fractures of Specimens Exhibiting Extreme Range in Efficiency, 49 Series 26 18. Typical Fractures of the 50 Series Specimens 27 19. Specimen 50-7B Showing Bulging and Tearing of Outer Plates 27 20. Typical Fractures of 51 Series with ¾-in. Rivets, Specimens from Two Fabricators 27 21. Typical Fractures of 51 Series with 1-in. Rivets, Specimens from Two Fabricators 28 22. Typical Failures of Joints with One Row of Rivets, Specimens from Two Fabricators 28 23. Location of Failures -Specimens 51-7, 8 and 9 29 24. Location of Failures - Specimens 51-10, 11 and 12 29 25. Stress-Slip Curves for Specimens 51-7 through 51-12 30 26. Relationship Between Bearing Ratio and g/d 31 FIGURES (Continued) 27. Theoretical Relationship Between Efficiency and g/d 32 28. Theoretical Relationship Between Efficiency and Bearing Ratio 32 29. Relationship Between Bearing Ratio and Weighted Value of g/d for Test Specimens 32 30. Variation in Efficiency with Bearing Ratio 33 31. Variation in Efficiency with g/d 34 32. Variation in Net Section Effectiveness with Bearing Ratio 35 33. Effect of Bearing Ratio on Rivet Shearing Strength 36 34. Longitudinal Strains on Gage Line A-A at Stress of 20,000 psi on Gross Section 36 35. Percentage of Load in Specimen Midway Between Transverse Rows of Holes 37 36. Percentage of Load in Outer Plates Midway Between Transverse Rows of Rivets 38 37. Variation of Efficiencies of 51-Series Tension Specimens 39 38. Variation of Gross Section Yield and Ultimate Compressive Stress with Bearing Ratio 40 TABLES 1. Allowable Working Stresses of Current Specifications 9 2. Dimensions of Tensile Specimens 12 3. Summary of Mechanical Properties of Plate Material 13 4. Summary of Mechanical Properties of Plate Material for Compression Specimens 14 5. Summary of Results of 49 Series of Static Tests 17 6. Summary of Results of 50 Series of Static Tests 19 7. Summary of Results of 51 Series of Static Tests 22 8. Summary of Results of Compression Tests 30 I. INTRODUCTION I. Bearing Pressure in Riveted Structural Connections Riveted tension connections which are designed in accordance with current specifications for build- ings or bridges are proportioned such that the stresses in the various parts or components of the connections are within certain allowable limits. These allowable working stress limits apply to the tensile stresses in the connected plates or members as well as the shearing stresses in the rivets and the bearing stresses in the rivets and plates. In evalu- ating the stresses for the design of these tension members it is generally assumed that the tension is uniformly distributed across the width of the connected members, and that the load is equally divided among the rivets. The average ultimate tensile and shearing strengths of riveted structural connections can be evaluated by tests, but the effect of bearing pres- sure upon the strength or behavior of such connections has been somewhat elusive. Some in- vestigators have studied the effect of bearing on slip in the connections, others the effect of bearing on the deformation, and some the effect of bearing on the ultimate strength of the members. Never- theless, since the effect of bearing appears to be of a secondary nature, it has been extremely difficult to evaluate. The origin of the allowable bearing pressures in our current specifications is uncertain. In fact, at one time some of the specifications did not include limiting stresses for bearing. Nevertheless, all of the major specifications for buildings or bridges now provide for a maximum allowable bearing pressure. The literature contains many references'1"* con- cerning riveted connections, but relatively few of these references involve studies of bearing pressure in riveted joints per se. One of the earliest refer- ences in which bearing was considered is that by A. B. W. Kennedy(2) wherein the author concludes that, "High bearing pressure weakens the joints mainly by causing such distortion of the metal * Superscripts in parentheses refer to references listed in the bibliography. that the stress becomes very unequally distributed, the intensity of stress at the point where fracture begins being much greater than its calculated aver- age value." Statements such as this probably were responsible, to a large extent, for the establishment of the allowable working stresses in bearing. In a 1911 report on tension tests of nickel steel riveted joints, Talbot and Moore(3) note that, "The limiting or safe bearing stress of the rivets or of the plate is ordinarily taken at 11/3 to 11/ times the tensile stress." The value of 11/_ has remained in most bridge specifications throughout the years; however, the principal American specification for buildings has permitted an increase to 2 times the tensile stress. For many years, the question of bearing pres- sure received attention in the German literature. (4, 5, 6, 7, 8, 9, 10) In these various references it will be found that some engineers favored the use of allow- able bearing values 21/2 times the allowable tension, while others favored the retention of a bearing value of 2 or less. Nevertheless, the German speci- fications for bridges have permitted the use of 21/ while their building specifications have retained a value of 2. Just as in Germany, the allowable bearing stresses in the United States vary from one specifi- cation to another. However, in the United States, the higher allowable bearing stresses are generally found in the building specifications rather than in those for bridges. The current allowable working stresses and the corresponding ratios of tension : shear : bearing for the principal American specifi- cations are given in Table 1. On the basis of the allowable stress shown above for conditions of double shear, bearing becomes Table 1. Allowable Tension, psi Shear, psi Bearing, psi (Double shear) (Single shear) T:S:B ratio (Double shear) (Single shear) Working Stresses of Current Specifications Specification AISC(0) AREA(") AASHO(1) (Bldgs.) (Bridges) (Bridges) 20,000 18,000 18,000 15,000 13,500 13,500 . ... . 27,000 27,000 40,000 32,000 1.0:0.75:2.0 1.0:0.75:1.6 1.00:0.75:1.5 1.0:0.75:1.5 ILLINOIS ENGINEERING EXPERIMENT STATION critical only when the thickness of the connected material is less than 0.785 times the rivet diameter for the AREA and AASHO specifications and only when the thickness becomes less than 0.59 times the rivet diameter for the AISC specification. Thus, the allowable bearing stresses are of consequence only when the connected material becomes rela- tively thin. 2. Object and Scope of Investigation Engineers have long sought a means of justify- ing or possibly increasing the allowable bearing stresses for structural connections subjected to ten- sile loads. One of the engineers who has most actively pursued this question of bearing pressure has been Mr. Jonathan Jones. For a number of years he has been chairman of a committee of the Research Council on Riveted and Bolted Structural Joints* which has been studying the question of rivet bearing. If an increase in bearing could be permitted, a saving would be realized in the cost of some riveted structures. The increase in bearing would obviously eliminate some rivets and thus save on the fabrica- tion and erection costs. However, in all probability, it would also provide the additional economy of reduced drafting room and shop costs by increasing the applicability of standard connections and re- ducing the number of standard connections which have to be redesigned because of high bearing. In considering fully the many aspects of the question of bearing pressure in tension, repeated loadings as well as static loading conditions must be taken into account. However, in this instance only static loading conditions will be considered. This type of loading is applicable to most buildings and the longer span bridges; it covers a large per- centage of the cases where bearing may be critical. In 1947 the Project 1 Committee of the Re- search Council on Riveted and Bolted Structural Joints initiated an experimental investigation at the University of Illinois to determine the effect of high rivet bearing on the behavior of riveted joints. Since a variation in the bearing pressure in * The Research Council on Riveted and Bolted Structural Joints was organized in 1947 to carry on investigations to determine the behavior of riveted and bolted connections. The organization and its research programs have been sponsored by the following groups: American Institute of Steel Construction, Inc.; American Iron and Steel Institute; American Society of Civil Engineers; Association of American Railroads; Canadian Institute of Steel Construction, Inc.; the Engineering Foundation; State of Illinois, Division of Highways; University of Illinois; Industrial Fasteners Institute; Northwestern University; U. S. Dept. of Commerce, Bureau of Public Roads; the University of Washington; and the Washington State Council for Highway Research. a riveted connection can be obtained only by vary- ing details in the joint design, the program also has included a number of other variables. These other variables involve such factors as plate thickness, rivet grip, transverse rivet spacing, rivet pattern, and the location of the critical section. Thus in any study of riveted joints it is impossible to consider the effect on the behavior of the joints of only one variable at a time. The first series of tests conducted, herein noted as the 49 Series, was limited to double-strap butt- type joints which were designed to fail in the center plate rather than in the outer strap plates. At the critical section, the rivets of the connections were in double shear. The second series of tests, the 50 Series, was planned to obtain information concerning the effect of bearing in double-strap butt-type joints designed to fail in the outer plates. These joints, as well as those of the previous study, were all tested stati- cally and at room temperature. The third and final phase of the investigation was designed to answer some of the questions which developed in the first two series of tests, and to pro- vide information concerning the effect of rivet bearing pressure on the behavior of compression joints. This third phase of the investigation will be referred to as the 50X Series and the 51 Series of tests. In these three studies 131 riveted connections have been tested. 3. Acknowledgments The experimental investigations described in this bulletin were a part of the research program of the Civil Engineering Department at the Univer- sity of Illinois and conducted in cooperation with the Illinois Division of Highways, the Department of Commerce-Bureau of Public Roads, and the Re- search Council on Riveted and Bolted Structural Joints. The work constitutes a part of the struc- tural research program of the Department of Civil Engineering, of which Dr. N. M. Newmark is Head. The 49 and 50 Series tests were made by W. K. Becker,"141 J. M. Massard,(15) as Research Assistants in Civil Engineering, working under the direct supervision of G. K. Sinnamon, Research As- sociate Professor of Civil Engineering, and the 51 Series tests by R. C. Bergendoff,16) also a Research Assistant in Civil Engineering. The entire investi- gation has been conducted under the general direc- tion of the author. Bul.454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS The details of the specimens and the scope of the program were planned in cooperation with the Project 1 Committee of the Research Council on Riveted and Bolted Structural Joints. This com- mittee is concerned with the effect of bearing pres- sure on the static and fatigue strength of riveted joints and composed of the following members: Jonathan Jones,t Chairman Formerly Bethlehem Steel Company Raymond Archibald J. E. Greiner Company Frank Baron University of California W. H. Munse University of Illinois C. Neufeld Canadian Pacific Railroad N. M. Newmark University of Illinois T. C. Sheddt University of Illinois W. M. Wilson* University of Illinois L. T. Wyly Northwestern University t Retired * Deceased II. DESCRIPTION OF SPECIMENS AND TESTS 4. Description of Specimens A total of 131 riveted specimens were tested in the three phases of this investigation. The first program, the 49 Series (49, 49X, and 49XX), con- sisted of 32 specimens in two groups, an original series and a retest series. In the original series there were ten different designs of joints each tested in duplicate. Five of the joints contained 34-in. rivets and five contained 1-in. rivets. The retest series consisted of six different joints tested in duplicate. All of the members in the 49 Series consisted of double-strap, butt-type, flat plate joints with five rivets connecting the plates. The details of the members are shown in Fig. 1 and the dimensions are summarized in Table 2. The 33 riveted specimens of the 50 Series were also double-strap butt-type joints fabricated with six rivets placed in two transverse rows. These members consisted of 11 different joint sizes, each of which was tested in triplicate. The dimensions and details of the 50 Series joints may be found in Table 2 and Fig. 1 also. Both tension and compression specimens were included in the 50X and 51 Series of tests. The tension specimens consisted of eight different joint designs furnished in triplicate by two fabricators. Thus, a total of 48 double-strap butt-type joints were tested in tension. Eighteen double-strap butt- type joints, three specimens each of six designs, were tested in compression. The details of these tension and compression specimens are given in Figs. 1 and 2 and in Table 2. In proportioning the specimens for each series of tests, the ratio of rivet shear to plate tension in the critical member was maintained constant. This eliminated the tension: shear ratio as a variable in I I -0 --- 0- -0--0--0- A -B-W»B- -4 C E --, (0) Series 49 and 49-X A - B 4-B A- 0-0---0- C ET - IP I I I -(s-----9- G0-0-0- S- - 4- -X Ses 8-XX (b}/ Series 49 -XX (C) Series 50-X (d) Series 50 and 5/ Fig. 1. Dimensions and Details of Tensile Specimens Table 2 Dimensions of Tensile Specimens Speci- Rivet men Diam. No. in. 49-1 49-2 49-3 ?4 49-4 49-5 49-6 49-7 49-8 1 49-9 49-10 49-1X % 49-4X " 49-6X 1 49-9X 1 49-1XX 4 49-6XX 1 50-1 50-2 % 50-3 50-4 50-5 50-6 A 50-7 50-8 50-9 50-10 1 50-11 50-4X .. 50-7X 51-1 51-2 % 51-3 51-4 51-5 1 51-6 50-X6 7A 50-X7 w ti 6.46 0.76 7.40 0.65 8.82 0.50 1.17 0.38 .05 0.32 8.53 1.00 9.97 0.82 2.30 0.64 4.82 0.50 .63 0.46 .47 0.73 .18 0.38 8.51 1.00 .82 0.50 .47 0.73 8.52 1.00 8.80 1 .38 1 .04 1 .02 1V .48 1½ .64 1 i .24 19 .26 1½1 .62 111 .50 1½ '.32 1 4 .02 ... '.24 ... .48 9/6 .34 11 .50 j/1 .84 116 .44 1mie .72 9i6 .22 1% .02 1½j 1 13 12 14 16 I6 11 14 i 10 13 17 11 12 17 17 12 14 17 11 17 10 13 15 8 10 Dimensions, in.* A B P 1.08 2.15 .... 1.23 2.47 1.47 2.94 . . 1.86 3.72 .. 2.17 4.35 .. 1.42 2.84 ... 1.66 3.32 ... 2.05 4.10 . . 2.47 4.94 . . 2.77 5.54 ... 1.08 2.16 1.08 1.86 3.73 1.86 1.42 2.84 1.42 2.47 4.94 2.47 1,08 2.16 1l\' 1.42 2.84 2 1.75 2.65 .... 1.75 3.44 .... 1.75 4.77 .... 1.88 3.13 .... 1.88 3.86 .... 1.88 4.94 .... 1.88 6.74 .... 2.00 3.63 .... 2.00 4.31 .... 2.00 5.25 ... 2.00 6.66 .... 1.88 3.13 .... 1.88 6.74 .... 1.58 3.16 .... 1.72 3.45 . 1.92 3.83 .... 1.97 3.95 .... 2.24 4.48 . 2.62 5.24 .... 1.37 2.74 .... 1.67 3.34 .... * See Fig. 1 for specimen details. Bul.454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS Specimen I 51-10 I I Fig. 2. Dimensions and Details of Compression Specimens the test program but made it necessary that the width and thickness of the connected sections be varied in order to obtain a range of values in the bearing ratio. By means of this procedure a varia- tion in bearing ratio of 1.28 to 3.05 was obtained for the 49 Series, 1.34 to 2.75 for the 50 Series, and 1.45 to 2.74 for the 51 Series of tension specimens. The variation in bearing: shear ratio for the compression specimens ranged from 1.78 to 4.21. Thus, a rela- tively wide range in bearing pressure was available for study in the investigation. In Table 2, a summary of the dimensions of the tensile specimens, it may be seen that the width of the members varied from 6.46 in. to 17.32 in. and the plates varied in thickness from 3/16 in. to 11/4 in. In addition, the rivet diameter was varied from % to 1 in. The fabrication of the test speci- mens was completed over a period of time in the shops of several large, prominent structural steel fabricators. Thus, the fabrication represents typ- ical large scale structural practice. In all cases the holes were subpunched and reamed, or drilled from the solid, all of the plate edges were milled to size, and the rivets were hot formed and hot driven with a pneumatic hammer. 518 3 14 Specimen 5/-7 * Coupon numbers followed by letters indicate Fabricator A. coupons are for specimens prepared by Fabricator B. t Each value is the average of three tests. All other 5. Properties of Materials All of the specimens were prepared from plates or members specified to be in accordance with ASTM Designation A-7 for structural grade steel. However, standard flat coupons were cut from the parent plates and tested in the laboratory to de- termine the actual mechancial properties of the parent material. The results of these coupon tests are summarized in Table 3 for the tension speci- mens; the results of the coupon tests for the com- pression specimens are presented in Table 4. All of these tests were performed in accordance with I Table 3 Summary of Mechanical Properties of Plate Material (Coupons Obtained from Same Plate Material as Specimens) Speci- Plate Yieldt Ultimatet Per Centt Per Centt men Thickness, Point Strength, Red. Elong., No.* in. ksi ksi Area. 8 in. 49-1 % 36.2 67.4 46.6 30.8 49-1X, 1XX % 30.0 60.2 55.6 29.9 49-2 % 36.9 66.4 47.9 25.6 49-3 i 34.5 63.0 51.7 29.4 49-4 % 39.5 66.6 46.3 24.8 49-4X % 36.0 62.0 54.9 30.3 49-5 4% 37.8 62.9 51.2 28.0 49-6 1 26.8 57.7 59.1 31.9 49-6X, 6XX 1 27.0 57.5 55.8 32.0 49-7 1i6 30.0 60.7 56.4 32.6 49-8 % 34.6 65.5 51.0 26.3 49-9 ½ 35.0 62.9 51.4 26.0 49-9X % 34.9 63.7 52.5 30.4 49-10 7e6 38.9 65.0 47.3 22.1 50-1,5 Me 37.8 63.4 52.4 28.4 50-2 ½ 37.0 59.7 53.4 30.0 50-3, 7X M«e 35.2 61.2 54.2 32.3 50-4, 4X % 36.0 62.0 54.9 30.3 50-6 Y 39.2 62.3 49.4 27.2 50-7 i 6 35.3 60.1 54.2 32.4 50-8 ?76 35.9 64.9 48.1 28.0 50-9 % 36.2 62.7 53.8 28.5 50-10 i6e 37.6 62.9 55.0 29.0 50-11 14 37.1 60.1 51.1 29.6 51-1 9/6 38.7 64.5 52.2 30.5 1AA is6 32.0 63.2 46.1 29.3 1AB /16 32.6 63.7 49.9 27.3 1AC 9ia 31.6 62.9 48.8 27.6 51-2 1/2 40.2 67.7 50.2 23.9 2AA ½1 37.4 64.2 48.8 24.9 2AB ½ 40.5 64.7 46.9 25.6 2AC t1 37.5 62.9 51.4 29.0 51-3 /1½ 39.7 65.5 50.4 26.5 3AA 7,1 39.4 67.2 46.1 26.0 3AB /e6 38.4 66.2 46.8 27.7 3AC 7/16 38.3 66.9 46.8 27.9 51-4 1ie6 38.1 67.0 51.2 26.2 4AA 1W6 31.8 66.8 28.3 24.2 4AB 1½6 31.4 66.7 40.7 25.9 4AC '316 32.0 66.1 37.8 25.4 51-5 As 35.4 66.8 49.2 28.6 5AA %s 38.2 62.1 46.8 27.8 5AB 1 ½6 32.5 63.4 50.6 27.2 5AC 1116 31.4 61 8 47.7 28.2 51-6 /16 37.6 64.1 51.3 30.4 6AA As6 33.6 60.5 49.8 27.1 6AB 916 36.0 63.2 48.6 25.2 6AC 916 32.1 61.6 50.8 28.3 50-X6 V 47.1 64.7 42.6 30.4 X6AA Y 43.3 69.6 47.1 27.3 X6AB ½ 40.9 64.4 46.5 26.3 X6AC Y 40.1 64.7 46.9 27.0 50-X7 lie 46.3 62.1 50.7 24.7 X7AA 418 47.2 65.5 45.2 30.0 X7AB '16 42.6 64.7 46.7 29.7 X7AC 316 43.7 65.1 45.4 27.5 ILLINOIS ENGINEERING EXPERIMENT STATION Fig. 4. Slip Gage on Tension Specimen Table 4 Summary of Mechanical Properties of Plate Material for Compression Specimens Specimen Plate Yield No. Thickness, Point, in. ksi 51-7 % 35.7 36.1C 51-8 3 40.5 42.1C 51-9 I 45.1 43.4C 51-10 Ma 47.0 49.1C 51-11 ' 43.5 43.7C 51-12 Yis 46.0 49.4C Fig. 3. 600,000 Lb. Testing Machine ASTM Designation E-8 for tension testing of metallic materials. The values of yield strength, ultimate strength, reduction of area, and elongation presented in Tables 3 and 4 indicate that in general, the mate- rials met the requirements of A-7. However, in a few instances the coupons did not comply fully with the strength requirements. This is particularly true of the coupon specimens for the 49 Series of tests. Nevertheless, it is believed that the materials used for the members of this program are typical of what would be obtained in practice when A-7 steel is specified. 6. Description of Equipment A 600,000 lb, screw-type Universal testing ma- Ultimate Strength, ksi 64.4 Per Cent Red. Area 51.4 Per Cent Elong., 8 in. 29.3 68.3 52.1 28.0 60.3 49.0 27.3 69.8 50.5 24.7 60.0 47.1 32.4 63.5 49.3 22.5 Note: C designates values obtained in compression tests. Each value is the average of two tests. chine was used for all of the tensile tests. This machine complete with a specimen may be seen in Fig. 3. In each test, a very carefully controlled consist- ent assembly and testing procedure was followed to eliminate from the tests any effects that might result from variations in the testing techniques. Pulling plates were welded to the ends of the test specimens and these plates, in turn, were bolted into pulling heads. The pulling heads were connected to the testing machine through pins which insured concentric loading on the test specimens. In the compression tests a loading block was clamped on the ends of the members for which the side or center plates were thin and required stiffen- ing to prevent local buckling. The members were Bul.454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS Fig. 6. Strain Gages Mounted on Specimen 50-5A Fig. 5. Slip Gages and Loading Blocks on Compression Specimens then placed in a 300,000 lb. screw-type Universal testing machine and loaded to failure. A number of measurements were made during the tension and compression tests; however, the principal measurement was the slip of the joints. For the slip of the tensile connections, dial gages were mounted on both edges of the specimen at the first transverse row of rivets. The manner in which these dials were mounted may be seen in Fig. 4. Slip measurements were made also on the com- pression specimens by means of mechanical dials. However, since these members differed in shape from the tension specimens, it was necessary to modify the slip measuring equipment for the com- pression tests. The arrangement of the loading block and the slip gages for the compression tests may be seen in Fig. 5. For the members of the 50 Series, electrical resistance strain gages were used to obtain an indi- cation of the strains in the outer critical plates during the tensile tests. An extensive pattern of strain measurements was used for the first two members tested, specimens 50-5A and 50-6B. The appearance of specimen 50-5A with its gages may be seen in Fig. 6. On the basis of the results of these first two tests, a standard gage pattern was selected for use with one specimen of each remaining type of joint to be tested. This standard gage pattern, the extensive patterns of gages for specimens 50-6B and 50-5A, and the gage patterns for plain plate specimens 50-4X and 50-7X are shown in Fig. 7. These strain gages, it was hoped, would help to ex- plain the general behavior of the riveted connec- tions when subjected to various tensile loads. In addition to the strain measurements, one specimen of each type in the 50 Series of tests was coated with "stresscoat."* Stresscoat was used to determine qualitatively the general pattern of strain distribution in the test specimens during the test. * A brittle lacquer coating which cracks when strained. It may be used to indicate the direction and magnitude of the principal strains. ILLINOIS ENGINEERING EXPERIMENT STATION Iand+ d locan and direction f train gges I and ÷ indicates location and direction of strain gages A A 50- 5A ._ _,_ A A___A A S4X V 7XB 50-4X6. TXB Fig. 7. Patterns of Strain Gages for Various 50 Series Specimens 7. Description of Tests As noted previously, the testing procedure was kept as uniform and consistent as possible through- out the entire program. The members were care- fully aligned as they were installed in the testing machine, carefully welded to pulling plates, and then loaded slightly before the entire assembly was bolted tight. This procedure reduced to a minimum the initial eccentricity of load in the joints. During the tests, load was applied to the speci- mens with the head of the testing machine moving at a uniform rate of 0.05 in. per minute. Although the same rate of loading was used during the entire test, the machine was stopped periodically to per- mit the reading of the slip and strain gages. Just prior to reaching the maximum load carrying ca- pacity of a member, the slip gages were removed and the joint then loaded to failure. III. RESULTS OF TESTS 8. Results of Tensile Tests (a) 49 Series. The results of the 32 tests of the 49 Series are summarized in Table 5. For each joint, the table lists values of ultimate net tensile, shearing and rivet bearing stress, the ratio of rivet bearing stress to plate tensile stress (bearing ratio) and the theoretical and test efficiencies. Although current specifications require that in computing the net area of a tensile member the diameter of the rivet hole shall be taken as 1/8 in. greater than the nominal diameter of the rivet, the net sections of the joints tested in this investigation have been based on the actual size of the rivet holes, a value 1/16 in. larger than the nominal rivet diameter. Theoretical efficiencies were obtained by the usual procedure of determining the ratio of critical net area to the gross area of the member. The test efficiencies are the ratio of the average ultimate tensile stress on the gross section of the specimen to the ultimate tensile coupon strength of the material used in the specimens. In general, there was good agreement between the ultimate strength of duplicate joints, the great- est difference being of the order of 7%. However, a comparison of the results of the various specimens shows that there was a rather large difference in the ultimate net tensile strengths of several very similar connections. Specimens 49-1B and 49- 1XXB exhibited strengths varying from 45,900 to 64,500 psi, although the geometry of these joints differed only slightly. In the original series of tests, the efficiencies of the 49-1 specimens were found to be extremely low and the efficiencies of the 49-6 specimens somewhat high. Since this behavior had not been expected, the 49-1X and 49-6X retest series of specimens were added to the program to ascertain whether these strengths were representative. In addition, the 49-1XX and 49-6XX joints of the retest series were included to determine whether the wide rivet spacing in the first transverse row of rivets might have been the cause for the low efficiency in the original series. However, the results of the tests clearly indicate that varying the rivet spacing in the first row had no consistent effect on the strength of the joints used in these tests. In the retest series, the efficiency of the 49-1X specimen was 20% greater than that of the dupli- cate joints (49-1) in the original series. Although considerable thought and study have been given to this variation in efficiency, it has not been possible to explain the extremely low efficiencies of the 49-1 specimens. As noted earlier, the load-slip behavior was ob- tained for each of the connections in the 49 Series of tests. These relationships, shown in Figs. 8 and 9, provide a means of comparing the relative defor- mations in the various joints. However, it is im- portant to realize that the slip as measured in these tests, using mechanical dials, presents a composite Table 5 Summary of Results of 49 Series of Static Tests Spec. Ultimate Ultimate Stress, ksi Bearing Efficiency of No. Load, ean Ratio Joint, kips Tensile Shear- Bearing percent ing Theo. By Test Original Series 49-iA 180.7 49.20 40.90 63.40 1.29 74.8 54.6 49-1B 168.6 45.9 38.2 59.1 1.29 74.8 51.0 49-2A 211.7 56.4 47.9 86.9 1.54 78.0 66.3 49-2B 214.2 56.9 48.5 87.6 1.54 78.0 66.9 49-3A 195.0 54.5 44.1 104.4 1.90 81.6 70.6 49-3B 196.0 54.1 44.4 103.7 1.92 81.6 70.0 49-4A 188.2 52.3 42.6 133.1 2.55 85.5 67.1 49-4B 202.0 55.1 45.7 140.3 2.55 85.5 70.7 49-5A 191.2 52.0 43.3 158.3 3.05 87.5 72.4 49-5B 194.2 52.5 44.Ot 159.8 3.05 87.5 73.0 49-6A 390.4 60.8 49.7* 78.0 1.28 75.1 >79.2 49-6B 389.9 61.1 49.6* 78.2 1.28 75.1 >79.5 49-7A 341.1 52.9 43.4 83.0 1.57 78.7 68.6 49-7B 334.4 52.2 42.6 81.9 1.57 78.7 67.6 49-8A 370.0 56.4 47.1 114.7 2.04 82.7 71.2 49-8B 369.0 56.2 47.0 114.4 2.03 82.7 71.0 49-9A 331.2 51.5 42.2 130.9 2.54 85.6 70.2 49-9B 328.6 51.2 41.8 129.9 2.54 85.6 69.7 49-10A 341.9 51.7 43.5t 149.9 2.90 87.2 69.4 49-10B 357.0 53.8 45.5 156.2 2.90 87.2 72.2 Retest Series 49-1XA 211.6 59.5 47.9 76.9 1.29 74.9 74.0 49-1XB 209.2 58.8 47.4 76.0 1.28 74.9 73.2 49-1XXA 208.9 58.7 47.3* 75.9 1.29 74.9 >73.1 49-1XXB 229.4 64.5 51.9 83.3 1.29 74.9 80.3 49-4XA 214.3 59.4 48.5 151.2 2.55 85.5 81.8 49-4XB 211.9 58.4 48.0 148.7 2.55 85.5 80.5 49-6XA 368.0 57.5 46.9* 73.6 1.28 75.1 >75.1 49-6XB 377.0 59.2 48.0 75.6 1.28 75.0 77.2 49-6XXA 376.0 58,7 47.9* 75.1 1.28 75.1 >76.7 49-6XXB 349.3 54.7 44.5* 69.9 1.28 75.0 >71.4 49-9XA 349.6 55.6 44.5t 141.3 2.54 85.7 74.8 49-9XB 350.3 55.7 44.6 141.3 2.54 85.7 74.9 * Denotes failure by shearing of the rivets. t Denotes combined plate and rivet failure. ILLINOIS ENGINEERING EXPERIMENT STATION Fig. 8. Stress-Slip Curves for Original 49 Series Fig. 9. Stress-Slip Curves for Retest 49 Series picture of deformation in the joints. The so-called slip measurement represents the slipping between the plates, some elastic and/or plastic deformation of the plates, and the shearing and bending distor- tion of the rivets. Thus, it indicates more than just the relative slipping of the plates at the rivets. From a comparison of the various stress-slip curves of Fig. 8 it is evident that the behavior of the duplicate specimens was generally quite con- sistent. The smoothness of the various curves indi- cates that the rivets filled or nearly filled the holes; however, the general shape of the curves shows that the greatest deformation occurred in those joints in which the plates were wide and thin (highest bearing). Since the joints with a small rivet grip may be expected to have tight rivets, it is obvious that the large slip exhibited in the figure results from a plastic straining of the plates and rivets. Another and possibly one of the most significant factors to be noted in this figure is the small amount Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS Table 6 Summary of Results of 50 Series of Static Tests Spec. Ultimate Ultimate Stress, ksi Bearing No. Load, ei s e Ratio kips Tensile Shear- Bearing ing 50-1A 50-1B 50-1C 50-2A 50-2B 50-2C 50-3A 50-3B 50-3C 50-4A 50-4B 50-4C 50-5A 50-5B 50-5C 50-6A 50-6B 50-6C 50-7A 50-7B 50-7C 50-8A 50-8B 50-8C 50-9A 50-9B 50-9C 50-10A 50-10B 50-10C 50-11A 50-11B 50-11C 50-4XA 50-4XB 50-7XA 50-7XB 271.1 269.2 270.3 246.6 244.0 245.5 225 6 240.9 232.8 358.3 355.8 360.3 358.3 358.6 361.5 347.0 351.9 337.6 288.8 295.3 285.2 442.7 444.5 442.2 436.7 448.9 454.8 465.2 471.5 460.8 393.3 392.2 399.5 180.4 179.8 160.3 165.5 51.1 50.8 51.0 46.5 46.9 46.3 42.6 45.4 43.9 49.7 49.3* 49.9* 49.7t 49.7t 50.1* 48.1* 48.8* 46.8* 40. Ot 40.9f 39.5t 47.0 47.2t 46.9* 46.3* 47.6* 48.3* 49.4t 50. ot 48.9t 42.4 41.6 42.4t * Denotes failure by shearing of the rivets. t Denotes combined plate and rivet failure. Efficiency of Joint, percent Theo. By Test 72.3 77.2 72.3 77.1 72.3 77.4 76.5 82.6 76.5 81.4 76.5 82.9 81.3 76.9 81.3 83.0 81.3 80.1 71.9 77.0 71.9 >76.5 71.9 >77.3 75.5 77.9 75.5 78.0 75.5 >79.4 79.4 >79.5 79.4 >81.2 79.4 >79.9 83.7 73.3 83.7 76.1 83.7 73.2 71.7 70.8 71.7 71.6 71.7 >71.5 74.7 >73.8 74.7 >75.9 74.7 >76.9 78.0 79.5 78.0 81.6 78.0 79.4 81.6 79.4 81.6 77.3 81.6 79.0 71.9 77.6 71.9 77.1 83.7 81.6 83.7 84.2 of slip present at the maximum load in the 49-1 specimens. For these specimens, the slip or deforma- tion at the ultimate load was about one third as great as the smallest corresponding slip for any of the other joints in this series. In Fig. 9 the stress-slip behavior of the 49-1 and 49-6 specimens are compared with the corre- sponding relationships obtained from the retest specimens. Here again, the relatively small amount of deformation in the 49-1 specimens is readily evident. However, the curves for all of the 49-6, -6X, and -6XX joints are in good agreement. (b) 50 Series. In the 50 Series the outer plates of the members were critical. The results of these tests are briefly summarized in Table 6 in a man- ner similar to that used for the 49 Series tests. It is immediately evident that the strengths of the joints in the 50 Series were more consistent than those obtained in the 49 Series and that the efficiencies of the members were higher than those of the 49 Series. The ultimate tensile strengths of the specimens ranged from 52,500 to 67,900 psi; the specimens having strengths less than 60,000 psi were those with high bearing pressures, wide thin outer plates, and the lower coupon strengths. Also included in this program were tests of plates which had open holes and were of the same widths, thicknesses, and hole patterns as the outer plates of specimens 50-4 and 50-7. The results of these plain plate tests are presented at the end of Table 6 and show that the strengths of the plain plate specimens were as great or greater than the strengths of the similar plates in the riveted joints. Slip of the joints, as measured at the first transverse row of rivets, is shown in Fig. 10. These curves differ from those of the 49 Series in that they exhibit a number of sharp breaks. These sudden jogs in the "elastic" regions of the curves may be attributed to an initial slip which occurs when the load overcomes the friction between the plates. For the 50-9 and 50-10 specimens these breaks in the curve are quite marked at a stress on the net sec- tion of about 20,000 psi. The more pronounced breaks in the upper regions of the stress-slip curves were probably caused by the plastic deformations and gradual slipping of the plates which occurred when the load was stopped for short periods of time to permit the taking of strain readings. During these load stops, usually 12 or so for each test, this slipping tendency or increase in deformation could readily be observed. The "yielding action" in the 50 Series joints generally occurred at a stress of between 40,000 and 50,000 psi on the net section, a value slightly above the yield strength of the plate material. Since the 49 Series exhibited a similar behavior, but at a stress approximately equal to the yield strength, it appears that the use of a full transverse row of rivets, three rather than two, produced an increase in the net stress at which this general yielding occurred. (c) 51 Series. The results of the third group of tensile tests, the 51 Series, are summarized in Table 7. The values presented in this table, as in the two previous tables, are based on the actual hole size and the measured dimensions of the specimens. The tensile specimens of the 51 Series were pre- pared in triplicate by two different fabricators (manufacturers A and B). Thus, a total of six identical specimens are presented for each type of specimen. The members prepared by fabricator A may be distinguished by the letter "A" included in the specimen number. All of the remaining speci- mens were prepared by fabricator B. In general, ILLINOIS ENGINEERING EXPERIMENT STATION 80 s/ip /0" 3/4 "rivets A B C C A C 8 A 0 I 2 3 40 %8 rivets A C B C B A C B A A 8 C 4 5 6 7 80 \---i--- 20 /" rivets A B C A B C A B C A B C r) - - ------ --------- -- I ------ I -- I ------------ Specimen numbers Fig. 10. Stress-Slip Curves for Specimens of the 50 Series Bul.454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS to to to to to to to Fig. I1. Stress-Slip Curves for S the ultimate strengths and test efficiencies were fairly consistent for the three duplicate specimens of each group. However, it may be seen that at the highest bearing ratios, 2.01 for the members with 34 in. rivets and 2.74 for those with 1 in. rivets, the members provided test efficiencies which are as much as 8 and 14%, respectively, below the theo- retical efficiency. As in the case of the 49 and 50 Series, slip meas- urements were made at the first transverse row of rivets for each of the specimens. The stress-slip relationships obtained in these tests may be seen in Fig. 11. Each of these curves, just as in the pre- vious cases, represents the average values of slip determined on the edges of the tension specimens. The agreement between these stress-slip curves for pecimens of the 51 and 50-X Series duplicate specimens of the same types of joints seem to be somewhat better for the specimens from fabricator A than for those from fabricator B, although the curves for the specimens from fab- ricator B are nearly always above those of the specimens from fabricator A. In general, however, the curves are typical of what may be expected for riveted tension members and are in good agreement with those obtained in most of the 49 Series of tests. 9. Strain Distribution in Plates Extensive studies were made in the tests of the 50 Series to determine the pattern of strains in the plates during the tests. Some of these specimens were coated with a "stresscoat" to show the gen- eral strain pattern. The photographs in Fig. 12 ILLINOIS ENGINEERING EXPERIMENT STATION Table 7 Summary of Results of 51 Series of Static Tests Spec. Ultimate No. Load, kips 51-1-1 2 3 51-1-1A 2A 3A 51-2-1 2 3 51-2-1A 2A 3A 51-3-1 2 3 51-3-1A 2A 3A 51-4-1 2 3 51-4-1A 2A 3A 51-5-1 2 3 51-5-1A 2A 3A 51-6-1 2 3 51-6-1A 2A 3A 50-X6-1 2 3 50-X6-1A 2A 3A 50-X7-1 2 3 50-X7-1A 2A 3A 267.9 245.0 244.6 228.8 248.9 238.9 279.2 280.0 247.2 261.9 231.3 241.8 266.6 267.9 244.2 229.0 242.6 251.0 443.2* 387.7* 400.0* 457.2 425.3 409.0 469.6 461.1 409.5 400.0 369.8 376.0 386.7 385.6 389.0 369.3 375.4 367.8 175.2t 167.7f 168.0 178.3* 184.2t 189.1 178.4t 169.0Ot 169.1 i 138.9t 137.5 136.81 Ultimate Stres Tensile Shear- ing * Denotes failure by shearing of the rivets. t Denotes combined plate and rivet failure. $ Denotes failure by tearing of the plate. s, ksi Bearing Efficiency of Ratio Joint, Bearing percent Then. By Test 103.9 1.56 72.5 76.4 95.5 1.56 72.5 70.0 95.0 1.56 72.5 69.7 90.2 1.56 72.5 67.6 95.4 1.56 72.5 71.5 94.0 1.56 72.5 70.4 123.7 1.76 74.8 80.5 123.7 1.76 74.8 79.5 109.2 1.76 74.8 70.1 116.3 1.76 74.8 78.9 101.5 1.76 74.8 68.8 106.1 1.76 74.8 72.7 131.7 2.01 77.2 78.8 133.4 2 01 77.2 79.7 121.6 2 01 77.2 72.6 119.2 2.01 77.2 69.2 125.5 2 01 77.2 72.9 129.7 2 01 77.2 75.2 89.3 1 45 71.7 >68.2 77.8 1.45 71.7 >59.3 80.2 1.45 71.7 >61.2 93.7 1.45 71.7 71.2 86.7 1 45 71.7 65.8 82.8 1.45 71.7 62.9 113.6 1.71 74.9 75.9 111.4 1.71 74.9 74.4 99.1 1.71 74.9 66.2 100.2 1.71 74.9 71.6 92.3 1.71 74.9 65.5 93.7 1.71 74.9 67.0 112.4 2.09 78.3 66.2 112.6 2.09 78.3 66.3 113.1 2.09 78.3 66.3 107.6 2.09 78.3 66.4 109.1 2.09 78.3 67.4 108.3 2.09 78.3 66.9 112.5 2.06 63.5 63.5 107.7 2.06 63.5 60.8 108.4 2.06 63.5 61.2 114.8 2.06 63.5 >62.9 118.5 2.06 63.5 64.9 121.1 2.06 63.5 66.4 146.6 2.74 70.2 70.6 139.8 2.74 70.2 66.9 138.9 2.74 70.2 66.9 123.6 2.74 70.2 57.1 123.7 2.74 70.2 58.1 122.4 2.74 70.2 56.3 46,650 psi net 34,40U psi net Fig. 12. Stresscoat Patterns for Specimen 50-1 IA illustrate the stresscoat patterns obtained for speci- men 50-11A at 46,650 and 54,460 psi on the net section of the joint. In general the cracks in the stresscoat developed first along the sides of the rivets at the first row and then spread transversely until the stresscoat at the critical section was extensively cracked. Luder's lines (at 45 deg. to the line of stress) next began to spread down into the gross section from their origin at the edges of the rivets. Some of these Luder's lines can be seen in the upper part of Fig. 12. After the formation of these 45-deg. lines, horizontal shear bands began to form in the gross section of the specimen, indicating the exist- ence of inelastic strains in the entire gross section of the joint. At least one specimen of each type in the 50 Series was tested with electrical strain gages ar- ranged to provide information concerning the quantitative values of strain as well as the general nature of the strain distribution in the joint. In addition, the gages provided data which illustrate the manner in which the plates function in resisting the loads to which they are subjected. The distribution of longitudinal strains on the various gage lines (see Fig. 7 for the location of the various gage lines and gage numbers) of speci- men 50-6B are shown in Figs. 13a and b. The longitudinal strain on gage line A-A, a transverse section midway between the two rows of rivets, shows that the longitudinal strains in the plate behind each of the rivets increased gradually in tension until the members began to yield and the Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS Gage ni (0a) Transverse distribution of longitudinal strains 'mber 2(nn1) 1600 1400 1200, /000 800 600 400' 200' 40 39 38 37 36 (b) Longitudinal distribution of longitudinal strains 12C 40 2C -20 -40 -60 0- 0 0 0 C C on 0 '0 -RO( Curves ore marked with load in kips at which s/rains were recorded 2224 19/3/9 -118.9 198 31 46 Goge number ' of rive/t \ -N \ \\ -vv Goge line D-D t. of rive/ & \ \ Fig. 13. Distribution of Longitudinal Strains, Specimen 50-68 Gage line C-C 250 /973 /575 //89 169 9 699 19.8 t ? I * 1 -800 ILLINOIS ENGINEERING EXPERIMENT STATION 60 40 Sages on Sline 4-4 400 x 10' inln Strain - - ----- 01 _____ _ Fig. 14. Stress-Strain Curves for Individual Gages Specimen 50-6B rivets slipped into bearing. After the joint had slipped slightly, the strain in the plate behind the rivets was reversed and went into compression. This same action is shown also on gage line DD, which presents the longitudinal distribution of longitudinal strains along the center row of rivets. Gages 1 and 5 of this diagram were located directly behind the rivets and show these compressive strains. Since these gages, because of their size and the space limitations, were mounted about 3/4 in. from the edge of the rivet holes, it is obvious that the compressive strains at the edges of the rivet holes were considerably higher than those meas- ured by gages 1 and 5. The strain concentrations at a point near the edges of the rivets are shown in Fig. 13a for gage line B-B. Again, because of the limitations imposed by the gage width and the size of the rivet head, the strains at the edge of the rivet were necessarily measured a short distance from the edge of the rivet hole. Nevertheless, the curves obtained from these gages indicate that in the initial stages of loading, the clamping force of the rivets tends to distribute the load uniformly to the plates. However, after the plates start to slip, the strain at the edge of the rivet heads increases at a much greater rate than does the strain in the balance of the section. Thus, as the rivets slip into bearing they produce a change in the strain distribution as well as the general behavior of the various connected parts. The strains on gage line C-C, a longitudinal line midway between the rivet line, are shown in Fig. 13b. It is evident from the strains measured by gage No. 38 that large plastic strains are reached on the entire net section somewhat before the gross section of the plate begins to yield. Curves of net tensile stress vs. strain for many of the individual gages of specimen 50-6B are shown in Fig. 14. From the curves for line B-B it can be seen that general yielding occurred on the net section at a stress of approximately 43,000 psi. However, a closer examination of the curves will indicate that some of the gages exhibited a marked change in rate of straining at a stress of as little as 20,000 psi on the net section or the stress at which the joint first slipped. In the lower portion of Fig. 14 are shown the strains for the AX-5 (two elements, cross-type) gages which were placed in front of and behind the rivets to indicate strains in both the transverse and longitudinal directions. The odd numbered gages (those shown by solid curves) indicate the longi- tudinal strains, and the even numbered gages indi- cate the transverse strains. Noting that strain to the right of the respective origins indicates a tensile strain, one can visualize the action of the plate material around the rivets. Curves 5 and 11, longi- tudinal gages directly behind rivets of the first transverse row, show that after having been in tension initially, the plate material behind these rivets went into compression as the joint slipped. At a stress on the net section of about 40,000 psi, these same gages showed a compressive yielding. The transverse distribution of longitudinal strains for the remainder of the specimens on which strain measurements were made are shown in Fig. 15. These diagrams show that the general nature of the strain distribution for all of the riveted specimens was similar to that of specimen 50-6B. From the strain gages placed on the plain plates with holes, specimens 50-4X and 50-7X, the pat- tern of strains which occurred as a result of the holes alone was obtained. The longitudinal strains in the plain plates remained in tension, of course, with no reversal such as occurred above the rivets Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS * 50-4XB 50- 5A -v0 W- --I rtf+-+1 - 50 --7X4 *50 - 7XA 50 - 8C 50-9C 50 I-/OC e 50- I/B Note:- Plates ore marked with load in kips at which strains were recorded * Plate with open holes Fig. 15. Transverse Distribution of Longitudinal Strains at Various Loads 246.9 2077 1579 118.5 1a 50- 4C * 50- 4XA 0 ILLINOIS ENGINEERING EXPERIMENT STATION 49-1B B =1.29 Et 51.0% 49-1XXB B 1.29 Et = 80.3% 49-6B 49-5B (Rivet Failure) (Rivet and Plate Failure) B =1.28 B 3.05 Fig. 16. Typical Fractures of the 49 Series Specimens in the riveted joints. When these are compared with the corresponding riveted specimens, 50-4C and 50-7C, a considerable difference in the strain dis- tribution obtained from the two types of specimens becomes evident. For specimen 50-4XA and 50-7XA a strain gage was placed in one of the open holes. The longi- tudinal strain concentration factors at the edge of this hole as computed from these gages were 2.3 for specimen 50-4XA and 2.6 for specimen 50-7XA based on the average net section strain. Although not shown in Fig. 7, a transverse line of longitudinal gages was placed on both outer plates of each specimen across the gross section of the member at a distance of 1/2 plate width below the free end of the center plate. The load distribu- tion as indicated by the strains measured at the gross section was not, in general, equal between the two outer plates; in one case there was about a 40% difference between the strains in the two plates. However, the average difference was 5 to 10%. The transverse distribution of these gross 49-4A 49-4XA B 2.55 Et - 67.1% B - 2.55 Et = 81.8% Fig. 17. Fractures of Specimens Exhibiting Extreme Range in Efficiency. 49 Series section strains in any particular plate was fairly uniform in all cases. 10. Fractures of Tensile Connections The locations of the fractures of the various tensile specimens are noted in the results, Tables 5, 6 and 7. For the 49 Series there were four general types of failure encountered: (1) a shear failure of the rivets, (2) a tension failure of the middle plate across a transverse section through the first row of rivets, (3) a tension failure of the middle plate on a zigzag section through the two rivets of the first row of rivets and the middle rivet of the second row of rivets, and (4) a shear failure of some of the rivets and a tensile or tearing failure in a part of the middle plate. Fractures of these four types may be seen in Fig. 16. The zigzag type of fracture occurred only in the joints of large widths, indicating that the geometry of the member may have some effect on the mode of fracture of joints which have similar shear and tensile areas. Another observation that may be made from the fractures of these test specimens is 49-3A (Plate Failure) B 1.90 49-9XB (Plate Failure) B 2.54 m. ,.- Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS Specimen 50-8A Specimen 50-8B B = 1.56 (Plate Failure) (Rivet and Plate Failure) B 1.34 B = 1.34 5 ./e >peci men ou-tý) pecImen ýU-/A (Rivet Failure) (Tearing Failure) B = 1.34 B = 2.75 Fig. 18. Typical Fractures of the 50 Series Specimens Fig. 19. Specimen 50-7B Showing Bulging and Tearing of Outer Plates the fact that a number of the rivets failed in shear. A shear ratio of 0.82* had been used in the design * This shear-tension ratio (the ratio of net plate to total shear area) is based on the nominal rivet diameter and the actual drilled hole size (nominal rivet diameter plus 1/16 in.). B = 2.01 (a) Fabricator B (b) Fabricator A Fig. 20. Typical Fractures of 51 Series with 3/4-in. Rivets. Specimens from Two Fabricators of the specimens and was considered low enough to insure failure of the plates. However, nine of the 49 Series members exhibited shear failures. The staggered rivet pattern of the 49 Series was chosen because it provided a "realistic" joint, one where the procedure of protecting the net section by omission of rivets in the first row was used. However, the zigzag fractures and those fractures in which the plates tore through the end indicate the presence of critical stagger spacings and/or end distances. Thus, it is necessary to have adequate rivet pitch and sufficient end distances in the joints ILLINOIS ENGINEERING EXPERIMENT STATION bS 1.43 B = 2.06 B = 1.71 D - z.uy (a) Fabricator B (b) Fabricator A Fig. 21. Typical Fractures of 51 Series with 1-in. Rivets. Specimens from Two Fabricators to prevent failure of the connected material on a zigzag path or the rivets from tearing or shearing through the ends of the members. In several instances extremely large variations were obtained in the efficiency of supposedly similar riveted joints. The fractures of two such cases may be seen in Fig. 17. In spite of the great range of efficiencies in these tests, the appearance of the fractures was not greatly different. This similarity B - 2.74 (a) Fabricator B (b) Fabricator A Fig. 22. Typical Failures of Joints with One Row of Rivets. Specimens from Two Fabricators in the fractures makes it extremely difficult to pro- vide an explanation for the significant variation in behavior obtained in the tests. The failures obtained in the 50 Series of tests were generally of two types: shear failures of the rivets, and tension failures of the outer plates. In some cases, however, a combination of the two occurred: a tension failure of the outer plate on one side of the joint and a shear failure of the rivets on the other. Typical failures of the 50 Series joints are shown in Fig. 18. Twenty of the 33 specimens tested in the 50 Series failed by shearing of the rivets, either com- pletely or in combination with the tearing of the plates. Since the ratio of rivet shear stress to plate tension stress was 0.75, this predominance of shear failures was wholly unexpected and indicates that, in many instances, the plate strength may have Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS 51-10 51-8 0-I I 31-Y Fig. 23. Location of Failures - Specimens 51-7, 8, 9 been somewhat higher or the strength of the rivet material somewhat lower than usual. The use of a very high bearing pressure in the 50-7 specimens resulted in wide, thin outer plates. The failures of these relatively thin plates of the 50-7 specimens were somewhat different from the failures obtained in the other members. The rivets appeared to tear out of the plates with an accom- panying bulging of the plates between the longi- tudinal rivet rows. This behavior is readily evi- dent in the photograph of Fig. 19. The fracture of the 51 Series specimens also exhibited several types or modes of failure as shown in Figs. 20, 21 and 22. Although the failures of these members were predominantly plate tension failures, four specimens failed by rivet shear, seven failed by a combination of rivet shear and plate tension and three failed by tearing of the side plates at the rivets accompanied by bending 51-12 Fig. 24. Location of Failures -Specimens 51-10, 11, 12 of the plates over the rivet heads. In addition, some of the members with one row of rivets, the 50-X series, failed by tearing through the ends of the plates in spite of the fact that the end distance was made relatively large. 1 1. Results of Compression Tests The results of the compression tests are sum- marized in Table 8. Included in these data are values of maximum plate compressive stress, rivet shear stress and bearing stress, the ratio of rivet bearing to shear stress, and the yield load. Failure of the compression specimens occurred by buckling of either the center or side plates in 14 of the 18 tests and by rivet shear in one case at a very high load relative to the load on the duplicate specimens. The maximum deflection as limited by the geometry of the specimens forced the termination of testing of the remaining three speci- ILLINOIS ENGINEERING EXPERIMENT STATION Fig. 25. Stress-Slip Curves for Specimens 57-7 through 51-12 Table 8 Summary of Results of Compression Tests Spec. No. 51-7-1 2 3 51-8-1 2 3 51-9-1 2 3 51-10-1 2 3 51-11-1 2 3 51-12-1 2 3 Maximum Load, kips 291.6 301.0 287.0 282.7 290.0 292.6 215.4* 220.0* 228.0* 285.9 352. 0t 329.0 271.1 343.0 270.0 238.6 225.5 244.0 Maximum Stress Compres- sions 49.8 51.4 49.1 47.6 48.9 49.6 36.6 37.4 38.8 46.4 55.9 54.1 44.0 55.7 43.7 38.5 36.7 38.4 Shear k, ksi Bearing- Bearing Shear Ratio 104.1 1.89 107.6 1.89 102.8 1.90 127.7 2.39 127.9 2.34 129.0 2.34 170.9 4.20 174.6 4.21 180.0 4.18 97.5 1.81 118.0 1.78 113.1 1.82 115.0 2.25 145.5 2.25 114.7 2.25 134.1 2.98 127.8 3.00 135.3 2.94 * Deflection forced termination of test; specimen still loading. t Denotes failure by shearing of the rivets. $ Compressive stress based on gross area of member. mens although the maximum load carrying capacity had not been reached. The compression specimens after failure may be seen in Figs. 23 and 24. Sev- eral of these members were loaded until the rivets sheared, although initial failure had occurred by buckling. The stress-slip curves for the compression speci- mens are given in Fig. 25. In general, the agree- ment for duplicate specimens failing in the center plate (upper diagram) was very good except for specimen 51-9-3, which had a considerably higher stress at slip than did its duplicates. The agree- ment among the curves for the side plate failure specimens (lower diagrams) was reasonably good for the initial slip although the spread became larger near failure. 30 60 50 1^ 14 C ES 0 1z 1^ 14 14) IV. ANALYSIS OF TEST RESULTS 12. Theoretical Efficiency of Tension Connections A simplified analysis is made herein of small connections to demonstrate a theoretical interrela- tionship between bearing, efficiency, number of rivet rows, and the ratio of gage to rivet diameter. By means of these relationships, neglecting such factors as stress concentration, etc., it will be possible to show the theoretical behavior that one might ex- pect from the simple riveted connections of various bearing ratios tested as a part of this investigation. To present the comparisons in simple relation- ships, several general assumptions have been made. The connections have been assumed to be small joints in which friction between the connected parts is neglected, the rivets have been assumed to fill the holes, and the actual size of the rivet hole has been used to determine the net area. In addition, simple joints of one gage width have been used wherein B, rotio of beaorinq stress to tensile stress Fig. 26. Relationship Between Bearing Ratio and g/d the load is assumed to be uniformly distributed to all of the fasteners. Since the bearing ratio is equal to the ratio of bearing stress to tensile stress or the tensile area to bearing area, it can readily be shown that the bearing ratio is equal to, t- (g - d)t 1 (g 1) B ba ndt n \d (d or - = Bn + 1 d wherein, ta ba B g = tensile area in sq in. = bearing area, sq in. = bearing ratio = gage, in. = rivet hole diameter, in. = number of rivets in a line = thickness, in. The relationship between bearing ratio and g/d presented in Eq. 1 is shown graphically in Fig. 26. From this figure and the following tabulations it can be seen immediately that if the ratio of gage B 2.25 g/d 5.25 n=1 n=2 n=3 n=4 3.25 5.50 7.75 10.0 B n=1 n=2 n=3 n=4 4.25 2.12 1.42 1.06 to rivet hole diameter is limited to about 5.25, (17) a recommendation based on a detailed study of the efficiency of many riveted joints, only members with one or at most two transverse rows of rivets would be involved in studies of high bearing pres- sures. Joints with three or more rows of rivets and a g/d of less than 5.25 will necessarily have bearing ratios less than 1.5. In a thesis study conducted by Schutz11( it is shown that the efficiency of a riveted connection can be expected to vary with the ratio of gage to hole diameter. This relationship can also be shown to exist for the simple members described above, ILLINOIS ENGINEERING EXPERIMENT STATION 40 2 3 4 5 6 7 8 /, gage divded by daomeler Fig. 27. Theoretical Relationship Between Efficiency and g/d for which the theoretical efficiency is the ratio of net width to gross width of the member. Thus, (w-nd) = (g - d) I(-- d (2) w g wherein, e, = theoretical efficiency w = width, in. The relationship given in Eq. 2 is shown in Fig. 27. It may be seen that the theoretical efficiency of a simple connection can be expected to increase with an increase in the ratio of gage to hole diameter. Since both the bearing and efficiency of the simple connection are functions of the ratio g/d, the relationship between bearing and theoretical efficiency may be expressed by the following equation. Bn et Bn + 1 (3) This relationship between theoretical efficiency and bearing ratio is presented in Fig. 28 and shows that the theoretical efficiency increases as the bearing ratio is increased. Therefore, since the design of a 5 row 4 row 3 row Sves n /6nroets In 5//6" daorn holes 0 I 2 3 4 5 6 B, bearing ratio Fig. 28. Theoretical Relationship Between Efficiency and Bearing Ratio 0 5 / 5 2 25 3 35 B, bearing ratio Fig. 29. Relationship Between Bearing Ratio and Weighted Value of g/d for Test Specimens tension member is based on the net section of the member, a high bearing value would, theoretically, be desirable for the most efficient use of the ma- terial in the member. However, this would not be true unless the theoretical efficiency of the member can be realized. In Fig. 28, the efficiencies have been indicated for various values of g/d. From this comparison, it can be seen that for a given value of g/d the bearing ratio depends upon the number of rows of fasteners and, at a given value of bearing ratio, the theoretical efficiency increases with an increase in the number of rows of fasteners. It should be borne in mind that the relationships discussed above are "theoretical" relationships based on the geometry of simple connections with one to five rivets in a single line. The behavior of an actual riveted connection is much more com- plicated than can be portrayed by this simplifica- tion. As a result, the behavior can be expected to be somewhat different from that represented by the theoretical curves. 13. Effect of Bearing and Gage on Test Efficiency Weighted values of g/d for the three series of tests in this investigation are plotted in Fig. 29 to show the relationship between the "gage-divided- by-hole-diameter" and the bearing ratio. In this 1 1 F 1 I S St 'S b S b St St Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS 1.25 1.5 1.75 2 2.25 /00 90 S80 _ 70 L5 60 50 B, bearing ratio Fig. 30. Variation in Efficiency with Bearing Ratio same figure, theoretical curves are shown for the 50-X Series and the 51 Series tests; the 50-X Series contained one transverse row of rivets while the 51 Series contained two rows. It may be noted that most of the specimens are found to fall between these two theoretical curves. Consequently, their behavior or efficiency might be expected to be between the values predicted for a one- and a two-row joint. One of the principal objectives of this investi- gation, as noted earlier, was to study the effect of bearing ratio on the efficiency of the riveted joints when loaded in tension. To show the variation in efficiency with bearing, a complete summary of the test results is plotted in Fig. 30. At first glance the data would seem to exhibit a scattered, shot- gun pattern. However, when the theoretical effi- ciency curves are shown for each series, a more consistent and meaningful picture of the results of the test program is obtained. Several pertinent observations may be made of the data presented in Fig. 30. Of considerable in- terest is the fact that two pairs of the 49 Series specimens exhibited extremely low efficiencies. These data, found at bearing ratios of 1.29 and 2.55, approach the theoretical curve for joints with one transverse row of rivets. However, the dupli- cate tests at a bearing ratio of 1.29 provided a much higher value in efficiency; they even exceeded the theoretical efficiency for the member. Thus, at a bearing ratio of 1.29 the spread in efficiency for the 49 Series tests was extremely great. The im- provement of the retest specimens 49-4X over 49-4 was found also to be considerable. For the 50-X Series, joints with one transverse row of rivets, the tests at a bearing of 2.06 are in reasonably good agreement with the theoretical curve, but, at a bearing ratio of 2.74, fell below the theoretical curve. Thus, the increase in strength expected with the increase in bearing was not realized. An increase in the end distance would probably provide a greater strength in some in- stances. However, for the members with the bear- ing ratio of 2.74 the failures were by a pulling-out of the rivets from the thin side plates which were required for the high bearing ratio (Fig. 22); it is doubtful that an increase in the end distance would improve the strength of the members which failed in this manner. The two remaining series, the 50 Series and the 51 Series, fall both above and below the theoretical curve. However, in general the 50 Series data fall slightly above the two-row curve while the 51 Series data fall slightly below. 3 3.25 o 49 series * 50 series All curves theorelical * 5/ series w 50-X series 3 row S 2 row, 50 and 51 series S(2 I / row, 50-X series S________________ ILLINOIS ENGINEERING EXPERIMENT STATION K %9/, gage divi Fig. 31. Variation On the basis of the data obtained in this inves- tigation, the Research Council on Riveted and Bolted Structural Joints, as reported by Jonathan Jones,"18 has concluded that, "Under static loading, the strength of a joint loaded in tension is not re- duced by reason of bearing pressure, if the ratio of this to the net tensile stress on the main material does not exceed 2.25." This conclusion certainly appears to be justified on the basis of the data shown in Fig. 30. However, it should be observed also that at the higher bearing ratios shown in Fig. 30, the increase in efficiency to be expected on the basis of theoretical relationships is generally not fully realized. Thus, similar relationships are obtained when one considers the effect of the bearing or g/d ratio on the efficiency of tension connections. In both instances the expected in- crease in efficiency resulting from the use of wide spacing and thin material (high values of bearing or g/d) is not realized in full; upper limits of effi- ciency seem to be reached at a g/d ratio of approxi- mately 5.25 and a bearing ratio somewhere in the neighborhood of 2.5. Comparing the results of the tests reported herein with those reported by Schutz, (17) one finds that the data from the specimens of the bearing tests seem to fall principally between Schutz's curve ded by hole diameter in Efficiency with g/d for specimen with punched roles (E,) and the em- pirical curve for members with drilled holes (Ed). This may be seen readily in Fig. 31, wherein the test efficiency is compared with the ratio of gage to hole diameter. In this figure it may be seen also that the efficiency increases somewhat with an increase in g/d; however, again the scatter in the results is found to be wider than the increase one would expect in efficiency for an increase in g/d from three to five. Because of this large scatter in test results the observations or conclusions drawn from these tests have been based on the average values. On this basis the general trends of the results ap- pear to agree reasonably well with the various theoretical relationships that have been presented. 14. Effect of Bearing on Strength of Joints in Tension If the ultimate strengths of the joints are com- pared at the various bearing ratios, a relatively large variation is found to exist between sup- posedly identical specimens. However, further study of the data shows that in many of the tests the difference in strength may be in part a result of the variation in strength of the base material. Thus, one of the most reasonable manners of com- paring the results of the various tests is on the basis of the theoretical and test efficiencies. Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS B, bearing ratlio Fig. 32. Variation in Net Section Effectiveness with Bearing Ratio When such a comparison is made, it is found that only 16% of the 49 Series specimens exhibited efficiencies greater than the theoretical efficiency. In the case of the 50 Series, 64% of the connections produced efficiencies which were greater than the theoretical efficiencies. For the 51 and 50-X Series the percentages were found to be 19% and 25% respectively. Thus, only the 50 Series tests ex- hibited strengths which approached the expected strength of the joints; the remaining series all fell below the expected strength. For bearing ratios up to approximately 2.25, the efficiencies appeared to range between 8% above to 16% below the theoretical efficiencies. Beyond a bearing ratio of 2.36 all of the strengths were found to be below the theoretical strength and be- coming increasingly lower as the bearing was increased. 1 5. Effect of Bearing on Strength of Materials In any study of the materials in the joints, the connected material and the rivets must be con- sidered. Obviously, the ultimate strength at the net section of the member will not present a realistic basis of comparison to evaluate the con- nected material because of the variation in ma- terial from one member to the next. However, the effectiveness of the material at the net section can be presented by a ratio of the average stress on the net section to the ultimate coupon strength of the material. Then, a comparison of this ratio with the bearing ratio will show the ability of the mem- bers to develop the strength of the material in the net section of the connection. Such a comparison is presented in Fig. 32, where it may be seen that the effectiveness of the material at the net section decreased as the bearing ratio was increased. This decrease in effectiveness of the connected material, when considered in connection with the theoretical increase in efficiency expected from the joints, has resulted in a reasonably constant value of test efficiency with a variation in bearing ratio. This is also borne out by the data presented in Fig. 30. Nevertheless, it is important to realize that the material in the connections may not be as effective when subjected to high bearing ratios as when the bearing ratio is relatively low, even though the joint strengths are not affected. If an equation is written for the general trend of variation in net section effectiveness with bear- ing ratio, a decrease of approximately 10% is found in the net section effectiveness with an in- crease in bearing from 1.5 to 2.5. In this same range of bearing ratio, the theoretical efficiencies ILLINOIS ENGINEERING EXPERIMENT STATION St B, beoring rotio Fig. 33. Effect of Bearing Ratio on Rivet Shearing Strength of the connections of this program increase by approximately 10%. An attempt has been made also to study the effect of bearing on the shearing strength of the rivets. However, since data were not available concerning the properties of the rivet material, the variation in the coupon strength of the rivets them- selves could not be taken into account. The average shear strength of the rivets in the specimens which failed in shear or combined shear and tension are shown in Fig. 33. This figure shows that the shear strength (shear failure only) ranged from approximately 41,100 psi at a bearing ratio of 1.45 to 50,000 psi at a bearing ratio of 1.65. In this instance, the minimum shear strength of the rivets is found to be 3.04 and 2.74 times as great as (a U U ZZ Fig. 34. Longitudinal Strains on Gage Line A-A at Stress of 20,000 psi on Gross Section the 13,500 and 15,000 psi permitted by our prin- cipal specifications for bridges and buildings. From the data there does not appear to be any consistent variation in shear strength with bearing ratios. The principal objectives of this study did not include an evaluation of the various materials. However, since the materials used in this investi- gation were thought to be reasonably typical of the structural steels in service, the tests seem to provide some indication of the variation in strength that may be expected in connections fabricated from ASTM A7 structural grade steel and rivets of ASTM A141 structural grade rivet material. In the coupon tests the properties of various heats of these materials varied considerably and, as a result, the strengths of structural connections can be ex- pected to vary also. This, no doubt, accounts for a large part of the scatter observed in the test data. 1 6. Effect of Bearing on Strain in Members To show the effect of bearing on the strain in the outer plates of the 50 Series joints, the strain distributions along gage line A-A, a transverse line midway between the rivet rows, have been com- pared for all specimens at a stress of 20,000 psi on the gross section of the members. The results of these comparisons are shown in Fig. 34, grouped together by rivet sizes. In general, the specimens having the thicker outer plates had the least varia- tion in strain across the section, while the speci- Bul. 454. EFFECT OF BEARING PRESSURE ON THE STATIC STRENGTH OF RIVETED CONNECTIONS /0 20 30 40 50 /6u 120 80 Specimen 50-7XA Gages on one side only /7 - ______________--------------------- /10 20 30 40 50 0 Nel tensile stress, ksi 160 120 q80 80 "3 o^ /0 20 30 40 50 Fig. 35. Percentage of Load in Specimen Midway Between Transverse Rows of Holes mens having thin outer plates (joints of high bearing pressure) had the widest variation of strain across the section. Thus, there may be an effect of the bearing ratio on the strain variation in the members, but the effect of the bearing ratio on the ultimate strength apparently is insignificant. An attempt was also made to determine, for all specimens on which strains were measured, the percentage of load remaining in the outer plates at the section midway between the two transverse rows of rivets. This was done by comparing the polygonal area under the strain distribution curves for the gages at the gross section to the area under the curves of strains for the gages on section A-A at each increment of load. The results of this study are presented in Figs. 35 and 36. It can be noted in Fig. 35 that the percentages of load passing the transverse row of holes, as determined for the plain plate specimens 50-4XA and 50-7XA, show a wide variation from the theoretical value of 100%. The final values for the 3/16-in. plate specimen 50-7XA approach 100%, but those for the 3/-in. plate 50-4XA do not. These values, however, as well as those for all of the riveted specimens of Fig. 36, were computed from gages mounted on only one side of one outer plate and do not account for the bending which may exist in the plates. In order to determine the effect of such bending, the two remaining plain plate specimens, 50-4XB and 50- 7XB, were tested with gages placed on both sides of the plates. The results of these tests, also shown in Fig. 35, indicate that when the bending was taken into account, the computed value of load present at the gage line A-A section was very close to 100%. The small error present is probably partly the result of using a polygonal determination for the strain-width area and partly a result of the strain concentrations at the open holes. In view of the large bending effect obtained in the plain plates, care must be exercised in in- terpreting the load distribution percentages shown in Fig. 36 for the riveted specimens. In tests of riveted joints, because of the extreme difficulty if not impossibility of placing gages on both sides of the plates in the joints, it is necessary to determine the percentages of load from gages placed on only the outside of the plates. Nevertheless, the average curves for the three rivet sizes show values which approach 50% for stresses between 15 and 35,000 psi, a result which is very encouraging. Specimen 50- 4XA Gages on one side only ' 160 Average /20 80 Specimen 50- 4XB Gages on both sides 40 0 /0 20 30 40 50 /60 120 Average 80 80 _______""--------- Specimen 50-7XB Gages on both sides i40 lb ILLINOIS ENGINEERING EXPERIMENT STATION 80 60 40 to 10 20 3 /0 Q0 .0 0 to 0 2 40 50 0 /0 20 30 40 50 0 /0 20 30 40 50 0 /0 20 3 Net tensile stress, A