m a. «am. an. 0 1.8V $3.3 . a? In ..d .31.. v o a! s M a “W. 1. o #047 do. 100‘- - Date a s 1 l ‘ ‘ J .u . L b - a..- . w t o -— —. u- u..-— _— —-‘—‘- J— ... nl—cn This is to certify that the thesis entitled AN INVESTIGATION OF METAL CULVERT PLATE presented by MATTHEW JOSEPH HUBER has been accepted towards fulfillment of the requirements for MASTER'Sdegl-ee in CIVIL ENGINEERING December 5 , 1950 Major professor -m ‘1 '— o-..-' - —— — .. -~--—‘¢o-o s .. AN INVESTIGATIJN OF MFTAL CULVERT PLATE BY Matthew Joseph Huber A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in oartiel fulfillment of the requirements for the degree of MASTER OF SCIENCE 1950 ,‘A-‘a-h’: ' I ‘- THES’S ACKNOWLEDGMENT This thesis would not have been possible without the 000peration of the Research Laboratory of the Michigan State Highway Department who furnished all of the equipment and assistance needed in the preparation of this thesis. Mr. E.A. Finney, L.D. Childs and R.W. Ormsby of the State Highway Department were especially helpful. The author is also indebted to the manufacturers, the Armco Culvert and Drainage Tnc.,Republic Steel Corp. and United Fabricators Inc. who furnished the specimens used in this test. I Wish to thank Dr. 0.0. Harris and Prof. C.M. Cede of the Department of Civil Engineering for their advice and assistance in t’e preparation of this thesis. Wes-9:! I SYNOPSIS A series of corrugated culvert plates with different sizes and shapes of corrugation and of various gages were tested as beams. There were three styles of cork rugation and four gages. The beam tests were made on plates formed to two curvatures. The_va1ue of different Joint fastenings were also considered. The outstanding results: (a) the load carrying capacities of the corrugated plates are in order, first, the 2 by 6 inch box type, second, the 2 by 6 inch circular arc, and third, the 1% by 6 inch circular arc: (b) for each type of corrugation the load carry-- ing capacity increased as the thickness increased; (c) the lap Joint is more efficient than the butt Joint when subJect to beam loading conditions; (d) the radius to which the beams are curved does not affect the unit fibre stress of the plates: (e) double bolting of Joints does not materially increase the efficiency of Joints subJect to beam action. THESM TABLE OF CONTFNTS Title Page . . . . . . . . . . . . . . Acknowledgement J. . . . . . . . , I Synonsis. . . . . . . , . , . . II Table of Figures_ . . . . . . . . . . . III Introduction . . . . . . . . . . . , . Purpose of Investigation, History and Use of Corrugated Metal Plate Outline of Tests. . . . . , . . . . . IV Materials Investigated. . ... . . . , . Sources . . . ._. .p. . . . . Physical Properties . . . . Outline of Tests. . . . . . . Identification of Specimens . Supplementary Tests . . . . . V Exnerimental Procedure. . . . . . . . . Description of Apparatus. . . . . . . Test Procedure . . . . . . . . . . . Miscellaneous. Tests. . . . . . . . . VI Experimental Results and Interpretation Load—Deflection Data. . . . . . . . Influence of Corrugation. . . . . . Effect of Gage . . . . . . . . Lap Joint vs. the Butt Joint. . . Single Bolting vs. Double Bolting Bolt Strains . . . . . . . . . . . . Effect of Varying the Radius of Curvature Bolt Torque Tests . . . . . . . . . VII Summary of Principal Conclusions . . . Appendix . . . . . . . . . . . . . . . . . Page 20 20 20 31 36 38 41 43 43 45 46 Z O (DCDQCDUHPOJNH II TABLE OF FIGURES Title The Six Fundamental Tests . . . . . . . . . . . Details of Plates and Joints. . . . . . . . . . Arrangement For Tests 5 and 6 . . . . . . . . . Load Transfer Head. . . . . . . . . . . . . . Stra.in Gage Attached to Bolt. . . . . . . . . Influence of Corrugation on Deflections- Test 5. Influence of Corrugetion on Deflections-Test_6. Typical Failures - Type A . . . . . . . . . . . . Typical Failures - Type R . . . . . . . . . . . Typical Failures - TVpe U . . . . . . . . . Influence of Metal Thickness on Deflections— TestS Influence of Metal Thicxness on Deflections- Testo Modulus of Rupture vs. Gage of Metal. . . . . . Double and Single Bolted Lapped Joint . . . . . . Bolt Strains in Butt Joint. . . . . . . . . . . 21 22 28 29 30 '79 U-‘J 33 37 42 42 -3- III INTRODUCTION Purpose of the Investigation I The purpose or this investigation is to conduct static load tests on corrugated metal plates of various cross— sections to determine their relative stability under different load conditions. At the present time the design of structures of corrugated metal plates is based wholly on empirical methods. Past experience has proven the best guide in the design of new structures is to use data already gathered from previous successful installations. Recently manufactur- ers have introduced two new variables which have made the use of data gathered from previous installations rather questionable. These two variables are the introduction of corrugation with a 1% inch and 2 inch depth in place of the 1% inch deep corrugation and second, a new type of corrugation, the "box” style which consists of rectangular cross-section rather than the circular cross—section. This investigation, then, is to answer the fOIIOWlng questions: 1) Is there any relationship between the section modulus of the plates and the load carrying capacity regardless of the size and shape of the corrugation? "may! 2) Do the types of fastenings used fully develop the strength of the metal when subJect to bending stress? History and Use of Corrugated Metal Plate Corrugated metal plate has long been a popular material for_construction of culverts in highway and railway work. Its chief advantages have been rapidity and ease of construction, high salvage value and ease of main- tenence. Pipes of this type are manufactured in sizes varying from 8 inches in diameter up to 96 inches in dia— meter. Beyond this size there are practical limitations of strength and shipping difficulties which make the 8 foot pipe the maximum usable size. To satisfy the demand for pipes of larger size Armco Drainage and Metal Products, Inc. in 1931 introduced nested sections of corrugated metal plate which are later bolted together in the field. The nesting of the sections overcame the shipping difficulties previously mentioned and to increase the strength of the plates the depth of the cross-section was increased from g inch to 1% inches thereby increasing the moment of inertia of the cross- section of the metal plates. Several manufacturers followed suit and manufactured plates of the same cross- section. This cross-section was used until the period immediately following World War II. All of the design THES‘S criteria of structures using sections of culvert plate were based on this style. Immediately following World War II the major manu- facturers of corrugated metal plate introduced a new style. of corrugation. One manufacturer increased the depth of his section to 12 inch, another increased the depth to 2 inches. A third manufacturer introduced a new shape of corrugation, the "box" type which was radically different from the existing styles of corrugation. The values of these changes in the size and shape of corrugation are being studied under laboratory studies such as this present series of tests as well as under field conditions in actual instal- lations. The principal use of corrugated metal plate is in highway and railroad culverts and in airport drainage structures. The sections are cut and punched in the shOp and are ready for assembly when received in the field. The finished assemblies may be of either the circular pipe or arch-type shape. Pipe culverts may be assembled in diameters ranging from 5 feet to 15 feet while arches may be constructed with spans ranging from 6 feet minimum to a maximum of 30 feet. Other uses of culverts of this style are as replacement or supplement for existing structures. In instances Where concrete or masonry arches have deteriorated beyond reason- THESIS 0" -5- able safety limits corrugated metal arches are assembled immediately beneath the existing structure on new or exist- ing footings and grout is forced between the bottom of the old arch and the tOp cf the new arch to insure transfer of load to the new arch. These plates are also used in some instances for constructing pipes used in sewerage and irrigation projects. Outline of the Tests In order to answer the questions relative to the new styles of corrugation, a series of 6 tests was developed. Three of the tests were to measure vertical and horizontal deflections of columns subject to loads applied at the ends of the column. A fourth test was devised to measure the slippage of joints subject to direct compression and the remaining two tests were used to measure horizontal and vertical deflections on plates acting as beams. The six tests are shown schematically in Fig. 1. This report is concerned only with the results and interpretation of the beam tests, tests 5 and 6. Test 5 consists of a simply supported beam, curved to a radius of 150 inches. A vertical load was applied at two points near the center of the beam and the horizontal and vertical movements were recorded. Both bolted and unbolted specimens were used for this test. Test 6 is identical to test 5 except that in this case 1' ' has»! ‘ : TtST Hi P 9 TEST *5 P TEST V Ex 6%.... 2 i p 2 150‘s. . I 52 3/4 r/ ._. \s/ W; 150' R © \ * THIS SAME JOINT IS REPEATED IN TESTS m. 3, 4, 5 AND 6 *fég SIX FUNDAMENTAL TESTS Figure 1 the radius of the beams was reduced to 5"l inches. Th,se two tests measured load carrying ability and Joint action of plates acting as beams. 111:5st -9- _I_y MATERIALS INVESTIGATED Sources The materials for the test were supplied by three manufacturers each of which uses a different type of corrugation. Each manufacturer in turn provided plates of four different gages in both bolted and unbolted sections. The style of corrugation used by manufacturer A is illustrated in Fig.13A. It is of the circular arc type with a pitch of 6 inches and a depth of 1% inches. The plates are fastened together with a lap Joint using high tensile bolts spaced as shown in BA. Manufacturer R also uses a circular type corrugation as illustrated in Fig 20. The pitch is again 6 inches but the depth of the section has been increased to 2 inches. A lap Joint is also used for this style corrugation and spacing of bolt holes are as illustrated in Fig. 20. The new "box" style of corrugation, developed by manufacturer U, is illustrated in Fig. 2E. The section is a modified trapeZOid with a 6 inch pitch and a 2 inch deep corrugation. The Joint used is the butt type which consists of a heavy butt plate welded at right angles to the cross—section of the corrugated metal plate. Two -10.. haA T- ., \ é“ . «h \ I - ' ; - 3 In. . — u. . - “T." . .. V ' O ‘ 3 ’ ‘ .. H.. ' I' _ _ a I - fi 349 I I Q 0 k i ‘ .N k a o a ' G 3/ / (J a TY'I A TYPE \ DETAILS .2 PLATES mg JOINTS Figure 2 -11- adJacent sections of this style plate are Jointed by bolting the two butt plates together. Bolt spacings are shown in Fig. 23. The lap Joint and the butt Joint are both illustrated in Fig. 2F. The lap Joint shown is the double-bolted Joint. In normal installation, the bolt holes are staggered and only one bolt is inserted in each valley and crest rather than the two shown. All of the plates furnished were 52% inches long before being formed to the different radii and were of the following width: type A 21% in. type R 22 in. type U . 21 in. Physical Properties Complete data showing details of each of the three styles of corrugation may be found in Table l of the appendix together with data for moment of inertia and section modulus of the plates. Chemical composition and hardness data for the different materials are found in Table II of the appendix. The dimensions of the bolts furnished with each of the three styles of corrugations are illustrated with their respective corrugations in Fig. 2. The bolts used for types A and R were high tensile strength bolts with an average ultimate strength value of approximately 132,000 psi. The bolts used for type U plate were of A-7 grade metal with lower strength characteristics than the other bolts used. Outline of Tests Tests 5 and 6 were made on both plain and bolted samples and in effect amounted to 4 different tests. Each of the manufacturers, A,R, and U provided samples for each of these 4 tests in 4 different gages, l, 7, 10 and 12 and enough identical samples were furnished so that each test could be repeated three times if necessary. (Manufacturer R provided 10 gage only for the unbolted ‘ portion of test 5.) Identification of Specimens In a test involving such large numbers of specimens an identification system was deemed necessary to facilitate classification of material and results. The code that was develOped consisted of a series of letters and numbers in the following sequence: source, test number, letter identifying which plate of three identical plates, metal gage and letter telling whether the plate was bolted or unbolted. The systen is as follows. The source may be A, R, or U. Test number 5 and 6. X,Y,and Z distinguished between the three identical plates. The gage symbol was 1, 7, 10 or 12. The last letter was either P (plain) or S (seam). In this system a plate identified as A6X128 indicates type A corrugation, test 6, first of three identical specimens, l2 gage, and has a Joint. RSZVP indicates a plate supplied by manufacturer R, test 5, the third of three identical specimens, 7 gage metal and an unbolted plate. Supplementary Tests Not all of the plates were tested as indicated in the above schedule. In most instances the information gathered from tests on plates X and Y provided all of the data needed for that particular test. The Z specimen was then used for supplementary studies. The supplementary studies discussed in this report include the following: 1. Seam strength Many of the bolted Z plates were reinforced at the seam by a double row of bolts before being subJect to beam loading. This test was an effort to determine if there was any merit in the practice of double-bolting Joints subJect to severe bending. 2. Bolt Stresses Strain measurements of bolts used in tests 5 and 6 were made at various phases of the test. SR—4 type A-B strain gages were attached to the bolts in order to measure tension in the bolt. 3. Bolt Torque In order to determine the maximum torque to which bolts should be subJected a limited number of bolts were twisted to failure. Measurements of torque were made with a torque wrench. -l4- V EXPERIMENTAL PROCEDURE Description of Apparatus The load for the beam tests was applied through a 50-ton.hand-pumped hydraulic Jack set in a frame constructed from I—beam and channel sections as shown in Fig. 3. The ends of the beams rested on two concrete block piers which were capped with 1 inch by 8 inch by 24 inch steel plates. The plates were machined to a smooth finish and set at the same elevation. The load is transfered to the plate by means of the loading head shown in Fig. 4. The dynamometer ring is used to measure the magnitude of the applied load. A 1 inch round ball bearing between the dynamometer ring and the steel loading head insured freedom of movement in all directions. The load transfer device itself consists of a reinforced channel section placed over a wooden pattern. The wooden patterns were cut out to fit the different types of cor- rugation and lined with rubber to insure a perfect fit. Freedom from restraint on the ends of the beam was guaranteed by the load transfer device shown in detail in Fig. 3. The ends of the plate rested in the vertex formed by a 2% by 2% inch steel angle. The angle rested in a groove in a machined flat steel plate. -15— m one o mBmME m0& mezwzmwzdmm< I m mmDUHh . V b . § r J. "r. -16.. FIGURE 4~ LOAD TRANSFER HEAD FIGURE 5 - STRAIN GAGE ATTACHED TO BOLT -17- U. The flat steel plate rested on three 1 inch steel rollers which acted as roller bearings on the steel caps of the piers. It was necessary to use two-point loading at the center of the beam since single-point loading would inter- fere with the fastenings used on the unbolted sections. The same pattern was used on the unbolted specimens to insure uniform loading conditions. Two dials, each graduated to l/lOOO inch were used in recording the deflection at the center of the beam. In order to insure that the deflection measured is that of the beam and not the compression of the loading device the rods leading to the dials do not touch the loading device. Instead they pass through holes in the loading head and bear directly on the metal plate. The dials are shown in position on either side of the hydraulic pump in Fig. 3. Horizontal measurements were made with a steel straight- edge graduated to 1/64 inch. Miscellaneous equipment used included a Baldwin Southwark indicator used to measure bolt strains and a torque wrench. A strain gage is shown in place on a bolt in Fig. 5. Test Procedure The procedure used in tests 5 and 6 was identical. The plates were inserted in the end loading devices and the -18... loading head slipped into place. After the plate was centered the load was applied in lOOO-lb. increments. Vertical and horizontal displacements were recorded as each load increment was applied. The load was continued until the ultimate loads were reached and further increases in deflection were possible without increases in load. The same procedure was followed with the bolted specimens except that the bolts in the Joint were tight- ened with a torque of 200 ft-lbs. A uniform torque was adopted after a series of tests showed that variation in torque effected the results of the load deflection studies. To determine a suitable torque, a wrench slightly smaller than that employed in the field, was used by five highway employees who found that they could apply an average torque of 157 ft—lbs. Assuming that the laborer in the field had a larger wrench and a better knack for using the tools, it was felt that a torque of 200 ft-lbs. would very nearly satisfy field conditions. Miscellaneous Tests In order to test the effectiveness of increasing the number of bolts in a Joint extra holes were drilled in those plates used and another set of bolts inserted. The rest of the procedure was as nreviouly indicated. By nature of the fastening used it was not possible to increase the number of bolts in the butt-type Joint. -19- Bolt strains were measured by inserting strain gages on the bolts and then placing them in the Joint. As each increment of load was applied strains were recorded from readings on the strain indicator. The maximum torque was determined by twisting the bolt to failure with a torque wrench. The torque at failure was recorded in ft-lbs. -20... VI EXPERIMENTAL RESULTS AND INTERPRETATION Load-Deflection Data The load deflection data for tests 5 and 6 is pre— sented graphically in Figs. 6 and 7. Each curve is the average of one, two or three Specimens, whichever number were used.for each particular test. Each group of curves is classified by gage of metal used and whether plain or bolted specimens. Those curves on the left side of the page represent the plain specimens and those on the right half of the page represent the bolted specimens. The type of corrugation used is indicated for each individual. curve. Included with the curves for the bolted specimens. are the curves for the double bolted specimens. These curves are noted by a symbol DB-( double bolted). Igfluence of Corrugation Figs. 6 and 7 have been arranged so that a graphical analysis may be made of the influence of corrugation on loadpdeflections. The nominal overall dimensions of each of the plates is the same; each curve is grouped with others of the same gage, so that for the unbolted specimens the only factor that determines the maximum load carried by the plates is the variation in type of corrugation. /’————— ———————— s 1 PLAIN 20 ,... . 0"”.‘\\ 33‘” .r "\__ — -TYPE u .2. -’ 220L- / /TYPE R 8 _/, 3 1 5 f TYPE A a __,,,,_-l 3 14— / ——————— 0 = J/-T""" '- f... "' E 4. 01/ 3 J 4 l J I 1 J I 0 2.0 3.0 4.0 A S LOAD IN THOUSANDS OF POUNDS VERTICAL DETLECTION IN INCHES ,J,’ TYPE u /.~/-—--°/°"'" ‘ ._r TYPE R ‘_‘____J_p_,. .xTYPE A 1 1 1 4 1 I.0 2.0 3.0 4.0 4.5 LOAD IN THOUSAI'DS OF PM 471 A LmD IN THOUSANDS N POUNDS . N --—‘1 VERTICAL OIFLECTION 111 mean I 1.0 2.0 3.0 vc1ch1. autumn 1111 111cm: I E —---“:’:_‘_‘J../"" A I L 1 1 1 1.0 1.0 5.0 4.0 4.5 vuchL 0EPLE¢T1011 111 11101115 I \-____ __.___._ ___..’ LOAD IN THOUSANDS OF POUNDS LOAD IN THOUSANDS OF POUNDS 4.5 40 2.0 3.0 VERTICAL DEFLECTIOI IN INCHES ,,-.-«-—-TYPE R /,TYPE 11-03 _ _ frTYPE u I -_.—'4 ” ’w-—_. a‘.’ ‘ "‘ TYPE A’DB l I I J I 1.0 2.0 5.0 4.0 4.5 : YuchL ozruc'nou 111 11101115 I , I 1 l 10— ‘ TYPE u 3 I g T- ._.____..--—°" ,_._.......—0 3 T- ...--—-'" ,,..l,—’———TYPE A x'" ,, TYPE A'DB g /. .2V 5 ‘b M O 3 L 1 1 1 J 4 l 1.0 2.0 10 4.0 4.5 I VERTICAL oerLEcnou m menu I ' i 3 "F —-—TYPE u g3 - TYPE 11-03 g; ',_-/TYPE 11 :2 lat-H" CPS A-oa - 4 38 “‘ " TYPE A l 1.0 2.0 3.0 4.0 4.5 : VERTICAL ocrLEcnou 111 111011;: J \___._._ ______ ._.- INFLWNCE OF CORRUGATION ON DEFLECTIONS TEST 5 Figure 6 LOAD IN THOUSANDS W POUNDS LOAD IN THOUSAN“ OF POUNDS LOAD 111 THOUSANDS OF P011110: LOAD IN THOUSANDS W POUNDS ’———_— 1 “91;;- _ _ __...-‘ -22- r TTTTTTTTTTT \1 1 | BOLTED . . I : 3‘F I I 3A___ I I ‘1‘ A 1 I \ C 1% 3 g 2 ”I u 8 + . /0 g ’ ~ BOLT SHEARED 0:- 14 I ‘7‘" R 2 ’——'—‘. ’a”’ g ' 0”.< ’ \_ A 0 1 1 1 u c l 1 i T 1.0 2.0 3.0 4.0 I 5.0 I 1.0 2.0 3.0 I 4.0 : YE11T1cAL DEFLECTION 111 11101155 I I VERTICAL ocrtecnou 111 menu I 1 ' 1m: ' ' 1 1 I I I I I l I g m_ I l J.- V " _ T" 3 1 ,J/ " u 10 1” R e .-" ._J a w .v IT" A 8 .. ’r A x . I P 411— I z I .. 1 1 1 1 1 3 .. 1 1 1 1 10 2.0 3.0 4.0 50 3 " 1.0 2.0 3.0 4.0 VERTICAL DEFLECTION IN INCHES ————d r I : YE11T1cAL DEPLEcnou 111 11101:: || 1 1 I 1 I I I I 3 10— z 15 5 I- 2 O 12I— ..r'"" U 3 12 F O . ’NT— ‘ A z .’ - O — ,0 g .I‘ . r I o—"“é_-‘ D l. A . l” o .3. ”A“. 4 I— )’ I o "T’ f X P" ‘I- {,QI/o/ )1 z I) 3' ' ,7 - o i I 1 1 4 I ' o .______.__ I._____ 1.__ -_.I 1.0 2.0 30 4.0 5.0 § 0 l 1.0 2.0 3.0 I 4.0 VERTICAL OEFLECTION 111 111011Es I T | VERTICAL OEFLECTION 111 111011E5 I I ——-————4 ————-— n ..,. s . D o O. 3 1 U) u S . O R g .I— /“’ 2 4 A I" 4" ‘J—4 A E (’0’ f 1 J 3 v ‘ l 1 L I 1.0 2.0 3.0 4.0 1 5.0 3 I 10 2.0 30 I 40 | VERTICAL DEFLECTION 111 ”1an5 ) 1 VERTICAL DEFLECTION 111 INCHES I \ _ _ _ _. _ _________ J \ ._. ._.. ._.. ________ ./ INFLUENCE or coseumnou 011 DEFLECTIONS' TEST 0 Figure 7 In both tests 5 and 6, plain specimens, it will be readily observed that the load carried by the type U corrugation is notably higher than the R style corrugation which in turn is able to support a greater total load than the A style corrugation. This relation- ship between the load carrying capacity of the different .types of corrugation is of the same pattern as the relationship between their respective section moduli. The section modulus for type U,is higher than for type R which in turn is higher than A. Such a trend would seem to indicate that there is a relationship between section modulus and load carrying capacity of a plate. In curves for bolted specimens the differences between types of corrugation are not nearly so evident. In this case the type of Joint used has also become a factor in determination of strength. It will also be noted that the presence of a Joint reduces to some extent the load carrying capacity of very nearly all of the plates regardless of the type of Joint used. In the elastic range of the curves for the heavier gages the lepes of the straight lines are very nearly parallel indicating that types U, R and A have comparable degrees of stiffness. The computed unit stress values at the elastic limit for tests 5 and 6 are tabulated in Tables 1 and 2. The actual values for the unit stress at -24- TMEEI UNIT STR ss AT ELASTIC LITIT - TBS T 5 'ir-I' ."X- X-'X--X '-"-'X--.'--..--.. Unit qtress at Average Specimen Load at Elastic Elastic Limit Lnut (1bs.) (psi) (281) 05x1? 17000 A0000 U5Y1? 17000 A0000 U521? 19000 AA800 A1600 U5X7? 11000 38800 05Y7? 11000 8800 u527? 12000 350 39983 U5x10? 9500 A3A00 USYlOP 9000 A1200 Uszlo? 9000 A1200 A2000 U5x12? 7000 A0800 USY12P 7000 A0800 05212? 5000 29200 36930 R5x1? 11000 - - _ RSYlP 12000 A5A00 R521? 12000 ASAOO hShoo 35x7? 7000 38700 ‘ R5Y7? 6000 33A00 RSZ7P 7000 38700 36930 RSXlOP 6000 A3900 RSYlOP 6000 A3900 RSZlOP 6000 A3900 A3900 R5x12? 500 32775 R5Y12? 000 37375 RSZIZP A000 37375 358A2 A5x1? 6000 25900 ASYlP 6000 25900 A521? 7000 30200 27320 A5x7? A500 28800 A5Y7? A500 28800 A527? 5000 31900 29830 A5x10? 3000 25100 A5Y10? 3000 25100 A5210? 3000 25100 25100 A5x12? 2000 21250 ASY12P 2000 21250 A5212? 2000 21250 21250 -25.. TABLE -2 UNIT STRESS AT ELASTIC LIMIT - TEST 6 Specimen Load at Unit Stress at Average Elastic Elastic Limit Lhut jlbs.) (psi) (psi) U6x1? 20000 AA800 U6Y1? 18000 A0300 U621? 19000 A2700 A2600 U6x7? 11500 8700 U6Y7P 12000 0A00 U627? 12000 AOA00 39800 06x10? 10000 A3800 U6Y10P 10000 A3800 U6210? 10000 A3800 A3800 06x12? 7000 8600 U6Y12P 7500 500 06212? 8000 AA200 A1A33 36x1? 12000 A3000 R6Y1P 12000 A3000 E621? 11000 39100 A1670 'R6X7P 7000 36800 R6Y7P 7000 6800 R627? 8000 600 38730 R6X12P A000 35500 R6Y12P A000 35500 R6212? A500 39700 36900 A6x1? 8000 32800 A6Y1? 8000 32800 A621? 7000 28800 31A50 A6x7? 5000 30300 A6Y7P 5000 30300 A627? 5000 30300 30300 A6x10? A000 32000 A6Y10P A000 32100 A6210? 3500 27900 30700 A6x12? 2000 20200 A6Y12? 2000 20200 A6212? 2000 20200 20200 -25- the elastic limit and the ultimate strength were deter- mined by the Bureau of Public Roads from samples of metal cut from the test specimens. This data presented in Table 3 of the appendix. Table 3 is a comparison of the values for unit stress at the elastic limit as determined directly by the Bureau of Public Roads and as computed from the information gained from the load—deflection curves. The table shows that for A and R there is very close agreement between the computed and measured values for unit stress and that for type U the agreement is reasonably good. This would indicate that the curves as drawn Show an accurate relationship between the different styles of corrugation up to the elastic limit. It would further indicate that up to the elastic limit the shape and style of the corru- gation does not greatly effect the relationship between the section modulus (I/c) and the load carried by the plates. Table 3 COTPUTED UNIT-STRESS VALUES vs. MEASURED UNIT STRESS VALUES (at elastic limit) Computed values Measured values type U 41014 35929 type R 39924 40669 type A 27008 29133 -27- Beyond the elastic limit unit stresses are not as readily determined. The "flexure formula" S = ¥E_ is applicable only when computing unit stresses in beams When the unit stress at the outer fibre does not exceed the elastic limit of the metal. As previously discussed, the ultimate loads, as indicated by the curves in Figs. 6 and 7, are in the same order as are the section moduli so that beyond the elastic limit there is still evidence that the relationship between section modulus and load carrying capacity is not effected by changes in the style of corrugation. Typical failures of circular-type corrugations (A & R) are illustrated in Figs. 8 and 9. The maximum deflection occur at the center of the plate as might be expected. In the bolted specimens there is tearing in the row of holes most distant from the punched end of the top plate in the lap Joint. Fig. 10 illustrates typical failures for the box type corrugation. In the plain specimens there is evidence of local failure in the corrugation while in the bolted Joint there is a "spread" failure in the butt-plate used for'the Joint. It is the failure of the butt plate that reduces the effectiveness of this type of Joint when subJect to bending. ASYIOS FIGURE 8 - TYPICAL FAILURES — TYPE A .. 29.. FIGURE -9- TYPICAL FAILURES - TYPE B FIGURE 10 - TYPICAL FAILURES - TYPF. U Effect of gage The load deflection curves for tests 5 & 6 have been regrouped in Figures 11 and 12 to graphically present the effect of gage on load carrying capacity of the metal culvert plates. In all styles of corr- ugation, both tests, and for plain and bolted specimens the load carrying capacity is of the same order as the thickness of metal. This further illustrates the premise that as the section modulus (a function of the gage) increases, the load carrying capacity of the plates is also increased. It will be readily seen from the curves that the stiffness of the corrugated sheet is influenced to a great extent by metal thickness. Comparison of l gage and 12 gage curves, for example, illustrate that an increase in metal thickness from 0.105 inches to 0.275 inches trebles the ability to carry loads. As a further basis of comparison, tables 4 & 5 have been prepared. These tables contain values for a 'Modulus of Rupture' which is found from the formula Sr = PKC/I where P is the ultimate load, K is the moment arm at the ultimate load and I/c is the section modulus of the plate. Both tests 5 and 6 are included in this table. The values for each gage and for each ’_——_- —————— ‘ ’——— ~-— —--_-— I \I I \ I PLAIN I T": U I BOLTED I I I I I 2. !.I- 33‘ ————-—-'l GAGE 8M- : g /,-.—-—l GAGE O // . ‘ 280 .."I- 3 o 3III- --""""""" 3 @- z : ,fl»? GAGE 3 \‘w -_.7 GAGE 3 3I o I ___. -_-, J-— - IO GAGE -—--"..—-—- "’"-’"'_ z z _ .O-" _\ - I_----- - ,. ...... \~——-I0 GAGE O N. O ...... ." 3 I; ‘~~-—\l_,h___ _ , _, ——I2 GAGE § \. " _. . ”-42 GAGE I J I I I l 4 J 1 1.0 go 3.0 I 4.0 I I.o 2.0 3.0 4.0 , 4.5 I vEnTIGAI. ocrLEcTIon m memes I I vchIGAL DEFLEGTION m meat: I I I I I I I I I I I I I I I l I I < I I l l I I I TYPE R I I I I I I a aI— I I In“ ”24» O O s g 03 0 20— .. I» '6 I I GAGE 8 3. 3 I6— , ~I GAGE z x 3 7 GAGE 3 g I “._.‘_____. 3 I2 ... E " ‘ ' 7 GAGE 5 ”—IO GAGE 2 . O O 3 I2 GAGE § I2 GAGE J ‘ 4 G J I I I 0 I l J r LG 20 3,0 I 4.0 I lb 2.0 3.0 4.0 4.5 I vEnTIcAI. DEFLEGTION m INCHES I I VERTICAL DEFLECTION IN INCHES I l I I i I I I I I I I I I I | I I I I I I I TYPE A I I z I | 20_ I I § § I IOI- 8 -I GAGE 2- “I z 3 J' 7 GAGE é ""'" ' 7 GAGE ; -» ~— A - Io GAGE ‘ r-‘Ti‘. Io GAGE - o . 3 7 , a I2 GAGE """ i I2 GAGE g j I o ' I L l I I m 2.0 3.0 I 4.0 Lo 10 to 4.0 4 s I venue“. ocrucnou m menu, I new» ocrLecnon m meat: I \_.________—J \___..__________/ INFLUENCE OF METAL THICKNESS ON DEFLECTIONS TEST 5 Figure 11 LOAD IN THOUSANDS OF POUNDS LOAD IN THOUSANDS OF POUNDS LOAD IN THOUSANDS -33- (’- ———————————————— \ I PLAIN I I I TYHEA “~- I I Gmx §” § "'I’ / 7 GAGE 13 § --IO GAGE §§ 3 &— I2 GAGE :8 J J l l I I.0 3.0 3.0 4.0 7 5.0 I I.0 8.0 30 I I vtIITIcAI. ocrLEcTIon IN INCHES I I VEIITIGAL 0EPLEGTI0u IN INGNS I I I I I I I I I 24 _ I I I . 20 ”T SPEARED /l GAGE I GAGE ,w“ I. ,_ ' _______ J 7 GAGE I2 I“ 7 GAGE l2 GAGE . ........ O I , I2 GAGE ’ -Im _ _i I i, I I d I.0 2.0 3.0 4.0 I I 30 I T. I VERTICAL OEFLECTION m INCHES I I venTIGAI. OEPLEGTIGN no menu I I I I I I I I I I I TYPE 0 I I 34 _ I I 3. - I I so as zaI. I GAGE III— -— 7 GAGE I‘ ’ ._. ._. — 4 .J’” I0 GAGE .——--'-" I0 ..." "" IZ GAGE o I I I A I I Ir I.0 2.0 3.0 4.0 I 2.0 3.0 I 4. I VERTICAL OEFLECTION IN INCHES I I VERTICAL DEFLECTION m INCHES II \ _______________ ..z \ ____________ ./ INFLUENCE OF METAL THICKNESS ON DEFLECTIONS TEST 6 Figure 12 -34- TABLE 8 MODULUS 0? RUPTURE - TEST 5 Specimen IGfiltimate Modulus of Load Rupture Avera 3 (lbs.) (psi) (psi? 05x1? 28000 66811 0511? 28000 6627 0521? 28000 66538 66806 U5X7? 16800 59663 USY7P 168 0 S97 _ u5z7? 162 0 578 6 59090 u5x10? 12000 55078 USYlOP 12000 55296 05210? 11800 52782 58385 u5x12? 8100 88298 USY12P 9000 2689 05212? 8000 9235 89235 R5X1? 17800 - - - RSYlP 19300 73539 RSZlP 18600 71368 72858 R5X7? 11520 6 7 R5Y7? 11800 6%3ug RSZ7P 11300 63586 68873 R5x10? 9720 7183 RSYlOP 10000 7382 RSZlOP 9550 70505 72055 35x12? 5720 53792 RSY12P 6500 61177 RSZlZP 6000 56801 57123 A5x1? 12180 52986 A5Y1? 12180 5276? A521? 12000 52031 52595 A5x7? 8000 51888 A5Y7P 8500 58717 A527? 8700 55993 58066 A5x10? - 6180 52065 ASYlOP 6125 51507 A5z10? 6550 55217 52929 A5X12? 3600 38 98 A5Y12P 620 8 32 A5z12? 000 750 39960 -35- TABLE 5 MODULUS OF RUPTURE - TEST 6 Specimen Ultimate Modulus of Average Load Rupture (lbs) (psi) (psi) U6x1? 33850 790 U6Y1P 33850 787 2 0621? 32000 75209 77672 u6x7? 17300 59966 U6Y7P 17200 60078 U627? 17800 60518 60185 06x10? 12300 55055 U6Y10P 12000 53610 06210? 13195 59376 56013 U6x12? 9180 50979 U6Y12P 9300 52132 06212? 9300 51986 51699 R6x1? 21000 78038 R6Y1? 21860 81521 R621? 23000 85321 81625 R6x7? 13800 75808 R6Y7P 1 650 75580 R627? 1 000 76887 76090 R6x12? 7220 66300 R6Y12? 7055 68528 R6212? 8000 73121 67982 A6x1? 1 650 58376 A6Y1? 1 000 59809 A621? 13000 55631 57939 A6x7? 9600 60128. A6Y7P 10000 6 1g8 A627? 8650 Sflh-S S9257 A6x10? 6800 56885 A6YlOP 7560 63009 A6210? 7810 61101 61813 A6x12? 385 hfi973 A6Y12P £220 -8 A6212? 8000 81910 88110 manufacturer are averaged and are used to produce Fig. 13. This illustrates the relationship between section modulus (a function of gage) and the modulus of rupture (a function of the load carrying capacity). Theoretically the modulus of rupture values for all gages should remain the same if each gage is equally efficient. For both type U and type R there is a tend- ency for the modulus of rupture to decrease as the thickness is decreased. In type A all of the gages illustrate very nearly the same trend except the number 12 gage. There is a definite decrease in the modulus of rupture which is indicative of stresses other than bending stresses when such thin metal gages are used. In all three styles the thin metal are not able to efficiently develop the metal strength to its fullest extent. There is some indication that in design that 10 gage may be a practical lower limit as to thickness of metal used for corrugations as deep as those used in these types of plates. The_Lap Joint vs. the Butt Joint In introducing the box style of corrugation the manufacturer used a new type of Joint, the butt Joint, which we have previously discussed and illustrated. So that the.Joints might be evaluated, the plates with seams were tested in a manner identical to that for plain plates. The efficiency of a fastening may then -37- O O ‘3 , O 3 O O IUPTURE '- (I O O O ) O T L— . I . _§_._; _ < Z 2' I c v .- 1 n MODULUS OF THOUSANDS OF LDS - P S I U 0 mousmos or us.-es. I. MODULUS OF RUPT URE- ~_‘_I/f—;Z;E;EIGAGE I I nouuwu.cmct _J IZIOl 7 IJ O 2 I01 71 I .05 .I0 '.Is .20 .23 130 .03 .I0' ‘W5 20 25 ‘.30 THICKNESS IN INGIIEs TI-II'GIINEss IN INCHES ' :N 1".1 .. '3 = I fl.‘ UdSO 118th— gI 0-» £340 TVA?! 3 3W; -L-_J’-- In ,7 35 3” a: I 32 NOMINAL GAGE II? '9: II I I 0‘ .05 V .02 .IS' 30 TH ICKONESS |IN INCHES MODU LUS RU PTU RE Vi. GAGE 07 METAL Figure 13 be computed by finding the ratio of the load carried by the bolted specimen to the load carried by the plain plate. ,The ratios, shown as percentages are found in Table 6. This is due in a main part to the fact that slippage and readjustment in the Joint produces an elastic limit lower than the elastic limit of the metal. For the lap Joint the efficiency at the ultimate load is quite high with but few exceptions, varying from 79 to 100 percent efficiency. The efficiency of the butt Joint is lower varying from 61 to 89 percent. The butt Joint apparently does not take advantage of the superior strength of the box—type corrugation. The failure of a butt Joint is not in the plate but in the butt plate at the Joint. This type failure is illustrated in Fig. 10. The failure in the lap Joint occurs in the metal of the plate itself and as such the Joint is weakened only by the holes punched for the bolts. Single Bolting Versus Double Belting The lap Joint was further tested by compiling data on the efficiency of double bolted Joints in Table 7. At the elastic limit the double bolted Joints show a significant increase in efficiency which is probably caused by a decrease in slippage and adJustment of the Joint. At the ultimate load there is no great increase LAP JOINT VS. ’1.) 9.. TABLE 8 BUTT JOINT TEST 5 Specimen Elastic limits 1% Eff. Ultimate loads ‘7'? Eff. plain bolted plain bolted U 1 ga 17870 000 51 28000 18800 87 U7 ga 11330 000 35 18800 11800 71 U 10 ga 9180 3000 33 11800 10300 87 U 12 ga 8330 2000 32 8800 7500 89 R 1 ga 11870 8000 89 18900 19000 100 R 7 ga 8870 000 75 11500 11900 100 R 12 ga 3830 000 100 8070 8800 100 A 1 ga 8330 uooo 83 12100 11100 92 A 7 ga L870 4000 88 8400 8h00 100 A 10 ga 3000 2000 87 8300 5700 90 A 12 ga 2000 2000 100 37u0 3900 100 TEST 8 U 1 ga 19000 11000 58 32800 20000 81 U 7 ga 12000 8000 50 17000 1u000 82 U 10 5a 10000 000 50 13000 11000 85 U 12 ga 7500 000 53 9000 8000 89 R 1 ga 11700 7000 80 22000 18000 82 R 7 ga 7300 8000 82 13800 12000 87 R 12 ga A200 3500 83 7800 8900 91 A 1 ga 8000 L000 50 13 00 12700 9h A 7 ga 5000 u000 80 9 00 8900 95 A 10 ga 3500 3000 88 7300 800 79 A 12 ga 2000 2000 100 A200 000 95 -40- ca cmmm mo coc com: oca cocm coH cocm cocm em ma c a o msem ca com come com comm cc cocm comm cm ca c c m cme mo coco cc o co ccc cc coo; cocm em a c a com cm H do comma co ma mo occ om coo: cocm mm H c 4 Ho cmoc Ho coco coca mo coo: mo comm com: em ma c m on cmeoa ac cccma comma cc coca mm ccoc coma em a c m mo _cccca ccomm cc coca coaaa am a c m mo comm ccH cocm cdam cca cocm cca cocm cocm em mm m a ca cocm co ccsm ccmc ccH cocm ac cocm cocm cm ca m a coa coco cca coco cosc cca cocm cc coo: one: am a m 4 so comcH Amo coaaa ccama cs cocm mc coo: ommc mm a m a cca coca ccH coco cscc ccH com: com ccc cmcm mm mm m m so ccmaa ooa cooaa comaa cc cccc me ccc cecc em a m m cca cocoa coa cocoa cocoa Icc cocoa cc cocm, cacaa em a m m cepaop cesaon beam a canccc .oom a cepacp caeac .oom a eacccc .cema cepaon caeac . seesacao easaa caemem cesaceom ozHqum mAMDOQ a mgmca .m> UZHBAOm HQUZHW -41.. in efficiency, the range being the same as for the single bolted Joints. Since in a flexible type culvert much of the strength of the culvert is derived from support at the sides of the culvert after the metal has passed the elastic limit, there is no great advantage derived by the extra expense and labor involved in the double bolting of Joints. A typical double-bolted Joint is shown in Fig. 14. Bolt'Strains On certain plates in test 5, strain gages were cemented to the bolts used in the plate seams for the purpose of observing the strain pattern. Figs. 14 and 15 were prepared on the basis obtained as a result of these tests. Fig. 15 illustrates the action for a butt~type Joint. The initial strain is introduced by tightening the bolts with zero load applied. As the load increases the strain in the A row (heavy line on graph) is decreased as the butt plate apparently is compressed more.tight1y at the top of the Joint. At a point Just before the elastic limit the strain increases and parallels the strain curve for the B row of bolts. The bolt strains for the lap Joint are shown in Fig. 14. For single bolting (solid lines) there is apparent relief in the A row of bolts while there is MAN LOAD IN Iowa: Iopoo I0,000 I 1,000 I0,000 . IgoooI 9- W -4 . —~—r s. I (.40: SINGLI: 00mm sun avuact or sYIAINs IN sous +3-4 I I I— I ' __i__I_ I GAGE “2,120 II I_ DOUBLI BOLTIO SIAM avuuct OI STRAIN: IN IOLYS Its I I N I/___ L—JL—A— COMPRESSION SIDE I I I TENSION Slot OF JOINT -4, I‘.0°° I A» — I I 'J'OOOI — 9] fir I2,000 +- I"OOO I ' (LI-she man or pun. IO’OOD I——-,-——q———+—-»—-II-——-o-— ———I.._—«—+ ,——1——~——T———-——J—— . I ' I i I 0,000 I- .-.-.-_ .1 -..L-_.L__- .I. -I ..L,_i_, I arnm nut: IN sous Amount IN BOLT swam I I /0N cowncssuou 3I0I. or JOIN? I I 0" ""90" 5"": 0,000 I -_ - T—-—— I» I . —— — + - r- ~-+ , - I ,— : . , I we: SINOLI OOLTED scum l ‘ i .\.__ I I I AVERAGE 0F SYIAINS IN BOLTS 7,000 »—— ¢ 1 a..- _.. "T —+.~_—_s.f + — + ——— -+—-— I. ——._ _+: . _4- '.2.3 0 4 1+ I I I I. I I I ' I I I ‘ ' ' I 1 i ‘ I 0,000 ——-+ _I..___. - \l \:\+ - ——-4 ——I 4 ——I K‘s—u - I - I — I» —-I I» I '. IGAG! ocustt 00am sun \N \ I . I I | "(not or s'rums IN BOLTS ‘ I I I . : ' , I 5,000 , SI’DS" __.t\.1,_-__ Jr...__1 . _ I if ‘I— J__ 4 i__.+_, ' ,_ 1L“ + T "T I I , __I I I I I I ' ‘000 I -+- —-—- k > L - -——— —— -- o r —4 . | ‘\ r I \ 1 . 'I GAGE LAM-:0 JOINT on sun. ; ET I 3.000 . _ I_ I I _ CULVI: PLATE SECTION uNDtfl 0:08 Tu? _ *7 _ 4r, _ Y _ A F—INITIAL STRAIN m sou \ A] T I I I ’ . %ou¢ to TIGHTENING to 4\h 1 I I I I 2,000 # I— 2 o H I.0 Tonout 'II— — ae—j a s - —— . ——~{ I —4 . I I . I I I I I I,000 — I - I T + 4 Y i _ _1_ ...__i__ ‘ ' ’ I I I I ' o I 1 z - I 0 00 I20 I00 200 000 020 000 540 000 000 120 700 040 000 000 I020 I000 n40 IZOD I200 I320 I300 I000 I500 I500 I020 I000 I700 I000 STRAIN IN MICRO-INCNIS,'¢I INCN ' BOLT STRAINS IN DOUBLE AND SINGLE BOLTED LAPPED JOINT Figure 14 A 0011 40m? 00 00mm I 0~-’ ”'L" 40"" mu: 00m: ORIGINALLV on I, I0000 Ttuslou not or J0IN1 —"" i I 0000 /- I A’ \mtst IOL‘YS omemuu ON 0000 I, counzsuou SID! or JOIN‘I "'"_' / 7000 f ) é / I ,z 4 =6 0000 a a?! J 1 I I1 I a r! (I/ "I a / 3 / J 4000 r I I0 00a 00x "'1 STIIL cuwtn? OLATI: scum 1 mm mm! 00mm 0071 .IOIN'I, 0000 /' NNtN 3004:0110 To 00. us! I ./ 2000 v / I000 I r’ A 1 T 0 00 I20 000 ‘000 I020 I000 II40 I200 I200 I020 I300 I000 I000 I500 I020 I000 I700 I000 I000 I020 I000 2000 2I00 BOLT STRAINS STRAIN IN IICIO ' INCH, "I INCH Figure 15 0017 JOINT -43- an increase in strain in the B row of bolts. The double- bolted Joint (dashed line) shows a marked change in the strain pattern for the B row of bolts. There is only a small increase in strain as the load is increased as compared to the large increase in strain in the B row of bolts for a single bolted Joint. The strain in the A row of bolts is very much the same for both types of Joint. Effect of Varying the Radius of Curvature The unit stresses at the elastic limit for specimens used in Test 5 and 6 are compared in Tables 1 and 2. The only difference in the plates used for the 2 tests was the radius to which the plates were curved. Test 5 had a radius of 150 inches while Test 6 had a radius of 50 inches. A comparison of the unit stresses for the two types of plates shows no significant difference in the pattern for unit stress. On the basis of this comparison it is apparent that the radius of curvature does not effect the action of the plate. gglt Torque Tests ‘ Specimens of each type of bolt furnished were twisted with a torque wrench to failure. The high tensile bolts furnished with the A & R bolts required about 700 ft-lb torque before failure occured. The bolts furnished for type U failed at a torque averaging -44v 590 ft-lbs. In either case the 200 ft—lb torque used in the tests is well within the working limits of the bolt metal. -45- VII SUMMARY OF PRINCIPAL CONCLUSIONS 1. Culverts may be designed on the basis of section modulus for all the styles of corrugation tested. 2. The standard lap Joint very nearly develops the strength of the metal at ultimate stresses but_is not as efficient at the elastic limit of the metal. Double bolting increases the efficiency of the Joint at the elastic limit but there is no increase in efficiency evident at the ultimate load. 3. The butt—type joint is not as good as the lap joint when subject to bending action. 4. Plate curvature has little effect on the unit stress of the plates. 8.223... .8 <23 2.33323. X.OZUtt( u u40.P 5440...... a a“? 4.41:4. -47- APPENDIX TABLE 2 CHEMICAL ANALYSIS AND BRINELL HARDKESS §pecimen BrinelI‘ Hardness C Mn S P Si Cu Mo. USZlP 90 .080 .300 .038 .016 .27 0521s 9 .080 .300 .0 8 .016 .27 U6ZlP 10 .090 .390 .042 .015 .25 06215 105 .090 .390 .042 .015 .25 U5Z7P 103 .019 .028 .026 .006 .004 05273 93 .019 .028 .026 .006 .004 06275 101 .019 .028 .026 .006 .004 052103 95 .019 .028 .026 .006 .004 062102 95 .019 .028 .026 .006 .004 062105 103 .019 .028 .026 .006 .004 25x12 107 .0E .13 .030 .014 .43 .07 25x13 101 . .11 .034 .010 .49 .08 R621? 107 .0 .13 .030 .014 .43 .07 R3218 10 .0 .11 .03 .010 .49 .08 25x72 11 .04 .13 .02 .011 .44 .08 25273 116 .04 .11 .033 .010 .48 .08 26x72 110 .04 .13 .026 .011 .44 .08 R6Y7S 114 .04 .11 .033 .010 .4 .08 RSXlOP 114 .05 .15 .025 .010 .54 .09 RSZlOP 124 .05 .15 .025 .010 .54 .09 25x12? 115 .05 .16 .030 .010 . .05 252123 112 .05 .16 .030 .010 .44 .05 R6X12P 121 .05 .16 .030 .010 .44 .05 A6213 90 A2375 lOS Typical limits - No specific data ASX7P 9 for this group ASXlOS 11 A521os 114 A52123 107 .02 .01 .015 .003 .04 A6X12P 92 to to to to A6212s 105 .02 .022 .007 .05 Typical analysis of Bolts Type U Bolts .20 .45 .05 .04 Type R Bolts 258 .39 .66 .033 .019 .25 Type A Bolts 269 .46 .80 .043 .010 Note - Chemical Analysis data furnished by manufacturers -48 .- APPENDIX TABLE 3 PHYSICAL TESTS ON PLATE SPECIMENS (by Bureau of Public Roads) Yield Modulus Specimen Strength Ultimate of No. Offset Strength Elasticity .05 percent (psi) (psi) x 103 U521? 30.444 49.427 30,393 05213 29,158 48,020 29.725 0621? 32,374 50,000 29,2 7 06213 ,29,675 0,397 29,0 1 0527P 9.781 8.798 30.6 USZ7S 3:25 51:39 30:2 3 052103 8,78 52,02 32,069 062103 3,153 56,348 32,241 Average 35,828 50,801 30,455 25x13 31,849 48,288 28,804 R3213 £4,530 49.378 29.783 35273 .737 52.053 29.497 36X7P 42.857 54.416 28.529 RSZlOP 41,250 50,76 30,119 352123 tfi.455 52.1 28.633 26x12? ,007 52,8 2 29,481 Average 40,669 51,422 29,264 A6213 20,430 41,219 29,885 A2X7s 31,380 46,183 30,676 A5X7P 35.196 43.296 29.707 ASXlos 38.923 48.154 29.945 A52123 2 ,779 41,681 28,471 A6Xl2P 2 ,091 41,182 27,049 Average 29,133 43,619 29,289 . 3“: 3 V Viv 5’. 2.. L H4 Jr" , . ' _ ROOM__ USE ,ONLY " MICHIGAN STATE UNIVERSITY L IBRARIES 2 1082 95 1 ' .“UIJJIJ