TESTS OF THE EFFECT OF BRACKETS 
 
 IN 
 
 REINFORCED CONCRETE RIGID FRAMES 
 
 BY 
 
 F^IANK ERWIN RICHART 
 
 B.S. in C.E. University of Illinois, 1914 
 M.S. in C.E. University of Illinois, 1915 
 
 THESIS 
 
 SUBMITTED IN PARTIAL FULFILLMENT OP THE REQUIREMENTS 
 ■ FOR THE DEGREE OP CIVIL ENGINEER 
 IN THE GRADUATE SCHOOL OP THE UNIVERSITY 
 OF ILLINOIS, 1922 
 
 URBANA, ILLINOIS 
 
Digitized by the Internet Archive 
 in 2015 
 
 https://archive.org/details/testsofeffectofbOOrich 
 
Ou. 
 
 UNIVERSITY OF ILLINOIS 
 
 THE GRADUATE SCHOOL 
 
 April 4^ 192^ 
 
 I HEREBY RECOMMEND THAT THE THESIS PREPARED BY. 
 
 VRAM K ERWTW RICHA RT . 
 
 ENTITLED TESTS O F THE EFFE CT OE BRACKETS IN RETTJ FjQBCEL. 
 
 CONCRETE RIGID FRAMES 
 
 BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE 
 
 PROFESSIONAL DEGREE OF 
 
 Head of Department of CIVTI. ENCTNEERTNC, 
 
 Recommendation concurred in: 
 
 
 
 Committee 
 
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CONTENTS 
 
 I. INTRODUCTION. Page 
 
 1. Preliminary 1 
 
 2, Nature of Investigation. i 2 
 
 II. ANALYTICAL TREATMENT. 
 
 3* Analysis of the Effect of Brackets 4 
 
 4. Effect of Brackets with Different Loadings ... .19 
 
 5. Effect of Brackets in Various Tjrpes of Frames. . .21 
 
 III. TEST SPECIMENS AND APPARATUS. 
 
 6. Description of Test Specimens 29 
 
 7. Materials and Making of Specimens. . 41 
 
 8. Testing Apparatus 44 
 
 IV. TEST DATA AND DISCUSSION OP RESULTS. 
 
 9. Procedure and Phenomena of Tests 48 
 
 10. Thrusts and Moments 60 
 
 11. Flexural Stresses and Deformations 64 
 
 12. Shearing Stresses. .74 
 
 13. Moment of Inertia. 77 
 
 14. Deflections 85 
 
 15. Conclusions 91 
 
 V. APPENDIX I. 
 
 16. Test Data and Drawings 98 
 
 VI. APPENDIX II. 
 
 17. Supplementary Tests of Paper Models. 131 
 
 -II- 
 
±;IST OF PIGUIilS 
 
 Wo. 
 
 Page 
 
 1. Outline Drawing: Used, in Analysis of i^'rame 
 
 2» Eelations between Moments and Eeactions* •••••••• 7 
 
 3. Eelations between Calculated Moment and i^lze of Bracket. 9 
 
 4. Calculated Effect of Bracket with Varying Proportions 
 
 of Frame 
 
 5. Eelation between Slenderness of Frame and Calculated 
 
 Eeduction in Moment Due to Bracket. 
 
 6 . Effect of Length of Clear Span upon Moment at Midspan. • 14 
 
 7. Calculated Moments in Frames of Varying Moments of Inertia. 18 
 
 8 . Influence Lines for Horizontal Eeactions of Frames.. . . EO 
 
 9. Moments at Midspan of Frames of Different Types and 
 
 Proportions 
 
 10 . iJistanoe hj, Contraflexnre. 25 
 
 11. Moments at Midspan of Continuous Beams with Brackets. . E 7 
 
 12. Details of Test Specimen 13A1. .,,*50 
 
 13. Details of Test Specimen 13A2. 
 
 14. Details of Test Specimen 13B1 ,52 
 
 15. Details of Test Specimen 13B2 
 
 16. Details of Test Specimen 13C1 
 
 17. Details of Test Specimen 13C2 ..55 
 
 18. Details of Test Specimen 13D1 
 
 19. Details of Test Specimen 13D2 
 
 20. Details of Test Specimen 13E1 
 
 21. General view of Test Apparatus. •••........,45 
 
 22. General Arrangement of Test Apparatus 
 
 23. Views of Specimen 13A1 and 13 aE after Test 50 
 
 -III- 
 
9 t ^ r A A * 
 
 5 
 
 
 1 
 
 1 
 
 1 
 
 \ 
 
 \ 
 
LIST OF FIGUi'OilS -Continued. 
 
 Lo. Page 
 
 24. Views of Specimen 13B1 and 13B2 after Test. 51 
 
 25. Viev/s of Specimen 13C1 and 1302 after Test 52 
 
 26. views of Specimen 13L1 and 13D2 after Test 53 
 
 27. Views of Specimen 1302, 13D2, and 13B1 after Test 54 
 
 28. Calculated and Observed Moments at Midspan 61 
 
 29. Relative Moments in Frames . . . 1^- 
 
 30. Observed Stresses in Specimen 13A1 65 
 
 31. Obsenred Stresses in Specimen 13 a2 65 
 
 32. Observed Stresses in Specimen 13B1 66 
 
 33. Observed Stresses in Specimen 13B2 66 
 
 34. Observed Stresses in Specimen 1301 67 
 
 35. Observed Stresses in Specimen 1302 67 
 
 36. Observed Stresses in Specimen 13L1 68 
 
 37. Observed Stresses in Specimen 13L2. . 68 
 
 38. Observed Stresses in Specimen 13iill 69 
 
 39. Relative stress Distribution in Frames 71 
 
 40. L'eutral Axes in Curved Beams 73 
 
 41. Shear Diagrams for Frames at Maximum Load 75 
 
 42. Member under Combined ilexure and Direct Stress 79 
 
 43. Variation in I with COmpressive Stress 81 
 
 44. '/ariation in I with Depth of Member 83 
 
 45. Calculated and Observed Deflections, Specimen 13A1 87 
 
 46. Calculated and Observed Deflections, Specimen 13B1 87 
 
 47. Calculated and Observed Deflections, Specimen 13C1 88 
 
 48. Calculated and Observed Deflections, Specimen 13D1. .... 88 
 
 -IV- 
 
LIST 0? JIG-UILIS- Continued 
 
 uo • Page 
 
 49. Calculated and Observed Deflections , Specimen ISEl. ... 89 
 
 50. Diagram Showing Decrease in Stiffness with Increasing 
 
 Load on Prames 92 
 
 51-68. Position of cage Lines and Cracks 113 
 
 69. Arrangement of Apparatus for Testing Paper Models. . . . 135 
 
 70. Values of H/f from Tests of Paper Models 136 
 
 71. Values of H/p from Calculations, using Aquation 5. . . .137 
 
 72. Values of H/p from Calculations and Tests of Type A Modell38 
 
 73. values of H/p from Calculations and Tests of Type D ModelJ.39 
 
 74. .Values of H/p from Calculations and Tests of Type C Model.140 
 
 75. Values of H/p from Calculations and Tests of Type D Model.141 
 
 76. influence Lines for Horizontal reactions 142 
 
 LIST OP TABLES 
 
 Ho. Page 
 
 1. Percentage of longitudinal Beinf orcement 40 
 
 2. rhysical properties of Steel Bars 41 
 
 3. Compressive Strength of Concrete .43 
 
 4. Data of Tests' 59 
 
 5. Comparison of Observed and Calculated Moments 62 
 
 6. Comparison of Observed and Calculated Tensile 
 
 Stresses in Beinf orcement 70 
 
 7. Maximum Observed Shearing Stresses in Prames .76 
 
 8. Calculated and Observed Deflections at Midspan 90 
 
 9. Data of Tests 98 
 
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1 . 
 
 TESTS OP EFFECT ^ BRACKETS 
 IN 
 
 REINFORCBB CONCRETE RIGID FRAIIES , 
 
 INTRODUCTION. 
 
 1. Preliminary*- This thesis is based upon the results of 
 one of a number of investigations conducted in 1918 by the Concrete 
 Ship Section of the Emergency Fleet Corporation in developing 
 the design and construction of reinforced concrete ships* The 
 immediate object of the investigation described herein was to 
 determine the effect produced upon the distribution of bending 
 moments in a transverse ship frame by using brackets or haunches 
 at the inside corners of the frame* The results of the investiga- 
 tion have a wider significance, however, as a contribution to presait 
 knowledge of the behavior of framed structures under stress, and 
 their greatest value undoubtedly lies in their application to the 
 general field of reinforced concrete construction* 
 
 In recent years considerable attention h^s been paid to 
 methods of analysis of rigidly connected frames and this theoreti- 
 cal treatment has been supplemented by a comparatively few tests 
 of reinforced concrete bents* However, there is little informa- 
 tion available as to the correct analysis of frames with haunches 
 or brackets at the intersections of members and apparently no test 
 data bearing upon this form of construction* A v/ell-known method 
 of analysis has been used here and although its application 
 requires a number of assumptions it seems to give satisfactory 
 results* 
 

 
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 The value of definite knmvledge regarding the effect of 
 ■brackets on stress distri'bution follows from the fact that the 
 bending moment at any section may be made to considerably 
 
 through their use and that the material used in brackets is 
 placed where it can resist the high local stresses which the 
 brackets attract to the corners of the frame, Praperly designed 
 brackets will produce a considerable economy of weight. 
 
 This investigation was made at the John Fritz Civil Engi- 
 neering Laboratory, Lehigh University, August to October, 1918, 
 by the Concrete Ship Section of the Emergency Fleet Corporation 
 under the direction of W, A. Slater, Engineer Physicist .United 
 States Bureau of Standards. Alter the armistice the data of the 
 tests were taken over by the Bureau of Standards and it is 
 through cooperation with tho-t Bureau that the data have been made 
 available for this thesis. It is expected th^.t the Bureau of ^ 
 St mdards will publish a Technologic Paper containing the sub;|ect 
 matter of this thesis. The opportunity of carrying out as ex- 
 tensive an investigation as is here reported is due largely to 
 the support of R. J. 7/ig, Head of the Concrete Ship Section, It 
 is desired also to express full appreciation of the assistance 
 afforded by Professor ¥/. P. McZibben and other officials of 
 Lehigh University in extending to the Concrete Ship Section the 
 use of the laboratory and equipment for this work. The investi- 
 gation was planned and carried out by the writer. Valuable 
 suggestions in laying out the tests were received from C. A, 
 Maney, Designing Engineer of the Concrete Ship Section, Major 
 W. M. Wilson and Major A. R. Lord, successively in charge of the 
 laboratory at Lehigh University for the Emergency Fleet Corpora- 
 tion, are entitled to acknowledgment for cooperation in carrying 
 

 out the tests, 
 
 2, Nature of Investip:ation ,~An important use of brackets in 
 ship construction is at the corners of transverse frames. Since 
 a sharp corner at the intersection of horizontal and vertical 
 members produces a section of highly concentrated fibre stress 
 combined with a large negative bending moment, a bracket is used 
 primarily to reduce the compressive stress at this place. In 
 addition, since in all t3rpes of statically indeterminate frames 
 the distribution of bending moments depends upon the relative 
 stiffness of the members or parts of which the structure is compos- 
 ed, the bracket produces two other effects; (1) it affects the dis- 
 tribution of moments throughout the frame because of the local 
 variation in stiffness which it produces, and (2) it affects the 
 magnitude of the negative moment as well as the distribution 
 of moments because it changes the shape of the axis of the members 
 at the corners of the frame. This^change in shape is sometimes 
 regarded as a shortening of the span of the members in which the 
 brackets are used. 
 
 In choosing the type of specimen for these tests, the object 
 was to secure a frame similar in form and loading to a ship fr^me, 
 and of fairly large size. A rectangular two-legged bent was 
 chosen as approximating, in the inverted position, the lower part of 
 a transverse ship frame. The columns v/ere made hinged at the bases 
 in order to simplify the interpretation of the results. The 
 
 brackets used were similar to those used in ship design. 
 
 In testing, all specimens were loaded to failure and observa- 
 tions of deformation a,nd deflection were made at regular increments 
 
 of lOw-d, The experimental data have been compared with analytical 
 deductions and in general a satisfactoiy agreement has been found. 
 

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 II. MALYTICAL TREAT5;TMT 
 
 3. Analysis of the Effect of Brackets. - Mathematical 
 analyses of rigidly connected frames are usually based upon the 
 assumption that the members of a frame are uniform in section 
 throughout their length, and there is little information on the 
 proper way of analyzing frames in which abrupt changes in cross 
 section occurs*. However, in the analysis which follows it was 
 considered sufficiently accurate for frames containing brackets 
 to draw in the approximate axis of the frame, and to consider as 
 fully effective the depth of the cross-section measured normal to 
 this axis. A semi -graphical method often used in arch analysis 
 was then applied to the frame. 
 
 In the analysis of the two hinged frame of Eig.l, which 
 shows one of the types that was tested, the outline of the frame 
 was first drawn to scale and the axis divided into a nimiber of 
 sections approximately equal in length. The length of a section 
 was denoted by the depth of cross-section by d, and the verti- 
 cal distance of the centroid of the section above the hinges by 
 2 ;. Values of d and y; were scaled from the drawing where 
 necessary for each section of the frame. Values of d were used to 
 calculate the moment of inertia, I, which for reasons to be dis- 
 cussed in Section 13, was considered to vary as d^A. Letting M 
 represent the bending moment at the centroid of a section due to 
 
 * Since the tests described herein were made and reported, a 
 very general theory for analyzing frames of this type has been 
 published by G. A. Maney, in Trans. A. S. C.E. , Vol.LXXXIII ,p664 , ^ 
 1919-20 
 
5 
 
 Fig. 1 
 
 Ontline Drawing Used in Analysis of Frame 
 
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vertical loads and reactions only, tne following general formula* 
 
 for the horizontal reaction of a two hinged arch was applied. 
 
 H = 
 
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 ^ Mt7 I 
 
 ds 
 
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 ( 1 ) 
 
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 Prom the conditions for static equilibrium of the frame the value 
 of the moment at midspan was found to be 
 
 ______ -(i^) 
 
 Substituting values of H from equation (1) in equation (2) values 
 
 Me = M -- Hh 
 ^ 6 
 
 of Mq ?/ere obtained, and for convenience have been expressed in 
 terms of the maximum moment, , for a simple beam loaded as the 
 top member was loaded. The reason for using the latter quantity 
 is that it simplifies the application of values of M to designing. 
 
 To illustrate the relations expressed by equation 2, let it 
 be assumed that the value of Me is known for the rectangular frame 
 of Pig. 2(a). Since the horizontal member is a partially restrain- 
 ed straight beam, the sum of the negative and positive moments is 
 
 equal to , and the trapezoid ABGD represents the moment diagram 
 6 
 
 for a simple beam. Hence laying off M„ fixes the value of the 
 negative moments at the corners and the entire moment diagram 
 for the frame is easily drav/n. It is further evident that if R is 
 
 Por derivation of this formula, see Johnson, Bryan and Turneaure, 
 "Modern Pramed Structures", Part II, pages 138 to 158. In this 
 derivation the effect of deformations due to internal shearing and 
 direct stresses are neglected. \^l/hile these effects are usually 
 negligible, they may be included in equation 1 by measuring ^ 
 to a point other than the centroid of each section. Such points 
 may be determined by use of the theory of the ellipse of elasticity 
 
8 
 
 the resultant of the horizontal and vertical reactions at the 
 base, the moment at any point left of ^ is This 
 
 relation is particularly useful in treating a frame having brackets 
 in which the axes of the horizontal and vertical members do not 
 meet at right angles, as in Fig, 2fb). Here the top member is not 
 straight and the sum of positive and negative moments is not equal 
 
 to, 
 
 
 However, it is possible to lay off the knom value of _M, 
 
 and the simple beam moment diagram ABCH. This determines the 
 moment diagram for the horizontal and vertical portions of the . 
 frame and locates the point of inflection 0, The resultant re- 
 action R must pass through 0 and since the moment at any section 
 
 j 
 
 to the left of B varies as the distance from R, the moment dia- 
 gram for the corner of the frame can be drawn in ijroportion to the 
 moment in the vertical portion of the frame. 
 
 Fig, 3 shows the results of analyses made by use of equation 
 (1) for the purpose of designing test specimens. Values of the 
 bending moment at midspan are plotted as ordinates against hori- 
 zontal lengths of brackets as abscissas. The points representing 
 the calculated moments are seen to lie nearly on a straight line. 
 The variation in moment at midspan is due almost entirely to the 
 variation in stiffness produced by the different lengths of bracket. 
 It is rather surprising, hov;ever, that the moment should vary so, 
 nearly as a linear function of the bracket length, and hence of 
 the clear span, for these particular frames. From the difficulty 
 of analyzing such a frame a straight line relation would not be 
 expected to obtain, and it is evident that the line does not apply 
 exactly at the * two extremities of the diagram where the bracket is 
 
9 
 
 
 Fi^. 3. Relation between Calculated Moment and Size of Bracket 
 

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 either very small or very large. 
 
 To determine whether similar curves may he drawn for frames 
 of other proportions further calculations have been made. Fig. 4 
 indicates the relative effectiveness of brackets when used in 
 frames having different ratios of height to span. It is seen 
 that the use of a given bracket has the greatest effect in chang- 
 ing the value of the moment at midspan when the ratio of height 
 to span of the frame is small. This is apparently due to the 
 fact that as the ratio of height to span decreases the bracket 
 occupies a larger portion of the region of high negative moment. 
 The principle involved here is sufficiently important to warrant 
 further elaboration. For illustration, if in any frame the moment 
 of inertia for a short portion of length be changed, there will 
 be a change in the bending moment at any other point in the frame. 
 This change is approximately proportional to the original bending, 
 moment at the section where the change in moment of inertia is 
 made. It will be seen, therefore, that an increase in the moment 
 of inertia such as that produced by a bracket or haunch will be 
 most effective if made where the original bending moment is larg- 
 est. Referring again to Fig. 4, when the ratio of height to 
 span is 1.0 the negative moment at the corner of a frame without 
 brackets is .40 and a 24 in. bracket reduces the moment at 
 midspan only 20 per cent. On the other hand, when the ratio of 
 height to span is 0.3, the negative moment at the corner of the 
 frame without brackets is .56 ^ and the 24 in. bracket reduces 
 the moment at midspan by 51 per cent. Hence for brackets to be 
 most effective both in changing moment distribution and in reduc- 
 
11 
 
jE^oc^: o:^ i^xobox^rTOUS o:^ LXOTJe 
 
ing stresses they must he used at points of high bending moments. 
 
 Another series of calculations was made to investigate the 
 effect of slenderness of members on the effectiveness of haunches. 
 With a constant ratio of height to span and a constant ratio of 
 bracket length to depth of member, 5’ig* 5 shows that the effect- 
 iveness of a bracket in reducing the moment at midspan is less 
 for the smaller depths of member. This should be true because 
 the frame is stiffened along a smaller portion of its length, and 
 because the change in shape of the axis of the frame at the 
 corners is less for the slenderer member. The information of 
 Fig. 4 and Fig. 5 has been replotted, using values of the moment 
 at midspan, Mq, as ordinates and the ratio of the clear span to 
 the total span, s/^ , as abscissas, producing the curves shown 
 in Fig. 6, Each curve represents a certain value of h/£ , the 
 ratio of height to span. The variation in clear span indicated 
 in this diagram is obtained by varying both the size of the 
 brackets and the slenderness of the members of the frame. 
 
 This diagram indicates that the moment at midspan varies 
 very nearly as a linear function of the clear span, or distance 
 between bracket edges, for frames of the proportions shown. That 
 is, just as in the case of the curve of Fig. 3, here a series of 
 straight lines seem to fit the several groups of calculated points 
 fairly well, the divergence from the linear relation being shown 
 at the extremities of the lines by dotted curves. The straight 
 portions of the curves represent the range of values ordinarily 
 encountered in the use of brackets; wi thbra'- ]^ets so small that the 
 ratio s/^ becomes 0.9 or more further tests are needed to deter- 
 
0.6 
 
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 06 0.8 lO /.2 !4 
 
 Depth of mem ber, d, m Feet 
 
 Fig. 5, Relation between Slenderness of Frame and Calculated Reduction in Moment Due to Bracket. 
 
14 
 
 E’ig. 6, Effect of Length of Clear Span upon Moment at Midspan. 
 
15 
 
 mine the exact effect upon the moment distribution. 
 
 It is significant that for the ratios of depth of span of 
 members to be found in practice, the moment is not greatly 
 affected by a variation in slenderness of members as long as the 
 clear span is not changed. This indicates that the clear span 
 is the variable of major importance. The effect of a variation 
 
 in slenderness is still less v:ith higher values of n than that 
 shown with values of n eg^ual to 0.25 and 3/7. 
 
 It is thought that an ec[uation representing the curves of 
 Fig. 6 may be found useful. Such an equation must naturally 
 reduce to the ordinary equation for rectangular frames when no 
 brackets are used. If n represents the ratio h/g for such a 
 frame without brackets, the moment at midspan due to a total 
 load P applied in equal parts at the 1/3 points of the span is 
 expressed by the equation* 
 
 Me = 
 
 
 2n + 1 
 2n + 3 
 
 (3) 
 
 ITow ivith regard to frames with brackets**, it is found that letting 
 
 * For demonstration leading to this equation see Bui. 108, 
 
 Eng. Expt. Sta., Univ. of 111., 1918, p.56» 
 
 **A method of analyzing frames similar to these is given by 
 E. Bjornstad, in "Die Berechnung von Steifrahmen nebst anderen 
 statisch unbestimmten Systeraen.” Berlin, 1909. One equation is used 
 for frames both with and without brackets by proper choice of the 
 terms corresponding to n. That is, the members which contain 
 brackets are considered replaced by ’’equivalent" members of con- 
 stant cross-section throughout. The section of the equivalent 
 member from which n is calculated obviously varies with the size of 
 bracket. This treatment of the subject from a purely theoretical 
 vie?;point neglects the change in shape of the axis of a frame con- 
 taining brackets; further the assumption is made that for a haunch 
 which varies uniformly in depth the moment of inertia also varies 
 as a linear function between the two extremities of the haunch. 
 
 The results obtained are stated to be approximate. 
 
16 
 
 m = s/^ , the ratio of clear span to total span, the straight 
 portion of the group of curves of Fig. 6 may all be expressed 
 by the equation 
 
 
 - 
 
 6 
 
 2n + 1 0.65 - 0.7 m 
 
 2n + S 
 
 (4) 
 
 nii" +” 0.8 
 
 This is an empirical equation fitted to the results of semi- 
 graphical analyses and hence has a theoretical basis. Its use, 
 however, should be limited to values of m between 0.5 and 0.93 
 and to values of n between 0.3 and 2.0. It may be noted that for 
 any particular value of n the effect of all sizes of brackets is 
 determined by calculating t?/o values of from equation{4][ , since 
 these are sufficient to fix the position of a straight line simi- 
 lar to those of Fig. 6. 
 
 The foregoing analysis has been based upon the use of equal 
 moments of inertia of columns and girder except at sections 
 occupied by brackets. In practice it is quite likely that the 
 columns and girders of a bent may have considerably different 
 cross-sections, with a resulting variation in the moments of 
 
 inertia. For columns without brackets equation (3) still applies 
 
 lih 
 
 ZT ■ 
 
 if the term n is considered equal to 'J - , fig = moment of 
 
 inertia of girder section, 1^ = moment of inertia of column sec- 
 tion) . It is therefore immaterial whether a variation in n is 
 caused by a variation in the ratio of height to span or of moments 
 of inertia or of both. However, when brackets are used, such a 
 general relation apparently does not obtain. 
 
 A number of calculations have been made, using a constant 
 
 value of h , and of moment of inertia, lo-, of girder, but varying 
 
 -e ^ 
 
*'.C- 
 
 ■’■Jm 
 
 
 ; I 
 
 ;«jpi ! 
 
 ,\a ' 
 
 -« A V 4 ..^ 
 
 jT ^*100 
 
 ■ •d: 
 
 yp 
 
 »!• 
 
 ti 
 
 _.J'- 'f'i'ri. 
 
 
 ■£ 1 . . 
 
 j • =i J ^,'V 
 
 ¥' 
 
 
 . - *' * 
 
 P 1 ' - >1. ■ t' ;7 t,7f 
 
 
 rt \ 
 
 
 ^ I : .M f> • .' 
 
 * ■ tjr •> 
 
 > ' 
 
 •:u •' 
 
 
 1 *li 
 
 •■ I I . ;■• 
 
 ■ovcw- 
 
 *< . ■»! 
 
 ^ X 0 nffi-, ' i r) t -iV f 
 i* ^.-)- 
 
 
 I 
 
 ..t' 
 
 
 • ^v. 
 
 ■' 4 ?^ 
 
 "■' ifeiV ■ i* 
 
 TC^ ': r 57 ; 5 (J) 0 <:: |f 
 
 - .,, ~ r'v’i.M-.' 
 
 i T’-' i a? ; .. , M • 
 ' • ' .'• ' 
 
 '•:t.‘ ’. ' . 2 L . 
 
 or.-;- ■ ,/r. 0 ci. : ;!i'c 
 
 
 i.Tj ,:0A' ,*y -v7 4 
 
 A . -r* ' ' 
 
 LU. rt#, , . f-^/rrt , ,.^ ■ (*) 'X^. 
 
 P'S 
 
 ‘j t- 
 
 !i ■ i-t'-'l’-tr:, r iT 
 
 ■ i -: ", oX.-io lo *r • 
 
 :o f'- ''r.'^:.; lo 
 
 i.<' 
 
 
 *i» - A • V. #v«*t 
 
 . (. . v| 
 •■ h 
 S\ 
 
 ,.x . A. ' .-■.'.- •..■f " ‘ «'f>-.-^l 
 
17 
 
 the moment of inertia of the portion of the columns below the 
 lower edge of the bracket* The values of thus determined are 
 
 plotted against values of the quantity Zg in Pig* 7. It will 
 
 be noted that with values of ^ equal to 3/7 and 1, respectively, 
 widely different values of Mq are found with the same value of 
 Furthermore, these values do not compare at all closely 
 
 is 
 
 With the moments obtained by assuming ig . h equal to n in 
 
 ^c T 
 
 Equation (4). It seems impracticable, therefore, to attempt to 
 use Equation (4) to investigate frsmies in which the moments of 
 inertia of girder and columns vary. Pig. 7 indicates the general 
 range of values of moments to be obtained in most cases of this 
 sort; frames of other proportions may be analyzed by the applica- 
 tion of Equation (1). 
 
 It has been shown that the moment at midspan decreases with 
 the increase in stiffness at the corners of the frame produced 
 by the use of brackets. If the corners of a rectangular frame 
 could be stiffnned x7ithout the use of brackets, a decrease in 
 moment at midspan would cause an equal increase in moment at the 
 comers, since in this case the numerical sum of the positive and 
 negative moments is equal to the maximimi moment for a simple 
 beam carrying the same vertical loading. However, where brackets 
 are used the axes of the members do not intersect at right angles, 
 but approach more nearly the pressure line of the resultant force 
 acting on the hinge. The resulting decrease in moment at the 
 corner due to this variation in shape of specimens with brackets 
 approximately offsets the increase in moment at the comer due to 
 the variation in stiffness of the different parts of the frame. 
 
p 
 
 *' . > 
 
 
 
 xO :’r.n;<: 
 
 ?.^r 
 
 .c-."j‘f ?■ 
 
 *1.’ 
 
 ^'Ar T 
 
 'i'^yroT.. 
 
 '.f" ' ‘-i-ivf.- 
 
 
 \v»- ‘C 
 
 V 
 
 
 \ 
 
 4M" 
 
 li ilL' ^'' •■.' 
 
 v-;j/‘V- . ... ,‘ 'TOrOT 
 
 ,’^ 4 : 0 1 >- ; 
 ■',> 
 
 
 '.,■ ,;j ^:v.ri^*'' ., {V' ,’. i-ij rit'''' 
 
 > ' , ; 
 
 
 ■- ... (k •' ' :■ -.. ' - "• ■■ 
 
 I ^ "n 
 
 ^ i ^ > 
 
 .•C.2 .r; 
 
 'J.6 .?JttTorr; 
 ‘"icrr 
 
 
 .. -r 
 
 li 
 
 4 .- ' 
 
 ■ ■ ’ 'V'T, 'c, ^ ..,, 
 
 .^ ■ ' '■ i' ' ‘ .!• : V cfve: ': . .' n.t 
 
 ".y . -''Of; • •.' if,, ■ ■ ; ' .r.i «.*)« 
 
 ' . -...TMdM , . ■ ■■•.,.,.4 c . . 
 
 .■.,'/r ^ -► "■ •- T .r;>.j.;;. b''trr^\ ': •'•M. .• ' bSrrco' 
 
 ' . '' ' 
 
 • >'.I t’>- r- V* • V 4'^i;;nTr-fr^:2fei- tneir.rj^*- 
 
 f- ■' 
 
 : •. ; •■■n l - . :•• ; ? TOTTj/ 
 
 •f 
 
 ^ — f 
 
 li,-D 
 
 .' I r < * J. 
 <■ 7 . T '. :kr' V 
 
 
 
 
 .'I 
 
 ■j.i 
 
 
 
 
 : J ti*:, i 
 
 'O'. 
 
 ' " Ai. , 
 
 .; -;C ,;> T ‘v 
 
 Itr 
 
 fl 
 
 :o C'o 
 
 i. ; 
 
 » - *. 
 
 i ■ } ’ r ■ "T f' j* . 
 
 0 ^ 
 
 
 
 ,r '■ 
 
 odt !‘>;f ■> * 
 
 ^3r.- 
 
 ■j ' 
 
 J :: 
 
 
 . i,‘V ■ 
 
 *»i f 4 ■ iyL".v ''>w) i f J r n ' 
 
 A .' ', 1 ,. ,'a* t',. ■ 'i/>> ''j. .-A'srk 
 
 . \li‘.- . Mil. 
 
 1 ' . 
 
 L 
 
 |(' 
 c ^ 
 
 
 . ko' 
 
 H ' 
 
 ^ ...'I 
 
18 
 
 Pig. 7* Calculated Moments in Frames of Varying Moments of Inertia 
 
19 
 
 Hence, the negative moments in the different types of frame are 
 nearly equal in magnitude for a given load, as will he noted 
 later from the results of tests, 
 
 of Brackets with Different Loadings .- Equation (4) 
 has been developed for the special case of third-point loading 
 which was used in the test frames. This form of loading is fre- 
 quently used in tests because it is easy to apply and produces 
 a moment diagram somewhat similar to that due to a uniformly dis- 
 tributed load, A study of the effect of other loadings shows that 
 equation (4) may be adapted to a form which gives the effect of 
 brackets for such cases. 
 
 Influence lines for the horizontal reactions of a two-hinged 
 frame under vertical loads are shown in Pig* 8.* That is, 
 the ordinates of any points on the influence line represent 
 relative values of the horizontal reactions due to equal vertical 
 loads at the corresponding points of the span. These relative 
 values are independent of the ratio of height to span of the 
 frame. Prom these curves it is found that certain common types 
 of loading (with equal total loads) produce the following relative 
 values of the horizontal reaction ,H, considering the reaction 
 
 * The construction of these influence lines is based upon the 
 follOY/ing theory: With a frame of the type used in this investiga- 
 tion suppose outward thrusts to be applied at the hinges, causing 
 the top member to deflect down\7ard, How from Maxi-Bell’s theorem 
 of reciprocal displacements it is known that the elastic curve of 
 the top member of this frame is an influence line for the horizon- 
 tal reactions of a similar frame lo ded with vertical loads on the 
 top member and having the hinges at the base held stationary. 
 
 Pig. 8 therefore was obtained by computing the shape of the 
 elastic curves of t\No extreme forms of top member; one having no 
 bracket and one having large 45° brackets extending to the quarter 
 points of the span. It is to be noted that these curves give only- 
 relative (not absolute) values of the horizontal reaction, and that 
 the curves can not be used to compare values of the reactions for 
 the two types of frame. However, relative values are sufficient to 
 compare loads at different points on the same frame, which is the 
 
 purpose of this diagram. 
 
r . 
 
 yP >. 
 
 "'. ::• .oj.t r'V • 'ar ’.>' I’i 
 
 
 
 
 '•» 
 
 I 
 
 
 Ai*!Cf 
 
 'ter, - 
 
 
 ■? > ■’■ 
 
 
 i ’.'’ :? iif.'' 
 
 
 ^ 0 ' 
 
 
 t*ii r j* 
 
 r .-b 4 
 
 t 3 ;-r * . 
 
 Ii."’ 
 
 •• ■ p.' 
 
 
 MA T>-i, 
 
 >1 
 
 o ^^ 0 J 
 
 '. 1 / ■■ ■' • 
 
 T.i' t.-taKv*:: . 
 
 .' r-’” 
 
 1 0 ir . { . - 3 tfr 5 . 45 ' 
 
 
 T ■ 
 1 
 
 l , 
 
 +- 
 
 t.v ■ 
 
 » t 
 
 k 
 
 ‘ 'hvX 0 ^, 10 , • 
 ■'ll ■ 
 
 i \ \ ' 
 1 » '' 
 
 1 , 
 
 ‘ 4, 
 
 f'Z i T, -/ 
 
 
 
 I r 
 
 ■i. r i. 
 
 •. o 
 
 I ‘ 
 
 feis t. . 
 
 t * n 
 
 ! . ' 
 
 
 I 
 
 . ♦ O' HiT, 
 
 . • • •. 5 -r, 
 
 t.-i «[•',<•*.■ 
 
 .. t?,<I . . ' '■'■ 
 
 *,■ ■ 1 ' . ■ 
 
 ':sr', -X 
 
 . 01 ,r 
 
 ■Uj -v;:-7 
 
 
 4 ..c:. .0 j; 
 
 r^. • 
 
 e ; .uiiiy or,.;' 
 
 0 1 'r' :> .' 
 
 
 i. -:oi ai 
 
 ♦ r J 
 
 'j ’: . 
 
 / 
 
 ' ..;■ -•. . ; ’ ;>:) '. 1 
 
 • -— •• 
 
 
 d'.. 1 ', i“* : 
 
 ‘ ■ ‘ ' 1 
 
 ■ J , . / ’ 
 
 • - ; i\i r -•. -■; .,, (• 
 
 
 i i. ■(" A 4 *> 
 
 
 ;.>'-o.roX 
 
 c 
 
 ■ ' r. ‘ >l:r, 
 
 ' • j r. 
 
 ^ ’j t • 
 
 
 
 *• .'tgX-t ' •■ 
 
 • • • ‘ A 
 
 ' ... .. . V ' ^ ■■ > - 
 
 ".kV / 
 
 ,! e> .‘i’dv' 
 
 0’^ 
 
 ^rot f 
 
 , f' ’T -•• . > 
 
 "’■:. I', ■' n'.rov 
 
 V* • 
 
 . ? ri A> «c '1 ■ 
 
 'th L ]>• ' ', 
 
 
 ■ TO ,i V>. . 
 
 ';■< .iw'ij ij.'.-,:.:, ■ • / ■ ; 
 
 
 '. li 4 , 
 
 ■ _ ■_. '•■* .; ' 
 
 :-:xT'.:r‘v3 *)« X f 
 
 ' -I'l’ 
 
 rv -V 
 
 • ^ 4 ' . 
 
 d.. ' fri.'.:/ : ■ • id 
 
 .0.CO.-? ;,.| ;jufv .t ; 
 
 t>;;’ I’d' 
 
 •I ' I i- ' ■ 
 
 ..d ^ 
 
 BfUi 
 
 ^ - j: ■ ' > 
 
 ■'•' 'ifa ■ - i i, 
 
 ' w w 
 
 • ;-ha ■ -.r ; ■ ‘ ’I'M 00 -^-.f 
 
 jM/d 1 
 
 Cl-, ■>'*; c-': 
 
 rft 
 
 
 ,o"v i ' 
 
 ■ '“T.^ ; ? •* d 
 
 
 ..'’rt ■ c.'d 
 
 ’■' ft -• 7 
 
 ,.0 : f ?4A~' Y 
 
 i: 
 
 'd-'x 
 
 * * 
 
 • /.to'. '■]••. .r t .• tori) 
 
 ^X'^;x, j I'ix V’,; j; ... ,^;ot '£ios<r . ■; d-. -n*- ^ 
 
 ■ ^ _ jjjj -;; gr^ .'iBij 
 
 Afc •' ■ '.•:'v : r ZV 
 
 . ' . ,i U/.' ^ .1 ^ ■■- Y» Cff 
 
 ■‘•-•ti-^oj:. ’ • ■' 
 
 •\ ' ' , .T^ : ; .. 
 
 
 . \ ’ V ; •• 7 ':“' 
 
 ^ iuliLlKKe ^0',.mrrC^. 
 
20 
 
 Fig. 8. Influence Lines for Horizontal Reactions of Frames. 
 
El 
 
 due to third-point loading as unity. 
 
 Third Point Uniform 
 Loads Load 
 
 No bracket, H = 1,00 H = .750 
 
 Large Bracket, H = 1,00 H = ,7E0 
 
 Concentrated 
 Center Load 
 
 H = 1.125 
 H = 1.167 
 
 It is evident that the relative values of H for a frame 
 Tvith no brackets will not be in error more than 4 per cent if 
 used for frames with brackets. 
 
 Prom equation (2) and (4), for the third point loading. 
 
 H = 
 
 Pi 
 
 6h 
 
 En + 5 
 
 0,65 - 0,7m 
 
 n^ + 0,8 j 
 
 (5) 
 
 Using the above ratios of H for the fr^me without brackets 
 and solving for M , gives 
 
 uniform load W, Mq = 
 
 
 fEn 
 
 + 1 
 
 0.65 
 
 - 0.7m / 
 
 8 
 
 l2n 
 
 + 3 
 
 n^ + 
 
 1 
 
 1 
 
 cc 
 
 . 
 
 o 
 
 Me = 
 
 u 
 
 En +1.5 _ 
 
 0.49 -0.53m 
 
 4 
 
 En + 3 
 
 n^ + 0,8 
 
 — (7) 
 
 For any other type of loading the relative values of H may be 
 found from Fig. 8, after which the moment is readily computed. 
 
 5. Effect of Brackets in Various Type s of Frames .- While 
 the results of the foregoing analyses should be useful in 
 the design of two hinged frames, the question immediately 
 arises as to what quantitative application may be made to 
 other kinds of frames. For example, brackets may well be used 
 in the closed rectangular frame, in the two-legged frame with 
 column bases fixed, in building or viaduct frames and similar 
 stride tu res. In 
 
E2 
 
 the absence of test data, theoretical analyses have been made for 
 two types of frame and it appears that an application of ecLuation 
 (4) may be made to these cases. 
 
 The frames analyzed are the closed rectangular, or quad- 
 rangular, frame in which the columns are assumed to be rigidly 
 attached at the bases to a horizontal member of equal section, 
 and the two-legged frame with the columns fixed at the bases. 
 
 Both of these frames have points of contraflexure in the columns 
 at a distance ho equal to 2/3 h or more from the tops of the 
 frames. In this case the portion of the frame above these points 
 of contraflexure may be considered as a two-hinged frame in which 
 the bases have been alio /ed to move apart a small amount. 
 
 Such an outward movement tends to increase the moment at midspan 
 in a two -hinged frame. 
 
 The analysis of these frames has been made by use of the 
 general theory of indeterminate structures,* The span and depth 
 of members used were the same as those used in the test specimens, 
 while the height and clear span of the frames were varied. 
 
 Fig, 9 shows values of the calculated moment at midspan for 
 varying proportions of these frames, and compares them with values 
 for the hvo-hinged frame. It is seen thi t for frames having the 
 same distance, hQ, from the top to the point of contraflexure, 
 the moments M are very nearly the same. The values for the 
 fixed base and quadrangular frames are slightly higher than for 
 the two-hinged frame because the columns at the point of contra- 
 
 * See Johnson, Bryan and Turneaure, Modern Framed Structures, 
 Part II, pp,386 
 
1 .. 
 
 tit* 
 
 ^w: ■ r 
 
 I f 
 
 
 -‘AC ^ 3 :*:v;.f. 
 V* ’ I 0 j j • T 
 
 - -. 
 
 ■ y 
 
 
 • - ; , '-'M 
 
 
 •vt.lv n ^ 
 
 
 
 'v.i "vi' '"i;.'. . 
 
 ■Jj 'V : I \ ' \r,' 'uO'> 7 i ' r 
 
 ■ ^ ■ ' . ■ 9 ;> 7 
 
 i:*' • ,C; ':i ’ ' 
 
 '/ 1 7 
 
 •* ■' ' ' A 
 
 i# ^ 
 
 ’ T 
 
 ' r . , X 
 
 .■,^.-d ‘.\: .-!• i 
 
 ■ u ‘UK*dJ t. - ^ ■"' 
 
 r,' :.*• ,. _ ‘'.*i*';:.iB..' j f. . 
 
 
 
 ' X j - 1 ■ T '.' 1 • ' ; ;J 
 
 • ■■ •! ii ’ . 
 
 fji''-*.'",.. j 
 
 ■.• ■ -•: f)., ■ • 
 
 ' - 
 
 '■■•■ .•' ; i' 
 
 ,?(■.' tRlw --- ■ *-; . 
 
 MV 
 
 "0.: 'w 
 
 X: -ur 
 
 
 V: • • . . r . -•• 
 
 i 
 
 ; 1 
 
 '■ ■•■ • r'/,^ 
 
 
 ■ ■■ rr.^.’T-' ; 
 
 
 " ■'■ ' T == , 
 
 • : ;> : i- .^qo n 
 
 
 .'■i ■ 
 
 ' ** C! ■ I 
 
 ; -O O . .' 
 
 ' 1 '; 0 ^ h'v ^ :ti' . 
 
 ^ • * 
 
 V I ;* ' 
 
 rt^ y - n: 
 
 V I T 
 
 ' ■*-' .' 
 
 V I'j r’ji- r .i/'; . i;,,-. . 
 
 > ' - ^ "i :.i5;.v •.;'!: r,i: 
 
 , y j .:- ^ • : : ' f-' 
 
 ■ c: . '.; •v-’. . ■ • ' ■ ^ ('rj L : 
 
 0 . .f ?. 
 
 ;i:; ; o. 
 
 
 
 iril 
 
 fiT. 
 
 ?. ■• ' A 
 
 V'v ■, A 
 
 
 r tJ*' 
 
 1 , 10 ':: 
 
 •■■’ :r. . 'X ri 
 
 'li"' Af;.in.rf£^4Mp 'SritS^l 
 
 '1 
 
 
 i'-'' •'■ 
 
 4 • I ^ • 
 
 'j- • -11 ■t--.;C 0 !. 
 
 . "r 
 
 ri v:r' 
 
 Ax: . 
 
 oyT 
 
 V • 
 
 ^ Tt. , 
 
 - ir . \, 1'.’-! 
 
Moment of M/depon /n terms 
 
 
 
 Fig. 9. 
 
 Moments at Midspan of Frames of Different Types and Proportions 
 
 Types of Frames 
 and corresponding symbo/s 
 Depth of members /-o" 
 
 , , Jpan /d'O" 
 
 ^ l \*~ I F 
 
 T I 
 
 _L 
 
 X— X— X 0-0-0 
 
 , I 
 
 d/nged f/xed Ooadrangu/or\ 
 
 I 
 
 .J d 5 .6 .7 T' 3 LG // 
 
 Va/ims . * 
 
ss 
 
 I •• 
 
 )' (> 
 
 r -..♦s 
 
 .. - 
 
 (■ . * 
 
 i 
 
 
 it 
 
 
 I 
 
 ■ f 
 
 t'f ti-. r. 
 
 
 
 '!« . 
 
 I « 
 8 ' • 
 
 l-v-.!: 
 
 ! i^i-’ 
 
 I 
 
 r 
 
 1 X] v^'vi . ■ -s.^ - ^ ik' Vxx ■’: 
 
 I', j 
 
 I r^-' VH ' h~ ^ J }^ JiH 
 
 ( rr~n ^ 
 
 
 i 
 
 j i~ 
 
 ,, , •: 
 
 
 ■c. J1.X: ?■■'•■■ .. ■ - ‘’^ ■■ ,f ■»' 
 
 r' '■ ?/j-, 
 
 ...>x"f 
 
 ■ ’■- -r^i 
 
 » 
 
 <f' 
 
 
 B«g^ *):o 5;/^ irf.cfsfciM ^ja a^iiemolT. .^.^ilT 
 
 ‘ ' - '‘- ■ '•■.■ . \ . 5 .V.- #: ., ''^ ^ '*•! ■• 
 
 '■ I- 
 
flexure have deflected outv/ard slightly. However, if the 
 value of ho could be determined it aj^ears that these frames 
 could all be treated as two hinged frames by use of equation (4 ) 
 without appreciable error, For this purpose Pig, 10, giving 
 values of h^, for frames of various proportions, may be used. 
 
 The data for this diagram were computed along with those for 
 Pig. 9. 
 
 The procedure in determining the effect of certain brackets 
 in a quadrangular or a "fixed-base” frame may be summed up as 
 follows: - 
 
 Knowing the proportions of the frame the position of the 
 points of contraflexure may be determined from the curves of 
 Pig, 10, Placing the value of h^^ equal to n in equation f4) 
 gives the value of Mq, the moment at midspan of the top member. 
 The moments at all other parts of the frame may be found from 
 the eqtiations of statics, ^'Thile the value of ^ may be slightly 
 inexact, the error is small. 
 
 The curves giving the position of the points of contra- 
 flexure are applicable for any loading on the top member that is 
 synmetrical about the center line of the frame. Hence, if uniform 
 or concentrated loads are used the procedure is the same except 
 that equations (6) and (7) must be nsed to determine the value 
 of Me* 
 
 One or two other trypes of rigidly connected structures 
 may well be mentioned here, Por example, the continuous beam of 
 three spans, with loads on the middle span only, may be treated 
 
25 
 
 <D 
 
 u 
 
 M 
 
 jH 
 
 o5 
 
 4 ^ 
 
 o 
 
 o 
 
 tH 
 
 O 
 
 -P 
 
 o 
 
 P 4 
 
 O 
 
 4 -» 
 
 ( 1 ) 
 
 0 
 
 
 o 
 
 ft 
 
 o 
 
 EH 
 
 0 
 
 o 
 
 h 
 
 O 
 
 Q) 
 
 O 
 
 0 } 
 
 -P 
 
 CQ 
 
 •H 
 
 P 
 
 O 
 
 P 
 
 bD 
 
 •H 
 
 ft 
 
26 
 
 as a two-legged frame with the coltimns swimg up into the hori- 
 zontal position. liThile certain features of the rectangular 
 frame such as column action, curved beam action and direct 
 compression due to horizontal thrust are absent in the continu- 
 ous beam, brackets used at the supports will occupy the same 
 region of bending moment in the two tjrpes of structure. Hence 
 equation (4) will give substantially correct results when used 
 with this special case of a continuous beam. 
 
 Another very common form of continuous beam is one having a 
 large number of spans of identical dimensions and with all spans 
 subjected to equal loads. To illustrate the effect of brackets 
 used at the supports in such a beam two numerical cases have been 
 analyzed by the method explained at the beginning of this section. 
 In one case brackets with a 45° or 1 to 1 slope were used at 
 each side of the supports; in the other case brackets having 
 a 2 to 1 slope (making an angle of 26^32' v/i/th the horizontal) 
 were used. The ratio of depth to span was one tenth, though 
 this quantity is shown in Pig. 6 to be relatively unimportant. 
 
 Pig, 11 shows values of the moment at midspan due to one- third 
 point loading, for various values of the ratio of clear span to 
 total span* Denoting this ratio by ra it is found that approximate 
 formulas for the moment at midspan are; 
 
 Por brackets with 1 to 1 slope. 
 
 Por brackets with 2 to 1 slope. 
 
 The moment over the supports in either case is 
 
27 
 
 03 
 
 ■P 
 
 M 
 
 o 
 
 o3 
 
 u 
 
 W 
 
 -P 
 
 •H 
 
 03 
 
 ® 
 
 PQ 
 
 OQ 
 
 pi 
 
 O 
 
 pi 
 
 Pi 
 
 •H 
 
 +3 
 
 Pi 
 
 O 
 
 o 
 
 O 
 
 PJ 
 
 o3 
 
 ft 
 
 03 
 
 fCJ 
 
 ■P 
 
 etJ 
 
 03 
 
 p» 
 
 Pi 
 
 © 
 
 S 
 
 p 
 
 to 
 
 •H 
 
 ft 
 
 i 
 
 i 
 
28 
 
 Ms Me --(10) 
 
 Equations (8), (9) ^.nd (10) may "be applied to the case of a 
 iiniformiy distributed load W on each span by replacing the quantity 
 ^ * These equations should not be used for values of m 
 
 smaller than thos e shown in Pig. 11. 
 
 The diagram shows clearly that with very large brackets, 
 corresponding to small values of ra, the bracket carries nearly all 
 of the load directly to the support, acting as a very stiff canti- 
 lever. The positive moment at midspan accordingly becomes very 
 small . 
 
I 
 
29 
 
 III. TEST SPECIMENS AND APPARATUS 
 6. Description of Test Specimens ,- Test specimens of 
 five types v/ere used; two specimens each of Types A, B, C, and 
 D, and one of Type E, All were two-legged frames with the 
 colnmns hinged at the bases. The details of these specimens 
 are indicated in Pig. 12 to 20. The cross-sections of types 
 A, B, C, and D were of T- shape, having the following nominal 
 dimensions; depth, 12 in.; thickness of flange, 3 in.; v/idth 
 of web, 8 in; width of flange, 30 in. The flanges were intended 
 to produce the effect of the shell of a ship adjacent to the 
 frame. The cross-section of type E was rectangular, being 
 nominally 12 in. deep and 8 in. wide. This type furnished a 
 comparison with type A to show the effect of the difference in 
 section. 
 
 All of the test specimens were made 15 ft. long and 7 ft. high, 
 overall. The span from center to center of hinges was 14 ft. 
 and the height from center of hinges to mid-depth of girder was 
 6 ft. Actual dimensions differed slightly from these nominal fig- 
 ures. 
 
 Specimens of Types A and E were made with square corners at 
 the intersection of horizontal and vertical members with the 
 exception of a 2-in. fillet at the interior corners. These 
 fillets were used to modify the extremely high stresses which 
 occur at a sharp corner, but were not regarded as capable of 
 exerting any appreciable effect as brackets. 
 
 Types B, C and D were made v;ith brackets similar to those 
 actually used in concrete ship construction. Type B had 45° 
 
 

 1 .1' n ■ I G 
 
 . •• 1 > 
 
 
 r 
 
 I 
 
 ■■^r- ■ i.’vvi’r 
 
 : ' . ' ' •,«-•■ .k 
 
 
30 
 
 r 
 
 ! 
 
 1 *? 
 
 ;--a 
 
 lU 
 
 0 
 
 
 
 <D i 1^ 
 
 7' 
 
 , \ 
 
 1 1 
 
 1 1 
 
 F=i r-i! 1 ^ 
 
 7 -K 
 
 3 
 
 I / 
 
 
 Fig, 12. Details of Test Specimen 13A1 
 
^ou'i'h Z^'cufh 
 
 31 
 
 V d 
 
 i ? 
 
 <o 
 
 4 
 
 
 
 c .4* J 
 
 'i 
 
 rr. 
 
 A 
 
 •' / 
 
 V 
 
 •m. 
 
 ' .- t'Z 
 „ rv c?r 
 
 J, 
 
 Fig. 13. Details of Test Specimen 13A2 
 

 Fig. 14. Details of Test Specimen 13B1 
 
U TJ 
 
S>ouih 5outh 
 
 36 
 
 Fig. 18, Details of Test Specimen 13D1 
 
5oui'h S>ouih A/orth 
 
 37 
 
 Pig, 19. Details of Test Specimen 13D2 
 
S>oufh 5c>t//A Horj-r< 
 
 38 
 
 
 
 Fig. 20. Details of Test Specimen 13E1 
 
59 5' 
 
 ■brackets, 12 in* in horizontal length; the exterior corners 
 were given a 45® chamfer eQ.Tial in size to the bracket, making 
 the depth of cross-section noimal to the face of the bracket 
 about 17 in. Type C was similar to Type B, but had a bracket 
 24 in. in horizontal length, making the depth of cross-section 
 at the corner approximately 25 in. Type I) was modified from 
 T3rpe C by filling in the angles bet;veen the bracket and the 
 main members i^lth two supplementary haunches, so that the inside 
 line of the frame approached the outline of a curved soffit. 
 
 The hinge detail at the bs^e of each column ?;as provided by 
 casting in place a steel shoe formed by 5/4 in. bearing plates 
 with a 5 in. pin-hole at each side of the column connected by 
 a 5 in. pipe sleeve 28 1/2 in. long. A 2 15/16 in. steel pin 
 passing through the pinlioles and pipe sleeves engaged similar 
 plates on the test base and formed a simple hinge. 
 
 In the design of the rei:of orcement used in the test speci- 
 mens the working stresses assumed were 16 000 lb. per sq.. in 
 for tension in the steel, and 1500 lb. per sq. in. for compression 
 in the concrete. The ratio of the modulus of elasticity cf steel 
 to that of concrete was taken as 8. The design provided for a 
 reversal of the direction of loading, so that all sections con- 
 tained a large percentage of compression as well as tension steel. 
 Details of the reinforcement used in the specimens are shown in 
 Pig. 12 to 20. 
 
 In designing the members the approximate bending and resist- 
 ing moments were calculated and the section at which failure by 
 
40 
 
 compression would probalDly occur was determined, From the 
 resisting moment in compression at this point the \Yorking load 
 for the specimen was calculated and sufficient tension reinfoice- 
 ment was provided at all points to withstand the external 
 bending moment . a The specimens were heavily reinforced with 
 bent bars and stirrups against diagonal tension failure. 
 
 Table 1 shows the percentage of longitudinal steel used in all 
 specimens, based 6n the area of oross-section exclusive of 
 flanges. 
 
 TABLE 1. 
 
 PERCENTAGE OF LONGITUDINAL RE ECFORCEIvIEl^T 
 
 Location 
 
 Stress 
 
 
 Spe c imen 
 
 Numbers* 
 
 
 of 
 
 in 
 
 13A1-: 
 
 2 13)B1-E 
 
 13C1-2 
 
 13D1-2 
 
 Section Reinforcement 
 
 13E1- 
 
 
 
 
 
 (Dovnward Loads) 
 
 
 
 
 
 Center of 
 
 ^(Tension 
 
 4.67 
 
 4.67 
 
 4.67 
 
 4.67 
 
 Girder 
 
 (Compression 
 
 5.61 
 
 7.48 
 
 3.74 
 
 3.74 
 
 Corner of 
 
 _ (Tension 
 
 4. 67 
 
 3.79 
 
 2.05 
 
 2.05 
 
 Frame** 
 
 (Compression 
 
 5.61 
 
 4.41 
 
 2.46 
 
 2.46 
 
 The main reinforcing bars were all 1 in. plain round bars, 
 and the stirrups ?;ere either 1/2 or 5/8 in. plain round bars. 
 
 The tee flanges were reinforced with cross rods to distribute 
 the stresses and to prevent transverse curvature of the flanges. 
 
 * This investigation was performed as Test Series 13; 
 hence the series number is used as a part of all specimen 
 numbers. 
 
 **Vertical section for Types A and E; section normal to 
 face of bracket in Types B, C and D. 
 
41 
 
 7. Materials and Making of Specimens . ~ Cemen t . - 
 Lehigh Portland cement was used in the making of all the test 
 specimens. It passed the requirements of the United States 
 Government Specifications for Portland Cement.* 
 
 Aggregate." The sand and gravel were obtained from local 
 deposits at South Bethlehem, Pennsylvania. The material was 
 siliceous, clean and gritty. It was carefully separated by 
 screening into three sizes; (l) fine sand consisting of grains 
 smaller than l/8 in. in diameter, (£) coarse sand falling 
 between l/8 in. andl/4 in. in diameter, and (3) gravel exceed- 
 ing l/4 in. but less than l/2 in. in diameter. The separation 
 of the sand into fine and coarse grades was clone for the pur- 
 pose of controlling the imifomity of the concrete made from it. 
 
 Steel. - The reinforcing bars were re-rolled from rejected 
 shrapnel steel billets of hi^ yield point. The physical 
 properties of this steel are shown in Table 2. Each value 
 in the table is the average of two tests. 
 
 TABLE 2. 
 
 PHYSICAL PROPERTIES OP STEEL BilRS 
 
 Liam. 
 
 in. 
 
 Yield Point 
 lb. per sq. in. 
 
 Ultimate Tensile 
 Strength 
 lb. per sq. in. 
 
 Elongation 
 in 8 in. 
 per cent 
 
 Reduction 
 in area 
 per cent 
 
 1/2 
 
 63 800 
 
 104 400 
 
 16.6 
 
 27.5 
 
 5/8 
 
 66 070 
 
 108 440 
 
 18.0 
 
 42.2 
 
 1 
 
 55 800 
 
 91 425 
 
 20.5 
 
 38.2 
 
 * Circular of the Bureau of Standards, Ho. 33. 
 
M .uru P U.7 
 
 . i 
 
 • ' O*' ■ 
 
 -f - ■. ^ 
 
 II? ,v; 
 
 0 j 
 
 Ofi 
 
 K^-f_ '1: 
 
 t’-j 
 
 . - . / r 
 
 . ■ .. j- 
 
 f 
 
 
 rui'tf-rrfQ 
 
 ‘I ^0-: .• 
 
 
 I' 
 
 rv 
 
 V 
 
 « . 1 
 
 <1 
 
 a 
 
 ■ \ 
 
 ■ iit:i 
 
 
42 
 
 Concrete . - The concrete used in this investigation was 
 mixed a]c:proximate 3y in the proportions 1:1:1. The actual 
 proportions hy volume were as follows: cement, 1 part; fine 
 sand* part; coarse sand, .20 part; gravel .99 part. In 
 preparation for mixing the concrete, each kind of aggregate 
 was thoroughly mixed by shoveling and determinations of the 
 moisture content were made upon samples taken at random* Enough 
 water was added when mixing the concrete to make the total water 
 13 per cent of the ccmbined weight of the dry materials, thus 
 producing a rather stiff mixture, considerably drier than is 
 generally used in reinforced concrete construction work. 
 
 Auxiliary Specimens .- Six 6 x 12 in. cylinders were made 
 with each test specimen and were stored under the same conditions 
 until tested. Three cylinders in each lot were tested when 7 days 
 old and the remaining three were tested when 40 days old, the 
 latter being the approximate age of the frames when tested. 
 
 The average compressive strength of the concrete is given in 
 Table 3. The initial modulus of elasticity of the concrete was 
 3/750 000 lb. per sq. in.; this value was found from a large 
 number of compression tests of concrete cylinders having identi- 
 cal proportions and materials, but made in connection with other 
 investigations at the laboratory. The stress-strain curves for 
 these cylinder tests were aloser to straight lines than is 
 usually expected with concrete. 
 
! 
 
 •% 
 
 1 
 
 
 ti 
 
 'T I 'h p -1. ‘},i ■ -.'J >0?: - . ^ •■ Toad^ *’-. ' y'.f' 
 
 s. '. ••;>• i. )mr. 
 
 . ■ < 
 
 ;:X'k7v'H=; 
 
 rf _ 
 
 »r . »->< 
 
 . MtiJ-V’ ,*• rt 
 
 C : '.J 
 
 0 'j:' o/’.. 
 
 
 •Ik 
 
 ^ ^ * ma 
 
 > &i| ) V. w. 
 
 
 ) ■ ■> «A 4 
 
 i . f 
 
 
 -' '>n 'r** 
 
 R - . . .t' 
 
 I t 
 
 
 ■ Lot:-..! 
 
 “n r* < 'T bv i .'♦TqiED 
 
 ircofT £':i‘7:rj:X 
 
 r* r 
 
 i. ■ 
 
 
 ■ ■ . J 
 
 
 
 ni'jeif 
 
 
 ' 
 
 ^S; . 
 
 bvXl- 
 
 ^ 6i\v} 
 
 Vl^' ■ J, 
 
 f: 0^'raJi!;'^ >os7t 
 
 V fi" . . 
 
 ' K4»/JT.* . 
 
 .,C 
 
 ■ t:: Oi 
 
 W*‘ :. 
 
 •• ' 
 
 ' K il:':- 
 
 ■ /I? 
 
 ft. 7 , .] Z.\z X . ■ ■- 
 
 , 
 
 V ‘ IJm. 
 
 
 ’*■ ** r»»ir^ 1 
 
 >.- Ir'. 
 
 'uurf li) >■■ 
 f 
 
 
 .“ -•3' Xc- w 
 
 I ; 1 ‘ , 
 
 • ' 
 
 JMa/. 
 
 ?r 
 
 
 
 /' ■' •. ■ j 
 
 ••:•.■ yp g*-: C 
 .:: *;»Ic 
 
 • , I r> 
 
 01? 
 
 J \ 
 
 
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 . c 7? 
 
 > ’ -r vcfffur;! 
 
 
 73 'fe - 
 rofroT$ X?o 
 
 c 
 
 ■ ; i: *■':;’ ■: 
 
 n;'.r j 
 
 'f •-.' ') ■' 
 
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 j:- 
 
 
45 
 
 TABLE 3. 
 
 COILPHESSIVE STRELGITH OF CONCRETE. 
 
 Each value represents the average of three 
 tests on 6 X IE in. cylinders. 
 
 Made with 
 Specimen 
 No. 
 
 Unit Strength 
 at age of 7 days 
 lb. per sq. in. 
 
 Unit Strength 
 at age of 40 days 
 lb. per sq. in 
 
 13A1 
 
 SEEO 
 
 3110 
 
 13AE 
 
 S975 
 
 3765 
 
 13B1 
 
 S880 
 
 4S60 
 
 13BE 
 
 E535 
 
 3665 
 
 13C1 
 
 S775 
 
 4505 
 
 13CE 
 
 E900 
 
 4040 
 
 131)1 
 
 E870 
 
 44E0 
 
 13 BE 
 
 3075 
 
 5860 
 
 13E1 
 
 S815 
 
 4995 
 
 Average 
 
 S785 
 
 4E90 
 
 Making of Specimens .- One wooden form was used for all 
 test specimens, and the inside corners of the form were designed 
 
 to provide for' the variation in shape of the brackets. The 
 inner surfaces of thie forms were well oiled. In order to insure 
 plumbing of the specimen and proper alignment of the hinges in 
 the columns of the test specimens, tlie form was erected in the 
 place arranged for making the load test, with the steel shoes 
 and hinge pins in position. The reinforcing bars were bent as 
 required in an Olsen cold-bend testing machine, and were wired 
 
• O' 
 
 i 
 
 
 
 :..rc .-6Xoo I’V :S.O ff 'i •; L • '•,•■ 
 
 
 
 
44 
 
 in place after "being set in the form. Concrete \ms dumped from 
 the mixer into a tight wooden "box, carried to the form "by a 
 traveling crane, and shoveled into the form* A considera"ble 
 amount of tamping and rapping was req_uired to get the concrete 
 into place, especially at the corners of the frame* The forms 
 were stripped when the concrete was about 24 hours old and the 
 specimen was lifted off of the test "base and transferred 
 to another place in the la"boratory. Wet burlap was kept around 
 the ^ ecimens up to the time of testing* 
 
 8* Testing Apparatus *- A heavy concrete test base was 
 made especially for this investigation* A general view of the 
 base with a specimen in position for testing is shorn in Fig* 21. 
 It ¥/as 22 ft* long, 5 1/2 ft* high and 2 l/2 ft. wide, and was 
 reinforced to withstand a reversal both of vertical loads and 
 horizontal thrusts. A vertical steel link at the end of the 
 base allowed for a practically frictionless horizontal move- 
 ment at the bottom of one leg of the specimen under test* A 
 60-ton hydraulic jack acting against this link was arranged to 
 produce a horizontal reaction through the axis of the hinge 
 and either to maintain a fixed distance between the two hinges 
 or to move the hinge in or out any desired amount* Such move- 
 ment was measured by means of a micrometer bar which had a range 
 of several inches* 
 
 Downward loads were applied on the top of all specimens at 
 two points 2 ft* 4 in. on each side of midspan. The distance 
 between them was one- third of the nominal span from center to 
 center of hinges* The diagram of Fig* 22 shows the arrangement 
 
>■ - 
 
 I 
 
 s' 
 
 
 
 
 
 * 
 
 ^ • 
 
 ’ ■ 'rr ■, ) 
 
 • 
 
 i|W « ,. . 
 
 ';, ■;> j,‘ n V 
 
 
 
 
 ■ ■ • ■ ; 
 
 •• n l.> / 
 
 (■ 
 
 
 ■'• 
 
 ;s , 
 
 i* .. 
 
 tf .1- ^ 
 
 ■ . ~ , '"CXx, 'Qa-t' ' 
 
 jA 
 
 -.-■I 
 
 
 
 r^.'rU'TtvO.’ 'f ;Tt'rft7' A* ^ • ’ x !?\ b'*“ : f 
 
 r‘ 
 
 
 fC‘ 
 
 s' 
 
 f.r 1 
 
 Tzr^ ;> ' ’ Rttw 
 
 ,*■ 
 
 •• 
 
 k 
 
 • ■' “C 
 
 J 
 
 ->.i: nJt .•• - Jv] ^ 
 
 '-r,. 
 
 
 
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 ‘ p ♦ : aa<>rri QSi ■ a* / '■ 
 
 • r. J 
 
 i?‘ 
 
 
 
 
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 V, ' ■ •’? 
 
 "V* 
 
 
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 . : ■ ' fciir. ■ ■ ii »( / Ct,' 8M. rf 
 
 n.v. gr/ . '■ ) 
 
 . 1 -. 
 
 1 ■ ' . ■ 
 
 O 
 
 i 
 
 j' . 
 
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 r ■ a 
 
 .1. .r. 
 
 ' fC ! ■ 
 
 • 'Xi . ‘ 
 
 ■- 'U 
 
 • ... J.^.rvv 
 
 .1 0- i. 
 
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 ; _jo' ’(TO :■ ■ .•.?.^^ocr' ' ’ j”#** 
 
 Vw -\r t;o’/ , ■. 't' — 
 
 ■ ■ X>jr;' .■.•:<'.[,?? Mai;' “■ 
 
 I ' j III /j r i.'L.' o^ i'l' rfi’ L9 .].•■ 
 
 ' -V ; 
 
 J,--, xo i:!i^ /air rj- *xo 
 
 ■ ' ' '^: .f • •' . 
 
 ■y > 
 
 
 K>.>. \y.tjn. '.; d \r.\j qc,', ^ 'n:; .tj \.r i t-u >r.. 
 
 . ' Vj.ij: Xj? ,!Ci 
 
 'Vc. ',• 
 
 . Ti , - . '."t- . f 
 
 ariVV •! vQ-,. -/>f 
 
 \. . -'"'Ac:! V 
 
 V. • ■ •'■ ■ :<’ i uX 
 
 i. 
 
 
 
 ar 
 
45 
 
 71 
 
 Fig. 21, General View of Test Apparatus. 
 
N 
 
47 
 
 for applying loads and reactions. The vertical loads were pro- 
 duced hy two 100-ton hydraulic ;)acks acting downward on a 
 steel "box girder which transmitted the pressure through a heavy 
 knife-edge casting and a roller to the specimen. Steel plates 
 ' embedded in plaster of paris were used to distribute the bearing 
 pressure over the concrete. The upward reaction of the jacks 
 was exerted against built up steel sections connected by six 
 tie rods to other steel sections beneath the test base. 
 
 Two strain gages were used in the tests, one of 4-in, gage 
 length being used for measuring deformations of concrete and one 
 of 8-in. gage length for measuring deformations in the steel 
 reinforcement, A continuous row of gage lines was located on 
 the reinforcement along the length of the outer face of the 
 specimen and a similar row was laid off along the inner face. 
 Deformations of the cnncrete were also measured on several 
 gage lines along the sides of the brackets. 
 
 Deflections were measured at points one foot apart on 
 both the horizontal member and the two columns, A black linen 
 thread was stretched at constant tension between points at the 
 two ends, at mid-depth of the girder. Similar threads were hung 
 as j3umb lines along the sides of the columns. Movement of the 
 ^ecimen with reference to the thread was observed by means of 
 paper scales pasted to small mirrors and attached to the speci- 
 men, Readings which were taken by lining up one edge of the 
 thread with its reflection in the mirror could be duplicated 
 
 within .01 inch 
 
I - 
 
 
 
 r ;} i ' 0 .' 
 
 
 
 ■ ^.oi* S Q . , 
 
 - j I J . . 
 
 * . i. -.t- 'J' 
 
 ‘ , * -I ‘i 
 
 ^ xr - ■-) ,:. r - ■ 
 
 -W ♦- V ' r ;.-:^ 
 
 
 bj| 
 
 ’^ '? r ■ 
 
 
 
 .>!' ^ I ■ 
 
 r 
 
 r 
 
 ' f'O 
 
 ■: ■' V ": ■ .'* r : r ^* 
 
 , >» 
 
 i-'X '**' ! -JM.-F 
 
 T 3 i . 
 
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 ■• riJ 
 
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 ■ ■ '■> 
 
 r oS ; 
 
 < 
 
 
 
 r •. • 
 
 
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 T' *■ ■ 
 
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 X‘;‘ 
 
 
 •x^n:- f'i 
 
 ,'.r, ,.'( 
 
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 r.00 ' riJT u'i 
 
 ; F * r 
 
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 vt^v. 
 
 % 
 
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 .1 ■- . . 
 
 t *L 
 
 i 
 
 vH..' •. r^t 
 
 r 
 
 •I .. • 
 
 .' ' 'i;'.' /I*- 
 
 W.-ffT "ij' 
 
 -•( - « »\ 
 
 a.t, 
 
 
 
 
 V Jfta >"■ 'i 
 
 
 i 
 
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 'i i 
 
 , ‘ : 
 
 nui'HissaM 
 
 w" is, 
 
 ■'''■ '•'<» ■ . . •> u't 
 
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 ^ ,no_ ' 
 
 ; : •;>: i 
 
 I 
 
 5 c. i;..O.r_. 
 
 } 
 
 fiJ f/' ;;.■•• 'iert:t.i.0.i 
 
 •■ ■ ■ 
 
 
 ' ■.•47 
 
 
 
 
 ^ii 
 
 .. : . '. Jjr . j * •; / ., •» i 
 
48 
 
 IV. TEST DATA AJJJD DISCUSSIOII OF RESULTS. 
 
 9. Procedure and Phenomena of Tests .- In general, 
 downward loads were applied to the test specimens in increments 
 of 30 000 lb., with the hinges at the bases of the coltimns held 
 in a stationary position. Zero readings were taken with no 
 dovmward load except that of the loading rig which weighed about 
 3 000 lb*, and with just enough horizontal pressure appliedat 
 the hinges to tighten up all movable parts of the hinge appara- 
 tus. 
 
 The effect of a reversal of stress was obtained in the 
 testing of each specimen in the following mfinner. After readings 
 of deformation and deflection had been taken under a load of 
 90 000 lb. all downward load was released. The movable hinged 
 end of the specimen was then pushed inward an amount sufficient 
 to produce maximum deformation readings at critical sections as 
 great as those observed under the 90 000 lb. load. Following 
 readings under this condition of loading and still without apply- 
 ing any vertical loads, the horizontal jack was swung around to 
 act on the inside of the hinge and the movable end of the column 
 was thrust outward until stresses were again produced ?vhich were 
 comparable to those observed under the 90 000 lb. load. The 
 change in distance between hinges was measured in both cases. 
 
 With the horizontal jack swimg back to the outside of the frame 
 and the distance between hinges brought back to its original 
 amount, vertical loading was resumed on the top of the frame. Com- 
 plete readings of deformation and deflection were taken at a load 
 of 120 000 lb., and at increments of 30 000 lb. up to the maximum 
 load. Final readings were t iken in each case after the maximum 
 

 
 ;-T:'j. I -'t C 
 
 
 'I'i 
 
 ' m 
 
 V 
 
 •j^l: 
 
 i 
 
 " ■ ' ••- .r^ii;..,: 
 
 1 
 
 '-' r .i,‘’V:.x Q.'re.’i > . 
 
 3 ^ " " ‘'' • '' '■ ■• >.v tsi . '.» '• ; fttAlltrr, ■ ,. 
 
 • ’’ ■ ‘ -■ '"•■ • 7’ ; ..-v 
 
 •% I . 
 
 .v>>;^ . m; r.\r~-/j 0^.^ ' ' o; I . ^ it|:j ...;! 
 
 ■ ^ V 
 
 A C : ^ ■ T 
 
 < 1 '</ : 
 
 ‘. '»-■ ■' } 
 
 . i' 
 
 .■^,tn\ ‘V" 
 
 
 r • 
 
 t r • » -J •» 
 
 
 .• ''r ^ s'* ;Syym 
 
 ,fi %. ;^,- ;-r ;< ’ 
 
 IV. f»| , I '-1^ lV o ,vX*''-<?*f V • ^ V 
 
 •; - : : 7 vr.( n . r r>-i '••r/rVo,o J.fja ogo C'A 
 
 .? fc/u'*-' MM-i 1 ^tfS .*' , .i'-'-.fCj 0<#gPilJ 
 K-.,ir ..- 1- A9if.">'V4 ■«* 
 
 • •. • .ic-v-4t-;»r:o ' :f fir*'- 
 
 ' ^ ■*'..'■* '-)' 
 
 *■• . '■' ’ 7..:r-5 T^- 
 
 . -,'f' 
 
 ^ V >C 3i; ■ •; ;> 
 
 n : 
 
 Cl 
 
 'i' ' - .■' , .1 '.- . t ,'. r 7'- S'L: , hT3\ ' 
 
 • VC ^ ^ 
 
 0. 
 
 -)r. 
 
 Xr-, 
 
 •-' • ' ' ■• ■'‘’ ' V”! •>:.; er'.* ; 
 
 ■ '■' '' •■'•V ’ ' :i" 'I. i,; 
 
 ■' ' ' '’ ‘M 
 
 r:./ L: r u . .' ; -v if.-.i C .$7-^ #- / /f:.hv 
 
 •■ ■*■ '•'■ •^' ^ j '.'tli.'i '? ' '>‘.t • f ’ 
 
 ‘ i v< • ■'. -i "f 5 c H X»zoS ■ ”'. , ' 
 
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 0.^ n . ^ ov . C-: 1-1 i, . '■ t:i \ - 
 
 V 
 
 J 
 
49 
 
 load was applied, in order to obtain information on the manner 
 of failure. Fig. 23 to 27 show views of the different speci- 
 mens after failure had taken place. The following paragraphs 
 -give a sliort description of the principal phenomena of the tests. 
 
 Specimen 13A1 »- Loads were applied as indicated in the 
 tabulated data of Section 16. Numerous cracks were observed 
 under the 60 000 and 90 000 lb. loads. After application of 
 end thrusts inward and outward with top load released, the 
 movable hinge did not return entirely to its original position, 
 but was pushed back into place mth little effort. Failure 
 occurred at a maximum load of 120 000 lb., with noticeable 
 crushing and spalling at the north inside comer. This spalling 
 was apparently due largely to slipping of bars at inside face of 
 column near corner. There was also apparent slipping of tension 
 bars near midspan. Tension cracks were numerous in middle 
 portion of frame, also across the tee-flanges on both vertical 
 and horizontal members near both corners. 
 
 Specimen 13A2 . - A number of tension cracks appeared near 
 midspan at the 30 000 lb. load. Cracks also appeared across the 
 tee-flanges about 15 inches frcm each corner on both horizontal 
 and vertical members. At loads of 60 000 lb. and 90 000 several 
 more cracks opened in same regions. V/ith inv/ard thrusts several 
 new cracks opened in the top face within the middle half of the 
 girder. With outward thrusts tension cracks were opened at the 
 inside corners of the frame. Failiii'e occurred through crushing 
 at the north inside corner and by tension in the steel at the 
 outside of the same corner. While the tension failure may have 
 
50 
 
 Fig. 23. Views of Specimens 13A1 and 13A2 after Test 
 

 
 ■I , 
 
 '*f,:i!l '■ ^ ^'•, ■ ■; 
 
 * ■ '* >5r i* ! 
 
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 • -■. , ' * •,* > 
 
 m 
 
 Utk 
 
 6i^ ' ^ 
 
 
 
 5s 
 
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 «• 
 
 WM 
 
 ...its*. ■■.. 
 
 
 
 Wi 
 
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 ..'r 
 
 I 
 
 X . . . .’. 
 
 
 
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 n6 u *r<‘’ , ■■ 
 
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 :v '%A 
 
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 b^' 
 
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 M 4 ,' 
 
53 
 
Pig. 27 
 
 Views of Specimens 1302, 13D2, and 13B1 after Test 
 

 ■.-<1 
 
 
 W" "' ■ ■'^‘' ^FyjM'^rS:^ 
 
 ;.-'s 4,, ■ w,.ii-w 
 
 l.!i> ''/t, 
 
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 w 
 
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 f ^ i.<^i , ■ . .-i ,ii ■'* » '■*--'*^ '' « 
 
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 ^ ® tM| 
 
 K'.| 
 
 V'Si 
 
 . '3> 
 
 •'^' -r'?^ 
 
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 r .-, ',i .„ ,- 
 
 
55 
 
 occured first, the yield point was exceeded in the compression 
 reinforcement at the comer, and also in the tension reinforce- 
 ment under the load points. There were pronoimced radial cracks 
 aronnd both corners of the frame. Maximian load, 119 000 Ih. 
 
 Spe cimen 12B1 .- failure began with crushing of the concrete 
 at the north inside corner at intersection of bracket and 
 girder. After this comer had yielded somewhat a large nxunber 
 of diagonal cracks appeared between the bracket and load point. 
 Cracks were not large at other parts of the frame. Horizontal 
 cracks in the tee-flange in the north end of girder indicated 
 that flange was shearing loose from the web, at failure. Large 
 tension cracks were observed on the top face of girder at the 
 north end. Some crushing occurred at the top of the south 
 bracket and at the bottom of the north bracket. Maximum load, 
 
 15£ 000 lb. 
 
 Specimen 15B2 .- At 30 000 lb. load there were a few 
 straight tension cracks on the lov/er side of girder. With a 
 load of 60 000 lb. a number of cracks opened up on the outside 
 faces of the legs and on the top face of the girder near the ends, 
 With inward thrusts, a few additional cracks appeared in the 
 top face of the girder, one being between the load points. With 
 outward thrusts, a few cracks opened at the junctions of girder 
 and brackets. At a load of 120 000 lb, piunounced diagonal 
 tension cracks developed in the web of the girder, running out- 
 ward from the load points at an angle of about 45 degrees. The 
 maximum load was reached at 138 000 lb. Failure came when the 
 yield point of the steel was reached in the outside face of the 
 south leg a.nd at midspan. At about the same time crushing 
 

 
 
 
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56 
 
 occurred at the jimction of the north leg and "bracket, and the 
 concrete spalled off considera"bly. There was a slight indication 
 of crushing at the south end, near the junction of leg and brack- 
 et* 
 
 Specimen 1501 * - Several cracks opened near midspan at a 
 load of 30 000 lb. At 60 000 lb. load cracks opened at about 
 midheight of the outside faces of both legs. With inv/ard thrusts 
 cracks opened in the outside faced and one or to'O at each end on 
 the top of girder. With outward thrusts cracks opened in upper 
 part of bracket and ran do^'n at about 45 degrees with the 
 horisontal, parallel to the face of the bracket. Cracks of this 
 type were produced in all frames with this kind of loading, and 
 were at right angles to those produced by inward thrusts. At 
 loads of 120 000 and 150 000 lbs. cracks began to run through 
 from the outer faces of the legs do\mward diagonally across the 
 webs tov/ard the inside faces of legs at junction of bracket and 
 leg. At the maximum lo d of 182 000 lb. crushing occurred at the 
 bottom of the north bracket. Large cracks opened in the outside 
 face opposite the crushed area and the yield point of the tension 
 steel was passed here and at midspan. 
 
 Sp ecimen 13G2 . - A few cracks were observed near midspan 
 at a load of 30 000 lb., and others opened up across the outer 
 face of both legs at the loads of 60 000 and 90 000 lb. Several 
 cracks opened in upper face of girder when inward thrusts were 
 applied alone, and with outward tlirusts the cracks were similar 
 to those found in Specimen 13C1, At a load of 120 000 lb, large 
 cracks opened in outside faces of legs. This specimen was 
 
57 
 
 weakened by the accidental omission of two of the four longitudi- 
 nal reinforcing bars in the outer face of each leg* Due to this, 
 failure occurred in the outside face of the south leg, opposite 
 the bottom of bracket where crushing fc^ilure rapidly followed. 
 
 The maximum load was 148 000 lb. 
 
 Specimen IgPl . - A few cr-^cks were observed near midspan at 
 the load of 30 000 lb*, and others opened up across the outer 
 faces of both legs at loads of 60 000 and 90 000 lb. Several 
 crocks opened in the upper f .~ce of the girder i7hen inward thrusts 
 were applied, and outside of the south load point. At later 
 loads this crack gave the impression of impending diagonal ten- 
 sion failure, however , failure did not occur in this part of the 
 frame. At a load of 180 000 lb, large cracks appeared at both 
 ends at the top of the veritcal faces of the legs. The maximum 
 load was 208 500. Failure occurred simultaneously when the 
 yield point of the reinforcement was re^^^ched in compression on 
 the inside face and tension on the outvSide face of the south leg 
 at about mid-height. The concrete crushed over a considerable 
 area in the locality of the failure. 
 
 Specimen 13 D2 , - A few cracks were observed on the outer faces 
 of the legs, near the corners, and near midspan at the 60 000 lb. 
 load. With inward thrusts several cracks opened on the top face. 
 With outward thrusts cracks on the tension side of the 
 girder were opened. Large cracks appeared under the 180 000 lb. 
 load across the face of the north leg, and failure occurred by 
 tension in the reinforcement of the north leg about three feet 
 from the top and crushing on the inside of the leg below the 
 
r. 
 
 «, - 
 
 j 
 
 
 
 •v/:-' 
 
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58 
 
 jiinction of bracket and lower haimch* A ntunber of diagonal cracks 
 ran between the sections of tension and crushing failure. 
 
 Specimen 15E1 .- In this specimen erf rectangular cross- 
 section the reinforcement was crowded together closely, and was 
 probably not as nearly in its designed position as in the other 
 specimens* At a load of 30 000 lb. there were a large number of 
 cracks near midspan, around the corners of the frame, and across 
 the outside faces of the legs. At 60 000 lb* load, several 
 diagonal cracks had opened betv;een the south load point and the 
 end of girder. At a load of 77 000 lb. the top of the specimen 
 began to crush just inside the south load point. The crushing 
 extended from the edge of the bearing plate for a distance of 
 several inches. With continued loading, the load dropped off 
 somewhat. Large tension cracks formed under the south load 
 point and at the south corner. It was noticeable that a large 
 number of tension cracks developed around the corners of the 
 frame, radiating tov/ard the inside corner as a center. These 
 cracks extended to ?/ithin 3 to 3 1/2 inches of the inside or 
 compression face. 
 
 Values of the ultimate loads and other data of the tests 
 are given in Table 4. 
 

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59 
 
 TABLE 4. 
 
 DATA OP TESTS. 
 
 Specimen 
 
 Ho. 
 
 Age 
 
 Days 
 
 Ultimate Loa 
 poimds 
 
 .d, 
 
 Manner of Failure 
 
 15A1 
 
 43 
 
 120 
 
 000 
 
 (Bond at outside of north corner 
 (followed hy crushing at inside of 
 (corner. Tension at middle between 
 (load-points. 
 
 13AE 
 
 39 
 
 119 
 
 000 
 
 (Compression at inside of north corner. 
 (Tension at outside of corner and at 
 (middle between load points. 
 
 Av. 
 
 41 
 
 119 
 
 500 
 
 
 13B1 
 
 42 
 
 152 
 
 000 
 
 (Compression at top of north bracket. 
 (Some shearing between tee-flange and 
 (web at north corner. 
 
 13B2 
 
 40 
 
 138 
 
 000 
 
 (Tension at middle of top member and at 
 (outside of north comer on leg; fol- 
 
 Av. 
 
 41 
 
 145 
 
 000 
 
 (lowed by crushing at bottom of north 
 (bracket. Shearing between tee and web 
 (at corner. 
 
 1301 
 
 39 
 
 182 
 
 000 
 
 (Compression at bottom of north bracket 
 (Tension at outside of hoc th bracket 
 (and in top member between load points. 
 
 1302 
 
 41 
 
 148 
 
 000 
 
 (Tension at south end in outside face 
 (at bottom of bracket, followed by 
 (crushing on inside at bottom of 
 
 Av. 
 
 40 
 
 165 
 
 000 
 
 (bracket. This specimen was weakened 
 (by the accidental omission of 2-1" 
 (round rods in outside face of each 
 (column where failure occurred. 
 
 13D1 
 
 40 
 
 208 
 
 500 
 
 (Compression at south end at middle 
 (of lower haunches and tension in 
 (outside face of column at bottom of 
 (bracket. 
 
 13D2 
 
 41 
 
 232 
 
 000 
 
 (Compression at north end at bottom of 
 (lower haunch, tension at outside face 
 
 Av. 
 
 41 
 
 220 
 
 250 
 
 (at bottom of bracket, and in top 
 (member between load points. 
 
 13E1 
 
 41 
 
 77 
 
 000 
 
 (Compression just inside of south load 
 (point. 
 

 * T* ■ ••"i**^* *: ' * i'' 
 
 j ‘- ' ’ ‘ ' ^ ••' ',-ro;ij®--’ “:r?xo.X> ”7"' '■ ,• ."■ 
 
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 • 3' " . - ■ ^ .i wO'. .;■ . *?'"' -V . , j. 
 
60 
 
 10* Thrusts and Moments. - The ratio of the end thrusts to 
 the downward load for the tests of frames with hinges held 
 stationary was calculated from the gage readings of the hydraulic 
 jacks. This ratio in general seemed about constant for each 
 specimen until near the maximum load v;hen it decreased consider- 
 ably. This could probably be ascribed to a decrease in the moment 
 of inertia of sections at points of high stress. Obviously at 
 stresses near the ultimate strength less elasticity of action woul( 
 be expected than at lower loads. 
 
 Table 5 presents (a) ratios of horizontal thrust to total 
 vertical load (average for all but ultimate loads), (b) average 
 actual bending moments calculated from measured vertical loads 
 and horizontal thrusts, and (c) bending moments by the analytical 
 method described in Section 3 on the assumptions that the moment 
 of inertia varied throughout all specimens, first as the cube 
 of the depth of section, and second as the 5/2 power of the depth 
 of section. A very fair agreement betv/een calculated and ob- 
 served moments is seen. 
 
 Values of the bending moment at midspan, taken from 
 Table 5 are plotted in Fig. 28 as ordinates against horizontal 
 lengths of bracket as abscissas. Since the frames of Type D 
 had a haunch different in shape from those of the other frames 
 it was found convenient to reduce it to an equivalent length of 
 45 degree bracket. From calculations it was found that the haunch 
 of Type D would produce the same moment at midspan as a 45 degree 
 bracket 32 inches in horizontal length. The points in Fig. 28 
 which represent actual bending moments as determined by test are 
 
;0 9LUJ9J, U/ uods'p/l^ J.U9LUOl^ 
 
 S rv 
 
 
 ;S 
 
 2^ >5^ 
 
 
 53^-^ 
 
 
 
 o 
 
 Nv 
 
 T^ C: 
 
 T'g c: 'fe 
 
 Li 
 
 Fig. 28. Calculated and Observed Moments at Midspan 
 
62 
 
 seen to agree fairly well with the calculated bending moments 
 based on Equation 1. Considering the variable nature of the 
 materials, the difference in details of design and dimensions, 
 and the various possible sources oferror in observations, this 
 might be expected. Eurthermore, it indicates that the analysis 
 of the elastic homogeneous rigid frame may be applied without 
 great error to the structure of reinforced concrete. 
 
 TABLE 5. 
 
 COMPARISON OP OBSERVED AND CALCULATED MOMENTS 
 
 Specimen 
 
 No. 
 
 H 
 
 Average 
 
 of 
 
 Test 
 
 
 
 Ratio 
 
 of Bending 
 
 Moment to 
 
 6 
 
 
 Prom Test 
 
 • Calculated f I=:kd^ i Calculated (L=M^' 
 
 At 
 
 Mid- span corner 
 
 • At At 
 
 : Mi d-€pen Corner 
 
 : At At 
 
 : Mid -span Comer 
 
 • 
 
 13A1 
 
 .168 
 
 .568 
 
 
 .432 
 
 
 
 
 
 15A2 
 
 .202 
 
 .480 
 
 
 .520 
 
 
 
 
 
 Av. 
 
 .185 
 
 .524 
 
 
 .476 
 
 .481 
 
 .519 
 
 .481 
 
 .519 
 
 13B1 
 
 .200 
 
 .486 
 
 
 .426 
 
 
 
 
 
 13B2 
 
 .236 
 
 .392 
 
 
 . 520 
 
 
 
 
 
 Av. 
 
 721F 
 
 .439 
 
 
 .47^' 
 
 .370 
 
 .524 
 
 .379 
 
 .517 
 
 le3Cl 
 
 .241 
 
 
 
 .438 
 
 
 
 
 
 13C2 
 
 .305 
 
 
 
 .602 
 
 
 
 
 
 Av. 
 
 .273 
 
 
 
 .520 
 
 .258 
 
 .536 
 
 .271 
 
 .526 
 
 13D1 
 
 .312 
 
 .198 
 
 
 7FT4“ 
 
 
 
 
 
 13D2 
 
 .352 
 
 .095 
 
 
 .674 
 
 
 
 
 
 Av. 
 
 .332 
 
 .146 
 
 
 .624 
 
 .186 
 
 .590 
 
 .203 
 
 .577 
 
 13E1 
 
 .218 
 
 .440 
 
 
 .560 
 
 .481 
 
 .519 
 
 .481 
 
 .519 
 
 The variation of bending moment throughout the frames may be 
 seen in Pig. 29 v/hich shows graphically the relative magnitude 
 of the actual bending moments and their distribution in the 
 different types of frame, as determined by the tests. This 
 variation is due to two distinct factors, variation in stiffness 
 

63 
 
 /?£rLf^T/V£: 
 
 /// 
 
 D£r£Rn/N£:o by Tf:sr.5 
 
 Pig, 29, Relative Moments in Frames, 
 
i»T 
 
 ¥ j- ■■ ' 
 
 ■* V. *■ . 
 
 K%.-''- «^- . ',■,- ,• .Tk’': 
 
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64 
 
 and variation in the shape of the axis of the frame, as noted 
 in Section 3* It is seen that while the moment at mid-span 
 vafies with the size of the "brackets, the moment at the corner 
 of the frame is about the same in all types of frame. 
 
 11. Flexural Stresses and Deformations .- Ta"bulated strain 
 gage data from the tests of all frames are given in Section 16, 
 which also contains diagrams showing the position of all gage 
 lines for measurement of deformations and deflections, and 
 shows the position with respect to these ga^ge lines of cracks 
 and crushed areas observed at the maximum loads. 
 
 Unit stresses in the steel reinforcing bars as determined 
 from strain gage measurements are sho?m graphically in Fig. 30 
 to 30. lYhile the stresses sh avn represent combined flexural 
 and direct stresses, the latter (which were compression for all 
 cases of downward loading) were comparatively small and did not 
 exceed 7 per cent of the total maximum stress in the extreme case 
 of the frames of Type D. For the other frames the direct stress- 
 es are much less and hence do not have an appreciable influence 
 upon the total stresses measured. 
 
 The calculation of stresses in concrete and steel of these 
 frames is quite laborious, due to the many changes in cross- 
 section, reinforcement, and the variation in the bending moment. 
 
 A sufficient nmber of calculations have been made, hov/ever, to 
 show a fair agreement with the resrkts of the tests. An 
 example of the comparison between calculated and observed stress- 
 es is shown in Table 6, which gives stresses in the tension 
 reinforcement at midspan due to a number of different loads. 
 
 
» ifj' 7r:- ui. .' 4 .. 
 
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66 
 
 ai- 
 
 nner 
 
 .‘^O'hc.5- , 
 
 w'ere m<zas>ur<zd on rizinforoincj bar£> 
 
 Tknsiion p!off<zd mv/ard on Jzff ha/f of fram<z- 
 and oufward on n^hf half of fram(Z^ 
 
 30 20 to O !0 20 30 
 3fr(zsiSr dhous^and lb per odj m 
 
 Specimen No /3A-I 
 
 30 ZO to o 
 fj fre S3 -thous^and 
 
 !0 20 30 
 lb per 3 f 
 
 - IZOOOO 
 
 -- >70000 
 
 - ^oooo 
 
 ■■ 30000 
 
 m 
 
 Fig, 50. Observed Stresses in Specimen 13A1. 
 
 Fig, 31. Observed Stresses in Specimen 13A2 
 

66 
 
 t Noi<z.s> . 
 
 AH 3fr^5>s>e.s> me.a^ur<z.d on nzinforcinc^ 
 
 Thns>':on piofiod mw^rd on left half of fran 
 - — and out yyard on nc^ht half of frames 
 
 vr , Specimen No I3B- 1 a 
 
 30 ZO to O !0 ZO 3>0 
 
 3 frzF^B>-fhous>nnd !t>. per 5-^. m. 
 
 !0 ZO 30 
 
 3lrcs>s>-fhou3>and !b per Sxj. m 
 
 Fig. 32. Olsserved Stresses in Specimen 13B1, 
 
jirf-*''" V®. “ 
 
67 
 
 Fig, 34, Observed Stresses in Specimen 13Cl, 
 
 Fig, 35, Observed Stresses in Specimen 1302 
 
68 
 
 >o 
 
 P= J 50000 
 
 'P- /zoooo 
 
 P‘ 90000 
 &0000 
 30000 
 
 30 ZO !(} O /O ZD 30 
 S>'/'re:5>£>-thous>iOJ7c/ /i> p/zrsx^./r?. 
 
 Specimen No /3D-I 
 
 30 ZO to O 
 5>lrss>3> -ihous>af7c/ 
 
 O ZO 30 
 
 /b. per 5 ^ /n 
 
 Fig, 36, Observed Stresses in Specimen 13D1, 
 
 P- 
 
 Z.'0.'’0C 
 
 
 
 ■ p = 
 
 50000 
 
 P’ 
 
 /zoooo 
 
 -p. 
 
 9rc~-0 
 
 p ^ 
 
 iOOC' 
 
 
 300CC 
 
 J-- j 
 
 O to ZD 30 
 iran^ J lb. Dzr 3 ^ m 
 
 Specimen No /3D-. 
 
 , o O >0 Z 
 lm,Z- -thouo tn J 't, or- 
 
 Pig, 37, Observed Stresses in Specimen 13D2, 
 

69 
 
 Pig, 38, Observed Stresses in Specimen 13E1, 
 
70 
 
 The observed stresses were determined from the average deforma- 
 tions measured on gage lines 22 and 22a of each specimen, while 
 the calculated stresses are based on bending moments computed 
 from the known loads and reactions on the frames, and include 
 the small compressive direct stresses which existed at the sec- 
 tion considered. The calculations ?i^ere made on the conventional 
 "Straight-line theory" of stress distribution and follow the 
 assumption that no tension is carried by the concrete. In most 
 cases the table shoves the calculated stress in the reinforcement 
 to be higher than tho.t found from test, thus indicating that seme 
 part of the tensile stress was carried by the concrete. 
 
 TABLE 6. 
 
 COUPARISOH OF CALCULATED AED OBSERVE!) TENSILE STRESSES 
 
 IN RSniFORCEIvENT. 
 
 Specimen Stress 
 
 Load on Specimen - lb. 
 
 
 No. 
 
 '30 000 60 000 90 000 l20 000 
 
 Maximum 
 
 Load 
 
 13A1 
 
 Calculated 
 
 11 
 
 500 
 
 32 
 
 000 
 
 42 
 
 300 
 
 61 400 
 
 61 400 
 
 
 Observed 
 
 12 
 
 000 
 
 21 
 
 800 
 
 31 
 
 600 
 
 Yield Point 
 
 Yield Point 
 
 13B1 
 
 C. 
 
 10 
 
 000 
 
 22 
 
 000 
 
 34 
 
 500 
 
 55 90b 
 
 60 400 
 
 
 0. 
 
 7 
 
 100 
 
 19 
 
 600 
 
 30 
 
 000 
 
 40 100 
 
 44 500 
 
 13C1 
 
 C. 
 
 7 
 
 100 
 
 13 
 
 000 
 
 23 
 
 600 
 
 45 500 
 
 46 500 
 
 
 0. 
 
 8 
 
 600 
 
 13 
 
 700 
 
 21 
 
 700 
 
 31 000 
 
 Yield Point 
 
 13D1 
 
 c. 
 
 5 
 
 300 
 
 11 
 
 700 
 
 12 
 
 900 
 
 18 500 
 
 50 000 
 
 
 0 
 
 7 
 
 500 
 
 11 
 
 000 
 
 18 
 
 200 
 
 20 200 
 
 58 200* 
 
 13E1 
 
 C. 
 
 8 
 
 600 
 
 32 
 
 400 
 
 
 
 
 42 900 
 
 
 0. 
 
 18 
 
 100 
 
 34 
 
 900 
 
 
 
 
 47 800 
 
 * Yield Point on steel - 55 000 to 60 000 lb. per sq. in. 
 
 As an aid to further comparison between observed and calculated 
 stresses, Fig. 39 shows in a general way the relative magnitude 
 and distribution of the tensile stresses in the steel and the com- 
 pressii© stresses in the concrete for all frames under any given 
 

 If ■ '■ . ' ■ ■-••,■ --r ■ 
 
 |: '■ "\y . : ji-rrnr n 
 
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 f; 
 
 f 
 
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71 
 
 
 A 
 
 7 
 
 A 
 
 
 
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 7yp<z£. 
 
 \ 
 
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 ■/■a in^rp 03 ^ £c io 
 as 7^ £>roken l/n<z5 Jnc//caJ‘<s^ 
 r(^/a//y<z honc/zne^ /Tycm^n:^ 
 
 Fig. 39. Relative Stress Distri^btition in Frames. 
 
7E 
 
 loading. This figure is merely an approximation, hut the shapes 
 of the stress diagrams compare very well with those shown in 
 Fig. 30 to 38. 
 
 When the radius of a curved member is small as compared to 
 the depth of the member, the well-known theory of curved beams* 
 indicates that a linear distribution of stress across the section 
 of the member does not exist, but that the stress on the concave 
 face is greater than it would be in a similar-sized straight 
 member subjected to the same moment. To investigate this feat- 
 ure of analysis, especially for specimens of Type A and E which 
 have only S-inch fillets at the inside corners, strain gage 
 readings were taken on the concrete on the side of the web at 
 one corner of all specimens. Using the measured deformations 
 of the concrete and the deformations in reinforcing bars in 
 the tension and compression faces of the specimens at the corners, 
 the position of the neutral axis for each specimen was determined, 
 as closely as possible and is plotted in Pig. 40. These de- 
 terminations were not exact because of the small number of gage 
 lines, and from the fact that all lines were not located to the 
 best advantage. The deformations used were chosen at loads 
 producing tensile stress in the reinforcement of from 20 000 to 
 30 000 lb. per sq. in. (^Deformations which were observed at the 
 60 000 lb. load exceed the deformations calculated as in a 
 straight beam by 20 per cent on Specimen 13A2 and by 65 per cent 
 for Specimen 13E1. It is evident that this high concentration 
 of fibre stress should be reduced and hence it would seem ad- 
 
 *See,for instance. Strength of Materials, p. 323, by J.E.Boyd. 
 
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 t¥ 
 
 ■'•' •;■’£/ - •> ,r:, • •> , ;■: .j' a li/ 
 
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73 
 
 Po^/rtoA^s or Nei/rj^/iL Px£rs 
 
 v5/ee/ >5tre33 =• 2*0000 /o 30,000 y/z /r?. 
 
 Pig, 40* Neutral Axes in Curved Beams, 
 
74 
 
 visalDle that some sort of fillet or bracket should always be used 
 in a sharp corner of this sort* The minimum size of bracket to 
 produce a satisfactory stress distribution is problematic, but 
 the horizontal length of the bracket should probably be not less 
 than one-half the depth of the adjoining members, and preferably 
 greater* A curved fillet or bracket should produce the best vari- 
 ation of stress around the corner* 
 
 IE* Shearing Stresses . - In all cases the frames were highly 
 reinforced against diagonal tension by the use of U-stirrups and 
 bent-up longitudinal bars. The ends of stirrups were hooked, being 
 bent out into the flange of the T- sections and bent inimrd in the 
 rectangular sections* The bent-up bars were also anchored by semi- 
 circular hooks having a radius of four diameters of bar. 
 
 The effectiveness of the web reinforcement was demonstrated by 
 the fact that none of the frames failed by diagonal tension, and 
 that diagonal cracks were in general guite small* Knowing this, 
 the shearing unit stresses which were developed seem q.uite note- 
 worthy, inasmuch as they are much higher tlian have been found in 
 any tests outside the investigations of the Concrete Ship Section. 
 
 Shear diagrams for the different frames at maximum load are 
 given in Pig* 41, and Table 7 gives values of the unit shearing 
 stresses developed, as calculated at sections of maximum shear 
 just outside the load points. Specimens 13A1 \nd 13D2 inclusive 
 were of T-section, having a flange 30 inches wide and 3 inches 
 thick, and the value of j used was 0.88. Specimen 13E1 was of 
 rectangular section, and the value j used was 0.83, A comparison 
 is also made in the table between the shearing unit stress, and the 
 compressive unit stress of the concrete as determined from tests 
 
\^=S3800 
 
 T^pe A 
 
 r=SZ50O 
 
 Type C 
 
 ?=33SOO 
 
 7Zf-00 
 
 
 Tf^peE 
 
 E=//a/oo 
 
 Fig. 41, Shear Diagrams for Frames 
 
 at Maximtira Loads 
 
76 
 
 of 6 X 12 in* cylinders made and tested vath the frames, 
 
 TABLE 7. 
 
 mxiimi OBSERVED SHEARING STRESSES IN FRAMES 
 
 (No fail-ore occ-urred through diagonal tension) • 
 
 Speci- 
 men No 
 
 Maxim-um 
 . Vertical 
 Shear 
 lb. 
 
 Width of Depth of 
 Section Section 
 in. in. 
 
 1 
 
 in. ^ 
 lb. 
 
 Shearing 
 
 Unit 
 
 Stress 
 
 V lb 
 
 per S(i.in, 
 
 Cylinder Ratio 
 Strength v 
 
 fc '^0 
 
 .per sq.in. 
 
 15A1 
 
 60 000 
 
 8,12 
 
 9.75 
 
 6 9.7 
 
 860 
 
 3110 
 
 .28 
 
 15A2 
 
 59 500 
 
 8,00 
 
 9,75 
 
 6 8. 6 
 
 865 
 
 3765 
 
 ,23 
 
 15B1 
 
 76 000 
 
 8.12 
 
 10.0 
 
 71.5 
 
 1060 
 
 4260 
 
 .25 
 
 13B2 
 
 6 9 000 
 
 8.00 
 
 9,75 
 
 68.6 
 
 1005 
 
 3665 
 
 .27 
 
 1301 
 
 91 000 
 
 8.25 
 
 9,75 
 
 70.8 
 
 1285 
 
 4505 
 
 .29 
 
 1502 
 
 74 000 
 
 8.27 
 
 9,75 
 
 71.8 
 
 1030 
 
 4040 
 
 .26 
 
 13D1 
 
 104 200 
 
 8.12 
 
 9,87 
 
 70.6 
 
 1475 
 
 4420 
 
 .33 
 
 13D2 
 
 116 000 
 
 8.12 
 
 10,12 
 
 72.3 
 
 1605 
 
 5860 
 
 .27 
 
 13 El 
 
 38 500 
 
 8.00 
 
 8,92 
 
 59.2 
 
 650 
 
 4995 
 
 .13 
 
 It will he noted that the shearing stress of 650 Ih, per sc[, 
 in, for th rectangular section is about as high in comparison 
 to the strength of the concrete as the highest values found in 
 previous test of ordinary beams, while the values for th© T-beaia 
 sections are much higher. It is true that shearing stresses were 
 accompanied by a small direct compression which balanced a little 
 of the stress in the tension side of frames, and may have reduced 
 somewhat the tendency to diagonal tension failure; still there were 
 generally fine vertical tension crachs present just outside the 
 load points at very low loads. It does not seem likely that the 
 
77 
 
 direct compression produced any consideralDle increase in the 
 resistance to diagonal tension. 
 
 Due to the fact that the positive and negative moments in 
 continuous frames may he equalized hy the ^‘udicious use of 
 haunches, the magnitude of the moments is kept comparatively 
 small; conversely, in such frames the shearing stresses x¥ill 
 be correspondin^y large. Hence it is of considerable value 
 to find that safe shearing strengths may be obtained which are 
 much greater than these caamonly allowed in building practice. 
 This is clearly dependent, however, upon the use of a suffi- 
 cient amount of web reinforcement, properly distributed and 
 anchored, and upon proper anchorage of the longitudinal rein- 
 forcement. 
 
 13. Moment of inertia . - It is well known that statically 
 indeterminate bending stresses are governed by the relative 
 stiffness of the various parts of a structure. The stiffness 
 of a member in flexure is iBually measured by two quantities; 1 , 
 the moment of inertia, which is a function of the size and 
 shape of the cross section, and E, the modulus of elasticity, 
 which is a physical property of the material. Ho¥/ever, in a 
 composite member of steel and concrete, the latter of which is 
 so deficient in tensile strength, both E and vary with the 
 stress in the member. A very large reduction in 1 occurs when 
 the concrete fails on the tension side of the member, and a 
 further reduction takes place in E and _I as the concrete fails 
 to take compressive stress in proportion to deformation. Through- 
 out this variation in stress distribution for the concrete part 
 

 
 
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78 
 
 of the member the neutral axis chr^nges and this in turn affects 
 the moment of inertia of the steel area slightly. 
 
 Aside from the question of the effect of stress, the 
 variation in the moment of inertia v;ith the shape of a member 
 must be considered. For rectangular areas of width ^ , snd 
 depth d, ^ varies as bd^. If such areas contain equal per- 
 centages of steel similarly placed, 1 still varies as bd^. 
 
 If such areas contain equal areas . A, of steel similarly placed, 
 1 for the steel varies as For a tee beam, 1 varies as 
 
 a 
 
 bd if the width of tee and the ratio of flange thiclmess to 
 
 p 
 
 depth remain constant and as something more than if the 
 flange thickness remains constant. Hence it is seen that I_ 
 for the frames tested v/ill vary as some power of d between d^ 
 and d^. 
 
 In calculating _I for the section of a reinforced concrete 
 beam, especially when combined flexure and direct stress are 
 encountered, a clear distinction must be made between center of 
 gravity and neutral axis of section. Consider the reaction H 
 acting at the hinge of a frame as shown in Fig. 42. Imagine 
 the portion of the frame ©ut away below the section A-A, leaving 
 the reaction R, acting as before. Assiuning that the concrete 
 may be cracked over some portion of the tension side of the 
 member, let the effective area of the section be the sum of the 
 uncracked area plus an imaginary concrete area which will carry 
 a stress equivalent to that in the reinf orceiment. The point 
 a represents the centroid of this effective area. By introduc- 
 
ri - 
 
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79 
 
 
 Fig, 42, Mera"ber under Combined Flexure and Direct Stress. 
 
80 
 
 ing a system of three balanced forces, Rj (equal but opposite 
 to R, } V, and H, all acting at a, the reaction R is resolved 
 into a shearing force H, an axial force V ^ couple R,e « 
 
 The couple produces flexural stresses varying from f^ to 
 fg^ being zero at the point a. The axial force V produces a 
 uniform compressive stress V over the effective area, so that 
 the resulting neutral axis due to combined flexure and c express- 
 ion is at the point b, 
 
 Pran the foregoing it follows that the center of gravity 
 of the effective area is to be used in finding the magnitude 
 of the bending moment and that it lies on the axis about which 
 the moment of inertia is to be found. The neutral axis is to 
 be used in determining how much tension may exist in the con- 
 crete at the section. 
 
 As a method of determining the value of the product M 
 from test data, use was made of the well-known flOJ^ure formula, 
 
 M = ~ . This may be written in the form El = ^ in which 
 e_ is unit-deformation and c_ is the distance from the neutral 
 axis to the point where _e is measured. M, £, and e_ were ob- 
 tained from test data. For convenience ^ has been considered 
 as having a constant value of 3,750,000 lb. per sq. in., which 
 is the initial modulus of elasticity for this concrete, and all 
 variation in the quantity M is taken care of in the single 
 quantity I. Pig. 43 shows the variation in I at different 
 values of the compressive stress in concrete as determined from 
 sections approximately 10.5 inches in effective depth.* The 
 
 A somewhat similar variation in the moment of inertia of a 
 reinforced concrete beam is described by Dr. P. von Emperger in an 
 article " Die Wahre Grosze des Tragheitsmoments im Eisenbeton - 
 balken . " Beton und Eisen, June 5,1916. 
 

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 Y .: 
 
 
Moment of /nert/o/~ 
 
 81 
 
 
 I 
 
 H 
 
 Fig, 43. Variation in with Compressive Stress. 
 
wide divergence of points shown may he sttrihuted to errors of 
 observation in M, c and e, to a considerable variation from the 
 nominal depth of 10,5 inches, to the variation from the design 
 dimensions of the section, and to the difference in the steel 
 area used in different specimens. 
 
 Moments of inertia calculated in the ordinary way frcm the 
 nominal dimensions of the cross-section of the test specimens 
 are also shown in Fig, 43. A section 10 l/E inches in effective 
 depth and having 4,75 per cent of steel in both tension and 
 compression has been used. Using a modulus of rupture of 450 lb. 
 per sc[, in. for this concrete and a value of n equal to 8, the 
 effective section at different stages of loading has been de- 
 termined. Values of 1 computed at the different loads have been 
 plotted in Fig, 43 against values of the calculated compressive 
 stress. 
 
 A general agreement bet?/een the calculated curves and the 
 experimental points is seen, although the latter are quite 
 scattering. It is seen that until the concrete in the tension 
 surface of the member began to fail, remained constant, and 
 was equal to about 3450 in,^. The tension failure of the con- 
 crete began when the compressive stress was about 500 lb. 
 per sq, in., and after this the moment of inertia decreased 
 rapidly. The average values of the experimental data are repre- 
 
 that a similar variation in moment of inertia occurs with 
 with different depths of member. Fig. 44 has been drawn. Logar- 
 ithms of moment of inertia and depth of member were plotted. 
 
 sented roughly by the hyperbola, I = 3450 
 
 To show 
 
1 
 
 ' ^ 
 
 j 0 
 
 f; 
 
 i 
 
 o: 
 
 
 J 
 
 .' ■* 
 
 ? . • • . 
 
 
 
 i 
 
 ( 
 
 5 
 
 » 
 
 i 
 
 ! 
 
 * 
 
 I 
 
 I 
 
Zc?qafr/y/7/773 of ffomen/3 of /ner^/a. 
 
 t 
 
 •s 
 
 oe 0.9 1.0 A/ 1.2 AJ A 4 
 
 Lo^Ofr/Z/jms of Dep//?5 of .5ecf /or?, cf. 
 
 Cu/?yE5 J/iOm/^6 ffEL/rr/ON OE LOO. I TO L06.d 
 
 6or?errf/ ^r^ooLf/o/? ^f? 3} . I =fbr?5fcnr?f OeJoiLi/ ^ =500an<f ./* 962^^ 
 
 Fig. 44. Variation in 1 with Depth of Meraher. 
 

 
 
 
 v< 1 
 
 ■ 
 
 
 
 
 
 ' V' ; 
 
 k; 
 
 -^i • ’ ' V - 'i^-' ■ ' ■ ■ f*' ' ' '■ ■» 
 
 'v ' 
 
 M ■■ 
 
 V.' ■ IV ■'•(*? 
 
 ■„ ■■ : >'!• 
 
 ;f« >- ii aB ' 
 
 * • >- --r 
 
 ’rr'gri 
 
 Id 
 
 ■ '•■^i'’'®’’^'^: -*±.: . •' •5; 
 
 ' ■■■;■'■ ' '‘ -(i 
 
 * - ‘’W , ‘ 
 
 K, S . * .; .'.■ ■ V '' 'V V^''--’' ''^v'’"’v‘'"' 
 
 ■ ■• i-v.ftftSaf /v.-'b 
 
 • * J ■ . '* ^ 
 
 »*i< 'rn.. . 
 
 }■/•, '.r:>.v-r 
 
 
 ‘■Jil?*!' 'r.l! 
 
 b- . '■; ',.■ « ’■ i.sai 
 
 • , ■ »:*> •.? .v.^ 4 , i” ■' •,« 
 
 ■0 
 
 >♦ 
 
 
 
 
 V-* ■•■ • ■ •' • ' --iA^ '■■■ -*'i 
 
 - *■■"'■' '•■ V.yv -• r -^.digSI '•' 
 
 «Hk,v, .. ... ^ mMsm ^ 
 
 ■ii 
 
 t.' . .Jf:, ., ■’.i' . ■ .iif 
 
 
 4 ». 
 
 
 .i .. A ,' iv ‘ 
 
84 
 
 taking the points along each curve from data obtained within a 
 certain range of compressive stress in the concrete. From the 
 slopes of these average curves _! is found to vary approximately 
 as d Hence each curve represents an ey^uation of the form, 
 
 I = kdV^. The values of k from Fig. 44 are found to decrease 
 as the values of fo become larger, in the same general way as 
 was shown in Fig. 43. 
 
 A general expression for the moment of inertia of sections 
 of the test specimens is found from the data of Fig. 44 to be 
 
 I = (9.6 d5/2) (3|0^Q_g ) 
 
 When the tensile strength of the concrete has not been ex- 
 ceeded, f_ may be assumed eq.ual to 500 which modifies equation 
 (11) to 
 
 I = 9.6 d 
 
 - (12) 
 
 
 
 Equation (11) shows that at a compressive stress of 1500 
 lb. per sq. in. in the concrete, the value of _! is only about 
 half as great as i t v/as before the tensile strength of the con- 
 crete was lost. Hence in analyzing a structure especially for 
 stresses above ordinary working stresses, the use of the assiuip- 
 tion that varies throughout directly as some power of the depth 
 of members is not exactly logical, and \iall give too high a 
 value of at points of hi^ stress. This is cnnfirmed by test 
 results of specimens of Tj^e B and C, though the variation is 
 not large. For preliminary design, especially if the structure is 
 to have fairly uniform stresses throu^out the region of high 
 bending moments, it will usually be satiisfaetory to use a relation 
 such as I = kd^, throughout all sections. For solving statically 
 indeterminate problems the value of k is usually immaterial, since 
 
I 
 
 ) 
 
 i 
 
 o 
 
 Zi.' 
 
 
 •t ’ t> 
 
 I/, 
 
 ■ ’JO - ■ 
 
— — 85 
 
 only relative values of ^ are required. 
 
 Equations (11) end (12) Ccji not be expected to apply 
 to members in which the sliape of cross-section, percentage 
 of steel or quality of concrete vary greatly from those used 
 in these tests. It is believed, however, that these equations 
 show the general way in which the moment of inertia varies 
 in a reiriforced concrete member. Further, the foregoing com- 
 parison indicates that within the range of working stresses _I 
 may be calculated according to its mathematical definition, 
 by the ordinary method of replacing the area of steel in a 
 section by an equivalent area of concrete, or vice versa. In 
 either case the value of E will be used which corresponds to 
 the material of the equivalent section, 
 
 14, Deflections ,- Measurements of deflections were made 
 on each frame, as explained in Section 8, at intervals of one 
 foot along the entire frame. Through the relation vhich 
 
 feiev 
 
 exists between deflections and the M diagrams for a 'number in 
 
 El 
 
 flexure, it was hoped that the deflections could be used to 
 
 study the variation in the quantity El, Deflection is a second 
 
 integral function of the quantity M • Since graphical differoat 
 
 El 
 
 iation is not practicable with any degree of accuracy, the 
 exact M diagram corresponding to a given elastic curve can not 
 
 ST 
 
 be found. The best that can be done is to perform the reverse 
 operation, Ehov/ing values of M, and assuming values of M, 
 deflection curves can be obtained T/hich may be compared with the 
 experimental curves. 
 
--irv 
 
 
 
 V 
 
 C '. : 0 
 
 ( ' 
 
 ': 5 J 
 
 J . ,: ) r ;« o ^ ■^'‘: li 
 
 7%') {.:.. 
 
 orii (C ': t & ocr &. ‘"'v 
 
 t ■■ I ' 
 
 ■ ff ’ .^ • 1 1 . ■•'?■ ; . 1 -; 
 
 n o u :• 
 
 SI / 
 
 
 
 . :zir ^:^^eto^ICK> '^j'-’-cC'ri ‘■‘.“■ 
 
 '-. ■ ■■: o ■ 
 
 1. > .. ‘ f '- 
 
 
 i ’ ■ Ji ,-*' '•■ oorfi i>f ■ J '/ aXi *'’ ad 
 
 , v . .; .rxo ' 
 
 
 
 m 
 
 '♦ «■' ■ i '^ 
 
 .10 ; ' * 
 
 E .1-. J 4 l > e » : '-. 
 
 
 |0> -• ' 
 
 
 
 
 
 ■■> '.■ . ■ I. ■ 
 
 
 •jvi-tt 
 
 *ju-: -7 .' ■- ■ 
 
 
 •“'.ir’ ,v' 
 
 "'■■■ •*' '."7 
 
 • f . 
 
 !#■ 
 
 f) ’• ■ ' . .' ■ r»f". ‘ ' 
 
 t • * « 
 
 ■•r'i. :ro ' 
 
 "■ ' >' L ) 1 . ' ’ 
 
 
 T-* 1 lH*Ji " ^ ''' ft*'** I 
 
 '^'tz 1 L 
 
 ': 4 -- 
 
 
 » < 
 
 .? i ’ ■ '7 .: o ^- (.' 
 
 O'l.. a-‘A »!fr:o.! .1 .';uJ.'roJj <• 
 
 
 
 
 t :' '.‘ O.-J 
 ; r -I '.• ./' *• 
 
 , 1 '' 
 
 .1/. ! ■ f . i'trT'-AKfl 
 
 - yJI . . • ' ' J 
 
 
 
 1 
 
 *1 
 
 * :> vi:r 
 
 'i.j ' r.'T'-*>»' *(rt>5 ''■ 'y.': rcojtCjt./ 
 
 '.■*•'( '•‘. ' iif ' 
 
 .' • V i '. e t.cc rJji ; o{j ^ •'. ' ■ .;; 
 
 ** f- 
 
 
 f . ':•■• 7 ) 
 
 .-.(• r •;• Jbr , •• 
 
 j ’>V ■ ■./'> l . iV - ■ ;!tfo 
 
 ‘ \ ,■ 
 
 y • 
 
 ■•' 7 .' a 
 
 <* t 2 EWT o . 
 
 ■] i : 
 
 “^ 7 X 1/0 n :. I : ■ 
 
 • A -' ./ ■ , ■ 
 
 /r ' W ' 
 
 t 'i f . 
 
 ; ! . 
 
 
 ,• A '. ' 
 
 ."V 
 
 l.•■^l VJi I * ■.i’,'*...i:i ''i.-i'ft! 
 
 i >’ 
 
 V. 
 
86 
 
 This has heen done for one loading on each type of specimen, 
 using a constant value of 3,750,000 Ih. per sq, ini for E, and 
 a value of 1 as obtained from equation (11), Pig* 45 to 49 show 
 calculated and observed deflections graphically for frames 13A1, 
 13B1, 13C1,13P1, and 13E1* The portion of these diagrams show- 
 ing calculated deflections have been constructed by making use 
 of the well-known second integral relation bet?/een force poly- 
 gons and funicular polygons. Here the "forces" laid off in the 
 vector diagram to the right are the values of M/l which have 
 been determined from the known forces acting on the frame and 
 from equation (11). Choosing the proper pole distance, which 
 depends upon the scales used in laying off the various quantities 
 a funicular polygon is drawn, starting from the corner of the 
 frame and making the string at point 15 horizontal. The funicu- 
 lar polygon represents the elastic curve for the specimen and 
 its ordinates agree very well with the deflections v;hich were 
 observed during the test. An exception is seen in the case of 
 frame 13E1, which differed in section from the others, and to 
 which equation (11) does not ^pear to apply particularly well. 
 
 For use with any rectangular frame without brackets, Maney’s 
 equation for deflection* is readily applicable. For a frame with 
 loads at the one- third points in which the maximum moment at the 
 center is Mq = "the maximum deflection at the center is 
 
 -4). Hence in Maney*s equation f = ^^(eg+ e^) , 
 the coefficient c becomes — )• The quantities gg and e^ 
 
 must be measured at the point at which the maximum moment is 
 
 measured. By the use of Maney*s equ ation, using steel deforma- 
 * "Relation between deformation and deflection in reinforced 
 concrete beams" by G. A, Maney. Proceedings A. S.T.M. -Technical 
 Papers, Vol.XIV p.310 -1914 
 
I 
 
 V ^ • 
 
 — J 
 
 . \ 
 
 i 
 
 r 
 
 t 
 
 \ 
 
 
 ■ 
 
87 
 
 C0MPAR130N OF OBbER^ED Am COMPUTED DeFLECT!ON3 
 AT EOAD OF 4,00 0 0 POUND5 
 
 C^P^C/MEN • /3 A 1 
 
 Pig. 45. Calculated and Observed Deflections, Specimen 15A1. 
 
 A T LOAD OF 4,00 0 0 POUNDS 
 
 3pf a men • /3 5 J 
 
 IS 
 
 
 /3 
 
 !Z 
 
 // 
 
 R 
 
 Pig. 46. Calculated and Observed Deflections, Specimen 15B1 
 
88 
 
 -/s 
 
 -H 
 
 /3 
 
 -/Z 
 
 ■-^-3 
 
 tii 
 
 COMPAR/3CN OF ObFERYFD AND COMPUTED DEFLECTIONS 
 AT LOAD OF 60000 P0UND3 
 
 Specimen - 13 Cl 
 
 Fig, 47, Calculated and Observed Deflections, Specimen 13C1, 
 
 
 AT LOAD OF 60000 POUND3 
 Op Ed MEN -/3D I 
 
 Fig,48, Calculated and Observed Deflections, Specimen 15D1, 
 
89 
 
 C0MPAR/30N OF OfFERFFD AND COMPUTED DeFLECT/ONS 
 AT LOAD OF 60000 POUND3 
 3 PEC/MEN - /3 £ I 
 
 ■IS 
 
 ■H 
 
 t3 
 
 ■/Z 
 
 // 
 
 ■/O 
 
 z 
 
 ±3 
 
 ■h*7 
 
 Pig. 49. Calctilated and OlDserved Deflections, Specimen 13E1. 
 

 
 '■'^M^y ■■■'•>■'■ ( 4 ' 
 
 'of ', •» ^iV 
 
 W.-.. 
 
 •A'‘.\«'«® 
 
 'iil ' ' 
 
 %"• ■'-I-- f, . 'W 
 
 *»!•.' 
 
 !«F "K' 
 
 
 l.v ' / , * 
 
 ^14 ‘ f ii 
 
 
 -:«' * ,1 \:'v‘ ■ i* Li 7'^ -'■•Vv '.fi • A# yiSil 
 
 ^•- .■■V’V-'S- ■ , ._ 7 ^'^ /»ii.^^||jiB| 
 
 ' ■• -‘J Js^V-'C -’^^'-S' *rs™S®*??l 
 
 i< ‘ , 4 '' ■ ‘..Vi^PKH '}- ■^‘■■■^, , 
 
 .X^X fremic^gP .oaoXiotJX':^^, iJ«:^«XttoX<»CN^® 0^ 
 
 ''•/' ■ 'i'Hi 
 
 .;• » /Uijr/;; 4 ^- , ' , , , _ 
 
 p 
 
 ' 1 ^: 
 
 
 
 /•if ; ' '/ 4 ' v. - ,.'.^ *jfl 
 
 'fli£<*'“ :<i'#t /,/'ps 
 
 ■ ■•\i 7-^V' !-• v^3iiv^^' '‘0 A'- ■ v' • Vw, ^ 
 
 ' 1 ^“'^ " I 
 
 r « - 
 
 
 
 j'..-,: A>j 
 
 w;? 
 
 /i’.'.:'"j«, ;f^. 
 
90 
 
 tions and using: for d the actual distance center to center of 
 the reinforcing bars upon r/hich readings were taken, the 
 quantities shown in Table 8 were obtained. 
 
 These two comparisons show a very close agreement between 
 calculated and observed readings, and give further evidence 
 that the theoretical relations which obtain between moments 
 and deflections hold true for these frames. 
 
 TABLE 8 
 
 CALCUL^ITEI) Am OBSERVED DEFLECTIOIJS AT MIDSPM 
 
 Specimen Load k* 
 
 lb. 
 
 0 (eg + eg) 
 
 Inches 
 
 g) Observed 
 Defl ection 
 Inches 
 
 13A1 
 
 30 
 
 000 .466 
 
 .085 
 
 .00052 
 
 .14 
 
 .14 
 
 tf tf 
 
 60 
 
 000 .648 
 
 .097 
 
 .00099 
 
 .31 
 
 .28 
 
 ff M 
 
 90 
 
 000 .590 
 
 .094 
 
 .00138 
 
 .42 
 
 .42 
 
 13A2 
 
 30 
 
 000 .400 
 
 .079 
 
 .00074 
 
 .16 
 
 .16 
 
 IT n 
 
 60 
 
 000 .536 
 
 .090 
 
 .00139 
 
 .39 
 
 .39 
 
 T» n 
 
 90 
 
 000 .500 
 
 .088 
 
 .00219 
 
 .60 
 
 .68 
 
 13E1 
 
 30 
 
 000 .314 
 
 .067 
 
 .00093 
 
 .23 
 
 .26 
 
 FT IT 
 
 60 
 
 000 .560 
 
 .091 
 
 .00186 
 
 .61 
 
 .55 
 
 Further use has been made of tne measured deflections 
 in studying the variation in stiffness of each frame as a 
 whole during the application of the test loads. In a homo- 
 geneous beam ivithin the elastic limit of the material, the 
 quantity M is constant and is proportional to the ratio of 
 load to deflection, P/f, In these test specimens the ratio 
 P/f varied, and hence the variation in which is proportional 
 to p/f may be calculated from measured values of P/f, On this 
 basis Fig, 50 has been constructed, using a relative value of 
 p/f equal to unity for the 30 000 lb. load on each frame. The 
 value of f used in each case was the average of measurements 
 
91 
 
 on deflection points 10,11,12 and 13, near midspan® ¥/hile the 
 decrease in stiffness ?/ith increasing load indicated in Fig,50 
 is similar to that shown by Fig. 43, it must be remembered that 
 in the former the deflections are influenced by the stiffness of 
 all sections of the frame. While the various parts of the 
 frame are subject to widely differing intensities of stress, the 
 sections most highly stresses have the greatest influence upon the 
 deflections at midspan. The decrease in stiffness under increas- 
 ing load, as shown by both deflection and deformation readings, 
 seems to be a typical phenomenon of reinforced concrete members. 
 
 15, Cone fusions . - In analyzing the test results it must 
 be remembered that the materials of which the specimens were made 
 are of rather unusual quality. The compressive strength and 
 modulus of elasticity of the concrete are much higher than are 
 usually encountered in reinforced concrete construction; in a 
 similar way the steel combined a high elastic limit with a fairly 
 high degree of ductility. Materials of this quality were of 
 especial advantage for investigational work, but may not be 
 considered as representative of materials generally available 
 for construction work. 
 
 The use of a large percentage of longitudinal reinforcement 
 made it possible to utilize much of the compressive strength of 
 the concrete, while the large amount of web reinforcement used 
 permitted the development of exceptionally high shearing stresses 
 without diagonal tension failures. 
 
 Certain definite effects have been determined from the use 
 of brackets in the particular test pieces described herein, but 
 
i/ \ 
 
 
 'H. * 
 
 
 ^ ff-, J,>oii "■ ■• 'c 
 
 ' . ■r"'— j r 
 
 \ a’;! 
 
 a. 
 
 
 ^ -.J - 
 
 I f’ 
 
 ’•• v,iojS'^-,‘4y* .roc*v«to -.‘ •:( 
 
 ^ u >16(B cr; : 
 
 -. f C 
 
 P A , 
 
 
 ^e- « 
 
 r *J 
 
 ■n- ' ^ 
 
 >1^ . 
 
 ■I I , •. 
 
 uonos crfc-i^j- '■ J^eigti^ 
 
 ‘ .• ' '?! 
 
 , 1 j 
 
 V ,, I. 
 
 .1-0; •' 
 
 • 'j. 
 
 _4i 
 
 ^ . -r 
 
 iUi 
 
 ■■*1 - 
 
 .J- 
 
 V 
 
 t f . 
 
 
 ,.'■' ‘£o l'y 
 
 -o 
 
 O > 
 
 :0*> f*it j 
 
 ■ y. ■'i ' 
 
 i'! ■ f .. i; 
 
 PM' 
 
 ' ‘ if 'll 
 
 r 1 ’ .i'-> 
 
 I - : 0, ' ’to:‘ 
 
 ':, r 'J? ‘ 
 
 ‘ ■■•'''•* li.’. [f 0 
 
 • .. i */ L i 
 
 p;:'"' ' ,i 
 
 ■ r>,A 
 
 
 
 
 I I'O 
 
 ! ' 
 
 *. ■.’ /. ' •; •*. ‘b: C,'i I ■.•rr»',,..*- 
 
 */■■ ' jjk' "rn i':-;:;:;:':' V 
 
 ■ .;o.-* 'tr. ", ^ .• , - 
 
 ' I " 
 
 ^.r or(T 
 
 f 
 
 no j-.ti ftiA-'- 
 
 . ‘ ^ 'r.C'' is-; 
 
 • a £^, ■ ■ 
 
 ►v 
 
 
 
 . ' V(< 
 
 ?* 
 
 ■ •'. ( V. ;\ L-'**'* .’ •■? hti.'io.'- c: • 
 
 
 
92 
 
 
 
 
 
 
 
 
 / 
 
 ^ 
 
 f 
 
 
 
 
 0 wo 
 
 
 
 
 
 
 _9 
 
 
 / 
 
 / 
 
 f 
 
 
 
 
 
 
 
 
 
 
 •h 
 
 r 
 
 / 
 
 / 
 
 4 
 
 
 □ 
 
 
 
 
 
 
 
 
 
 < 
 
 / ‘ 
 
 / 
 
 
 
 
 
 
 
 A 
 
 X 
 
 
 - 
 
 / 
 
 / 
 
 
 ■ 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 / ^ 
 
 / 
 
 • 
 
 
 
 
 
 
 
 
 
 
 ! 
 
 / 
 
 
 □ 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 ( 
 
 
 ■ 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 / 
 
 - 1 
 
 e 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 Mi 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 ■o 
 
 3 
 
 ' 1 
 + / 
 / 
 
 
 ( 
 
 ) 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 + 
 
 1 
 
 1 
 
 1 
 
 - f - 
 
 — f — 
 
 1 
 
 < 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ \ \ 
 
 O □ < • 
 
 0^ N-^ tsr^ 
 
 • ■ << + X 
 
 
 
 
 
 
 
 
 + 
 
 9> 
 
 1 
 
 L 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 § ^ ^ ^ ^ 
 
 ■99LUVJJ./0 e^3uj;i^Q aboj^AD bu/4D9ipui j2jo93nidA pai^di?^ 
 
 Proportion of maximum load on frame 
 
 Fig, 50, Diagram Showing Decrease in Stiffness with Increasing Loads on Frames 
 
many more tests are necessary before any broad generalization 
 can be made concerning the effectiveness which a bracket will 
 
 have in different types and shapes of frames* A niimber of 
 tentative conclusions, ] 3 .owever, may be formulated* 
 
 (1) From an analysis of the test data it appears that the 
 reinforced concrete frame can be treated with a fair degree of 
 accuracy by analytical methods similar to those used in arch 
 analysis* A study has been made as to the validity of some of 
 the assumptions usually employed in such an analysis. 
 
 (2) For the purpose of determining the distribution of 
 bending moments, it seems to be sufficiently correct to consider 
 the entire section of a specimen as effective, even at points 
 
 of sudden change of shape* The effect of such a change in 
 shape upon the stress in the member is a matter ?/hich needs 
 further experimental investigation. 
 
 (3) In the analysis of statically indeterminate frames the 
 modulus of elasticity of the material and the moment of inertia 
 of the cross section are quantities of primary importance* With- 
 in the range of working stresses, the value of the product M 
 
 as determined from a large number of test readings agrees closely 
 with the value of M as calculated mathematically, using the 
 common method of replacing the steel area by an equivalent con- 
 crete area and neglecting the tension area of the concrete if the 
 tensile stress is high. At higher stresses the tests indicate a 
 decrease in the value ofS, resulting in a relative loss of 
 rigidity at points thus stressed* This might produce a slight 
 readjustment of the moment distribution, and some leeway should 
 
 J 
 

94 
 
 be allowed in the design of the structure to accomodate such 
 an occurrence. It is to be noted, however, that if the struc- 
 ture can be designed so as to develop nearly uniform stresses 
 throughout, there will be little variation in rigidity under 
 the higher loads, 
 
 (4) Fairly consistent q.uantitative informatinn as to the 
 variation in M has been obtained from the tests of tbe differ- 
 ent specimens. Until the concrete begins to fail on the 
 tension side of the member the value of M appears to vary 
 about as the 5/2 power of the depth of the section. After the 
 concrete begins to fail in tension the value of ^ gradually 
 decreases, in the manner indicated by equation (11), 
 
 The assumption that M can be expressed by a simple equation, 
 El = kd^ is evidently not correct, but will usually be satis- 
 factory for preliminary designs. An exponent n equal to 5/2 
 in the above expression applied Very well to these highly re- 
 inforced members; with a smaller amount of reinforcement an 
 exponent n equal to 3 may be expected to apply, as it would 
 also for rectangular sections of a homogeneous material. For 
 determining bending moment distribution the relative magnitudes 
 only of the quantities ^ at different sections are needed, so 
 that the value of the coefficient k is immaterial for such 
 calculations, 
 
 (5) Calculated deflections of the test specimens based on 
 values of moment of inertia from equation (11) agree very well 
 with measured deflections, and also with deflections calculated 
 by use of Maney*s equation. This is significant as showing a 
 
95 
 
 fairly consistent agreement among the various data of the 
 test, 
 
 (6) From calculations, the basis of ¥/hich is confirmed 
 by the tests, it is found that the effect of brackets on the 
 bending moments in a frame may be expressed as a function of 
 the clear span(from edge to edge of brackets) , of the ratio 
 of height to span of fra.me, and of the given loading. The 
 importance of the various factors is indicated in eq.uation (4) . 
 
 (7) The effect of brackets if sometimes thought of as a 
 shortening of the span of the loaded member. That is, the 
 bracket is considered a part of the end support and thus the 
 center of bearing is brought out from the center line of the 
 column. It has been found that this shortening of the span is 
 not constant for a given bracket, but also varies with the 
 ratio of height to span of the frame. For the frames tested, 
 the total span may be considered as reduced by about t^.vo-thirds 
 of the horizontal length of the bracket at each end. While 
 
 the total moment has been reduced in this way, its distribu- 
 tion between positive and negative sections has varied. The 
 proportional amount of negative moment increases considerably 
 as the size of bracket increases. Hence while the decrease 
 in total moment is in effect a shortening of the span, this 
 viewpoint does not lead to logical conclusions, since the 
 negative moment actually increases as the span shortens. 
 
 (8) The use of 45^ brackets in these tests is not intended 
 to imply that this shape is the most effective. For any given 
 frame and loading, the mdst desirable shape of bracket may 
 

 ■i 
 
 
 « • 
 
 
 
 . 'Tv «;\t c 
 
 
 . ■•••i ..V < V- 
 
 • 
 
 
 ■ ’ rn-Jo 
 
 
 
 '*V 
 
 <*'* t)-a5'- t iC" ■ , ' '•: 
 
 
 * 
 
 ‘ ■ •' ^ t-. 
 
 ,■••'•-'■ In rs2^«i ■ 
 
 ■ ■'■.’ '.i 
 
 •: L: 
 
 
 V 
 
 
 
 
 -- ^ ‘ '^-4 
 
 '■;■> 
 
 « 
 
 . ’ .' ' f' H ' ■ 
 
 \ * 
 
 ' i - '■ikiJk'* 
 .-*y*^55.5r •- 
 
 
 ^-:o <- '< ■ ? • 
 
 
 
 
 ■• » •. *-■• '■ ' • : 
 
 
 *: ‘ 1 '■ ■* 
 
 
 r-.- ,■ .. . •■ ' '■•roo '■ 
 
 
 . f. 
 
 ^ -W’ • '0-) ;S;.r. 
 
 A 
 
 <? 
 
 r/ 
 
 . ' ’■ - [ .xi ,'r,v's<^ 
 
 
96 
 
 iie determined. The general rale should he kept in mind that 
 the bending moment diagram for a frame of uniform section is 
 an approximate influence line for the e ffectiveness of brackets 
 or haunches. That is, an ordinate at any point of this diagram 
 represents the relative usefulness of an increase in section 
 at that point. 
 
 (9) \^/hile brackets will usually have rectilinear outlines, 
 it is evident that the brackets of Specimen 151)1 and 13I)E, which 
 approach a curved form, have certain advantages. This shape 
 
 of bracket was very effective in reducing the moment at midspan, 
 and it also produced a fairly uniform distribution of stress 
 throughout. The result was that these frames withstood a much 
 greater load than any frames of the other types. 
 
 (10) Brackets should not be used for the purpose of 
 reducing stresses, without also determining what effect they 
 will produce upon moment distribution. A large bracket may 
 produce a hi^ moment at a section where it would not occur 
 without the bracket and where the member consequently is not 
 reinforced suff iciently. For example, it is seen from the test 
 of Specimen 131)1 that while the bracket was deep enough to 
 provide for the large moment at the corner, it caused failure 
 to occur at the weaker section at midheight of the column. 
 
 (11) The results of these tests confirm the theoretical 
 deduction that brackets can be used to effect a considerable 
 saving of material and of dead weight in a structure. The 
 bracket eliminates the high local stress which is found at the 
 sharp comer of a frame; it produces a more uniform variation 
 in stress along the frame, thus minimizing the tendency for the 
 
97 
 
 formation of cracks; and it reduces bond and shearing stresses 
 at the corners of the frame. Fiirther, by the careful choice 
 of the brackets the bending moments may be varied considerably 
 and thus a proper balance may be secured between the stresses 
 in regions of positive and negative moments. 
 
 The desirable features mentioned apply to all forms of 
 continuous beam and frame construction. In reinforced concrete 
 work the formation^ of brackets and haunches is comparatively 
 easy, and in important structures the saving of material should 
 considerably overbalance the extra cost of construction. 
 

 
 
 
 ri’.Tw^ 
 
 ■’'W'’* ' ■ '• ■ --r-^vs r ■ r t . - • T • .^...-, •'sw.-i 
 
 ^tT2"ji.ejfr» t ia3itiotb 
 
 
 • f V -3 ^ 
 
 'o^i 
 
 iT?r 
 
 Itttaf'.o <afv‘ x^ ,'i'ySiJi^ \\esM 
 
 / . -■ ~'^l * •*/'," *’ ' ■ .c^Jj '* •'5' F 
 
 S*} 
 
 -Vi*' 
 
 
 K ^»1^;* S<f A^TxroAti J&jj ooxwXjrcT. 0D^ 5^Vi 
 
 i' ' J ■' '' ' ■ '^'^ ''' ''“^ ■ '*^|««pilr 
 
 ^ '‘-^ ■ ' ■ -V .^/ ' 
 
 
 «» 
 
 XX* of OQC^IS'IXU^ OOT^7^gO'^: OX<fiTl%;Vi'* 
 
 : - /:• '■' ■■•■-' ■ J- ■ ■• ; ■ '.^, .-V' 
 
 - .Q ’*'4^ 
 
 ? .rfaiot‘vt<*Jio«^*i-o feVo Mfii > »4f 
 
 V, 
 
 - - .1 
 
 
 ’V 
 
 * 
 
 
 K X 
 
 vis 
 
 4.;V-'‘-l .: Si4r 
 
 ^ ... 
 
 ■ <j 4 ' 1 
 
 'V\' 
 
 
 .T V 
 
 
 \,-h- 
 
 y>^‘/S 
 
 
 
 V- 
 
 ■j^ 
 
 ■■s;; 
 
 V. >. '* 
 
 *!■-*. ■i'V 
 
 1 -*,fc • 
 
 •>.r- 11 
 
 fc-:; 
 
 
 « V,' >ijD '• ■■■ ’f^'v’^' ‘'J' ^-'’.^..t.^ 
 
 ^ ■' ‘ /...^ ''ii. 
 
APPENDIX I 
 
 16. Test Data and Drawing .- Detailed data of all 
 stressf^ deformations, deflections, loads and reactions ob- 
 served in the tests are given in Table 9. While these data 
 have been presented elsewhere in the form of curves or 
 diagrams, they are tabulated here to add to the completeness 
 of the thesis. 
 
 Following Table 9, detailed sketches showing the 
 position of all strain gage lines and deflection points, as 
 well as the position of cracks at failure, are given in 
 Fig. 51 to 67. It will be noted that strain gage points on 
 steel are marked by solid circles, those on concrete by open 
 circles, and deflection points by open sq.uares. The gage 
 lines are numbered to correspond with the data of Table 9. 
 
 It is felt triat the crack drawings fizrnish considerable informa- 
 tion regarding the behavior of the frames under load. 
 
 TABLE 9. 
 
 DATA OF TESTS 
 
 Note.- In the table loads are recorded in pounds, 
 deflections or movements in inches, unit stresses in thousands 
 of lb. per sq. in., and unit deformations in thousandths of an 
 inch per inch. The + sign indicates tensile stress or deforma- 
 tion and upward or outward deflection, and the - sign indicates 
 the opposite. 
 

 SPECIIvISU 
 
 13A1 
 
 
 
 99. 
 
 
 Load on Specimen - 
 
 lb. 
 
 
 Base 
 
 Observation 
 
 30 000 
 
 30 000 
 
 60 000 
 
 90^ bO(J" 
 
 '120 oob 
 
 Moved 
 
 
 
 
 
 
 
 Outward 
 
 End Thmst-lb. 
 
 6 200 
 
 6 200 
 
 8 200 
 
 14 300 
 
 17 600 
 
 
 End Movement- in. 
 
 -.01 
 
 0 
 
 ^.01 
 
 —.04 
 
 -.01 
 
 +164 
 
 Unit Stress 
 
 
 
 
 
 • 
 
 
 on G. L. 37 
 
 -4.5 
 
 -3.7 
 
 -4.5 
 
 -6.8 
 
 -9.8 
 
 
 36 
 
 -3.4 
 
 -4.1 
 
 -6.0 
 
 -9.4 
 
 -14.9 
 
 
 35 
 
 -10.8 
 
 -6.4 
 
 -6.0 
 
 -10.1 
 
 -18.8 
 
 + 9.0 
 
 34 
 
 +3,4 
 
 -7.1 
 
 -9.4 
 
 -16.1 
 
 -28.5 
 
 +3.4 
 
 30 
 
 -4.5 
 
 -7.5 
 
 -7.5 
 
 -10.5 
 
 -7.1 
 
 +13.9 
 
 29 
 
 -2.6 
 
 -3.0 
 
 -2.6 
 
 -1.5 
 
 + 3.4 
 
 
 28 
 
 -1.5 
 
 0 
 
 +3.8 
 
 + 6.0 
 
 +18,0 
 
 
 27 
 
 +4.9 
 
 + 3.8 
 
 +8.3 
 
 +13.9 
 
 + 21.4 
 
 
 26 
 
 + 6.8 
 
 + 7.1 
 
 +13. f 
 
 +19.9 
 
 + 25 . 2 
 
 
 25 
 
 + 9.4 
 
 +8.6 
 
 + 21.0 
 
 + 30.0 
 
 +52.5 
 
 
 24 
 
 + 13.5 
 
 +14.7 
 
 + 23.2 
 
 +33.0 
 
 +52,2 
 
 
 23 
 
 + 7.9 
 
 + 9.8 
 
 + 19.5 
 
 +29.6 
 
 Y.P. 
 
 
 22 
 
 +13.1 
 
 +12.4 
 
 + 22.9 
 
 +32.2 
 
 + 54.8 
 
 +14.6 
 
 21 
 
 + 10.1 
 
 +13.9 
 
 + 21.8 
 
 + 31.1 
 
 +Y.P. 
 
 +12.8 
 
 22a 
 
 + 10.1 
 
 + 12.4 
 
 + 20.6 
 
 + 31 . 1 
 
 +Y.P. 
 
 +11.3 
 
 23a 
 
 + 11.6 
 
 + 14.2 
 
 + 22.5 
 
 + 34.1 
 
 +Y.P. 
 
 
 24a 
 
 7.9 
 
 + 7.9 
 
 + 21.0 
 
 +30.4 
 
 +Y.P. 
 
 
 25a 
 
 + 10.5 
 
 +12.4 
 
 +15.4 
 
 — 
 
 +Y.P. 
 
 
 26 a 
 
 + 9.4 
 
 + 9.0 
 
 + 18,0 
 
 + 25.5 
 
 + 34.9 
 
 
 27 a 
 
 + 2.6 
 
 +5.6 
 
 +10.9 
 
 +18.4 
 
 — 
 
 
 28 a 
 
 + 5.2 
 
 + 6.4 
 
 +3.0 
 
 +8.3 
 
 +15.0 
 
 
 29a 
 
 -1.1 
 
 0 
 
 -4,1 
 
 -2.7 
 
 +3,4 
 
 + 15.4 
 
 30a 
 
 -2.2 
 
 -5.2 
 
 -6.0 
 
 -9,8 
 
 -17.6 
 
 + 12.8 
 
 34 a 
 
 -4.9 
 
 -4.9 
 
 -3.0 
 
 -13.5 
 
 -22.1 
 
 +5.3 
 
 35 a 
 
 -5.6 
 
 +0.4 
 
 -1.1 
 
 -3.0 
 
 -10.1 
 
 +14.3 
 
 36 a 
 
 -5. 6 
 
 -4.5 
 
 -2.2 
 
 -0.8 
 
 -8.3 
 
 
 87 a 
 
 -3.4 
 
 + 6.0 
 
 -1,8 
 
 + 2.3 
 
 -0.4 
 
 
 17a 
 
 0 
 
 +1.1 
 
 + 2.3 
 
 + 5.6 
 
 +18.4 
 
 
 16a 
 
 +0.4 
 
 +1.5 
 
 + 6.0 
 
 + 11.3 
 
 +24.4 
 
 
 .15a 
 
 +4.5 
 
 + 6.4 
 
 + 10.5 
 
 +15.4 
 
 + 27.0 
 
 
 14 a 
 
 + 3.8 
 
 + 6.0 
 
 +9.4 
 
 + 16.1 
 
 +25.2 
 
 -5.6 
 
 13 a 
 
 -f-3.8 
 
 +4.1 
 
 + 7.5 
 
 +13.5 
 
 +30.8 
 
 -7.1 
 
 12a 
 
 +7.1 
 
 + 9.8 
 
 + 12.4 
 
 +20.3 
 
 +47.7 
 
 0 
 
 10a 
 
 +1.9 
 
 + 6,4 
 
 + 13.1 
 
 +16.9 
 
 +28.9 
 
 -10.9 
 
 9a 
 
 + 4.5 
 
 +4.5 
 
 + 7.5 
 
 + 10.9 
 
 +9.4 
 
 -3.8 
 
 8a 
 
 + 2.6 
 
 +3.4 
 
 + 7.9 
 
 +12.0 
 
 +48 .0 
 
 
 7a 
 
 -1.9 
 
 -1.5 
 
 -1.1 
 
 +4.9 
 
 +15.0 
 
 
 6a 
 
 -1.1 
 
 -0.4 
 
 -2.6 
 
 — 
 
 +14.3 
 
 
 3a 
 
 -5.3 
 
 -4.5 
 
 -9.0 
 
 -9.0 
 
 +7.1 
 
 
 2a 
 
 -3.8 
 
 -4.1 
 
 -7.9 
 
 -10.5 
 
 -9.0 
 
 -2.6 
 
 1 
 
 -4.9 
 
 -4.1 
 
 -7.9 
 
 -9.4 
 
 -2.3 
 
 -3.4 
 
 2 
 
 -4.9 
 
 -3.8 
 
 -9.0 
 
 -10.9 
 
 -3.8 
 
 -2.3 
 
 3 
 
 — 
 
 -2.3 
 
 -7.1 
 
 -10.1 
 
 -1.1 
 
 
 6 
 
 -3.0 
 
 -1.9 
 
 -4.5 
 
 -5.6 
 
 -3.4 
 
 
 7 
 
 0 
 
 +1.1 
 
 0 
 
 +1.5 
 
 +14.3 
 
 
it 
 
 
100 
 
 T.-iBIE 9. 
 
 DATA OP TESTS, Continued 
 SPECIMEN 13A1 Cont, 
 
 I Load on Specimen - lb. Base 
 
 Observation 3d000 SoUUD 606b0 96000 12OO00 Moved 
 
 Outward 
 
 8 
 
 -1.1 
 
 +0.8 
 
 +1.1 N 
 
 1 +3.4 
 
 +10.9 
 
 
 9 
 
 +1.9 
 
 + 3.4 
 
 +5.6 
 
 ' +8.3 
 
 
 
 0 
 
 10 
 
 + 6.5 
 
 + 10.1 
 
 +15.8 
 
 + 24.0 
 
 +53.6 —4.5 
 
 11 
 
 + 7.5 
 
 +10.5 
 
 +15.8 
 
 +23.6 
 
 +48.4 +3.8 
 
 12 
 
 +3.0 
 
 +4.9 
 
 +8.3 
 
 +16.9 
 
 +36.8 -4.5 
 
 13 
 
 + 5.3 
 
 +8.6 
 
 +11.3 
 
 +19.5 
 
 +56.3 -8.6 
 
 14 
 
 +4.1 
 
 + 6.4 
 
 +16.9 
 
 +22.9 
 
 +34.5 +0.4 
 
 15 
 
 + 3.0 
 
 +4.9 
 
 +10.5 
 
 +19.5 
 
 +33.8 
 
 
 16 
 
 +0.4 
 
 +4.5 
 
 +4.5 
 
 +9.4 
 
 + 28.5 
 
 
 17 
 
 0 
 
 +2.3 
 
 + 2.3 
 
 +4.9 
 
 + 18.0 
 
 
 Unit Deform. 
 
 
 
 
 
 
 
 on G.L.lOl 
 
 -.04 
 
 + . 04 
 
 -.04 
 
 -.11 
 
 -.89 
 
 
 102 
 
 -.07 
 
 -.06 
 
 -.15 
 
 -.24 
 
 -.02 
 
 .26 
 
 103 
 
 -.15 
 
 -.15 
 
 -.22 
 
 -.13 
 
 -.63 
 
 .52 
 
 104 
 
 + .07 
 
 + .13 
 
 +.26 
 
 + .69 
 
 — 
 
 2.03 
 
 105 
 
 + .15 
 
 -.04 
 
 -.02 
 
 -.04 
 
 — 
 
 + .11 
 
 106 
 
 + .11 
 
 0 
 
 • 
 
 1 
 
 0 
 
 + .26 
 
 +.94+1.26 
 
 Def lec tion-in. 
 
 
 
 
 
 
 
 on Point D1 
 
 + .01 
 
 -.01 
 
 +.02 
 
 + . 01 
 
 -.44 
 
 +0.4Y 
 
 D2 
 
 + .01 
 
 0 
 
 + .03 
 
 + .04 
 
 -.22 
 
 + . 32 
 
 D3 
 
 +01 
 
 + .01 
 
 + ,03 
 
 + .03 
 
 -.02 
 
 + .17 
 
 D4 
 
 0 
 
 + .01 
 
 + .01 
 
 + .02 
 
 + .06 
 
 + .04 
 
 D5 
 
 0 
 
 0 
 
 0 
 
 -.01 
 
 -.05 
 
 -.04 
 
 D6 
 
 -.03 
 
 -.02 
 
 -.07 
 
 -.10 
 
 -.43 
 
 -.10 
 
 D7 
 
 -.07 
 
 -.07 
 
 -.13 
 
 -.19 
 
 -.83 
 
 -.14 
 
 D8 
 
 -.09 
 
 -.09 
 
 -.18 
 
 -.27 
 
 -1.20 
 
 -.18 
 
 D9 
 
 -.11 
 
 -.12 
 
 -.22 
 
 -.34 
 
 -l.EO 
 
 -.20 
 
 DIO 
 
 -.13 
 
 -.14 
 
 -.26 
 
 -.39 
 
 -1.86 
 
 -.22 
 
 Dll 
 
 -.15 
 
 -.15 
 
 -.28 
 
 -.42 
 
 -2.07 
 
 -.24 
 
 D12 
 
 -.13 
 
 -.14 
 
 -.28 
 
 -.42 
 
 -2.13 
 
 -.23 
 
 D13 
 
 -.13 
 
 -.14 
 
 -.26 
 
 -.40 
 
 -2.10 
 
 -.23 
 
 D14 
 
 -.11 
 
 -.12 
 
 -.23 
 
 -.36 
 
 -1.81 
 
 -.20 
 
 D15 
 
 -.09 
 
 -.10 
 
 -.19 
 
 -.27 
 
 -1.37 
 
 -.17 
 
 D16 
 
 -.06 
 
 -.07 
 
 -.12 
 
 -.18 
 
 -.93 
 
 -.13 
 
 D17 
 
 -.05 
 
 -.04 
 
 -.07 
 
 -.10 
 
 -.52 
 
 -.10 
 
 D18 
 
 -.01 
 
 -.01 
 
 -.02 
 
 -.02 
 
 -.10 
 
 -.04 
 
 D19 
 
 + .01 
 
 0 
 
 + .01 
 
 + .01 
 
 + .08 
 
 •f*. 03 
 
 D20 
 
 + .01 
 
 + .01 
 
 + .03 
 
 + .04 
 
 + .28 
 
 + .13 
 
 D21 
 
 + .02 
 
 + .03 
 
 + .04 
 
 + .04 
 
 + .44 
 
 + • 25 
 
 D22 
 
 + .01 
 
 + .01 
 
 + . 03 
 
 + .03 
 
 + .57 
 
 + . 36 
 
101 
 
 TABLE 9. 
 
 LATA OP TESTS, contirmed 
 
 SPECIIJEU 13A2 
 
 Observation 
 
 Load 
 
 30000 
 
 on Specimen • 
 60000 90000 
 
 - lb. 
 
 119000 
 
 Base 
 
 Moved 
 
 Outward 
 
 End Thrust- lb. 
 
 ^0 
 
 10800 17500 
 
 17>/00 
 
 4^00 
 
 End Movement -in, 
 
 • +0.02 
 
 +0.01 +0.01 
 
 +0.03 
 
 +1.66 
 
 Unit Stress 
 
 on G. L. 37 
 
 -1.5 
 
 -6.4 -8.3 
 
 -10.1 
 
 +0.4 
 
 36 
 
 -2.3 
 
 -6.8 -10.5 
 
 -18.4 
 
 + 1.1 
 
 35 
 
 -3.8 
 
 -9.4 -15.0 
 
 -35.3 
 
 + 2.6 
 
 34 
 
 -5.3 
 
 -13.5 -21.0 
 
 -44.3 
 
 +1.5 
 
 33 
 
 -10.1 
 
 -18.8 -33.0 
 
 +Y.P. 
 
 -0.4 
 
 30 
 
 -3.0 
 
 -6.4 +1.1 
 
 + 22.1 
 
 +12.4 
 
 29 
 
 -1.9 
 
 -1.5 +13.5 
 
 +13.5 
 
 +19.5 
 
 28 
 
 -0.8 
 
 +5.3 +18.0 
 
 + 28.9 
 
 +13.5 
 
 27 
 
 + 1.5 
 
 +13.9 +25.9 
 
 +33.4 
 
 +8.3 
 
 26 
 
 +8.3 
 
 +19.1 +28.5 
 
 +35.0 
 
 +8 . 3 
 
 25 
 
 + 10.1 
 
 +23.6 +42.4 
 
 +70.5 
 
 +9.8 
 
 22 
 
 + 18.4 
 
 +31.9 +46.9 
 
 +Y.P. 
 
 +12.3 
 
 22a 
 
 +14.3 
 
 +28.1 +48.0 
 
 +Y.P. 
 
 +10.1 
 
 30 a 
 
 - 3.8 
 
 -7.1 +0.4 
 
 + 21.0 
 
 +12.8 
 
 33a 
 
 -7.5 
 
 -14.2 -20.3 
 
 —21.8 
 
 +3.0 
 
 ^ 13a 
 
 -*-12.4 
 
 +14.6 +24.4 
 
 +33.0 
 
 -2.2 
 
 10a 
 
 +1.5 
 
 +1 .5 +2.6 
 
 +3.4 
 
 +1.1 
 
 2a 
 
 -6.8 
 
 -12.0 -19.5 
 
 +24.0 
 
 -6.4 
 
 2 
 
 -4.9 
 
 -11.3 -17.3 
 
 -17.3 
 
 -4.1 
 
 6 
 
 -4.1 
 
 -6.4 -5.3 
 
 + 9.8 
 
 -1.5 
 
 7 
 
 -1.5 
 
 -6.4 -2.3 
 
 + 10.2 
 
 -1.9 
 
 8 
 
 -2.3 
 
 0 +3.4 
 
 + 8.6 
 
 -3.8 
 
 9 
 
 +1.9 
 
 +6.4 +8.3 
 
 + 7.1 
 
 -6.8 
 
 10 
 
 + 7.5 
 
 +15.0 +22.5 
 
 +30.0 
 
 -10.9 
 
 11 
 
 + 6.0 
 
 +16.9 +30.4 
 
 + Y.P. 
 
 -3.4 
 
 12 
 
 +9.8 
 
 + 23 . 6 +42 . 8 
 
 + Y.P. 
 
 -3.0 
 
 13 
 
 +10.5 
 
 +22.9 +34.1 
 
 +61.1 
 
 -1.9 
 
 14 
 
 +4.9 
 
 +12.8 +22.5 
 
 + 28.9 
 
 +0.9 
 
 15 
 
 + 2.3 
 
 +8.3 +15.5 
 
 + 23.6 
 
 -0.4 
 
 16 
 
 + 2.3 
 
 +4.5 +11.3 
 
 +16.1 
 
 +0.4 
 
 17 
 
 -1.9 
 
 -0.4 +0.8 
 
 + 1.5 
 
 -4.1 
 
 IMit Deform* n 
 
 on G.L. 101 
 
 -0.07 
 
 -0.17 -0.46 
 
 
 +0 . 66 
 
 102 
 
 - .20 
 
 - .53 - .85 
 
 
 + 1.22 
 
 103 
 
 - .30 
 
 - .77 -1.66 
 
 
 + 0.68 
 
 104 
 
 0 
 
 - .09 - .15 
 
 -2.52 
 
 +3.19 
 
 105 
 
 + .06 
 
 + .46 +1.18 
 
 +4.50 
 
 +1.16 
 
 106 
 
 - .20 
 
 - .28 ^.35 
 
 
 +2.71 
 
Vn 
 

 TABLE 9. 
 
 DATA OP TESTS, continued 
 SPECIMEN 13A2 continued 
 
 102. 
 
 
 Load on Specimen 
 
 -lb. 
 
 Base 
 
 Observation 
 
 30000 
 
 60000 90000 
 
 119000 
 
 Moved 
 
 
 
 
 
 Outward 
 
 De flection- in* 
 
 
 
 
 
 on Point D1 
 
 0 
 
 +0.01 -0.03 
 
 -0.84 
 
 +0.34 
 
 DZ 
 
 +0.01 
 
 0 0 
 
 -.47 
 
 + .25 
 
 D3 
 
 + .02 
 
 + * 03 + * 04 
 
 -.10 
 
 + .12 
 
 D4 
 
 + .01 
 
 +.02 + .04 
 
 + .13 
 
 + .03 
 
 D5 
 
 -.01 
 
 -.02 - .03 
 
 
 -.03 
 
 D6 
 
 - .04 
 
 -.09 - .16 
 
 -0.51 
 
 -.10 
 
 D7 
 
 - .07 
 
 -.17 - .30 
 
 - .98 
 
 -.14 
 
 D8 
 
 - .11 
 
 -.25 - .45 
 
 -1.47 
 
 -.21 
 
 1)9 
 
 - .13 
 
 - . 32 - . 58 
 
 -1.93 
 
 -.25 
 
 PIO 
 
 - .15 
 
 -.37 - .66 
 
 -2.27 
 
 -.27 
 
 mi 
 
 - .16 
 
 -.39 - .68 
 
 -2.47 
 
 -.28 
 
 m2 
 
 - .16 
 
 -.38 - .68 
 
 -2.5e 
 
 -.28 
 
 ms 
 
 - .14 
 
 -.35 - .63 
 
 -2.34 
 
 -.26 
 
 m4 
 
 - .13 
 
 -.31 - .56 
 
 -2.00 
 
 -.24 
 
 ms 
 
 - .10 
 
 -.24 - .44 
 
 -1.55 
 
 -.20 
 
 me 
 
 - .06 
 
 -.16 - .30 
 
 -1.07 
 
 -.14 
 
 m? 
 
 - .04 
 
 -.09 - .17 
 
 -.61 
 
 -.10 
 
 ms 
 
 0 
 
 -.OS - .03 
 
 -.13 
 
 -.03 
 
 D19 
 
 + .01 
 
 + * OS + * 03 
 
 + .10 
 
 + .03 
 
 P20 
 
 + .01 
 
 + .03 + .06 
 
 + .40 
 
 + .14 
 
 D21 
 
 + .02 
 
 +.04 + .10 
 
 + .68 
 
 + .29 
 
 1)22 
 
 + .02 
 
 + . 04 + * 10 
 
 + .96 
 
 + .43 
 
 
 
 TABLE 9. 
 
 
 
 
 DATA OP TESTS, continued 
 
 
 
 
 SPECIIMT 13B1 
 
 
 
 
 Load on Specimen-lb. 
 
 Base 
 
 Observation 
 
 30000 
 
 60000 90000 120000 152000 
 
 Moved 
 
 
 
 
 
 Outward 
 
 End Thrnst-ib* 
 
 6750 
 
 12600 18200 
 
 19500 26706 
 
 9100 
 
 End Movement- in. 
 
 +•0.02 
 
 +0.02 +0.02 
 
 +0.06 -0.01 
 
 +1.81 
 
 Unit Stress 
 
 
 
 
 
 on G.L. 35 
 
 00.4 
 
 -6.8 -1.6 
 
 -3.2 
 
 +8. 6 
 
 32 
 
 -3.4 
 
 -10.5 -15.4 
 
 -23.3 -28.5 
 
 -3.8 
 
 28 
 
 -1.1 
 
 -3.0 +4.5 +10.5 
 
 +19.9 
 
 22 
 
 +9.0 +20.6 +30.0 +40.1 +34.9 
 
 +15.4 
 
 22 a 
 
 +5.3 +18.7 +29.9 +40.1 +54.4 
 
 +13.9 
 
 23a 
 
 + 7.1 
 
 f20.3 +29.6 + 40.9 +43.1 
 
 +15.4 
 
 24a 
 
 + 8.6 +19.9 -hZe.6 +3^,0 +34.5 
 
 +14.6 
 
 25a 
 
 + 6.7 
 
 fl8.4 +29.8 +40.9 J-58.1 
 
 +16.1 
 
 26a 
 
 + 6.4 +14.2 +244 +24.4 
 
 +17.6 
 
■i^'m 
 

 TABLE 9 
 
 DATA OP TESTS, continued 
 SPECII.'IEIT 13B1 continued 
 
 
 103. 
 
 
 
 Load on Specimen - lb. 
 
 
 Base 
 
 Observation 
 
 30000 
 
 60000 
 
 90000 
 
 120000 
 
 152000 
 
 Moved 
 
 Outward 
 
 Unit Stress 
 
 on G. L. 27a 
 
 + 3,4 
 
 + 10.1 
 
 +14.3 
 
 + 21.0 
 
 + 26,6 
 
 ^12.4 
 
 28 a 
 
 0 
 
 + 1.1 
 
 + 4.5 
 
 + 10.1 
 
 + 24.0 
 
 + 24.0 
 
 51a 
 
 +1.1 
 
 - 4.5 
 
 ^ 9,0 
 
 - 7.3 
 
 -12.0 
 
 + 23.3 
 
 36a 
 
 -1.9 
 
 - 9.0 
 
 -17.6 
 
 -23,3 
 
 -22.9 
 
 + 3.0 
 
 36a 
 
 -1.5 
 
 - 4.9 
 
 -12.8 
 
 -16.9 
 
 -17.3 
 
 + 6.6 
 
 37a 
 
 -2.6 
 
 - 5.6 
 
 -12.4 
 
 -14.6 
 
 -13.9 
 
 + 0.4 
 
 17a 
 
 -1.5 
 
 -I- 3.4 
 
 + 2.6 
 
 + 6.4 
 
 + 14.3 
 
 - 3.8 
 
 16a 
 
 +2.6 
 
 + 11*3 
 
 +18.0 
 
 + 18.5 
 
 + 26.3 
 
 - 1.9 
 
 15a 
 
 +0.4 
 
 + 3.8 
 
 +18.8 
 
 + 27.4 
 
 + 31 .1 
 
 - 0.4 
 
 14 a 
 
 +1.5 
 
 +10.5 
 
 +20.3 
 
 + 27.8 
 
 +27.8 
 
 - 5.3 
 
 13a 
 
 +1.9 
 
 + 9.8 
 
 +18.8 
 
 + 22.4 
 
 +37.5 
 
 - 3.0 
 
 11a 
 
 +0.8 
 
 + 4.5 
 
 + 9.8 
 
 + 17.6 
 
 +20.3 
 
 - 1.9 
 
 10a 
 
 + 2,6 
 
 + 7.1 
 
 -^14.5 
 
 +20.3 
 
 + 20.3 
 
 + 2.3 
 
 9a 
 
 +4.1 
 
 + 8,3 
 
 +14.5 
 
 +16.1 
 
 +22, 9 
 
 - 2.3 
 
 8a 
 
 +2.6 
 
 + 7.5 
 
 + 7.9 
 
 +11.3 
 
 + 8.3 
 
 - 1,6 
 
 7a 
 
 +0,8 
 
 + 3.0 
 
 + 3.0 
 
 + 6.4 
 
 +10.9 
 
 + 0.4 
 
 6a 
 
 +0.8 
 
 + 1.1 
 
 + 1.1 
 
 + 6.4 
 
 +12 .4 
 
 - 0.4 
 
 2a 
 
 +1.1 
 
 - 0.4 
 
 - 8.6 
 
 - 8.3 
 
 + 6.4 
 
 f 0,4 
 
 2 
 
 +0.8 
 
 - 2.6 
 
 - 5.3 
 
 - 4.5 
 
 
 
 .0 
 
 9 
 
 +1.5 
 
 + 3.4 
 
 + 6.4 
 
 +10.3 
 
 
 + 4.9 
 
 11 
 
 +3.4 
 
 + 5.6 
 
 + 15.8 
 
 +38,1 
 
 +21.4 
 
 + 1.9 
 
 14 
 
 +4.5 
 
 +11.3 
 
 +18.0 
 
 +46 . 5 
 
 + 27.8 
 
 - 5.6 
 
 Unit Deform 
 
 on G.L. 101 
 
 -0.17 
 
 -0.39 
 
 -0.40 
 
 -1.47 
 
 -- — 
 
 — 
 
 102 
 
 -.13 
 
 - ,30 
 
 -.52 
 
 - .99 
 
 -1.03 
 
 -0.24 
 
 103 
 
 -.18 
 
 -.39 
 
 -.74 
 
 -1.05 
 
 -.90 
 
 + 1.79 
 
 104 
 
 -.09 
 
 -.30 
 
 -.13 
 
 - .20 
 
 — 
 
 +1.25 
 
 105 
 
 -.18 
 
 -.41 
 
 -.53 
 
 - .81 
 
 -.74 
 
 -.22 
 
 106 
 
 -.04 
 
 - .28 
 
 -.15 
 
 -.24 
 
 + .40 
 
 -.18 
 
 Deflection-in, 
 
 on Point D1 
 
 + .02 
 
 + .03 
 
 + .03 
 
 .04 
 
 -.35 
 
 +0.46 
 
 D2 
 
 + .04 
 
 + .03 
 
 + .05 
 
 .06 
 
 -.21 
 
 + • 30 
 
 D3 
 
 + .01 
 
 + . 02 
 
 + .04 
 
 .06 
 
 — 
 
 + .15 
 
 D4 
 
 -.01 
 
 0 
 
 0 
 
 .01 
 
 -.04 
 
 + . 02 
 
 D5 
 
 0 
 
 -.01 
 
 -.Gi 
 
 .01 
 
 + .01 
 
 -.02 
 
 D6 
 
 -.02 
 
 -.04 
 
 -.06 
 
 .10 
 
 — 
 
 -.18 
 
 D7 
 
 -.04 
 
 -.08 
 
 -.15 
 
 .25 
 
 — 
 
 -.23 
 
 DB 
 
 -.05 
 
 -.13 
 
 -.23 
 
 .40 
 
 -1.30 
 
 -.27 
 
 D9 
 
 -.06 
 
 -.16 
 
 -.32 
 
 .57 
 
 -1.67 
 
 -.32 
 
 DIO 
 
 -.08 
 
 -.19 
 
 -.37 
 
 .66 
 
 -1.73 
 
 -.36 
 
 Dll 
 
 -.08 
 
 -.20 • 
 
 -.39 
 
 .69 
 
 -1.67 
 
 9.36 
 
 D12 
 
 -.08 
 
 -.20. 
 
 -.39 
 
 .68 
 
 -1.56 
 
 -.35 
 
 D13 
 
 -.08 
 
 -.19 
 
 -.37 
 
 .66 
 
 -1.53 
 
 -.34 
 
« 
 
 
 : 
 
 
 
 
 i 
 
 * 1 
 
 4 
 
 r 
 
 
TABLE 9 104 . 
 
 LATA OP TESTS, continued 
 SPECBIEN 13B1, continued 
 
 Load on Specimen -lb, Base 
 
 Observations 
 
 30000 
 
 60000 
 
 90000 
 
 lEOOOO 
 
 152000 
 
 Moved 
 
 Outward 
 
 Deflection-in, 
 on Point D14 
 
 -.05 
 
 -.15 
 
 -.30 
 
 -.56 
 
 -1.21 
 
 -.27 
 
 D15 
 
 -.05 
 
 -.13 
 
 -.24 
 
 -.43 
 
 —.90 
 
 -.25 
 
 D16 
 
 -.04 
 
 -.08 
 
 -.15 
 
 -.28 
 
 -.56 
 
 -.21 
 
 D17 
 
 T . OE 
 
 -.04 
 
 -.06 
 
 — 
 
 — 
 
 -.14 
 
 L18 
 
 - 0 
 
 0 
 
 0 
 
 -.01 
 
 -.01 
 
 -.02 
 
 LI 9 
 
 0 
 
 0 
 
 0 
 
 0 
 
 + .02 
 
 + .01 
 
 L20 
 
 + .0E 
 
 + .03 
 
 + .06 
 
 + . 08 
 
 + .20 
 
 + .13 
 
 LEI 
 
 + ,0E 
 
 + .05 
 
 + .07 
 
 + .10 
 
 + .33 
 
 + .25 
 
 LEE 
 
 + .03 
 
 + .05 
 
 + .07 
 
 +.11 
 
 + .44 
 
 + .34 
 
 
 TABLE 9 
 
 LATA OP TESTS, continued 
 SPECIMEN 13B2 
 
 
 
 Load on Specimen -lb. 
 
 Base 
 
 Observations 
 
 30000 60000 90000 120000 138000 
 
 Moved 
 
 Outward 
 
 End thrust -lb. 
 
 5800 
 
 1500023000 
 
 30000 
 
 31500 
 
 8300 
 
 End Mov’t-in. 
 IMit stress 
 
 +0.04 
 
 +0.04 +0.05 +0.08 
 
 +0.07 
 
 +1.65 
 
 on G.L. 
 
 35 
 
 - 2.6 
 
 -11.3 
 
 -15.0 
 
 -21.4 
 
 -55.1 
 
 + 7.1 
 
 
 32 
 
 -3.8 
 
 -13.5 
 
 -18.4 
 
 - 22.1 
 
 -16.5 
 
 + 1.9 
 
 
 28 
 
 -2.3 
 
 - 3.0 
 
 + 6.0 
 
 +13.1 
 
 -«-10.3 
 
 +€ 0.6 
 
 
 22 
 
 + 8.6 
 
 + 21.0 
 
 + 36.0 
 
 + 54 . oj 
 
 Y.P. 
 
 +15.0 
 
 
 22 a 
 
 + 8,6 
 
 +19.1 
 
 +35.6 
 
 +5f. C 
 
 Y.P. 
 
 +19.1 
 
 
 25a 
 
 +4.9 
 
 +17.6 
 
 +31.9 
 
 +49,0 
 
 + 66 . 4 
 
 +15.0 
 
 
 26a 
 
 +2.3 
 
 + 13.9 
 
 + 26.6 
 
 +46.5 
 
 ^58.2 
 
 +16.9 
 
 
 27a 
 
 - 0.8 
 
 + 0.8 
 
 + 12.0 
 
 +20.3 
 
 +25.5 
 
 +10.5 
 
 
 28 a 
 
 -1.5 
 
 + 1.9 
 
 + 10.1 
 
 + 21.0 
 
 + 24.0 
 
 + 19.9 
 
 
 31a 
 
 -3.8 
 
 - 12,8 
 
 -14.3 
 
 +15.0 
 
 -12.7 
 
 + 11.6 
 
 
 32a 
 
 -4.5 
 
 - 7.5 
 
 -15.4 
 
 -24.0 
 
 -24.0 
 
 -1.9 
 
 
 35a 
 
 -2.3 
 
 - 9.8 
 
 -15.0 
 
 -21.7 
 
 -23.6 
 
 + 5.3 
 
 
 36a 
 
 -2.3 
 
 - 8.3 
 
 -14.6 
 
 -2 0.6 
 
 - 20.2 
 
 + 3.0 
 
 
 37a 
 
 -3.4 
 
 -7.9 
 
 -12.4 
 
 -17.6 
 
 -18.8 
 
 0 
 
 
 17a 
 
 -2.2 
 
 1.5 
 
 + 5.6 
 
 +14.6 
 
 +13.2 
 
 + 0.4 
 
 
 16a 
 
 0 
 
 + £.8 
 
 +16.5 
 
 +31.5 
 
 +30.0 
 
 +O .4 
 
 
 14a 
 
 +1.1 
 
 +12.4 
 
 + 25.5 
 
 +39.0 
 
 +36.8 
 
 + 0.4 
 
 
 13a 
 
 +1.5 
 
 ^ 7.5 
 
 + ES.1 
 
 +34.1 
 
 +34.8 
 
 - ^.3 
 
 
 11 a 
 
 + 0.8 
 
 + 2.5 
 
 +15.4 
 
 + 28.9 
 
 +27.8 
 
 - 0.8 
 
 
 10 a 
 
 - 2.6 
 
 + 6.0 
 
 + 12.0 
 
 + 13.3 
 
 + 0.8 
 
 - 4.9 
 
 
 9a 
 
 +1.5 
 
 + 7.5 
 
 + 12.0 
 
 + 9,0 
 
 +4.9 
 
 - 8.6 
 
 
 8 a 
 
 -0.4 
 
 + 3.4 
 
 + 3.8 
 
 4 . 3.8 
 
 -0,4 
 
 - 4.5 
 
 
 8 b 
 
 -1.1 
 
 + 0.8 
 
 + 4.1 
 
 + 3.8 
 
 +1.1 
 
 - 3.0 
 
 
 ©c 
 
 -0.4 
 
 + 3.4 
 
 + 9.8 
 
 ^10.3 
 
 + 8.6 
 
 - 4.5 
 
 
 7a 
 
 -3.0 
 
 - 4.1 
 
 + 0.4 
 
 + 4.9 
 
 +4.1 
 
 - 5.6 
 
i 
 

 TABLE 9 
 
 DATA OP TESTS, continued 
 SPECILCEU 13B2, cent. 
 
 
 
 105. 
 
 
 Load on Specimen - lb. 
 
 
 
 Base 
 
 OlDservations 
 
 30000 
 
 60000 
 
 90000 
 
 120000 
 
 138000 
 
 Moved 
 
 
 
 
 
 
 
 Outward 
 
 Unit Stress. 
 
 
 
 
 
 
 
 
 on G, L. 6a 
 
 -1.9 
 
 -1.9 . 
 
 -0.4 
 
 + 1.1 
 
 -2.6 
 
 
 -1.1 
 
 2a 
 
 -2.6 
 
 -8.6 
 
 -4.1 
 
 -9.8 
 
 -24.0 
 
 
 -2.6 
 
 2 
 
 -2.6 
 
 -8.6 
 
 -14.3 
 
 -11.3 
 
 -18.0 
 
 
 -4.5 
 
 9 
 
 +1.9 
 
 + 9*0 + 22 . 1 
 
 + 31.1 
 
 +48.4 
 
 
 -1.9 
 
 11 
 
 0 
 
 +9.0 +20.3 
 
 +32.6 
 
 + 72.0 
 
 
 -7.9 
 
 14 
 
 +4.5 
 
 +14.6 +29.6 
 
 +45.0 
 
 Y.P. 
 
 
 -6.4 
 
 IMit Deform. 
 
 
 
 
 
 
 
 
 on G.L. 101 
 
 +0.03 
 
 -0.23 
 
 -0.40 
 
 1 
 
 o 
 
 * 
 
 o 
 
 -1.40 
 
 
 + 6.50 
 
 102 
 
 - .03 
 
 -.40 
 
 -.55 
 
 -.63 
 
 -.65 
 
 
 -0.30 
 
 103 
 
 - .45 
 
 -.63 
 
 -1.03 
 
 -1.03 
 
 -2.05 
 
 
 + 6.90 
 
 104 
 
 + . 03 
 
 + .03 
 
 + . 03 
 
 + .68 
 
 -.68 
 
 
 + 1.70 
 
 105 
 
 - .55 
 
 -.18 
 
 -.30 
 
 -.80 
 
 -.95 
 
 
 -0.45 
 
 106 
 
 + .70 
 
 + .73 
 
 + .73 
 
 +1.05 
 
 +3.60 
 
 
 + 2.25 
 
 Deflections-in. 
 
 
 
 
 
 
 
 
 on Point D1 
 
 +0.01 
 
 +0.01 
 
 +0 * 02 
 
 + .03 
 
 +0.35 
 
 
 +0.43 
 
 D2 
 
 + .01 
 
 + .02 
 
 + .04 
 
 + .07 
 
 - -- 
 
 
 + .28 
 
 D3 
 
 + .01 
 
 4i.03 
 
 + .06 
 
 + .09 
 
 
 
 + .14 
 
 D6 
 
 -.01 
 
 -.04 
 
 -.07 
 
 -.12 
 
 -.30 
 
 
 -.13 
 
 D7 
 
 -.03 
 
 -.09 
 
 -.18 
 
 *-.30 
 
 -.65 
 
 
 -.19 
 
 D8 
 
 -.05 
 
 -.14 
 
 -.28 
 
 -.49 
 
 -1.00 
 
 
 -.24 
 
 D9 
 
 -.07 
 
 -.20 
 
 -.39 
 
 -.69 
 
 -1.36 
 
 
 -.20 
 
 DIO 
 
 -.08 
 
 -.23 
 
 -.45 
 
 -.79 
 
 -1.F8 
 
 
 -.32 
 
 Dll 
 
 -.08 
 
 -.24 
 
 -.48 
 
 -.54 
 
 -l.f4 
 
 
 -.33 
 
 D12 
 
 -.08 
 
 -.24 
 
 -.49 
 
 -.33 
 
 -1.80 
 
 
 -.32 
 
 D13 
 
 -.09 
 
 -.24 
 
 -.47 
 
 -.82 
 
 -1.73 
 
 
 -.32 
 
 DD4 
 
 -.07 
 
 -.21 
 
 -.42 
 
 -.74 
 
 -1.49 
 
 
 -.30 
 
 D15 
 
 -.05 
 
 -.16 
 
 -.32 
 
 -.57 
 
 -1.17 
 
 
 -.25 
 
 D16 
 
 -.03 
 
 -.10 
 
 -.19 
 
 -.30 
 
 -.74 
 
 
 -.18 
 
 D17 
 
 -.02 
 
 -.05 
 
 -.09 
 
 -.16 
 
 -.37 
 
 
 -.13 
 
 D20 
 
 + .01 
 
 + .04 
 
 + .06 
 
 + .11 
 
 + .32 
 
 
 + .11 
 
 D21 
 
 + .02 
 
 + .05 
 
 + .08 
 
 + .15 
 
 + .53 
 
 
 +.21 
 
 D22 
 
 + .03 
 
 + .05 
 
 + .08 
 
 + .16 
 
 + .72 
 
 
 + .31 
 
 
 
 TABLE 
 
 9 
 
 
 
 
 
 
 
 DATA OP TESTS, continued 
 
 
 
 
 
 SPECIMEN 13 ( 
 
 >1 
 
 
 
 
 
 
 Load 
 
 on Specimen - 
 
 lb. 
 
 
 Base 
 
 Observations 
 
 30000 
 
 60000 
 
 90000 120000 150000 182000 
 
 Moved 
 
 
 
 
 
 
 
 
 Outward 
 
 End Thrust -lb. 
 
 8200 
 
 17000 
 
 23600 
 
 25000 
 
 26700 
 
 48000 
 
 8200 
 
 End Mov't.-in. 
 
 + .02 
 
 + .02 
 
 + .02 
 
 + .02 
 
 o 
 
 -.03 
 
 +1.79 
 
 Unit Stress 
 
 
 
 
 
 
 
 
 on G. L. 37 
 
 -4.9 
 
 -9.4 
 
 -15.4 
 
 -22.1 
 
 -27.7 
 
 -56.3 
 
 -1.9 
 
 36 
 
 -4.1 
 
 -13.1 
 
 -20.3 
 
 -27.8 
 
 -38.3 
 
 r-p 
 
 0 
 
 33 
 
 -3.0 
 
 -6.4 
 
 -10.5 
 
 -17.3 
 
 -15.4 
 
 r-p 
 
 + 2.6 
 
> 
 
 V 
 
 J 
 
 \ 
 

 
 TABLE 9 
 
 TEST DATA, continued 
 SPECILIEU 15 C-1 cont. 
 
 
 106. 
 
 
 
 Load on Specimen 
 
 • 
 
 H 
 
 1 
 
 
 ' Base 
 
 Observations 
 
 30000 
 
 60600 POODO 12OOO0 
 
 150000 182000 
 
 Moved 
 
 
 
 
 
 Outward 
 
 Unit Stress 
 
 
 
 
 
 
 on G. I. 52 
 
 -2,5 
 
 -4.1 -6.4 -9.8 
 
 -12.4 
 
 -25.1 
 
 +2,6 
 
 51 
 
 -5,0 
 
 -5.4 - 6.8 -10.2 
 
 -10,9 
 
 -19.5 
 
 -0,4 
 
 50 
 
 +1,9 
 
 -5.0 - 6.8 -10.9 
 
 -11.6 
 
 +12.8 
 
 -0.8 
 
 27 
 
 +1,1 
 
 +0.8 + 2.6 + 4.9 
 
 + 15.1 
 
 +41.2 
 
 +26.7 
 
 26 
 
 + 2,5 
 
 +4,5 + 8.5 +12.8 
 
 + 20.5 
 
 +45. 0 
 
 + 27.7 
 
 25 
 
 +4,1 
 
 +9.4 +16.9 +21.0 
 
 + 51,8 
 
 Vf. 
 
 + 25,1 
 
 22 
 
 +8,5 
 
 +12 *0 +19,9 +29,5 
 
 +41.0 
 
 + 68.0 
 
 +16.5 
 
 22a 
 
 + 9,0 
 
 +15.4 +25.6 +52,6 
 
 +42.4 
 
 y:p. 
 
 + 21.4 
 
 27a 
 
 -2.6 
 
 - 2,3 + 1.5 + 5,5 
 
 +14.5 
 
 +42.7 
 
 +30.4 
 
 52a 
 
 0 
 
 - 2.6 - 5. 6 - 7.5 
 
 - 8.5 
 
 -12.8 
 
 + 6.4 
 
 56a 
 
 -4.9 
 
 -10.5 -17.7 -24.0 
 
 -29.6 
 
 -35.3 
 
 + 1.1 
 
 15a 
 
 +4.9 
 
 +12.4 +17,5 +25,5 
 
 +30.0 
 
 +32 .5 
 
 - 3.4 
 
 11a 
 
 + 1.9 
 
 + 1.1 + 5.0 + 6.0 
 
 + 9.0 
 
 y:r 
 
 - 0.4 
 
 8a 
 
 +1.1 
 
 + 5.4 + 7,5 +11.3 
 
 + 9.0 
 
 + .4 
 
 -15.9 
 
 2a 
 
 -2.6 
 
 - 6.0 - 9.0 -12.8 
 
 -15.4 
 
 -30.4 
 
 - 4.9 
 
 2 
 
 -5.0 
 
 - 5,6 - 8,6 - 9,0 
 
 -12.4 
 
 -18,0 
 
 + 1.1 
 
 6 
 
 -2.6 
 
 - 3.4 - 4.1 - 5.0 
 
 - 3.4 
 
 - 1.9 
 
 -10.5 
 
 V 
 
 -1.5 
 
 - 0,4 + 1.5 + 1.9 
 
 + 0 « 8 
 
 0 
 
 -11.6 
 
 8 
 
 +8 , 6 
 
 +10.2 +14.6 +22.1 
 
 + 21.8 
 
 +18.4 
 
 - 4.1 
 
 9 
 
 +1 , 6 
 
 0 + 5,4 + 9.0 
 
 + 7.5 
 
 +10.1 
 
 - 3.0 
 
 10 
 
 - 4 
 
 + ,4 +1.9 + 6.8 
 
 + 6.4 
 
 + 17.5 
 
 - 2.3 
 
 11 
 
 + 1.5 
 
 + 6.8 +12.4 +16.9 
 
 + 20.6 
 
 + 34.1 
 
 0 
 
 15 
 
 +1.9 
 
 + 1,5 + 2.3 +15.4 
 
 + 22.5 
 
 r.f? 
 
 -..1.9 
 
 14 
 
 -1.1 
 
 +3.0+ 7.9 +27.8 
 
 +40 . 8 
 
 t?. 
 
 - 1.5 
 
 15 
 
 +1.5 
 
 +10.5 +20.6 +28.5 
 
 +40.8 
 
 Y.e. 
 
 - 1.9 
 
 16 
 
 +1.1 
 
 +11.6 +19.9 +30.8 
 
 +41.6 
 
 + 55.0 
 
 - 1.2 
 
 Unit Deform, 
 
 
 
 
 
 
 on G. L. 101 
 
 -.48 
 
 -.54 -.81 -.95 
 
 -1.27 
 
 -1.23 
 
 — - 
 
 102 
 
 -.05 
 
 +.14 -.09 -.18 
 
 - .16 
 
 -.53 
 
 + .02 
 
 105 
 
 -.22 
 
 -.48 -.54 -.95 
 
 -1.03 
 
 
 + .46 
 
 104 
 
 -.05 
 
 -.11 -.20 0 
 
 - .56 
 
 -.36 
 
 + 5.7 
 
 105 
 
 -.16 
 
 -.01 -.14 -.18 
 
 - .11 
 
 -.66 
 
 + .04 
 
 106 
 
 -.01 
 
 0 0 + • 24 
 
 + .73 
 
 -.64 
 
 + .39 
 
 Deflection-in, 
 
 
 
 
 
 
 on Point D1 
 
 .05 
 
 + .05 + ,08 + ,11 
 
 + .22 
 
 — 
 
 + . 43 
 
 D2 
 
 + ,02 
 
 + .04 + , 0 % + .11 
 
 + .21 
 
 
 + . 28 
 
 D5 
 
 + .01 
 
 + .02 ^ .04 +.07 
 
 + .12 
 
 4. .31 
 
 + .16 
 
 D6 
 
 -.05 
 
 -.03 ..04 -.07 
 
 -.11 
 
 - .30 
 
 -.15 
 
 D7 
 
 -.02 
 
 -.05 _.08 -.15 
 
 -.22 
 
 _ .58 
 
 -.28 
 
 D8 
 
 -.04 
 
 -.09 .,14 -.23 
 
 -.36 
 
 _ .89 
 
 -.54 
 
 D9 
 
 -.04 
 
 -.11 ..21 -.32 
 
 -.49 
 
 -1.18 
 
 -.37 
 
 DIO 
 
 -.08 
 
 -.14 ..24 -.58 
 
 -.58 
 
 -1.40 
 
 -.40 
 
 Dll 
 
 -.08 
 
 -.15 ..25 -.40 
 
 -.61 
 
 -1..51 -.41 
 
 D12 
 
 —08 
 
 -.15 _.26 -.41 
 
 -.62 
 
 _1.55 
 
 -.42 
 
 D15 
 
 -.07 
 
 -.14 ..E4 -.39 
 
 -.58 
 
 -1.47 
 
 -.40 
 
 D14 
 
 -.05 
 
 -.11 -.19 -.21 
 
 -.46 
 
 -1.26 
 
 -.37 
 
 D15 
 
 -.05 
 
 -.09 -.15 -.24 
 
 -.37 
 
 - .97 
 
 -.35 
 
4 
 
 ,1 
 
 i 
 
107 
 
 TABLE 9 
 DATA OP TESTS 
 SPECIMEN 13 C-1, continued 
 
 
 
 Load 
 
 on Specimen -15 
 
 • 
 
 
 Base 
 
 Observations 
 
 30000 
 
 600U0 
 
 90000 
 
 lEOOOO 
 
 150000 
 
 18E000 
 
 Moved 
 
 Outward 
 
 Deflection-in. 
 on Point D16 
 
 -.OE 
 
 -.05 
 
 -.08 
 
 -.14 
 
 -.EE 
 
 -.63 
 
 -.S8 
 
 D17 
 
 -.OE 
 
 -.01 
 
 -.05 
 
 -.07 
 
 -.11 
 
 -.33 
 
 -.15 
 
 DEO 
 
 0 
 
 + .0S 
 
 + .04 
 
 + .05 
 
 + .09 
 
 + .30 
 
 + .13 
 
 DEI 
 
 + .0E 
 
 + .05 
 
 + .08 
 
 + .l£ 
 
 + .18 
 
 + .64 
 
 + .E8 
 
 DEE 
 
 + .0S 
 
 + .05 
 
 -«-.08 
 
 + .1E 
 
 + .S1 
 
 + .81 
 
 + .41 
 
 TABLE 9 
 DATA OP TESTS 
 SPECIIvElT 13 C-E 
 
 
 Load on 
 
 Specimen - lb. 
 
 Base 
 
 Observations 
 
 30000 
 
 60000 
 
 90000 
 
 12000 148000 
 
 Moved 
 
 Outward 
 
 End Thrust-lb. 
 
 11700 
 
 16750 
 
 E5E00 
 
 ^3500 30500 
 
 13700 
 
 End Mov*t-in. 
 
 +0.0E 
 
 +0.03 +0.04 
 
 +0.03 +0.03 
 
 +1.88 
 
 Unit Stress 
 on G. L. 37 
 
 36 
 33 
 3E 
 31 
 30 
 
 -E.3 
 
 -3.4 
 
 -3.7 
 
 -1.1 
 
 -1.1 
 
 -3.0 
 
 -5.6 
 
 -7.9 
 
 -4.1 
 
 -3.0 
 
 -S.3 
 
 -4.1 
 
 “13.1 
 “17.6 
 “ 9.0 
 “ 7.9 
 “ 6.8 
 “ 6.8 
 
 -15.0 -13.9 
 
 -E9.1 -46.1 
 
 -11.3 - 6.8 
 
 - 9.8 -10.1 
 
 -9.4 - 8.6 
 
 - 9.8 - 7.5 
 
 +3.8 
 + 3.0 
 + 2.3 
 +1.1 
 -1.1 
 -9.4 
 
 26 
 
 + .8 
 
 + 1.9 +1S.4 
 
 EE 
 
 -^8.3 
 
 a.^2.8 +-22.1 
 
 EEa 
 
 +8.6 
 
 + 13.5 +24.4 
 
 E7a 
 
 -2.3 
 
 + .4 + 5*6 
 
 32a 
 
 -E.6 
 
 - 5.3 “ 7.5 
 
 36a 
 
 —4 . 9 
 
 -13.9 
 
 15a 
 
 +4.9 
 
 + 13.5 +21.4 
 
 11a 
 
 +1.1 
 
 + 1.5 + -^'2 
 
 8a 
 
 +E.6 
 
 + 3.8 + 
 
 2a 
 
 -5.6 
 
 - 7.9 - '<^.9 
 
 2 
 
 -4.1 
 
 _ 4.9 “ ^*6 
 
 6 
 
 -2.3 
 
 - 3.0 “3.4 
 
 7 
 
 -1.9 
 
 - .4 + 1-2 
 
 8 
 
 +2.6 
 
 +7.9 + 6*0 
 
 9 
 
 +0.4 
 
 +1.9 + 3.4 
 
 10 
 
 «0.4 
 
 + ^ 
 
 11 
 
 +E.6 
 
 +11.3 +4.2 
 
 13 
 
 + 0 
 
 +1.5 4.5 
 
 14 
 
 ->-1.9 
 
 +4.9 +13.9 
 
 15 
 
 +2.6 
 
 +10.1 ■^^2. 9 
 
 16 
 
 +E.6 
 
 +13.5 
 
 17 
 
 + 2.6 
 
 + 6.0 +21.4 
 
 + 19.5 
 
 +40.5 
 
 + 19.1 
 
 + 33.8 
 
 + 57.8 
 
 + 18.0 
 
 ^33.8 
 
 + 60.4 
 
 + 19.1 
 
 + 4.9 
 
 + 25.9 
 
 + 19.1 
 
 -IE. 4 
 
 -12.4 
 
 - 3.8 
 
 -33 .0 
 
 -60.4 
 
 + 3.0 
 
 + 31.1 
 
 + 21.0 
 
 - 5.6 
 
 + 7.5 
 
 + 9.8 
 
 - 1.1 
 
 + 13.1 
 
 - 3.4 
 
 -12.8 
 
 -14.6 
 
 -21.8 
 
 - 6.0 
 
 -12.8 
 
 -18.4 
 
 - 4.1 
 
 + 0,8 
 
 - 4.5 
 
 - 6.8 
 
 + 3.0 
 
 - 6.0 
 
 - 7.5 
 
 + 10.9 
 
 -'3.0 
 
 -14.3 
 
 + 5.3 
 
 - 3.0 
 
 - 7.1 
 
 + 4.9 
 
 - 1.1 
 
 - 3.4 
 
 + 7.5 
 
 + 4.-9 
 
 - .8 
 
 + 15.8 
 
 + 17.6 
 
 -2.3 
 
 +31.5 
 
 + 31.1 
 
 - 0.4 
 
 + 34. 9 
 
 +31 .9 
 
 - 4.1 
 
 +49.2 
 
 -^35'..9 
 
 - 2.3 
 
 +48.4 
 
 +51..7 
 
 - 1.1 
 
4 ' 
 
 \ 
 
 ( 
 

 
 
 
 
 
 
 108. 
 
 
 
 
 TABLE 
 
 9 
 
 
 
 
 
 
 
 Data of 
 
 Test 
 
 
 
 
 
 
 spEcncau 
 
 13 C-2 
 
 continued 
 
 
 
 
 
 Load on Specimen - 
 
 lb. 
 
 Base 
 
 Oliservations 
 
 30000 
 
 60000 90000 
 
 120000 
 
 148000 
 
 Moved 
 
 
 
 
 
 
 
 
 Outward 
 
 Unit Deform 
 
 
 
 
 
 
 
 
 on Gr«D* 101 
 
 -.35 
 
 -.35 - 
 
 .75 
 
 -.67 
 
 -.90 
 
 — 
 
 102 
 
 0 
 
 -.32 - 
 
 .37 
 
 -.02 
 
 -.05 
 
 + .22 
 
 103 
 
 -.20 
 
 -.50 - 
 
 .75 
 
 -.25 
 
 -.25 
 
 + .63 
 
 104 
 
 -.10 
 
 -.12 - 
 
 .40 
 
 + .52 
 
 -5 
 
 — 
 
 105 
 
 + .07 
 
 -.17 - 
 
 .40 
 
 -.12 
 
 -.28 
 
 -.12 
 
 106 
 
 + .05 
 
 -.15 - 
 
 .20 
 
 + .52 
 
 
 + .38 
 
 Deflect ion- in* 
 
 
 
 
 
 
 
 
 on Point D1 
 
 + .01 
 
 + .04 + 
 
 .09 
 
 + .13 
 
 + .53 
 
 + .48 
 
 D2 
 
 + .01 
 
 + . 04 + 
 
 .08 
 
 + .16 
 
 ++40 
 
 + .32 
 
 D3 
 
 + .01 
 
 + f 02 + 
 
 .06 
 
 + .10 
 
 + .24 
 
 + .16 
 
 D6 
 
 -.01 
 
 -.02 - 
 
 .05 
 
 -.08 
 
 -.20 
 
 -.13 
 
 D7 
 
 -.02 
 
 -.04 - 
 
 t09 
 
 -.16 
 
 -.40 
 
 -.27 
 
 D 8 
 
 -.04 
 
 -.08 - 
 
 .15 
 
 -.27 
 
 -.61 
 
 -.32 
 
 D9 
 
 -.07 
 
 -.12 - 
 
 .24 
 
 -.40 
 
 -.86 
 
 -.37 
 
 DlU 
 
 -.08 
 
 -.14 - 
 
 .27 
 
 -.46 
 
 -.95 
 
 -.40 
 
 Dll -.09 
 
 -.15 - 
 
 .29 
 
 -.48 
 
 -1.00 
 
 -.42 
 
 D12 
 
 -.09 
 
 -.16 - 
 
 .29 
 
 -.49 
 
 -l.OZ 
 
 -.42 
 
 D13 -.08 
 
 -.14 - 
 
 .27 
 
 -.46 
 
 -.97 
 
 -.42 
 
 D14 
 
 -.07 
 
 -.12 - 
 
 .23 
 
 -.41 
 
 -.89 
 
 -.39 
 
 D15 
 
 -.04 
 
 -.08 - 
 
 16 
 
 -.29 
 
 -.65 
 
 -.36 
 
 D16 -.03 
 
 -.06 - 
 
 .10 
 
 -.18 
 
 — 
 
 -.32 
 
 D17 
 
 -.02 
 
 -.03 - 
 
 .06 
 
 - r 09 
 
 -.24 
 
 -.18 
 
 D20 
 
 + .01 
 
 + .03 + 
 
 + 
 
 .04 
 
 + .08 
 
 + .21 
 
 + .16 
 
 
 
 
 TABLE 9 
 
 
 
 
 
 
 
 DA.TA OP TESTS 
 
 
 
 
 
 SPECIIM 13D1. 
 
 
 
 
 
 
 
 Load 
 
 on Specimen$-lb. 
 
 Base 
 
 Observations 
 
 300006000090000120000150000180000208500 
 
 Moved 
 
 End Thrust-lb. 
 
 90001750028400 
 
 37300 
 
 50000 
 
 57300 58500 
 
 17500 
 
 End Mov't.-in. 
 
 + 0 . 01 +C 
 
 1.03+0.04 
 
 +0.07 
 
 +0 .08 
 
 +0.05 +0.06 
 
 + 2.04 
 
 Unit Stress 
 
 - 3.8 
 
 • 
 
 7.5-12.4 
 
 -16.1 
 
 -24.0 
 
 -34.5 -37.9 
 
 + 4.5 
 
 on G.L. 37 
 
 
 
 
 
 
 
 ' 
 
 32 
 
 - 4.1 
 
 — 
 
 4.9- 9.8 
 
 -15.0 
 
 -19.5 
 
 -23.3 -23.1 
 
 + 3.4 
 
 27 
 
 0 
 
 
 2.6- 1.5 
 
 + 0.4 
 
 + 3.0 
 
 + 4.5 +13.5 
 
 + 30.0 
 
 22 
 
 + 6.8+10.5+18.0 
 
 +19.5 
 
 + 27.8 
 
 +33.4 +48.4 
 
 +34.5 
 
 22a 
 
 + 8.6 
 
 -^11.6+18.4 
 
 + 21.0 
 
 + 28.5 
 
 +34.5 +67.9 
 
 +35.7 
 
 25a 
 
 + 4.1+ 
 
 7.1+10.9 
 
 + 23.3 
 
 + 34.5 
 
 +40.5 +51.4 
 
 +46.1 
 
 26a 
 
 + 1.9+ 
 
 3.8+ 0.4 
 
 +36.8 
 
 +38.6 
 
 +38.3 +55.9 
 
 — 
 
 27a 
 
 - 0.4 
 
 — 
 
 0.8- 3.4 
 
 — 4.5 
 
 - 3.0 
 
 - 1.1 +13.9 
 
 + 33.0 
 
 28a 
 
 - 1.9 
 
 — 
 
 3.8- 8.3 
 
 - 7.9 
 
 - 8.6 
 
 — 9.8 + 9.0 
 
 + 27.8 
 
 31a 
 
 - 1.9 
 
 
 7.1-10.9 
 
 -14.3 
 
 -18.0 
 
 -24.4 -20.1 
 
 + 7.5 
 
 32a 
 
 - 1.5 
 
 
 6.4- 8.6 
 
 -12.8 
 
 -17.3 
 
 -22.5 -21.8 
 
 + 1.9 
 

 Ji 
 
 ! 
 
 A 
 
 i 
 
110 . 
 
 TABLE 9 
 
 BATA OP TESTS, Continued. 
 
 SPEC lira 15B2, 
 
 OLserv’ 
 
 
 
 
 Load on Specimen- 
 
 •lb. 
 
 
 Base 
 
 "^30000 
 
 60000 
 
 90000 120000 
 
 150000 
 
 180000 
 
 210000 
 
 232000 
 
 ivio V e 0. 
 
 Out 
 
 End 
 
 Thrust, 
 
 a.12000 
 
 27500 
 
 31500 
 
 41700 
 
 50000 
 
 59200 
 
 67100 
 
 66300 
 
 16800 
 
 End 
 
 Mov't, +0.02 
 Unit Stress 
 
 +0.02 
 
 +0.02 
 
 +0.05 
 
 +0.06 
 
 +0.06 
 
 +0.07 
 
 +0.08 
 
 +1.74 
 
 on G.L. 
 
 37 
 
 - 5.6 
 
 - 9.4 
 
 - 15.4 
 
 -22.9 
 
 -27.8 
 
 -36.4 
 
 -48,4 
 
 .X K. 
 
 + 8.6 
 
 32 
 
 - 3.4 
 
 - 7.1 
 
 -10.9 
 
 -13.9 
 
 -21.0 
 
 -22.9 
 
 -27.8 
 
 -27.7 
 
 + 5.3 
 
 27 
 
 - 2.3 
 
 - 5.3 
 
 - 6.0 
 
 - 5.6 
 
 - 5.6 
 
 - 4.9 
 
 - 0.4 
 
 +16.5 
 
 + 27.4 
 
 22 
 
 + 5.3 
 
 + 8.3 
 
 + 8.6 
 
 +18.0 
 
 + 22.5 
 
 + 28.9 
 
 +37.2 
 
 + 59 . 2 
 
 + 27.0 
 
 22a 
 
 + 6.4 
 
 + 8.3 
 
 + 12.4 
 
 + 16.9 
 
 + 23.3 
 
 + 28.9 
 
 +35.6 
 
 +55,5 
 
 + 27.5 
 
 23a 
 
 + 6.4 
 
 ^ 7.5 
 
 + 15.8 
 
 + 22.5 
 
 + 29.3 
 
 +33.8 
 
 + 42.4 
 
 y:p. 
 
 + 34.1 
 
 24 a 
 
 + 3.8 
 
 + 7.9 
 
 + 15.8 
 
 + 20.3 
 
 + 25.5 
 
 +31,9 
 
 + 39,0 
 
 - V.p . 
 
 +35.3 
 
 25a 
 
 + 2.3 
 
 + 3.4 
 
 + 10.5 
 
 + 16.9 
 
 + 20.7 
 
 + 26.6 
 
 +34.5 
 
 + 59.6 
 
 + 28.8 
 
 26a 
 
 - 0.4 
 
 - 1.5 
 
 + 2.6 
 
 +17.6 
 
 +19.9 
 
 + 22.5 
 
 +30,0 
 
 + 63,4 
 
 + 64.1 
 
 27a 
 
 - 6.0 
 
 - 5.6 
 
 - 0.4 
 
 + 0.8 
 
 2.3 
 
 + 5.3 
 
 +12.4 
 
 +31.5 
 
 + 35.6 
 
 28a 
 
 - 2.6 
 
 - 6.0 
 
 - 8.6 
 
 - 7.1 
 
 - 6.8 
 
 - 5.6 
 
 - 0.8 
 
 + 25,5 
 
 +36.4 
 
 31a 
 
 - 4.1 
 
 -11.3 
 
 - 13.9 
 
 -1^.6 
 
 -18.0 
 
 -19.5 
 
 -23.3 
 
 -23.3 
 
 + 9.4 
 
 32a 
 
 - 3.0 
 
 - 8.6 
 
 - 11.6 
 
 -13.9 
 
 -18.0 
 
 -19.5 
 
 -25.5 
 
 -24.4 
 
 +11.6 
 
 35a 
 
 - 4.1 
 
 -10.9 
 
 - 15.0 
 
 -21.0 
 
 -25.9 
 
 -33.4 
 
 -40.9 
 
 -45.4 
 
 + 7.9 
 
 36a 
 
 -7.9 
 
 -13.5 
 
 - 14.6 
 
 -20.0 
 
 -25.1 
 
 -33.0 
 
 -46.1 
 
 -51.4 
 
 + 4.1 
 
 37a 
 
 - 5.6 
 
 -12.0 
 
 -12.0 
 
 -20.7 
 
 -24.7 
 
 -32.3 
 
 -44.3 
 
 -48.0 
 
 + 4.9 
 
 17a 
 
 + 1.5 
 
 + 9.4 
 
 + 8.3 
 
 + 16.5 
 
 +19.5 
 
 + 23.3 
 
 +31.5 
 
 +34.5 
 
 - 2.6 
 
 16a 
 
 + 3.0 
 
 +13.8 
 
 + 9.8 
 
 +17.3 
 
 + 21.8 
 
 + 27.0 
 
 +39.4 
 
 +41.3 
 
 - 2.3 
 
 15a 
 
 + 1.5 
 
 +11.6 
 
 + 9.8 
 
 +18.4 
 
 + 23.3 
 
 +33,8 
 
 + 53.0 
 
 •YCf. 
 
 - 1.1 
 
 14a 
 
 + 2.6 
 
 +10.2 
 
 + 9.0 
 
 +17.3 
 
 + 20.6 
 
 + 33,4 
 
 +48,4 
 
 + 52.2 
 
 - 1.1 
 
 13a 
 
 + 1.5 
 
 + 4.1 
 
 + 7.1 
 
 + 22.1 
 
 +36.8 
 
 +49.2 
 
 + 68,3 
 
 -Y.f. 
 
 - 0.4 
 
 11a 
 
 + 0.8 
 
 + 5.3 
 
 + 1.1 
 
 +10.1 
 
 + 13.5 
 
 + 18.8 
 
 +31.5 
 
 +33.8 
 
 - 1.9 
 
 10a 
 
 + 3.0 
 
 + 1.9 
 
 + 1.1 
 
 + 6.8 
 
 + 8.6 
 
 +10.9 
 
 +13.9 
 
 +13.9 
 
 - 3.4 
 
 9a 
 
 + 2.3 
 
 +12.7 
 
 + 15.8 
 
 +18.8 
 
 + 20.3 
 
 + 25.9 
 
 + 28.9 
 
 + 22.9 
 
 0 
 
 8a 
 
 + 1.1 
 
 + 9.8 
 
 + 9.4 
 
 +15.4 
 
 + 19.9 
 
 + 24,0 
 
 ■^26.6 
 
 +18 . 8 
 
 - 3.8 
 
 7a 
 
 + 0.8 
 
 + 5.3 
 
 + 2.3 
 
 + 13.5 
 
 + 15.4 
 
 + 18.8 
 
 +20.3 
 
 +19.9 
 
 + 0.4 
 
 6a 
 
 - 0.8 
 
 + 3.0 
 
 - 2.6 
 
 + 4.9 
 
 + 8.6 
 
 + 12.0 
 
 +16.1 
 
 +15.4 
 
 - 4.5 
 
 2a 
 
 -Q.4 
 
 3.4 
 
 - 6.4 
 
 - 4.8 
 
 - 4.9 
 
 - 5.3 
 
 - 5.6 
 
 - 0.8 
 
 - 2.6 
 
 2 
 
 - 3.0 
 
 - 6.4 
 
 - 9.8 
 
 - 8.3 
 
 - 8.3 
 
 - 9.4 
 
 -10.2 
 
 - 4.9 
 
 - 4.5 
 
 8 
 
 + 1.9 
 
 + 6.0 
 
 + 6.8 
 
 + 21.8 
 
 + 24.0 
 
 +31.4 
 
 +37.9 
 
 +47.6 
 
 + 2,3 
 
 11 
 
 + 2.3 
 
 + 2.3 
 
 + 2.6 
 
 + 9.8 
 
 + 15.4 
 
 + 22.5 
 
 + 30.4 
 
 + 36.8 
 
 - 3.0 
 
 17 + 2.3 + 9.8 
 
 Unit Beform.on 
 
 + 9.4 
 
 +19.1 
 
 + 26.6 
 
 +33.0 
 
 +42.4 
 
 -V.K 
 
 . 2.6 
 
 G.L. 101 
 
 -0.25 
 
 -0.44 
 
 -0.52 
 
 -0.61 
 
 -0.81 
 
 -0.94 
 
 -1.28 
 
 -1.54 
 
 -1.39 
 
 102 
 
 -0.05 
 
 -0.24 
 
 -0.31 
 
 -0.44 
 
 -0.59 
 
 -0.66 
 
 -0.72 
 
 -0.93 
 
 +0.04 
 
 103 
 
 -0.18 
 
 -0.35 
 
 -0.37 
 
 -0.70 
 
 -0.81 
 
 -1.18 
 
 -1.18 
 
 -1.18 
 
 +0.13 
 
 104 
 
 -0.12 
 
 -0.20 
 
 -0.17 
 
 -0.40 
 
 -0.40 
 
 -0.54 
 
 -0.63 
 
 -0.81 
 
 +0.15 
 
 105 
 
 -0.20 
 
 -0.20-0.26 
 
 -0.40 
 
 -0.37 
 
 -0.31 
 
 -0.35 
 
 -0.72 
 
 +0.04 
 
 106 
 
 -0.10 
 
 -0.15 
 
 -0.18 
 
 -0.26 
 
 -0.24 
 
 -0.28 
 
 -0.24 
 
 -0.40 
 
 +0.09 
 

 
 
 TABLE 9 
 
 DATA OF TESTS, Continued . 
 SPECIHEE 13D2,Cont. 
 
 
 
 111. 
 
 
 
 
 
 Load 
 
 on Specimen- 
 
 lb. 
 
 
 Base 
 
 Observ’ 
 
 n 
 
 
 
 
 
 
 
 
 . Moved 
 
 
 30000 
 
 60000 
 
 90000 120000 
 
 150000 
 
 180000 
 
 210000 
 
 232000 
 
 Out 
 
 Deflection at 
 
 
 
 
 
 
 
 
 
 pt.Dl 
 
 + .02 
 
 + . 04 
 
 + .04 
 
 + .05 
 
 + .08 
 
 + .10 
 
 + .14 
 
 — 
 
 + .38 
 
 D2 
 
 + .01 
 
 + .03 
 
 + .04 
 
 + .05 
 
 + .08 
 
 + .11 
 
 + .14 
 
 + .45 
 
 + .26 
 
 D3 
 
 + .01 
 
 ^.02 
 
 + .03 
 
 + . 04 
 
 + .06 
 
 + .08 
 
 + .10 
 
 + .27 
 
 + .14 
 
 D6 
 
 -.01 
 
 -.01 
 
 -.02 
 
 -.03 
 
 -.05 
 
 -.06 
 
 -.09 
 
 -.21 
 
 -.12 
 
 D7 
 
 -.03 
 
 -.05 
 
 -.06 
 
 -.09 
 
 -.12 
 
 -.16 
 
 -.21 
 
 -.46 
 
 -.25 
 
 D8 
 
 -.03 
 
 -.08 
 
 -.09 
 
 -.15 
 
 -.21 
 
 -.27 
 
 -.36 
 
 — 
 
 -.35 
 
 D9 
 
 -.05 
 
 -.12 
 
 -.14 
 
 -.23 
 
 -.30 
 
 -.39 
 
 -.53 
 
 -1.05 
 
 -.42 
 
 DIO 
 
 -.07 
 
 -.15 
 
 -.18 
 
 -.28 
 
 -.36 
 
 -.47 
 
 -.62 
 
 -1.22 
 
 -.47 
 
 Dll 
 
 -.06 
 
 -.15 
 
 -.18 
 
 -.29 
 
 -.38 
 
 -.50 
 
 -.66 
 
 -1.32 
 
 -.47 
 
 D12 
 
 -.07 
 
 -.16 
 
 -.19 
 
 -.30 
 
 -.39 
 
 -.51 
 
 -.68 
 
 -1.36 
 
 -.50 
 
 D13 
 
 -.05 
 
 -.15 
 
 -.18 
 
 -.29 
 
 -.38 
 
 -.47 
 
 -.65 
 
 -1.33 
 
 -.48 
 
 D14 
 
 -.05 
 
 -.13 
 
 -.15 
 
 -.25 
 
 -.34 
 
 -.44 
 
 -.58 
 
 -1.18 
 
 -.44 
 
 D15 
 
 -.03 
 
 -.08 
 
 -.10 
 
 -.17 
 
 -.23 
 
 -.30 
 
 -.41 
 
 -.88 
 
 -.37 
 
 D16 
 
 -.03 
 
 -.06 
 
 -.07 
 
 -.12 
 
 -.15 
 
 -.19 
 
 -.26 
 
 -.57 
 
 -.29 
 
 D17 
 
 -.02 
 
 -.04 
 
 -.04 
 
 -.06 
 
 -.07 
 
 -.10 
 
 -.13 
 
 -.30 
 
 -.16 
 
 D20 
 
 + .01 
 
 + .03 
 
 + .03 
 
 + .06 
 
 + .07 
 
 + .08 
 
 + .11 
 
 + .23 
 
 + .14 
 
 D21 
 
 + .02 
 
 + .04 
 
 + .06 
 
 + .08 
 
 + .10 
 
 + .13 
 
 + .18 
 
 + .43 
 
 + .27 
 
 D22 
 
 + .02 
 
 + .05 
 
 + .06 
 
 + .09 
 
 + .12 
 
 + .15 
 
 + .20 
 
 + .57 
 
 + .40 
 
 
 
 
 
 DATA OF 
 
 TESTS 
 
 
 
 
 
 
 
 
 
 SPECIMEN 
 
 13E1 
 
 
 
 
 
 
 
 
 
 Load 
 
 on Specimen 
 
 - lb. 
 
 
 
 
 1 • 
 
 
 
 
 
 
 
 
 
 UDservaxion 
 
 
 
 
 
 
 
 
 
 
 
 
 30000 
 
 60000 
 
 
 77000 
 
 
 
 End Thrust ,1b. 
 
 
 8000 
 
 10100 
 
 
 14500 
 
 
 
 End Movement, in. 
 
 0.06 
 
 0.05 
 
 
 0.05 
 
 
 
 Unit Stress on 
 
 
 
 
 
 
 
 
 Gage Line 37 
 
 
 - 
 
 1.9 
 
 - 4.9 
 
 
 - 6,4 
 
 
 
 
 36 
 
 
 — 
 
 4.9 
 
 -.9.0 
 
 
 -11.3 
 
 
 
 
 35 
 
 
 — 
 
 6.0 
 
 -12.0 
 
 
 -14.1 
 
 
 
 
 34 
 
 
 - 
 
 7.9 
 
 -15.0 
 
 
 -18.0 
 
 
 
 
 33 
 
 
 - 
 
 9.0 
 
 -16.1 
 
 
 -19,1 
 
 
 
 
 30 
 
 
 - 
 
 4.1 
 
 - 7.1 
 
 
 - 7.9 
 
 
 
 
 29 
 
 
 — 
 
 3.8 
 
 - 3.4 
 
 
 + 2.6 
 
 
 
 
 28 
 
 
 — 
 
 2.3 
 
 + 0.7 
 
 
 + 6.8 
 
 
 
 
 27 
 
 
 + 
 
 4.1 
 
 +12.4 
 
 
 +19.5 
 
 
 
 
 26 
 
 
 4- 
 
 9.0 
 
 + 22.5 
 
 
 + 29.2 
 
 
 
 
 25 
 
 
 + 15.0 
 
 + 32.6 
 
 
 +42.8 
 
 
 
 
 22 
 
 
 + 17.2 
 
 +32.3 
 
 
 +43.6 
 
 
 
 
 22a 
 
 +19.1 
 
 + 37.5 
 
 
 + 52.1 
 
 
 
118 . 
 
 TABLE 9 
 
 BATA OP TESTS, Continued 
 SPECniEil 15E1, Gont. 
 
 OLserv'n 
 
 Load on Specimen- lb. 
 
 on 
 
 Specimen 
 
 . 
 
 H 
 
 1 
 
 30000 
 
 60000 
 
 77000 
 
 
 30000 
 
 60000 
 
 77000 
 
 Unit Stress on 
 
 
 
 Beflection 
 
 at 
 
 
 
 G, L . 
 
 
 
 
 Point 
 
 
 
 
 30a 
 
 - 9.0 
 
 -12.8 
 
 - 1.5 
 
 B1 
 
 + .04 
 
 + .09 
 
 + .31 
 
 33a 
 
 - 8.6 
 
 -16.1 
 
 -12.4 
 
 B2 
 
 + .05 
 
 + .09 
 
 + . 26 
 
 13a 
 
 + 10.5 
 
 +19.1 
 
 +21 . 8 
 
 B3 
 
 + .03 
 
 + .07 
 
 + .18 
 
 10a 
 
 + 9.4 
 
 + 19.1 
 
 + 25.4 
 
 B4 
 
 + .02 
 
 + .04 
 
 + .10 
 
 2a 
 
 9.4 
 
 -21.0 
 
 -11.6 
 
 B5 
 
 -.01 
 
 -.03 
 
 -.08 
 
 2 
 
 -10.1 
 
 -21.0 
 
 + 9.0 
 
 B6 
 
 -.07 
 
 + .14 
 
 -.31 
 
 6 
 
 - 4.5 
 
 - 9.0 
 
 - 1.5 
 
 B7 
 
 -.12 
 
 -.25 
 
 -.55 
 
 7 
 
 + 3.4 
 
 + 4.5 
 
 + 12.4 
 
 B8 
 
 -.17 
 
 -.35 
 
 -.79 
 
 8 
 
 + 1.9 
 
 + 4.1 
 
 + 9.0 
 
 B9 
 
 -.21 
 
 -.45 
 
 -1.02 
 
 9 
 
 + 4.5 
 
 + 9.0 
 
 + 10.9 
 
 BIO 
 
 -.25 
 
 -.52 
 
 -1.15 
 
 10 
 
 + 6.4 
 
 +14.2 
 
 +16.5 
 
 Bll 
 
 -.26 
 
 -.55 
 
 -1.36 
 
 11 
 
 + 9.0 
 
 + 17.6 
 
 + 24.8 
 
 B12 
 
 -.26 
 
 -.55 
 
 -1.46 
 
 12 
 
 + 7.1 
 
 +15.0 
 
 + 13.9 
 
 B13 
 
 -.24 
 
 -.52 
 
 -1.43 
 
 13 
 
 + 8.2 
 
 + 16.9 
 
 + 19.5 
 
 B14 
 
 -.22 
 
 -.46 
 
 -1.23 
 
 14 
 
 + 5.6 
 
 + 12.0 
 
 + 14.6 
 
 B15 
 
 -.17 
 
 -.35 
 
 — .88 
 
 15 
 
 + 6.0 
 
 +12.4 
 
 + 15.4 
 
 B16 
 
 -.12 
 
 -.25 
 
 -.57 
 
 16 
 
 + 1.5 
 
 + 6.8 
 
 +10.1 
 
 B17 
 
 -.06 
 
 -.13 
 
 -.27 
 
 17 
 
 + 3.9 
 
 + 5.3 
 
 ^+ 6.4 
 
 B18 
 
 -.01 
 
 -.02 
 
 -.01 
 
 
 
 
 
 B19 
 
 + .02 
 
 + .02 
 
 + .01 
 
 Unit Beformation 
 
 
 
 B20 
 
 + .03 
 
 + .04 
 
 -.03 
 
 on (x. L. 
 
 
 
 
 B21 
 
 + .06 
 
 -.06 
 
 -.07 
 
 101 
 
 -0.22 
 
 -0.37 
 
 -0.64 
 
 B22 
 
 + .07 
 
 + .06 
 
 -.14 
 
 102 
 
 -0i44 
 
 -0.92 
 
 -1.60 
 
 
 
 
 
 103 
 
 -0.28 
 
 -0.39 
 
 -0.53 
 
 
 
 
 
 104 
 
 -0.05 
 
 -0.13 
 
 -0.09 
 
 
 
 
 
 105 
 
 -0.02 
 
 +0.97 
 
 +2.39 
 
 
 
 
 
 106 
 
 -0.09 
 
 +0.02 
 
 0 
 
 
 
 
 
•’€/ ^9-/ ^9/ ^// 
 
 
 
 
 
 VSJ 
 
 N 
 
 QCi 
 
 O) 
 
 Si 
 
 
 ^ a 
 
 a 
 
 
 'O 
 
 d 
 
 n 
 
 tt 
 
 <5 
 
 'J^ 
 
 N 
 
 M 
 
 N 
 
 S3 
 
 js 
 
 Si 
 
 "t-e »s^ ‘’9e 
 
 
 
 o 
 
 k 
 
 ^ f 
 
 ^ I 
 
 I 
 
 |l 
 
 1 2,^ ^ 
 
 
 
 ii: 
 
 irC S€ 9£ l€ 
 
 a 
 
 a 
 
 N 
 
 o 
 
 
 -k 
 
 'i> 
 
 % 
 
 5; 
 
 Z/ £/ tr/ 9/ 9/ Z/ 
 
 
 Fig. 51. Position of Gage Lines and Cracks, Specimen 15A1 
 
?r • TU_-.djl^i»SC. „ -sSisi,^j!4*^,tiI--|»4. I: jCJitia- m'& ., ^ . T s:..::.isrffcs!t:^ J5 »i3 e / > »-^' '- -- -V ^1 •... 
 
 ^ SXI 
 
 P: 
 
 t 
 
 K 
 
 'Vf 
 
 ■ I 
 
 
 , ^ 
 
 W } 
 
 E->’r 
 
 •I 
 
 Vn 
 
 >■ 
 
 \X 
 
 >*l 
 
 c 
 
 r!- 
 
 <0 
 
 ►t-’ 
 
 fc 
 
 c: 
 
 Uf, 
 
 o 
 
 cr' 
 
 / ::, 
 
 ;<» 
 
 a'? 
 
 4l> 
 
 o 
 
 a. 
 
 o 
 
 T 1 * 
 
 &c 
 
 »-l 
 
 .*1 
 
 }-?r 
 
 (•jil 
 
 
 
 
 
 i;5» ^ 
 
 Vj? \y 
 
 .•■ r- .,ii 0 .ii I ■.-^~. ^'' i||I .%r. )»i. 
 
 4<5\ 
 
 .i| 
 
 , ,* 
 
 r, J,'. ■• -V'. 
 
 V • 
 
 
 A-*! 
 
 c£- 
 
 r-= 
 
 /V 
 
 
 
 
 
 ,«■' .' 
 
 , 1^1 ii 4 i ^^- |. , 
 
 • ' /A 
 
 -5.'^ 
 
 >^4 S 
 
 U. (*0 (/ 
 
 '1i i' 
 
 a 5 « r; 5 
 
 ^ j 
 
 B-til ^ 
 
 0 
 
 L 
 
 
 ■ ■ 
 
 
 
 
 V^'l 
 
 . ■•.*»»:- 5 BiCi*:^-=. ■ — ^-■r' _ - , _ ^ ^ ^ 
 
 '-V' -- -'•‘“.•J #•■'-. 1 / ■' '■ , •■ ■ • . •, ■'' V- , 
 
 . i.-:.«rf>’"'» Mbit..': -'. ’ " i »' • .W • • ,*>.' A* ^'i_'- >. 
 
 r ! I 
 
 1.^, 'i^ ~',T 
 
 / W VJD V.J, \^l \XLA 
 
 / \'i \^ -S, \t. \'S; 
 
 v/ 
 
 
115 
 
116 
 
 
 
 Fig, 54. Position of Gage Lines and Cracks, Specimen 13A2 
 
117 
 
 f^/ 
 
 
 I 
 
 
 
 fij 
 
 ig. 55, Position of G-age Lines and Cracks, Specimen 13B1 
 

 n x iihmii 
 
 i 
 
 W’> \^ ^ ' 
 
 - *• iCih ■ 
 
 tr:' 
 
 .: X 
 
 W',’ 
 
 ■.s'' _ ;ji 
 
 
 Nil V'- ‘ »-^;t ■ 
 
 i ^ 
 
 ■ ■ %f‘ 
 
 .-9 No^v •' * ■ 1 
 
 ^ 0 \^ w . I 
 
 If, h 
 
 t. ’t'®' . 
 
 j ^ .* 
 
 ,'SJ 
 
 ■% 
 
 l!i>. 
 
 yr ! 5^ 
 
 iKa !'L-- 
 
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Pig. 65 o Position of Gage Lines and Cracks, Specimen 131)2 
 
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APPENDIX II 
 
 li^l, 
 
 17. Supplementary Tests of Paper Models .- In February, 
 1922, a method was described by Prof. G. E. Beggs* whereby 
 stresses in indeterminate structures might be determined by 
 measuring certain deflections in a paper or cardboard model of 
 the structure. It was evident that the method, if practicable, 
 would be extremely useful in connection with the problems of 
 this thesis. Accordingly, through the assistance of lAr.R. L. 
 BroYm of the Engineering Experiment Station Staff, in the 
 limited time available since the method was published, the 
 effects of several types of brackets have been measured by 
 the use of this method. 
 
 The theory used in the tests of models is not new, being 
 based upon Max?;ell’s v/ell-knovm "Theorem of Reciprocal Dis- 
 placements". The novel feature is the use of small models of 
 paper or other isotropic material and the measurement of de- 
 flections by means of microscopes and micrometer gages. The 
 theory and procedure in the tests may be described with reference 
 to Pig. 69, which shows the arrangement of apparatus which was 
 utilized for the purpose. The model of the frame to be tested is 
 placed on a horizontal surface and supported on ball bearings to 
 reduce friction. The hinge B is held stationary by means of a 
 needle, while the hinge A is attached by means of another needle 
 to the screw micrometer D. The formation of the hinge between 
 paper and needle is difficult, as the fit must not be tight 
 
 ^ "An Accurate Mechanical Solution of Statically indeterminate 
 Structures by Use of Paper Models and Special Gages", by G.E. 
 Beggs. Proc. American Concrete Institute, 1922. 
 
152 
 
 enough to cause high frictional resistance to turning and it 
 
 must not be loose enough to allow play in the hinge* Assuming 
 
 that it is desired to find the horizontal reaction H at A and 
 
 B due to a load P acting at the point C, the procedure is to 
 
 move the hinge A to the ri^t a distance d by means of the 
 
 a 
 
 micrometer I) and with the microscope to read the movement do 
 
 of the point C in the direction of the load P (which is taken 
 
 in this case to be at right angles to the direction BA)* By 
 
 ^c H 
 
 the application of Maxwell’s theorem the ratio = p ♦ or the 
 horizontal reaction H = P 
 
 In practice it was found 
 
 "a 
 
 advisable to repeat the operation, moving the hinge A to the 
 left of its initial position and measuring d^, and using the 
 numerical average of several sets of observations in calculating 
 the value of H* 
 
 The paper models tested were of Types A,B,C,and B, as 
 described in Section 6, except that eight different heights of 
 each type of frame were used* To eliminate differences in the 
 q,uality of the paper of the models, all were made from one 
 sheet of paper, the frame of Type D being first cut out and 
 tested without damaging it, the brackets then cut down to the 
 form of Tjrpe C and later of Types B and A* The paper showed 
 some variability in stiffness and the values recorded were the 
 average of a number of observations* The values of H/P, 
 the ratio of horizontal reaction to vertical load applied at 
 the 1/3 points of the top member of the bent, are plotted in 
 Pig* 70* For comparison, values of H/P have been calculated 
 from equation 5, assuming the haunch of Type I) to be equiva- 
 lent to a 45® bracket 4/3 as long as that of Type C, 
 
133 
 
 toid are plotted in Fig, 71, The values from the model tests and 
 from the calculations are also plotted for the four types of 
 frame in Fig, 72 to 75, inclusive. The agreement in the results 
 from the two methods is very close and may he considered a 
 satisfactory verification of equations 4 and 5, 
 
 Another use has been made of the models in determining 
 relative deflections at various points on the top member of 
 the frame. Fig, 76 shows relative deflections of the top 
 members of the models of Types A, B and C, These curves are 
 in effect influence lines* for the horizontal reactions of 
 the frame with a vertical load on the top member. It should 
 be noted, however, that the purpose of these curves is to 
 compare values of H/P with loads at different points on the 
 same frame and not to compare values bet>.veen different types 
 of frame. It is found that the horizontal reactions with loads 
 at midspan and at the l/3 points are in the ratios of 1.15, 
 
 1.16, and 1.17, for Types A, B and C, respectively; with uni- 
 form loads and l/3 point loads the reactions are in the 
 ratios 0.75, 0.73 and 0.71 for the frames, respectively. Com- 
 paring these ratios with those calculated in Section 4, where 
 for Type A the ratio bet^;/een the reactions for loads at midspan 
 and 1/3 points ivas taken at 1.125 and the ratio for uniform 
 load and l/3 point load was taken at 0.75, the agreement is 
 seen to be very close and the correctness of the basis of 
 equations 6 and 7 is thus verified. 
 
 In conclusion it may be said that the tests on paper 
 models gave results which were remarkably close to those found 
 
 * See footnote on page 19, 
 

154 
 
 by analysis. However, individual observations varied consider- 
 ably from 131 e mean value found and it was necessary to take 
 quite a number of readings to eliminate errors of observation 
 and manipulation. Further, preliminary tests ?7ith these 
 models indicated that some grades of paper are not isotropic 
 or are not uniform in certain properties, so that great care 
 must be used in the selection of the material if such tests 
 are to be used for scientific work. 
 

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Fig. 7! Va/ues of H/p from CalculaHom, u^ing FguaFon 5. 
 

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 Hj. 72 Valuer of H/p from Cnlcu/aflono and Teoh of d Model 
 

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