RIVETED SEMI-RIGID BEAM-TO-COLUMN BUILDING CONNECTIONSdigital.lib.lehigh.edu/fritz/pdf/191_3.pdf · BEAM-TO-COLUMN BUILDING CONNECTIONS ... PROPOSED METHOD OF DESIGN FOR BEAMS WITH

LEHIGH UNIVERSITY LIBRARIES

1/ II 111111111111111 111111111111111111111 1/11111111111111111111113 9151 00904069 8 No 206

-""-

RIVETED SEMI-RIGID

BEAM-TO-COLUMN BUILDING CONNECTIONS

PROGRESS REPORT NUMBER 1

,BY ROBERT A. HECHTMAN AND BRUCE G. JOHNSTON

AMERICAN INSTITUTE OF" STEEL CONSTRUCTION

RESEARCH AT LEHIGH UNIVERSITY

COMMITTEE ON STEEL STRUCTURES RESEARCH

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

· \. .,

fRITZ ENG~NlpERnW LABORATORYLEHIGH UNIVERSITY

BETHLEHEM, PENNSYI.VANIA

RIVETED SEMI-RIGID



I~I~

III.

I~

I

RIVETED SEMI-RIGID



BY ROBERT A. HECHTMAN AND BRUCE G. JOHNSTON

AM E RI CAN INS TIT UTE 0 F STEEL CONSTRUCTION

RESEARCH AT LEHIGH UNIVERSITY

COMMITTEE ON STEEL STRUCTURES RESEARCH

AMERICAN INSTITUTE OF STEEL CONSTRUCTION

NOVEMBER,1947

COPYRIGHTED 1948

BY

AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.Printed in United States of America

CONTENTS

Page

FOREWORD. . . • . . . . . • . . . . . . . . . . . .. 7

NOMENCLATURE

INTRODtj"CTION . . . . . . .

TEST PROCEDURE

9

11

15

GENERAL TEST PROGRAM . . . . . . . . . . . . . . .. 19

EVALUATION OF SEMI-RIGID CONNECTIONS WITH RESPECT TO

BEAM DESIGN REQUIREMENTS . .. 23

TEST RESULTS . 31

ADAPTABILITY OF THE SEMI-RIGID CONNECTIONS TESTED TO

BEAM DESIGN " . . . . . • . . . . . 39

PROPOSED METHOD OF DESIGN FOR BEAMS WITH SEMI-RIGID

CONNECTIONS . . . . . . . . . . . . . . . . . . . 52

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . .. 65

ILLUSTRATIVE EXAMPLES

ApPENDIX A

ApPENDIX B .

[ 5]

66

71

81

FOREWORD

THE restraining effect of beam-to-column connections, in frameaction, and the potential economy that might result from the

recognition of partial continuity in beam design, are subjects whichhave commanded the attention of investigators for many years. Because of the numerous variables involved in the functioning of theseconnections, progress toward the promulgation of a semi-rigid designtechnique has been slow, although the complete logic for such atechnique has been freely admitted.

In approaching the problem, the American Institute of Steel Construction and the authors of this report have been guided by theconsiderations that:

1. To be of any real practical value the technique should besimple of application, and

2. That it must give "safe" results.

The first consideration suggests that the limiting, or critical, conditions of loading should· be investigated and that simple generalformulas, which will yield "safe" results even for these limiting cases,should be devised-the alternate being a solution by continuousframe analysis, modified for the semi-rigid characteristics of theseveral joints.

The second consideration requires that the actual moment-rotationof each approved type of connection be investigated experimentallyto determine (1) the relationship between these variables for anycondition of loading, size of beam, and required span length, and (2)to insure the presence of a dependable minimum factor of safetyunder any condition of service.

These two considerations are the basis for the following report.Mineographed copies of an earlier edition of this report were cir":

culated in April 1942, when the war interrupted plans for a generalpublication at that time.

In the opinion of the American Institute of Steel ConstructionCommittee on Steel Structures Research, the authors have made amost valuable contribution in the field of the semi-rigid design of

[ 7]

steel frame buildings-one which can now be put into practice eventhough the experimental research to date has not developed a qualifiedsemi-rigid connection for every size beam the designer may haveoccasion to use. Those connections which have met the necessaryrequirements will be found to cover the bulk of the beam tonnageusually specified in tier building construction. The design proceduredeveloped in this report is one which can be applied to anyone, orany number, of the beams in a frame otherwise designed as Type 2construction, as defined in the A.I.S.C. Standard Specification, without affecting the rest of the beam framing.

T. R. HIGGINS

Director of Engineering

An:erican Institute of Steel Construction, Inc.

[8 ]

NOMENCLATU,RE

d Depth of a beam in inches.

E Modulus of elasticity-taken as 29,000,000, lb. per in.2

F Redesign coefficient, applicable to a particular beam as loaded.

I Moment of inertia of a member.

K Ratio, Ill, of any member in a frame.

K B Ratio, Ill, for a beam in a frame.

K c Ratio, Ill, for a column in a frame.

Length of a beam or column between joints, in inches ..

M Moment in a member at a joint.

Me Positive moment in a restrained beam.

M R Moment at the ends of a beam which would be induced by agiven loading if the connections were fully continuous and thesupporting columns did not rotate. (Full fixed end moment.)

Mr Moment at the ends of a beam which would produce a specifiedtensile stress in the tension rivets in its semi-rigid connections.

M. Simple span moment in a beam resulting from given gravityloading.

P A concentrated load on a beam.

p Percentage of rigidity of a semi-rigid connection.

S Section modulus of a·member.

w Uniform load per unit length of a beam.

cP Angle of rotation at the end of a beam; also the angle of rota-tion, produced by M, within a semi-rigid connection.

cPo Angle of rotation at end of a beam, due to simple span loading.

U r Specified unit tensile stress for rivets.

Uw Specified unit flexural stress for beams.

o Angle of rotation of a column at a joint, due to frame action.Subscript designates joint; thus OA indicates the rotation ofthe column at joint A.

r9]

PROGRESS REPORT NO. I

RIVETED SEMI-RIGID BEAM-TO-COLUMNBUILDING CONNECTIONS

American Institute of Steel ConstructionResearch at Lehigh University

By ROBERT A. HECHTMAN* and BRUCE G. JOHNSTONt

I-INTRODUCTION

This is a report on tests of semi-rigid beam-to-column connections,such as may permit the weight of beams to be reduced as comparedwith results -of usual design practice in which end supports are assumed to be without bending restraint. With this purpose in view,tests of forty-seven riveted beam-to-column connections were madeat the Fritz Engineering Laboratory of Lehigh University. The testresults are interpreted and a simple design procedure is developed.The investigation was sponsored and financed by the American Institute of Steel Construction, which, through its Committee on SteelStructures Research authorized the initial work to begin in September1939. Actual testing was completed in June 1941, and the study ofthe test data was virtually completed by January 1942, but the warinterrupted plans for publication.

The design requirements for a beam-to-column connection in asteel building frame will include the following:

1. The connection must have vertical shear strength sufficient tocarry safely the vertical beam end reaction.

2. If lateral forces on the building, such as wind loads, are tobe considered, the connection must have moment strengthas well as shear strength.

3. If the connection is designed only for vertical loads it musteither be (a) flexible, or non-moment resisting, or (b) momentresisting with moment strength inversely proportional to itsflexibility.

---* Formerly American Institute of Steel Construction Research Fellow, Lehigh

University ; now Research Engineer, University of Illinois, Urbana, Illinois.t Professor of Civil Engineering and Director, Fritz Engineerin~ Laboratory,

Lehigh University, Bethlehem, Pennsylvania.

[ 11 ]

12 S E M I - RIG I D B E A M - T 0 - COL U M NCO NNE C T ION S

4. The connection should be economical in design and convenientfor erection.

Building connections may be classified under three different headingswith respect to their moment-rotation characteristics.

1. "Rigid" Connections are those in which the relative rotation between theend of the beam and the column is reduced to a minimum by the use of stiffconnections, as in the case of continuous frames where full continuity isassumed in the analysis. (See Fig. lea) ).

2. Flexible Connections are those which are capable of carrying the end shear,but which allow relatively free rotation between the end of the beam andthe column, as illustrated in Fig. l(c). A flexible connection approachesthe common assumption of pin end supports, in which case the beams aredesigned for full simple beam moment .. This has been the general practicein the case of standard riveted building connections.

3. Semi-Rigid Connections are intermediate between rigid and flexible connections and transmit appreciable bending moment, with .some rotationbetween the end of the beam and the column. (See Fig. l(b)). Manyconnections assumed as "flexible" are inherently "semi-rigid", therebydeveloping end moments which have not been considered in the design .

Connections

~~~ Less t-han~ JFlxed~nd

Mo,.,.,,,nt-

Beam -Column Connections

In echon Point

. (b) Semi-Rigid

(0) Rigid 5earn-Column

¢ ¢.,...-Le55 t-han Simple e>eam

Rotahon

..--____Nol2otohon-.............

If- __

.__0 .-- 1\ fl J '-

SImple f>eamRotation

NoEnd Mome..

(c) Flexible 5eom-Column Connections

Fig. I.-Three classifications of beam to column connections.

The design of the connections that were tested followed standardpractice as closely as possible and the details were checked by a fabricator's drafting department.

In each semi-rigid beam-to-column connection test the relativerotation at the connection, between the end of the beam and the adjacent column, was recorded for successive increments of applied

PROGRESS REPORT NUMBER ONE 13

connection moment. Such data permit evaluation of the actual moments developed at the ends of beams so connected in a building frame.This evaluation makes possible the design of beams in building frames,using somewhat less than the maximum simple beam moments andthereby saves weight.

A considerable background of information on semi-rigid connectionshas been developed, in this country and in England, by work on (1)tests, (2) analysis and (3) design.

Tests of six riveted connections of a variety of types were made atthe University of Illinois1 in 1917, and a few tests of riveted buildingconnections at the University of Toronto2• During 1931-1936 theSteel Structures Research Committee of the Department of Scientificand Industrial Research of Great Britain3 tested about thirty-fiveriveted connections. During the same period eighteen riveted connection tests sponsored by the American Institute of Steel Construction were made at the College of the City of New York4• Tests alsohave been made in Great Britain to study the effect of concrete encasement5 .

Methods of analysis are fundamental to the development of generalized design procedures. The application of both the slope-deflectionand moment-distribution methods to the analysis of frames withsemi-rigid connections was made by the British6,7. Similar methods ofanalysis have been presented by one of the authors8 •

The question of both beam and column design was considered ingreat detail by the British Steel Structures Research Committee3 •

A "Joint Committee of the Institution of Civil Engineers and theInstitution of Structural Engineers" (Great Britain) concluded that

1 W. M. Wilson and H. F. Moore, "Tests to Determine the Rigidity of RivetedJoints in Steel Structures", Bulletin 104, Engineering Experiment Station, Universityof Illinois. .

2 C. R. Young and K.B. Jackson, "The Relative Rigidity of Riveted and WeldedConnections",. Canadian Journal of Research, Vol. 11, p. 62, 1934. ,

3 First, Second and Final Reports of the Steel Structures Research Committeeof the Department of Scientific and Industrial Research, Great Britain, 1931-1936.

4 J. Charles Rathbun, "Elastic Properties of Riveted ConnectioJ1's", Transactions,A.S.C.E., Vol. 101, p. 524, 1936. !

5 C. Batho, "The Effect of Concrete Encasement on the Behavior of Beam andStanchion Connections", "The Structural Engineer", December 1938.

6 J. F. Baker, "Method of Stress Analysis", First Report of the Steel StructuresResearch Committee Department of Scientific and Industrial Research of GreatBritain, p. 179; Second Report, p. 200. .

7 A. J. S. Pippard and J. F. Baker, "The Analysis of Engineering Structures",Longmans, Green & Co., New York, 1936.

8 Bruce G. Johnston and E. H. Mount, "Analysis of Building Frames with SemiRigid Connections", Transactions, A.S.C.E., Vol. 107-1942, pp. 993-1019.

14 SEMI-RIGID BEAM-TO-COLUMN CONNECTIONS

the British Steel Structures Research Committee design procedureswere "far more laborious than those in generitl use". This JointCommittee recommended instead, the making of minor reductions incalculated simple-span maximum moment, using top and seat angleconnections.

The authors9 have suggested a simplified design procedure applicableto a wide range of connection stiffness. The National Building Codeof Canada also has formulated simplified design procedureslO basedon the work of the British Steel Structures Research Committee. Thepresent tests have been made because it was felt that previous investigations were not sufficiently complete to furnish data coveringa wide range of beam depths, beam sections and span lengths. Extensive tests of connections for beams of both light and fairly heavyweight from 12 to 18 in. in depth were carried out, and exploratorytests made on 21 and 24 in. beams.

The following are the more important factors which have beeninvestigated experimentally:

1. Variation of beam depth.2. Variation of top angle thickness.3. Variation of rivet diameter.4. Effect of approximately doubling the beam flange thickness.5. Difference between like connections to the column web and

to the column flange.6. Variation in identical connections fabricated in different shops.

The following information has been obtained from the test results:L .Moment, angle-change relationship of each connection.2. Reaction value of typical connections,3. Observation of initial and final failure of each connection.4. Location of the center of rotation, and division of rotation

into component contril;mting parts, in the case of 28 tests.5. Suitable design range and moment restraint values of each

connection.The results have been summarized, correlated and certain recom

mendations for design procedure have been developed.

9 Bruce G. Johnston and R. A. Hechtman, "Economical Design Through Restraintin Beam Connections", Engineering News-Record, Vol. 125, No. 15, October 10,1940, pp. 484-487.

10 S. D. Lash, "The Design of Beams in Steel Frame Buildings", The EngineeringJournal, April 1941.


II-TEST PROCEDURE

A typical set-up to test the moment and rotation requirements of aconnection is shown, in the diagram, Fig. 2, and by photograph inFig. 3. The test assemblage, consisting of two beam stubs rivetedto a column stub, is supported in an inverted position. The supportsapply shear and moment at the connection approximately equivalentto the shear and moment at the end of a building beam framed ateach end to a column. After a preliminary determination of themoment-rotation characteristics of the connection at low loads, themoment arm length "a" can be adjusted so that the ratio between

a

f)/q/s to measvre

!I(V'I.ronf'q/l11Ovenrent

and cenff>r orrOf'af/Dn

a

Machine Base

a

Fig. 2.-Typical arrangement for mome,t-rotation test.


Fig. 3.-Photograph of typical set-up.


moment and shear will simulate any desired beam length and loadcondition. This ratio of moment to shear would remain eonstant ifthere were a linear relation between moment and rotation during thetest.

Fig. 2 shows the rotation bars used to measure relative rotationbetween beam and column by use of a 20 in. level bar of the same typeused and described in a previous investigationS. This level bar wassensitive to changes in angle of 1/20,000th of a radian. Fig. 2 alsoshows 1/1000 in. dial gages in position to measure horizontal movement of the beam flanges relative to the column face, thereby locating

7t'O',.---....,....---r----,----r----,

6001---·-t+--+---+---+---~

soo

\:-(;:\>

~.~ Test No./6~ J()O

~

~~

~ 2QQ

8 /2 /6 20

Angle Chunge m RCTq/uns x /0'.1

Fig.· 4.-Comparisonof constant-load and constant-maximumstress beam lines applied to a typical test.

8 Bruce G. Johnston and E. H. Mount, "Analysis of Building Frames with Semi-;' Rigid Connections", Transactions, A.S.C.E., Vol. 107-1942, pp. 993-1019.


the center of rotation. Additional dial measurements were taken forthe purpose of evaluating the contribution of rivet slip and connectionangle flexure to rotation.

From the rotation readings obtained by the level-bar, curves havebeen drawn showing the relation between connection moment "M"and span-end rotation "cJ>" between the beam and the column. Fig. 4shows typical moment-rotation, or (M,cJ» curves for Test No. 16.Since each test assemblage consisted of two connections, two curveswere obtained from each test.

The connection passes through three stages: first, an initital stagewith moment approximately proportional to rotation; second, agradual spread of yielding in the connection; and third, a stage ofaccelerated rotation, finally resulting in either failure or very eX'lessivedeformation.

Applied Load

1% .~

'-*"""II

i b.Q

i::>+ I\f)

IBeam stub Ic ,~

E p'CT" ~:>0U Support

Testing MachineBase-?-

Fig. 5.-Arrangement for supplementary shear. testafter moment-rotation test.

As the connections began to yield, the rotations increased disproportionately to the moments. In an actual beam framed in a buildingthe non-linear increase in rotation would result in an increasing ratioof vertical reaction to connection moment. In some of the tests theload point was moved in toward the column to simulate this conditionand to study the effect· of a change in the moment-shear relationship; -",


By removing the applied moment from the connection, at variousstages of the tests, the unioading and reloading (M,</» curves and theamount of initial set and rivet slip were found as shown in Fig. 4 ..

As a routine check of their adequacy to take reaction, four connections were so tested, after the moment-rotation tests were completed.The ends of the beam stubs were supported (see Fig. 5) and the loadapplied close to the connection. The top angles of top and seat angleconnections were removed. Stiffeners were used at the reaction pointto prevent beam web crippling. The results of this study are reportedunder "Failure of Connections in Reaction", on page 37.

III-GENERAL TEST PROGRAM

Forty-seven separate test assemblages were fabricated and tested.Except for a series of five similar assemblages made by differentfabricators from the same detail drawing, each assemblage was ofdifferent design. Each assemblage, however, consisted of two identicalconnections tested under the same ·conditions. Two test curves arereported for each assemblage, the maximum reported load being thatat which one or both connections of the assemblage failed.

Table I shows in summary the general program of connection tests,indicating the factor investigated, beam depth-, type of connection,column face connected to, and rivet diameter.

Shop details of the various assemblages are sl:lOwn in Appendix Bof the report. Fabrication was carried out j~ regular fabricatingshops under conditions simulating shop and field,'practice. The following notes were listed on the drawings as furnishe<;l,the fabricator:

Material: All material to' m~et A.S.T:M. Standard Specification A7-39 forBuilding Steel and to be free'from rust, with mill scale.inta:ct. All sections ofsame size should be cut from material of same heat and rolling, and a 1 ft. 4 in.extra length for laboratory coupons shall be provided. ' ,Holes: Punch I~ in. dia. for %: in. dia. rivets. Punch 1§{6:in. dia. for ~ in.dia. rivets. :.Rivets: % in. dia. and ~ in. dia. as noted. Allrivets to be'driven by pneumatic hammers by methods correspondingto best field driving practice.Paint: No paint.Shop Note: Clip angles to be riveted to the column sections before beam stubsare placed. Rivets, through the beam flanges and outstanding legs of angles,to be driven last, are shown as open holes.


Table I.

TEST PROGRAM OF CONNECTIONS-

Test No. for Col.Factor Beam Depth of Type of Face Riv.

Investigated Connection Conn. Diam.

12 14 16 18 21 24 to in.

- - - - ---2 20 22 9 ·. · . Top and Seat Angles Flange %

Beam 19 21 23 12 " " " " Web %· . · .Depth 35 24 " " " " Flange ~.. · . ·. · .

25 26 " " " " " Va· . · . ·. · .3 7 Web Angles " %· . · . · . · .

- - - - ---I Top and Seat Angles " %· . · . ·. · . ·.

16 5 " " " " " %· . · . · . ..2 20 22 9 " " " " " %· . · .

Top Angle 10 " " " " " %· . · . · . · . · .Thickness 6 " " " " " %· . · . · . · . · .

17 11 " " " " Web %.. · . · . · .19 21 23 12 " " " " " %· . ·.

13 " " " " " %·. · . ·. · . · .14 " " " " " %· . · . · . ·. ..

- - - - ------17 " " " " " %·. · . ·. · . · .18 " " " " " %.. · . ·. · . ·.

Beam Flange 14 " " " " " %.. · . · . · . · .Thickness 15 " " " " " %· . · . · . · . · .

25 26 " " " " Flange Va· . · . · . · .32 31 " " " " " Va· . · . · . · .

- - - - ---2 20 22 9 " " " " " %·. · .

19 21 23 12 " " " " Web %·. · .16 5 " " " " Flange %· . · . · . · .17 11 " " " " Web %· . ·. · . · .

Column Face 10 " " " " Flange %·. · . ·. ·. · .Connected to 13 " " " " Web %· . ·. · . · . · .

6 " " " " Flange %· . · . ·. · . · .14 " " " " Web %· . · . · . ·. · .

· . 47 · . · . ·. .. Top and Seat Angles-Top Story Flange ~

·. 46 · . .. · . ·. Top and Seat Angles-

ITop Story Web ~

On this page, Test Nos. on same horiz. line have top details cut from sa.me section.

PROGRESS REPORT NUMBER ONE

Table I.-(Cont'd)

TEST PROGRAM OF CONNECTIONS

21

Test No. for Col.Factor Beam Depth of Type of Face Riv.

Investigated -- Connection Conn. Diam.

12 14 16 18 21 24 to in.

- - - - --·. · . 22 · . .. · . Top and Seat Angles Flange %:

27 " " " " " %:· . ·. · . · . · .Fabricator 28 " " " " " %:· . · . · . · . · .

29 " " " " " %:· . · . · . · . · .30 " ", " " " %· . · . · . · . · .

- - - - ------Rivet 2 23 9 " " " " " %:·. · . · .

Diameter 35 40 24 " " " " " Y8· . · . · .- - - - ---

3 Standard "H3" Conn. " %:· . · . · . .. · .Web Angle 4 Web Angles " %:· . · . · . · . · .

Size 7 Standard "H4" Cohn. " %:· . · . · . · . ·.8 Standard "B4" Conn. " %:· . · . · . · . · .

- - - - ---Conn. to One · . · . · . 36 · . · . Top and Seat Angles Web Y8Side Col. Web · . · . · . 37 · . · . Top and Seat Angles~

Web Stiffened " Y8- - - - -

T & Seat Angle 34 33 Tee and Seat Angle " Y8· . · . · . · .- - - -

T-Connection 44 Tee Connection " Y8· . · . · . · . · .- - - - --

T-Conn. and · . · . · . 45 · . · . Tee Conn. andWeb Ls Web Angles " Y8

- - - -Length of Vert. · . · . · . 24 · . · . Top and Seat Angles Flange Y8Leg oi Top L 42 " " " " " Y8· . ·. · . · . ·.

- - - -Top, Seat, and · . · . 41 43 .. · . Top, Seat, and

Web Ls Web Angles " Y8----- - - - - -

Top Story 38 Web Clip and Seat Angles " Y8· . · . ·. ·. ·.Connections 47 Top and Seat Angles " Y8· . · . · . · . · .

46 " " " " Web Y8· . · . · . · . · .


The specimens were ordered in six different groups, successivegroups being designed after the results of the preceding tests had beenstudied. All details conformed as closely as possible with standardshop details and were checked for this feature by the fabricator.

The forty-seven test assemblages can be classified as follows:Top and seat angles ,34Top and seat angles to one side of column web. . . . . . . . .. 2Top, seat and web angles , 2Standard web angle connections , . . . . . . . . . . . .. 4Tee and seat angle , 2Web clip and seat angles ' 1Tees on both beam flanges 1Tees on both beam flanges and web angles 1

In the case of top and seat angle, tee and seat angle, and teeconnections,' one-eighth inch shims were used under the top beamflange detail. All holes were punched and rivets were driven bypneumatic hammers.

Wide-flange sections were used for both beams and columns, the beamdepths varying from 12 in. to 24 in., the columns from 8 in. to 14 in.Connection tests using beams of 12 to 18 in. in depth were quite numerous, while only exploratory tests using 21 and 24 in. beams weremade. Twenty-eight of the connections were made to the columnflange and nineteen to the column web. Three-fourth in. rivets wereused on twenty-eight connections and Y8 in. on nineteen. Both lightand medium weight beam sections were included in the program, andthe following is a summary of the number of tests on each beam size:

10-12 vv: 25 15-18 vv: 472-12 vv: 50 3-18 vv: 854-14 vv: 34 1-21 vv: 597-16 vv: 40 1-21 vv: 1082-16 vv: 78 1-24 vv: 74

1-24 vv: 120

The tests on 12 vv: 25 and 18 vv: 47 sections covered the range ofconnection variables. The results of these tests provided the basisfor designing the other specimens..

All specimens except assemblages No. 27, 28, 29 and 30 were fabricated in the same shop. The latter were fabricated in other shops,and together with No. 22, constituted the "Fabricator Series", inwhich the differences in materials and fabricating practice werestudied.


IV-EVALUATION OF SEMI-RIGID CONNECTIONS WITHRESPECT TO BEAM DESIGN REQUIREMENTS

When a beam is framed with semi-rigid connections to columns ofmulti-story buildings, the magnitude and location of the maximumbending moment in the beam will depend both upon the behavior ofthe frame as a whole and· upon the characteristics of the semi-rigid

'connections. The maxImum moment in the beam could be either anegative moment at the end or a positive moment at or near the midspan. The effect of frame action as a whole will be considered laterin the report. For the present, columns will be assumed as fixedagainst rotation at the beam connections, and consideration will begiven to the effect of the connection alone.

Since the (M,c/J) relationship of a semi-rigid connection is non-linear,the amount of restraint afforded by such connections will vary, in anon-linear fashion, for any given span of a particular beam, as theloading is increased. Hence. it is necessary, in order to determine theamount of restraint actually afforded, to consider each beam size,beam span and loading as a separate problem. With the (M,c/J)characteristics of a particular semi-rigid connection determined experimentally, a curve representing this relationship may be plotted with c/Jvalues as abscissa and M values as ordinates, as explained on page 18.In order to determine the specific M and c/J values which will obtainwhen a semi-rigid connection is used for a particular beam, span andloading, a graphical construction, first developed byC. BathoS, couldbe used. The constant-load-beam line illustrated in Fig. 4 is Batho'sconstruction. In this report a "constant-maximum-stress beam line",also shown in Fig. 4, has been employed.

The intersection of the constant-load-beam line with the experimental (M,c/J) curve, determines the actual amount of end momentand rotation wpich a given connection will develop for a given beamon a given span under it given load. This method was followed in arecent study of welded beam connectionsll . The most economicalbeam size sufficient to support a particular load, on a particular span,restra:ned at the ends by semi-rigid connections, can be determined

3 First, Second and Final 'Reports of the Steel Structures Research Committeeof the Department of Scientific and Industrial Research, Great Britain, 1931-1936.

11 Bruce G. Johnston and Gordon R. Deits, "Tests of Miscellaneous Welded BuildingConnections", Journal of the American Welding S:>ciety, Vol. 21, No.1, January191;2, Research Supplement, pp 5·S to 27~S.


only if the amount of restraint afforded by these connections is known.However, using the constant-load-beam line construction., the loadassumed for a given beam and span length probably will not be the onewhich would stress the beam to the allowable design stress. The constant-load-beam line construction, therefore, is at best a cut-and-trymethod.

The constant-maximum-stress beam line method, on the other hand,considers the case where the beam size, the span and the load are sorelated that the mid-span bending moment will have a constant valueequal to uwS (allowable bending stress times section modulus). Thismethod leads to a design procedure whereby the permissible load maybe increased as the connection stiffness increases, or, stated anotherway, using this method, the beam size for a given load may be decreased as the connection stiffness increases. It is better adapted tothe usual design problem, since the object is to determine the mostefficient beam size which the specified bending stress for the beam, andthe actual restraint from the connections, will afford. The methodis, of course, limited to cases in which the connection stiffness willproduce end moments no greater than the moment at mid-span,because, with greater fixity, the point of critical moment in the beamwould be transferred from mid-span to the supports. For uniformloading the limiting case is one in which the connection provides notmore than 75% of full end fixity; for a single concentrated load atmid-span the end moments in no case will exceed the mid-span moment.

For any beam symmetrically! loaded, with identical semi-rigidconnections at its ends, let the' release from imaginary fixed-endmoment, M R , to the actual end resisting moment, M, permit rotationof each end of the beam throug~ the angle, cP. Then, since the resulting change of slope from end to end of the beam equals the areaof the M / EI diagram,

2 _ (MR - M)l'" - EI

or

(1)

For any given span length and symmetrically disposed given loading, M R is a constant whose value may be readily calculated. Forany given beam of given span, E, I and l are also corstants. Therefore Eq. (1) represents a straight line in terms of the variables, M andcP. This line has been defined as the "constant-load-beam line". It


expresses the relationship of .p to M for all combinations, from thecase where .p = 0 and M = M R to the case where M = 0 and .p =.p.,where .p. is the rotation angle at the ends of the beam when completelyunrestrained (simple span). When M = 0 it may be seen from Eq. 1that

MRlq,. = 2EI

As is shown in Fig. 4, both the line for Eq. 1 and the test resultsfor a given connection may be plotted to the same coordinates-eachset of coupled (M,.p) values obtained from the test yielding one pointon the test curve. The intersection of this Gurve with a beam linedefines a connection moment and rotation (M,.p) exactly consistentwith the I, l and load assumed for the beam. The (M,.p) value atthis intersection point is the only value relevant to the given problem.

Thus far M R has been treated as a constant, which is the case whenthe magnitude of the loading is fixed. However, in the case of theconstant-maximum-stress beam line, M R is variable, because theamount of load which a given beam may carry and still retain a constant bending stress at the mid-span is dependent upon the degree ofrestraint afforded by the end connections.

To derive the equation for the constant-maximum-stress beam line,the center span moment, Me, is held equal to uwS (allowable bendingstress in beam times its section modulus).

Considering first the condition of uniform loading and noting that Mis the actual restraining end moment,

wl2Me = 8-M

h u'l2 'h 'I b d' 'I b S' h f IIwere 8 IS t e eqUiva ent en mg moment on a simp e span earn. mce t e u y

fixed end moment, M R = % of this value, Me = ~MR - M = fTwS, and

2M R = 3(M + fTwS).

Substituting this value of M R in Eq. 1

M = ~M + ~fT S _ 2Elq,3 3 w l

M = 2fT S _ 6Elq,W l

M = 2fT .') _ 3ESq,w lid

or

or

(2)

(3)

26 SEMI-RIGID BEAM-.TO-COLUMN CONNECTIONS

which is the equation for the constant-maximum-stress beam linefor the condition of uniform loading.

Similarly, for a concentrated mid-span load,

PIMe = 4 - M.

In this case the magnitude of M R is one-half that of the equivalentsimple span bending moment,

1M R = 2 (M + uwS).

and, substituting this value in Eq. 1,

4Elq,M ~ uwS - -1- or

(4)

(5)M =(1 _ 2ESq,Uw'J lid

Eq. 3, 5 or a similarly derived equation for any other type of loading, may be plotted for any number of arbitrarily chosen values oflid for a given beam. These lines will radiate downward to the rightfrom the common point (c/J = 0, M = M R) • At the intersectionpoint Of these lines with a connection test curve, the (M,c/J) valuesobtained will measure the moment-rotation characteristics of thatconnection for the chosen lid ratio for the given beam, and the magnitude of loading will be just sufficient to produce the specified bendingstress, (Jw, at mid-span. The end moments thus derived can beexpressed; in terms of the full fixed end moment M R , as a percentageof rigidity. Thus the "percentage of rigidity" will be

Mp = MR X 100.

The percentage of rigidity is proportional to the dependa,ble M fromthe case where p = 100 when M = M R , to the case where p = 0whenM = O. .

On diagrams employing the constant-maximum-stress beani line,M R is not constant;

for uniform load M R = ~ (M + uwS) (Eq. 2)

and100M 150

p = =~M+~uwS 1 +uwS3 3 M

(6)


For concentrated mid-span load MR = ~M + ~"wS (Eq.4)

and200

1 + "WSM

(7)

In this case the percentage of rigidity is not linearly proportionalto M.

The beam and its connections should be designed so as to have anadequate factor of safety. Consider the case of a beam designed for aparticular percentage of connection rigidity and a maximum workingstress O'w equal to 20 k.s.i. Assume that the connection test curvecrosses the design constant-maximum-stress beam line at a momentM' (see ~Fig. 6) at a point exactly corresponding to the percentagerigidity assumed in design. If a linear relationship existed between Mand q, up to a connection moment of 1.65 M' , it would be possible to

Fig. b.-Typical test No. 16 showing construction to obtainpermissible percentage rigidity for a particular beam.

Con a.nt Mo.~\ InumStye 0:. Bea.m Ine:o:.for Po.d,c.ul Bea.mfor ZO II}' for 33 K5\

) ,"Mo.. Mot. "'ICo

( \bor1

I

I

/ T"..t Cut:---..-:..--p. I

p. 50%\~I ......-V7 c

1\M"

~~1V .\,",,,,,,,'

I I-

I/ [;(01.1 ~ \1<'5

IV 1\ \l"

800

'00

",00

oil

'"~z

sooo.:i.

~

~400..

i0

::?:2 3000;::\J..ZZ 'l000

U

'00

0

° 0.004 0 00& a-olt. O·Ol(D

l'>."ulE C"""uE IN R"t>.""r.OOz.o OOt4


put 1.65 times the design load on the beam before stressing the beamup to the specified mimimum yield point of structural steel, viz.,33 k.s.i. But since the connection has a non-linear (M,q,) relationship,loads corresponding to 1.65 M' would produce an end moment nogreater than Mit. Therefore the bending moment at the mid-spanwould be larger than that required to stress the beam to 33 k.s.i.

In order to insure in all cases a load factor of safety equal to the usualstress factor of safety of 1.65, a straight line will be drawn in Fig. 6 frompoint A to point C. Point C is the intersection of the test curve and aconstant-maximum-stress beam line obtained by substituting 33 k.s.i.for U w in Eq. 3 (or in Eq. 5, as the type of loading may indicate).The intersection at B of Line A-C with the constant-maximum-stressbeam line for the condition U w equals 20 k.s.i., gives a reduced value

for the end moment which is 1.~5 times the end moment, Mit, that

would obtain if the beam were loaded 1.65 times the intended designload. The percentage rigidity represented by point B (40% in thiscase), since it will afford the 1.65 load factor of safety, will be usedinstead of the percentage of rigidity as determined by the end momentM' (50%) actually produced by the connection at the specified working stress for the beam.

The horizontal lines (p = 30%, p = 40%, etc.) are plotted on thediagram in accordance with Eq. 6.

Pursuing the same line of reasoning, a similar limitation can beplaced on the tensile stress in the rivets connecting the top fitting tothe column. While this tensile stress usually will not be a governingfactor in the determination of the percentage of rigidity, it must beinvestigated and, when the p-value derived by the straight line construction outlined above, is larger than one based upon a limitingrivet tensile stress, the latter should control.

The tensile stress in the rivets may be expressed as

M<T = d' nA

whered' the vertical distance from the center line of the tension

rivets to the top of the seat anglen number of tension rivetsA area of one rivet.

Let M r be the end restraining moment which will produce a stress u,in the rivets, 1.65 times the permitted design rivet stress, when thebeam is loaded 1.65 times its design load.

Then


M, = ",d'nA

29

This moment is represented in Fig. 7 by a horizontal line intersecting the test curve at C', .

If, as in Case I, Fig. 7, C, should fall to the right of point C (theintersection of the test curve and the constant-load beam line for thecondition of 65% overload), rivet stress will not be the governingfactor.

~con..to"t - lood beom line for

De",q" load (o"..tonl- \.<D5 t.m"" de...qn load.loo.d 'oeG.m hne where ei'sreqa.rdmq rl"e.\ s"re.ossr\Vet 5tre~~ qove.rns ~I

M.lEI_' -'-(Mr + r)-y- 1.<05 e; e;.

e;o

De",qn lood co""tont1-~4=~'-!--;>",e...+"t-"'""f';:-'1mo..""mum - 'S+re"50Sbe.QM

line.M.<DEIll·405

-1-

Fig. 7.-Construction to determine permissible percentagerigidity determined by rivet stress.

Consider now Case II, where C, falls to the left of point C.

M R = M + 2~Irf> (Eq.1)

Substituting MT and cPT' the particular values at point C, , for Mand cP in Eq. 1, M R will then have a definite value in terms of M TandcPT'

Thus: M R = MT+ 2E{rf>r

30 S E M I - RIG I D B E AM - T 0 - COL U M NCO NNE C T ION S

A line from this value of M R at cP = 0 through point C', whereM = M r and cP = cPr, establishes the constant-load beam line, definedby Eq. 1, representing the case where the load is of just sufficientmagnitude to produce the limiting rivet 'tensile stress with givenvalues for I and l. For a given beam having a moment of inertia Iand span length l, the fully-fixed end moment, M R,will be directlyproportioned to the magnitude of the loading. If a load factor ofsafety of 1.65 is to be maintained with respect to the load which willproduce 1.65 times the limiting rivet tensile stress, it may be applieddirectly to the foregoing expression for the fully-fixed end moment.The general expression for M and cP, as determined by permissiblerivet stress, then takes the form, from Eq. 1, of

M + 2Elq, = _l_(M + 2Elq,,) (8)I 1.65' I

But, if the design bending stress, uw , at the mid-span of the beamis 20 k.s.i.,

M + 6Elq, = 408I

(Eq.3)

which is the general expression for M and cP as determined by maximumallowable bending stress in the beam.

Solving these two expressions as simultaneous equations, eachcontaining to the left of the equality sign, the value for M and cP whichwill satisfy both the condition of load safety factor and maximumdesign bending stress in the beam, cP may be eliminated, leaving Min terms of M r and cPr.

3 ( 2Elq,,)M = 2 X 1.65 M r + -1- - 208.

Substituting this expression for M in Eq. 6,

P= 100[1.50 - (M, :3~) ]

where p is the largest percentage of rigidity which will provide a loadfactor of safety of 1.65 when tensile stress in the rivets is the criterion.

For the loading condition of a concentrated load at mid-span, thecorresponding equation for percentage of rigidity, when rivet tensilestress governs, will be found to be

P = 100[2 -

I'I


f,

If pu is the maximum percentage of rigidity that can be used for agiven beam designed for uniform loading on a given span, when rivetstress is the criterion, and pc is the corresponding maximum percentagewhen the same beam, using the same semi-rigid connections, is designed for a concentrated load at mid-span, it can be shown that

3(Mr +~) - 668

pu = ( 2EIA. ) • Pc4 M r + -l-",r - 668

from which it will be seen that the condition of uniform loading requires the larger reduction in allowable percentage of rigidity when

. rivet tensile stress is the limiting factor.

V-TEST RESULTS

The quality of material used in the connections was checked bymeans of sixty-three tensile coupon tests, made in the direction ofrolling, from samples of all material used. All of these tests satisfiedthe ductility requirements for A.S.T.M. A7 Specification for Structural Steel. Only three samples out of 63 had upper yield pointsbelow the specification requirement Of 33 kips per sq. in., and mostof the upper yield 'points were between 35 and 40 kips per sq. in.Most of the steels had nominal ultimate strengths between 60 and 65kips per sq. in. Fifteen out of 63 samples had nominal ultimatestrengths below 60 kips per sq. in., several of these being in the neighborhood of 55 kips per sq. in. The single sample with the loweststrength had an upper yield point of 29.8 kips per sq. in., and a nominal ultimate of 53.9 ki~s per sq. in. The 'sample w.ith the higheststrength had a yield point of 42.7 kips per sq. in. and ~ nominal ultimate of 71.2 kips per sq. in.

Results of representative. connection tests are presented in theAppendix B. With each test the following information is given:

a. Brief record or "log" of test.b. Shop details.c. Photograph(s) after test.d. Moment-angle change relationship in design range, correlated with constant

maximum stress beam lines which indicate the range of beam design requirements.

e. Graphical subdivision of moment-angle change diagram (tests 20 to 47) intocomponents assignable to the following causes:1. Bending of top angle and column tlange, and extension of tension rivets.2. Slip of top beam flange rivets.3. Bending of seat angle.4. Slip of bottom flange rivets.


TABLE No. IIGeneral Summary of Test Results

0 DLTAJl.~ O~ 5tAM FlA/'IGL~ WL~ Anm Coc,n... ,..ToP D[TA1~ 5LAT DtTAIL c

.... c

'" ... r: C '" ""~~"' 8N J5 o C N

"'.~,; 6 IS c e :3 Iii '"A~L£

III &~ C (. r

'" 0 l-.sIZ£

~

:'>Ize 3 ~£ ;~Jf- 3 ~v uJ ~~ :'l,Z£...~ ~~<: " 0 0 > .. , 111

~lH.:l ~ v v & ::: ~ ~ 6 Ii,Jlx

I Z. 3 4- 5 6 7 89 10 " 12. 1~ 14- IS 16 171 :!> IZIYZ5 IOIY4~ Flanq< )/. 6·4-·l,8! 66J2,

2- 4- do do do J' ""j.&! 6 6 It

3 , . dO do do do 6,hi,"'l t • ",,<O.t,"l ,4b44 I.. do do Uo do "',.,i''''} z • do 4 + 14

5 L do do dO do <O.4o,l,'~ 2. 4 do 4414

6 /7 do do Web do 604.1,'1 t • do 4 .. 14

7 /9 do IOII'"~ do do '.4,! ,61 z 4 do 4 4 14

a 3S do JOII'"4'i fla."", 'Ie ",4,I.Si 2 4 6."'.hsi 4 4 14

9 :!>4 do SIYlI Web do STlOII'"41.7! 4-4 Stlf(entd" 4 " 1810 38 do IOlf49 FlanqE' do '."'.t.S! .+- 6..... ,6 + 4 16II /8 '2W"5O do Web 'to "'.t.a Z • 6..G",he + 4 H-

12 39 do IZ\'f65 do 18 ,.4,i,~ ~.6,6.,.9 4415

13 lO 14W"* do FiOr<le ~ 6.4·10''0' 44 6.6.,,7, 4 • I~

1+ ZI do 1+11'"58 Web do "'••".10 + 4 do 4 4- I~

15 4-6 do do do i'e a:';:'•. Ilk 44 Il."". lit 4 4 16

16 47 do 211'"65 F1on9\' do .:.:'r: ... 01 4 4- 8.'.1,9 4 +- 1617 2.2. 1E>\'f4<) do do 14 " .....1'0' 4 4 ••6.t.n 44- 10

18 27 do do do do do .. 4 do 44"I~ 2ll do do do do do 44 do 44 16

2.D Z9 do do do do do 4t do 4416

ZI 30 do do do dO do .. 4 do 4· 4 I.22 23 do 1+1'fS8 Web cb 6...4',1& .. 10· 44 do 441623 40 do do do rs ' ••• I.II! •• 6,".1.lIi 4 4 '"24 41 IbI'f'18 1ZW"65 FlQnqe do ~'.I."Oi 4 • "."'.1.9 44 4·Ji·l·lli 4& III

25 44 do 1411'"58 Web do STIlWJ7.1~ 8 (, Sld(e~edT " (, to2fo 7 I8W47 IZW65 F1anqe ~ 6.4.1.1I! 8 8 "l7 a do do do do 4,4•••lIt 4 & It

18 5 ·00 do do do 6.·4-,. r.1~O· 44- ,.G.i.n 44'"Z9 9 do do do do ,.4... 1'0' 4 4 do 44 ,(,

.30 /0 do do do do (,.4.~.1'0· 44 do 4 4/(,

?>I (, do do do do .'+.8.1'0· 4 4 do 44 lb·3l 1/ do 14.\'f58 Web do 6.4.t.10 4 + d: 441.

?>?> Il do do do do 6.4o.A.IO 44 do 4416

* 13 do do do do 6.4.1".10 44 do 4- 4- ",:!>S 1+ do . do do do 6.4••• 10 4. 4- do 44-1.

?>" l'lo do 1211"<05 FJanqe JB ,.4.~.l'o; 4 4- do 4 4 I.37 42 do do do do ",.6·1 ":0; 4 'lo 6'''.i.&!. 4- 4 16

.38 ,)3 do IOW41 Web do STIOW41.7i 44 SI,ffen,d L 461839 ?>6 dO J4W56 ontS...

do 6.4.!.lIt 44 6... ,&./14 4416w••40 37 do do dO do f"f~tt:J~~i 44 do 44'"4/ 15 1811"85 do Web l> 6.4.1.10 44 (,.6.1.9 4416oil 4-3 do 12.\'f65 Flo",!" % 6.,.~.I:Oi 44 ,.6.1.9 44 4.3i·i.lI! 48lB43 45 do 1411"58 Web do STIZW37JII. a" STIlWX9 .. 4 4.3;"1.81 3 6 '344 25 21W59 14\'fBT Flano' do 6.4.1.1'2. 44 S1ff,.,.j L 461845 3Z 2IWJ03 do do do do 'lo4 40 4- (, IB

46 ZG 2.411"74 do do do do 44- do 46"1847 ~1 Z4VfI?f. do do do do 4- 4 do 4618


TABLE No. II.-(Cont'd)General Summary of Test Results

33

I'II

\.l

COM Mof'l It' \(,P In PEIt.c.LnTAGE.,..

'AC.TOIl

2U;;;IOITY roq ~It'! DL~IGf'\ RA"~£.

~!11IO" U""ro.."",-'f~

TvpF. Ut'lI~Oll.1"\ LoAo R.OT AT

~~~~~~~L::o...... 0 LoA!) MA'I1.1.o"'0

d c ~ or f .... '-Ull.E ''''TOq or 1.65 ~~ <W W (oro .... :\Q L, , n ~! 0.. """,.. !.: ~l:

~oZO If,jo3Q ~ I~'IO Ild'ZO 1f,j.3Q a~ ,~.Z1J ~.30.:l Vd" O

I 18 Iq 2D 2.1 2.2 n ~4 2.5 lob l.7· 2.8, 68 'lS "'" ~z.o 'E.1I.'C!$~1". DeformotLOr'l 14.~ lO.6 ZH· 40' 4j\. :.~-

2 0) I~I 1~7 z.tJe TOD'Rwe; In Col Lta of Co,," <. rOil" 17» U••Z 30.+ t.O ~o- Z.O·, 144 171 1'1+ ~50 chc:.'~lv, O.formatlon W ~3,4. ~9 .0- 1\.,. :'>.5

• las tza 255 ~I~ RIVet ,n VerI. leo of roo ( ro".d ~4,6 40+ 419 '0. al. 5...

5 US 2.8+ 3110 7+7 .rrac+urt of Too' 40.0 47~ ~7 +0' 511 +.06 1'7 ~~ 258 558 liva+ In \ieI'''' Lea of Too <. Fall.d. 304~ +1.2 ...~ SO, 6'1 U

7 1-5'1 !J07 ,~, 67'1 . E..c. •••'v. O.fo"",Qtion #3 +q.q .~ ~- 60 +JII /..b7 31.7 ~, 8~5 RIY~+ i" Vel'. leq 0'" Top' Hal\f'i 4~1 ~z.o 5Sa 46 7.5 SJ9 ~14 37' +18 75:l R.tvt+ \1'1 Verl- UlQ of Te.e FQ,I.d 50.5 5'0.8 "-\5 18 Zq 20lO L05 Zql 5:l+ To, llVet Col Laq of w.b Anqle loilol 37.4 .8.1 I~ 17 ~1/ LIt loSZ 1.77 .s~ Il,..,t ,n V.d L.eq of Top (r.,Iod V.I 2.4-4- U.5 40- 5.0 .).~

IZ 4:>0 53=' 616 1060 E.xc.e'Sos,i". ,o.iormaHon. ~H +~ 4M 11 1.+ 1.7

13 ..3~ 47' 54-5 005 d. 3'l.q .4'1.7 05'0 60+ as 6./I. <4007 510 5''1 1'!lO0 d. +4.4- '51.8 .55.-4- 50' 75 5.215 .%5 3'11. ~qZ 1067 do 41.0 4~.3 ~3 ZOo.. 2.& 1/1-16 l:l<O 33+ ~'10 1071 d. 2~+ .:36.5 4l2. 40' 5." III17 45ll '81. 657 14'1+ do Yl.4 44.8 50.7 50- 7.1 5.018 481 5" '-60 1512. do 40.7 4-7"; saa 5+ 7& S.,

" 42.0 555 ,:30 12.& de ~70 45.1. ~ :6.10 5.0 35ID +l.5 530 6/5 12/5 do );1.2. 43.7 48.," zs- ~ 242J 4-45 !fI3 6+2 /580 do :le.6 4(;.2. 50.0 60' 8.6 s.q

2Z 50'1 62+ 6q4 /2.33 Yield in £1Y.ts \1\ Wo,.it. Lee; Top" 42.1> ~.1 52.f> 168 1..5 172.3 ~~O 1085 River.. ,n l/ert leq of Top L Foiled 4'1.3 6 Inof In..f.

24 666 B80 10/8 2.'135 IlJvets faded in ~O"lt. leq Top L 31.1 .38.8 ~8 32.- 4.:'> .10

ts 1/35 I4-QS 1550 ~4'1 Rive+$ln top of Tee fad.d 4"2 53.3 5h.7 +0' 6.1. ..~2.6 lSI 2.03 2.28 480 E.'lCc.cs~IY~ DeformQ+ion 12..6 16.~ 18.3 +0+ +.7 U

1.7 108 1+5 flOQ 37+ d. qZ I~.Z. I 14-.0 +0' +7 :\1

1.8 4~S 5co3 1054 12.00 RlVe~ \n Ver'hcol Leq Top t failed 31+ :l8.3 42..' U'" 35 2.52'1 5IZ 6+7 7Z.7 1706 R.lwb In Horu. Le. Top I. Fooled 35.5 42.+ «..0 40· 5.5 3.&!JO 5Z5 6~0 781 1850 do 3(,Z 44+ 4-8.~ +5- 6.3 44-

" 480 654- 754- 1800 l'll.co'!o~IV. Defot"mQtlof\. 31'1 +27 47.Z 43' 60 .,3Z 4'1+ 582. 650 15+6 Rivet '" Vorl. Leq Top L .olled 34.7 3Yl +loS 40- ~.. 3.735 558 ~78 750 15'10 ~,vQb In Vel"! leq Top <. ,ailed 380 HB 47.0 31.4- 4.4- !>D

'* 5% 7::>4- 8:>4- 1+72. R.1'J8+ In Horn l.eq Top L Fai led ;}qq +2Z 51.2. ".... 2.3 1.7

M 5~Z 700 810 ''-50 Riv~h ,n Vert Leq Top L toded ~6 #8 4~6 2.5 3.5 1..5

.% 6/8 780 870 1'1% [",ce!o~i ....e Deforrna+ion 41.0 4a3 52.0 5~ 7.8 s.+~7 +'1Z 650 74-2 2.+74- Rivet ,n Veri le. Top L Foiled '. .}4,5 42.+ +66 40- 15+ 311

38 'SO 810 '100 22.15 Rivet In Ve,~ Face of Tee foiled 43.'1 4~5 530 50 74 5.1:)q 788 Rivet an Vert Lea of TopL Foiled 7... In"f, I.,f

Ml 658 &~7 '1-:;'7 2+57 do 42..'1 50.5 54~ 55- 8.Z S7

41 7?>O 8'10 '1'10 Iq5~ R.lveb In HoYll. L4P4 of Top <. Fai \K 2.8.5 ~~~ :\02- 34- +.+ ~.O

42. 700 '1'15 1/55 ~23 l.ee,. Def and Web{T.a, 275 ~3 4010 4<). 53 3.6

+3 /2'15 /510 IS7~ '!lO72. Rivets. If' Top of Tee failed +4.0 4a.q 5O:l 2.Q +.3 U.. 850 /090 1Z.~5 2486 Rivet in Hori. leo Top ( Foi led Y1.+ 4.10 51.2. 31' 4.5 3.1

+5 1010 12.6l. 1540 ~I05 Rivet an Vert. lO<j 100 <. Foiled ~ ~.3 ~9 34- 4-4- ~O

46 '14<) 11.00 1~+5 Zq()4. RIVllh!. In ~ori~. leq Topl. Failed 32..4 !fl.1 4-l.S 40- 5.4- 40

47 1255 2.755 Rivet In Ved leo ToP L I'Giled Z~O lu'u In..f. [.,f.


Essential information regarding details of connection~, togetherwith the more significant test results, are summarized in Table II.The test results presented in this table have been rearranged to startwith the lightest weight 12 in. \/IF section tested and end with theheaviest 24 in. \/IF section. Columns 3 to 17 give essential detailsregarding the type and make-up of the connections tested.Moments and Type of Failure-Columns 18, 19 and 20 give thedependable moment values of the connection, for span-depth ratiosof lid = 10, 20 and 30, respectively (calculated as shown in Fig. 6),based on the straight-line construction to give a safety factor of 1.65(see page 28). The real factor of safety is the total reserve of connection rotation beyond the ~otation at design load. Because of thestraight-line construction there will be the same apparent factor ofsafety for' moment at working load as for rotation. Actually, atworking loads the true connection moment will be larger and theconnection rotation will be slightly smaller than indicated by thestraight line construction, as the constant-maximum-stress beam linewill intersect the (M,¢» curve above and to the left of its intersectionwith the straight construction line. Nevertheless, this is of secondaryimportance, since the ratio of beam load at connection failure toworking load will be equal to or greater than the chosen factor ofsafety. The amount of moment calculated at working load by thestraight line procedure determines the usable restraint value of theconnection. Blank spaces in columns 18, 19 and 20 are cases of connection rotation factors of safety insufficient to satisfy the foregoingconstruction.

Column 21 of Table II indicates the maximum test moment either atfailure or at a deformation so excessive that the test was stopped.In the latter case the test load was usually increasing at a very slowrate. In some cases failure of one or more rivets occurred at loadsbelow the maximum test load, without prod ucing a general failure ofthe connection as a whole.

Column 22 indicates the type of failure. In summary, eighteenconnections failed by excessive deformation; one because of fractureof the top angle; the remaining twenty-eight because of general tensionfailure of the rivets. All rivets failed near the middle of the shankexcept in the case of connections No.5 and 40, where failure was justunder the rivet head.

All failures of the top-and-seat-angle type of connections were in thetop angle or top angle rivets. Seat angles were adequate in all the

. test specimens and showed signs of yielding only where extreme rota-


tion and/or high reactions were developed. Where connections weremade to light column flanges, the column flanges bent considerablybut the upstanding leg of the top angle tended to remain comparativelystraight, throwing greater tension into the rivets nearer the centerlineof the column. With connections on both sides of the column web,a more equal division of the tension took place among the rivets ofthe upstanding leg of the top angle. In the case of a connection toone side of the column web only, the outer rivets were most severelystressed. In the case of light beam flanges the top angle rotated as awhole and caused considerable deformation of the beam flange at

Fig. S.-Ductile and brittle failure of 'l's-in. rivets. Rivet on right is from test No. 40.

high moments. The greatest deformation of the beam flanges occurredin the connection having the greatest thickness of top angle, and theleast in those having the least thickness of top angle. Considerableslip occurred in the rivets fastening the top angle to the beam flanges.Two shims were used between the flange and angle in twenty-fiveconnections and one shim in nine connections. Relatively little slipoccurred in the rivets connecting the beam to the seat angle.

Standard web angle connections failed by excessive deformationin the case of web angle thicknesses of three-eighths inch; by fractureof the end rivet in tension for a web angle thickness of five-eighthsinch. Slip of the rivets connecting the angles to the 12 inch beamwebs were observed at moments within the working range of the connection. However, in the deeper connection to the eighteen inchbeams, no such slip occurred to a degree observable by eye.

36. SEMI-RIGID BEAM-TO-COLUMN CONNECTIONS

All tee connections failed by fracture of rivets in the flange of thetee, even when fewer rivets were in the stem.

Columns 23, 24 and 25 indicate the dependable percentage of rigidityof the connection as compared with the actual moments tabulated incolumns 18, 19 and 20, assuming no column rotation, and based onthe straight-line load factor of 1.65.

Maximum C-onnection Rotation-C~lumn 26 gives the maximummeasured or estimated rotation between the end of the beam and thecolumn for each test, based on the minimum of the two connections.In a few cases, where the rotation at failure was not obtained, a tangentto the (M,q,) curve was extended from the last measured value up tothe moment at failure. This procedure would be expected to give lessthan the actual maximum rotation because of the normally convexupward shape of the usual (M,q,) curve, and hence yields conservativeresults.

Connection Factor oof Safety-In evaluating semi-rigid connectionbehavior, a factor of safety with respect to rotation is of greater significance than one with respect to the moment producing rotation. Forany given beam and system of applied loading, the actual amount ofend rotation is limited to something less than that which would takeplace if no end restraint were present. The ability of a semi-rigidconnection to rotate more than this amount, as demonstrated byactual tests, is of far more importance than the magnitude of themoment which would have to be employed-or the relationship ofthis moment to any actual end moments at service loads.

Columns 27 and 28 give the factor of safety of each connection,for lid = 20 and 30, at working load. In the case of Test No. 36(line 39) the insufficient factor of safety may be explained by the factthat the connection is made to only one side of the column web. Thethin web has little flexural stiffness and most of the tensile force iscarried by the outside rivets adjacent to the column.

Components of Rotation-The division of the rotation into components (due to deformation of various parts of the assemblage) wasmade from data obtained by 1/1000 in. dial readings. Since thesedata vary as much as fifteen percent from the more accurate level-barreadings, they were adjusted to agree with the latter. Typical figuresfor Tests 20 to 47, in the appendix, show the plotted components ofrotation. The curve nearest the bottom of the page is the mean(M,q,) curve of the two connections in each assemblage.

These curves indicate that only a small part of the rotation is dueto bending of the seat angle and slip of the bottom beam flange rivets.


TABLE No. IIIFailure of Connections in Reaction

((Mil. &'11m ~d ut'OrL WebL 1-&0 s....7j~of(i:;nl1t'Clbh ~eelli>n VZ~

7j~ 01' FqiluI'e .J'",,"JJ

Alo. IJioI1l Size uize '!lin .N.1tJ

illS ins. iIM I(i~ I~,.I ;op Ij,JeQI An/IdS IZ~ ,L t l6·;"; IU-I Beqm Web Crij>pled Izso~

Z do do 3 do 'It.! ~11i9'i:'l1t'r on 81'11111 Web Bldlell Sll+J ~hI.<dlln:f ffeDlUwn do J 6,/·5->81 IH.5 ~-?k:r biNllfdebm.-'Yi blnil'lli'lhlIIlfleD 5-1.7:,:..; "hf>ISt'4t A~/lIS 18W--17 3 6·'·f·ri fiT-a RII'ef.s in Column .sIJeqreti 151.9~

Top A/lqle rel71"Yed on Top ~ .seqT Al1ffk (:"""ee Ii",.,

Most of the rotation is due to bending of the top detail and slip andextension of its rivets. Also, these curves show that in the case of topand seat angle connections, and tee and seat angle connections, thedesign of the top detail, for all practical purposes determines therigidity and strength characteristics of the connection.

The five test assemblages, Numbers 22, 27, 28, 29 and 30, of samedesign but fabricated by different companies, had moment-rotationcurves that did not differ greatly, as shown by Fig. 9.

00404 0 .....

L..---:::-~ -

.--::;:;;;;;,i --::::::;;0

~

:~'IfIf

o ,

...

_t,

··,:1 100

·~! ....

J·9~•i .,"

Fig. 9.-M, '" curves for I0 connections of same design made by five different fabricators.


TABLE No. IVCenter of Rotation

Cam 7jp~ 01'{oN",,,

8Nm Cenkr or Rototion ot{on"Foce

,-w,. Conn..etion Conn. FirJft-d 02UItAi. tHUIt/hn 06UItAl"", tUUItMomIt> .koc~

1- -1 9: -9 ~No

All M M M AIq Top I Sellt Anglt!s Flange ISW." 60 O.S JlIZ (151 '1i.4 0.61 !A?U6 077 IJI,f '110 do do d. 181 QTI 370 0.61 740 051 1110 0.73 1410 10

II do Web ·do 120 a" JOf. 0.67 618.4 QJ6 9L7.6 0.73 1lJ'. II

12 do do do 2-10 Q£/ 311 0'1 '36 061 "S9 0" l27l 1213 do d. .0 120 aso 252 060 S04 07L 756 010 Wi all 13

14 do do do 21() OZJ 3j() 0.13 660 aJI 'i'9O 0.71 IJ20 an u1.5 do do IIWiS 160 0,27 3'10.6 0.£/ 71lt 0.13 1171.1 0."1 'S6U 0.'16 1516 do fla"'lS 12W25 '16 068 12.ll 0.'" IN.I 0.7-1 362' 0.7' -I'I?I 0.83 1617 do We/) do 32 O.SO {(J7.' 068 ?1S.2 tJ.SS 32lJ 0.92 13M 0.'16 1718 do i/o IZWSO 336 0 //3.6 U?l 0.'13 J4QJ 0.99 !-fJU 100 18

1'1 do do 12W'LS JU 135.8 ?71.J M8 (()l~ 0.71 Jl12 0.81 1'1

20 do Fla"ge 14/Y.31 36 a7Z 261 a7.J 5Ll 071 713 O/lf I()H 2021 ab Wo6 do J6 O.JO 260 aS8 52U a7l 730 0.87 1010 a9~ 21

ZZ do Flange 16W40 36.2 0.50 2fll 074 5"6 0.73 196.1 an IIfU 0.19 222.3 do Well do 108 ;:WI, 0.16 1'lJ.2 0.92 739.1 0.'13 "8M 0.'15 2JN do FltmJe IIW'-I7 60 OJ7 .J89.2 a&J 7744 0.75 fl,7.i 084 '!Su 0.91 24-205 do do lilt'S" 66 o.S5 19!L a6S 99#.1 0.69 H'll-' 0.76 198U 086 2S

26 do do ';!~1Y71 ",2 O.SS~ 0.£8 11U.6 OoiV 1TN.4 014~ 0.'11 2627 do do 16IY.fO ..JI, 100 3IJl:# a" iIJI.J a70 '101.2 all ~OI!' 27

28 do do tlo ..JI, aH 2SU 0.#1 SR.8 0.61 76tl 0.78 ~6 0.17 282'1 do do d. 36 0.14 lO au 166 060 72'/ Qrz 972 081 29..30 do do 110 36 O.!I 3/6 0.67 ~3L 0.71 'H8 071 ILi~ .30

.31 do de 2-1WlZO 18 ass IILI a6() lIS-' (U6 ILJ&j 0.71 IWZ 0.74 .31

.3Z do do 21WKJJ 66 0.24 '21 06J IlIl a7S 1163 atS 1z4H J23.3 ~, l- SeQt A"9'" WeD 18W", #) 0.,0 413 a'll 816 artS 1329 0.96 177L .J.)

.H do do 12IYZS -18 07/ lHo.6 a7S 1Z91Z 0.76 13'£1 aID SA' au ..uJS "Top If Sel1t Angl". I1t/'¥" do 32 0.12 /67 0.62 334 0.74 SOl 0.15 "8 J.S36 do WeIJ 18/Y-I1 80 0./9 loMl aH Z97.6 06J HM 0.69 S9S2 .J6.17 do do do 80 0.6" 4fL-I 0.66 91L.J 0.6'1 IfNz 0.77 1.£6 .J7J8 l%'h Clip 8Sorlt~ Fhnge IZWZS 32 O~3 ff..l 0.64 I'M au 2"-6 o.6S 3f'.1 0.70 .38

.39 T"p l.5eot A"9'''' Well IZIYSO 64 060 2/6 06/ 432 065 648 075 1864 OM J940 do dt> 1""40 'l/6 OM Z/7 082 43f 073 651 0.70 868 076 40-1/ 7(,,,,.5,,"t 4-~DA",1as FlIl_ J'W'78 144- 100 435 0<'31 810 Q~ 1305 0.40 1740 41

-IZ lOp , St!l1t A"91u do 11W'17 240 06 495 0.68 '390 075 1485 1980 424J ~p, Sel1t 4W~AA",es do 18W8S 132 054- 540 0.48 080 055 16CC 066 ~60 OX) 4.3

-If- Tee Conned;'n W,/) 16W'78 3Z0 05I:J 709 104-9 "II" 062 llZl 078 2836 OM 44

405 u:.-U>." ,..,fh HWo U dt> 18IY8S 328 045 614 1044 1228 1047 I~l 0.5J Z456 . 4S46 lOp 4- St!t1t A",lrs II. 14W.34 1'14 0.85 ll4- 083 428 0.76 rA2 tJ56 46

47 do FIll., do ll6 09Z ZII on 428 0.96 6;2 098 856 47

g·dl.st4lfCe I'rl1l11 bp DHlf1l fllln~ IrI ce~ 01' rl1tlltlon d= Deahl tiepth


II

V

VI-ADAPTABILITY OF THE SEMI-RIGID CONNECTIONSTESTED TO BEAM DESIGN

The connection details will now be considered in relation to applicability to semi-rigid design as determined by permissible percentageof rigidity. The principal factors affecting the behav or of a semirigid connection have been outlined in Table I. In the evaluation of aparticular variable it is preferable to make a series of tests in whichonly that variable is changed. In view of the many different factorsaffecting the test results, the complete experimental study of anyoneparticular type of connection would require a great many more teststhan could be made in this program. However, enough tests havebeen made to arrive at definite conclusions as to the adaptability ofthe top and seat angle type of riveted connection to semi-rigid design,within a specified range of beam sizes.

Standard Beam Web Angle Connections-The results of standardweb angle type connection tests are tabulated in Table II (Tests3, .4, 7 and 8). The percentages of rigidity developed by these connections were lower than results obtainable with a similar number ofrivets in top and seat angle connections.

By increasing the rivet size to Y8 in. diam. about 25 per cent rigidity,for lid = 20, probably could be allowed in the case of the 12 VF 25beam, scaling downward to about 15 per cent for the 18 VF 47 beam.Further reduction in allowable percentage of rigidity would have tobe made for smaller lid ratios or for heavier beam sizes.

It was evident from the first series of web angle tests that the topand seat angle connection offered greater end restraint effectivenessand the remainder of the program was devoted to this type connection or some variation thereof.

Top and Seat Angle Connections-Thirty-eight tests were made onthis type of connection to investigate the principal variables.

The beam depth was the principal variable in two series of testswhich will be denoted as Series A and B.

Series A (Tests 20, 22 and 9) had the following factors maintainedconstant:

(1) Lightest or next to lightest weight beam for each particular·beam depth.

(2) Connection to flange of 12 VF 65 column.(3) 6 X 4 X % X 12 in. top angle;(4) Four % in. diam. rivets in each leg of top angle.


For Series B (Tests 21, 23 and 12) the preceqing four items weremaintained as follows:

(1) Same as Series A.(2) Connection to web of 12 VIF 58 column.(3) 6 X 4 X % X 10 in. top angle.(4) Same as Series A.

Series A and B

Allowable Percentage Rigidity for lid = 20Beam Size Series A14 VIF 34 49.716 VIF 40 46.818 VIF 47 42.4

Series B51.849.143.8

Tests Numbers 25, 26,31 and 32 provide a study of relatively deepbeams in both light and medium weight sizes. The tests are groupedtogether on the last four lines of Table II.

The thickness of the top angle was the variable in four differentgroups of tests, namely:

3 tests of 12 VIF 25 beam connections to column flange (No.1,16,2)

2 tests of 12 VIF 25 beam connections to column web (No. 17and 19)

4 tests of 18 VIF 47 beam connections to column flange (No.5,9, 10,6)

4 tests of 18 VIF 47 beam connections to column web (No. 11,12, 13, 14)

The results of these tests are presented graphically in Fig. 10, whichshows that connections on each side of the column web, when testedagainst each other, were somewhat stiffer than similar connections tothe column flange. The columns used in the tests were relatively lightsections, and the bending of the column flanges contributed to thedifference in behavior. Hence these two types of test represent twoextremes of condition. A column with very heavy flanges wouldincrease the stiffness of a top-angle-to-column-flange connection, ascompared with the lighter weight column sizesused, but not more thanthe amount indicated for connections in pairs on each side of a columnweb.

,I

pnOGRESS' REPORT NUMBER ONE 41

S5._-.,...----.,...----.,...-- ---__--..

. 50 1--+---.."...--,,~'_;_-::+-6_-"""2f=_+_---+____i

4SI---+-----:--t---J~'--+_~~-+_--..3Ioo,pI,_--I

~~.~

.~ 40J--~--___J~Y~-HI_+--+_.:_:_:___:__+_--fct~

t~ 35

et30J--~---f--!.----r_---r_---+_--f

20L-.....L---....L---~---""""- __........~.....

J~ 'lZ % 3A1rhickn~ss of'TOI' Angle

Fig. 10.-EfFect of variable top angle thickness-percentages ofrigidity shown are for lid = 20.


Tests Numbers 36 and 37 (Lines 39 and 40 in Table II) simulateda connection to the web of an outer column in a building where theconnection frames to one side only. The specimens were identicalexcept for the addition of a reinforcing angle on the outside of thecolumn web in Test No. 37, as shown in the details. Test No. 36 hadthe poorest relative strength of any test in the whole program, whereasTest No. 37 was considerably above average. These two tests indicatethe desirability of reinforcement for the column web for web connections to one side of a column.

The effect of approximately doubling the ratio of connection ~hear

to connection moment was evaluated in the case of Assemblies Nos. 32,33, 35 and 37. Considerable increase in shear increased the slope ofthe (M, c/» curve by only a small amount. In the case of heavily loadedbeam connections, an unstiffened seat angle may be insufficient tocarry the reaction, while a stiffened seat in some cases may not be permissible because of building clearance requirements. Beam web connecting angles may be provided in this case to furnish the reactioncapacity. Tests 41 and 43 are of this type. (Lines 24 and 42 in TableII.)

The rivet pattern of the tension rivets in the vertical leg of the topangle is a factor influencing the behavior of the connection. In mostof the tests the vertical leg was the four-inch leg of a 6 by 4 angle andthe tension rivets were all in one line. On a small column it may notbe possible to get four rivets in one line. Two lines of rivets requireeither a 6 by 6 top angle, or a structural tee connection. Tests 41,42and 43 (Lines 24, 37 and 42 in Table II) made use of two lines ofrivets in the vertical leg of a 6 by 6 angle. Of these, only test 42 maybe compared to a similar test using a 6 by 4 top angle. (Test 24,Line 36, is exactly the same as Test 42 in other respects.) Tests 24and 42 both gave good results, although 42 was somewhat strongerthan 24. The rivet pattern in the vertical leg of the top angle inTest 42 should be noted. Two rivets with the short gage lengthare placed at the ends of the angle where the greatest column flangeflexibility obtains. An improvement in equilization of tensile rivetstress is obtained by this pattern. It seems probable that a reversedrivet pattern to that used in No. 42 would be preferable in a columnweb connection when two rows are necessary.

Connections W1'th Structural Tee Replacing Top Angle-The structural tee is particularly adapted to connections to a column web, wherespace will not allow a sufficient number of efficiently placed tensionrivets in a top angle. It also has possibilities in connecting heavier


beams when a top angle becomes inadequate to the task of developingan appreciable semi-rigid moment.

Four tests were made using a structural tee at the top, namely,Tests 34, 44,33 and 45, reported on Lines 9,25,38 and 43 of Table II.All of these connections were to the.column web. Their safety factors,with respect to rotation, are summarized below from the data in TableII. Test 45 had beam web angles in addition to the structural tees.

RotationLine in Test No. No. Factor ofTable No. Beam Size Tee Size Tensile Shear SafetyII Rivets Rivets lid = --

10 20--------------

9 34 12W25 10 W41 X 772 4 4 2.9 2.0

25 44 16W78 12 W37 X llU 8 6 6.2 + 4.3 +38 33 18W47 lOW 41 X 772 4 4 7.4 5.1

43 45 18W85 12W37 X llU 8 6 4.3 2.9

The tests made by Rathbun4 include a number of tee connections,most of which were of a wind-bracing type, somewhat heavier andwith more rivets than those tested in this program.

Roof Connections-Three assemblages were designed with the top ofthe beam flush with the top end of the column, so as to simulate theusual conditions at roof framing. Test 38 (Line 10, Table II) madeuse of a seat angle with beam web angles rear the top of the beam.This test indicated a rather low factor of safety. Two tests, Nos. 46and 47 (Lines 15 and 16, Table II) had inverted 8 by 6 top anglesThese tests had good factors of safety but developed somewhat lessrigidity in proportion to strength than most of the other connections,this being particularly true of the column flange connection. Theflanges of the column bent rather easily at the ·end of the column.

Development of Semi-Rigid Connection Standards-This programof tests provides the necessary data for the preparation of Tables Vto VIII, giving dependable restraint values, p, for the five types oftop and seat angle connections shown in Fig. 11, within the range ofbeam sizes covered by this investigation. In the preparation of thesedata the estimate of dependable restraints has been based on the

(J. Charles Rathbun, "Elastic Properties of Riveted Connections", Transactions,A.S.C.E., Vol. 101, p. 524, 1936.

NOTES-

~"tRIVETS FOR TYPE 1 a TYPE lIr CONNECTIONS.

r t BOLTS AS NOTED, AND f tRIVETS, FOR TYPE ]I CONN£CTS,"tr RIVETS FOR TYPE 111 AND TYPE V CONNECTIONS.

>!'oo....

Ult'Jis:...,:ll...0...t:i

I:l:lt'J>is:,..,0,

"88"CO)

0t"qis:Z

CO)

0ZZt'JCO)..,0ZUl

CUT HEREt OPTIONAL)

8+

91"

SECT"AA"FOR TYPES IV av

SECT "At1.'FOR TYPES I, n am

- • I' •(MIN.) 8 i (MIN.)

Il.. r .~ --..;..: - -Ir " " I ," I '-' ~'-' '-' '-'

2 i " " I"L L 6". <r• .!."~

~

rL ,"~ ~

z '-' '-'

FILLS· - lit•( OPTIONAL) 1 HIGH STRENGTH• BOLTS·TYPE ]I ONLY

"" " " " ~

~ '"

AJ. .\. SIZE OF SEAT ANGLE AND RIVErS FASTENIN\; ,)

IT TO COLUMN AS REQUIRED BY BEAM REACTION-

Fig. I I.-Suggested standard semi-rigid connections.


straight-line construction of Fig. 6, with an over-load factor of 1.65.As previously discussed in connection with Fig. 7, the values have beenreduced where necessary so that the average rivet tensile stress will,in no case, exceed 1.65 times 15 k.s.i. when the beam is subjected to a65% overload. The rivet value of 15 k.s.i. has been chosen to'provide an additional factor of safety, with respect to the working valuerecommended by the American Institute of Steel Construction, inorder to cover uncertainties as to individual rivet loading where thepermitted reduction in beam size is directly a function of rivet stress.

In one type of connection (Type II) where rivet stress is frequentlythe determining factor, dependable restraint values are based on theuse of high strength bolts meeting the requirements of A.S.T.M:Specification A-261 , with the proviso that such bolts shall be tightenedto a specified torque. The amount of this torque has been determinedfrom a study of the experimental work of the British Steel StructuresResearch Committee12 •

A 6 X 4 X % in. angle has been adopted as a standard in the proposed design tables. This is % in. thinner than might have beenselected on the basis of the majority of the tests, but it has beenchosen to provide added flexibility (even at the sacrifice of somewhatgreater possible restraint percentages), thereby minimizing the possibility of too Iowa rotation.

The shear rivets of the seat angle (and of web angles if they arerequired by the beam reaction) must, of course, provide sufficientbeam reaction capacity, based on the' specified allowable workingstress in shear.

A suggested supplement to the A.I.S.C. Standard Specificationcovering the use of these semi-rigid beam-to-column connectionsfollows:

""Final Report of the Steel Structures Res3arch Committee", pp. 284-287.


SUGGESTED SUPPLEMENT *TO

A.I.S.C. SPECIFICATION FOR STRUCTURAL STEEL FOR BUILDINGS(As Revised February 1946)

TO COVER

SEMI-RiGID BEAM-TO-COLUMN CONNECTIONS

Section I. Application

(a) Specific Citation Required

Where the "Specification for the Design, Fabrication and Erectionof Structural Steel for Buildings" of the American Institute of SteelConstruction has been adopted by citation in a Building Code orOrdinance, or is used in the design and construction of a building, thisTentative Supplement is not in force, except by specific citation.

(b) Reference

When this Supplement IS III force, beams framed to columns bymeans of approved semi-rigid connections may be designed on thehasis of partial end restraint, as specified in Section 14 (b) and limitedby Section.21 (e) of the Standard Specification.

Section 2. Semi-Rigid Connections(a) Types

Only the five types of semi-rigid b3am-to-column connections shownin Fig. 11 are approved under this supplement.

(b) Percentage of Rigidity

The maximum amount of end restraint which may be used in computing the moment, for which a semi-rigidly connected beam may bedesigned for the given loading, shall not exceed the percentage ofrigidity given in Tables V to VIII, for the beam and connection selected.If dissimilar connection types are employed at opposite ends of a beam,the percentage of rigidity used in the computations shall not exceedthe value tabulated for the more flexible type.

* This supplement is included to show the reader how the proposed design techniquemight be made to operate within the framework of the present A.I.S.C. Specification, and to invite comment. It does not constitute a design recommendation of theInstitute at this time, as it has not been studied by the Committee on Specifications.


\\

(c) H1'gh Strength Bolts

If high strength bolts are substituted for the tension rivets, as inType II connections, they shall conform to A.S.T.M. A-261-44T.Their holes may be either drilled or punched. Bolts used in lieu oftension rivets shall be tightened in the field to a torque of not less than125 lb. ft.

(d) Beam Reactions

Beam seats, unstiffened or stiffened, and/or web angle connections,shall be adequate to provide for the beam reactions, using the allowable unit stresses prescribed in Section 15 of the Standard Specification.

(e) Connections on One Side of Column Webs Only

When beams are not located on opposite sides of a column web soas to permit the use of the same tension rivets or bolts to connect thetop angle of both connections, a reinforcing angle shall be placed, onthe side of the column web away from the beam connection, in linewith the top angle of the connection.

Section 3. Supporting Members

(a) Alignment

Columns, used to support beams designed, on the basis of partialrestraint by virtue of the approved semi-rigid connections, shall havetheir axes approximately in line with these beams.

(b) Other Requirements

A semi-rigid connection shall not be considered as affording restraint at the end of a beam when the flange of a column to which itframes is less than one-half inch in thickness, unless the column flangeis stiffened to resist an outward deflection caused by the pull of thetension rivets or bolts.

A semi-rigid connection shall not be considered as affording restraint at the end of a beam unless the top of the column extendsabove the center line of the tension rivets a distance at least equal tothe width of the column flange.


Table V.DEPENDABLE PERCENTAGE OF RIGIDITY, p, FOR

TYPE I & TYPE II SEMI-RIGID CONNECTIONS(See Fig. 11 for Details)

2 - %" 4> Tension Rivets (Type I)2 - %" 4> Tension Bolts (Type II)

BEAMSPAN IN FEET

8 10 12 14 16 18 20 22 24 26 28 30

34

43

48

36

45

25

50

38

31

14 W 30

12 W27

10 W 21

------ --------------------------,----

37 39 40 42 I 35 27 I 20 14 9 4 - I -37 39 40 42 43 44 45 46 46 47 47 47

29 32 -;4- 35--12516-1-7- --------

29 32 ~_~_~_~_~_ 39 ~_~_ 41 42

29 27 29 30 1 29 18 8 -- -- -- 1 -- -- --~_~_~_~_~_~ 34_~_~_~_~_~_

29 31 32 1 32 22 10 -- ~ I --29 31 ~_~_ 34 ~_~_ 37 38_ 38_ 38 39

25 27 29 27 16 5 I -- -- I --25 27 ~_~_ 31 ~_~_ 34 _34_~_ 35 35

22 24 25 22 10 -- -- -- -- -- -- -22 24 25 27 27 28 29 30 30 30 31 31

40 ~f ~f ~(I ~( 2f 26~ 27~ 27- 28 __ 28 _ 28 _ 29-

18 20 21 114 -- -- -- -- -- I -- -- 1--;; ; iil~:::I:]:1::: :] ::-::1:::27 29 31 I 26 15 4 1 -- 1 -- -- 1 -- -- --27 29 ~_~_~_~~~__36_~_~_~_~_

~1 ~~ ~: -' ~g 13~ _ 31 J321 32 _ 33__ 33 _~_ 34_

21 23 25 116 1 -- -- I -- I -- -- -- --21 23 ~_ "':'6_.!!_...:.s_~_~_~_~_~~~

20 21 22 111 -- I -- -- I -- -- --20 21 22 23 24 25 26 26 27 27 28 28

~: ~g ~g - 2i - 22 -I 23 -I 24 -I 24 - 25 - 25 - 25 - 25-

53 ~-~-~~-~121T21 -1 22 -1 22 -1 23T23~ 23 - 23-

Upper Lines Give p-Values for Type 1.Lower Lines Give p-Values for Type II.

10'


Table VI.

DEPENDABLE PERCENTAGE OF RIGIDITY, p, FORTYPE IiI SEMI-RIGID CONNECTIONS

(See Fig. 11 for Details)

49

2 - Ys" <I> Tension Rivets

SPAN IN FEETBEAM

8 10 12 14 16 18 20 22 24 26 28 30---

10 W 21 ~146J~_ 49 I 51 I 52 ~J~_ 42 38 ~J~_----1--25 38 40 42 43 45 46 40 35 30 25 21 17------------------- -----

29 34 36 38 39 40 39 32 26 20 15 10 6-------------------------

12 W 27 34 36 38 39 40 41 41 35 29 24 19 15---------------------------

31 30 32 34 35 36 37 36 29 23 17 12 7-----.-1---------1-----7- -1-1-='-36 27 29 30 I 32 33 34 29 21 14

40 24 2"6T"27T2;- 30- 31 "22T14--7--=- -'=--I-'=--24T25- -;;-127- --1------ -=-I-'=-r=-45 23 28 18 9 -

50 21 22-12;- 24-125- 24 14-1-5- -=-- -='-T='-I-='-

14W 30 30 32 ]-34 ~ -36 ~ ~!8 ~ 39 40 ]-33] 27 ~ -2'T17T"-34 27 29 31 32 34 35 34 1 27 I 20

14-1-8--3-

38 24 26- 28- -30-\-3i--: 32 29"-122-1-14- -7-1--l-r--

43 22 24- 2"6- 27TZS- 29 23T14-1-6- -'=--1-'=--1-=-48 19 21- 23 - 24 r2"5- 26 19TIOI-I--'=--I-=T=---r---r-- --15-1-6 -1-=- -'=-r=-I-=-53 19 20 21 22 23 24

4 - %" '" Tension Rivets

BEAM

50 SEMI-HIGID BEAM-TO-COLUMN CONNECTIONS

Table VII.

DEPENDABLE PERCENTAGE OF RIGIDITY, p, FORTYPE IV SEMI-RIGID CONNECTIONS


SPAN IN FEET

10 12 14 16 18 20 22 24 26 28 30 32 34

14 W 30 ~I~I~~~I~~I~~~~I~~34 S2 35 137 39 40 42· 43 44 45 46 47 I 45 42

38 30 32 34· 36 37 39 40 41 42 43 42 I 38 -':5

43 '-'7 29 31 33 34 35 36 37 38 39 35 30 26

48 25 27 28 30 31 32 33 34 35 35 30 25 20

53 23 25 26 28 29 30 31 32 33 31 26 21 16

16 W 36 31 I 34 36 38 39 41 42 44 45 46 42. 39 36

40 28 31 33 35 ~ 38 39 40 41 40 35 30 26

45 26 28 30 32 3335 36 37 38 35 30 25 21

4 - '!/slit/> Tension RivetF


Table VIII.

DEPENDABLE PERCENTAGE OF RIGIDITY, P, FORTYPE V SEMI-RIGID CONNECTIONS


51

SPAN IN FEETBEAM

10 12 14 16 18 20 22 24 26 28 30 32 34.--

14 w: 30 41 44 47 49 51 52 54 55 56 57 58 59 60--------------------------

34 38 41 43 45 47 49 50 51 52 53 53 54 54--------------------------

38 35 38 40 42 44 45 46 47 48 49 50 51 51---------------------------

43 32 34 36 38 40 41 42 43 44 45 46 47 48---------------------- - --

48 29 32 35 36 37 38 39 40 41 42 43 44 44---------------------- - --

53 27 29 31 33 34 36 37 38 38 39 40 41 41--------------------------

16 w: 36 35 38 41 43 45 47 48 49 50 51 52 53 53--------------------------

40 32 35 37 40 42 43 44 45 46 47 48 49 49--------------------------

45 30 32 34 36 38 40 41 42 43 44 44 45 45--------------------------

50 27 30 32 34 35 37 38 39 40 40 41 41 42--------------------------

58 24 26 28 30 31 33 34 35 36 36 37 38 39--------------------------

64 22 24 26 28 29 30 31 32 33 34 34 35 35--------------------------

71 21 23 24 26 27 28 29 30 31 32 32 33 33------ ------------------

78 19 21 22 24 25 26 27 28 28 29 30 31 31--------------------------

18 w: 50 27 30 32 34 35 36 37 38 39 40 40 41 41--------------------------

55 25 28 30 32 33 34 35 36 36 37 38 39 39--------------------------

60 24 26 28 29 30 31 32 33 34 35 35 36 36--------------------------

64 22 24 26 28 29 30 30 31 32 33 33 34 34--------------------------

70 21 23 24 26 27 28 29 30 30 31 31 32 32--------------------------

77 19 21 22 24 25 26 26 27 28 29 29 30 30--------------------------

85 17 19 21 22 23 24 24 25 26 27 27 28 28--------------------------

21 'N'62 22 24 26 28 29 30 31 32 33 34 34 35 35-- ----------------------

68 20 22 24 26 27 28 29 30 30 31 31 32 32--------------------------

73 19 21 23 24 25 26 27 28 29 30 30 31 31


VII-PROPOSED METHOD OF DESIGN FOR BEAMSWITH SEMI-RIGID CONNECTIONS

It has been shown (page 13) that, for uniformly loaded beams, aconnection rigidity of 75 percent is needed to produce negative moments at the ends of a beam equal to the positive moment at midspan, and that a connection rigidity of lOOpercent is similarly requiredfor beams supporting a concentrated load at mid-span. In the methodof design proposed, only connections which will function with considerably less rigidity than 75 percent will be used, so that, in everycase, the beam may be proportioned for the positive moment. Thismoment will be less than the one which would exist if no end restraintwere present, the extent of the reduction being determined by theamount of dependable restraint afforded by the semi-rigid connectionsused, and by the contributory effect of frame action.

To obtain the section moduli required for beams framed by connections having dependable amounts of restraint, "redesign coefficients" will be derived for critical conditions of loading with respectto frame action, and for various types of beam loading. The "redesigncoefficients", multiplied by the section modulus required for thecondition of no end restraint, will immediately give a "safe" reducedsection modulus, based on the dependable effect of the semi-rigidconnections under the least favorable frame action likely to exist.While this reduced section modulus will always be greater than theone which might be derived by an accurate analysis of the momentsin the given frame containing the particular beam under consideration,the sacrifice of some of the possible economy can be justified by theconsiderable reduction in the design computations involved.

Six factors influence the effect of frame action on the positivemoment produced by gravity loading in any semi-rigidly framed beamin a tier building. These factors are:

(1) The relative length of adjacent spans.(2) The relative size of adjacent beams.(3) The relative size of adjacent columns.(4) The relative rigidity of the several end' connections.(5) The symmetry or asymmetry of loading on each beam.(6) The arrangement of loading of adjacent spans-both at the

level of the beam under com;ideration and alRo at adjar.entlevels.


Assuming, first, a complete symmetry of frame with respect tothe first five of these factors, the arrangement of span loadings shownin Fig. 12 (a) is the most critical one possible for A-B, an interiorbeam in a frame several bays wide and several stories high. Althoughits occurrence is highly improbable, this arrangement is frequentlyassumed, in analyzing the effect of live loading on continuous-frametier buildings, to obtain results that are bound to be on the safe side.

Joints A and B, as well as joints C, D, E and F, are restrained againstrotation by the stiffness of the column sections above and below thejoint. They are also restrained by the stiffness of the unloaded beamsin the adjacent bays, but this restraint will be diminished, in comparison with the condition of full continuity, by reason of the flexibility of the connections framing these beams to the columns. If thislatter restraint were assumed to be removed completely, joints A, B,C, D, E and F would rotate somewhat more, and the positive momentin beam A-B would thereby be increased. Since the results will err onthe "safe" side without too much loss of economy, such a simplifyingassumption will be made. This assumption will also have the effectof largely eliminating (1) and (2) from the list of factors which otherwise would have to be investigated in analyzing the effect of frameaction.

A requirement that the same connection type be used in framingboth ends of a given beam will eliminate (4) as a factor. If differenttypes of connections are used at the ends of a beam and the beamsize is determined by the rigidity given for the more flexible type ofconnection, (4) will also be eliminated as a factor.

At first it will be assumed that columns CAE and DBF (Fig. 12 (b))are the same size, and that the loading on beam A-B is symmetricallydisposed about the center of span.

The dotted lines in Fig. 12 (c) indicate the actual moment diagram;the solid lines show the moments which would result if the unloadedbeams were removed (assumed as taking no moment).

In Section IV a method of evaluating the dependable percentage ofrigidity of semi-rigid connections was developed, based on the assumption of no rotation of the columns. As joints A and B rotate throughangles BA and BR (Fig. 12 (b)) the restraining end moments are teduced(shifted to mid-span) and, therefore, the connections actually are lessheavily loaded than previously assumed. Because of the non-linear(M,cfJ) relationship of semi-rigid connections, any reduction in theassumed connection moment results in a proportionately smaller angle


I ~ I ~

~ ~

I I c: o I I

A j • B

I I j IE F

~ ~

lea \'2. b

\"2. c.

Fig. 12.-Analysis of semi-rigidly connected frame forcritical loading condition.


of rotation of the connection, thus increasing its actual percentage ofrigidity under this condition of frame action.

Note, in Fig. 12 (c), that the moments induced in the columns areof constant magnitude between joints, and that the negative momentsat the ends of the loaded beams are also of equal magnitude at eachjoint, although opposite in sense at the two ends of anyone beam.

Because of the symmetry of the frame and loading, a direct distribution of the moments induced by frame action can be made in oneoperation in accordance with the Hardy Cross procedure, with no"carry-over". Under this procedure the joints are first assumed aslocked against rotation and the fixed-end moments produced by thebeam loading are assigned to the joints where the beam ends frame tothe columns. As the joints are simultaneously "unlocked", thelocked-up unbalanced moments at the joints are distributed to eachmember in proportion to its "bending stiffness" and in the case of theloaded beams, subtracted from the fixed-end moments to obtain theactual moments induced by the frame action. Bep.ding stiffness maybe defined as the ratio of applied moment to corresponding anglechange, i.e., the amount of moment required to produce a unit anglechange-M/4>. Since the moments induced by frame action in thisproblem are of constant magnitude throughout the entire length ofeach member (beams and columns), the change in slope from one end

of the member to the other is, by the moment-area principle,~J,where

l is the length of the member. And, since the change of slope is ofequal magnitude at both ends of the member, it may be expressed,for either end, as

or

where K = 1/1.

cf> = 2:K' (equals OA in Figure 12 (b)

Then the bending stiffness, M/¢, equals 2EK.This value is correct for the columns and the total bending stiffness

of the column (above and below joint A) may be written as T-2EKc .The actual bending stiffness of the beams, taken together with their

connections however, by reason of the connection flexibility, willhave to be modified. Such a modification may easily be made if the(M, 4» relationship of the semi-rigid connection is assumed to beconstant.


Let M 1 be end moments applied to the connections at each end of abeam, such that M 1 is constant throughout the length of the beam.If the connections are 100% rigid (p = 100) the angle change 01 , atthe ends of the beam, will be, by the moment-area principle

(9)

Iwhere KB = Y for the beam.

Now, if the connections are "semi-rigid" (p < 100%), let M 2 =the end moment required to rotate each end of the beam through anangle 1/>2, such that

</>' + </>c = (Ii

where cPo is the angle of rotation produced in the connection by reasonof its flexibility, between the end of the beam and the point of application of M 2 • If the connections were very flexible and approached thecondition of zero stiffness (p + 0), the rotation cPo could be producedby a moment M 2 that approaches zero, and the ends of the beam inthe limiting case would not rotate, i.e., cP2 = O. The "percentage ofrigidity" of the connection as defined in Section IV, may now be expressed as the percentage of cP2 to 01or M 2 to M1, i.e.,

substituting lIf. = 2EKB 8.

into Eq. 10,

p </>' lIf,100 = -0. = lIf.

(Eq.9)

p lIf,100 = 2EKB 8.

(10)

and the stiffness of the member consisting of the beam and its semi~

rigid connections, becomes .

lIf, p0; = 100 (2EKB ).

The unbalanced moments produced by unlocking the joints cannow be distributed to the ends of the members forming the joints.Since the "distribution factor'·' is the ratio of the bending stiffness ofany particular member to the sum of the bending stiffnesses of allthe members entering the joint, the distribution factor for beamA-B in Fig. 12 (b) will be


p100· 2EKB

};2EKc + L .2EKB100

p100· KB

};Kc + _E_ • KB100

But, due to the flexibility of the connections, the moment at theends of the beam, when the joints were "locked" against rotation,

was not the full fixed-end moment, but 1~0 • MR. Unlocking the joints,

this moment will be lessened by the proportional part of the unbalancedmoment distributed to it, i.e., by

(L. K B

)pMR . 100100 p

I.Kc + 100 • K B

and the net moment remaining at the end of the beam will be

(__T!- • KB) ( )M A = pMR _ pMR 100 _ M R 1

100 100};K + _P_ K - 100 + K B

C 100 B .. P };Kc

The positive moment at the mid-span of the beam equals

(11)

(12)

(13)

where M s = the moment produced by the same loading on a simplespan.

The desired redesign coefficient then equals

F = ~ = 1 - ~~ = 1 - ~:(}!!!! :~)p };Kc

For any particular type of loading (uniform, concentrated load

at mid-span, etc.) Z: is a readily derived constant. Then the only

variables affecting F for a given type of loading are (1) the percentageof rigidity of the connections used and (2) the relationship of beamstiffness to the total stiffness of the column.

The adequacy of frames designed in accordance with the foregoing procedure has been tested by recomputing the bending stressesin both exterior and interior beams in several frames designed by thisprocedure, where the ratio of bay widths was varied through a considerable range. In recomputing these stresses the more accurate

58 S E M I - RIG I D BE AM - T 0 - COL U M NCO NNE C Ti 0 N S

A B

D oJ

01:," ,.~ " irrr ",,,,1. .1z. .1,

c

Lond of 3.5 KIps per ft "£1 1z.Center shess III Klp~ per ~.\"

on benms as 'E.nown AB C.D BG OJ

~".\ 18.5 AnQI~f>1

I? ' 24' •11· :!> Iq·"2. De""qn

~114- 1&.1 AnCl\'(SI~

1"2.' "2.4'fr

\) J 18.0 18.lDDe""qn

~18l 18.4- AnCl\Y~ls

"2.4' 1.4'Iq.z.

fr18·lD Deslqn

~IBlD 18:' AllCllyslS

1.4' "2..4' ..o J Iq Z. 18 lD [)e'c>lqn

~\8·\ 114 Al\Qlysls

2.4' 1"2.'ir

IE!>.lD p.(one""qn

A 6

~18·<0 11 Z. AIlQI'(sIS

2.4-' \"2.' ..Iq z. 113 l)eslqn

4 5tress by deslqn procedure would be eltacH~ ,0 K.5 I. ,tsechon modulus o-f ne.tual beam were snrne 0.'" that Yeo.\l"e~

Fig, 13.-Calculated maximum beam stresses in frames designed byproposed design procedure.

i-' PROGRESS REPORT NUMBER ONE 59

'.

but more tedious moment distribution method, as modified for use insemi-rigidly connected frames7,a was employed.

The results of this study are given in Fig. 13 and indicate surprisinglygood agreement. In every case the stresses derived by means of themore precise moment distribution analysis prove to be less than thoseobtained by use of the proposed ,method. This may be largely accounted for by reason of the actual restraining effect of the unloadedbeams, which is ignored in the proposed design method, but whichwas. included in making the moment distribution analysis. In thecase of the three equal 24' spans the difference in stress by the twomethods is practically constant for all parts of the frame. Even whenthe ratio of interior to exterior span lengths was changed by as muchas 100%, the true stresses resulting from inequality of span length,in no case exceeded or even quite equalled the stresses derived by theproposed method. The fact that all of these stresses range from a lowof 17.1 to a high of 19.2 k.s.i., instead of being 20 k.s.i., is of courseexplained by the fact that the available beam sizes which most nearlymeet the design requirements have section moduli slightly in excessof actual requirements. This is typical of the condition encounteredin every day design practice and, where it occurs, provides an additional factor of safety which is frequently overlooked.

Curves based on Eq. 13, for various percentages of connectionrigidity and various types of loading, are plotted as solid lines in Figs.14, 15 and Hi.

If all the spans were equal; all the story heights were the same;and every span were equally loaded (as, for example, by dead load)there would be no rotation of the joints (i.e., no frame action) at the

ends of interior beams. Then the term ::'0 would not appear in Eq

(13). Assume such a frame with one-third of the total loading causedby dead load. Let F D be the redesign coefficient associated with thisdead ioading, and let FL be the redesign coefficient associated with thelive loading arranged to give the critical condition assumed in theearlier discussion. Then, dividing the problem into two parts (deadload and live load), and applying the principle of superposition, the

7 A. J. S. Pippard and J. F. Baker, "The Analysis of Engineering Structures"Longmans, Green & Co., New York, 1936.

8 Bruce G. Johnston and E. H. Mount, "Analysis of Building Frames with SemiRigid Connections", Transactions, A.S.C.E., Vol. 1Q7-:---:1942, pp. 993-1019.


redesign coefficient expressing the effect of the combined loading wouldbe

where

and

Then

(

1 + pKB

)MR .~.-1 -- . - M s 100 + KB .

p ~Ko

\

(Eq. 13)

(Eq. 13)

(14)

Curves based on Eq. 14 are shown as dotted lines on Figs. 14, 15and 16. For frames having nearly equal bay widths, "safe" F-coefficients for interior beams may be read directly from the appropriatedotted-line curves. If F-coefficients are read from the solid linecurves for exterior bay beams, and for interior beams when the baysare unequal by more than a moderate amount, it is obvious that,since the balancing effect of dead load is entirely neglected, a widemargin of safety is afforded.

Assume now that column CAE (Fig. 12 (a)) is stiffer (larger) thancolumn DBF. Since the conditions at beam A-B are no longer completely symmetrical, a precise solution of the problem by the HardyCross method involves a "carry-over" and cannot be completed inone cycle. However, if the stiffness of column CAE is assumed equalto the lesser stiffness of column DBF the resulting redesign coefficient

will err on the "safe" side and, within the usual working range of ::'0the error will be small.

Analysis of the case of unsymmetrically loaded beams requires asomewhat different attack. It is given in Appendix A. It will be seenfrom this analysis that, for. asymmetrical loading, F-values taken from

oZl".l

0.71

0.1'1

0.88

0."

0.114

0.10

0.82

0.74

0.'6

10 10 0::::--:: '""":- f- :::-- :..-=-...;.~~~~ .---

° __ I 20 ,/" ."". ?;I::?"f--- -... ~-t_- ..../ ~ ::?' ---

I...---__ 0._ -1---

...-~ ~-~ /:;~ 1--' ----~- ---- - ~ 30 ~7/ 1-- f---- '" 1;2 1--- ---

V V -- oJ';:: ~ '/"., .......... -- ---1--- .-/ 'a p:-.::= ,,0 -

~~- .-/..,- ....~ -4J.~ // -- _...

V ~~- ~ /'" ....- /'" /,,'"

,,/ _I--...:t- w -/"V_~1-- V / 1 1 1 1 1 I 1

....' V ,/...- I ./ I--

k / ...- ,,0

V V- I-- h p \-p .L I---- 5 3.....-::;

I I '---

1/ V...... V ,-......

~/ 1/

-.... 1--....

1/' /,,1/ -I

V/t/

1//0.60

o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 5.0 4.0 $.0 60 7.0 8.0 '.0 10.0

STIFFNESS' RATIO {f.

0.118

0.116

0.'4

0.'2

0.'0

0.88

0.86.... 0.84.~z 0.82!!!..;:: 0.80.......... 0.78z..0; 0.76........ 0.74a:

0.72

0.70

0.68

0.66

0.64

0.62

Fig. 14.-Redesign coefficient curves-uniform and third-point loadin9'

r .- l- i-.

'0 '0

~-~ :;;..- --20 .....-?"':~ ::::?'-- - .-

.- -' ~. =.2~ / -0 7 -- --.. 30 --- _. .----- --'§- 0 ------ co 30 40 -- -- --C

~l-- --- -- L--~- ~ r%-'"

V ...-1---- ~- ---- ~ k::: &0 --- -- --

~ V ~~:;;;;>'"~r--- ... --~ ~-:. ..- ....-

V t:::/ I" V..

V"--- ... 110./ ---- ...--

~

_...

V~~-

1--- V./

&0__-

/'V -7' -----""

~ ,," / "",-

~ /I-"

L -I- P -I- L

" "2 I "2

" T

/. V"'"

IV ,

STifFNESS RA710 i=cFig. IS.-Redesign coefficient curve--c:oncentrated load at mid-span.

0 ...

0."

0.'4

0.12

0.10

OM

.. 0.8...., 0.84..2..

0.82....0uz 0.80coiii..

0.7'0..a:

0.7'

0.74

0.72

0.70

0."

o 02 0.4 0.8 0.8 1.0 12 I.. 1.8 I.' 2.0 3.0 4.0 11.0 8.0 7.0 '.0 • .0

0."

0."

0.'4

0.12

0.'0

0."

0."

0.'•

0.'2

0.80

10.0

C":loZZt<JC":l0-3

oZUl

.......-~.........~ - ~------~ ~-.._-~ -- ·If.~

oZto!

0.90

098

094

092

096

088

0.84

088

0 ..80

0.82

07'

0.78

" -...

\0 -:::-.- .-' :::.-I- ~10 -.--->.... '-- .--~~~~~- --

20 V / ~~).=

.- - -'b-:"-~- - -=.2.2-

-~O __V -0V 1-'- --- -- ,. ---- .-- >;:~..- /~ 1'" --- --%-- 40 --f.-- ~-

~~ If --- ----- ...- " --- "~O "

~ -~

,,4 V 1:- ,/ ,,-- ----,...- 'i~~I_AO ,/ .--

V'./"

V ~~---V7 ,/,/ ",..- ... ./ "V ...-- /'7' V --~~--./

~>...- /' ~- --

./ -- /60

V' V V-- --- .-~ -- PTI11/ // / -----

/- ./ / //.. /

II' / ./' "v./

~V

r082 0 0.2 04 0.6 0.8 1.0 '.2 1.4 1.6 1.8 2.0 3.0 4.0 ~.O 60 7.0 8.0 9.0 10.0

~STIFFNESS RATIO IKe

0.88

0.64

09,8

0.98

0.94

092

0.90

0.88

0.88

."- 0.84..z'" 0.82U;;:"- OBO'"0uz 0.78

"in'" 0.78e0:

074

0.72

0.70

0.68

Fig. 16.-Redesign c:oeffic:ient c:urves---,quarter-point loading.


Fig. 15 provide redesign coefficients which are on the safe side, andthat, within the usual working range, any consequent error will be toosmall to warrant further refinement.

When the bending moment in a beam is produced by a combinationof two or more types of loading, an adjusted redesign coefficient maybe obtained by weighting the coefficients for each type of loading (readfrom the curves) in proportion to the contribution of each type ofload to the total moment.

Assume for example, that a total moment is 40% due to uniformloading and 60% due to a concentrated load. Also assume that, foruniform loading, F = .81 and, for the concentrated load, F = .86.

For the combined loading

F = .4 X .81 + .6 X .86 = .84.From Figs. 14, 15 and 16 it will be seen that the greatest reductions

apply to the condition of uniform loading, and that the least reductionsapply to the condition of a single concentrated load at mid-spanwith the case of equal concentrated loads at the three quarter-pointsintermediate between these limits. A little study of these curves willenable the designer to select, by inspection, a reduction factor whichwill be very close to, and on the safe side of, the actual value, evenfor a complicated system of loads.

The proposed method of design may be summarized in the followingrules of procedure:

1. Design the beam for maximum b.ending moment, assumingsimple support& (no restraint).

2. Calculate the stiffness con~tants for the next lighter beamsize and the less stiff, or minimum T.Kc , of the two supporting

columns, and then compute the ratio KB/T.Kc . (KB = f for

the beam, and T.Kc = T. f for the column above and below the

beam.)3. Select the type of semi-rigid connection to be used and obtain,

from the appropriate Table V, VI, VII or VIII, the dependablepercentage of rigidity for this next lighter beam size, on therequired span.

4. Choosing the curves appropriate for the required type ofloading, enter Fig. 14, 15 or 16, with the computed KBIT.Kcand move vertically upward to an intersection with the dependable percentage of rigidity obtained from the tables,

\.1

PROGRESS REPORT NUMBER nNE 65

II

l'~ .

5.r("

I

6.

interpolating between the plotted curves when necessary.Move horizontally to the left and read the redesign coefficient,F, from the vertical scale. For interior spans in frames havingnearly equal bay widths, the dotted curves may be used;otherwise use the solid line percentage curves. If the bendingis produced by a combination of uniform loading and concentrated loads a weighted F-coefficient may be derived fromthe F-value3 obtained individually, from Figs. 14 and 15, orFig. 14 and 16. A single concentrated load may be assumedas located at mid-span, regardless of its actual location, forthe purpose of obtaining its F-coefficient.

Multiply the required section modulus previously calculatedfor the simple span design, by the redesign coefficient, andselect the lightest beam which will provide a section modulusequal so the product of this multiplication.

When a particular beam is repeated under identical loadingconditions a number of times in a frame, so as to justify theextra work, and the size determined by step (5) is less than thatassumed in step (2), a further economy may sometimes beeffected by repeating the procedure until K B in step (2) exactly agrees with the beam size actually used.

VIII-ACKNOWLEDGEMENTS

The authors acknowledge the advice and cooperation of the sponsors,the American Institute of Steel Construction, through the Committeeon Steel Structures Research. Mr. Frankland, Director of Engineering and Chairman of the Research Committee at the time of the testwork, and Mr. Higgins, present Director of Engineering of the Institute, have been particularly helpful. Mr. Jonathan Jones, ChiefEngineer of the Bethlehem Steel Company, and his assistants, contributed freely with advice on connection details and in the expeditingof the fabrication of test specimens.

The progress of the work was aided by the research staff of theFritz Engineering Laboratory, including in particular, Mr. H. J.Godfrey and Mr. Robert M. Mains, former Engineers of Tests.


ILLUSTRATIVE EXAMPLES

Example A

Given: Uniformly loaded beams, framing between columns spaced26 feet on centers. Total load on each beam, 30 kips (45% live,55% dead). Story heights 10 feet. Columns, 12 w: 53 atthe sixth floor, and 12 w: 79 at the fourth floor. Beams willframe to column flanges.

Required: Size of beams, at the sixth and fourth floors, semi-rigidlyframed to columns.

Ms= 30 ~ 26 = 97.5 kip-feet = 1170 kip-inches-

1170Req. 8 = 20 = 58.5

Required simple beam, 16 w: 40 (8 =64.4) or 14 w: 43 (8 = 62.7).Since the simple beam requirements would almost be satisfied with

the next lighter section, the redesign computations will be made atonce using the second lighter section.

At the sixth floor, Type II semi-rigid connections will be specified.From Table V, p = 33% for a 14 w: 34 beam on a 26 foot span.

K 339.2B = 26 X 12 = 1.09

KB = 1.09 = 153~Kc 7.10 .

2 X 426.2and ~Kc = 10 X 12 = 7.10

Interpolating between the solid line curves for p = 30% and p =40% in Fig. 14, a redesign coefficient, F = .79, is obtained (note thatthe maximum effect of frame action in this problem, as indicated by

the relationship ~~c' is so small that there is little difference between

F-values derived by the solid and dotted curves; hence the more conservative solid line value may be taken for both interior and end bays).

Req. redesign 8 = 58.5 X .79 = 46.2

use 14 VF 34 (8 = 48.5)

Saving in weight, 15%Saving in depth, 2 inches.


At the fourth floor, Type V semi-rigid connections may be used.A 14 \/IF 30 beam will be tried. From Table VIII, p = 56% for a 14\/IF 30 beam on a 26 foot span.

289.6K B = 26 X 12 = .93

T-K = 2 X 663.0 = 11 05c 10 X 12 .

K B .93T-Kc = 11.05 = .084

Interpolating between p = 50% and p = 60% in Fig. 14, an Fvalue of .64 is obtained.

Req. redesign 8 = 58.5 X .64 = 37.4

use 14 \/IF 30 (8 = 41.8)

Saving in weight, 25%.

Example B

Required: To design a line of girder beams, each spanning 24 feetand supporting 31 kip concentrated loads at its third points.Story height 10 feet. Exterior beams frame to flange of 12 \/IF65 wall columns. Interior columns, 12 \/IF 79 with webs normal to webs of girder beams.

Ms = 31 X 8 = 248 kip-feet = 2976 kip-inches

2976Req. 8 = 20 = 148.8

Required simple beam, 21 \/IF 73 (8 = 150.7)

Type V semi-rigid connections will be specified. From Table VIII,p = 30% for a 21 \/IF 68 beam on a 24 foot span.

K = 1478.3 = 5 15B 24 X 12 .

The lesser T-Kc = 21~ ~1~24 (minor axis of 12 \/IF 79) = 3.6)

K B = 5.13 = 1 43"1:Kc 3;61 .

68 S E M I - RIG I D B E A M - T 0 - COL U M NCO N N EC T ION S

From Fig. 14,

F = .86 for'end bays (from solid lines)

F '= .84 for interior bays (from dotted lines).

For end bays, Req. redesign 8 = 148.8 X .86 = 128.0

Use 21 \/IF 68 (8 = 139.9).

For interior bays, Req. redesign 8 = 148.8 X .84 = 125.0

Use 21 \/IF 62 (8 = 126.4)

KB(Actually, for a 21 \/IF 62 beam, P = 32%; K B = 4.64; -K = 1.28;2: c

F = .83 instead of .84; and Req. redesign 8 = 123.5)

Saving in weight, 7% in end bays.Saving in weight, 15% in interior bays.

Example C

Required: To'design a semi-rigidly connected beam to carry a uniformload of 1.7 kips per linear foot, and a concentrated load of 22kips located 7 feet from one end, when the c. to c. of supportingcolumns is 20 feet. Columns just below the beam are 12 W'72 and story height is 12 feet; columns immediately above thebeam are 12 W' 65 and this story height is 10 feet. Beam willframe to webs of supporting columns.

M, occurs at point of concentrated load.22 X 13 X 7 .

M,(due to concentrated load) = 20 = 100.1 kIp-feet

M,(due to uniform load) = (1.7XI0X7) -(1.7X7X3.5) = 77.3 kip-feetTotal M. 177.4 kip-feet

2129 kip-inches2129

Req. 8 = 20 = 106.5.

Required simple beam = 18 \/IF 60 (8 = 107.8).

If Type IV semi-rigid connections are specified, p18 W' 55 beam on a 20 foot span.

889.9For an 18 \/IF 55, K B = 20 X 12 = 3.70

174.6 195.32:Kc = 10 X 12 + 12 X 12 = 2.81

KB =3.70 = 1 32'1:.Kc 2.81 .

29% for an


Moment due to uniform loading = ~~~:~ = .57 of total moment.

Frpm Fig. 14, F = .86 for uniform loading.M()ment due to concentrated load = .43 of total moment.

69

Although the concentrated load is not at mid-span, the F-valueobtained from Fig. 15 (F = .90) will err on the "safe" side (see p. 64).

A weighted F-value, for the combination of uniform and concen-trated loading, may be computed as

F == .57 X .86 plus .43 X .90 = .88.Req. redesign S = 106.5 X .88 = 93.7.Use 18 W 55 (S = 98.2).Saving = 8}% = 100 pounds of plain material.

Had Type V semi-rigid connections been specified, p would equal36% for an 18 \/IF 50 beam on a 20 foot span, instead of 29% for the

18 \/IF 55 beam; :~c would have been 1.18 instead of 1.32; the

weighted F-value would have been .86 ; and the required redesign Swould have been 91.6. Th\i.s it will be seen that a 1272% increase inthe rigidity of the connections, resulting from the use of '!/s" ep insteadof %" ep tension rivets, would produce but a 2~% decrease in therequired section modulus, which would be insufficient to permit tEeuse of this next lighter beam. Had the lighter beam proven to beadequate using the larger rivets, the added saving in main materialwould have been 100 pounds. Such a saving would probably nothave warranted changing to '!/s" ep tension rivets here, if the balanceof the fabrication was based on using %" ep rivets.

PROGRESS REPORT NUMBER. ONE

APPENDIX A

REDESIGN COEFFICIENTS FOR UNSYMMETRICAL LOADING

71

On page 26 the percentage rigidity, p, of a connection was defined inreference to a symmetrically loaded beam. On pages 52 to 60 theredesign coefficient, F, was derived, in terms of p ; the load distribution;and the relative beam and column stiffness. The redesign coefficient,F, for an unsymmetrically loaded beam, as for example the case of asingle concentrated load placed anywhere on a single bent span asshown in Fig. 17, can also be derived. It will be shown in the followingderivation for this case, involving both sidesway and unsymmetricalloading, that, while the expression for F is too involved for frequentuse in design problems, nevertheless a handy design short cut is available-that the F-values, already given in Fig. 15 for the special casewhen this load is placed at mid-span (symmetrical loading) , can be substituted for the true values to give results which are on the safe sideand, at the same time, are but slightly in error.

(

h

C1 b

o

Fig. 17.-Single bent with concentrated load-P at any location.


The slope deflection procedure of frame analysis, modified to takeinto consideration the rotational effect of semi-rigid column connections, will be used in the derivation.

Fig. 18.

Fig. 18 shows the deflected and bent shape of any beam, AB. Identical semi-rigid connections are assumed at A and B. The followingnotation, indicated in Fig. 18, will be used:

OA, OB = Rotation of column axes, at A and B, respectively, at theirintersection with the beam axis. (Positive when clockwise.)

6 = Deflection of B relative to A, taken transversely to thebeam axis. (Positive when causing clockwise rotation of astraight line between A and B.)

M A, 101B = Final moments acting on the ends of the beam (and throughthe semi-rigid connections, on the columns) at A and E,respectively. (Positive when acting clockwise on end ofbeam.)

VA, VB = Shears at A and B, respectively. (Positive when tendingto rotate the beam clockwise.)

'Y = A constant (assumed) ratio between the moments transmitted by the semi-rigid connections and the consequentrotations, between the ends of the beam and adjacentcolumns, produced by these connections. (Note: Identiealconnections are assumed at A and B.)

By tbese definitions, 'YMA is the rotation within the connection atA and 'YM B is the rotation within the connection at B, as shown inFig. 18.

It has been shown (page 24) that when no column rotation takesplace, the moment at the ends of a symmetrically loaded, semi-rigidlyconnected beam will be

(Fq.l)


But, by the definition of 'Y, which assumes a linear relationshipbetween M and cf>,

Hence

Cancelling; out M,

q, = 'YM, and

MR

= 100Mp

M = 100M _ 2EIM'Yp I

'Y = _1_(100 _1)2EK p

(15)

Since the tabulated "dependable" values for p (Tables V to VIIIinclusive), for a given semi-rigid connection have been determined bythe type and limiting magnitude of the symmetrically disposed loadingthat ~ay be placed on a beam of given span and moment of inertia,the angles of rotation within the connections at ends A and B in Fig. 18may be expressed, respectively, as

'YMA = 2~~C~0 -1) and

'YMB = M B (100 _1)2EK p

Equations for M A and M B , in terms of 8A , 8B and ~, commonlycalled the "slope-deflection" equations, can now be derived. It isassumed that the reader is familiar with the "moment-area" procedurefor obtaining slopes and deflections given in most texts on strengthof materials and indeterminate structures. By this procedure thechange in slope between any two points along a straight member may

be obtained directly as the area of the ; diagram between these .two

points.In Fig. 18 the slope of AB at A is seen to be

IIA _ MA (10.0 _1)2EK p

At B it is

liB - MB(100 -1)2EK p

74 S E M I - RIG I D B E A M - T 0 -C 0 L U M NCO NNE C T ION S

Hence, the change in slope between A and B is equal to

The bending moment anywhere along beam AB may be obtained byadding algebraically the three separate parts shown in Fig. 19, i.e.,

(a) the moment for a simply supported beam, plus

(b) the proportionate contribution of end moment M A, as indicated in the triangle having M A as the ordinate at the leftend, plus

(c) the proportionate contribution of end moment M B.

If beam AB has a uniform cross-section, the total area of the ;

diagram between A and B equals

;I[As + ~(MA - MB)Jwhere A. = the area of the simple beam moment diagram.

This expression for the change in slope may be equated to the expression, in terms of (j and M, already derived, giving, after minorrearrangements,

(16)

To obtain separate expressions for M A and M B a second equationcontaining M A and M B is needed. This equation may be written byapplying the moment-area procedure for determining deflections. Thedeflection of any point, B, along the axis of a deflected beam, withreference to the tangent through any point A, is equal to the moment

of the area of the ~ diagram between points A and B, taken about

pointB.As shown in Fig. 18, the tangent to the deflected beam axis at A

makes an angle equal to

IJA - D. - 'YMAl

with respect to the straight line connecting A and B. Substitutingthe expression for 'Y given in Eq. 15, the deflection of B, with referenceto the tangent at A, may be expressed as

l[IJA - D. _ MA (100 - l)Jl 2EK P


MReferring to Fig. 19, the algebraic sum of the moments of the Ef

diagrams, about point B, is equal to

A.x +(~Al) (~) - (~Bl) G)

C. G. OF SIMPLE BEAMMOMENT DIAGRAM

MOMENT DUE TO SPANLOAD ASSUMING SIMPLESUPPORTS

AREA· As

Fig. 19.

When this expression is equated to the previously derived expressionfor the deflection at B, we get, after rearrangement,

MAe~o - 1)- M B = 6EK(OA - f)- 6~2.x (17)

Simultaneous Equations 16 and 17 may now be solved for M A andM B, giving the slope-deflection equations for a beam having semirigid connections. Thus

MA = 30~~~P[ (3 - l~O)OA + 1~0 OB - 3~ - :iC; - 1~0)J(18)

2pEK [( p ) p 36 A.(3(1 - x) p )JM B = 300 _ 2p 3 - 100 OB + 100 OA - T + EI I - 100

76 SEMI-R.IGID BEAM-TO-COLUMN CONN-ECTIONS

When p = 100, Eq. 18 reduce to the familiar equations for a fullyrestrained (fixed-ended) beam.

[ - - 3.6. A.(3X I)JM A = 2EK 20A + OB - T - EI T - -

(19)

M B = 2EK[20B + OA- 3~ + :iC(1 ~ x) - I)JFor the beam AB in Fig. 17, the vertical displacement of B, with

respect to A, may be assumed equal to zero, i.e., ~ = O. For the

case of the single load, P, the maximum simple beam moment isPabequal to -1-'

Hence A. =(P~b)G)=P;b

(21

and the distance, X, from end B to the centroid of the simple beam

; diagram, may be written

x = l (21 - a)3

For this special case, Eq. 18 becomes

(20)

The first subscript after M indicates the end of the member underconsideration and the two subscripts, together, identify the member,

For columns AC and BD, full continuity is assumed and Eqs. 19apply. Since no transverse (lateral) loads are applied, the last termin Eqs. 19 drop out. Also the rotations at the column bases (Oc and On)equal zero. With these assumptions, the four slope-deflection equationsfor the two columns in Fig. 17 become

MAC = 2EKc( 20A _ 3/:)M CA = 2EKc( OA _ 3::)M BD = 2EKc( 20B _ 3/:)M DB = 2EKc(OB _ 3::)


These expressions for moments (Eqs. 20 and 21) contain three unknown deformation quantities, OA, OR and A. By writing threeequations based on conditions of static equilibrium, these deformationquantities may be evaluated in terms of the applied loading, the properties of the members, and the semi-rigid characteristics of the beamconnections. These values may then be substituted in Eqs. 20 and\21to obtain usable expressions for all of the moments.

Two conditions .of equilibrium can be obtained by equating thesum of the moments acting at joints A and at B to zero. A thirdcondition can be obtained by equating the moments acting on thecolumns to zero. These equilibrium equations would be

M AB + MAC = 0

MBA + MBD = OJ

MAC + M CA + M BD + M DB = 0

(22)

To reduce the labor of solving Eqs. 22, the following substitutionof constants will be made:

C - P1-300-2p

C, = 2EKBC{3- 1~0)

C - 2pEKBCI,- 100

C, = Ci(Z - 1~0)

C. = C{l - 1~0)

The substitution of Eqs. 20 and 21 into Eqs. 22 now gives

(C, + 4EKc ) OA + /:::,.. Pab2 Pa2bC,Oo - 6EKcT = C'T + C' T

/:::,. Pa~ Pab2C. OA + (C, + 4EKc) 00 - 6EKcT =- C'T - c. T

+ 90 4/:::,. = 0h

78 SE MI-RI GID BE A M-TO-C OLUMN CONN E CTI 0 N S

The solution of these simultaneous equations gives

[ . Jh~(JA = C,C. - EKe (1.5C' - 2.5C.) + C.C. T +

[ ]Pab2

C,C. + EKe (2.5C. - 1.5C.) + C.C. T

[ ]Pa2b

(JB = - C,C. + EKe (2.5C. -.1.5C.) + C.C. l2

[. ] Pab2- C,C. - EKe (1.5C. - 2.5C.) + C.C. l2

(23)

a = ~ «(JA + (JB), but does not need to be evaluated since it does

not appear in Eqs. 20 for M AB and MBA, which are the only jointmoments required for the derivation of the redesign coefficient, F.The evaluation of M AB and MBA is now possible by substituting theforegoing expressions for (JA and (JB (Eqs. 23) into Eqs. 20. However,since these expressions are lengthy, and are but an intermediate stepin the derivation of the redesign coefficient, they will be omitted here.

Referring to Fig. 19, it may be seen that the moment causing compression in the top flange ("positive" moment, according to the usualbeam convention) at any point along the beam shown in Fig. 17can be written

M = M. + M;Bb _ M~Aa

In all problems where the proposed design procedure may be advantageously applied, the maximum moment in the semi-rigidlyconnected beam will be equal, or very nearly equal, to the momentat the point where M s , the simple beam moment, is also maximum.Then

MABb MBAaM max = M. max) + -l- - -l-

The redesign coefficient, as previously defined on page 57, equals

or. in the special case of the single concentrated load in Fig. 17,

1F = 1 + Pab (MABb - MBAa) (24)


The substitution of M AB and MBA, obtained from Eqs. 23, intoEq. 24 finally leads to the expression

[

4(KB + 200) (~ _~) + .(13KB + 800 _4)]

F = 1 _ K c P 12 1 K c P12(KB)2+ 2KB (1500 _2) + 400 (300 _2)

K c K c p p p

As a varies with respect to l, the location of the load, P, giving amaximum or minimum value for F is determined by setting the firstderivative of Eq. 25 equal to zero.

dF = 0da

The only part of Eq. 25 affected by a is the first term in the numerator within the brackets, from which it is readily apparent that amaximum or minimum value for F occurs when

1a=2

or, when the load is at mid-spanFurthermore, it is also evident that the second derivative of. F,

with respect to a, is always negative. Hence F is always maximum

when the load is at mid-span. For example, letting p = 50 and ~;2.0, the following values of F are obtained from Eq. 25:

all F0.1 0.8130.2. 0.8220.3 0.8280.4 0.8320.5 0.833

When all = 0.5 there is no sidesway and the case is similar to theconditions which are the basis for Fig. 15, where F = 0.833 when p =50 and :llc = 1.0. In making a comparison of the two cases it should

be noted that the columns in Fig. 17 are fixed at their bases. Acolumn so fixed is effectively twice as stiff at joint A as it would be in alimitless frame as is, for example, column AE in Fig. 12 (b).

Since F is maximum for the symmetrical case, when the concentratedload is at mid-span, use of Fig. 15, in the design of a beam for anyasymmetrical positioning of the load, will give the least reduction inrequired section modulus that need be considered and the design willerr on the safe side.

, ,

.. ,)

\ ~

JI; ,

r

APPENDIX B

[ 81 ]

TEST NO.2 (PILOT SERIES)

•bb

-++H.-t-tLt b

_,oJcO

3'- of'

I 10 W @49* 3'-0" MIE2 12 W@ ?-5* ,3'-0·2 L5 (0"4,, ~"(,,i +b2 L5 eo" ("" i" eat bb4 - da. TEST SPEC\MEN NO. Co

DETAILS

LOG OF TEST NO. 2

REMARKS

20.00

23.05

SHEAR

(KIPS)

15.75

737.6

MOMENT

(IN .-KIPS)

504

640

Strain lines inside column flange near topangle rivets.

Top angle pulling away with vertical legremaining nearly straight.

Fracture through horizontal leg of top angle,at fillet.

GENERAL NOTES: The fracture of the top angle is of particular interest.A complete lack of ductility was noted and the fracture took placealong the fillet where stress distribution is uniform rather than throughthe rivet holes, where stress concentrations are localized and the netsectional area less. The connection had good rotation prior to fractureand developed between forty and fifty per cent rigidity.

[82 ]

TEST NO.2 (PILOT SERIES)

0.02.4-O.O'Z.O0.004 a.ooe a.ort

Tel' o.nd S ~t Anqle

f>~'lo%

~~, \ Unlfor Loo.~

.-R~oo/.V

"""10 Flo. qe of 10~49Col.!.,o TopL- lD~4xh~1

5eo.\ -4>x.<ox~ eol

1/\ ~~I<,v'+ -~-

?-C?.y.

40%\Mo.~. fJiom.74 K"

~~ \ ,~, --' Ro\'o>O.O1 >=o \)0

Mo.x. o Ro.d.d 0'0

150

\ --!

/(onten'1 p.led l.o", 0.+ M,d pO."

Io

o

'00

700

~Ul:;~ ~oo

zo

5w 100Zz

<'3

~

~ sao

~oo

RO'TP,,"T'ON BE,WEEN END OF BEPt.M Pt.NO

COLUMN IN RAtllA.N5

M- r; CURVE FOR CONN. No.2 RELATED TO

MOMENT- ROTATION BEAM DE51(,N REQUIREMENTS

...!!

'"c:«a.

N 0I-

ei Iz.... N~ ei..I- Z

....~..

I-

[ 83 ]

TEST 'NO. 5 (PILOT SERIES)

TEST SPECIMEN NO.5DETAILS

-11-~I- :--

~Nt--r

-R-_,N 1 ~N

~ ~

:~t--l ~1t [J-~'-

30'_ Bl" +c----' 3'- e'i~

3'- 3l" i .! l~lii 3'- 31.~

tc /hlb

hlb -/S'

r -,~

'"18W@4,'" 3'-8'tf),9' .,.,

18W@41""G>~ ..

1 ~:q. j:.- 3'- 8"

~

bC<I', Ff':"f----=:i:~~

i

f1Ir~5'" 4'-5" MIE , :~! I I, T3,"" 3'-B"

1 '-

II?-W@("2 18W"@42 L5 ("~4~<.~ \ 0 +<:21:(,,~(O~~~7ibc.

2 SHIMS 5~~ "- 7 db

LOG OF TEST NO. 5

REMARKS

27.00

SHEAR(KIPS)

13.05

26.00

MOMENT(IN.-KIPS)

522

1040

1080

Scaling in column fillet opposite seat angle.

Scaling in column face above top angleopposite column fillets.

Scaling in column face below top angleopposite column fillets.

1180 29.50 Two rivets broke in vertical leg of top angle.

GENERAL NOTES: Most of the bending in the top angle. Good rotationfactor of safety and between thirty and forty per cent rigidity.

[84 ]

M- r/> CURVE FOR (ONN. No.5 RELPI'TED 'TO

MOMEN'T- ROl'PlI'ION BEAM DE51GN REQUIREMENl'S

U'I

-ImVI-I

ZP

.....,.r0-O-I

VIm:II'-mVI-

0·0'1.40.004 o·OOB 0·011. 0.01<0 0,0'1.0

RO"TI\"TION BE,.WEEN ENe OF BEI\M "ND

COLUMN IN RllIelll.NS

Top p.nd Seo.-t Anqles

p' <00% L-----\ .1. - Unlfprm Loo.d

------\

1 ~u~q~ of \2 W"CoSCol.d. •10 "\ ~ TopL (O)(4)(~ I'· 0

50 % Seo.t -Cox <Ox x7i

,J( j Rivet 3"

p. Cooj ~. 4-

r-,I

\50% r4-_-l \ j 110m' \,2( O.K"

i,Io\)\ \ Mu)(.\W ~\ Mo.)(. ot.'";> 0.2~Co Ro.d\

Ie :r. \ \(once tra.+ed. L o.d 0.+ M dspo.n

3~L __ ~

IIo

o

1400

Test No.5-Top Angle

1'1.00

iJlILl

1000"UZa.

:2

~800

I-Test No.5 2w

:l0

:2 IDOO

Z00 0(Tl 5

ILlZ 4-00Z0

V

1.00

TESTS NO.9 AND NO. 10 (SECOND SERIES)

~,

T.5

CIMEN NO.9 &10DETAILS

, .. i I ~I- B~"31• Ba

~'- ~~.. <ii, ! :~'1.l' 3>'" 3> 1"

\ <;\O\\M d.o., ! ~o.- ! , ')\o\IM d.o.-:::~

-IV ill

IBltF41 :'ICO"<t

..9 18W"41 3'-8"3'-8" LI1

0-

il"..9 11~~

:~C:::lM:"'f"

-

\<05 4~5" M2.E~bo._

47 3~&"'V~·q.RIVE:"o/a .1~O"ta. -TE~T ·9 ,

4<Y4<''o'tb'T~----#I ~ rift:'> 5'8"7do.';N - - - TEST SPECo 7 " V"B" a bn --"" - .- "T'

I 12.\IF2. 18vF2. ~ "'''42 ~G"

Z SHIM2 \? (""

LOG OF TEST NO. 9 LOG OF TEST NO. 10

REMARKS REMARKSMOMENT SHEAR(IN .-KIPS) (KIPS)

706 17.65 Scaling in column filletsopposite heel of seatangle.

850 21.25 Opening of ~6 in. between beam and topangle.

1706 42.65 Rivets sheared betweenbeam and West topangle.

GENERAL NOTES: Good rotation factor ofsafety with between thirty-five and fortyfive per cent rigidity. Distortion balancedbetween bending in top angle and columnflanges.

MOMENT SHEAR(IN .-KIPS) (KIPS)

542 13.55 Scaling in column filletsopposite heel of seatangle.

900 22.50 Scaling at center columnflange face above topangles.

1850 46.25, Rivets sheared betweenbeam flange and Easttop angle.

GENERAL NOTES: Most of the bending inbeam and column flanges. Good rotationfactor of safety with thirty-five to fiftyper cent rigidity, nearly the same as TestNo.9 with lighter angle. Detail of connection same as that for Test No.9.

[86 ]

TESTS NO.9 AND NO. 10 (SECOND SERIES)

Test No. 10

Test No.9

[ 87 ]

Test No.9-Top Angle

Top nnd C eat Anqle

~

~p

~

I~V

p./o

i \ /

j "0 I zoV 30\arm LaMUn,

'r~J !-IX soJ lflO5 ColI To FI nee of 12I

~I \ j Top L fox4x,i 1'-0\<00% Seat L-fo",fox x7i\7 R,ve 3"

5-4.-/rl (j~a:!~i, 10[ zol 30\ Concen+' jated. Loa140"'~ at M, spo.n

V Mll'l..MoIn= 1,850. "

Max.RaI .=~0.O45 Rad..

RO,.A,.,ON BE,.WEEN £NO .0F .. BEAM ANO

(OLUM;:' .\~ 'RA;'ANS

-fmell-fell

ZP

-o-ellmnozICII

ellm

O.OZ4 :!!mell-

0.004- O.OOB a.Oll. O.OUD 0.01.0

RO,.P'TlON BE,.WEEN ENo 01' BEAM AND

COLUMN IN RPlOIPlNS

Top and C eat Angl s

~~

~V

p' <00"/0

izo\ 3~#- '10

\ rs-u"

1',10· [I,y form Load.r-

kFiDSCol.I soY. To FI nae of 12I

'k\\ ~~Top L-<O",4'1.~ 1'-0

I /o0~ Sent L-fox <0 x] di~-I R,ve 3"\

5-4-

D7~~--\.Q -dOlO 0\ 30\

(onc.ent nted LoatC44 ,

1. \ ....I at M d.5pan

I Mo;~.Mo .= 1,10Co.""Max. Rot. ~O.O40 ad.

U

oa

14-00

IZOO

IIIW:t

1000V

~Q.

:<::et-

eooZw~0

:2t /000

9t;wZ7-0 400

U

ZOO

o.o2.~0.01.0a·olCe»O.OIZ0.0080.004-

I'Z.OO

,~oo

1/000

:!l:t

~- 1000..~

oa

~

~ 800..~0

Z(Xl "Z

<000(Xl 0

Gw"Z"Z0

U 400

zoo

M-" CURVE FOR CONN. No. 10 RELA'EO 10

MOMEN'- ROl"",\I0N BEAM DESIGN REQUIREMENTS

M- 'I CURVE FOR CONN. No. 9 RELI\IED TO

MOMENT ROTI\TION BEI\M DESIGN REQUIREMENTS

TEST NO. 11 (SECOND SERIES)

SEE NEXT PAGE

[ 89 ]


I ' ,:l:l-

~I~

1--

t:;: r:;;

..9

-

1-- ~ ~'N

1-- K ~':

'2~t~-

TEST SPECIMEN NO. I IDETAILS

_~bW©-""_. ..,N_<t " , . '-~

_!...ot --

JBj:~_'N

N

-~ -...-~ l±: M""-~

?:l'- Bt' -.!..ot ~'- Bf

I ?-~ ~I3'- 3!" 'Z.i ~:,,! '"3'- "!>'\-

teo kID, I':>IIIM dn

\':>IIIM dn

11~~:I~fN

.,4III

i iii" :'I((l

IBII'F41 3'- B", 'i1'1

., IE>1I'F41

i Iill: ' - 3'-e"11 11 ,

'.1I ILt;,t-t;fF~

bn ~', 1411'F5B 4'-5"

"~4'-5" MZE r i o/4'ol> RIYET.53'-5"

\ \4I1'FSB

C \8W'4i2. LS <O~4)(~ ~ 10' +cC LS <O,,(o,,~x7i bn

2. SHIM 5~~"i d.n

LOG OF TEST NO. I I

MOMENT(IN.-KIPS)

1546

1360

SHEAR(KIPS)

38.0

34.0

REMARKS

Maximum Load.

Tension Fracture of one rivet III vertical

leg of top angle.

GENERAL NOTES: Nearly all bending in top angle. Good rotationreserve with thirty-five to fifty per cent rigidity. Compare with Te,stNo.5, similar except connected to column flange.

[90 ]

--- ------ -~------,

RO,.A,.\ON BETWE.EN END OF BEllM AND

COLUMN IN RAOIANS

o O"----0-.....00-4---0-.o....o-e---0-,O....IZ---O-.0...1"'---O-.O....Z-0---0--'.OZ4

14QQ ,...----r-----,.---"""T----r----r----,

IZOO

If)W:I:\JZ 1000

d' IOll.

:.:: p.10% -Ir- m

~ '"I -It- 800Z Zw~ p0

2 -'Z 6>00 -9 --0 r ti '"w m

z nz 00 400U Z

IClI

'"ml,oo

;:Ill

m

'"

Test No. II M - t) CURVE FOR CONN. No. II REL",TED TO

MOMENT- ROTATION BEAM DESIGN REQUIREMENTS


'";,'- 0;:

'2.'-..,1"

I 5HIM d.e

I'2.W253'- 0"

3'- o~"

'1.'-,1"I 5HINI d.e

--m.;.--i--,Li._~. -IV

1'2V'F253'- 0"

be

I IOW49 3'-0" M2EZ IZW25 :"-0"2 t: <"'1A><'1 l\ <o!- thZ LSCo><.Co'l<l><<"l,be2. SHIM 5 l\~ l\ 1'04- de

3/~'+ RIVE.TS

TEST SPECIMEN NO. \(0

DETAILS

LOG OF TEST NO. 16

REMARKSSHEAR

(KIPS)

19.25

MOMENT

(IN.-KIPS)

616 Tensile fracture of one rivet in vertical legof top angle.

GENERAL NOTES: Most of bending in top angle. Excellent rotationreserve and between thirty and forty-five per cent rigidity.

[92 ]

-iOO r----~---...---r_--___.---_r--____,

-ImCIt-I

ZP

-CItmnozcCItm::amCIt-

°0~---0-...J.O-O"':"4--0-:.0i..:0-:8--0-....Lo-:\'t---:O..J.OL,CO:----:O~.o:1:'t:-:o:--~O~.O't4

RO,PITION BE.1"WEEN END OF I:>E.P-M P-ND

COLUMN IN RP-C\P-NS

Top ~nd. Seo.+ An<jlesTo Flp.nqe of I bW4-9 (:>l.

IDOO 1-------+----+----="'::....:-F'F-~,.___'_fT_'_'_;__., ~.---=t--------iTop -(O ....4xax(o"!:Sea: L- (0 x Co i x Co lR,ve 5-~"

500 1------+---+---+--------j----+------1(l.

~

~ p~c.o% Untform Loa.d ~~~ 400 ~T-----1;:t=~;;;~~=:..:..:.=F::::;~s12::::::...-+----1

~ ~:~O% zot~o~.~~om"<OI<t: K"C r-, h FL- \ I \ 50(0 Ma.x. ot.:~O.O ,0 Ra.d.

300 1--+--4=f=;'7JIA~*==\_--I--.:..:.:..:::.::~~--=-=+--=-~

§ 'r'-Jo ~ \ \S~~ \ \ 40%\i 'too I-/W~';w====~\t--_+t----__t---T--_____jo f!'IO c. '.Zo '3O\\r---..... \u L40170 \ 130%~ \

- - Concent" :ted LOo.d0.+ M, spa.n

Test No. 16

M-" CURVE FOR CONN _ No. ICo RELA,EO ,0

MOMEN'T- ROTA'TION BEAM DESIGN RE.QUIREMENTS


=..'- o~"

'2.'-1 ~ ..

+h

12W25 3'-0"

belIOW49 3'-0"

~og 12W"253'-0"

..,d>cO

f---Hl+H-I-II-

, ,

-~ iI

I IOW49 3'- 0" M2EZ IZW"2.5 3'-0"'2. LSCo"4,,heoi t"Z LS eo" <0.. l" eo! be:'2. SHIMS 5>< ~"eo~ d.e

TEST SPECIMEN NO.nDETAILS

LOG OF TEST NO. 17

REMARKSSHEAR(KIPS)

16.80538 Tensile fracture of one rivet III verticalleg of top angle.

GENERAL NOTES: Most of bending in top angle. Good rotation reservewith between thirty-five and forty-five per cent rigidity.

MOMENT(IN.-KIPS)

[94 ]

-tmCIt-t

ZP

-CItmnozcCItm2!!mCIt-

-.....

0.01.40.004- O.OOB 0·011. O.OIe.. 0.01.0

RO,A,ION BE'WE.E.N ENO OF BE.AM AND

COLUMN IN R"C\"NS

Top nd Sent AnqlesTo ......~b of 10W"49 ColOp L-(O~4)(H(O!Sea: L- (0)( (0)( h<olR\liE

3"ts- 4

~

Unl prm LoClJp--p= CDO% .--:;::.~'IO

~~V-- K"d ro- Ma.')(.. Mom·S B.

P=10",Mo.'/(. Rob?O. 5\ ROod.r-

~'IO#' ~o:1 \ 40~1.0 30\

d. ilL \ 50"!~- Concent o.+ed Lo d

I0.+ Mid pa.n

,o

o

"TOO

Test No. 17

CDOO

If1ll!:I:lJ

500Z

~~

~ 400

~W~0

2 300

-0 Z<.n 0

t~ ZOOZ0

U

100

M- 'f CURVE FOR CONN. No. 11 RELPo.'EO ,0

MOMENT- RO'Po.T10N BEPo.M DESIGN REQUIREMENTS

---------------------------------- -


'"~l_ 0'2.

L'-l i"

I Z V\F50 ;\'- 0"

~'- or

-b IZW-50, 3'-0"

..~...

-t:\l'l.il~li

I IOW49 3'-0" MlEl leW-50 3'-0"l I.: (O"4,,i l< B tmZ I.: (",,(0"1"& bdZ. SHIM 5,,~,,8 dd

TEST SPECIMEN NO. 18DETA\LS

LOG OF TEST NO. 18

REMARKSSHEAR(KIPS)

17.75568 Tensile failure of one rivet in vertical leg oftop angle.

GENERAL NOTES: Between twenty and thirty per cent rigidity. Good

rotation reserve.

MOMENT(IN.-KIPS)

[96 ]

oo

Top Q.l'ld Seat Al'lqlesTo Neb of IPW"49 C01.

Top L- (ov.4~ b. 8Sec tL-(ov. pv. heRlV !'

ets - ~

.tp-40% Concentrctee Loo.d

~J,IO Ii!n ~~P - '50"1.r- .,-~

i °'0 ~

~~

\

~o m Loo.d~J:

~o"l"

~---\

1- \ ~~~

lOS/, \

I Mo.1(. Moment· 5lD8~'

Mo.v.. Rot. =~ o. 45 Ro.d..

"700

cooo

~ox:\J2 500

~

:lz- 400t-ZWro~ 300

ZQ

CwZ lOO1-o

U

100

0.004 O.OOB 0.01"l 0.0110 O·OW

RO.,.P,TION BE.,.WE-EN E.ND OF" BEAM FINO

COLUMN IN R"O''''NS

0.01.4

....mCIl....ZP...CD

CIlmoozcCIlm

"mCIl-

M - '/J CURVE FOR CONN. No. 18 RELATED ,0

MOMENT- ROTATION BE~M "DESIEaN REQUIREMENTS

TEST NO. 20 (THIRD SERIES)

TEST SPECIMEN NO. toDETAILS

.,~~-~---

~Q-;1f-- 7 ~-

-; -~ -:....v-".~- --';L-="'" - ",OJ

--- _---'-N

3'- 41." ;' 4~"

<'-lIr '2.} ! ~l~ ~I 2.'- I\~"

<-SH\~1l~+b~

-I --, l-- ...__<- SHIMS dllN 1=

I,

-,ot -:q-14'/IF34- ,'-4" ": U1 \4 '/IF34- 3'-4":-

I ~ i ii '-IS '!"""'I' ~

£"!1"_oN 1--- ---oJ ,--_ --t;

~bb-

<il5 4'- I" M'2.E -----.!134 3'-4"\ \'('/IF

2. \4-W"2. ~Co".4x~,,\'-O" tb2. ~Co)«jn~,,7~ bb4 SHIMS Sx~"Co~ <ill

LOG OF TEST NO. 20

MOMENT(IN.-KIPS)

1305

SHEAR(KIPS)

36.25

REMARKS

Ultimate load. No failure.

GENERAL NOTES: Excellent rotation reserve with forty to fifty-fiveper cent rigidity. Test stopped because of excessive deformations, withbalanced bending in column flange, beam flange, and seat angle.

[98 ]


MO"

ROT",.'ON B~r.~", ENO 010 Bu."" _0

Co\..UNlN '101 R#.O""MS

=-~-E

-' ~

i -;;~s,wl ~ ... t..J]

11'1> ~, .:; ~"0 ~ -: - ~r~ J?

nio ~.8OJ",

T JUI § ~

7/; '/00

(I!II

0o.ooe. O.OIl. O.OI~ 0.010 0.0

TopL-l'D 4)(1..... '·-,5eo.iL-/D eo'.(ell-IR.veJs.-l

lOp .n' ' ..I A"'I1e

To FI.nne 01 12W'lD rnl

"" 'o·t.. Uniform

Lond.

o L--olo-""----,ol.o--o-,-.-~::::---"l=---o~.0;:;,:;;o-,0;;.oROTATION BE'TWE~N ENe O~ Bu,Nl

(OLUMN IN R",c,,,,N.:!>

."

M- '" CURVE FOR CONN. No. 2.0 RELATED TO

MOMENT - ROT~TION BE~M DESIGN REQUIREMENTSM- '" CURVE FOR CONNECTION No. cOSHOWING COMPONENTS OF ROi",.\ON

2.

Test No. 20

[99 ]

TEST NO. 22 (THIRD SEIUESJ

TEST SPECIMEN NO, 2.2.DETAILS

",-.r--~- -~- ---ttl.c()-iiI--- ~f':"" f--- -

~=N

----1 I -I'--;:t -- i'"

~- "''''~'" N

~l_ 4~" i '30'- 4~"

Z'- III zi ! ~zi "2.'- \Ii

l SHIMS_~~I . f---+b-2 SHIMS do.

~<t

:",ot 111 -ICo W40 3'-4' J ,9 ICo\fF40 3'-4"

1i ~ il~

-t/ """"" ~- ('l""'!'!--- ~_,N('lol L.-..-- _ -----j

~--

( f--- be ---)

~<OS 4'-3" M2E40 3'-4"

SA'o!> RIVETS

"',

lOG OF TEST NO. 22

MOMENT SHEAR REMARKS(IN .-KIPS) (KIPS)

1494 41.50 Ultimate load. Test stopped prior to failure.

GENERAL NOTES: Good rotation reserve with between forty and fiftyper cent rigidity. Bending distributed between column flange, horizontalleg of top angle, and top of beam flange.

[ 100]


~ t11-:; t

~ ~ ! ~t

J~i I I';~; ;: J ;1r~ , r.

0

Hl ~jt.

./" 10

V V f-'""

/ 00

//~

IIV11/1/

RO"''''''O!\l B£TWIU.. EMOO"S_ ~D

CO\.UHlt-l""~-0

0 0_004 o.ooa a_olt. O.OIfoo O,OlO 0.01.

0004 0006 0

ROTl'.'\ON B!:"fWl!EN END OF BEP.t(I

CO\.UMN IN R"'O'"NS

Top (lnd eQ~ &\f\ql

f'.'10~

~~

i '''\ ,,\ }()LYn'farm~

rt:~IY M.. Mo - \.494.Mu Rot ->0.054 Rna..

p,10'i\, f/\ .o~ To Fla.nq of IlW" 5 Col.r-,I \ Top L- (" 4)(1)(. " 00

<oyj

Sea:+ L- l~Coll+lC. 4'/!" -~ J Rlveh. .!'101 '0 ""1-~"'~

o /Co"tenn-- f<>l Lood.

oJ MId. pon

0110

0" o Ole. 002.0 DO

o-l!

'0

.~

l2.g

j

~1 \000

M- ~ CURVE FOR CONN. No. 22 REl~TED TO

MOMEloIT- ROT~TION BE~M OE51<;N REQUIREMENT5M-1> CURVE FOR COlollolECTION No. 22SHOWINc::. COMPONENTS OF ROiATION

Test No. 22

[ 101 ]

TEST NO. 23· (THIRD SERIES)

'",

TEST SPEC.IMEN NO. 23DETAILS

L ':>HIM':> do.

IIDW40 ;>"-4"

be

=~=="'·l-"",,,,'"-,,...

';..."'

o/4-"~ RIVETS

3'- 4-{"

I 14W"58 3'-4" MlEl ItoW"40 3'-4"2. t: to .. 4 .. ~ '" 10 te2. t: <o"to"'~'" 7~ be4 SHIMS 5" t '" Co~ do.

LOG OF TEST NO. 23.REMARKSSHEAR

(KIPS)

34.25 Combine shear and tensile failure of outerrivets in horizontal leg of top angle.

GENERAL NOTES: Rotation reserve is ample, but considerably less thancompanion Test No. 22 to column flange. Deformation largely due todeformation of rivets in horizontal leg of top angle and tension deformation in vertical leg rivets.

MOMENT(IN.-KIPS)

1233

[ 102]


~Co 1000

.!

Top a.nd 5 n+ A"qle

-- --p.,o% Uniform / ---1 - ~7:i.: ",0

Y::Y MIlt...Mo ... 1,233. .. ~

,... Mall Roi >0.1(,,8 .d.,-,I \

YV \ 50~\\!...~"\It'", ToWell ot 14'1;"58 01.I t7,10\ '" 'oP L- Co 4)(.5 x.\

71...1---' 5eo.t L- )(.(O)(.lx 7\ Rwt:\'!>-l

//~.Y. __1-rconc.enh- .. Lo<d

f o.tMla pM

0004 oooe

Ro"t ":flOW BE'TWE.EN END 01' BEIl.M

(OI.\,lNlW \N R"'D\"'N'!o

i i ".,.... 1 .... -,~ £ U~"1i

1~-,

~ H

)AV

/b::""

0/

/jV/'{

RtTT""llOfo1 BETWU.N [ND 01' B "'1Il~O

COI..UM 'N RI<oOI ........

0 0.0 o. . ,

M-';' CURVE FOR. CONN. No. 23 RELA,ED TO

MOMENT- RO,ATION BEAM DESIGN REQUIREMENTS

M - r/J CURVE FOR. CONNEC..,\ON No. 23SHOWING COMPONENTS OF RO'TATIOtol.

Test No. 23

[ 103]


TEST SPECIMEN NO. 2.4DETAILS

I

I' r~4f--.

~ p

OJ

,

f'-.F~ ~

f-.

"'i

-~

~8"" RIVETS

;it(~----

m-:r1- ~-,.,.,.,",-~C-_

3'- 81" ~'- B~"

~'-3~" d.l.!. ' , ~I ,'- ,1"- '-_td_

~b/ SHIMS2 SHIMS db db

_INr-- --N

'Lf)

I:"Id,)

-,..18WA, ..9 IB\llF41

3'-8" Lf)'- :1

,s

I i3'" 8"

~~

"N - r::rr-is t=:.-=: .==::;4'-5"

CI-bd- D \S ..CoS M'2.E

~HOLES: PUNCH iCD ~

47 3'-B" RWET5: r ~

"4,,",, 1'-01 td

I IZWZ IBWZLs<a e ~

Z LS <a"<D,,~,,'i bd4 SKIMS 5,,~ di d:b

LOG OF TEST NO. 24

MOMENT SHEAR REMARKS(IN .-KIPS) (KIPS)

1946 48.65 Near maximum load. Test stopped.

GENERAL NOTES: Compare with Test No.9 which is same exceptfor rivet size. Good rotation factor of safety and between forty andfifty-five per cent rigidity.

[ 104]


o.OQ& O.Olflo o.a!.o

RO"''''''IOH BlETwu.w ENe Of' BOJooI "NOC_U..,N IN RIo.O'''N!I

M- 16 CUR.VE FOR CONNECTION No. 24SHOWING COMPONENTS OF ROTA"TION

l1 L----, ..----~

'OtJ ~ / ~.:~ /' h re:

t

r~~~~ /~ :

'"Ir#V 1 j]f-

I~VI, ""T ,

rJ{ 1JIff ;, ':.

~

1

0 0.004

0

VTop ond lent At'lqlt

/".1'0%Uniform ood

l- W3 ~ " /VTo FlaMe of IZW 5 Cot

,... AE:l Topl·lD 4)1, l)l, I' 0ts.ol L-( xlDlt ~ '4 ~

IT\ ); \ R",et~·!

I

o 1'~ ~ W .o.~~o.!!\I

~ oo~ j \ MuMOI '·'.94~.0<;-"\ Mo.'l Ro~,')0.053 RodNf- L~~

Concellh led Lo~

Q~ MId PO'

IfII

0 00 00' 0

~J. 100

,~

M-" CURVE FOR CONN. No. c4 RELA'ED ,0

MOMEN'· ROT"-'ON BEAM DESIC,N REQUIREMEN,S

0<

RO'TlIITlON BETwEEN ENO OF" BEAM AND

(Ol,.UM"l 11'4 R"'OI"'N~

Test No. 24

[ 105 ]


I

~l;!~IHi '

I'; 1""

fi' ~~

I--- _II 1IIIt - -['II--LL f'!

'"iI

~,

o

TEST SPECIMEN NO. '2.5ETAILS

HOLES UNc..H 1(0 ¢RWE"T5 r q,

~=l~···.~~ 0

'"-~ =-:.- , --. --- 1 - -~

4'- 0"l I,,,

4'- Oz.

3'- 1 i" 1.~4te_ ~l~~ ~I 3'· 1~·

L SH~~~;k 1-- 2 SHIMS de

I I

I

.--:10;0 to'

ZIW"59';' ~':;>

I

ZIW"594'- 0" -- ~""'

4'-0'-

~_... ,.----I' ber---4VoF87 5'-0" MZE ~ 1-- b P--IW594'-0"

5(ox4xixl'-,Z" te-~ ==-.t: ""-- 21.? ko.

s(oX(oXlx9i, be FILL fo.

s4"4xi,,,el ko. -.!1ILlS 3 x t x 9 ito. ,p '.?"

I IZ Z2 l:2 L:4 L:Z F4 SHIMS 5)(~x 8 de

LOG OF TEST NO. 25

REMARKS

56.50

SHEAR

(KIPS)

43.50

2486

MOMENT

(IN.-KIPS)

Scaling at bearing toe of seat stiffenerangles.

Shear failure of outer rivets in horizontalleg of top angle.

GENERAL NOTES: Good rotation reserve, but deformation largely incolumn flange. Between forty and fifty-five per cent rigidity.

1914

[ 106]


To Flo.nq of 14W" 7 Col.lOP L-r" 4<4 <I' z50.+ L- <,,<!<9! r.>hHonedR,vets-~

Top o.nd eo.+ Anq\ 5

01---+---+----1----1----1----1

00

h..! ~ i

"-. .'" J-'J! -' ,1 0 , 1.Rd IJ' '"';;J! ' jp - 1,\

I I.-- T :..:k. v---::~

~~~

/;~f/

It'rTf

RClT"'Tl0~ BETWEEN [NO OF B ,",WI MIa

COUIMN \ iU.l)l"NS. .- 0_

i1

II0004 eooe 0.01l.

RO""""I',ot4 BETWU':N END Of' BE"'''''

COLUMN ,~ R"'CI"'NS

o i'~i.~I Conc.enh ted. load.

oJ M,d po.n

~ p.l0. I ..........L---~ 1.000 t-_t-+--b__~U"'n"-oi"'o".m"l_"lo"'."'.~~~=-____j____j-_l

~ f.'o'-Ro "VVM' .0 K'~ G.X III m.-2.40

:; 1,,"00 1-_--t-t--I'""~X~r__+_-M-O-K-R+_+,-.'_0_,_0+1_R_.d=-,----,

3 I Y \l ;:,~x 1/\ "",,\

40~

M- ~ CURVE FOR CONN, No, 25 RELATED TO

MOMENT- ROTA,ION BEAM DESIGN REQUIREMENTS

M-, CURVE FOR CONNECTION No.255HOWING COMPONENTS OF ROU.TION

Test No, 25

[ 107 ]


I

I3 'Z.~'Li 3

I I

IE ;:oF!

I

1- -If ~~110' ·:011LL, UJ

,~

iI

:..

ino

TEST SPECIMEN NO. '2CoDETAILS

?4V\F74 4'-4":'I~o

-;~?~----~~=~

"' I 1 'I "'..., l 1)- _,1'1

~'--- -- '"r 4'-4~4'-41.-

1:::::::=====::=:l==;1;::t4j._ be ,_ lll;;:~=======:l",.!...v ~_ _ ~ ,

"'-- r-----; =-=.t: ~--

I 14V\F87 5'-3" MtEt ?4V\F74 4-'.4-"e. t: ro",4",~", I'-f' to.e. L'" "''''''''''1 ,,9~ be4- L'" 4",4", i,,,,e~ ko.e. FILLS "''''i,,9i to.4 SH\MS S",~" e de

LOG OF TEST NO. 26

REMARKS

60.50

SHEAR(KIPS)

55.00 Scaling at bearing toe of seat stiffenerangles.

Shear failure of rivets in horizontal leg oftop angle.

GENERAL NOTES: Good rotation reserve. Between thirty and forty-fiveper cent rigidity.

2904

MOMENT(IN.-KIPS)

2640

[ 108]

TEST NO 26 (THIRD SERIES)

,

t&oo',--,-__,-__-,__,.-__--,__--,

10p Q"d pool A"'II 5

0.004 O.COl!> 0012. 0'''' 0.0

ROTATION B£TWE£I>I ENe 0'1"" B~"M "'NO

COLUMN IN R"OI",N'S

M-, CURVE FOR CONN. No. 210 REL",.EQ,.O

MOMEN,. - RO"""'ON BE"M DES'C.N REQU'REMEN1"S

Test No. 26

[ 109]

"!'ti .i-ii'

,,~ ::& .. ,.~{" '.t .~'li .. ~

I{ ~ ~J.... r>'JH ~1 il-"

"- II IJ

/V ~V-

~.-V~~

~oo

1/r/,,- //1eo<>

YI.~

Rou."T\O+.I ~W~ ENO 01" """""'-NOCo\'UWlN I R"OI"N

0

M-; CURVE FOR CONloJEC.T\ON No. 2bSHOWING COMPONENTS OF ROT"TION

TEST NO. 31

4'_ 4f

Z4W'12.0 4'-4"- Me.

----#-+ +I--~_,..~I__ --H+-#-~-""...1.I

~zi! --\-,--"1.----t~1.i, lb

~=

?AW'I2.04'-4·'-me.

1- L8xro"i" I'-oi - be2.- Ls<O,,4,,~,,8~ -k"1- FlL. 3" i " 8 i -f"

-,v

~..-,

lIT.,N~~ Ii. 11

"",eO . ,"<t l'".9-',

--

'~ :E----l-I-I~,~III=I-<D.>+--J.jl------'-:'+'i I ~ ~~

-- -~-.l..--I~,I~-----l...- '----:le."-- I----~' be.

\~TEST SPEC.\MEN NO.3\ : --l~~ 1-:,;'DET~\LS - +--"--

LOG OF TEST NO. 3\

REMARKSSHEAR(KIPS)

43.00

172.00

229.40

MOMENT(IN .-KIPS)

2060

2064

2755

Tension rivets in vertical leg of top anglenear failure.

(New lever arm).

Maximum load. Tensile failure of rivets.Exact load at failure unknown.

GENERAL NOTES: Although moment-rotation curve shows no rotationreserve, there was some degree of unmeasured rotation beyond themeasured values. Nevertheless, this connection is apparently deficientin rotation reserve, while developing between twenty-five or more percent rigidity.

[ 110]

I TEST NO. 31

I

~3 '1.000..;.

~Top anG eat Anq s

:..:::.:L C

/F//

U1dsponc..Uot load a.tJ ''''1 to 1>0 //

I I I / 40·.

I"'.. I /1' II

W" to ~'\'I '0I ~",form 00'I

\ " ---t

1~ 0'.Ixl \ MQ1 Mo .-'2.155'"I

I Mo.Yo Ro+ • >0.012 R••.

fL I~1!L __

f "To Flonqt of 14W 7 Col.Top L' G,4,1, I-lSeo.t L-BxG:lIth.I~OiShHened.

Rivets •

0.004. c.coe. c.ote

ROTATION BE,.WU:N END OF BE&\"'1

COLUM~ IN RADIANS

M- ~ CURVE FOR CONN. No. 31 RELA,.EO,.O

MoMENr ROTA,.,ON BE""I\ DE51C>N REQUIREMEN,.S

Test No. 31

[ " I ]

0.004 oooa

RClTIIlTION &Twu:N El>lo 01" BU.M ""'0

CoI.UMN IN R"o,,,"..

M-, CURVE FOR CONNECTION No. 31SHOWING COMPONENTS OF ROlA"fION

TEST NO. 32

I-l B~G:>'J.i~9i - bb

.<J2-L!> <O~4)C:~~Bl-ka. /' ---~-.f-... I-FIL. :h-f'J.9-f -fa.

~ ~----,_,N . -:Q~

~~~ ~4--~

11 Ii .D -----~,oJ ;1 'Zl ! It.{~~ I'-~"

<l- I <11~

-9

, !-,oJ

--' 4'-01" ,~, ' ,, tl 4- o '!

i r:, '4>.D-.l

-'N qosh-lot bi''" 1--, uJ

I

iti , 0 zi

_,N ;"It Z\'l'FIO~ ~+l~ i

.- I4'-0 '? ~ 1.1 'I'F 103 4'-0 mbmb--

'"-:.. [jj l~ 3

-!-ot" ~

~~t+. '10Si./ l~~ Ir'

II ~"'I - '" -<'<0 - I------

-- :'l'lt %.... RIYE-T~, i 0

~I.,:.

! I , . '"mi- I . h bb

4 TEST SPECIMEN NO.3! '-: .r-

I -.:;'jDETA\LS - L W

LOG OF TEST NO. 32REMARKSSHEAR

(KIPS)

2823

MOMENT(IN .-KIPS)

3105 Tensile fracture of rivet in vertical leg oftop angle.

GENERAL NOTES: Good rotation reserve with between twenty-five andforty per cent I'igidity. Rotation largely accounted for by bending incolumn flange and slip of beam flange rivets.

[ 112]

TEST NO. 32

to> O.(lU)

Rcn""uON ~::::t\;N;":~,,,~:"'~ \NOM-'; CURVE FOR CONNECTION No. 32

5HOWING_ COMPONENTS OF R9n,"IO~

,

Ji.t

~:t. !

:;;i , t" r t ... '"

, ... " ~ - ~5

.$ ~ 1< 'li 5

..':11 ! q0

dG i< Ji~

~

) .JV)/~~

!Jw0

7!!

a 0·004 0·008 001t. 0.0.

T- and 5., i Anq'~5

1/r:-.--./'

! _10

so"!. / V"...1'",a

f~ tx n Unlfcwm ood

I

I

~-~ \ Ma< Mo -3,105~01:

~.~\J \to 30\Ma, Rol '0341 od.

I~ ""Con<:enh ~ed. load.

Q.~ M. pan

II To Flono of 14W 81 Col.'Top l-" 4 .. 1~ " 2SeQ+ L- ~ (ind.)( 9i

II R\"et~ - e-

o o. O~ 0006 0.012. 0,020 0.01.4

RO"l"A,"tION B£'W~t!:N E~o OP" BEllM "'NO

COLUMN IN R"'OI"'N~

M- ¢ CURVE FOR CONN. No. 32 RELA"TED "TO

MOMENT- ROTA"TION BEAM DE51uN REQUIREMENTS

zo

i8

.Z ll;>OO

1

Test No. 32

[ I 13 ]

TEST NO. 35

:",<0o

l,l- \0 4Z~

td I ~'"dd ~

_!~~I~I_---L"''''

-.9

I -d~f\J

• ,-d,," ,

3'-o·f • I oJ 3'· ot'"_,. N, 11 ''''

~U~"3hw~

\?V'F?5 ''l~l ,0 , ¥ I?WZ5~I~ i~ I 3,'-0 mel3'-Q md rr '" i i'\, ~~./ i

<t' ;rr~

I

9

JL_I

I!

~"q, RIVET~ TEST SPECIMEN NO. 35DETAILS

LOG OF TEST NO. 35REMARKSSHEAR

(KIPS)

17.50

41.75

560

835

Column flange scaling at top angle.

Tensile failure of rivet in vertical leg oftop angle.

GENERAL NOTES: Fair. rotation reserve with forty-five to fifty-fiveper cent rigidity. Rotation primarily due to bending of top angle andextension of tension rivets.

MOMENT

(IN.-KIPS)

[ 114]

TEST NO. 35

~'E0 -' ~ •

.e ~ '_q~1'~]j ~ rf ~r.: I~' r :

~H $~ ~\R£~~

IT

:?~/

JffI/;,

ROT/ll'TIOH IBETWEEN NO OF B IIt.M ",NO

COLUMN \ R",nlll,NSo

0 00 •

j.~%

DoOll. o.ot.o

RO"''''TION B£lWEEN £'folD Of" B~"N\ ",,",0

COLUMN IN RIlt.OU\N!o

Top Gnd ••1 i\nq\,

V V

,o~.

~~

i,,, U..I"~ Lo.'

w~ .\&£Y. I/, ""\ \

~~ \ '"~Mo.... Mom " 835.l(~

''''' Mo.... Rot. >0.048 .d.r-i,t:: w \",---\

\ (oncentro. ed loo.d 1 M,d,,,,~oX .1

I To FIGnqt. ot IOW4 Col.To. L- '" 4-. 5 .Bi50<.1 L', • • Co'lti "'&1R·w:n.·a

. 0.004-

j.'"~~!:2§

~2

J 200

M - ,. CURVE FOR CONN. No. 35 RELA'EO TO

MOM'NT-RmATION BEAM DES'(,N REOUIREMEN'S

M-;' CURVE FOR (oNN.n,oN No. 35SHOWING COMPONENTS OF ROTA"T\ON

Test No. 3S

[ I 15 ]

L -

TESTS NO. 36 AND NO. 37

Dm¥CO" W~ >: -::!..'1""','" ~~ ;;s.., ~ ~,,"

"_HI dl <t u~ ,

3>'- 81 '" J d

t~I ~ :t.... ~

I '" I

L" ~-..9 l;:;

:' '"« «

9·'h If 0

o..c.:l...-1...

-,. ~

~ I ~~ IBI"F4? ~2'" ,'-e,

~ 0-

-- mp -- ~ , i I "" --~ d

ad)1--- _,

-~

~~

~-1bp -is'

+ C}~ ~~ :"I't .9I"

<t

t~.9 ;,

r" !\1 i 7I

4,l~

~l,

0.<1. bp

{"J~,-....'"

D' fHt«, , %"~RIVE.T5 J', , _,N u: l. .... 4 t, ,

~, ,II ~j'I' , TEST SPECIMEN NO. '3(0 a. 37

DETAILS

LOG OF TEST NO. 36 LOG OF TEST NO. 37

Top and Seat Angle Connection toOne Side of Column Web

REMARKS

95.0

122.852457

Scaling on vertical leg ofseat angles adjacent tofillets.

Scaling in beam webabove seat. '

Tension failure of allfour rivets in top angle.

GENERAL NOTES: Good rotation reservewith between forty and fifty-five per centrigidity. Comparison with No. 36 shows themarked improvement produced by stiffeningthe opposite side of the column web, therebyforcing bending to take place in top angleand distributing load between top anglerivets.

Details of this connection similar to thatof Test No. 36, except for web reinforcement.

1900

MOMENT SHEAR(IN .-KIPS) (KIPS)

1800 90.0

Top and Seat Angle Connection toOne Side of Column Web with

Web StiffenedREMARKSMOMENT SHEAR

(IN .-KIPS) (KIPS)

640 16.0 Strain lines due to bending of column web adjacent to ends of topangle.

744 18.6 Tensile rivet fracture intop angle at end.

988 24.7 Second tensile rivet fail-ure in top angle.

GENERAL NOTES: Insufficient rotation reserve. Flexibility of column web throws alltensile load in outer or end rivets of topangle. The desirability of a reinforcing angleon the opposite side of the column is indicated.

[ 116]


Test No. 36

Test No. 37

[ 117]


ROTATlO\ol BE'TWEEN END OF EIlo.M AND

COLUMN IN RA,Q1F>.N

0.004

,Top (lnQ. eo.t AnqleIf

so%,

J Rlve+ FQ.I\ I"'e

f· LO "'1/

l Uniform o.d<00

V\ 40%

rt +~o:~\ I Cont.~n+" 1e.cl. Loo.d. +Mtdspo.n

1··~ ..II

"'\I IL4<l'b ~o%

I Mo.x.Mom -988'·Mo.... RoT >O.OIZ' d.

! C~n hon 10 C e Sul.e Co~mnWebW.bU ~hHened..

Top L-<Dxj4xAlt \14Seo:t L-,~ CD1.~l( \1!Rlveh.-e,

ROTF>.'TION BCfWEEN NO OF B~N\ ",NO

COl.UNlN \ RA.DIA,NS

0' 0'0 0.02.

M- .p CURVE FOR CON". No. 3(0 RELAOEO TO

MOME"T- ROTATION BEAM DESIGN REQUIREMENTSM-" CURVE FOR CO....ECTION No.3"

SHOWING COMPONENTS OF ROTI\TION

B

ROTA-nON BETWEEN ENt> Of' BEAM

COLUMN IN R"'OIANSM-" CURVE FOR CO"..ECTION No. 31SHOWING COMPONE"TS OF ROTI\TION

...J"Oj! E ...J ~

;~~ HHf0

f ~I ~ (J..;:: rJ. ~

~!j t£ ~~f£

) )) ~

1/;/~IV!

If;1/

WIII

0 0.004 000 0

<00

j

%o

5"%%

.3

lop o.nd. !eat Anql.,

/V

V,-

"TO·I.

~ .10

"'\ 3O~fO m LaM

80Y.. V~J Max.Mom ·Z,451. K"

; \ 1\ / \ Mo.... Rot. >0.05(0 ",d.

I 1'1 j~o:d~~, \I

i I I ,,'.1& 10 1 to\I <00"

\,C nc.entra+E d. Loo.d. MHI,''!Ipo.t- L~'"/~

Conn chon +0 (r' ""de C um" WebWeb hHened.

UTop L-(D 4)(1\11- I

SeQt L~. )(fo)l. eo x 14-RI''W1!.t'S.-e.

RO"T"','ON BET ....... EEN ENO OF Ell.M ""NO

COLUMN \ RP,OlAI'II'i

0 0,0 4. O. 00

M- .p CURVE FOR CO..... No. 37 RELATEO TO

MOME..T-RoTATION BEAM DESIGN REQUIREMENTS

%o

i(j

[ 118]

Documents

RIVETED SEMI-RIGID BEAM-TO-COLUMN BUILDING CONNECTIONSdigital.lib.lehigh.edu/fritz/pdf/191_3.pdf · BEAM-TO-COLUMN BUILDING CONNECTIONS ... PROPOSED METHOD OF DESIGN FOR BEAMS WITH