t::1 ,3

. CIVIL ENGINEERING STUDIES STRUCTURAL RESEARCH SERIES NO. 159

STATIC AND DYNA IC TESTS

f STEEL FRA E STRUCTURES tNT THE

INELASTIC RANGE F DEF RMATI N

by

J. M. Massard

final Report to

RESEARCH DIRECTORATE

AIR fORCE SPECIAL WEAPONS CENTER

Air Research and Development Command

Contract AF 3 3 (61 6) - 17 0

Project 1 080

Task 10803

UNIVERSITY OF ILLINOIS

URBANA; ILLINOIS

MAY 1957

AFSWC ~1'R"" 57 =23

FINAL REPOR.T

STATIC ~D DYN~IC TESTS OF STEEL FRAME STRUCTURES

Project ~

Task Contract~

INTO TH:E.i INELASTIC RANGE OF DEFORMATION

by

Jo Mo Massard

Approved by

No Mo Ne-wmark

University of Illinois

Department of Civil Engineering

May 1957

RESEARCH DIRECTORATE AIR FORCE SPECIAL WEAPONS CENTER.

Air Research and Development Command Ki.rtla.nd Air Force Base, New Mexico

1080 10803

Approved~

AF 33( 616) -170 Eric lio Wang Chief} Structures Division

STATIC .AND DYNAMIC TESTS OF STEEL FRAME STRUCTURES INTO THE

INELASTIC RANGE OF DEFORMATION

CONTENTS

10 INTRODUCTION

10 Purpose and Scope

20 Acknowledgment S 0

110 CONCLUSIONS

10 Comment

20 Conclusions 0 0

1110 GENERAL COMMENTS

General Commentso 0

IV 0 SUMMARY OF THE IN\lESTIGATION

Summary of the Investigation 0

Vo REVIEW OF THE INVESTIGATION

Survey of Literature 0

20 General Nature of the Investigation o 0'

30 .Analytical Studieso 0

40 Devel.opment of Testing Apparatus"

50 Experimental Investigations

BIBLIOGRAPHY " 0 0 " " 0 0 0 0 6 0 0

APPENDIX A~ ABSTRACTS OF REPORTS PREPARED UNDER CONTRACT

1

1

3

6

7

9

9

10

11

12

15

AF 33( 616) =1700 0 0 6 0 0 0 0 0 0 0 ; 0 0 0 0 17

APPENDIX B ~ TABULATION OF TESTS PERFORMED UNDER CONTRACT AF 33(616)=1700 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46

TABLE OF NOTATION FOR APPENDIX Boo 47

STATIC AND Dl'NAMIC TESTS OF STEEL FRAME STRUCTURES INTO THE

INELASTIC RANGE OF DEFORMATION

10 INTRODUCTION

10 Purpose and Scope

The purpose of the program which has been conducted at the

University of Illinois under Contract AF 33(616) ... 170, Task 10803, Project

1080, can be stated in general terms as Uthe performance of tests and

analyses to obtain basic information concerning the behavior of steel

structural frames and elements when subjected to known static and dyn~ic

loadings that produce extensive inelastic deformationso Jtr

The project was begun in July of 1952 and., in its various phases J

has been carried on continuously since then 0 During this time three Final

Reports 3, 9 have been writteno However, since this is to be the last

F"inal, Report on the contract J the entire project will be summarized" The

review of such an extensive program. must necessarily be cursory; however,

it is hoped that this presentation will provide the reader with enough

information to permit his understanding the investigation as regards its

purpose J scope J results produced and their appli.cabili ty to problems per.,.,

taining to the inelastic behavior of steel frame structureso

2" Acknowledgments

lhe investigation described in this report was performed by staff

members of the University of Illinois in cooperation 1.;ri th the Wright Air

* The numbers refer to entries in the Bibliography presented at the end of the text 0

Development Center and the Air Force Special Weapons Center, Department of

the Air Force, under Contract AF 33(616)~170 as Task 10803, Project 10800

The project was conducted in the structural Research Laboratory

of the Department of Civil Engineering under the general direction of

No Mo Newmark, Professor of Civil Engineering and Head of the Department.

Project supervisors have been, in chronological order; Go Ko Sinnamon,

Research Assistant Professor of Civil Enginee~~ng; Fe Lo Howland, Research

Associate in Civil Engineering, and Jo Mo Massard, Research Assistant

Professor of Civil Engineeringo

The many re.search assistants and research associates who have

been associated directly with the project include Ro Jo Munz, Ro 30

Mayerj~, Wo Egger} Ro Fa Wojcieszak, Jo Ho Sams, Co Lo Wilkinson, Lo Wo

Heilmann, Ae Aug, and D. McDonald 0

One Technical Report produced with project funds was based upon a

doctoral dissertatioD. by Wo 30 Rallo

The instrumentation used throughout the investigation was, in

general, the responsibillty of V 0 J 0 McDonald, Research Assistant Professor

of Civil Engineeringo In additi.on to those individuals named many other

members of the staff of the university of Illinois have aided the advance-

ment of the program 0 Not the least of these were the personnel of the

Civil Engineering Shop, and the many student helpers employed to perform

the routine computational work necessaryo

IIG CONCLUSIONS

10 Comment

The conclusions described below were reached as the result of

tests performed under the following conditionso The material in all cases

was mild structural steel which nominally met the requirements of ASTM

Specification A7 = 56To All of the tests were performed at room tempera-

ture and at rates which were either nslowli (maximum load and deflection

reached in several minutes, or a few hours in some cases) or YVrapidit

(maximums reached i.n times on the order of fifteen to fifty milliseconds ) 0

The configurations of the test systems were such that specimen resistances

were not limited by buckling of any type until the maximum strains were

well into the range of strain hardeningo All failures were ductile; i .. eo,

no brittle fractures 0

20 Conclusions

lo The actual resistance of a mild steel structural element to

an imposed inelastic deformation increases with the rate of that deforma­

and is also dependent upon the time involved!Y 8, 9, 11

20 In most of the specimen types in which it occurred,. local

inelastic buckling was less pronounced in the rapid tests than in the slow

ones:1 which indicates that the effecti veness of the 'beam section was

t t 5, 8, 11 increased wih the rapidi y of deformationo

3

)0 An axial load on a structural member decreases the ability of

the member to resist lateral load, but does not affect appreciably the

total resistance of the member to an external moment except in the limited

range of deformation immediately following ini tialf-l:yieldingo 3, 6, 8, 11

4

40 The effect of shear upon the moment capacity of an 8 WF 58

section loaded laterally and slowly in the plane of the major axis was

found to be negligible even for a beam having an equivalent cantilever span

to depth ratio as low as two 0 However» in a region of constant shear but

gra~ient moment, the development of a general shear yielding condition in

the we-b caused. deflections considerably greater than those which resulted

I 2 from concentrated yielding primarily caused by momento

50 In most of the structural elements and models tested, the

ini.ti.al Uelastic H region of the resistance""deflection relationship had a

slope less than that derived using elementary theory and assumed ideal

condi.tions of support 0

60 .A static resistance"",deflection function for a simpl;e struc'"

t1rral element or a relatively simple structure can be determined with good

accuracy by usi.ng practicable approximations to relate strains to deflec-

tions, and then computi.ng resistance on the basis of the known static

stress-strain characteristics of the material involvedo 1 , 3, 4

70 For research purposes requi.ring good accuracy, an equivalent

resistance-deflection function for a relatively simply structure subjected

to rapid deformation can be determined in a manner similar to that mentioned

above USing, of course, the dynamic properties of the material in the deter:...

mtnation of the resistance 0 The procedure should be such that the equiva ....

lent resistance is computed using instantaneous material stresses at the

critical sections which are c.ompatible with the strains, straining rates,

and times involvedo The total resistance so determined (which does not in-'

clude inertia forces) is actually a function of ttme and velocity as well as

displacement (as was indicated tn paragraph 110201)7 andy therefore, is

5

strictly valid only for the particular case considered, or for others very

. . 1 dId' ft· d ttl f' t . 11 Slml ar as regar s oalng unc lon an s.ruc ura con 19ura lono

80 However, since the effect of delayed yielding is probably

important only in cases of short duration impulse, and the general yielding

reSl,stance of mild steel is relatively insensitive to changes of straining

rates wi thin one or two orders of magnitude , suitable accuracy can be

obtained in most practical problems (where the dynamic loading function is

seldom kno'WIl with great accuracy) simply by increasing the static inelastic

resistance of the structure (as determi,ned by use of the procedure outlined

in paragraph 1102 .. 6) in accordance with the straining rates estimated to

exist at critical locations in the structure as it responds to the rapid

loading imposed0 7,. 8, 9

90 Methods were developed for analyzing indeterminate frame

structures deformed inelasticallY08, 10 In these procedures the resisting

moment.s throughout the structure which correspond to a compatible deflec-

tion confi,guration are determined" The methods are ill,ustrated with the

solution of nstatic~g problems 0 However, they could be used with slight

mod,ification in the timewise step .... by-step solution of problems involving

structural response under rapid loading" Their use in this manner would be

most practicable with the use of a high speed digital computer 0

100 The analytical procedures which have been developed on this

program were intended for use in research applications,," 4, 8, 10, 11

Ho'Wever J they should be useful not only in the planning of testing programs

and the evaluation of experimental results but also in determining the rela-

tive accuracy of simpler methods which are more suitable for purposes of

design and routine analysis d

6

1110 GENERAL COMMENTS

10 General Comments

Irhe experimental studies made under Contract AF 33( 616) ... l70 to

obtain basic information concerning structural behavior and for corirelation

with the analytical studies were inevitably of relatively narrow scope

compared with the entire range of structural usageo However, the results

of the program. are applicable) at least indirectly, to much of the field

which the studies were intended to cover, the effect of blast loadings on

structures 0 The major omissions in the program were tests of connections

other than the rigid welded ones used, and tests of fairly large scale

frames 0

The first omission is being covered by an experimental study of

various typical riveted and bolted connections now being con=

ducted under Contract AF 33(616)=37800 It is expected that the work on

this will be concluded within a few months and that the information

perta,ining to the slow and rapid deformation behavior of column~ base and

beam=to-column connections will be made available as an MSWC Technical

Report 0

As regards tests of large scale frames under slow and rapid load-

app~.ied illlder conditions it is not believed that the value

of the resu~ts produced in to the funds expended would compare

favorably with other research possibilities such as wider lnvestigations of

the behavior of the

conditions q

structural elements under different force-time

7

IV 0 SUMJ!,Af..A,RY OF TEE I1~1ESTIGATION

10 Summary of the Investigation

10 A br:i.ef survey has been made of the literature pertaining to

the static and dynamic behavior of mild steel structural frames and elements

d ot· f d·d d· 2, 3J 7, 10, 11 under can l lons 0 slow an rapl loa lngo

2" Experimental resistance-deflection-time information has been

obtained from slow and rapid tests of beams and beam-columns deformed i.nta

the ine.lastic rangeo l } 3, 5) 6, 7 In the slow tests, failures were produced

in times of several minutes to a few hours} while the times involved in the

rapid tests were on the order of tens ofm:i.ilisecondso

30 A combined analytical and experimental investigation of the

behavior of 'beams under oblique loading has been madeo" 4

4'0 A brief analytical and experimental study has been made of

the effect of high shearing forces on the deflection of beamso 2

50 The behavior of simple model frames when subjected to slow

and rapid loadings has been investigated experimentally 0 5 J 8

60 Analytical correlati.on studies based upon si.mple mathematical

representations of material behavior have been made of several d.ynami.c tests

of beams and s:i.mple frames 0 9

accurate procedures for determining the

inelastic deflection=resistance characteristics of redundant frame struc-

tures have been developed 0

80 The behavior of material obtained from a few rolled sections

of structural steel has been determined experimentally under rapid loadingo 1l

90 The behavior of several series of beams which were tested

statically and one series which was tested dynamically to extensive

inelastic deformations has been correlated fairly well with the known

properties of the specimen material.s as obtained under reasohably compara­

ble conditions of stress, strain, and time 0 3, 8, 11

100 Rapid loading equipment capable of applying forces as large

8

as ± 60,000 lb in times as short as 10 milliseconds to small structures and

12 structural ele~ents has been. developedo

9

v " REVIEW OF THE INVESTIGATION

10 Survey of the Literature

In 1952 three publications13.? 14J 15 became available i.n which

were summarized c'ollectively the state of knowledge pertaining to nSteel

Beams, Connections, Columns and Frames iV under loading conditions ranging

from iU static uu to transient Ii dynamicV~ rates 0 The availability of these

reports made unnecessary an extensive survey of the literature concerning

steel and steel frame structures, and, in addition, greatly simplified the

finding of specific information useful in the advancement of thE:; investiga-

tion being conducted at the University of Illinoiso Of course, during the

ensuing years J technical publications have been continuously monitored for

pertinent informationo Such references are listed in the various Technical

Reports produced under Contract AF 33(616)-1700 Abstracts of these reports

form Appendix Ao

20 General Nature of the Investigation

The investigation summarized in this report can be divided some-

what arbitrarily into three phases; (1) the development where necessary of

analytical procedures and methods of computation which would he useful in

the planning of test programs, interpretation of test results, and the

general analysis of steel frame structures under slow and rapid loadings

producing inelastic deformation; (2) the development of apparatus with

which the required experiments could be performed; and (3) the experimental

testing program" Each of these phases will be discussed in the following

sectiono

10

30 Analytical Studies

The analytical phase of the project has included a study of the

elementary theory of inelastic flexure of beams loaded laterally in the

planes of major, minor and oblique axes; an investigation of various anal-

ytical expressions with which it might be possible to include the effects

of various parameters believed to be important in the behavior of structures

under rapid transi.ent loading conditions producing extensive inelastic

deformations; and the development of basic procedures useful in the analysiS

of indeterminate structures whose elements undergo inelastic deformation 0

It was found in the first studylj 2, 3; 4, through correlations

with the experimental work, that the elementary theory of inelastic flexure

when used with realistic stress-strain relationships including strain

hardening permitted the computation of accurate resistance-deformation

relationships for beams subjected to lateral loading applied slowly in the

planes of the major, minor, or oblique axes provided that the beam section

was of such geometrical proportions that the secti.on was not made less

effective by buckling effects"

The investigation pertaini.ng to the development of analytical

expressions including in parametric form the variables considered important

in structural hehavior formed the basis of a doctoral dissertation by Mro

F 0 La Howland 7 0 This procedure was used in the correlation studies presented

in the Final Report for the period 1 September 1954 through 31 August 1955<>

Mro Ro Jo Mayerjak and Mro Ao Ang investigated possible methods

for anB;lyzing indeterminate frame structures when deformed inelasticallyo

The procedure which resulted from these studies8j 10 permits the determina=

tion of the resisting moments tb...roughout the framework of an indeterminate

structure for any inelastic deflection configurationo From these moments

the loadings which could have produced them can be computedo While the

procedure only determines resistance for an assumed deflection configura­

tion, it is not limited to cases of ~~staticiV loading, since, with a

suitable adjustment of the material properties to take into account

increased resistance in accordance with known or expected straining rates

at critical in the structure, it would be possible to analyze,

proceeding step by step as regards time, the behavior of a structure sub=

to dynamic loadi.ngs 0 In Reference No., 8 the material properties

were (by increasing the yield stress 15 percent) to account for

11

d.ynamic loading conditionso The solution of such a problem by this method

would be tedl.ous by hand but it should be quite practicable by

high digital computer 0

40 Development of Testing Apparatus

In the early of the investigati.on, which were concerned

with slow deformation tests of beams and beam=columns, the testing apparatus

used was fabricated from the various loading frames and hydraulic jacking

equipment available in the However, with the incidence of

dynamic it became apparent that the drop weight eqUipment available

would be inadequate for any except those concerned with rela­

small structural elements 0 it was decided to develop

rapid loading eqUipment with whi.ch it would be possible to apply forces as

large as :t 60)000 lb in times as short as 10 to 15 milliseconds, maintain

these loadings as long as and then release them in times as short

as 20 to 30 millisecondso The successful development of this apparatus

12

provided the laboratory staff with means of applying controlled loadings to

structural elements of reasona'ble size 0 12

50 Experimental Investigations

The first of the experimental investigations were concerned with

the behavior of beams and beam-columns made of I J wide flange, B} and M

structural sections when subjected to slow lateral deformation in the plane

f th ". 45°' 1, 2, 3, 4 CIt· f th . ° . e maJor) mlnor} or axlS 0 orre a lon 0 ese experl-

ments with the analytical studies indicated that the resistance of such

structural elements can be computed with good accuracy if the actual stress-

strain properties of the materials including strain hardening are used in

conj'unction with an elementary theory of inelastic flexure based upon

assumed planar distributi.on of strai.n throughout a section. These methods

yield results that are accurate even well into the range of strain hardening

if the configuration of the specimen, its sectional properties) and restraint

condi tions are such that the primary ma,de of failure is not associated with

lateral} local} or torsional bucklingo

A closely related phase of the experimental investigation was

concerned with beams and beam=columns which were tested with two types of

rapid loading, pulses applied. with a drop weight machine 3, 6" 7 and loadings

which were applied in about 15 milliseconds to constant levels thereafter

• +" d b th . l' t" h" d 11, 12 maln~alne y. Ie specla_ teslng mac lne use c>

In addition to the beam and beam-column tests, information concern-

ing the behavior of frame structures was obtained from slow and rapid tests

of small single bay bents whose elements were quarter scale models of 6,WF 25

,"" t... 3, 5, 8 ~ec lonS6

13

Throughout the project, the behavior of structural elements and

model frames was correlated where possible with the properties of the

materials from which they were made. Through 1955, the properties of the

actual materials used could be determined only for the slow tests. The

material behavior under rapid loading could only be estimated from informa­

tion obtained by other investigators for similar steelso For the last

series of beam and beam~column tests performed in 1956, both the slow and

rapid loading properties were determined for material cut from the parent

sections from which the beam and, beam=column specimens were obtained"ll

As was the case with the specimens tested slowly it was found

that the resistances of beams and model frames tested rapidly were in good

agreement with those determined on the basis of the known rapid stress-;

strain=time behavior of the materials involved 0

Where local inelastic buckling vras observed in a test series, it

was less severe in the specimens tested rapidly than in those tested slowly.

A partial explanation for this behavior may be obtained from consideration

of the dynamic nature of the buckling process excluding time dependent

effects in the materiale 17 However, these effects as they pertain to the

straining rate dependence of the yielding resistance of mild steel

may be the most important factor in these tests, since the greater the rate

of center deflection of' a beam with respect to the Ii flow H rate (rate of

at a

of the "beam the could be

As was mentioned,

ments which have been

possible to the static and

the were madeo

the more widespread along the length

to be"

the behavior of the structural ele-

experimentally' has been related where

properties of the materials from whi.ch

the determ:Lnation of material

14

properties under both slowly and rapidly applied uniaxial stress has been

an important phase of the projecto This work has progressed concurrently

with the beam and beam=column specimen tests, and within itself has yielded,

in the case of the dynamic material studies, new information pertaining to

the behavior of materials in rolled structural sections under conditions of

rapid deformationo ll A related phase of the beam and beam-column investiga­

tion was the determination of existing residual strains in the specimen

parent sections as received from the mill, and also strains induced in the

specimens as a result of fabrication by weldingo ll

In another phase of the program, the effect of shear on the

inelastic behavior of wide flange beams subjected to static loading was

investigated experimentally and analytically by W. Jo Hall as the subject

of his doctoral dissertationo 2 The beams tested were 8 WF 58 members which

have sectional properties such that local buckling is not criticalo A

shear stress~strain curve was derived which can be used to estimate the

component of deflection caused by general shear yieldingo From the results

of this study it was concluded that the effect of shear on the moment capac­

ity of a wide flange beam is negligible for the usual range of structural

practice, but that general shear yielding should be avoided since it leads

to excessive deformation 0

The several series of tests of beams, beam=columns, and model

frames are summarized in the tables which are presented in Appendix Eo

15

BIBLIOGRAPHY

10 Howland, Fo Lo} iVStatic Load Deflection Tests of Be81D.~Columns, Y? Univo of 1110 Civil Engro Studies, Structo Reso Series Noo 65, Contract AF 33(616)=170, Deco 19530

20 Hall, W 0 J 0, uiShear Deflection of Wide Flange Steel Beams in the Plastic Range,UVUnivo of 1110 Civil Engro Studies, Structo Reso Series Noo 86, Contract AF 33( =170, Novo 19540

30 Howland, Fo Lo, Egger, Wo, Mayerjak, Ro Jo, and Munz, Ro Jo, HStatic and Dynamic Load Deflection Tests of Steel Structures, Ii Uni Va of 1110 Civil Engro Stuclies~ str'ucto Reso Series Noo 92, Contract AF 33(616)=170, Febo 19550

40 Egger, W 0 ,VINotes on the Analysis of Obliquely Loaded Beams in the Inelastic Range J

ii Univo of 1110 Civil Engro Stu.,dies, Structo Reso Series Noo 98, Contract AF 33(616)=170y April 19550

50 Wilkinson, CoLo, and Howland, F 0 Lo, iiTheResponse of Model Frames Subjected to Dynamic Lateral Loads,ui Univo of 1110 Civil Engro Studies, Struco Resa Series NoD 99, Contract AF 33(616)=170~ June 19550

60 WOjcieszak, Ro Fa J and Howland, F 0 La, liThe Response of Beam=Columns Subjected to Dynamic Lateral Loads, Ii Univo of Ill" Civil Engro Studies, Structo Reso Series Noo Contract AF 33(616)=170, June 19550

70 Howland, F 0 La, iiInelastic Behavior of Mild Steel Beams Subjected to Transverse Impact/v Univo of 1110 Civil Engro Studies, Structo Reso Series No a 106 J Contract .AF 33( 616) =170, August 19550

80 Mayerjak, Ro J 0, of the Resistance of Model Frames to Dynamic Lateral Load,iv Univo of 1110 Civil Engro Studies, Structo Reso Series Noo 108, Contract AF' 33( August 19550

9 0 Howland~ F 0 Lo J and Egger, W 0, iiCorrelati.ons of Reaul ts of Dynamic Tests of Beams and Model Frames~iU Univo of Illo Civil Engro Studies, Structo Reso Series NOO Contract AF 33(616) Septa 19550

100 Aug, Ao) and Massard, Jo Mo, Method for the Analysis of Frames to Inelastic Deformation into the Range of Strain Hardening J Ii

Univo of 1110 Dept a of Civil Engro J Techo Hepto to the Air Force Special Weapons Center -TR.-56=47)~ Contract AF 33(616)0170, Novo 19560

110 WOjcieszak, Ro F 0, and Massard) J 0 Mo, uUSlow and Rapid Lateral Loading Tests of Simply Supported Beams and Beam=Colu:rnns J Vi Univo of 1110 Dept 0

of Civil Engro, Techo Hepto to the Air Force Special Weapons Center (AFSWC-TR=57=21), Contract AF' 33(616) Febo 19570

BIBLIOGRAPHY (Concluded)

120 Egger J W 0' IV 6o-Kip Capacity Slow or Rapid Loading Apparatus, Ii Uni v 0 of 1110 Depta of Civil Engro J Techo Repto to the Air Force Special Weapons Center (AFSWC=TR-57~22), Contract AF 33(616)-110, June 19570

130 Hu, La So, Byce, Ro Co, and JohnstonJ Bruce GO}~IStee1 Beams, Coll.lilllls and F'rames, TI~ University of Michigan, Dept" of

Civil Engro) Engineering Reso Institute Projo M948, Report to Sandia Corporation, March 19520

140 rUBuilding in the Atomic Age,IU Proceedings of the Conference on, Massachusetts Institute of Technology, Dept 0 of Civil and Sanitary Engineering, June 16 and 19520

150 iUEarthquaj(e and Blast Effects on Structures) Ii Proceedings of the Symposium on, Earthquake Engineering Research Institute and University of California, June 19520

160 Clark, DoS 0' Behavior of Metals Under Dynamic Loading, Ii Trans 0 ASM, Volo 46, 1954, po 340

170 Hoff, NoJTo, 'iBuck1ing and Stability,VU Jo Royo Aero 0 Soco, Vo10 58, NoD ( 1954), po 30

APPENDIX A

ABSTRACTS OF TECHNICAL REPORTS PREPARED UNDER

CONTRACT AF 33(616)-170

10 Static Load Deflection Tests of Beam-Columns

by

F 0 L 0 Howland

University of Illinois Civil Engineering Studies

Structural Research Series Noo 65 December 1953

18

This report is listed as the final report for the period of 1 July

1952 to 15 September 19530 The work described in this report included a

series of static tests of beam-column specimenso These were lateral loadings

of beam=columns under axial load with the lateral loading applied in both the

strong and weak direction of resistanceo In addition some information was

included on the influence of axial loads on the response of beam-column

specimens 0 The report also indicates that a brief analytical study had been

mad.e of the effect of olJlique loading on beams 0

A total of nine beam=column specimens were testedo These included

two, 3 I sections, two 7 4 M sections and five, 6 I sections 0 Actually only

two of these specimens, one a 6 I and one a 4 M, were subjected to axial

load in addition to lateral loadQ The results of the tests are summarized

well in a series of three tableso

The effect of non=symmetrical bending including ideal plasticity,

(that is, the case in which yielding occurs at a constant stress without

strain hardening) is presented brieflyo The results are presented in the

form of an interaction diagram which relates the bending moments about the

principal axes of a section as a function of the maximum fiber strain or the

depth of yieldingo

20 Shear Deflection of Wide Flange Steel Beams

in the Plastic Range

by

W 0 J 0 Hall

University of Illinois Civil Engineering Studies

Structural Research Series Noo 86 November 1954

Methods of utilizing the reserve plastic strength of steel in

19

structural design applications have merited considerable attention in recent

years 0 Since deflections, rather than loads and stresses, often may be the

controlling factors in such design, it is imperative that it be possible to

calculate or at least make an estimate of the deflections under a specified

loading in the plastic range 0 A review of the literature indicates that the

discussions of the deflection of structures loaded beyond the elastic limit

have been restricted to bending alone 0 Little theoretical or experimental

information is available on the plastic defonmation of structural beam

sections in which high shear forces are presento

In order to study the deflection characteristics of beams sub-

jected to high shear forces, two continuous beams of 8 WF 58 as=rolled

section were testedo The main span of the beams was 9 ft and the overhangs

used to maintain the end fixity of the latter span were 4 ft 5 in. long 0

The central load points were symmetrically spaced at the one~third points

for the first beam. and at the one-sixth points for the second beamo Each

beam. thus had sections subjected to pure bending, bending combined with low

shear, and bending combined with high shearD Loads, strains, and deflections

were measured, and pictures of the whitewashed portions were taken to record

20

the yield patternso In order to made the pertinent data available to other

investigators, the load, shear, moment, and deflection data at key points

are tabulated in the reporto The detailed results of the tests are pre­

sented in tables and figureso In analyzing the data it was assumed that the

deflections due to bending and shear could be separated and that their

combined effect could be obtained by superpositiono From the shear versus

shear strain data, a shear stress-strain curve was derived which can be used

to estimate the component of deflection caused by shear when regions of the

beam have undergone general shear yielding 0 As far as is known from the

literature} these tests represent the first large-scale tests of continuous

beams loaded far into the plastic range in which extremely high shear forces

are present 0 On the basis of these tests it is concluded that no measurable

reduction in the moment capacity (for the section and span used) was

indicatedo

The importance of the shear aspect and its effect on the behavior

of beams is evaluated brieflyo Theoretical examples are presented which

illustrate the effects of general shear yielding of the web on the deforma­

tion characteristics of beamso This could be of major importance when shear

yielding of the web occurSo

**** A paper of the same title by W 0 J 0 Hall and No Mo Newmark has been

published as Proceedings Separate Vola 81, Noo 814 of the American Society

of Civil Engineers and a somewhat more condensed version will appear in the

1957 AGCE Transactions 0 The :proceedings paper i.s a condensed summary of the

data presented in the above report but in addition compares some of the test

results with current design specificationso Portions of the test results

21

indicate that where large shear forces are present the factors of safety may

be somewhat lowo This would seem to be particularly true for loadings of

the type used in these testso Since general shear yielding in the web can

cause excessive deflections, the recommended practice is to avoid high shear

when possibleo

30 static and Dynamic Load Deflection Tests

of Steel structures

by

University of Illinois Civil Engineering Studies

Structural Research Series Noo 92 Novet;n.ber 1954

Part one of this report presents a survey of the literature

pertaining to elasto-plastic and inelastic behavior of structureso

22

Part two describes static tests to failure of steel beam columns,

an analytical study of the effect of axial loads on the response of wide

flange beams, and the description of specimens, test apparatus, instrumenta ...

tion, and results pertaining to the beam-column study 0

The third part is a delPcription of model studies of frames

subjected to static lateral loads along with the description of the speci-

mens, the apparatus, the analysis used and the results of the testso

In part four the static oblique loading of steel beam columns is

described including the analytical investigation, the experimental investi=

gation and the summary of resultso

In part five the dynamic response of beams is discussed including

a criterion for determining the dynamic yield stress and description of a

dynamic test in a drop testing machine of one 3 I specimen including

instrumentation procedure, results and conclusionso

The conclusions listed in this report state that this program has

indicated that the static response of steel frames and frame elements can

be predicted with a theory that is similar to the elasto=plastic theory but

23

which includes the effect of strain hardening of the materialo However,

the tests have also indicated that the mode of failure can cause significant

deviations from the predicted response even though strain hardening has been

includedo For nearly all of the tests the experimentally determined capac­

itywas between that predicted by the elasto-plastic theory as a lower bound

and that predicted by a theory that includes strain hardening as an upper

bound a In the weak direction of loading, although failures generally

occurred by local buckling and the load capacity was restricted, the re­

sponse nevertheless approached the upper boundo In the strong direction

tests, however, the failures by lateral buckling cause significant deviations

from the upper bound predictions and, in many cases, the elasto-plastic

theory, which neglects strain hardening, provided the best predictions"

However, the deviation depends on many factors such as the restraint

conditions which are not incorporated in the theories at this timeo

In the application of these theories to the prediction of response,

the effect of axial load must be includedo In the weak. direction tests, the

thrust had only a small effect on the moment curvature relationship and had

to be included only in the computation of the applied momentso In the strong

direction tests, the thrust had to be included in the computations of the

bending moments and of the curvatures corresponding to these momentsa

The dynamic tests of the beam specimens have indicated that the

resistance to dynamic loads differs significantly from the static resistance 0

The change i.n resistance noted occurs because of an increase in the yield

stress of the material 0 This increase is, at first, a result of the delay

yield phenomenon which extends the elastic range of the responseo After

yielding occurs the resistance decays to a level that is greater than the

24

static resistance" The results of dynamic tests that were reported are of

a preliminary nature and continued investigation5J 6, 7, 8, 9, II has

produced a better understanding of the dynamic behavior of steel structures 0

40 Notes on the Analysis of Obliquely Loaded Beams

in the Inelastic Range

by

Wo Egger

University of Illinois Civil Engineering Studies

Structural Research Series Noo 98 April 1955

* The previous investigation of the static load capacity and

25

response of obliquely loaded beams in the inelastic range was restricted to

a small range of deflections by limiting the maximum magnitude of the

strains to the so-called Hflat H portion of the stress-strain relationship"

This restriction excluded the influence of the strain-hardening of the

material on the load-capacity of the beam 0 The e1asto""plastic theory

described in the report, though describing the behavior of the structure

reasonably well, was not suitable for a practical solution of the oblique

loading problem"

In order to overcome the limitation of the elasto-plastic theory

on the strain magnitude, the theoretical solution has been extended to

include the influence of strain=hardening of the material on the load

capacity so that the response can be predicted up to deflections of approx ...

imately 20 times the elastic limit displacement 0 It was f01.md that the

contri"bution of the strain=hardening to the load-capacity could be obtained

directly from the previous elasto-plastic analysis so that a minimum of

additional computation is required to extend the range of applicability of

the theory 0

* Howland, Fo Lo, Egger, Wo, Mayerjak, Ro Jo, and Munz, Ro Jo, "Static and Dynamic Load ... DeflectionTests of Steel Structures n Civil Engineering Studies, Structural Research Series Noo 92, University of Illinois, 19550

By means of the extended theoretical solution it was possible to

evaluate the applicability of the rigid-plastic analysis method by comparing

the response and load=carrying capacity of a cantilever beam. for various

directions of load applicationo This comparison has indicated that the

rigid~plastic analysis can be used to predict the deflection path with

sufficient accuracy except for the cases in which the load is applied at a

small angle to the web or Y=axis of the section.. Major differences between

the results of the theories occur in the predicted load-capacity since the

limiting capacity of the rigid-plastic theory is the Ii fully ... plastic Ii resist­

ance for the structure which neglects the contribution of the strain""

hardening of the material to the load-capacityo

50 The Response of Model Frames Subjected to

Dynamic Lateral Loads

by

Co Lo WilkinsollJ and Fo Lo Howland

University of Illinois Civil Engineering Studies

Structural Research Series Noo 99 June 1955

27

The principal objective of this investigation was to determine the

inelastic resistance of model frames subjected to dynamic lateral loadso In

this studYJ the observed dynamic resistance of the model frames is compared

with the V~theoreticalVi and observed static resistance 0 This comparison aids

the eValuation of the parameters which determine the static and the dynamic

resistanceo A study was made of assumed forms of the dynamic resistance of

the frames on the basis of the relationship between the energy inputs and

the mac~imum deflections 0 This was a simple and convenient procedure from

which many of the trends of the dynamic resistances could be determinedo

Four model frames specimens were tested by subjecting each specimen

to a dynamic lateral load applied along the axis of the top girder 0 The

specimens were essentially ideal frames with fixed-column bases and column

sections which were one-quarter scale models of a 6WF25 sectiono The applied

loadJ accelerations, deflections, and maximum fiber strains were recorded as

functions of time during each testo

The dynamic resistance of each specimen was computed from the ob-

served loads, accelerations, and deflections by means of a single-degr~e-of-

freedom system analysis 0 The dynamic resistance curves of all frames had an

elastic slope less than the theoretical static resistance J but approximately

28

the same as the observed static resistanceo The dynamic resistance was

greater than the static resistances when general yielding occurred and

retained this increase until a deflection of from 8 to 11 times the theoret­

ical static elastic limit deflection was obtained 0 .After this deflection

had been reached, the dynamic resistances closely approached the theoretical

static resistance for the remainder of the testo The increase in the observed

dynamic resistance over the theoretical static resistance has been predicted

reasonably well by consideration of the strain rates in the frame 0

Conclusions 0 The dynamic resistance of the frames tested in this

investigation was found to be higher at yielding than the static yield

resistance 0 After yielding occurred, the inelastic resistance approached the

theoretical static response and in the later stages of loading the dynamic

resistance can be considered to be the same as the theoretical static resist­

anceo For large deflections, the theoretical static curves are a good

approximation for the dynamic resistance since the increase in dynamic

resistance at yielding contributed only a small amount to the total energyo

The dynamic resistance was found to be significantly higher than.the observed

static resistance since the local buckling and twisting of the columns, which

reduced the capacity of the frame in the static tests JI did not have time to

occur during the dynamic tests 0

Although these tests do not provide enough i.nformation to permit

determination of the response of any frame Jl they do give a general picture

of the response of frames and show what can be expected under conditions

used in these testso

6 a The Response of Beam-(blumnsSubj ected

to Dynamic Lat~ral Loads

by

Ra Fa Wojcieszak

University of Illinois Civil Engineering Studies

structural Research Series Noo 100 June 1955

The investigation of the response of dynamically loaded beam-

columns consisted of testing in a drop test machine four pin"" ended beams

with an effective span of 80 ina The beams were fabricated from 4 M 1300

29

rolled sections which were normalized to obtain 1llliform material propertieso

One p~ir of the specimens was tested in the strong direction while the other

pair was tested with the section oriented in the weak direction with respect

to the appli.ed lateral loado One specimen in each pair was subj ected to a

constant axial load in addition to the dynamic lateral loado

A test consisted of dropping the 500-lb weight of the drop test

machine from several heights to vary the energy inputo In each test the

lateral load, deflected shape of the beam, strains, and axial load, if

present, were recorded as functions of timeo

The test results indicate that increasing the energy input

increases the duration and amplitude of the load, and the maximum deflec-

tiona In general} the axial load did not appreciably affect the resistance

to lateral deformation of the beam-columns oriented in the strong direction

when the center deflection was small, approximately less than three times

the static yield deflectiono For larger deflections the axial load had the

effect of causing the response to decay toward the theoretical static

response curve and the resistance of the specimen was often considerably

less than the resistance of the specimen without axial loado With the weak

direction specimens, as was expected, the resistance-deflection relationship

was affected more by the axial load than was the case in the tests of the

specimens with the section oriented in the strong direction~

The correlation of the dynamic resistance to lateral deformation

with the theoretical static resistance was obtained by comparing the actual

energy-input and maximum deflections with the strain energy predicted from

the theoretical static resistance-deflection relationship at the same

deflectiono When the energy input at the maximum deflection was gr'eater

than the corresponding strain energy predicted using the theoretical static

resistance, the yield stress used for the static resistance deflection

relationship was increased until the strain energy approximately equaled the \

energy input measured in the testa

.By comparing the energy=maximum deflection relationships obtained

from these tests, it was found that higher values of the yield stress were

required as the energy input increasedo It was also found that the axial

load had little effect on the resistance in the deflection range from

approximately zero to three times the static yield deflectiono However;1 for

larger deflections the axial load caused the resistance to decrease with

increasing deflections in the same manner as was noted in the static tests

of beam=cplumnso In the case of the weak direction specimens the increase

in yield stress with increased energy=input was smaller than noted in the

strong direction tests p

70 Inelastic Behavior of Mild Steel Beams Subjected

to Transverse Impact

by

F Q L.. Howland

University of Illinois Civil Engineering Studies

Structural Research Series Noo 106 August 1955

The response and resistance of a dynamically loaded mild steel

beam has been approximated using a single-degree-of ... freedommodelo The

resistance of the beam and model has been considered to consist of the

following phases~ (1) an initial elastic resistance; (2) a subsequent

31

inelastic resistance whi.ch may be a function of the displacement, velocity,

and time; and (3) finallYJ a recovery resistance that is essentially elas~

tico The elastic phases of the resistance are fUnctions of the displace-

ment only and1have not been considered in this investigationo

The initial phase of the inelastic resistance of the model was

found to be a function of the velocitYJ the time:! and the static elasto-

plastic resistanceo This time-dependent resistance has been assumed to be

given by the following expression~

where w and R are the rate of change of the displacement and resistance,

respectively, with respect to time; K i:s the elastic spring constant; R is

the resistance; and Rfp is the static iifully=plastic H resistanceo The

time-dependent resisting function is applicable until the time when it is

32

equal to or less than the static resistance, which includes the effect of

strain-hardening of the materialo

From the information in the literature, and from a consideration

of the static inelastic deformation process, it was found that the parameter

a could be expressed as follows~

aKT

where u g is a dimensionless velocitYJl T is the period of the beam, and f3, C,

and n are constants 0 The constant f3, which is determined by the load

distribution along the beam, relates the velocityu V to the maximum strain-

rate 0 Because of the derived form of f3, the time-dependent resisting

function is restricted to statically determinate beams" The constant C is

essentially a dynamic shape factor 0 Both C and n are determined, in part,

by the relationship between the lower yield stress of the material and the

strain-rate"

The applicability of the procedure was investigated by predicting

the response of several beams and frames for known loads and comparing the

predicted response with the response measured in testso This comparison has

indi.cated that the magnitude of the derived constants are essentially correct

but that further adjustment of the constant f3 is necessaryo

From a brief study of the time""dependent resistance, an a:pproxi-

mate method has been outlined for estimating a dynamic iYfully .... plastic H

resistance to replace the more complex time-dependent resistanceo

Two additional investigations are included as Appendices~ (1) A

criterion for estimating the dynamic elastic limit resistance and displace-

ment of the structure 0 This criterion is based on the available information

Room . . .4 ng Department Civil Engineer ......

BI06 C,E. BUlld~ng . • .l-~,. of TIllnolS

UniverSlllJ -;LllinoiS (;

U,1;;~~'.lU

33

concerning the delay time for yielding 0 (2) A semigraphical procedure for

including the effect of strain=hardening of the material on the static

resistance and response of inelastically deformed structureso

Summary 0 From this investigation of the inelastic resistance of

mild steel beams subjected to transverse impact it has been found that~

10 in the early stages of the inelastic response J the resistance of mild

steel beams exhibits a defi.nite time dependent character; 20 when the

displacement of the beam becomes sufficiently large, the resistance of the

structure is the static load deflection relationship for the beam if strain

hardening of the material is included in the stati.c analysis; 30 if an

inelastic resisting function for the beam is assumed, the parameters requi.red

in the function can be derived from the information available from the lit ...

erature and by considering the static elasto=plastic behavior of the

structureJ 40 from a study of the inelastic resistance during time dependent

resistance portion of the response, an approximate procedure for estimating

the dynamic fully plastic resistance can be developedo

80 A Study of the Resistance of Model Frames

to Dynamic Lateral Load

by

Ro J 0 Mayerjak.

University of Illinois Civil Engineering Studies

Structural Research Series NoD 108 August 1955

The resistance of model steel frames subjected to dynamically

34

applied lateral loads which produce large deflections (nearly 30 times the

elastic limit deflection) is studieda The results of static and dynamic

tests are presented. These provide a basis for the comparison of the

dynamic with the static resist~Jnce of model frames a

The models used in these tests were made from ASTM A=7 steel and

were machined to be approximately 1/4 scale replicas of a standard 6 WF 25

sectiono In all of the tests the sections were tested in their strong

direction of resistanceo There were two center loaded simple beam tests;

one third point loaded simple beam test} four rigid top girder frame tests}

and six flexible top girder frame testso In two of the flexible top girder

frame tests:! axial loads were applied to the columns of the frames in addi-

tion to the lateral load. The rigid top girder frames were square bents

approximately 15 ina by 15 ina The flexible top girder frames were rectang ...

ular bents approximately 1665 ina high and 30 in6 long 0

The experimentally determined resistance functions for the frames

tested in this investigation are in good agreement with those theoretically

predictedo It was found that the characteristics of the resistance function

for dynamic loading conditions can be explained and predicted by taking into

35

account the dynamic stress-strain properties determined from investigations

of tensile coupons of a similar materialo

Relationships for estimating the resistance function of full sized

structures subjected to dynamically applied loads are developede Tb~e proce­

dures are based on dimensionless relationships which enable one to determine

the angle change in a member subjected to large inelastic deformations. When

this is done, the load-deflection analysis can be made by conventional

procedure~.

90 Correlations of Results of Dynamic Tests of Beams and

Model Frames

by

Fo Lo Howland and Wo Egger

University of Illinois Civil Engineering Studies

Structural Research Series Noo 109 September 1955

The object of this program is to determine the effects of blast on

buildings and structures by investigating the load capacity of steel struc-

tures and elements under both static and dynamic conditions 0 For a static

load the load capacity can be obtained in the form of load-deflection and

moment-curvature relationships for the structure 0 When the structure is

loaded dynamically, the resistance or load capacity no longer is a function

only of the deflecti.on but can depend also on the strain rate and possibly

the time 0 Thus, a second objective of the program is the correlation of the

dynamic and the static resistances 0

Previously the emphasis of the program has been concentrated on

investigations of the static resistance of steel structures 0 The results of

these investigations have been summariz.ed in the report which is the final

report of the program for the period 15 September 1953 to 1 September 19540 3

These studies have indicated that the static resistance or load-deflection

relationship can be obtained by means of the available theory of plasticity

if the influence of strain hardening of the material is included in the

analysis and if the structure does not develop a lateral or local failure

during the loading process o. A limited study of two aspects of the static

response problem has been included in the present contract and the results

of these studies have peen distributed as technical reportso The first of

37

these investigations is concerned with the influence of strain hardening of

the material on the response and resistance of obliquely loaded steel beamso

The second investigation was a study of the effect of combined bending and

shearon the resistance and .deflection of steel wide flange beamso Abstracts

of these reports are included in the appendix 0

The major emphasis during the present contract has been placed on

the investigation of the dynamic resistance of :mild steel structures o The

determination of the dynamic resistance and the correlation of the dynamic

and static resistances for various structures have been studied by both 0

experimental and analytical methodso In the experimental studies, several

types of specimens have been tested under a variety of loading conditions 0

The results of the various experimental investigations have been reported in

references 5 through 80 Abstracts of the contents of these reports are

included in the appendix 0 The information obtained from the various experi­

mental investigations has been used~ 10 to determine the dynamic resistances

for the structures; 20 to determine the variations in the form of the dynamic

resistance; and 30 to provide experimental data for use in checking the

applicabili ty and validity of the methods of analysis that have neen developed 0

From the results of the tests it has been found that the dynamic

resistance of a structural element can differ appreciably from the static

resistanceo

The dynamic behaviors of test structures were analyzed by assuming

that the actual test structures could be approximated as single-degree-of=

freedom systems 0 Roweverj slightly different approximations to the form of

the dynamic resistances of the structures were made by tne two principal

investigators, Howland and Mayerjako

Howland assumed that the resistance of the structure was of an

elasto=plastic nature similar to the resistance of mild steel to uniform

axial deformation if the upper and delayed yield effects are neglected but

dependence of the instantaneous resistance stress upon the rate of general

yielding is retainedo After general yielding is completed and strain harden­

ing begins, it is assumed that the dynamic resistance is the same as the

static resistance 0 In the formulation of the resisting function, parameters

were included to take into account the distribution of load, the boundary

conditions} the shape of the cross section of the structural element} and the

material from which it was madeo

Mayerjak based his computations on the stress .... strain relationship

for the material rather than the overall resistance of the structure 0 The

dynamic increase in resistance was taken into account by increasing the

stress level of general yielding in accordance with the average strain rates

expectedo This procedure is fairly accurate since the relation between the

stress level and the rate of general yielding for mild steel is relatively

insensitive to changes of strain rate no greater than one order of magnitude)

a range which includes the average strain rates encountered in the testso

Using the dynamic stress=Etrain relationship} Mayerjak computed

dy-namic resistance deflection relationships for his frames by the same general

method useo. in obtaining the static load ... deflection curves if inertia effects

are neglectedo This procedure is not restricted to statically determinant

systems or those which can be approximated by single-degree-of-freedom analogso

Howland later modified his procedure to a simpler approximate method

in which the general form of the dynamic resistance function for the structure

is the same as that for static loading except for an increase in the iLevel of

the fully plastic resistance 0 This level is determined by a consideration of

39

the elastic response of the structure as compf'ed to the dynamic resistance

computed using the. velocity de~endent relationship of Howlandis first methodo

The approximate method Was used to compute values for the dynamic fully

plastic resistances of the specimens as they were tested with their various

loadings 0 These results are compared, with the values of fully plastic

resistance obtained.by tests in which the data are interpreted on the basis

of the single-degree-of-freedom analogo

Conclusions 0 Comparisons of the specimen resistances obtained

experimentally with those computed using the approximate method indicate

that~ 10 The ratio of the dynamic fully plastic resistance to the static

fully plastic resistance is not changed appreciably by the changing of·~the

orientation of the cr'oss section) span of the beam, or shape of the cross

section" (This indicates that the increased resistance is a function of the

specimen material and not the conformation of the specimena) 20 For the

tests considered, the dynamic fully plastic resistance can be related to the

static lower yield stress of the materiald (This indicates that the actual

critical strain rates occurring in the test structures were of the same

order ofmagni tude or else that the material is relatively insensi ti.ve to

changes in strain rateo) 30 The addition of a constant axial load did not

change the total internal resistance of the structure appreciably from the

value it would have had if not~rust were presento

Major differences in the form of the dynamic resistance deflection

relationship were noted when the resistance of the determinant and the

indeterminant structures were compared 0

10. A Method for the Analysis of Frames Subjected to Inelastic

Deformation into the Range of Strain Hardening

by

AoAng and J 0 Mo Massard

University of Illinois, Department of Civil Engineering Tec[J.nical Report to

The Air Force Special Weapons Center (AFSWC-TR.,.,56=47) November 1956

A method for determining the resistance of frame structures

40

composed of elements having individual resistance-deformation characteris ...

tics of any monotonically increasing form that can be described graphically

is presentedo The resisting moments in a structure which correspond to a

given set of displacements of the loaded joints are found by a trial and

error procedure made convenient by use of moment-end slope relationships

for the individual memberso After the resisting moments have been obtained,

the corresponding set of loads required to produce the particular joint

displacements are computedo

By solving a set of such problems.1 load.;.joint displacement

relationships can be obtained for a range of loads:; or conversely for a

range of displacements"

The general nature of the method is such that it is perhaps most

useful i.n research applications 0

A simplified procedure for the analysis of independent frqrnes

using moment distribution with bilinear approximations to the moment-end

slope relationships is presented in the appendix 0

The pr'ocedure used in this report involves assuming displacemeIl,ts

of the loaded joints (the general deflected shape of the structure), and

41

obtaining the resistance of the structure to that particular deformation

pattern assuming that a reversal of strain does not occur any place in the

structure 0 The practicability of the method depends upon a convenient

means of relating the resistance of a member to its deflected shape" In

this method, the resisting moments at the ends of a member are related by

graphical representation to the end slopes of the membero Using these

relationships (which apply to any wide flange section within the limits of

error given below) resisting moments can be found for the assumed deflected

shape of the frame structure using an iterative trial and error procedureo

After the resisting moments have been found, the combination of loads that

could produce the assumed deflection configuration of the structure can be

computed 0 The moment curvature relationships presented in this report can

be used with an error of less than ± 3 % in the resisting moments for all

structural wide flange sections"

Neither 'of the methods presented in this report takes into

account the effect of non""rigid connections on the behavior of the frame

consideredo It is expected that the procedures will be extended to include

this effect as a part of the work in the Contract AF 33(616)""37800

110 Slow and Rapid Lateral Loading Tests of Simply Supported

Beams and Beam-Columns

by

R. Fo Wojcieszak and Jo M. Massard

University of Illinois, Department of Civil Engineering Technical Report to

The Air Force Special Weapons Center (AFSWC-TR- 57-21) February 1957

The two major purposes of the program described in this report

were to determine experimentally the resistance of beam and beam-column

specimens to inelastic deformations applied slowly and rapidly; and, if

possible, to correlate these resistances with the static and dynamic

properties of the material from which the specimens were made.

The results obtained indicate that, beyond the static elastic

limit, the resistance of a mild steel beam or beam-column to a lateral

displacement produced rapidly is greater than that corresponding to the

same lateral displacement produced slowly, and that the increase in the

42

resistance of the beam with the rapidity of the lateral deformation can be

explained with an experimental error in the limited range of strain in

which comparisons were possible, by consideration of experimentally deter-

mined dynamic properties of the specimen material which included delayed

yielding and rate of general yielding behaviors typical of mild steel.

The experimental work described in the report includes the deter-

mination of the mechani.cal properties in the specimen materials, the

determination of the residual strains in the beam specimens, the beam and

beam-column investigation which included a total of nine individual specimen

tests and a correlation of the beam resistance with the material propertieso

Conclusions 0 ao Beyond the static elastic limit, the resistance

of a mild steel beam or beam-column to a lateral displacement produced

rapidly is greater than corresponding to the same lateral displacement pro­

duced slowly 0 bo The increase in the resistance of a beam with the

rapidity of the lateral deformation can be explained, within the limits of

measured strain anp. .experimental error, by consideration of the delayed

yielding and rate of general yielding behavior of the specimen material

corresponding to stress-strain-time conditions comparable to those produced

in the beamo co When under a .constant axial load, the resistance of a

beam-column specimen to a rapidly or slowly applied lateral deformation is

less than that of a similar beam without axial loado do A beam which is

tested slowly with increments of displacement W'ill have a resistance at any

inelastic displacement less than that exhibited by a beam loaded slowly but

continuously 0 eo The delayed yielding and rate of general yielding be­

havior determined experimentally from the coupons which were cut from the

structural sections tested were comparable to those that had been obtained

at the University of Illinoi.s and elsewhere for mild. steela

Time did not permit a correlation of the slow and rapid loading

behavior of the beam-column 6pecimens with the properties of materials from

which they were made as was done for the beam specimenso However, the

authors believe that, as in the case with the beam specimens, the differ­

ence in slow and rapid loading behavior could be explained in terms of the

stress-strain-time properties of the specimen materialso

Even though the scope of the investigation, at least as regards

the beam and beam-column tests described in this report, is rather limited,

it is believed that some procedure of determining the dynamic resistance of

a structural element from considerations of the dynamic properties of

44

the material from which it is made is generally applicable to problems of

determining the response of steel frame structures to conditions of loading

or deforming that vary in time from slow or static conditions to those in

the range which structures of this type might be expected to resist under

atomic bomb attack or earthquake shocko

120 6o-Kip Capacity Slow or Rapid Loading Apparatus

by

Wo Egger

University of IllinOis, Department of Civil Engineering Technical Report to

The Air Force Special Weapons Center (AFSWC-TR-57-22) May 1957

In this report is described the design, construction and opera-

tional characteristics of the 60-kip slow and rapid loading units developed

at the University of Illinois under Contract AF 33(616)-1700 The desired

operational characteristics of the units as described in the contract cover ...

ing their construction were largely met by the units as completedo These

were~ that it be possible to apply a loading either slowly or rapidly of a

magnitude oft 50 kips; that the units have maximum stroke of 18 inches;

that it be pOEfsible to apply the maximum load in a time on the order of and

if possible less than 10 milliseconds; and that it be possible to release

the load in a controlled time of approximately 30 millisecondso In the

report the actual load versus time relationships obtained through the use

of these units are compared with load time relationships which were obtained

from thermodynamic considerations of the mass rate of flow of the gases in-

volvedo In the region in which the theoretica:].. relationships are applicable

the agreement is quite goodo

APPENDIX B

TABULATION OF TESTS PERFORMED UNDER CONTRACT

AF 33( 616) -170

The values presented in the Tables were obtained directly from

information given in the report listed as the ret'erence" In some cases

where the same test information was used in more than one report minor

discrepancies may be evident.

Notation

TABLE OF NOTATION FOR

APPENDIX B

The following notation has been used in this appendix~

NA

NR

P m P e

~ Qe T m T e

x m x e xx

yy

Loading~

A

L

Loading Device~

C

j:.1

HJI

PJ

S

W

20k

60k

Not Applicable

Not Reported

Maximum Applied Lateral Load

Applied Lateral Load which Would Initiate Inelastic Behavior with No Axial Thrust

Maximum Lateral Load Resistance

Elastic Limit Resistance

Applied Axial Thrust

Axial Thrust which Would stress the Entire Cross Section to Yield

Maximum Center of Span Deflection

Center of Span Deflection Corresponding to Yield

Strong Direction Orientation

= Weak Direction Orientation

Axial

Lateral

l20k Baldwin. Machine

3000k

Machine

Hydraulic Jack

Pneumatic Jack

Springs

500-lb Drop Weight

20k Slow or Rapi d Machine

60k Slow or Rapid Machine

47

stJMMARI OF EFAMil l?EAM-COIDHN, AND MODEL FP.AME TESTS • -- - -- III> e 1 ! s:: i .. · Lateral Load Axial Phenomena Measu.red :3 a .-t

I .~.. ct~ (CofIcentra~J ..'l1i~t (MaJdJDuIn values. llsted, 1 ~ ~ ~ ~ ~ . "f"'4 S _ ,~ III cF ~ PI I). . I 0 v ~ 4 • ~ *tj ~ ~ ~. f) R+l

I ·~ @) ~ t) til ~ J:: ,x d 4!IS ~ !Ill C'4.. ......,.-.1 'es:: • til 0 Q.. Ii cod , '+l . ~ ~ ., , rI

I .! ~ I ...... til ~ ~ t) O?J ~ . ~ S ,~~ s::: ~ C" . 0 ., 0 (!) () ~ S:::o ~....,. t:; -4' ~ "0 XOf-:t ~ c i ro ~ "C ...,.. ert "" i~ s:: ~ c..... b.O ·r-!O rj ,&:l .tlO CD «t-4 i.t: 0 ~ +>:9. I C1J 5

:;!:O t) S C '0 C ~ ~ +l ...:to -+' 0 s:: C! +> 5O!O s::: s:: 0 +l p... 0 ~ ~ '-a .... L M f.4.cr« 0 ...-4 ~ .... ~ . H .s:: erl ci-f r-! cr. ~'H til tD m ' , ~ I!tl

~ G) (l . .....c III) ~ "d •.. +' C'D 41)'''0 s.. a c)Cl.l 0 +'..G "0 C> G:! :::s C) p... ''«:3,'~ ro r-l ~ ! o..~ ;,t ~ m ~ G) m ~ &Ii ~ ~ U "f"f ., 0 ~ g ~ 0 fiQ () II) .,... ~ +' ~-" @15 d 10-4, S m 0 f'l I w .. ~ .. I ~ ~ ~ 0 ~ . 0 ~ e; 0 ,.«> ...-! ~ «> m tj me ~ k rF! I ~ ~ tf'~o.ai .. ~\ O'l) ,II rll. Qj I E-t ~ to Q 8 ~ c:. U C::l tf) ttl O. E-4 H ,.A f---.. 1-4 tJ) _E-t ;..;: ::::> ~ -< t;-o 1 ~ A.a -< f-4 .....l ~ c:. x 0 P::: tt) I ~

~-'l-------l --, t, IIIncremental! Ma.n~1 JL'I,. , I,.! +1' I 1317•5 ,1 317.5 ~ ,1 x-x' flection l!lour L-HJ None, 1.29 0 NA--J-2,.9~8,2;,_1 .. 29 -<7,_~' 1205 ! I I I! I I 'I I! I lID-.5 i 1 I IDe5 .. I 401 x-xli " !" I "i .. II 2.21 0 I NA kr~~21 7~ !6Os' I I . i ! II I:·! ~n2. 5 i 1 fU2.5 "11361 X"X .. ! n .. .. [I 1.34 0 i NA J.O'~---.;2:..34; 9 I 0-l i20S I I ' , I! [ 1 I . ~.5 : 1 i" .. i 40! x-x,1 .. I" I"+," 111.99 1. 0 I IV. ;29. 4 !1..:9911 91 0

1425 :! 1 t I ! II.. 1 I L-HJ I Con~tant;j I I: : .._ ;6Il2 .. 5: 11 " :~~---l Be1 x-xl n ! n A-HJ 10 .. 0 ksil 1 .. 59 10 .. 26' NA i 8 .. 13 : 1,,5911 910

i6Yos il I ~.. I . I I . I !,: l6112 .. 5 11! n ~ 1~ y-y If tv L-HJ None 1 .. 82 0 NA P.O.4 11 .. 821 81 0

12YOO· ! I . I I·' l6I12.5 ,1 n n 40 y~y, .. .. .. " 2.51 0 NA 22.9 2.51 810 1=3.0 11 lOO3.0 n 88 x-x n " n .. 1.64 0 NA 7.02 1.64 9! 0 ,4].53 \1 . t ·L-HJ Constant \ ': :4MJ.3 .. 0 ~ " ~.s=-O--a"'" 88 x-x n 99 A .... HJ i6.6 ksi! 1 .. 35 0 .. 32 NA 5 .. 89 1.35 9 0 r I !

I f

+ (l)

NA 22~8 'I '

0 NR 9 0

,---i i B-1 I

.2 I BWF58

I f-

• ~ ~ tl- Incremental. Many A a NA x .... x

99 I 9 1 0 0 NAf.Q~- NR

8; " H :1 .. 38 t 0 INA JIB .. l . 1m I .L-~ l ,0

,f t -+ + I NA x-x Ii'II " I 7s: JI

1 + .. NA " " J1 :a x .... x

1 I

T I .

! .:B-2a .~ 1 2 "

B-2b I 2~ n 1 1

·References are listec nt end or text (1) .p .... bas~on beginning of general. shear y1el~ ..

stMMAF.:I OF, BEAMt.BEAM-COlnHN~ AND lviODEL FPȣE TES'TS

s: '0 ~ .., () .. .ID &:

'ltl::! 0 Q ~ «:) s::+> § 0 e

I ~ I !l E. ¥ I "'I ,,~ I ~ "'-' (Dr!: ID m Q...Cl> I

f:-I ~ tf.j 0 I I I' I

40s I I I. 4Ml3.0" I~~:;$O I

\ 415 I 1_~~3.,O~3 14yOS i 1100..3 .. 013

" u'

" !..4Y1S

1.4Ml3.0 I 3 .

1~2. st L6!)2. 5 r 141S I ; 6I12 .. 5, :; : 6yos .6112 .. 53 -, 4n.s . I 6n2 .. 53

1t

tv

'IIY

j40S ,l ; 6B15 .. S!3 16]3].5 .. 5 I4lS ! : ·61U5 .. 513 . i 4YOS! I i 6Bl.5 .. 5' 3 1 -' -.--~

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I

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:~ .(; ~ ()

ID £: A ~ 0

W ~~ J:!o

'"'C ,"1"'11 eM

t5 'f,~ ~ ~ '''0 f;; ." ,t;'~ s:: ~00

£-io::~O

t ~ I 88!X-X

.. 1"

1t

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iV

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tV

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1t

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ft

- I 881 " 886

m ~+-88:1 n

t I

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l:;6:y-yl 1

. I ~ I B81 'Wt

f 88!x .... x I

I ~I 88i ff

. 88 y-y ! j

T-IIP fl ~ 88' " 1.4Y1S '·1 '6B15 .. s13 1\1

~ ~-I

j , ., Lj

.' '-References. nre listed at -end of' terl

.Lateral Load (Concentrated)

4"'0 X d .... ~ I$S

~ ~ ~. ;~~ if~ ..r! s.; I s.:4 S:;::...-I.....-t

ID"t:! J.., 0 ID 0 o+=..c"'d p...a:lo~ '[:+>01:001'1')

~~ Q G.l.1 """" ,~ CD, ro, d III 8~ 0 E-<~tr.!E--.::"::::::>

Axial ThI"l.lSt

4-4 o +'

.-1(.'.. ID cd !';S ~

t.:;... "ri "'" ~"x ..c 8<8

Phenomena '}~easuroo ':3 -:1 e-f

(l~ valueslfsted) ~. .c:: t':i ",CF t! ~ 16

'"0 ~ -+l +'b' <0 $2, ~ ~ m . r::: (.A.. as &. • ..,:::;- ,we o !:.1 ¥ s::: ~'m"- ...... " ~ ~ ~_ CO., I o .. ~ C2 CD

~ ~ £' t :s $ ~ ~ uf-i

~ (l) rl m Cl ::1 m (!) ~ m E--. "0 rl ~ C-."rI ~ I ~ +> ((j 0 c...... E f1.l 0 Vl Ild~ 11~o Q~'Oa> r-I m ~p.., . <~...:J QX O~ til ~

I'~I l.,46 I 0 INA I 7 .. 11 ;10461 S) :0

3~ 10.)0 iNA I 5.~9-;1~35 9 10

'Many Increme~taJ.1 Hours I L-l1J None ~. DefiectJ.On .. .L-:sJ consta.n~

n A-ill 17 .. 3 ks tv

T I

" n 'L-RJ I None 1 .. 88 I 0 IliA 112 .. 1 i 1 .. 88 9 ! 0

I .. 78 f O.32INA ! 6,,81 11~ 78 9 10 . I

1 .. 33 10 ! Na .\10.4 11 .. 33119! 0

L-HJ Constant

" IA-ro ].4 .. 8 kef

n L .... ID. Hone

n

n

L-RJ I Constant 1- . 8.13 11 ;59!1 9 \0 .. IA-F.J i 10.9 ks! ,I 1.59 0 .. 24 NA ~~' .

" IT HJ . l' ' 1 79 o UA 7 .. 78 11 .. 79 II 8 I 0 i .L,u- lone G . '. I . . .. ~ '\ '

L-HJ I Constant. n' I A...;HJ 7 .. 6 ksi I 1 .. 57 o,,16NA I 5 .. 34 11 .. 3719 jO

:' I I n I L-m! . None 111.34 ! 0 INA Ilo~~.34119 10

L-HJ r Constant i

: ;:~:r3·;o::~I! :~:: 1°:361: I::: 1:~~:II:I:

L-HJ ! Constant I .. I A-HJ 9·0 kS~1.37 .. /o.22INAI13.111.371161 0 I I . ... . ... I··· . I ~

.l.

rr

ft

n

n

1'1

n

~

m _~.l.

Ew~-cornEN~ Al~D MODEL FP~1E TESTS

r- r ,. 1m J Lateral Load Axial. Phenomena :s,:J M

g:l~1 (Concentrated) Thrust (Haximum vaJ:ues@:;' .~ ~ 15 !l~ <»"0 "'d ~ +> +> ~9 § I 8. ID CJ :S§ t.; 2 ~ ~ +> ~ ~ ~. ~ ~ ~.~

ID I ~ I m ~ ~ (!) ~ t:; ;:: ~ ~ ~ s:: ... c.. () $ .. ~ r~ o ~ ¥ I ~ 0 i> ~ ~ b::: ...c eM .'. crl 'U "0 5 <J"-<l ...... n;,-"

eO t:: I '-'" "'T"t.-r. sM ru's;;:.s I c..... ~ ..,..-l .O·.-j Qb.O .. i:D . r-i b 0 +J ....J C) .:3- I--.....,-~ $... I' !i E I O~' f ~ "6 ...:11 3 r;:: 0 !l ~ 1

1

' +' ~ wg ~ ;.1 11"""1 ~ ~ ~ 0... ~ m ~ t!fl

Q 0 ...-f r 0 .+-1 "0 ID ~+' lD O"d NO. CD 0). 0 '+'. ..c; "0. ID iJ.\l .~ (!) A.a ~ 8 "dri X .r-.... -ri 11 ;:: \ .p-ro Ilf.: I p..."O ff.j ~ .c....:. 0. "'rill p.. d O·(;.;,i , E: +' Q1 UlO (0 P..,,-I ~ +J..........] ........... \ ~ 0 c..... "'" S \1.l . 0 ID Q. ID ~ t:l CD (:) ~' • ~ .;:-. q m I..,...;'" (j) «>'!;j OJ i :> .. }Ii ..s:::: Ilt1 ~ ~ 0 0 iD .. ~ 0 0.> rl Q'j

til Q 8 crl h {,) a:il tfJ· 'Ell 0 f:-4 ....... Q b ;:t tr:l E-.; :..: :::> I f-i" -< f-i ....:t (l;., . [-I ...:J -< Q X (.) P:: c,'l I ;::.....

I Frame~! 12/4 sell ttl jll··Incremental! I' 1111 I Beam 1.: 3' 16'WF25 j..iii A INA. y-y II D~nect~'2n Hours kC Nc~ne I Frame I I . I I +-.... . I E. e. ~a 7: 3 ~, I ti INA .. I x-,x n n L-C n . .l.., I Frame i ! ~. I I

"Beam 4, 3 ,,! -" t A T5 i y-y " lUi I,,-c In! i ! ! ..! I' I

iFrame I' I .. , 1 I I t-=,·-'t I

I Beam 613 1 Wi I 111 15 I x-x " .1 tt L-C. . ... 'v. _ ... _' .. '.. c:. i---' ! I I ! 'jl 1 I .1 . I:

: I I I ., I' i -V .. 3 I 4 i 0 , I

!1" 4 '0

I I l .. 7511410

~OTNA ~ 70

I I

1 I

0 NA ; 140

tO~2 0 NA. 90

!hame Incremental: fl· I ; 1 Deflection I Hours! L-FJ None I 3 .. 3

i---- .

iFrame ! I' ! I : I .

2 ! 3 '" 115 I y~' ! "n 1" 7 Fr I I i

i arne I F9-! j

_,3 1:2 j n l·~ 115 l x-xl " n None II 1 .. 15 Frame I i I II' I L-EJ I Constant Ii ;~

4 ~ __ , " t15 ,x-~·_ it n J A-S j8" 73 ksill 1.,45 0 .. ;23 NA 9Q. 1,,4511410

1 '

1- ... . I' -----n I I I! /l L ______ ~,l" "

i4XYos T I 'I 1 ·11 Increm.entaJ..1 Many ·1· -.,' II . I .' I , - 1 . .11

j'

! 6B 3 !6B15 .. :5 -, 87 45° Defie,ction Hours L-HJ None I 2 .. ,3E) .... /0 NA 39 2 .. 36 1130

4ms I rt t I I II L jL-HJ Iconstantll I I I ·II! I l t

1

6B 1~316B15. 5 l-.A --u--,.-, B7 ! 41' .. ." I" f A-ilJ ,10 ksi ;. 1.64 "0. 25. NA . 23 11.64 13 0 ~ 'I 1, . I

·Reference~· are "lis+ c.:atetld·of terl

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.. ~8 ..to Q)

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.fo ecUJ4 ~o 0 0

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== :: ~ ~

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0 ;:. ;: ::: 3! .~ ;: g: ::: atd~c eAllooJJ3 cp

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tc'\

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(\,j f{'\ ..:t U"\ \0 t- eo 0\ Tanlrnlrl II.!! t sa '" t

4 : . "" "''1' ~&l. ~ AI.f\ \.0 .11 g:; :: :::: :: ::: ::: :: ;: ~ .. .. g: I: :;i$! ;: .... l~ ..:::tt--

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. I

.... ~..... ~- ~ -- . f" -l 0\ ~ l '~~;~-~::b-8r-ro t=J ~ . "

-" .. - .... -.... -- ---' _._ ... - -- _ .. _-- • ---#--.. --.-----.... - ....... ;... ......... ~ ........

'. \J1 V1 V1 Vi V1 \ V1 neforance'· ,

, ~ l'··--'~· r--' '--l J 'J'J -, .~~ s-;:-:'l~~n ~~ti:h I ~r-c-, J+~ ... , ," _ _ ',_ ~_. .' · S ,-n ~ , :~:~~nt~~ [I I . I t I . t I I I I 'I 'J....... T.Y'PC .. ' or $.' ~.' eitnen C;) d'

~ :I :t

IJj

tl.tld Ehd , . J:ontt-nint :: ::

t Cond1tlon~ ~

~r-r .. ·.,.·.·. -.·.c~t·~.·~ -~. ---.~~.~:~ --:~. · ~. ,~~~ .. e~~J~lii I.·.·. ;i r .' t·t . · i·, .'., · , .. action. ,

. . . x O:r~~~,f).!:io~ ~ ~=t=..~~~·:.4 .. ·· t~ ~.~ ... ------ ~

e I ~ 11-'* ~ ~. ~ Typ~ of § ..::: PJ (l). (l)(1l Loadin lt1 ........ ~

~ p.. 0 a . F, D ~ ~ ~ 0 or 0 fi'. ~

g £" De(onnlnrl, ~ go ~

I:

. -_._ .. +-•. ., .......

·----,,··t·--t--~+- I I I ~- .- - -- . ---' . ~-t:='

, ,I I I' I:: :: :: ~, I ~ ~:~inO ,_,_.+_-+-,,~_,, ___ ~, -.!- 4-. I --.-J-~U

::

I I

~ ~ e ~ ~ ~ .

..- IH ~. tc3t-al Load ~ ... ~ ~ ~

., = 1 = I. 'I. 151 Type of i;'!' ~ ~ Axial ~ ~ ~ 1 I Thrunt r> .... ~+=~==-~--=!= j 'j. I' I' =+ -I II

i~

tl) ... · ~!.~ It-' ~

r I t--~---+-.-. I ~-

-.l. (jJ I-' co -J ..... \.>I \.N

.1 L·· '. .... '!".

• 8j' Q

-l V1 P Jp ti ~

r1 e tl

o 0 Wal Thrust : I __ Tr/T e ~

8'1 Load Point ~ .. f o 10" 0 10 -P-:-E--~--~---~-+----I

-A Ie.' ; ~~

i

~---L-L-L-~ "C3' I~ Ij

...... _ . ..---- -~

~i .. ]'8 Den .. ecti(')rH'!,~~ ft .\.». . "n/Xe Ld 41 Ft [. e III . . e . "

I- ' .. --. 1-- -"I Lj'''-' '.... • __ ._ J r- '.1-' .'-. . : e;..'~ . Computed Lat. Ld.

-~."';""~.:..-i----t=.:::i= !:::.:--i== <J\ V1 Re!liatance, Qd'Qe

~ I~ ~ j~ '-+-'---+---.. -~. ----~--. ;.,' .. ~

o .~ \0 I~ 0\ 0 \.» ('X)

~ ~ ~ ~

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~ ~

o o

Slo\,' I' 1 ate rln} -~Coupons Fast Tested

I t t

~ ~ W

E-1

1 !. it,; io Ie j~ im 1<-. 'CD 'e:.:..:

l:: o ~ ,.:> .(J .~ J,;; tij 0 ...... J:~ o ~ E F .....4 ___

o "'I'"'l .u cr. ~tJ

tel 0

1 ~ I ;..:. .. .....{

! u 1 ~ i 0.- 1l'J ! t!1 ,~s:: ! ;: c I ~"'C """" e,-!

j o~ f~ , (;) "''0

P-."O ~ s= , ~CQ 0

j ~ ~ ~o

40XD t I !

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--j

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STn.A,a~ NIt:" 'ICn;"At! 'h'L"'UJ raory",,,,,,, jiI'Vn 1.,I("',"r''r.'i ~d\V":' l1"1:'IC'1TtC" UrAVAA.::_.J. v.::: ,L;~~'9 .,_'!dl·t.n~J...IW~..;J.t'l n..;.J,.J rl .... lJ~ r L,I"\;' • .to. _£&.J ... .J

j ~ J 11 La teraJ. Load Axial II,' ,.....f -! II I ! e.'::;; Ii (Concentrated) Thrust I

1·~ 4. . I *"0 I r:; "c: ~II i X d , ... c'l dOl I <D t.j "'f"'lj t::: I",::"....::a :> a ~' c I-

l...-l tu~ s:::: ~ t:....; ~ .,.-; " 0 rlI c.:;, t:!' 0 ~ d +JiO...... 0 s::: ~ +" Gli"O J: £:: 0 '-+, 'II O..,...jC 4f'"i ~ ~ C....-f..n M :.: W ..,J Clj ~ <"(j $..a 0 Q; 0 ,0 ~ ..c "'0 (l) cd :3 -

&:...j 0 ."f"'I p., 1i1S 0 ~ f2,.J (j to 0 ,G) P.."f"'I s... j f.!)"" ~ CD .....4~<DQ.)dm ~.&k..= ra L~tIl 0 E-< oS CI IE-<..::I til E-< :i: ::> E-< ..: E-< II

rc.; m

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Drop Weight, 500Th 12mlo .. 0241 L-W NOlle 11 1 ... 25

rr----8a IX-X

f! tV

I !

n ! " ..1

500 1.b -24:in1 0.0221 'f

j 5001b 48mj 0,,007' n

" 1. .. 64 -

,v 1 .. 93

I ;00 ~b 72m! 0,,(1)71' tv

__ . ____ <Ii ~I " --r-n- 'TV 4

'4DW ! -4M-l I

I .2 I !

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16

3 6

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I

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r I I" f 11

,

500 1b 24 mt t?, .. 022 fi

I '( ! t" "J " I 500 ~b 48i:lj O~OO7!: "

" 2 .. 82

Constant I 8 .. 93 .ksi II 1 .. 23 Constant! I - ..... B.72 ks!!1 1.49

t Constap;t I 7 .. 14 ksl:

T Constant I

1 .. 63

¥

! ~¥. &:: s::-t: ,·8~

~ 41

~ 8 <"d ~ ~~ fd g <E-t 3c<

11,1 n' ,:1 500 lb72 fir 1+ 161 _1. '" 'n

, I,· , , 1 «, ' ,

j , j , I -6.24 kS111 2.82 ~11

, I.

I .. _~ __ jl ~J I I !I

I ~ Ijr~ 1" I 1 1\1 " I f • ; \' rr--,I . , . " r I , { 1 j I'll' , l' ,~ I f I, '- , "~ . , ' I ________ ""'----'-'--___ j. _____ ~~ __ i.~IL~ _____ . ____ l. _ ___L 1 . Fr=r~----' r~~1 --J-~ ---1· - I --:-- ._] . J~ __ _ ____ ~ ___ ~ ...... ~ __ ..L ~ __ 1 i :-1 -~ '1-11"---' ~~-~-~'~l'" --~l' '. '. ,f

___ 1-..-'___ _1.___ '_ h_.~_~~~ '-_~ ____ L __ ~_.~,J_ _ 1,iL...,.J!L 'f'-, ;"

. .¥ tI. p." s:: o Q/t

j:9 v i1) CD rl~ ~,. o xc::.

-Reference!' aTe 11'stee :at e!1dof text '-' .l:1Oom Departm,ent, '

University of IllinOis ~A&UtiJil, T"'I "1.Jl_. 6180.4"

<1> GJl *1j'3 ~) M t: Cd

@ .. ,"f"'I. ,':: ~ +l, $..')(0 (d Go (l) 0-'''''

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~ ~ Spe.:!irnen Section " ::: ::: ::: :l;' :: YJ Desirnntion

c~ 0 hJ.; " (J3 •• -.-.- _ .. '--

c~ .,' " ~, • " , ,; '~ ~' T,YPO 0 f S, pee itna.:n ~ ....... .1.nd F .. nd ,-+ ... +:: ~ - .. Fef1trnlnt

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~ (·'"",c·I.• n H ~ • :: ~ ::l :: ::: I .J 9 lJ10

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Slow B-1 11 111 11 n Loading _I 300 1L-60k

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B-3 in" .. .. I "Ii n o I,

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