Cheney, L. T.

English

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Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1938
Short steel columns, 1938 Proposal
L. T. Cheney
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Cheney, L. T., "Short steel columns, 1938 Proposal" (1938). Fritz Laboratory Reports. Paper 1221.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1221
\, FRITZ fNGfNEERi'NG LABORATORY
LEHIGH UNIVERSITY I
BETHLEHEM, PENNSYLVANIA '
I fo-r 'Ct}'0fl,~
Preliminary Study of Tes t Prog"ram - It is the purpose of
this preliminary report to present to the A.I.S.C. Tech-
nical Research Comnittee further details in regard to the
Short Steel Column program, together with questions 'which
have arisen, as a consequence of further study and thought
given to this investigation. It is desired either to ob-
tain wri tten cOlirrJent, on these mattel~S from individual
members of the co~nittee or to hold another meeting of
the committee in the near future for the plJ.rpose of their
discussion. In ths mefu"'1while pilot tests will be proceed-
ing on the first pal"t of the program.·
. At the October 5th meeting of the 'l'echnical Hesearch
Commi itee the pY-ogram for the Sb,ort Steel Column investiga-
tion was discussed and the general objectives of the inves-
,tigation were placed under two heacllngs.
1. Flange CriPLJl:lng of Short Columns.
2. Strength of Short Colu'mns wi th Varying
Eccentricitios of End rrhr,ust.
Each of the.so progr%lS wiil now, be eli scUssod in
greater dotail than at tho Octobsr 5th moeting and the
qUGstions on which comment are desired will oe numbered
for reference purposes in consecutive order.
~. Flange Crippling of Short Colm;ms - Theoretical solu-
tions* for the clastic buckling of n thl~ plate with one
side unsupported are already available for the two extreme
~----~--------~-~-----~~-----~-----~-~--~--~---~-~----~--~
~ Timoshenko, ELASTIC STlillILITY, pp. 339 and 342
(
.~ :..
2condi tions shmvn in 1i':1.£:. la~ (supported side simply sup-
ported) and Fig. Ib (supported sida fixed). Tho outstand-
ing leg of one-half of tho flanGe of a rollod column
section (Fig.lc) is in a condition somewhere between that
of Fig. la and lb. Timoshenko also gives solutions for
this case UJlcler the hoading iIOnesidc olastically built in"
(loc.cit. p.344). It is sufficient for tho present discus-
sion to point out that even for tho weakest condition as
shown in Fig. la all co~~only rollod shapes and A.R.E.A.
specificatlons for built up colurms givo proportions for
which tho critical strossos arc above the yield point evon
in tho case of structural nicl{ol s tool. Tho 6 x 8 x 7/16-
in. angle, with 8-in. logs outstanding is in a doubtful
rogion and is tho only exception.
Quostion 1. Is it desirab13 to study tho crippling
strength of outstand::tng 108s of co11lliills in such ca,ses where
the critical loads are above tho yield point?
For all standard scctions this problom would be one
of plastic buckling. For short colunills with L/r 50 the
critical buckling stress of the column as a whole is ap-
proximately equal to t;l}C yield-point stross of the material.
Since tho strength ag~inst local crippling insofar as axial
loads ar8 concer'ned is alroady above the yield point a de-
tailed study of this problem is of doubtful practical im-
portance.
Question 2. Would it not be desirable to limit
elastic buckling tests to a relatively small progrru~·to
check Timoshonkols theory?
3Close cOl'rclati,on wJ th l'imosl1cmko t s theory has
already aoon found for anGlo struts.-)to
Whatever the anSW61'S to Questions No. 1 and No. 2
may be, a very im,portant practical problem remains. If
localized bending stresses arc present in one or both
flanges of a col~mm section, what then will be the axial
load which will produ,ce flange j)llCkling? Such localized
stresses are induced by clip and seat angles in a beam-to-
COlunrrl connection. The local buckling strength of the
column flange under this comb:i.nedstrcss condition may
possibly be much low,')r than £'01' the caso of &xiul load
alon'e. Very nearly the sane problem occurs at the cutoff
points of covor platos of the compression flange of a plate
girder, duo in this caso to tho eccontricity of load trans-
fer. Little attention appoars to have been given to a
thooretical analysis of thi~ very practical problem. It is
proposed thereforo that a serios of tests be made using the
setup shown in I"ig. 3, and that this problem be given par-
ticular attention.
Question 3'. Is a program of' tests as shown in Fig.3
advisable?
Proposed Program for Plango Crip:)ling Tests - Part Ia
A series of ton tests of short Il-beam soction with
flanges planod to varying thickness. Axial load will be ap-
plied along the linos indicated in Fig. 4a and 4'0. The local
buckling of tho flanges is not a function of Z/r of tho whole
* SOHE NE1N EXPEIITl.illNrCS ON PUCI~LInG OF THIN V'JALT-J CONSTRUCTION
by Bridget, Jeromo, and Vos seller - 'rrarlsactions, Am. Soc.
Mach.Ensr. Applied !\;oJchardcs Divisi.on, Vol.65, p.569, 1934
4column but deponds rather on tho ratio of blh of the indi-
vidual flanGe. (Soo Fig. 1 for notation).
Tost Program 10.
Material: Structural Silicon Stael
10 sections of 10 x 10 at 49 lb. WF beam
sections e~ch 4 ft. 4 in. long with ands milled at right
angles with the longitudinal axis. Plane the outside of
the flang'Js to fivo difforQnt thicknoss·,:;s as follows:
(2 with flangos planed to 0.20 in. thickness
(
(2 with flancos planod to 0.235 in. thickness
10 (
columns (2 with flangos planed to 0.27 in. thickness
in all (
(2 with flanges plunod to 0.305 in. thiclmoss
(
{2 with flanges plnned to 0.34 in. thicknoss
Test Progra~n Ib
Flange crippling tests en colLunns with loaded beam
connections.
ThrGe colLmm s1 zo s, probabl~r:
10 x 10 WF at 77 lb POl'" foot
10 x 10 WF at 49 lb pOl'" foot
10 x 10 VIF at 49 lb. 'wi th flanges plcmed to
0.34 in. thickness
Throe typos of connection LlS shown in Fig. 5a, b, and c.
Three tests on each of the c,bovo vlith different amounts
of load on the c8.ntilovor arms.
Tho forogoing progr~m Ib calls for 27 tests in all,
with exact details to be worked out lator aftor cOlmrront by
tho conIlnitto<3.
5II. ?hort Steel Col~n_ Program - At the October 5th meeting
it was decided that Part II of the program would be a general
study of short steel colw;ms eccentrically loaded. The ~/r
ratio of these columns was to be in the 20-30-40 range.
The purpose of this work is primarily that of determ-
ining simple workable formulas for column design which are
both safe and economical when used in the design of columns
in building frames. It is aSSUIIled that the eccentricity of
load ac ting on the end of the colulll.."1 is knovm. Methods for
deterrllning this eccentricity in ~ny actual bUilding column
depend on many factors and are outside the scope of the pre-
sent investigatio~. In laying out a program, however, it is
necessary to give some thought to tIle structural behavior of
a bUilding frame. Considerable vvork along thi s line has
already been accomplished by the British Steel Structures
ResGarch Committee-X- and their r'eports have been studied in
detail. The last noted reference presents the final recom-
mendations on the design of col1.J.llms. The allowable stresses
are presented in tho form of a chart based on theoretical
analyses which is presented her0 in Fig. 6, because of its
usefulness in laying out a colll!nn program. If anything 'sim-
ilar to Fig. 6 should resUlt from the present investigation
it seems likely that the results could b~ presented in the
for~m of an empirical formula as suggested at the meeting of
the conn:nlttee. The chart in Fig. 6 is based on the worst'
---------------"---------------------------------------------
* First Report of tho Steel Structures Research COlnmittee
. pp. 211-224
Second Report of the Steol Structures Hesearch Committoe
pp. 13 - 43
Final Report of the Stool Structul'CS He search Cornmi t too
pp. 436-545, pp.559-565
6probable: concH tion which m1c..ht ariso in a buildil1£colurnn
regardless of whether the bending is in the form of single
or double curvature. (No reduction of rib ratio of tho COlll-
pression flango has boen made in this chart.)
The results of the British Steel Structures Research
Connni ttee show that the proport~ons of colurlffis in buildings
usually allow them to be designed with practically the same
allowable stress as is used in beam design provided the
colQml1s are designed for known eccentricities of load. The
"l/r of building colurll1s is larGe only in the UPl)er stories
of a building where the axial loads al~e small as compared
with the bending moments. For such a condition, as for ex-
ample, a I'atio of direct stress to bending stress of 1:4,
the allowable combinod stress from Fig. 6 vVQuld be 17,500 p.
s.i. for an r/r as hieh as 100, as conwared with a basic allow-
able stress of 18,000 p.s.i. [01' short columns. When the axial
load becomes the major factor, as in the lower stories of a
building, the 1/1' of the columns decreases along with the crit-
ical value which allmvs design on the basi s of such high work-
ing stresses. For 95 per cent axial stress the coluliU1 may be
designed for 17,000 p.s.i. maximum. stress if the Z/r is 30 or
less.
It seems evident from Fig. 6 and from'the foregoing
discussion that for 'short c.olumns In the 20-40 range of r/i!
as proposed for this investigation, failure will not result
until the rnaximum stress in the colunm very nearly reaches,
the yield point of the material. The experimental check on
7this question is one of the primary purposes of Part II of
the short colurn.i'J. program. It nO'IN seems desirable, in addi-
tion' to test collli~ns of higher ~/r - up to 100 - for cases
where the eccentricities of load are high. These tests
would tie the program in with other work and permit much
more general and complete conclusions to be reached. In
general, the tests should' cover the follovling range:
Ratio of Average
Axial Stress to
Maxinn..1..'TI. BendinG
Stress
---
o - 1
1 - 4
1 - 2
1 - 1
2 - 1
4 - 1
1 - 0
Ranse of ~/r
to be Tested
100 - 140 -(only 3
80 - 120 (tests
60 - 100 (above 100
40 - 80
20 - 60
20 - 40
20 - 40
Question 4. Is this modification of the :program
desirable?
The method of testing is another problem concerned
with Part II of this program. In a building, if the beams
framing into a column are symmetrically loaded so as to in-
troduce no eccentricity of load into the column, the beams
will then provide a restrainlng action at the column ends.
In this case a reductIon of ~/r would be permissible in cal-
cUlating crltical loads. On the other hand, if the beams
introduce bending into the colu.iiill, the tendency for buckling
will be increased.
Three different methods of testing colwnns with com-
bined thrust and mo'ment will noyl" be dlscllssod.
8Method 1 - The colu.mn is loaded axially in the testing
machine with varying eccentricities of load and the buckling
or yielding strength determined. (See Fig. 7£1..)
Advantages: 1. Simple fabrlcation of test colur:ms.
2. Simple test procedure.
Disadvantage: 1·. Eccentricities limited to core sec-
tion of column, unless special pro-
vision is provided to develop ten-
sion between one side of column and
testing machine head.
Method 2 - The axial load would in each test be applied
in line wlth the centroidal axes of the column. End moments
would be introduced through riveted beam-to-column connect-
ions with detachable loading beE,rns 8S shown in Fig. 7b.
During the test definite end moments could be applied
to the colura...'1 after which axial load v/Ould be applied until
the colunm yielded and failed.
Advantages: 1. A:Jplied end moments 8.ccurately knovm
and colUlim a1wa"J'·s 1 ocated in center
of testing 111achine.
2. Large range of equi vB.lent eccentri-
city easily obtained.
3. Actual conditions closely simulated.
Disadvantages: 1. Hore expensive ane. complicated
test set -up than r.:ethod 1.
2. ECiui valent eccentricity of axial
lose:. r'Lecl"oc.ses during test, but
can bo calClllatecl roadily for any
given load.
9Method 3 - Column testcd as part of a frame as shown in
}'ig. 7c. End mor.lGnt s d.eveloped i.n column by tightening
turnbuckle and loading spring.
During test. defini te end moments would be develo·ped
after which axial load would be applied until the column
·yielded and failed.
Advantages: 1. A still closer simulation of actual
conditions in a building frame.
2. Large range of eccentricity easily
obtained.
3. Set~lp is simpler than Method 2.
Disadvantages: 1. Introduces a new variable.
2. Calculation of end moments is a
s t[~tically indeterminato problem.·
SlJHMARY OF PROPOSED PROGRAM
Part I - Flange Cri::;pling.
a. Pilot tests on 10 x 10-in. WFshort columns at
49 lb. to tryout test methDds.
b. Test series Ia - 10 ·.short cohunns w:t th flanges
planed to variable thickness.
c. Tcst series Ib - 27 short colw~ls with loaded
beam connections. Three flange thiclm.essc)s, three types
of cop....,.'1octions, three differm1.t beam loads.
d. Theoretical analysis of flange crippling prob-
lem, c.orrclation with test results, and design reco:mmend-
ations.
- 10
Part II - Columns Vii th End MOIlJ.onts.
a. About 6 columns with zoro eccentricity of load
and variable 1/r (20-40) tested by Mothod 1.
b. Between 20 and 30 collulills tested by Hethod 2
with varying t/r and varylnc ratio of end moment to axial
load. Details to be decided on after tests in Part I are
finished.
c. Study of results and presentation of design
methods~
Tho preceding program may exceed slightly the limit-
ation of time and money availablo but is proposod in this
form so that alterations m2Y be ltw.de in lino with rocommend-
ations of the committoe.
APP:8HDIX A
e :====0 ..-=e
The material contained in this appendix consists
of the comment advanced by the members of the Structural
Research Con~ittee of the American Institute of Steel
Construction after their review of the foregoing report.
It does not seem desirable to go farther with a
study of the crippling strength of outstanding legs of
columns except throu6h a relatively small program to
check Timoshenko's theory. Test Program Ia is the part
of the program offered for this topic. It apparently
studies width to thickness ratios of flange from 15 to
25 within which range it should be possible to make the
flange criyple before the yield point of the column is
reached. It seems this is worth doing. It not only
woulde~1ibit the sufficiency of the A.R.E.A. rules as
plotted on Fig. 2, but it would also give a designer not
governed by stande.rd speciflcations some leeway in mat-
ters of design which might cause him some consternation
'\
if he were not aware that it would be possible to devi-
ate from the usual flange thickness rules in case of
necessity.
It seems very in:portant to test columns not only
under idealized conditions covered by Fig. 2, where the
only load on the flange is the axial load~ but also for
actual conditions in a bUilding, where portions of the
- 2
flange are under transverse r:loments large in comparison
with axial stresses. Program Ib is directed toward this
topic and additional suggestions and criticism concern-
ing the types of cOl~ections are needed.
The investigation of co~)ined axial load and bend-
ing in the range indicated by the table on page 7 appears
to be justified in view of the evidence presented. This
will dispose directly of Section 6(a) of the A.I.S.C. spe-
cification which is an afu:1itted rule of thumb and fre~
quently criticized.
As to the testing methods indicated on Fig. 7a,
7b, 7c, it seems the most desirable would be 7c cutting
off the two beams to the right of the spring connection
and omitting the rest of the beams and auxiliary columns.
This would make the end moments Qeterminate instead of in-
determinate. In this arrangement, however, a problem
arises. As the axial load is increased the column will
gradually bend prior to buckling and the load in the
spring will decrease as a result of the bending. The
applied moment, therefore, will likewise be decreased.
Just how serious a matter this would be in an actual test
is a problem which will require further study, This is a
detail which may be settled later following additionaland
morc widespread C01TImCnt.









Short steel columns, 1938 Proposal

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