Driscoll, G. C., Jr.

Lu, L. W.

Yen, Y. C.

English

Lehigh University: Lehigh Preserve

Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1962
Proposal for the investigation of instability of multi-
story frames, 1962
Y. C. Yen
L. W. Lu
G. C. Driscoll Jr.
Follow this and additional works at: http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-
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Recommended Citation
Yen, Y. C.; Lu, L. W.; and Driscoll, G. C. Jr., "Proposal for the investigation of instability of multi-story frames, 1962" (1962). Fritz
Laboratory Reports. Paper 1755.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1755
276.11 i
PRO,JECT 276
PROPOSAL FOR INVESTIGATION OF
INSTABILITY OFMULTI-STORY'FRAMES ,
Yu-Chin Ye'n, Le-Wu Lu and
George "C. Driscoll, Jr.,
TA~LE OF CONTENTS
RECOMMENDATION OF A SIMPLIFIED METHOD'
'OF ANALYSIS • • • • .,' . • . . . .'.
. . . . . . . . . . . . .
STATEMENT OF THE PROBLEMS, .
PROPOSED THEORETICAL STUDIES' .,
EXPERIMENTAL PROGRAM • ". . . .
3
6
9
1
I)
17 '
11
12
Page
. . .
. . .
. . . . .
. . . . . .
• 0' • • • • •
. . . . . . . . .
o • • • •
.~ .. '.. ~
., .
. . . . . . . .
. . . . . . . .
TABLES AND FIGURES
R~~EN CES .'. ., • ., ~
INTRODUCTION
FINAN,dES
I.
II.
III.
lit tv.
V.
VI.
,VII.
VIII.
•276.11
..'
, 1. INTRODUCTION
-1-
According to the r.sults oE some single
In plastic design' 9f "multi-story fr,ames, the mem,,:,
bers are proportioned by a, crj.~e~ion based on the load'lead-
ing to the form~tion of- a failure me~hanism. ~~' i~ is
possible ~hat the frame ~ay buckle at a load~ s~81Ie~
than the ultimate load correspon~i1ng to' the" failure mechan·ism.
Therefore ipstability problems may gov~rn the design of
multi-story frames.
story r.ectangular frame tests, the load-carrying capacity. of
a frame is only eO to 90% of the pla~tic load~ ('1) It is b~,
eved that the situation W9uld become more serious when the
number of stories is increased.
Th~ problem of fr~lJ1e. instabilfty in tall building
frames is be~omi~g'increasinglyimportant because.of recent,'
developments in the fields' of materials,' architecture, and.
structures. Lighter building materials, modern curtain
, "
, '
walls, the plastic method of design, and compo_ite design of
the rloor eYstems~l contrJbute very much to the reduct~on
of dead load on frames. On the other hand high-strength
steels and improved methods of design as adopted in the new
AISC Specification fuzither contribut'e,to the reduction of
the member size. conseqUentlY~der'columndesign
gives rise to the more dangerous problem of frame instabi-
lity.
, .
276.11
From the ,point o~ view o~ structural design, the
reduction in dead IOa~agnirie. the importance or wind
load which is considered as an important ~actor in the pro-
blem o~ ~rame instability. 'There~ore a siD1ple ~rame sub-
jected to working ver.tical load and varying horizontal load
should be investigated as a pr,eliminary study into the be-
havior o~ multi-story ~rames subjected to wind loads as well
,
as v~rt~cal lo~dso
It is well known that bracing in building rram.~
and partition walls pro.,lde considerable sway resistance to
@ structures. Braced $'rames under', vertical loads tend to
~buckle iri a symmetrical con~iguration ,which corresponds to
: a ~igher buckling load G that o~ an anti-symmetrical 90n-
figuration. Moreover, the brac,1,ng provides the mos't e~~(§t'0
ivt;' means for resisting horizontal load applied to ~rames.
There~qre the ~nvestigation should include the solution of
,"
braced ~rames '~or determination o~ the minimum bracing' re'-
,~ ~.
quire,lI'lent.
'Accor~i~g to a literature survey, (~there is ~o
exact theory to analyze the ins,tability probl~m~ of muJ,..ti-
story frames in the inelastic range. Furthermore, lar'ge
scale instability tests are also n~eded. Therefor~ this pro-
posal in6lude~ th~ development o~ theory, its experimental
veri~ication, and preparation of a recomme,ndation ~or an,
approximate method o~ checking the stability o~ fr~m~s.
276.11
-3-
2., STATEMENT OF THE PROBLEM '
There are many factors which affect the buckling
, "
load of a frame. It' is essential to understand clearly each
of these variables before the twe of~ame instabl1ity
,problem can be classified. Once the individual type of pr6)
blem is formulated, the suitable variables can be chosen for
investigation according to practical neces!3ity and their
importance.
The factors affecting frame instability loads are
the following:
, h(1) ,Slenderness ratio of columns rz0 This is the
II
most important factor governing the buckling load of ,a fram~.
(2) Stiffness of beams
The stiffness of beams is the second important
factor. For example, frames with beam stiffness approaching
zero can buckle regardless of the stiffness of the columns •
.This suggests that the stiffness of the floor slab be in-
cluded for ecqnd~lc8l analysis, particularly in the case of
... ~ -~_ ...
,composite ,design.
(3) Degree, ot restraint at supports.
,~ -·partial-fixed or fix-ended conditions
su~stantia~luenceon the critical load ofa frame.
(4) 'Types of, steel.
have
'I'
Since the stress-strain ourves and moment-curva-
... relations vary with different types of materials, thei
buckling loads of frames differ accordingly.
276.11
(5) Cross-sectional shapes
, , ,
Only wide-flange shapes with typical residual
stf;~sS patterns will be investigated~,..
:'.,
(6) 'Loading conal'tions
-4,:"
L •
Whether the loads are symmetrically applied or
whether they produce primary bending mome~t in the frames
are "all imptU't_!!.'nt factors. Though the structl;1re might be in
the most critical state when possibl~ ~~~mic ~9ads are av
lied, the investigation of the et;fec,t ..of_,·'4yna~ic- loads is
not included in this proposal.
(7) Loading sequence
In the inelastic range, the behavior of a str~~-
I - I
ture is non-conservative in its nature: Therefore,th~ final
'status of the structure depends on the' loading history. :Fqr
I'rOPOreallYi~craas ing ::~~=ca~ and horIzo~t~l"l~a~~.::"
a frame , no strs,in revers,~l would occur _in its members. -How-
ev~r, a, structure may undergo unloading in -some part of the
\llemberS~f' 'the vel'tical loads aresppl1ed f'1rst snd then
th~ horizontal loads _follow.
- ~
(8) Existence of shear wall-'6r bracing. ,
I~ actual bUilding t'l'ameS~he_wallS,0", ev,,,,, PV
ition's help resist sway cori'sid:erably. The eff~c~t of bracing
csn~ the f'rames to buckle in symmetrical mOdes, which
result in much higher critical loads thanAanti-symmetrical
modes. '\
....'j
276.11 -5-
Types ·of frame instability are classified accord-
ingto thelr loading cond,,,",tions in Figure 1.
Type A .is c~racterized by the bifurcation of
ilibrium position at the critical vertical load. Since it
is an initial motion problem, strain reversal will not be an
important factor forevaluatiC?n of the buckling load. If
the loads are not symmetrical, horizontal deflection develops
immediately after the vertical loads are applied as shown in
Type B. Type C is' characte;rized by the a_pplication o'f pl'O-
portional horizontal and vert~cal loads. This is a typica~
problem to be found in.most of the literature. However, type
D is a more practical -situation. ~The frames under vertical
loads are sUbjected, to gradually_increasing horizontal loads.
The windward corners will unde~go considerable strain rever-
sal. To neglect this effect would result in a conservative
analysis. However its quantitative picture is totally un-
know. Therefore It is necessary to investigate this pheno-
menon.
When the frame is prevented from sidesway by brac-
ing, the instability mode is always symmetrical (shown as
type E~. Methods for determining- the ultimate strength
corresponding to _this type of failure are be~ng developed in
connecti_on with the multi-story frame project~. (273)
279.11
·~~1I1
./ l-\r cy'5J;J~
~ '\ -6-
3. PROPOSED THEoRETICAL· STUDIES
~~e r~eoretical solution,of fra~einstability;pro-
·blems bec.:omes verry complicated due to the high degree of
.
'lndetermitiacy, non-linearity of thrust-moment-curvaturere-
~ationshiPs, and the n.on~conservat1ve naturs. ot(5 str~~::)·
ures in· the inelasti9 range. However the problem can be. s~,
ved by systematic investigation of the in~ividual column and
beam elements of which the frames are composed. Therefore
colUlDIl and bsam detlection curv~s~nd end~moment .vs.snd=
rotation curves for various axial load.and end-translations
should be developed. In order to solve problem type D
described in the previous· section , the effect of unloading
.. due to sway displacement should be included in analyzing the
coluplns. For·the sake of accuracy and efficiency, computer
,pro~aIJ¥D.ingwill be ,developed as much as practical. With
these data available, it is possible to develqp a method
which is feasible for an accurate solution of frame stability
problems.
~ Ho~ever, it is necessary but not sufficient to
,
developan·'ccurate theoretical method. Afairlyslmple
approximate method should be recommended for practical design
purposes. Unless the true behavior of frames is explored
theoretically and confirmed by experiments, it is not ~.
quate to estimate and recommend any approximate method of
analysis. Moreover a purely exp~~imental approach to inves-
tigate all variables would result in a tremendous number of
test~~ Theret'ore, it is essential to deve,lop a ..general
276.11 -:-7-
theory to analyze the structure under various loading condi-
tions. The proposed theoretical studies can ,.be summarized
as follows:
(1) Completion'of individual column and beam data
curves.
Before the problem can be solved, more information
about the individual columns and beams are necessaI'Y.' ,Pre-'
j ~
para1:iory work includes the following items:;
r (a) Column deflection curves
I
(b) Column end-m~ment vs. end-rotation curves
(c) Beam deflection curves
)(d') Beam; end-momentvs. end-rotation curves
(e) Item (a) includes the ~way effect
,(f) Item (b) includes the sway ef'fect
(2) Development of methods for analyzing partially I
yield~d frames.
~astic-plast~c analysis of frames can be perf~
med by using data (a) to (d) inclusive. Moment, rotation
, '
and deflection of members throughout the frames are to he
determined by these data under any sypmletrically applied
vertical loads. T~refore the method can be used as the
first step to the solution of' problem type A.By repeating
the process for different vertical load, problem type E
cQUld also be solved.
••. '~. "~. l' .~
•276.11
ability.
-8-
() Analysis of frames with bifurcation type inst-
".
A m~thod will be developed to solve tqe buckling
of frames under vertical load~~ (shown as type A in Article
2)." At first the fra~e is atialyzed by the prevJously-menti-
!
The solution to problem types Band Cwill be
treated using" the data (e) and (f) list"ed in it~m (l). Lit-
erally the method is an elastic-plastic analysi~ of frames
including the sidesway effect. Since there is no reversal
of strain anywhere during the loading process, the "solution
is unique. The instability loads are characterized by the
maximum points on the load"':'defler tlon curves. Actually the
solution of prol;>lem (J) resembles that of the p:resent prob~
lem. The difference between these two problems is that" the
sway deflection is real in one a"nd ficticious ifl the qt:Qer.
I
276.11 -9-
Before concluding the' article, it should be point-
ed out that the proposed studies are oriented toward the
I
following dIrections • First" for the sake of eff~ciency,
I
accuracy and versatility, a digital computer will be used as
mU9h as practical. . Second, the possibility Of non~~iimenv
()!faJ}.zing-.the data will be _inyesti~atedao that the r~sults
9btained_from ,the 8WF)1 section can be applied, to any other
WFsections. Third, the deformed shap'es Of tr~me~,' in, pa,rt-
fc~iar; the poaition of tha polpta of cObtran&: in"the
columns, will be studied.- Last,- becaus"e of the possible
advantage of extending the stability check to include the
effect of dynamic load, an energymethorl will be attempted.
4. ~XPERIMENTAL' PROGMM__
Since there ar,e so many factors affecting the frame
!~Hl~~1p.i~!ty load and some of, ~l:l.~;1r ,individual eff~?~~_vfliln::>ot
be iriy.estigated precisely by a purely theoretical.mE3tnod,
!=lxper:i,mental work is necessary. The theory can be applied
for practical analysis only when it is· verified by:t;;es1;;s.
However a purely experimental approach to investigate all
vari,ables would require a tremendous number of tests. It is
believed that valuable information can be obtained by first
condu¢ting a series of carefully planned tests when enough
!
progress
tested.
has be,en made in the theoretical studies.
~a~'r\oposed. that six lIIodel multi-story frames be
The proposed test program and its oqjectives are as
276.11
follows:
-10-
(1) Unbraced frames under vertical loads (10k6 Ij)
CTestframes U-l, U-2, U-3, and U-4) This series
of test~as shown +n Table 1, is intended to check the val~
I . Jk~,'~dity of'tpe theory of anti-symmetrical buckling of multi- ~~. ~
story. f'r~mes sul>j ected to. symmetrical vertical loads. The ~~~
succe.. of' this seri.s of'test would also partly conf'irm the >. .validit~ Of the theory of' symmetrical instability ref'erred ~
to 'as TyPE! E in Article 2. _~
Howev~r, it has long be en a q,uestion how much
:t>ra~ing is required in ord~:r to in.crease the vertical load
up to the symmetric.a.l instability load ... Therefore the next
, .
seri~s 9f tests recommended is:
(2)' Braced frames under vertical loeds tr~~)
I #
(Test frames B-.l, and B-2) This series aims at
the find.ing of the minlmuJ,n requfrements for bracing. At the
sam&- tlm~ it will check the. validity of the theory o~ the
·.symmetrical in's'tability of m-cliti-story frame·s·. In other
words, the test r~:8:Ults will justify the method of elastic-
plastic analysis pr9posed in the previous chapter. ,The
series of test.~ is summarized in Table 2.
Depending On results of these tests and theory,
the work will be extended to' include the following investi-
gationsl
(3) Single··",frames under horizontal and vertical
276.11
loads
loads
loads
-11-
(4) Unbraced frames under horizontal and vertical
(5) Braced frames under horizontal and vertical
The loading system and test apparatus for the pro-
posed tests are siml1arin principle to those reported in
Rei'. 1. The load will be applied on the i'rames by lever lJS.1}jfn
'systems a~~ight. However some minor~~ and.\ rOn~
improvement are neg.;essary. It is expected tha':tcn-~lties ~ ~
"'---------
will be encountered in alignment of the loading system for
the tests of three-story frames. To remedy this, special
device~ will be attached to the lever system for adjustment
I "';
,-
of ~he load distribution on the frames.
5. RECOMMENDATION OF A SIMPLIFIED METHOD OF ANALYSIS
Accurate analytical method and experimental veri-
fication arie possible only for relatively simple frames. For
highly indetermi~ate structures, such as tall building frames
with a large number of bays, the preciseapalysis and test
may not be feasible. Therefore a simp11fied method of a~
lysis against frame instability is needed. The approxim~
method has to be based on some simplifying assumptions. The
Iproposed studies should be able to evaluate approximately the
error involved in each assumptior, the approximate method can
!
then
276.11 -12':'
.' be used to analyze more complicated frames with reasonable
confidence. For example, the investigation of the effect o~,
strain reversal, the measurement of angular change at each
.
corner of the frames, measurement 'of'---deformed shape of
frames, espt!cially the position of inflection points, ----
all are orient~d towards the ,justification of the ass~
ions to be made ,in an approximate soluti.on. Therefore the
I ' . I
ultimate purpose of the proposed studies lies not so much. in
the theories and their verification but in the 'recozmnendatio,n
of a simplified method of analysis.
6. FINANCES
Enough funds have been included in the 1962-1963
proposal to cover planning and those tests that can be'done
in the current year. Costs of individual tests and total
~est progra~ can n~t be certain until the test setup has been
pesigned.
.-
, -.'
276.11
7. TABLES~!ID FIGURES
-13-
.- ••• ·0
-------
,Frame ~,f)_. Column /f- $ -1: /Noo ,span size Qn) l Heifht size .1L ~pL (in) r v h in) rx (in) rv
-
.- .
- \.../- -
- -
- I
JU-l 60 5" 10095 54·8 33 c3 I3·7 1.095 30 "~ I307 I'" t~ . ~:
- -
_.
U=2 60 2.5 13-7 10095 54·8 44 2.~ 13.7 1.095 40 ~ f I"5 ,,' " ~p.. ~
-... Q) /
U-3 60 31507 1.230 4808 2,5 131 I'C) ~~33 1.095 30 1ra4'v-" (5_._.- ..._- --- .-.--- .._- .' - . ~ - mlP>
--_.
2-2 t~ L .,U=4 60 3I507 10.230 48.8 44 13,7 100~5 40
. ~. 8
, .
Note: Loads on beams will consist of either two or three concentrated. loads.
I ,
. I
TABLE 1 PROFOSED TESTS OF UNBRACED 'FRAMES UNDER VERTICAL LOADS
"
.-
t...;'i ,
,.,~., "."
~j" ,••,,,: ;~' ~,
'It~f.
'I
-.
4044 c3g 13·7 1.095
Cclumn
size rx(in) h
r T
5408 33 5 10095 302,813.7
54·8
Beam
size
2~I3.7 1.095
60
60
TABLE 2 PROPOSED TESTS OF BRACED FR!'MESUNDER VERTICAL LOADS
The_member size of bracing will be determined acc
..
din~-to ~he instabili~y load obtained from the pre-
vious unbraced frame test results •
B=l
B=2
Frame
_No.
~--,.,--+-----+-----jf-----+----1----I------+----+----l.s:;
tc')
II
r
@-*===:I:===!!=~I
. "
: ..~.
276.11
(A) Symmetrical
vertical loads
=16~
L...------~J
(B) Unsymmetrical
vertical loads
\
\
JL- -...,.~cf
t> ~cSloE- P
Proportional O{~ ------(C)
application of·
vertical and oq:> /----- ---- ."horizonta·l. loads t
."",O(p
------
,,;,:
J
H
vertical H(D) Constant
l~ads with varying
horizontal loads H
/-~
H
..
P
(E) Braced frame under
vertical loads ~~
FIG. 1 TYPES OF FRAME INSTABfLITY
276.11
,; , .~ ..:-
8. REFERENCES
-17.-
".
1. Yen, Y:U-Chin, Lu, Le-Wu~,.. apd Driscoll, G. C., J~ •. I
t1'~ESTS .. O:N T~. STAB~LITY~. OF WELDED ST.EEL ~RAI1ES"~. )j',
Fritz Engine~ring..Laborat6ry Report No. 276~9',"
Sept. 1961. Also'Weldirig Research Council Bulletin
~o. 81, Sept. 1962~ .
2. Lu, Le-Wu
"A SURVEY QF LITERATURE ON THE STABILITY OF -FRAMES"
'FritzEilgirieering Laboratory Report No. 216 ~ 2,' '"
Dec. 1961. Also Welding Research Council Bulletin
No. 81, sept. 1962~


Proposal for the investigation of instability of multi-story frames, 1962

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