Error involved in isolating one floor of a building frame for design purposes
by Pete Boyaci
A THESIS Submitted to the Graduate Committee in partial fulfillment of the requirements for the
degree of Master of Science in Civil Engineering
Montana State University
© Copyright by Pete Boyaci (1952)
Abstract:
This thesis presents an investigation of the errors made in calculating the design moments of the beams
in a continuous frame, when this frame is analyzed in accordance with article 702 of the American
Concrete Institute (A.C.I.) specifications which is followed in the designs of multiple story building
frames.
In Part I of this thesis the analysis of the frame is based on the A.C.I. specifications where every floor
is treated independently, as if it were a complete structure in itself. Thus, the design moments for the
beams of the frame are determined.
In Part II the frame is analyzed as a single unit and the effects of all loading combinations are included
in the design moments for the beams. The comparison of the moments obtained in Part I, where each
floor is treated as an isolated unit, to the moments obtained in Part II, where the frame is treated as a
unit, reveals the errors made when analysis is based on the A.C.I. specifications.
The results of the two parts show discrepancies up to twenty percent in the design moments. The frame
proves to be underdesigned if analyzed according to the A.C.I. code. isBoaoR mro&Tm m .
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ACKNCttVLEDGMENT
I am. in d e b te d to E. R. Dodge, Pb*D ., A s s o c ia te
P r o f e s s o r R. C. D eH art, and N ic h o la s B a e s a r, J r . ,
A s s is ta n t P r o f e s s o r , a l l o f th e D epartm ent o f C i v il
E n g in e e rin g of Montana S ta te C o lle g e f o r t h e i r g u id ­
ance end h e l p f u l in fo rm a tio n .
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PROCEDDBE
Part I
.
.
B peelflc a tlo a e , =..- . « « * ^ ■*,'*
.» ,
is
O utllno 0r Prooedtire follow ed ■< +
*- «♦
l§
Design of
Blabs . * * * .
Design of Oelurfins
Design of
+ * .» «. .* 9 . «» ■ i s
'* . , * , . * < -» » .4. y
Beams * ■, i » » t *
s>.
1@
, , . » < - gl
B fIffn sss factors* . . . * * . .
. *
%%
D istribution- fa c to rs * .....................* .
%%..
Fixed End, Moments*
34
Moment D is trib u tio n . . . . 4
,
35 ,
A nalysis o f tiie frame as a sin g le D n lt» »■
<59
&ppro&ob* * , * . * * + * . * % . -*
g#
Part 11
&* *
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^ITSmmRE OIBBD AND GONgQLgED, , *. » » '» . . *
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TAB&B W ,
DESCRIPTION
I
D e s ig n o f E d o f S la D s S I a n d SS . , *
10
II
D e s ig n o f S l a b s S i a n d SB f o y F l o o r s
Ijj <s ano. 0 * * 4- * , & « * *
* *
I^
IH
D e s ig n o f C o lw m s C l t K r c m # C 8 *
« ».
10
IT
Design o f Oolomas 09 through 016
* *
80
T
F i x e d B a d M o m en ts f o r M axim um Condit r o n s 6 ». » -e e 6 #' *' -is 3 & C , I* *
26
TI
M om ent D i s t r i b u t i o n f o r i s o l a t e d
R oO f * 4 = 6 « O8 9 8 fi # It 8 -iji 8
28
TH
M om ent D i s t r i b u t i o n f o r i s o l a t e d 5 *.
F lo o r* P a r t a , » » + * * . , . * *
a*
Page
T ill
M om ent D i s t r i b u t i o n f o r I s o l a t e d
F loor, P a r t bo , . * , » » t ,
m
M om ent D i s t r i b u t i o n - f o r I s o l a t e d B»
F l o o r , P a r t a* » & * ^ ? # & & * *
SI
x
M om ent D i s t r i b u t i o n f o r i s o l a t e d 8 *
F l o o r , Part b» , * » , *, » '» * %,
52
XI
M om ent D i s t r i b u t i o n f o r I s o l a t e d I 6
F loor, Part a* *, . # * + , * **
&0
X#
M om ent D i s t r i b u t i o n f o r i s o l a t e d IdF l o o r , P a r t b» , *
*
84
X III
B a l a n o e d M oments- f o r F ra m e s , l o a d e d
^ D a n lAB * O « e 6 . 8 8 8 8 » b 0 b8
40
H f
B a l a n c e d M om ents f o r F ra m e * L o a d e d
8p a n BO * <? ^ & &* * ^ » 9 ^
^
41
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'B a la n c e d M om ents f o r F ram e* L o a d e d
S p a n CD* * * * * * * * * * $ * * *
48
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L I # QF TABLES
TABLE BQp
BESO&IFTIO#
-
Pag#
ZVI
Balaneed Momenta t o t T£m,e-f loaded
-Spaii SET#. * * »' $. > #• p k -p b. »• 4
dBi
%V3I
Balance# Momentn f a t Btame* -loaded
Span Ferf. 4'. t ' ♦? i ' * P # # -i I f 'y
44
X V III
Balanced Momenta f o r Btaae^ loaded
xn:
Balanced Moments to n tz m & f loaded
Span H e ■*', 4: ¥ « S O » d ' e e f *'
xx
Balanoed -Mment 8 '
leaded- '
Span 1M# ?■ *. ■* -ft -* e- * » » e -ft s
4V
xxi
Balanced Moment a t o r Frame»: loaded'-, ■
Span. SIS.ft « <» .»■ 4 ft1 *■ 4 ft; '-«■ ft. ft *
48.
XXII
Balance#' Momnnte' to p ' B rm ef l e a d # '' Span PB? * .4, » -4 ft ,ft .1 ,ft . e, »
49
XZIII
Balanced' Moment o t o r 1Frames loaded:
ZXIV
Balanced' Moments1f o r Frame* lo ad ed
Span ST*.- .# =-. *• . ft «r *. * .ft. ft ?■ ft
ZZV
Final memento when Frame in • • - • ■'
XZVI -
F in a l Momenta when Frame- i n
T reated as a S in g le # # *
* -"
* .*.
55
ZZVii
Final. Eomente when-Frame- la ■■
T reated a#' n
W i t \ .* * »
5$
z x v iii
Final Momenta when Frame "le '
Treated as a sin gle % it * » ^ ^
55-
ZXIX
Final Momenta 'Wen frame i f ■ ' ; ■ ■
Treated as: a Single-U nit % * * %
SB
Sp an 0B« »■ * * *. 4 f p % •« s- v --$■
Span. BSft. ?-. 6 & » ft. *■ * »: s * ft $'
T reated as. a S in g le U nit * * *. %
—
. ■-
4$
1 46
•
50
51
52
L3S# OF %AR&08
m m # %%
38% ' ZXZI
zxz#:'
Pnge
Q^xWwm - p w # v ^ .
OdBd'y.’bi.OlX'S/ ;<»,■,"A' #. .«- •* * 6 ',» f #■ f
#'
- ' ' 'UM Moments fo r MWdmim P o sitiv e
Gpndi t i oil s' |r' * s,..i . f. » f.
f, p ■i
Ga
' ' 'Brror W IsplntdAg 0#p Ulppr Pf a
Urampf ? % *■ f
^ ..^ * ^ „ „ ,&
W
fM s th e s is present s an in v e stig a tio n of the errors
made in ca lcu la tin g the Se sign moments of.' the beams, in & -..
continuous. Irarae5. when t h is frame is analyse S' in accorSance
with a r t ic le 70$ o f th e American Concrete in s t it u t e . (AaGpJp}
s p e c ific a tio n s which in fellow eS in the .Sesighs of m u ltip le•
Ster^ h u llsin g frames^
In Part I of t h is th e s is the an a ly sis of th e frame is
bases on the -A»c»lo sp e c ific a tio n s where every' f l e e r i s
treated insepehsehtlyy as- i f l i ' were a complete stru ctu re'
in i t s e l f it W uhf the--Se-si@n; moments' f o r th e beams of th e
frame are determined,
L
'v
In Part % the frame i s analysed as a sin g le unit- and
the .e ffe c ts of a ll-lea d in g , combinations are included; Sn- the
design moments fo r the beams* Ihe comparison e f th e moments
obtained In Part %&. where each flo o r i s treated as am is o ­
la ted unit* to the- moments, obtained in part II* where the
frame i s trea ted as a" unit*. rev ea ls the errors ma.de-when an­
a ly s is is based - Sn the- A ,0 ,1 , sp ecifica tio n s*
Ihe r e s u lts o f the two parts show Slaorepameies up. to
twenty percent .in the design moments* Ihe frame proves to
be underdesigned i f analysed according to the A,.O,,I , code.
' ,
STTRGDUGTOT
Object
prim ary o b jectiv e of t h i s paper i s to in v e s tig a te
th e p ercentage e:3?rdr involved l a is o la tin g ope f lo o r of a
eontinuous b u ild in g frame and t r e a ti n g every f lo o r independ e n tly ,
T h e .a p p lic a tio n of th e moment. d is tr ib u tio n concept
provided th e most d ir e c t and convenient method in determ in­
ing tills error.
H isto ry .
# e m u ltip le s to ry b u ild in g has been, u t i l i s e d f o r
many y ears in the b u ild in g h isto ry * and was the most success­
f u l s o lu tio n of th e c e n tr a lis a tio n problem and* a t the same
time.* th e b e s t use of h ig h -p ric e d land*.
H isto ry re v e a ls th a t the b u ild in g m a te ria ls used* from
th e tim e our a n c e s to rs emerged from eaves to th e present*
p lay ed d e f i n i t e l y th e most, im portant r o l e - i n construction*
Hrom th e branches and leav
/ e s t o s tr u c tu r a l s te e l and r e in fo rc ed co n c rete, from a r t and experience to modern methods
o f an a ly sin g a Structure*,.- th e y ears th a t elapsed were a
challenge, to c r e a tiv e minds*.
' fh e b u ild in g m aterials used thousands of y ears ago
l i k e stone* brick* wood and many o th e rs ■-**■ th en in a prim­
i t i v e form
a r e s t i l l used.
fh© development- Of the co nverter by-Hehry' Hessemer
in E n g la n d a n d o f th e open-hearth Iw n a e e hy W illiam
Siemens i n M en lea between 1800 and 1870'» made p o s sib le
the p ro d u ctio n of a w te h i& l whose p ro p e rtie s could be
properly bent w i l e d and e&uld be oaa# and r o lle d !Saito da*
sired shapes * lBie new mater M l# k#ew&: a@. st&el# is one of
the g re a te st achievements M building hi story <= ' S teel has
contributed a m aterial th a t enables not only speedy strength,r ig id ity and 'lig h tn ess of e re c tio n s^ but also ra p id ity of
dem olition# Another m aterial^ e q u a lly im portant^ m s .u s e d
■:
•.; •
■ ..
..
'
by t h e $gyptlone and ^ o m n ere^ ly in the h isto r y o f t&oapi
s tr u c tlo n i Sn. a massive- form and in the n in e te e n th century
re in fo rc e d w ith steel*, was adapted a s one o f th e major
b u ild in g materials.*.
B iis m a te ria l i s known a s ' s?co u crete5J?
and w ith , s te e l in t Be1Sody- of th e Cbhcrete* known a s
^ rein fo rced concrete**
As f h r a$- d esig n i s -concerned* i n ' t w e a rly ; yearA
' .I
:
a rt and eeperlenoe replaced ob% utatlons * !Bbe ##&t and
l i n t e l c o n s tru c tio n 8 th a t was s ta r te d in Egypt and P e rs ia
became th e most w idely uged method o f construction,, h a ter,
the Simple supported beam Idee* based on the peat and
I in t e i sta rted te grow*, m u ltip le story b u ild in gs were
li-.' "* )m teiclaie'a% methbde. b& A r # L % # % i ^ o n s t r u b b K ^
Tby
sons* Iho«» HeT* p, W
Sq-, - Ib id p# S
published by fab# Wiiey and
oil these ,simple supported beam p rin cip les ana the
s t a t i b a i l r 'deterM nate an a ly sis«,
^a.tb&.y&Q# 1015%
&# Maaey Asreloped the wide+.
Slope p a f le o tla # MetbsA wbiSb pnorl&Q# a& eeabom*
I o a l a ssig n , eoEtparea t o th e p netiens ones, w ith th e he*
q u ire d th e o r e tic a l a n a ly s is of th e s t a t ib a lly In d e tem $na te trams.*
EdVi/ever<S; th e te d io u s d esig n , re q u irin g th e
s o lu tio n o f numerous simultaneous equations* was tod- eom*
p lic a te d compared to th e a% a% sl# Of determ inate structures,*
A new technique^ based on p re rio u s th e o rie s^ lik e ' th e lb eo ry
of H sian a tio n , was IntrodUoed by Hardy c ro ss i n 1958»
This
new tech n iq u e, Mown a s wThe Moment H istrib U tlon^was adopted
by th e engineers?
Then the American Concrete institute.* with amorous
assumptions* made the analysis Of a reinforced concrete
frame comparatively shorter*, ana th e A»l*s*Q* rea& ## the
work In w ired in s te e l design?
Importance
A rtic le VOS o f th e AWvlo specifications s ta te s wThe
l i r e load may be considered to be ,applied only to the flo o r’
■under consideration*, end the f a r ends of the columns may be
assumed as
. #&e'l#erta&&@' of Obin-ObealO' 1# to-investigate how ''
much e rro r is involved in th e analysis' of a frame- it- # e
i s aesigned aocoz-iing to t h is A r tic le fGS e f the
sp s e i f Ih a t lone ' ' '
' ■■■■■
'
■ ■'• ■
P apt
a
-
'
:
A .pl.aa r i m o f ■a continuous re in fo rc e d concrete
frame i s shown in Fig* I*
$he se c tio n 1-1 of t h i s frame
i s to he am l^ z eg according to HoCsI 0 s p e c ific a tio n s „
given lo a d s I
l i v e lo ad f o r Roof, 50 pounds p er square fo o t
l i v e load f o r a l l o ther f lo o r s ^ 180 pounds pep
square f o o t
. . .
S p e c ific a tio n s
th e SB day* u ltim a te stren g th o f concrete i s
250G pounds p er square inch.
Wo way s la b s a re to he used i n th e analysis*
o u tlin e o f th e Procedure follow ed
A*
$he. th ic k n e ss Of the s l a t e Ie determ ined
B»
OOlumnS a re designed
O4 Beams ■a re d esig n ed ,
l a Fig* 8 a l l j o in ts are. l e t t e r e d ;
columns and
beams are numbered and they .w ill be re fe rre d to in t h is
:
manner#
Design of; .slab#.
The design of sla b s fo r roof and a l l other flo o r s fa
shown fa fa b le s %end # »
She two governing fa c to r s that
have to be given consideration in the design ere as follows*
a 6 The minimum th ic k n e ss to s a t i s f y d e fle c tio n
■14-
r
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Si
32,
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U r
P la n View
S e c tio n I - I
F ig . I
P la n V ie w and S e c tio n I - I of th e Frame to be
A nalyzed.
15
X ^#5-
fig . s
I d e n t if ic a t io n o f th e Members to be A nalyzed.
I
—1 6 »
TABLE I :
P7EStGN OF l?OOF 3LA05
5 1 £ SZ,
si
5 Z
L. r f o p* f
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L.
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L. L = ^ O
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5 - 2.0 '
m - I
= [20 + 20 _ ±L I '3 ^fTfTo
L
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w lir r< M - ^ o '
t -s: f - 5 5 in.
Mo m^n4
Cf
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co< (. (or
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17.0 0
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d , I M
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n
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in = - 4
t - f fi v 2o - .^L- I ,z * 1^ . ? ° °
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w Li fe r e Kl = 5"£>'
t = 5 -^ 4 m
C 1 co e.f.
C 2.
c o e {-(}ci e n i s
(or Necp Mom. erf Conf.
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MicJapon
M((JspO0
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M -j =
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M o m e n t
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1
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W=
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M2 -
1-92
fn . kips
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2.
lops
P2.51
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4 2 in .
fnclnes
#
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in. kips.
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-I? TABLE
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Fog
FLOORS
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M,
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for
Me<^. M o m
a f d i s c . f Jc je
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fo s .
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M i
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M
ii
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ii
M om
d-i7 T
Listf-
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fn. k i p s
4-4 9 o
=
y. y
-
S =
2 .0 0
=
coe. f ^ ic i e n ^
fo r
I
I
M1
ii
N e ^ . M o m . a"f c o n f t f ^ e
Fos
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M 1J s jy p r j
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=
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M orjT —
d = I M
xl K b
-
in.
rn = . 4 -
fn.
co< z(.
M
2 ^ .2 0
c \S 5 u m tr d
M ie/spon
I W 5 Z
=
p s f{-
fv[ o i n t n t
C1
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' (fst
"t
=
=
4-
/ S z 2 -2 0
—. F z
/
in .
in. pou .
in .
requirem ents of th e s p e c if ic a tio n s
P_e
minimum th ick n ess to s a t i s f i ' th e design
moment: requirem ents.
f
The design moments shown In th e ta b le s f o r the s la b s a re
obtained i n accordance w ith the s p e c if ic a tio n s .
The max­
imum moments fo r -two ad jac en t s la b s are computed based
on the moment c o e f f ic ie n ts given
by
th e JU-G,1» code.
These: moments are balanced' assuming th a t W ' supporting
beam between the two adjacent slabs takes one-third of
the unbalanced moment and the remaining twc^thirds bal*
aneed based on the s t if f n e s s of the slab s,
00sign of Columns?
With the determined' th ic k n e s s of slabs- a very close ' /
approximation of the loads on the commas of the frame la made.
These loads and the a e sig # of the columns ere show# i n Tables
111 ana # 4 . a l l columns e r e .designed'.based on e x la i load"
lng conditions*
The dimensions of columns Cl through 04
a re determined by th e ISO square inches minimum a re a .require­
ment of the s p e c ific a tio n s ^
The dimensions, of Columns OS'
through 01#/ a f t e r being determined* based on the lo a d s,
are a r b itr a r ily increased two inches in each d irectio n to
s a t is f y th e bending .moments^
The design,though not a tho#f
ough one, la sa tisfa cto ry , fbr the purpose,
being to determine th e
th e a n a ly s is .
Th* mere object
s t if f n e s s o f the columns needed In
19-
TABLE III : PESlGN OE COLUMNS
Loacis
Gl
on
GI - G8
Loads
R o o f 5} a h Si
Assum ed
Bi
A s s u m e d ci'irders
on
C5
I. Floof- Slot? S I
Assu med
B4Assumed nirdcrs
Loadt Eor'
Cl
2 4.
^
i
3 .0
1 Cl
I.f
12oop
eki,s
Assumecf
Assumed
Cf
Min
Use
Assumed
"try 10 a
|?= . o l
IZ col
L oads on
Si x s z .
girders
BI JJ BZ
CZ
-52
^
A. F lo o r
F
J ao A
I.
5 8 IC
Silaho
4
51 jj SZ
T
ArGd required by S p e c s . \ 2 o
4.
8
C (0
Assumed
BA
Assumed direfers
CG
Lo ad for
GZ
Lf
<
lt.
ICue I2 '' f o r CS
K
CS IJ tn h c o I Ac CF
dimensions i n c r e a s e d Z inches in
bcNi directions do accoflnT forbendino
Mom.
UsG IZzzX I4Z/ for G5 % CS
CZ
identical i c
z
C a r r y mcj t a p .
NlL ^ N (I ? - . 0 3 4 )
N = 7 2 * »I okI col.
R ta u m zd A = -J2 -eo.Jo = 4-5 5 in
Cl iJ#nTi Co I -fo CA
UsG IoV IZ' ^or Gland c 4
on
50
8?
p = .01
N = A [-Igff t .^zfy p ] = rJ ooA
Recjii'ired
A = Az
m
Min. £o(. clim<ns/on5 Io'a IZ
Loads
Z
4
07
Ih a v e s h1 o rIt column
? 0 ’° *
j ^ IO '- ^ iz- = IZ i ^ IGafor SL rf
assumed
45
G^
Iry I O k. I Z
Lon^ Co I.
Assumed
Retjuiracl
£»l*"
Z
4
2
F®
107 *
Ni = i£ I - 11 4-K
p=. .0 2 5
A — 114 -so. 94 -
1Zi
C7 iden dicq I f 0 C (0
(dsZ
*
IZZZ> I 4 Z/for GG f C7
-n
TA0 LE IV
•.
PESlGNOF
Lood^ o n
Load)
Loads
As> u m t
Assumfe
COLUMNS
C9
Loads on
Uoqda on
Loods for
Loads from
for
Assum 6 p - . 0 Z 2 Y
Assu me 5 liort Column
N = A C ^4-0 + 5 6 0 )
Required A- =■ 2.10 ^ cJ. in.
dl(y
C 12.
C9 onJ
69
^
IC 7
I 7 6 K-
Assu me p -=. . 0 2 y
Assume
skord column
M = A- ( ^ 4 o +■400 )
Recyuired A = 1 8 7 sep m
cm
i den "fi Cd/ Ao c IO
Use
19^ 17" f o r
Use
i d e n f i c a l -fo Cl^
I ( c \ 17' for- c i 5 f
Loods on
CIO
06
Z . Floor
CIO
I5 4>K
55
189 K
K-
p = .OZi
S borf Column
|4 \
C 15
Loa Js f o r
c9
Loo d a from -I. Floor
for C f]
^rom 2. Floor
M = A ( 4o ¥ 556,)
Rfecjuirtd A =. 15"*7 s^j. in.
C I2 idfenli'co I f o
C9
d5E
C 9 - C/6
Jf.
Loads f o r
loa ds from
C I4
Clo
d. f l o o r
<7
G9
Z4-F ^
Assume p = .0255
Assume 5 Iiorf C o l u m n
Nl = A [ A-o -¥ 4 o f )
Reejiui're-d A = Z^-T s ^ - ’in
Ciy
CU
ci6
Use
1
denfica I i~o
17L
(9
fo r
CL14C 14-
C iy
Design o f Beamsi
Theye i s no d irect method fttf which th e dim ensions of
th e haems can he determined*
flie hash end most convenient
one i s to assume th e dimensions; and* a f t e r th e an aly sis, is.
completes check the assumed, dimensions * With the follow*Ing te n ta tiv e he am dimensions i n inches
BI and
B8
ID &18
B8
E&, B&, B9* #9*
8 %1#
BlOand 318
18 %8&
3 $ , 3 8 and B l l
1 0 %M
The a n a ly s is i s made hy Moment D is trih h tio n applied to
is o la te d flo o rs*
4#
The information- needed i s as follows*
S tif f n e s s f a c to r s f o r a l l members
B« D is trib u tio n fa c to rs f o r a l l jo in ts
Ge
Fisted end moments f o r a l l beams*
■Stiffness fa c to r s I
The s t i f f n e s s f a c to r , commonly known as k*values is.
the r a tio o f the moment of i n e r t i a to th e le n g th of the
member*
Thus Ic f o r member AB equals
I
%A& *
3^A & 3 *
'
I
*
'
"3 # AG 2 l$S/&0 % 18 *
80,0 in&
The s t i f f n e s s f a c t o r f o r a l l th e member#, are given below*
obtained as: th e s flffn e s S f a c to r fo r 43 was. computed in
th e example
F=BSr--
Member
.
BI and B3
80*2
PB '
88,-1
a l , 48% G8 and 04
18
84, 86* B?* 89, 810 and BlB
67
B&, 89* and B ll
83 (['0
06% 06* G# aa& 08
8&#a
09 and OlB
B2,&
010 and o i l
61*8
* 015 and 016
54,5
014 and 015
81*0
D is trib u tio n facto rs'?
B&sed 6%, th e s t i f f n e s s factcxs? k obtained in th e pre->
Seding p arag rap h ? th e d is tr ib u tio n factors fo r a l l member#
a t a l l jo in ts a re determ ined a s fo llo w s i
fhe d istrib u tio n f a c to r s fo r the member Bi* a t.th e
jo in t ® is
^4
where
represents the sum o f the k
TE
values for a l l members meeting at. the j o i n t , or the d is*
trib u tio n fa cto r M a t jo in t $
is ,
**
In a s im ila r way, d i s t r i b u ti o n fa c to rs f o r a l l mem­
b e rs a t a l l jo in ts were determ ined and a re given below t
CV .
3:oint
Member
• ■- A
A
.B
•B
B'
’ S -'
. %
01
Bi
BI
B# .
(58 '
Ol
Y„ <3!5 .
M
BA
. f.
02
.
OB
. f
BB
OB
- %
09
a '
B?
■ K
■B
B?
OB
%
019
B
I
Be
P
OO
019
•P
BlO
P
BlO
a
GlO
B
014
B
n
BH
lo in t
B
. B
. *
a
G
B;
I
S
&
G
#
0
#
W
.MM'
M
M
t
S
T
e
«
8
a '
.
04
BB
BS - . '
B8
OS
'04
ds BB
. BG
OS
07 ^
BB
08
GlS
B9 ' .
B9
07
O il
B8
018
016
B18
'813
O il
OlS
BH
S7^
SB#
48$&
88#
18#
88#
. $6#
SS#
%Wa
IS#
19#
19#
86#
65#
W
14#
SI#
14#
81#
SS#
44#
SO#
80#
06#
11#
To sim p lify th e niomelit d is tr ib u tio n p rao ess when symmetri-r
d s l lo ad in g co n d itio n s e x is t # d sin c e the f lo o r s are
^symmetricai^^an o th er s e t o f d is tr ib u tio n f a c to r s a re ob*
ta in e d fo r th e i n t e r i o r jo in ts ,
ih e e x te r io r j o i n t s do n o t
d i f f e r a t all*
“^ W e o ^ r b f Modern
Vo X r^ f7 ^ y ™ 1 7 ^ ^
arintef,# p u b lish ed by th e Macmillan Oo*, •
pp,ll& *
11 9*
Member
> - '■
•1
BI
CC
. BB
IsMo •
CO
SB
OS
B8
1#
■E ’
E
E
E
B4
CC
OS
#&
#
.0
O
0"
BC
os.
CV
BC
OGg
W
80#
10^,
%
E
%.
. %
cy
06
ClC
38
M
M
M
M
BC
CV
CU
#8
IB fa
R
B
B
B
- mo
CIO
Cl4
mi
B
^ '
B
m&
C ll
C ls
BH
08$
84$
88$
c$-
d o in t
. B
B
. 'B
■
Member
46$6
44$&
SS#
Fixed Snd Moments"'
th e re a r e th re e p a r ts combined to g if e th e t o t a l
fix ed end moments
a»: Fixed Snd moment due to dead load o f the beam'
Th . Fixed End moment'due "to'Sead ■load o f slab -per
AnO+I* sp e o ifio a tions a r t i c l e . #15.
.6* Fixed End moment due to l i v e lo ad on th e flo o r
p e r AsCeIo s p e c lfio a tio n a a r t i e l e 815*
Fixed end moments f o r ro o f member' w ill always in ­
clude a l l th re e p a r ts ' a s l i r e load cannot be o m itte d «
4»
1Wixed End Moment C o e ffle le n fa $$%■ Beams o f Uniform.
Cross Section** by &,
Cesterlin g, C ivil Engineer
lng vol* 4» Wa 1C* PBf C48KC#f
fW a ll otbse floor members the ■
e l# #
SM momemta w ill
aHcw&9b1&'%%%P@#*9*#11 W. lboiudea o# G&attoa
o p .tw '
$lee&
^B aisiena #o&88 te Beoa&ee d,#
at
pee#'# of
These t&&e$ p a # # #3#
etmetWOf
#embiae& t& g&# f&#&a
eaa moments f e e e i$ Wmhem i& f a b le %
ia ssi SleiSsstisaE
.
fo Obtaib-Ibe. a # e i 0 &.memebta' g e r %b# 'beams, th e fix e d
e%a 'memehte &fe aistflbhted lit fables
tweegh jcscg&t.
IRXwB;4&%nsa^gr'dLarO#&gpk*aa\a^3j6*33&& eh#r% 3# f i g , -04 gxgx&etel; f #
th e ro o f .whebe- 1 1 # load, 0 abbot h e om itted ,from @#y a # h # WOo p e ra tio n s of. b a le s e ib i m # e # # ane- performed:*
f t i e 1#»
portent to n o te th a t ffom new on moments producing compress
slon -at th e top and- te n sio n at. th e bottom of a beam w i l l be
referred to as .positive- moWnt#*.
..-
Jitomonts prohuolng.
■
'
■
. ■
......................
- t W a |# at.-%&' t # - oh#
WHWA Hf- s #W&
w i l l be re fe rr e d t o as negative moments^
The sig n convention followed in balancing moments is.
a r b i t r a r i l y oho sen c A clocM ’i s e moment is. given, a ■^+8Bigng
and a eounteroiooln-vi.se moment^ a
**' sign,,
These..signs
w i l l be o f ,help i n defermtining w hether 6 moment i s ' po#&,
Mre.- or negative^'- referring He- th e a b e # .paragraphs - .'.
fn -part
.
.
• -
th@ le e # n g he#*
d ltio n e a re so chosen to give mam.lmW& p ositive moments
-2 6 "MfHE
V
F. E. M .
c •
- F i x E P EMp
^or
Fo £
J L tu I^ - -L 1 6 8 x Z o ^ x i z
IZ
IZ
X
-LwIz -
6 7
a
2 0 a Z c L x IZ
—
I y . OO
=
7 2. 7. OO
X
%
9 <3 x Zo X Z o 2-X I 2 -
for
L w l z =
(7
X lV la = - L
9 <U
cH ,
L 1 2 7 *<s2 * 12IZ
W IZ =-
'
_L
96
cl
b
C
X 8 Zx ' 2
-
^
=
X
%
(or
X
j2
L w r
-
X
X Wlz
-
b
I6.O0
F E M
96
96
M
F.E.M
=
i n - ki'j>6
xJ 0 . O c
-r
6 ^ x Z o a z o 2 x 12
l o o . OO
=
Tn-^iL
i
<7
4 .
5 2 7.00
.
-
A b S r-OO
170 x Z o x 2 o 2x 1 2
=
rJ f O - O O
F.E .M .
-
\ \ J f .00
I ZOX S z X i Z
=
X
8 z x IZ
c
2o, 80
S
x
s^xun
-
4 7 . OO
96
X
7 .7 P
67 X8
in.
k.
in-kips
in-
lops
q+ b
4 -o .o o
itox
96
F- E . (/I
A 55 0 m t - J
F.E
=
m - k / -^>5
9 ?
=
TJ
i n - k/^>s
94-
for
-EwI2
96
I
c
20. 8 O
- L w I ^ = - L
2 Fo x Zo-2X |%
12
IZ
F.E.M
8 . Oo
=
T O x 8 x S z x 12.
7
96
vvIz
C>*p O . O O
=
4<5U m e-rl
F. E. M
-
9%
a
cJ
in c h - k i j z s
2 .1 ? O . OO
F.E.M
C-
Oo N P I T I O N S
96
96
F. E M
MAXIMUM
9/
=
o
MOMENTS
-
60. 0 0
i n . ki f>»
for
97
<an<j
8 IO
5dm E
d S
F.E .M
for -
90
end
P If
^am e-
as
F E M
----------------------- d -------------------
assum ed
fo r
f or
P4
p F
27
F ig . 3
••
I s o l a t e d F lo o r s f o r D esign P u rp o se s
28T A 0 /-E
v/z : M O M E N T
PI 5T £ I I^uTlOM
F£)I? I 5 < 3 L A T E P
—If4-
*
- 77
RooF
29
TA0LEVII: MOMENT PI5T i? I (I TlOW
FO lZ ISOL.fl.TE17 3 . FLOOR
PAgT o(:
A
BA
I2
BK
ZZ
+ I 42
-h2 78
-I- <72
+ loo
+
T
-+ I
+ 200
+
I O
+ I
%
«>
EF
66
-117?
+ 77?
- 4 yo
+ 29#
- 4A
+ 29
- 4
+ 2.
F E
?9
FL
20
F a
IO
FB
11
F
—4-o
+ /'7 ?
+ 3 87
- 900 - 3 o + —C (e> - 1«32
+ (A9
- 88
- 30
+ I?
- 9
— ^
— 2
i-72.9 - 3 3 ?
-184
—f
_
+ 569 - ? 6 9
K
1
-2 0 6
I-
r
7 A0 LE VIU
M O M E N T pi S T R I ^ U T i o N
FOR
iS o u A T E P
FLOOR .
!7art f?:
4 80
-598
- 1AI
4 97
-( 87
-------------------------------------------- =SL=______________________
IX : M O M E N T P ' S T K I B L I T I O N
table
FOR
ISOLATE P
a .
FLOOR
Pakt o< :
E
K
K- B
19
+ Z Z ?
P
2 . C,
4"^0(.
F
K L
L K
L F
L R
L M
T fT
4 4
I T
3 3
8
- I i T F
+ IITF
4
+
? 2 5
-
(2-4Z.
6. A L .
- 7 2 '
4
4
4-
+ 2 8 6
+
8 ?
f
/ 7 7
-
2-0
-
P
4-
I I
+
-
+ ? 9 4
- d
82.
<
L
—2 .2 .0
- 4 - 8 0
- ' 3
- z s >
-
7
—
—
I
- I f ^
4 8 8
9 9
f
2.
+ 9 o
8
—
1
- 2 3 4 .
I
- J t o
'
O
rr
- 4 o
R
1- I 6 4 -
TAgLE /
' MD M E N T
PlST K I B U TfD N
FOR ISO LATE P
2.
FLOOR
PaKt
KL
I9
K
+2.23
+ 9?
+ 4
-H77
+3o<o +F4F
-Z90
+ VT + iFo
+ 6?
- 27
+
17
- 4
+ I
+ I
+Z
+287 +780 -F7 I
LK LF
LR
41
' 4
71
L
+ H79
+ 327
- 700 -198 -442
+ 60
—4-^9 - ' 7 - 3 7
+ 7
- 8
- 2
- T
6
H
—
80
ML
14
+ 80
-198
-9 9
+3 I
- '7
+ 10
-+ 42 + 4 2 4738 + 182.
- 6
-142.
4-21 +Zi + 40 + 4 2
LM
14.
Md MS
/4 3 )
M
-2
+ 991 - 2.7 -482 -274
—
I
+ 79
~
I
- 7
MN
41
-425"
NM M14 N T
19
24
79
N
442.7-
+ 91
- 2 8 4 - 9 8 -134
+ 6
- 3
-31
+ 14 + 4
-3S
F
+- 9
+217 - 9 2 -127
+82 +181 -328
I
P
2
S
/ J ^
r
-r
--------------------------------------------------:____________________________________________
t a b le
>m
*.
m o m e n t
i>is
t
r i
e u
t i on
f o r
/s
o l a t e d
a.
f l o o
e.
Pact «<
'
L
K
-
PK
Z I
Pw
3T
+ 4'Z
1-4 7
+ 76
4 Z
+ Z
P(2
44
P
-1174
+ T'7
-2.2?
+ 96
-
8
+ 4
+Z9 7 + 492- - 787
ZP
? 2
ZL
2 4
RX
36
C
-4 0
+ U74
+ 248
- 4 46 - 4 3 4 - ? 3 0 —B 7
4 49
- I6 —IZ - / 8 - 3
+ 2
I
- I
4loZ( -"946 - 7 4 p -12 ^
j
W
777TTTT
R5
I6
y
T A B L E Xll : M O M El NT
Pa
PI 5TRI BUf I ON
ISOLATED
/I.
FLOOR.
r t
K
Pw
PB
4-4P
- "7?
PK
Z I
4 41% r Z 4 < , 4 T n
+ 71
t
FOR.
4
+ 45
+ 2.
4 487 +291
-24 5
+ 89
L
R P
50
GX
Z3
34
G
4H7T
+ 258
- 4 o 6 -3M
-
+ 4-
+ Z
-
-I 6
Z
-
Z
-+IOpZ - 3 2 9
W
rrrrrrr
K.S
SR
Sm
II
II
23
- ao
+ 80
- 4 87 - 1 4 9
+ 44
-25
- 7
-
+ IZ
- ?
+ 4
- i
-T 'T
-Zog
X
5Y
34
6
Sr
3o
-42y
T N
TZ
Zl
3 F
T
+ 425"
TS
44-
- Tf
*25
+ 4-5
-IO
-778
RL
+94 +i TZ +124
-108
4
+?9
+z4
+4-0 + 3 4
+122 +192
-575
+ 45
- Z ' f - 1 0 2 -171
+ 17
- 8
+282
r
- 4
- 7
- t o y -177
ZL
in the ex terion beam ana a t the; same time give maximum
negative Bioments in the, ©xtevion beams,; where the extern
iqr-beams meet the e x t e r i # ' 'ee%##s^
in p a rt
# a loading: e e n a itia h e , a re ekeeen to
give maximum n eg a tiv e moments fo r both ex te r io r ana in* .
te r io r beams where both beams m eet.the in t e r io r . ooInmnw
#h@ ma&dmwm p o s itiv e momonts are obtained by eimpi#
s t a t ic s .from, the balencea end moments' obtained "in part
’a" and the loads on.the beams*
the
Won example# to Obtain
p o s it iv e moment &#
.# 6 9 in ch k ip s &t B .and
(hieing tension at the tq p t
W
bn& # m # t 8'"Wre
ln # k # a at
p%#»
By tak in g moments around p
the rea ctio n a t . S i s determined} and by taking moments
a t the oe&tap of tko bean# the p o s itiv e # m # t i s &#&#*!Md*
This p o s itiv e mommt a t th e O m te r o f th e b e a m #
V6S in ch k ip s and fo r a l l p ra etio a l purposes i s the max*
imw p o s itiv e moment in the beam,*
The mozimm positive morneate
the laterlo# %eem$
a#e &ot OOBeWfea* beeauee the ln te fie r beapte, hevlag a
shert span of eight fe e t ^ w ill never pro t o e p ositive
momenta to be the gpveWn&ag # a l # moment* fo r the teama*
Both mazimtim positive ana negative moments for. a l l
beams given, in inehes kips are. show below an# the design
moments are Ohosen whieh w ill determine the beam dimensions
Beam Maz0NegoMom0 Maz0P o s itoMom0
8B8
894
88G
889
881
BBO
981
884
981
1058
BOB
1058
Bi
BB
B8
B4
BS
BO
B?
m
B9
BlO
BH
BlB
518
f'■'%
618
894
618
886
551
886
951
854
961
1058
898
1088
■wPr
618
V68
»
768
688
<=,.
688
688
BG8
The design moments f o r the beams a # need- in the fo l­
lowing design where the determined dimensions are com­
pared'w ith the assumed ones.*
Design Moment M # § fokjbd2 where f c “ ' 0*4S f ?o ,
k % O040
j,
I #
b is the width of the beam and d is
tha distance.to the center of reinforcing steel*
’ Beam Bi assumed dimensions
M*
$1 8 , 0 9 0 * b a 1 1 , #8 %
10
t
10
$ # IGyQ in<
Seam BS assumed damans 1021s .
M & 294,000 , b « B, ds •« 294,000
196 t>
Beam-' B4 assumed dlmensio'jis
I * BSO,000
4 *
"1 2 %' '24 ■
bu #. iws , d&
v*. -*» ~SSOjg
p OOO
^ Lt
d *
18+? la*
10 % %4
Beam. B5 assumed dimensions:
% * 6$i,ooo,: b ^ 1 0 , a^
13*6 in* {
$ 4 & 15*4 in ,
-
L:
'
■Beam Bi? assumed .dimensions
M * 951,000, %/* 12, ds
+»
s
.12 % 2:4
d
Beam BB assumed dim ensions
.
M * 854*000, b S 10» df *
2% 00p, ^
Beam BlO assumed dimensions
I nOSB4OOO
M * 1052,000, b # 1 2 ,
#
10 %. ;i4
a .* 11,91%,
12 z
a
208,000, "b #' IG 9 d2 s
24
- - SI *2 in ,
10 % 14
Beam BH assumed dimensions
MS
80*1 in .
2
a
-
1 0 ,3 in .
Beam BS id e n tic a l to Bi
Beam B0' id e n tic a l to B4
Beam B9 id e n tic a l to B?
Beam B. 12 id e n tic a l to B10,
r
A
' *
‘ •■
.study of th e r equired beam dimensions shows that;
t h e p dim ensions',are f o r a l l p r a c t ic a l purposes very close
to the assumed .ones.*,- as th e »a» dimensions -are only the
d ista n c e to th e c e n te r o f reinforcem ent and not the t o t a l
depth of th e beams, ■ The assumed dimensions; w ill be used
in th e second p a r t of th e paper where th e frame, i s
am iyged. ae a s in g le u n it ,
& 39-
BAB# I&
M a ly s is
mg, Frame a s a ^inglS IM it
MproaQh
,
convenieiit; loads are assumed stiela th a t p applied,
to one "beam a t a time produce, fix ed end moments equal
to 1000 i&tih pounds and i f th ese fix e d end moments' a re
halanded s e p a ra te ly fo r th e e n t i r e frame, th e "balanced
moments f o r fix e d end moments o f any magnitude can he
ooMUted a t any p la c e in the frame "by proportion=,
such, fix e d end moments are assumed^ and th e f i n a l
balanced moments a re in d ic a te d i n Tables %li% through
ZZiy.
Based on th e r e s u l t s , th e f i n a l maximum negative
moments f o r the beams are obtained b y combining s p e c ific
fa v o rab le lo ad in g co n d itio n s in Tables 2£l? through XXlZl
A lso, th e end moments, which in t u r n .w i l l give maximum
p o s itiv e moments by sim ple s t a t i c s as shown on page 35
are o b tain ed by combining d e sira b le loading conditions
in Tables tg $ and XIXl»; I t is obvious th a t f o r every
beam th re e maximum moments a re computed | two n eg ativ e
a t the two ends and a p o s itiv e moment Very, OlOee to the
ce n te r..
However, a g a in p o s itiv e moments f o r th e i n te r s
l o r beams a re em itted as in the f i r s t p a r t of th e anal­
ysis*
In T ab le XlXS which is a summary of the r e s u l t s of
T A 9 L E Xlll
; SAUW eECTM O M EN TS
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TH E F R A M E . L O A P E P
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+
-
I
K
E F
AA
CR
5 <A
2
I
3 <T
+Ct’fG) - 2 3 3 -42$yz>7.7 Z .
TABLE XXV : FINAL MOMENTS WUEN FRAME ISTtfEATED AS
FI NAL
LoA-D ON
BI
MOMENTS
F inal
i
5_
Fo a.
Moment
At
A
69-0
-L
/00
- 2l
69-0
7&
1177
IOO
B4
Final Momeni At
6
= - 2 9 2 .0 0
-LL
-
=
J l-
4. p
t
10
IOo
=
70.p
U .
Mom en ts
Fo R E?3
Ar
D
Mo m e n t s
Load on Final
Bi
52.
63
6 TO
'
IOO
Fo
R
wIoment
C p
by
OO
e
Ar
Ar
- -
7^8 00
00
+ HO. OO
I. Go
-
At
C
= T I I0. OQ
JZJ. fo.
- -
5 7 .OO
= +
3 7 5 •OO
IOO
J2_ eyo
loo
loo
INCH- K IfS
- 707.17
IOO
3y.
=
Moment
LLcp
J_
" 7?
6>7 00
+ 7 0 1 17
C
F inal
IOO
T5T
——
52
LL Gp
So
Ho. 9 o
SyiTi mefrv
+ 57/
LLL p
IOO '
-L 100
- +-
= -+ 11.77
,N fW -K lP s
00
+ 7 4 0 .0 0
= T I G>. 40
1177
IOO
T3?
- 3 7 1.
Final
p
loo
I7.00
-
6, / p .
Ioo
= -
BL,
F INA-L
S 1N6 LE UNIT
BI
ICO
B%
A
loo
1175"
80
= +
- -h
11 .7 7
I. Co
i I- 7 1
2 96,. 59“
I N c H-
KIfS
-+
2 9 6 .9 7
b 3-
Xxvi
TABLE
F
i n
a
l
m
F I N A L M O M E N rs> W H E N F R A M E
o
Load on
m
F
BI
e
n
t
F
s
M
i n a l
o
o
m
.
r
e
n
0
E
— — I. ^o
G-TO
I OO
-4-5" G- 11y-y
I OO
54
= -
777
go
— G?T°
loo
-5_ G-^o
|0O
— -T
+
1 9 . To
ilL
too
117T
- +-
7 9 0 .0 0
80
%
= +
4 7.00
57
too
5U
U
57
JU -
l
IOo
IOO
IiTT
-
II7T
a
-
5 4 .
2^i_
2 0
100
-LL
IOO
INCH - KlPS
i
n
a
l
m
o
m
e
n
t
F
s
o
.
r
At
f
i n
a
l
LOAD ON
m
o
F
m
e
n
i n a l
t
s
M
f
o
m
o
e
-
+ T0 -lJ s
M7T
=.
4
I N C H -
+
K i P S
1 2 . 9 0
9 2 . 3 .
9
t
Ar
Ar
7 4 9 - 0 0
F
=t
<3
_
9 2 7 .9 0
-t-
F
Z
9.
20
i n a l
M
o
m
e
n
At
t
L i - GTo
G7
+
7
- 80
loo
——
IOO
7. 80
-
2
9
. 2
0
100
54
&7
too
,17?
B9
88.7
IOo
flo
= -
7 1 8.00
« _
2 . 10
88.7
10 0
Ao
=
2 TM
|/7 T
T= +-
? I8.00
+
,2.90
too
67
-LL H 7 7
-*•
7. | o
ICO
B
9
-LL
0
S?
r
n
117?"
'
J?y SYmmt^rv
+
M
A l G-To
loo
B I
749.00
BG-
-
2 £>.00
- 5?. 2.0
69
F
UNIT
Moment A t F
Fi n a l
sr — 91.00
JOO
B?
ASA SINGLE
TREATEP
4
AT
t
S
=
"7T
—
12 9 o
IO O
inch
- ki ps
- 3iA-. 6»0
IN-KlPS
-F
916.60
-54
i AB LE XKyiI '■ FI NAL M O M E N T S W U E n F R A M E
fi nal
Loa-P ON
E-I
B5
M
P oe
MOMENTS
F inal Moment
iil_
4o o
6^0
At
l<
+
=
-
.=- -
1177
iitF
-=. -
IO- 2* & O
=,
—
Bf
_!_
/00
nrr
=
-
•=.
-
loo
r 2.
loo
lJL 6.70
^
_
t-fo
4 . JO
3-1
loo
6 70
=
+
20.2o
62.20
Zj-tIOO
M /?
=.
-T
2 7 - 00
l-l
I 00
II 7
rr-f-
I 2.. P O
78.4
iitE
=
u 7s '
S . /
11.
e,
O
IOO
•41.S' flo
loo
3 .S
IOO
• Q
/O O
- 810.87
I N - K -IPS
Mo m e n t s
F o e
Kl
09
+ 8 1 0 . 87
922.00
+
— 4.
33.20
rr
1. 2 0
B I2
f i nal
L
Ce, f j 8 . OO
BE
B Io
^t
IOO
B.C.
5T-9
lo o
Final Moment
44-70
loo
B7
S IN G L E UNIT
B7
-
■Lg.— 6.70
IOO
7
15 T R E A T E D A S A
1177
= -i- 4 I. 2 . 0
II7S
=r
9. 4 0
--------------------------
IfJ-KiPS
-4-
-4 o L j , 4 - o
SyPime-ITy
A t
M
— -4 o4j. 4o
*
-
55 -
TA6LE XJCvm: FINAL MOME NT ^ WWfN FRAME 15 T g E A T E P
o
a
d
o n
F
inal
for
b
Moment At
L
8
Final
8.
loo
B4JL L
so
-*=
—
Qo
.
J lL
o
m
e n
H76
t
At
M
= +
9.4o
6 0
ioo
l o o
B 4,
M
03
O
L
moments
Il
+
final
AS A SINGLE U N i T
L & _
1/7-7"
w
| , 7 T
=
—
A-O
9 .
l o o
67
65
' 9
-
2
2
?
.
O O
IOO
9 1 . 2
I 0
8 0
-
-
O o
O
91-2
60
-
T 7 ? . OO
M l f)
=
+
-=
-t
IOO
69
19
l oo
g IO
9
1177
OO
1 0
. y0
loo
BII
I I
8 0
•sr
• 6
O
I O O
& 12.
_ 2
_
M
=
7 9
—
*• I
loo
So
-
—
1 0 . 7 0
IOO
i n c h
- K
i
-
P S
\
3 1 7 . 7 0
I N C W -
Kl PS
4- 7 1 7 . 70
-do
—5 6 —
table
Mix
F in a l
LOAD ON
B7
: F inal
momentaw w en
m o m e n t s
F inal
is
TREATED
FoR
1175
B l O AT
-
too
P
-
T inal M o m e n t
. 80
89
6 io
8
117E
-
[OO
-
tJ L
117 7
— T
1177
T
-
-
8 3 8 .8 0
B 1 2.
by
+
8 5 8 . 8 0
>
-I
H
f o r
1177
/W-KiPS
+
R
a t
■= -v
30-4loo
INCH- - Kl PS
Fo r . b i o
1177
loo
m o m e n t s
u n it
-1 -1 .
100
7 7 5 .0 0
B/l
f in a l
AS A SINGLE
8 IO
fo r
Mo m e n t
fram e
Jd- 8 0
8. 2.0
IO^O-OO
+
24.4-0
1 /0 1 .4 -0
S ym m eiry
At
S
—
I IOl . 4 o
«
B 4
F or.
Fin a l m o m e n t
• 4IOO
B i/
Fod
B H AT
/ , 7*7
R.
P inal Mo m e n t
B 6,
•8
loo
B-i o
<3.9
IOO
a i i
9 9 .6
IO o
— —
S
h
77
-C +-
4 .7 0
u-8IDC
11 7 f
■=. -h
9. 4 0
6
=
1.00
0
+
l.o o
I DO
-c- —
1177
h
7<7
-= —
80
9.4-0
1 6 /1 .0 0
C
vT1
0
0
£ 9
8 0
H
I
J - 2 I.
too
B h At
l 4 l ..
100
£ 7
E S
Fo r
O
L o a d on
m o m e n t s
It
I
FIN A L
& 12.
INCH - K i Pd
-
. 10
•
9 3 6
IOO
80
=
T
1 J.O O
13.9
I0 a
M 7f
C-V
I ( o j ■0 °
4
2 -7 5 .1 0
TA 8 LE XXX.
' EN D M o M E NT" 5 p o £ MAKi
mum
Po s i t i v e
Co
nditions
Foe. BI
LoAP ON
Mo m e n t
A
At
Moment
At
8
Bi
- 2.9 2 . 0 0
+
J4o.00
62,
+
+ .fo
+-
2-0. S O
S3
—
I 3 .0 0
—
A 7 . 00
N/e<j Iec "f
65
1wci4 -KiPS
Po a
6^
Mo m e n t
-
B o i.y o
At
—
inc.i4-K.ips
G
I.
4- 4 94.. Oo
Mom En t
P
Ar
BI
-
82,
N(-<j Uc'f
83
—
84
-
5137.
OO
-t
B Co
-
57
2.0
—
Be
NE (ec-i
inch, C-1P5
FoR
B3
_
At
5 . 80
I•
4-
Fo
p
>
B 4,
2-4.00
+
1 9 .7 0
790.
OO
S> 2*.
Dy
ini c H- ic 1PS
4
rJ A C o .
Mo me n t
At
C.
—4
^ O t . 5-3
9 4 .0 0
Sym m e Iry
Mo m e n t
At
444- Co Ig 4.
Oo
5 . 4-0
by 5Ymm e "j"rY
MoMEN T
Foe
9l.oo
6 C A.
80
MoM EkT
At
G
-
74 6 .5 0
-----------------------------------------------T A B L E X<XI : E N D
FOR.
---------------------------- —----- -------------------------------------
MOMENTS
FoK
M A X IM U M
PO SITIV E
CO N D ITIO N S
£> 7
Lo A P ok
Moment
At
K.
B-I
M oment
At
L
4
t i . 70
-
8.|o
4-
Ufccj | f c c f
-
B3
65
-
1. 9 o
2 0 . z. O
3 . 10
6 7
—
ET8 . 0 0
+
9 2 2 . OO
B e
-
i ( . 7 5
—
4»6? . 0 0
Ni
B-Il
1M C l V
FoR
B IO
-
K l
PS
MOMENT
(fccf
— (0 (0 ( 0 .
At
At
-
5. 9 0
-f
I 0 30.00
2, 4 . 8 0
7.00
INCM - K i P5
by
6 9
-
7 7 0. 60
4
9 9 5 .
FO
s y tr> t n c i r y
M om ent
At
Mo m e n t
n|
4
B 12
50
5 .6 o
77? . 0 0
B 12
8 9 7
K
Uecj I e c f
B io
F o e
M oment
9 . 4-0
B 8
FoR
-+
5
F7
+
B4
1
3 .9 0
f y
A t
M
_
15
897.
sym m fcfry
M o m e n t
At
T
-V
7 7 0 . 60
M o MENT
A r
5
-
9 9 5". 50
-5 9 table xxxji
B eam
: Geeoe
in
AT IN G ONE
Pe R c t N T fosiTWE Moment ^Bcent
Le f t End
Error
Riii-MT E n J>
EBEoR-
%B?
^o 5
34.
444
749
928
14
909
* 34
B7
*B7
.7
4. T
II. 5
Zo
4.0
M o me n t s
10. Z
—
-
_
—
1 S- 8
444
3. 5
390
in
THE
17 8
ONES
IN CU - K l P S
4 •0
O B T Al N E
A CONTINUOUS
I
_
—
53 3
838
"
3.
_
78 8
Al? E
1. 0
ES 3
253
3 3
1.0
438
IIOI
i7- 8
Ai» AN AL y Z-EP AS
E -
444
4, 38
444
Zo 8
1032.
II OI
M OM ieN TS
_
Zo
1 0 5 7,
j se
233
10 . 5
610
Io-S
13
743
9 31
10 4 3
234
3'7
48Z
13 .8
1045
« PU
NOT
-
749
ZoS
VV
—
11. 2
BH
* Tnese
18- Z
9Z?
Si 7
4 BIZ
I/. Z
74,3
444
I 1. I
S3&
-
7o 4
II. I
? Sio
_
14
314
820
931
_
371
331
5 14
444
69
* 69
Bio
-
4 I5
9 Z3
234
13
.7
U .3
as
# PB
f$
7o4
294
JI4
8 zo
482
8 1o
BlZ
4.5
E rror
294-
3?i
<ey
,
FEAME
Moment A t
?2S
♦ B4-
TLooR of - A
Percent
294294
* B 2.
l
Moment At
314371
Bi
x BI
BZ
5o
P
W W E N
STRUCTURE
330
TWE
F R A M E
3 .1
Part I asicl Part Pp6 the th ree morneatg fo r each he am ob­
tain ed by both methods are tabulated and the d iscrapan cles
between the moments obtained by the two methods
are expressed as perdent errors based on the ta ln es
obtained by Part I I 6 which i s assumed'to be more ao«
curate „
Zn analyzing a continuous fram e, a number of a s­
sumptions bare to be made..
The assum ptions made are
Of major im peftaiide throughout th e analysis-;,, and -the
f i n a l r e s u l t s must be in te rp re te d on th e b a s is of these
assum ptions^
-
I n f a r t - I .th e assu m p tio n s made Could be summ arised .
•as follows:
Xn
.
The l i r e load, was considered to be ap p lied .
Only to the floor under consideration* ana
th e f o r ends Of th e columns .were .assumed as
fixed#
B9.
The frame under c o n sid e ra tio n was- analyzed
in two dim ensions w hile a c tu a lly a continuous
frame is e three-dimensional structure#
8*.
giabs were to bare no e ffe c t on the rig id ity
of th e frames:
dtt
5 ».
Garry-o^er factors ware take# as one-half s
■
Distribution factors-; were based on th e s t i f f -
nee# of rectangularamd&bers,'
Ay
eidesway was o # t ,t # 4 ; -
y,
Footings were t r e a t e d 'a s fix e d .
8* .
B#lU al settlemenb of foundations was. omitted,
9f
,tflOw
nett considered^
These eame aeew&tio&B were uae& &a P a r t 3% 6%oe#t
f o r th e f i r s t one, which was s u b s titu te d hy a c tu a l eona itio n s s
T h erefo re? th e r e s u l t s show th e e r r o r o f the
f i r s t assum ption made. in analyzing th e frame according
to th e -AeOvXo spec ! f l o a t Ions,
The r e s u l t s undoubtedly, would be in flu en ce d by th e
a c tu a l co n d itio n s i f th e s e c o n d itio n s were to re p la c e '
th e assumed ones'^ . Thie-,* in-tur% :. re q u ire s th e l n r e s t l f
g atio n ' of the ,fe e t-o f'th e : assump'tiO'ne--add t h e i r " e ffe c t
OE -the f in a l, results.^ Howerer.,^.: the- hW hef of indeterm *
I n a te i f a c to r s is- so la rg e th a t' the, a n a ly sis though n o t
impossibles-wou ld be a very com plicated one«
. The e r ro rs computed show d iscre p an cies up to twenty
p ercen t in ■some p a r ts of th e structure-* and th e se dis*
CrepanCies are- n o t' immaterial;* .but th ere-■i s one m ajor ,
f a c to r to be. given co n sid eratio n b e fo re reaching ■any
conclusions.from th e s e resu lts*
The allowable stre sse s given by-the sp ecificatio n s
a re used when -.all the' .assumptions' .made agree with the
ones used* i f Ihe analysis- follows- the sp ecifIcationsx
These allow able s tre sse s make provisions for the' assumed
Conditions*
A ' study of Table 3CI2E1I ,shoT/s. t h a t th e ■moment s obrtai&@8 ty th e a n a ly s is in P a r t ' # a re greater.#,'w ith one
except io n -/th a n th e moments Tornid in P a rt I /
SoweYer4,
t h i s .does not n e c e s s a rily mean, t h a t the "beam dimensions
have to be ehangea, ear if a i l fram e m re to be analysed
by th e more exact method, followed, i n Bart. H 4Z th e .allows
able s tr e s s e s of th e s p e c if i e a t io n s would have been .mod­
i f i e d aeeo rd in g ly end -probably in e re a SOdsAvhich#. in
terms'^ would b r ih $ 'th e - h e s n ite e l a s e r to the r e s u l t s eb&
ta in e d by th e method follow ed in Part. I*
Gmsa m o. GGmmTm
Gay* c* SE, agd Parke# &»?, ISSO*' . '*&GazBI%
Bg[AJEd3 .AND S#mOD3
OlP AaoaimOTlWl, GOI^TmOT^e^, * JOkB Wiley
and S o n s,. I n e «, * N.Y»
G rinter jr l /
, 1949,*. lf5rI1HEOET OF MODEM SlEBL STRHOlHEES
Tols IXt Macmillan Gp.*, HsT5
Peabody* m*. 1.990t "THE REGM OF WBEDRGBD GONGRETE
STM0TWE8," Jokn Wiley .-ekd" Sons, %o+% N^Ts
"■' vn j ,
1 0 3 O l 5)
M O NTA NA ST A T E U N IV E R S IT Y L IB R A R IE S
Illilililillll
762 100 3095 2
N378
-------------c o p . 2_________ 1 0 3 0 1 9
author
__B o y a c i r Petm
T,T^ r ? ? r i n v o l Yed i n i s o l a t i n g
OI10 f l OQr—* ma fo T d e s i f m mi*rmr»€»£k<s
d a te d u e
b o r r o w e r s na m e
xV
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!A l,'
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MAR I
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M 3 / 8
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