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Ieutr a1 Axis

The Ventral Axis of a homogeneous Lean —- Let us teLe a
wooden beam slung between txo sup orts at its ends and put on it
sufficient weight at the center to cause it to break. Ugon ex-
amiLation of the broken wooden beei it will be seen tlr J the bot-
tom fibres have been torn apart by stretching or tension and the
top fibres are crushed by compression.

How, it will be obvious that if the top portion of the
bean is being cruehee or ;horteneu by com oreesion anc tee oottom
portion is being stretc‘MLei or tc rn by tension then there must be
so. 1e line or point at which these stnesses chauge s? 1:, and; at
this line tLere can not be env stress because at it there is no
tendency eitim rto shorten or stretch. This line, not being

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SUUJQCD to Cpurrfibfiifln or tezision, is inan as the ”neutr; C‘Js”

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”uiie Jne liger 3L tee bee:: lfl LilCh it is situatec is 1n3 n 22
‘. . 4— . .
tie ”neutral :T,ne"

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;he gosition of the neutral axis is aegcnurnt on the
change from co; rescion to tension atre s 33f tie mange in the
stress frov he one LGt to the ctner is grewugl tnrougttut tie
degth of tie We; . The greetsst cemcressicn will be in tie ts;
fibres, era this ; :th'll“ decreeses until the neutral layer is
reachec, g“ere it oiaazgcars ent’1elj. The greatest tension is in
the bottom fibres and ttis iirinishes ngards until the neutral
layer is reached, JLETH again this stress becomes zero, es she n
y the shade; fort'cr in Pi . 3.

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The 'ucertence of a knowledge of the Position of the

neutr»l l?”u? will be L; reci
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niddle of it" length ens that

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0

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roment of resistance just calculs*~€, then the ‘aap nould ?e
safe ur’er thoee leféihw confitigfie.

77. square roe is .5?* sq. in., so t”

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Sue tovgl cross-section o» t.e -Viue ut-M is l1 x w
. - a -' , 2.. ,. -‘, ., .7 - V.“ ' ,.
(assure ; in. Ior coverlnu the steel rots), so it .ill “Blkfi
”‘5“. 1}: /.(.\+ + 7" “Luca tr ‘Lrl 7'3“" 1d 3 x“ +7 ‘1 '1' “A r” 4: P 6'11/ 1“
CPL. - )0; .1. LI. , 0.. u; ‘.. O ". ( t... 1;}: ...c' 'o‘ k i u fi. L 'T. _--. A. 3." c --‘-.l0
¢hicrzths eve flxr ti TYflnwtefi.
Go t?e “wrrir” movofit 'b t“? certer ““ tle 2e;: one to
&.4
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1‘: ' = —— : c-n-z —————————————
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The Renoir wowent caused bv a safe exterral uniqir
U
‘ a . " ‘ - ' - ‘V . {\
load CI Il l1”. ler foot r41 is
* 7' rue/3‘ .r w" '7 "\
‘ l = R - ' = 17' ,C""‘-’ "’ lC“‘i‘.’ U
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(1 , :‘r‘. - 4.
= ‘..L":.,L.1'.U‘V b0‘lb.
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_ “r“ . .0...
- 1,13»? Ila/lb.

Therefore

load of 1,153 lb.

Tee-Deans —- It i

sistence to compression i
be

EJ-

overcome this difficulty

 

«-- _W---— - -‘-.— __‘—.-._.--—

fe tor of co

C
C

we er but for envenienc
teLen es 150 lb./cu. ft.

safe for

to “rovio sufficient re—

a.”

e

n the ordinary rectangular sectioned

yhere heavy losds here to be carried and so in orqer to

t] 18

fleeivned

\J

1e bee;

 

ncrete

v. w-w.--.———- --- - __'—— .——— _.—_...—._—- -

2.1 tires the

e the w ht of concrete

(2
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37
with a wide flerge to give more concrete in the top pert of
the lsrzi releIJAKE'to the :i'ifi'tifi the iUJWG e as stRHi i: Fig. 1C?
4‘, b _ :1
Ahdfiavwzqynuwaal%qye I
7/ 13»
£36
/ , /A l
4 H /7///
/751.&3
The Construction of this Tee-beam then consists of a
what is like a slab which is stiffened by a ecccrete rib o: the
uncerEZQe, or a gid>r slab cum its ribs (or Lirier) are built at

to.“~

V

D

'Liiel“,

Lil-LIL

and these ribs

. .0 1-‘ ,. . . '1. f. . .‘-. —‘~ 1,, , r~ r; l ,3 .-«~., .
garts oi tie schS (or ubimp) are elem Cclleu lee-he:.s.
'7", - .f‘, ' ‘1 ' , . r~ .55-? 1, .2. -. .-. ‘ ,- ' ,.
-OJ Te_UTTlF; to «19 1%, “lies Shaun a very nice rec-

renewnerec tnef

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. ‘ “ ' j ': "‘ ‘1‘...’ 'W' I“ -: I ' '\ , '9 .. ' .‘~ - -r- f~ r \ - . * ’-
ticn must we rerlec,em in bio resign, so cdet the t.Q CTEQS are m
g 1 r‘ 1@(1 l", hz\+ 7"] 3",? .3.’_‘ ()1‘r‘fi. Q r‘ 1‘. 31'v~lfi $1C'tf‘ 1 T". ‘3‘? ‘ 1" '. N r r
\- II." t \' ...l are _. 'v J . :eE.L-C4;_‘ C. .'..E\ .. L. O O .'.‘J-l .’e ' E - 1-; .. A L‘ {1(A Ir! J... L) - If. LLL ..LIJ (.‘.113
r‘ i . h . r\ -: .,«.- ‘r‘ ‘+ ’ . ‘ -0 '. -..' f.‘ ' - '. 1‘ .
reashreole w;r re uclrp t-e strengtn a; tre ' g . ln etier
words, the strerwth of ,Le rib fior tie slab fo: 3 oren’ h b act-
. ‘ " " fl . ”,1 (- 1"". f f‘ '1 "L r‘ “.r‘ r ‘~ V". I I '-- ‘ 1
1r; togetuer 15 e Hgl to tlot 9‘ a IQCMCL;u1aT beam 0: bredoth o
and of The same oegtn o, QTCVitiMD ire steel :bic‘ ‘oulc he uses
’ -‘ r -. 4-r ‘ - “ ~ ‘ -- «n»- «- ’ ~—‘-
in toe lar;er recchLUlar seam is HOT concentratec into tie
, ,. --o_\ 1 H1-“ '.,, ‘ ..L. ' x : ., .. ..' '2
narrow rlu. luis ingroveuent lS cumiously very econogicol ens

 

l Faber & Rowie, Reinforced Concrete Design, Vol. I

, pp. 38

co
m

is largely the cause of the economy of reinforced concrete con—
struction.
From first has been said, it is clear that a lee-bead

q

may be designed as a rectangular beam of breadth b and Ceith d.
ihoueverg :hi case rigriree-bearéndJEit have a guuxyter brcaflfifll'Qf slafiu
as their compression Lember than can he called into plav therefore
the r sistance moment should be calculated from the amount of

tension steel uses. 80 Tee-beams may Fe cclculatec from the

following formula:

where R

I I
*‘5
i .2
U"
} .J
U“
Ci
‘1)
*3
O
(D
b
3)
5%
LJ
5’
1..)
i

I
H
C

A - area of steel in sq. in.

A
,.
II

—| V , + . .
ceyth of beam in in.
, . . . . 2
IS: safe tens1le stress in steel in lb./in.
from which formula it is easy to calculate B when A, d, and fS
are known, or to calculate the area of steel needed to give a
required value for R.
how the question arises, what limits the breadth b of
the Tee-beam? The width b that can be considered as acting with
the beam will depend on circumstances, but it must not exceed
0 1‘ '0 - ' 1

either of the following:

(a) one-third of the effective span of the Tee-beam

(b) three-fourths of the distance from center to

center of the ribs of successive Tee-beams
(c) twelve times the thickness of the slab

(d) six times the width of the rib of the Tee-beam

+ . r -1 1 . . a 1 .
leasurec irom the top face of the coupresseo portion to the center
of the tensile steel

1 Faber & Bowie, Reinforced Concrete Design,

r. ~ .. _ Vol. I, pp. 38
cutnerlano & Clifford, Reinforced Concrete

N ‘ . \ . I . l ‘ rt
1165.21.5'11‘ 1).).(K‘L‘1LJ.

- ;.h

CC

VJ
To make sure that the slab will act with the beans, it
is necessarv that there shall be bars in tne slab across the beam.
These be s naturally exist when the slab is continzo s and spans

from besm to been, but if the b am in question hangers to be a

main beam (carrying only secondary beams and not slabs as well)
then such steel might not ordinarily be provided, but yet its
n
—‘ q o o o ,. o -, A. O ' . x is
accition 1s acXisacle. as a rule, 5 in. roos at 6 in. center to
3

center for the breadth b will be suitable. See Fig. 19.
gfa//%Mbd%%mv
(jgfléfihflta%CF6hmév3

F; —:
'1
I
fly, /9

Then what limits the width of rib (hr)? The nidth of rib

 

6.— 1%

 

 

d

F"

3’

 

,lg- diam»

I
.Sccaoabtyl
|

 

 

 

 

 

 

is also ligited by three considerations --

(a) It mute not be less than one-third of the bean

(b) The shear stress must not be too great. (This
will be exglained later . It can be shown from
this considerztion that the width of the rib
should not be less than -;-: where Y is load on
beam in bounds i
and d : depth in inches
and, even then, shearing reinforcement is required.
(0) If the beam is a continuous one, then, as erylained

previously (see Jigs. 15 and lGi), it has to re-

sist a negative Lending nonent over tge snogorts.
his negative moment is about equal to the posi-

l

. — - — - as. “1. '1‘. :.. -' 1‘.- I
titwezhonern;zree_ ziits J11. liffCLlelELi e

H

-.1 . ‘

that, at the suggort, the bottom of the beans is
in congression, and therefore at the support the
slab does not help. hence the beam will be too
weak in congression at the supgort, if br is made
very much less then b. This effect can be, and
often 's, overcome by increasing the oepth of the

beam near The suogort by means of haunches to the

.rv to add co:—

U

columns, but it may also be necess‘

\D

pression reinforcement and then tension reinforce-
ment will be needeo of length .3 seen in slab
over column and set yarallel to beam's length.
Even so, it will be found that these negative

moment at column supports will often determine the

minimum width of the rib.

To make sure that the comoression slab is reallv strone
.L a L;

enough, all that is necessary is to see that the percentage of

steel, calculated relative to the value of b x d, does not exceed

.675 per cent.

If it does, the safe strength of the beam would

fbe Proportionately reduced, or a larger beam would have to be useo.

The above discussion assumes that the neutral axis falls

either within
the slab. _If
concides with
then it means

in the shaded

the slab or that it concides with the bottom of

ne neutral axis neither falls within the slab nor
the bottom of the slab, but falls below the slab,
that we have not only omitted the concrete shown

area in Fig. 18 which was unstressed, but also a “art

-C»..L.
J

41
of that which was only slightly stressed in compression and so
also somewhat of use. To check up for this it is only necessary
to test whether the thickness of the slab is equal to or greater
than .36d.

If the thickness of slab is only slightly less than .36d
then the neutral axis falls below the slab and if the thickness
of slab is not less than .BOd then for such cases the amount of
concrete between the underside of the slab and the neutral axis
is so small, and the stress value there is so low, on account.
of its nearness to the neutral axis that the consequent'reouction
in the resistance of the beam to congression can be neglected in
actual calculations.l

To deal fully with the exact formulat used in the design
of a Tee-beam whose neutral axis falls below the slab is too
complicated for us to give here. however, the following approxi-
1nate method is civered for practical requirements.2

.. - . 4 . . .
ihen cs 18 smaller than 5 m as shown in Fig. 20, take ~-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 ii
m nA '1
d nA + bds SELL / l—
- Gs IfihwéuVVQnS) . ‘b
R - d -- ----0 19/46
H: ‘
r
Then C .'.: ‘ *é’
d.
d—( _.t‘i)

2 F9, 20

 

_— _‘—-. —

 

].clones, h. E., Reinforced Concrete, pp. ice-105
:3.Eaber d Bowie, Reinforced Concrete Design, Vol. I, “M 39-40

I": ‘

 

 

{‘1
C.. = ----
m bds
. m

C : (3m X ”dc:

m-—(—~—)
2

K

A : ‘
d

S
(d— ) f

2 S

where m = distance from top surface of
neutral axis
E
n : modular ratio (——9
E
A = area of steel
K : bending moment
R = radius arm
C = total compression
Cm = mean compression stress

c = maximum compressive stress in

f8 = safe tensile stress in steel
As an example of Tee—beam deSign, let us she
ous beam 20 ft. Span, carrying a 6-in. slab, the load
200 lb. per sq. ft. inclusive of dead weight, and the
being spaced 10 ft. apart.
The load per beam is : -
J = 20 x 10 x 200 = so,ooo lb.

111

57‘}.
La

m 1r' -‘. 4.1,. 1 1
4.8..4".1I.l;" one oeno

3—6'1, 'd'e h?ve : ‘-

 

senaing moment

slab to

concrete

a continu-
being

beans

= ‘0,“90 in.-lb.

ence to Table II (gage £7) s1

overall, reinforced with B-fi in.

gives a resistarce moment of
16 required.

The next stezt is to see

to carry the congression stresses

0 , OC’O i1] 0 -113 0’

whether the slab is 1i'ficient

width is °

of & ft bree

6.57 in.

roufih u,Jrox1'cticn we see

sistance moment

one-third of the eff:ective

01‘ tile I~|ee-}DQEJ)‘L O O O O O O O O O O O O O O I C O O O O O O O C
three-fourths of the disten
center to fienter of the ribs

_.ee_h|ea£‘:1000000000.0.0.000...0.0.0.000...

t' lve times the th iclzness

six times ne thickness of the rib

Of ti’le'.:_'€e- 1314513.]. ooooooooooooooooooooooo.

the smallest of these, we

nth x G in. thick.
le II sho that the berm requires
thick. lhou;h our slab is not
'thickness, this is here then com; heated

beine more thin required.

,

continuous beem has n beaming moment

I
I

s r; ;.;.:)111ent of .._ ..._: {at the 8‘11)

/
..--A

vx - 1 ,_ '
sue ort the compression is at

no
is

LT:

ailsble a

L\')

n.)

C"

(D

H.

1 U
7 .‘.-

. _
1111(13 35'}?

iiven in Uth II c~ line

5~rLJ-- .... .rH

only to
U
beam, and so does not a 91y

t1e lotiwv,

beam 20” X 8”

round rods,

more than

.4.

note the t tn e liziting

C3

, J
C+

(r‘
}_J
"n
U

CD
}J-
:1

but the re—
center
C‘.‘ .~.‘-.'\r - -
1...-..L/LJOI‘1J, be

efifi there~

 

 

ii iii

44
fore the concrete slab, which so greatly assists at the center
section, is not available for compression at the ends.

If the end of the beam were to be calculated as a rectangu-
lar one of breadth R in. and depth 19% in., its resistance mo-
ment would be

R = as x a x (19g)2 = 253,000 in.-lb.
But this would really be somewhat larger, because the percentage
of steel is considerably greater than .675 per cent.,'and there
would also be some steel on the compression side, but there is no
need here to go further with this claculstion here.

To make the beam strong enough at the support, it is
therefore desirable to increase this moment of resistance nea ly
four times, which is usually covered by doubling the depth at
the end, since it will be remembered that the resistance moment
of a beam varies with the square of the depth. Referring again
to diagram iiin Fig. 16 shows that the reverse moment near the
support dies away rapidly along the beam. Therefore the in—

creased depth at the support may also be gradually reduced form-

 

 

 

 

 

 

 

 

 

 

 

ing a haunch extending for t ;—cih“p of the span of the beam.
~§ EchIZfiflza?
t a 1'-
zr 3?: \ NY
A, \ K, . a,
. g 11
afi::::1L '
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éhc~afflwé
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x97. 2/

fl gener al rule tor nestguing the overall depth of the beau at
support is o “the +he be:m t are tuice the overall depth at
milsI‘ an, as shoun in Fig. 21.

fhe depth fr” lendth of hcunch s1nyla ee le'sure? at
anr from the edye of the colv n, as she n in tbe Pipure.

This beam shculd now as checked for the tension re1n‘orce—
ment at the top surface of the beam ‘crtss the col:;-n to see if
. . . XL
it is trot enov h to carry one negative bequn; moment m TB
t‘fire 0y tre sting the be?M sectitn as doubly reinforced heal
'“ich really is.

The arranIenent 01 th reinforcement cannot he det;r-
mined until we have consi red the question of she r.

ll-Ue11 -- In some cases beams are required ”hich
have a slab on one side only as for example those acting as

trinu'ne rs eroun

s imilar .'i urI 30s s,

‘uith a Tee-

the compressive re

section as shown i

3y the h at

SBCtl-‘Dn.

.,\

L]

d an 0 strircese, lift, or

and then it is not pos- design the beams

If it the slab in

EJ-

\ N 1“ j
s st11ce

beam becomes an ell-

€31

T1 1‘ 15' ill-

8

J-LT'

 

 

-////////
13

 

 

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o—-4k;
h———J 1

fig. 22

 

 

 

1 ‘1 - ' 7“,
one; portion. 3:

,1-

 

, r'
!

‘xi‘r

f the beam is limited to four times be thick-

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t thickness only if sgeciel extra sheer reinforce-
ment is provided to deal w'th the complicated stress that is set

up in a one-sioet flenee section.

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SUJ‘.’ .Or‘beu OI: COlU-:.-NS _L; .L La. 1.1}. 1.31;; 111 Due v; ‘LJ QLOIL- o
11_ 1 , I x ‘O , _ . ._ _'I_: _ l. .1, ‘, ~_- _, fl- 4 ’ ,_L
1— x 8 l1") V'- . Ff fl I C u f ' ‘5“: ‘J A _ L, L. J. -l {3; :\:‘_ l. L5G” (J- .‘. {)1} ..; , kt. ..L'.
‘_J

”‘ " .. L. -'-‘-~'-- ’ A " - - 1 v-r “ .’-». wxe 17,. . ”v c": A“
3110:: LClQ I, he S.“ 11. _LW'KAU L);‘.' 1:; Lila, I LAMAR '. ,i \ _(;.('j-)_,‘T3;g.l "3 .'.L‘ o .n

 

0 14. Till Te rethrefl, end the t'hle Ilsa f;Vee tn: ¢0LCDL CL
-_ “2', n - ._,~- ,. ~ (m .- ’1'
111mm] :1 OJ- b.7116 berm :‘b 51.-.,» ’ -LII. , ..memCrC—B

F' r”)

- ‘. ,yfi; .le— "f‘
2 — _ - QKJO'.
" (7

{-1 \ 1'. ' - fi_ -‘ V. 4' 1~ I - r- . v ‘ -' - . ,\ - ,V-\ A. L \
...‘tC L811]: we 18'1” en 0; the La --' 111 17101185; (3; 1L”).

_ e ‘1
‘I ~ I. ~- . _\ '1 _ '7- -v- .‘ _‘r'. C _ — q ‘ ‘ ‘0 _ , > _ ‘ ... 0‘ _I _ _ .‘y f _ J .' '1‘ '
rulerl 11?0.1 t;a}a_ea AJLl., .'e A33'c: a1191J L153 710:;e11t <3C’ -‘_w7‘e;': Le ” ‘ 4) .vt

whence ‘”0

T7

[.1 <5, 0 ” ~ f‘ p .‘_ ‘ U r- ' V" ‘. _ ‘ .
Laulrg A as u LOT ouuslee COlUflwS, Le nave

'r‘ P. v
- J C

‘i‘ _ kl.‘
"JCT ".24:

£41.) ObWJ

I!
I
Y)
Q

 

from Table VII it will Te SsCfl that the bencing moment correeroye-

 

 

Vfi '1, ,.
' ~< ““’ — . H. « r-r‘ 1"' I ":‘-. . a r r- ". \
1?; to 7*.- C.u 4e flHth ' , ni-Ch 1n our Cdze is
D 17.3
"71"“ .r ( ‘f‘ v ‘7 {W X 1‘7)
, .. .. ~~4~~~ A» ~-‘~' w _.rv c-r - -
140‘ o “ - 217,:JKIO lac-1.00
f
l7.d
7"— x 1 ‘J \ ‘l ‘. ‘4‘ r ‘ ‘ _I' “ - . "I F: ‘ -. V
, AOJ the stress n the \lung fine to wenelpb e xiveu
.L
?d

_ 1,- *~_ A- 1 , . _,‘
he UGTQLML moment

L
d = the Gieyeter of column (

I '-
F’)
‘J
*3
(D
O
(u
n}
H
1‘
*5
"J
’:__J

v . '.-. .»‘ . 4 '.~ 1
1L3; 1c ween u 48 tee Le-

(H
CL
(0
F"
”D
x.)
o

I = 'he Loment of inerti

£17

or in our case

 

 

lb“
5)
H)

‘1 1‘ ,’ 1". “r. T3. ' ‘I _— _ _J --, I H ~r ~' (-
l bauer 6 DOale, gel OICEM Concrete ue51;n, v31. i, gt. 150

277,500 x 14

 

so

9
a23 lb./in.‘

'— 0.0000000...
:1; y €1,1IC -.
_. ‘{
Che oirect strt, ‘19 b0 lo'd is a
A“;
l“ COG . , . 2
: ”.’- oooooooooooooooooz ('1': lD./ll’lo

a‘o

 

a . 2 +
Adding gives a total = so? lb./in.
There 3 is the reaction and A is the total area of concrete and
steel in the column, as given in Table II.

Th? calculation for the foregoing column was for the

top floor, that is, for one which StOJgeu at the beam it su;;ert-

ed. Such a column is subjected to greater bending stresses thané‘
column in a loJer story which also runs up above the beam it
carries, because in that case the bending monent from the beam is

the leniith

V

carrfieg gartly by of column above the bean and partly

by the column below it.

Let us consider an outside column 14 in. X la in. that
is Sipporting a standard Tee—bean 18 in. x 8 in. X 20 ft. span,
carrying 20,000 lb. distributed load at roof level, and also
supporting a similar beam and load at next floor, 12 ft 6 in.
lower, a smmilar beam and load 12 ft. 6 in. lower still, and so on.

low the stresses in the column of the top floor will be exactly as

calculated above (asSLning hat the roof dead loaning intensity is

same as floor loading). hut, as an example, those in the floor

next lower to the top floor will now be calculated.

Column carries 10,000 lb. from roof level

Column carries l0,000 lb. from floor level

g... r..-

Total

I
+ lhese

stresses do not include those due to wind pressure, which
{JrOUlC—‘l

be important and greatest near the ground.

Frcm Tasle III on gage 86 the equivalent area of a

11 'n. X 11 in. column is given as 230 sq. in. ;““70 re the

N
.._—10
.3
’D
O
C
(.0
d
H
m
U‘
H-
(I)
j
)
..)
D
H

‘1“ p C C I (-3 r- n A '1 _ n _J. _r

f h : 144L— : 3n ‘w to ‘ptmfipo “Wt 'l‘ Q"1QPDPCS OP
--OIJ D _AU .1J‘-' v-5.) ‘.)4 - V 4’ IJKA k) ‘E4 5.; KJ.~.~ 4- 4b.. ....
r
J:(\’
‘ - -~ . ‘ I»-—‘ v" .’j 1 ”\ - u. ’L (x "‘ r.“ V 'l"~ .‘.. l‘". ,r-I‘
the column is Made no 01 two rgrbm, One inove the lloor, and

... 1, J." - r1r ..° 1,. '17- x: ‘ n __’
one belch the lloor. iahint h as o as beiore, t1w m1,

0 K {N
-pfi — -\ 1 .- f‘ ~ .d; . .‘ d — L: /\
a, above tn” . nor - c X - —— - lu7ok2
an
- vx.
" (3&0
”#1 ._1 . -1 -'1 , I, _ n L L, ._ '1 ['f ”(j
to below the fLoor — o X ”a... - lo7.Cs

 

:_: llil . 2":
v ‘ x r- P r ""l r‘ -f1 - ‘ . .11... .'. - 4. ‘. '3’ 1‘ '3' ' ' 1‘
netce tie tot;1 a3 as elfectin; the JOlub oetueen the

column and the floor Leam ecuals 515.;1, whenie

 

From Table VII on page 98 the mouent factor at the Joint
due to this is .058 TL and the bendirr mtment 18,
H = .008 X 20,000 X 20 X 12
= 31;,600 in.-1h.
As stated previously, half of this moment is carried by
the upper length of column, and half by the lower len th, so that

the column under the first floor below the top floor (roof ) 011v

r—’.
TD

C.PT--

(‘0

 

ny1‘ ‘ a, . A- . I"
Lhe stress one to the 12en: :19 is
“‘3'? 1E1,” ’ “.'.(W V 3,4. 2
g“ = 3.1-:01- = 278 loo/in
L’J t—l :‘C U,uh§':)
so that the La 1um stress there is 278 + 97 = BPS lb./in.
1" w ' ~ r:-~.'~~ (\‘* v r 1‘ ' ’ — r--' 1,. ‘ "O
grow the Blamyle suohn above, it #111 be seen that Jhlle
-LT : .‘. ‘ :- r- . -1. . ' ~ ' -
toe cireCt stress is oouble (as the lower coluxn carries tuo

instead of

\ w, - :-' . .‘
one; tue bend in: stress

'—

If .9 13’1_rc-c:+'1_ the. SJL)1“F?E_‘SQQ for

the rect 1o”er lloor, ue shall get,

. <2(‘..(‘r*fl 1 . 2
LlI‘E’CL. tress ="+-+-:’;--=-- = 13.10./1n.

recs Cue to bendir‘ Moment = 2.3 l1»./in.

 

l 0.1.18.1 “208 1-13. [’11,] o .

From this, it 311] be seen that in outside colunns the
stresses are often 'rootest in the top fltor or under the roof,
an» that the sect on of the outer colugn reiuired for the to;
floor bill also be stron; enough for several tiers no n. It
i EIIVEJWXAJEDUS, inierefknne, to Links tlmatlut 1 glu. 'the seam:
size on all floors for a builting of not gore tuan four to si
stories in height, for the reason that the c as ant section
enables the column moulds to be useL a;3in glieh is often a

ore i ortant cotsiCerativn than the sevxr cf a {Eu 1 ches of
cvrocw°etxa 11r \ff. Irrigfl‘ ifiwe sjecfiyioil 5*? tise (x)lit;u.

- ”1-(3

T‘ _ _'
get- I"-
" “H u

the Interior Columns --

oolunns, the bending it: nt generally tlayso less i VO?‘Clt
fart. It will be note} that the dead load is noic goiu; to
cause any b {Cir soments in t~e column, since the read lowo is
balanced. She only bending moments on the iytsrior ccluen ill
be the live lo ad .hen the yanel on one si.e is 1o Gen an» that
on the other is unloaueu as shown in wig. 38. Eherefcre, in
'Ial1e VIII, I is the live load only whereas for Table VII, J is

'the sum of

eflection

1
q ...v
:1 1

'en'1

live lo

pg

.1 I“ "T \ (I '- ~"‘
‘r- L » .LO .3. 5: 1‘0 LLUC 6-: Ll

<1 in; the co 11.11111] .

ll

Begging moments on irtericr colnnns 35; he SQLBtlQHS
_ o - . o - ... -: q . ‘ . ,— - i A. . .‘
neVlecteo witncmt “nert TlSi Wfille to no so in outer columns is
' V ' k7:
verv c rvpr»mg.

Afilfielam/ Afiifielamd #4AdeZbaa’

 

 

 

 

\

7/?0 5/005, me ff/{é’ /0oa{°a’
fig 36

r“. . , v ‘ 4 .- , '. * 1“ '
.-::e FEURPE‘J. ‘,.i.*:.*-;;,ii I'. ,- ' " 1-1.01’ CO.u;.:;

 

75/23: gag/75, Cam/0r a/I/aaaé'a’

‘ TJ“ I - - n r.- ‘ .‘- - \ ‘ r‘ " . ’- 'fi '1 .4 ., " t“~ ‘- r.“‘ " $31“ " " " ‘ i ‘
ulven . _L p 1 ...- ne (3 9E: S :4“ .‘.r to Stat»? 117‘: 67?; If m : L-j ; l‘T'Lll- ._€:_.1E311L O. L... Le
U U V

vertical Evr: Inf tte literal binding in the column seetion. As

,w ' “51'.r7 1. j: ,1.,_., ..‘\ ' , ..-~,, 7,.” .’o -.. .n . ~-

SilC.Jl 13 s11;. 13:, 'tila ci£{_1€i1 (5;; If: time CCM_JUIRJgtJ.:OImJ cl :PelJl-
.‘. " ‘ _.,_I‘. 1 . ‘ -. W‘ '1 f. ‘_ . a “a _ _ 1' _. _1’ r‘ ‘ _1_ ‘1 '11 < _ _1_1' ‘J _' 'Vfi' _
..L OI‘CQU (123111-411 by L c; .‘.L 5,1. . 111. U 1" "L; 1.938 :10;le8 . [X.‘.L€.L‘. bil€.b Q '9 .1 L:

‘1 't 1 . ' ‘ ‘ 1‘. fl -v V 1 -‘ . ‘ ‘. < f'. . \ .‘ . -- ‘ . 4‘ —: l- , --/ r. .. \
170.:s :xre ;;eru3rzillwr M£;€C.1lr;'LQ f3: :3.. 111. :g; tL;e a.;.kdcc_a (13;.

It xill We noticefi thqt the rOes are uleced near the

.‘

- . _:~. ‘9 _‘ '1 f _|_ K r“ _;_ 1}~ ‘ -. ‘ ’_ ~. 7 4 -\ -\~ “4 ' - . ‘. ‘ I“ ‘—
eCi-j GS OL trim COJJLLLI] re. one-1" bllaih tr)..€-:-1"GS the: Center. lne realm:

4.1 ' ' , 1. 1 , 4.1.. F .1...‘ ,‘ _c- .u. 1 ‘ ’ -- ‘ _' .. ,_ .2 ' ,_. _ '
TfOI‘ ““13 7i: MECflMSG tflfézm3licn Ol LAN: POLfi gm. spinelr;l.;"to
A I
...t, r\ “1" “f “t ' _. . - ~ r w ~ - 'f‘ i‘} ' ‘ - _. “ .‘ t ‘ f c ‘.
tc;+‘>.e IlllJ Ell; ellsion nuts-1.01]. .3511“ OC‘31._11‘. ' 11.1.».‘(4‘ Khi‘tl- JL‘L.) ’ -1-«, ‘5 (.1](_1|k

t
'tension exists onl

iiiet the rods are tlecec. It should he noticeo elso twat as the

f: a r- ."\ I‘ _ r- ---' T - w :5 r' .- ~ -3 . —. . - r '1 _ ‘, .._ .- .A _ ' _
wals ere i_,l«a.<.‘.eu U93? tne ecge Lnu are in generel vex; lOHQ in

... 3n .’1. v'\r\~f‘| .'.-'I‘ ...- .7 ...,‘w . ‘ _L'r ~ , y? ’f‘ U _‘r4‘_ I _ ‘_ ‘ '1 _v '_.-|'\
Caul;arlsoL to cneln dllneter bgej ”mule le eltrelelr llgwle to
'1 .‘l F1 : ‘ ('I'J‘ " r-O 4- ‘.r—\ r‘\ '1 f‘ ’ -. -— H. —‘ . a . 1,,— . .0 f .A _. _ q.‘
rMLCLle, anu s. bursting the smell coverlnb sLin oi concrete

EITNJNQ them en?” frog the core ox the column and thus allowinS

-L '1 l -, v-1--: \
r it. lo i,reMent tnls

)

‘1 'I‘ .‘.\ 1 -- .. __' ‘ -v'~.- 1 ‘ \
tne rocs to I,-1_1c.-.le Outfl'er-s (no so (_.e._tro

"" -: '1‘} 1 r5 - 1 " . ‘ v ~ r--~ ‘l -O 1" ’ A ‘ "3 “ ‘3 ' 1 q -" r '3 "
the vertlcel TObE c “e .[lt-flw 11’] by -.ecfn, Cl L'J.]1‘_._Jli'-=S ($3 5.;10‘..n in

o
C
o
I"
F J
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,4

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C
O
C
(“F

Ib'
H.
:1
1—1.
‘3'
'15
{0+

rouse roos, ans occur at stout C in. centers in the column, an;

a ‘ . -J— n . ‘~ .1 f
Wmlfl&l TBlHL’?C€mjnb UL?: swoulu

‘nou. 4’ Imare Tfl1sn :4 LGI‘<38TfiL. roI' Less 1J1 n {3.5 Lifl“ cern;. of“u.e

7:, ‘A -. . 1 u. v- "A A v r- — «.4- 3 " ,_ -‘ -. r. - q r .~ ‘ -. 1". 1 - —. ~ . A r ‘ \
;--€’:l 0:11-; .: UUI‘ Kip! L;lC;.*.l T's‘CL 1:1”: 111:8 SCH-1341*: ‘v"'-H“1--Iip£
l"~ 4' 1 ‘1 .4‘ ": w -\ .K ’. 1 r -,- v c- N ~4“ ' ' q,“ - ‘ ': "‘ '1 " R I“ a — .
ET‘B all on? o M: 1:6“; -,‘::._,~:..=‘U.r , who were e49 '* 1"” .t. LI”: Lop A “$111-, C:

“iig‘xsula nos be eifective in reve:ot wi1j the rods in the
midole of the faces from bursting outulrcs, since consiceraflie
goveaent ould take wlsce before the binning could become effec—
tive. inerefore limittwrzl lmi u”invs l€"e to he uses rs indicateu
in (J’LC‘_LL'I‘?J.L (L) in .311". 3'7.

{mother Iorn oi reinxorcexenc for columns is the spiral
Jiniinw indie? ea in Fir. 37 (c). This was first thoroughly

1 .. x u . . W. .,

'ateq by Eons. Co-s;oere. bgiral binning consioerably

u re: ¢1e11s the concrete by ureventin; it from bulging uhen the

 

+ There is no raticnsl method of dete1u Hui the size of the

L—I.

01-091 rod t1 be used :tor a la: teral tie A ~czfe rule

. L
to follox is to ure 3 ber of such Ciameter oust t r
its section is not less than 2 oer cent. of the sectio

c'1e lonL_ itudinsl T81 niorcenent held in glece My t 'i

:4
7“
(I-
T
.-.-I

«D O
C
'rJ

Lutullanfll |.;.. ..

$.4:« -"_-,._.. 1 -9, ,1 _‘0 N .;-“.. . ,~ 4—,
Te L1; .3. .‘1 I- i 3‘; Ilrg:.— -L-S “I. '\rl1" i1.) )9 S1\J.“'-A‘C‘1‘-t) Oi egyr‘ LIL or "d 3‘. ”far .

H rs " - 'I‘ -u ,7. (~ ~ A .‘-. - ‘1 - ’1 .'fi . ‘ 4' -' x
as 01 : structure above ground -- In bulé bgofl

rJ

‘Lq‘ (S \ n-.- "r- r“ -r .‘. ‘1 ',‘r ...». r'{‘1 “t. “-1 w '0‘: . .‘I .1— ? 'ny— '\
toe wylls ere L;lgil- lJ t,e n:tUte 1. -onb'b iill1r— in set men

3
1
«.1 A. {.._x

L;

‘~ ‘ t‘ . ‘. /"4‘.“" I" 1 V ‘. 2‘ ~1‘ 1 ~"."‘-, ’. ‘ ~ '1’) 'i 1'" ‘ 4:. ~ (‘2; - ‘A ”‘1‘ ¢\'-"\ '7 '- ' '. ~.'~~I-
:e Izrgrlll WGJ-» .qli-C-t-T-Efln; 1:-€—§l.11..-E?l b ('1. one .13": .8 win, glib 1.10 ILL-I Dz: o

"L A - "" Tr . ’ . ~ ' -. - ~ —‘ 1‘ a « -.. 1 ‘ " “ v r: -. 'V. l' I » “
StreuLtu is rec:ireo «scatse t ese Laiels cereli LCL as a screen
4' V‘ " 'J'fi‘ - ..\ I‘ ‘ v .‘. v' ”1"": J'Tltw'1 “- - 'x-s - r'zlw
DO 1’». Q L? OUT; (A 1e we 9t} 1817' 0 U 33193." 441:; 5; {ti LT...;.1.WL’1L_'. , b! 1 *L‘. t; e Lizzie lb 1-. f5."

be of any thickness not less oflan » ”s. end it is r:re on,o Hare
than 6 in. is refluireo when they ere not losden that is when all
loses qua'trs s jiflrxf Ciractj¢r‘to the fizgxnxnfla of the stinurmire.
Each panel in sny external wall is gensrflly designed to sefcly

resist a horizontcl wine greasure of at least 30 lb./ft. assum-

ing thst this gressure 1s ectin; unitwrmlo

n-V

f1
‘1

over the area of one
panel from either side. It should be said that the Jamel must

be strong enouvh to rzsist tressure outxc‘:

I (3 1.
.-. L. . v... x-.. . u -»L.,

r)
U)

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\10 T”? ‘6 z-‘-:€ I. '31" 11.2.6 5 :31.) blur] ti); L. QCCUi‘L, L 13 one --9<.‘.. ..il“ 5:.- _1_'_: t: L;
‘
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0': 1 ." ‘ . “'1 ‘ . if ‘v f, f 1.1- ‘ , ._ f; , , ' ' ' ~ ' . \. ‘1~1_~ Lu . ' = a
:1. £111.14 _L.']_ «111-14- ;4 - ,le . ac- sits to ll)... .Lor .,rc_:,=.,1_: u L. . -r
_ L.‘ \_..~ A. U
- _ ‘ .. _.-‘ — . O 4- .'- ‘1 I I - Q '1 : '1
\f‘ P w '5 r ‘ '7."1' r r .‘. a 1 rr- - 3 . §
L2: , 188% L" I c '6‘? 1- .4; E: 1' c--s~v (L 4-11:; o b! F: 1-1. 1 nil e sue :1 J.-L 1—
J
7 r (‘7 , q r r ‘IL A ' 'I' f ( " uq -: ,'-~ -.~ ' 3 I‘ v u- "- “'4 ‘7 , - fir .' r r
1“ 7 ”“4 “40 us“: Lu. NJ: u' '- lt‘f. .- 1C . i o ...».Lo 63 out? ‘4 £21-02-
: .‘.. .1. 1. 3 3 _.l, I" . '\5 _ ‘1 .1“ "\ ‘_ 3‘ I. a 'r‘ ‘1 A .‘.. -'.. '7 7L 7' q ‘1 . ‘Q J v ' f\ _A '-‘ . . .
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.5 , ‘. ...1 ..J- ' - .I .V -"
r-. (.'1 v» -- '1 ‘ "',»"' 1 m - W ~~- , 1- -- r ’1
“Ids... L/C-L’... ...DE, Jupntil ..lJ . f_ {1.1091,} ILHL'I‘l "Chap.

‘- V
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0 1o , j 1‘ _,] I — *1 _ 1 _ _' r‘ r '
' 5‘ ‘ *z‘. ‘ ' 1 \ ' D ’I ‘ 1 ‘
la: +9191.“ 6 1 ' 9:} _t :1 g). £—' -- 1”-“ ,_ ‘-* i _ _ v..'_-- ._ . ,v 7, Is ._ -_ m
L’ 7‘ V » r 7 L
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81f”) ‘V tui t L; H ’r' . “J 1 ’1'. 'J P 2:. . I 1-..‘12': v- .. L JOU .Lu kn.

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ff .'.: lg.-. trill-2.x - e ,1“. I ,1 .f J 1 1:” -. ”my .--:, (.'.-.41: Men ..I(,(: mm,” H:
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