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Ala YS Te OF AL UNSW! UPTRICAL
PPIN’ O.CRED CONCH LTE
&i.Cn
This trereat)e fe resvectfully sublsitted

to the Civil Th tarering Peomrtment

hicrigen Arricvultvrrl ‘Ccltere

Aen es ontem for the Cerree of

Pershelor of SCci-nce

June 9, 1679
TnHesiS
 

Porevwore

Tvevic lize to @exycress ry anorrecisaticn te Mr. VY. BintzZz

‘

City Frpineer fer the City cf Tensirg Tor “is sesistarce, and
eilso Trofessor Veccer ard Trefieecr Allen of the Civil
Engireering Terertr«ec4 of the tichigan Acrienlture] Collere.

for thier eld given to tre euthor.

1O1G6%5
prt Ter Ry
Pyr ara varee ¢

Heol, Vol. #. cr weinforcec ccr-ccte.
HOLL s-a Johnson. Corerste Orgpinervs! Eandbook.
we locim, Gréephic Statics,

Hone, £<. Toretise on Arches,
(4)

The following rapes Cro71l with the sreivsis
of en uneyretric¢sl reinforced concrete arch, The arch is
one of tuo thet form the imin eupeert of Elm ®treet
Pricge of Tensing,, Wichigan,

The bricre wes ceeienec Ly YY. Pintz new
City Engiresrr of Iircing, The bricce wae bvrilt hr

7. larshell ance Son cf Crarc Réaoices Turing the verr cf

Tre outtor bLevware trtirectec in the bricre

reis the rcrch beasrure be porkedA on the

v
Vv -

cnc vertec to rral

pricpge threnrt) cut the ecnetruction es Cereral Sunerentean-

Cent, arc beeruse cf bis tetrest fia reinferecec conercte

The bricse consists in tye sein cf two
RC'-O'' srehes with cn eloatic pier, the erches are of
retrforcec cererste,. Tie roncerate use wee a T3 234
mixture. Tie steel vsec was cbhtrirec from the Carraicfre
CLeel Company arc wes theretcre rece steel. Vert of

the crevel wee cbtaired rron Tattic Creck, *hat of tre

local ;ite Leins reicot. The corevs*@ vas nixec on c7
Sice of the river anc sas *wvensnorteé by reere cf carts

to where Lt ars vented,
A thirce of esch arch wee pourec rt a tixe, thus -«* hing

of crvch yreciic*l’y three persrsic erchea, tre concrete
was put in lesyere ovo r the @ntire etretech thve rreventire

unecual settlerert cf the falsevork, the cererets
4

"as well ter>-erd erounc the steel in ercet to Insure

s gocd bore, Turine the nrocess of nourtng the tro

errohese vere LullnesceR off of the certre cf the pier

so it ves only neoessery to work on cre arch rt - tine,
The victh cf tte arck is 42°-3" ere

cf ecfcerelk, ti.> tottl sicth of the cicewelt)

~9

~

‘eing 81-3", There sre neste tireice of the spoerncre?
well eennsetirg the sicerslk to tre arch whicl takes

care cf the erv'tlever effect cf the uelk.

The eleveticn st t** crenmn ig T2C.00, the

"

elevation at the “iphect. pcint of *** intraccse i
T290,00 rehire a9 thichrecs of the erch rine st the

crown cf 7.2%3' or TS". Tr > thictrese at the ebuterm rt
soringirg line is €'-.", thre clevettion et the abuterert
Brrincine line isIII,45 -ckine - rice of T7,55',

The ere> fies 2 three centered curve, tre reius

being shown or blue nrint No, 2, The Cleterce from the

frrincirg line (cutstce) to the erorvn point is 398 ,

we
ce
a oa
¢]
i)
b
C3)
a
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crf
’
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Oy
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rs
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Y
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short of beine 28 erretiriael] erch,
In @rstysing *hts orech the nethod

o

tet tee eutror firet used iv ounce in Fool vol. 2

of Reinforecrc Concrete, this nethod is pert of the

elastic theortie,. Irsete'@ of taking the totel losc,

unite boscs were taken st cefirite pointe, The first
»

thing that was cone wes to fret the I civisions, this

wes Cone by the frachicsl methoc, The unite loacs

were then pleced at the center of gravity of these

divisions ond merments for a@ lord at esch secticn were

then founc about the crown gecticn.,

As the author workec these thru
sccorcing te tke formulas he found thst the only ve lue
that cane cut es it shoulc was H, , the values of
Vo were allricht for half of the srchn but they then
became tooirreruler, the values of M, were negative
for the first three civisicns ard t:ey then startec to
incresse end kept increzsing over the rer-ining vart
of the arch. All of these vslues when plotted shouleé
show rerculer curves and should Cecres#3e to zero
st e#rch springing lire.

Wy comrcutetions were checked over *bout
fifteen tives but no mistake eculc be found, as the

time wos cettirg short the avthor then turned to the
mf

grephicel solution «? the arch, The method used in Hool
end Johngon's Concrete Engineers Honc Pocock nes first
tried kur the line of turust fell belon the arch. As
there ere a ni’ licn Funiculars polygons to @ groblen
there te cnly one trat titLs any case, The one that

had to fit the etsn cof the unsyustriccel arch wes to

pase the polygon thru three points, tre tyo sprirgline

line: anc tha ereir, The reathod used is cn the follcnine

&
QM
at c'. Then Tot srl BIA perresert the perctiona of tre

forces to tie left cf bh, aetire thru the scintsa brnc a

ry

res eetfully,. Feint C' is eorron to all forne anlrrors

tom of >t

Barnes. ard vsoirt tS ec ron to

for tre siven ors

pli force volyoms for tre foraes to the Left os bd.

From the ceirts Ct ered Tl, crew the lines resrectively

*.
-~

4

paicvlle® to se ( tre line cmnectinge cf t+ 4 piven pat rts

w.

are the civicirg 1 58 @orressonctineg ta tee closing

etrirce

cf the recutrec firtevlar pelyfon, ard there inter

a)

cetion
Cort cetersdve te o> pels ierthis pclibor. “tth tris
pole C , so7merce et a, anc crey the recutredc funteulor
poelroon, which must race thro tls three fier roirts

@, bh, Cye or, if the pole G is cn the lire C'O , the

>. $ ~rVeur wo 4 vo v. 4 - £ 5
funjiculer nelyran noch :31se thru the roirts a and ec

>
we
ny
3

?)

pte
rs
p—te
ce
—dle
™
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3
—>
-
‘x
ry
Wd
am)

» te funteulsr relrren wust

Nite :- This page should
Tolliow the wext
"Tf. TT
a wal Ca

V~ . s ~~ 4 ? ™~ ' vy . 7 ’ $ - v
‘ The creblen ic te trae tbpe Punievler Tolycon
threugh trree civen points, the tuo enmrincires lines orc

‘se Crowne

The verticsl losd lire rerresernts in we-
nituce end cireecticn a system of forces which #re ‘he
eeirhts of the Ciffttrert Civittors of the recuced lad
line certure erf rectine thru trere center of previty,

Take corr nole Of, snc crow tre raye, Conm-

%
7
3
vd
pute

re at mam cereterat te. Punteuitr sc.yronm anc cc:

tie veolveon by crewirs the coher aw rey, Prem the pole
O' craw the Civicirge ray C'Cc' cuttine the ecnilitrant
Ch tte fepossyet C8 then “Cle c CTA re wre ants tha

ten proert tin

tno rerattiors rhose Lire of acticrs ere ec! arc cla,

anc whic! cessthrougch «¢ znd 2@ respectfully, Now Crew

the Lire 7 end A which in this case is vertical, which
represente the ecuilibrant of the forces to the left, of
be Throurh b Craw the Line Eb! verallet to [TA , connect
the points » bt, aré the ncoints 2 or@ b bry the lines

strin

@b' sré sb, whi mes cf the funicular

cr)

4, ere tre chosing

polyson for the forces to theleft cf b. Throush O', drew

the Civicirg rey Of PB! ceitiel to ad! cutting the load line
el uCIFICATIONS

Dead Toads,

The cead losac shall consist of ‘he computed
weight of the material veed in the construction. In
cetermining weights fhe following units will oe
arsumed.

Pewerests ( inclucing bese) 130 # / sq, ft.

Reinforcec Concrete T50 # / sq. ft,
Perth fill 100 # / sqf ft.
Crevel end Broken satcne 130 # / Sq. it,

Live loads,
Whichever of the follow ng¢ livel@wds es
will give the mavyiunm stresses,
A. Concentrated live lescs,
Yotor trucks of the followirg ci-ensions anc
weights occupying #8 much of tre riscrry as je necessary

for urxiur stresses,

Totel yeigrnt 40,000 2d8.
Welght on rear axl es £8,000 "
Distance bet een axies Te ft,

Ficth of tresd of resFfr
wheels 24 fn,

Tistencebetween centers cof
rear wheels 6 ft,

Dietence betree
Koad s;sce occupied, wicth IO ft,
Length spece " . " 50 ft.
Be Uniformly Listributed Live [Icac.

QO ne honcred forty (T40) rounds per stare
foot. The ahove uniform loscing may ve assured to occupy
eé11 on such portinrs of the roacway ares not ccreuvnied
by the motor truck lovcing eS in necessary Tamium slresses,
Termverature,

Strecass cue to en everape tenmversture variation
of ec? Shell be provicec “77, Tren temosreture stresses
are eacea ta cera sic Live loacs stresses the alioraole
unit my be incr esec 26%,

Tinpact,
For concrete «:cnes witm So.necrel filled
of one fact or fore no allcwetie im,act eheil be

>

On ccrnerete siahe, girders anc cpen Envancrel

arches cllon 25%,

Listribution of Concentretec Loscs Throuch Tartnh Tilles.
Concerti*rtec loacs qm esrth fillings two

feet or rore in centh shel? be agsusec to be uniformy

Cistributec over en ares tre sice of -hicn is euurl to

the wicthof the soreertretec load olus the Geoth of tis

filling.
UNIT otha

Unite streseers

in the Iciloring tables f

Class & con
oP B
L

Conerete in wmpr

ype s. ton
(flexuirl strescees

Sé.

fy be
ve

)

Bearing om concrete (wher
Barfece to which losd
is aprilied «t least tern
times the loedec oraa)

Axisl compression on
rlein eoncret® venticrs
of members whose lencin
is les: *5sn six tBimes
the Least cioanrention,

Oohesr, usedg cf a wersure
cf cjoronal tensicn,
on plain concrete
fectlicns,

ec 7e.
ond dad ad at

ere ll not exeeera tne valucs civen

or te cl-ss of concrete incicatec.

crete 1:13: mix
w T:2:4 "9
" t325:5 "

Glass of Concrete

A B CG

 

 

 

500 CoO oC?
e

CVO 7OO cul

O79 450 650

LO £0 VO

Too T40 99
Smear, usec 6s 2 xensure of
Ciz; onal tension, on
secticus, fully rein‘ reea
for cie¢gerncl ters ion in
eveess of thet allcwec
cer tlajn corcrets.

Bor:c on plain bears

4

ec bor

i)

Fone cn Ccetor
Ratio of Vocul’li of Flsct-
jcity steel to concrete

wn"

pd $
Corarete in

Eteeat iy teneicn

Steel ir cecurression ( where
irteccuec in conercte)
is "yy" the stress in
currevy “ing concrete ena in
no

O43.

a;

 

ro
O

 

lbc:per Lbs:per
Ge THe SGe ine

 

ceee Shoulc exceed 16 ,0cos#/ SG. in,

a)
WW
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a
On

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CY)
qn

To
O Q

16,coc"/ sq. in.
{t-

tre ercwm

4

thrust CF

e

it ehcrs

rece of only
mia
tersion er.c

1

tn

cecl of s

cid net knc

plage
ecreavece

ere

~~
-
ww

rei: livs bee
hours crent
results birt.

LOCC»

CChOCLU. TON

autkor kas ehowr, by the use of the rere ohiecl
f-e@ aren is sate on the richt sice of
eticn, “hits on the icft cice *he Line cf
net ores tru the wicets third erd thereto
ungouncnecs Yn the creh, F.', **ts can be
r kLeerucs *its tieory orlv se slies to iirtn
meg, teare Pore Ff this oprah bac of bean
sccrarete Gtoreo 7A ef been ruck thicker,
rerkress of the erect is tho.n in eaderesster
this iss taken otre of by the use cf 7 frert
l.
futher strtes that ne found

out thet he

9

very much about enelrsis cf a reinfeor

7m
ws we

3

hence ke whl not ve setéeried? wtiilt ws

r rralogreec sore other wey. The arcunt or
on this thesiszrckrbly ©9 not slow much
thew hove cone the savthor se great ceel of
c>
2

SEOUTS TICKS

Dicck “oc Eo. cence 2025 fF CO Cistarce off nerter,
9 vt Po —~_——-—e Fann J exe ” vt 1
vt A) 3 ._—-—--— me PTES5 Lf On a] " ”
A] “ee ween TOH d c.I a 1 1?
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" 7) Cy eee Pe ER 00 " tt t
1? " Fee ae 790 f° O.1 tt " "
tl vt a. ae 2TT5 y? re it) " 1
" ” ©. mewn FOOD r are tt " tt
8 ve Te . ——-- HE, oO a Cc "? " tt

Thes# ecemputetions ere for the righi sice
of tre crown, *S fchorn the lire cf thrust follows very
reariv the certer of tree cren screwirg thet the sroris

very eofe,
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——

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—————

MICHIGAN STATE UNIV. LIBRAR

31293009915