AN INVESTIGATION OF AN EXISTING
NON-PARALLEL CHORD TRUSS
FOR INCREASED LOADING

THESIS FOR THE DEGREE OF B. 8.

Lloyd L. Arnold
1931

 

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An Investigation of An Existing
Hon-larallel Chord Truss For

Increased Loading

A Thesis Submitted to

The Faculty of
RICH GAR “TATE COLLEGE
of

AGRICULTURE AKD AffLIED SCIEN 3

By
Lloyd L. Arnold

Candidate for the Degree of

Bachelor of Science

May 1951

 

 

MEsw

93793

TJ'

-A.

Dead load CfmfutlthnS
Investigation of stringers
Design of new stringer

Investigati“r of flc r beam

Invwst'gitiar of fl or beam connections
to truss

Investigation of tr rs.

l. Tni“ rm live load stress com‘utqtions
l

I. Go cent: ted live load stress com-
Lutations
3. Investigati~n o? congression members

4. Distribution of live loads
5. Combinsti'n of stresses

Conclusion

 

F‘REWCRD

The author virhes t n01n<wl d e the assistance

given *y tee I ,hw y Detar ment Bridge
Divisi n in gurn’shins the mmt*ridl ffr svbject of this
thesis and the Val a
illen of the Civil Thaineering Department C?
State Co‘lege nd Kr. yOYLVd Sheldon, Chief Draftsman
of the Bridge Division, as consultants.

This brldge is loomted North of Zscmnaba and Rest
of Glulstene over the Leewnabu river. It is on a c nnty

l ' ' 1

s in n ed 0? resurfacing. A 91X incn concrete

H.

rt 1d -1nd

’I

slab 11s Iroiooed for it, necessitating the" frre an ex-
aminau? n as to whether or rrt it :as cwgaole o? saFely

-‘

Stifldi 5 increased loadire. Tr. C. B. Trxtten innard-

H‘
*3

.aly made an eximination of t.e sL' cture on “*vemher

15, 1970 and submitted his d t1 to tho Bridge Divisi n
from wfion the author Ontmired I photcstat cogy.

1

fiany o? the d nifUOtU‘G W

(D

re V?

I."
l...’
CO
0
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c+
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vague.

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Ehe s wv R'acine was not even m arurfifl in the VEeld ex-

l

I
' '. 1“ A I. , . "Iva, I 3,... m : HI,
amtnatlon nor «are tne c:n re s: n newoers Urn~zslcred

H

, .c - I ,_I _ I _ '. .. , «-..- z . _ _ 4:“. A. - ,, ° , °
?Ld/¢“1L¢tutl; , .ES 11% fin“ éfl.fi.iL: t.l.fl . 13 .»;rtduceo‘12L it

t :90? re heedme necessary to ertirate s: e o? UT“ d‘m—

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9'0
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(-4"
T)
(4.
L.
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'55
'3
i' 11
{4-
1;)

leave fat 0 We Jeratirn o“ the TTTX Hr Cir; ent rely.

' . ~~ h . ‘ — 4 7 #— OI
lhls mw‘ s be” to d we ex e U P 1 “U P \Y ’nce of
, D I a h 4‘— ' 1 1 ~ 1 ' 4 1., “I
t? ‘y d 19 O‘1LIClUflbl3 . ll ‘Ccd l t 13 lg, Ur.n

.,
, . ~.1 I ‘.

will additirnally increase the sti?fness of the structure.

Egon c.ns ltitirr with Hr. Shelden it was decided to be

unnecessary to invertiLate the ewqy and lateral bracing,
and the only remainirc ‘hings lent to do were to analyse

the Pl cr lemme stririers, ccenecti he, 3rd the truss.

’

5
icles tris inveeti at fin and analyse may

”‘4

Ehe guthcr
be of srme use tc the Bridge Division if the concrete
is ever *ut in, 1nd tc the Bridée Divisicn he

readmm”

\
I.

dedicates this trrk.

LLCYD l. ARVCLD

 

Channels st

1 11. 5/16

Lattice tire say 3.npl

Total

BOttOm Ch'

1 -

7/€”X 3 h s e1?-
V rticsl:-----

2 _ 6”

channels ? 9. “ x 7;

Sway Bracing at

DiaLcnils at 51v

0/
literal Bracing at F‘v

Sub Total

Total fit. f Truss ecuals 3734 X 1C.02

Stringers 6 - 6"4X 12" X lECZ' ecudls

4 - 4" x 12" X 18.02 eouils
Floor Beams 15" Cl:.?# X 19.67 eeuals

6" Slab 75fxl9xl€.02 ecuals

Ht. {3? lanel

Ccncrete
Total

eich truss enuals 18,400#

Assame 75$ of Dflmd Load on lower chord

Ft " " " " upper "

X Z3 ediyils lffil..93_'

per

Larel as tyfiCQI)

.4.

1...:
m
Q
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n
13
7 ‘

p. 0 fl
IXEQRC-r

6.003

N.
,\

,-

v

c o

C)

w.

40.00%

is nnfl
'..-',’ .\x V ,'

332.74?Ler

eouzl86000.00#ye“ Inl

Conn b"
RLLVK 0.4, r]:

 

:er ganel
efiuals 13,800#

v 4.600%

INVISTIGATILN L? STRTVCTES

 

 

{+— /e~’0é EB, +0 EB. —’“>I

I I . I
Resume -ve. ein7 1 of {recent stringers qt s’p-
- - -. e n .
rox'n1tely s' —u” c. tc c.

1/

£5 -
r “j /ZDE’¢fimflibo¢%fifi7

I'-
I V« 1
AAA 1

§ é/zlzvcrefe qwbi) 3

downw—

 

/ fl 1 / .1 I” I/
.5142 &&2’ éflrAZ

L,‘ 2—0,. *9 2:10“- ,J

IrchV‘rs e Sec. Thru Strir¢ers

: m in 1_ . :,- .. .H. - .4- V.
Accord.ng to lehlng State HLChKQL DGIJIUTF t

U)

loci? 1czt1’rs Lhe loading ccnd t CPS shill he as
follows:—-—--

igtwar loudly s. ----- ill structires and

c ironent farts sha i be deei red for maxim1m stresses
based on the g f a iiir on true its on each trQOfic
lane. The t sites and concert: ti he 1tsurned
shill Fe t} WC ty.icsl or standard truck shown in
figure 5.

u I VV=Zafi1/rwwqfif

_1 'L_._ln

.zw CD aw

(0:3

 

 

 

 

 

 

 

 

 

%__/_-z_'—:a” H-.. 1 f 61“” 1
E13 c::iT<w “Sififi
‘ LVflflh? Cf?€06%7/1%W‘ five
1 égzefls /303r finv'cvpfb-J/
LtJ [m#3:é <. htfifl0f¢U’/@JUtU//715k

5K6 inml sis cf Eristing structures. ----- ”or the
yur$ose of sex :Cis o? existivg struct res, tre legal
loading s ecifie by current statutes, in Eenersil, corr-
es;onds very C70 ly with, and may be ccnsidered is the
ecuivalent cf, H - 1:} loading. -----

 

".E.l.3 For 19099es, 81rd9rs, ’fli Zrchvs. ---~-

Deck tr1"ses, Lirdxro, and arches, :id t rou h trusses

or Lirde 3, ircludrL heirirLs 1rd suhstricthrfis, sh1ll
he designed fer the stresses [reduced h; 1 101d on each
tr1“fic life 0 T osed c? 1 1ni“crm load ;9r line r fact
of lwhe Lith m c*9C"tr ted lozc “Pic? skull he ccrsider-
ed as the afrreximate grictical ecviv l=rt o? the truck
trn'ns re 1'ed tc in Sectich F, 1 d vhich shall be con-
sil red as locited longitudihs1lv a" to ,roduce max-
imum stress These leads sl1ll be subject to red1iction

Cso

es.
as hereina: ter s so fied or t:e imgrchibility of full
load on multiyle l9ré brid,cs. The concentrated load shill
be cor911cred s unif urmlv distributed trsnsv rsely on a
line ha"ng 1 10flith Gfiuil to the ridth of the line. The
stnhdsrd truck clearance :idth of 9 feet st9l1 he srsumed
as 0 net itutir the width of she trs”f1 l1re. These
1:sumed equivaicot lowdirLs still he classified as follows:
Ed ivalert icidirg H - 121. A tctal
101d on each trsfl-ic lane ccmycsld c?
a VhiPcrm 101d of 37? rounds per lin—
ear foot hd a sihile c hcertrited 101d
0? l? 5”“ lhs

5
tkose due t. 9'
wind 29d liter

----- A I live load stresses except
i ‘cuds thd centrifuge , tractive,
ces shall he ircre 99d b“ an s'low-
an e fer dynxmic, V ratorv -1rd ig1act enfects.
?Cr ehd flocr beams, fl or beim hthgers, columns
su jortih; oloor beam ccncentratirhs and all floor heém
9hd strihber corrections, the imrsct nllowsrce shall he

a)
H
a

H 0

..--

60% o? the live load stress.

For all other Iortifhs 0? Mt uctures, the ispsct
QIIOW1nce or increxert is ~) res sed as s coef’icieht of
the live lcsd stress, *sryirz 5ith the loaded length of
the structures 31d tie u‘dth of road“1y ares. Its in-
tehsitg is determined by the followiri ?Crmulss in which
edu-ls impact cos Sicieht

” loaded length of s11n in ft.1ro-
duc ing the m9x.st1tic stress in the tem-

t4H

I eouils L rise 25“

10 I “ 5‘9
1‘ . . the msximum value of ”I," as
he shove P rnuls, qull not exceed 0.39.

 

A’sume tire distributier ecuwls l" Ier tdn tatil
'vt C? IC‘ 611 True "tfitfl11rould ecusl lEiW"‘7dth in this
ones or 993 a“.

The land is 1ssumed tc he echcertr'ted d‘rectly

ov~r tTe light 4” X 12” strip 9r, to Ircdxce m Xinum

stress in that stringer. .ow tke load msv he 19sumed

to He distributed Lurtial‘v ts the GWAcert strirters hr
1 t.

memes c? the 6” c ncrete slab, 1" “831; greyortiergte.

ts the ilexibilitg of this slab, so it is necessary to

figure the resists cc of tris slab. TO do tkis the miidle
é X 12 stringer mmy he assumed as rexcved c5 tEe sign
gzng flared as shown helcw.

P

—..—

r2

 

 

1

 

I
L

T

3’—é”

mi '

Lcccrdi~g t? tfie Tic?.bsn Szate Pigkway Degsrtment
SyecifiCiticns, (see ?igure 14 under Bridge Design)

lbs.

fer a concrete sls

b with tr reverse reinforcing

’

lhen l X 1.75 - E X .25 eeuuls LZTCX
a; C;
l
6
,hence l e“utls L5 -- .7? eeuuls 7“”C#

O

which is the load wkich the 6‘ cone slab will transmit

to the adiscent stringers.

iced

:LO Hi t2fl er: by
II

M

ier rear u

1’1”.” f‘ 3’
\J. '.

'heel efluils

adjacent stringers " EFTO
“ i X 12 stringer " 7C7C?

7cm 3”“

 

I

I ~

(3

 

w

0

_g X

 

mozent in 4" X

eduxls El,

 

senals

........

. \

l2” strirter wculd be
5’0 ft. lbs. or 378,000 in lbs.

 

Z?8,”OO X 6 X l: eeuals ”940 lbs.
4 X l; X I; X l;
is ech"s1ve).

1here? re the l X l" strin

Ch

’ I’

18

tco

new strircers will have to be grovided.

b
V

It

’1
+

8

very

TI‘O-

‘.

bible anyhow thut the gresent wood strinéers are rather

rotten 1rd in n'ed cf re lacing.

T‘\“("

 

lJJJu 'Ul _ i k; u.)

Assume 2;;roximately ”'—6" sg‘cirg c. to c. of
strirC rs 2s sh:wn.

The loidine fgr the ‘esigr o? the stringers srmll
be taien is the H-lfi leidLVE, that is, cne 15 ton truck,
because 0? tie ”act that in a e}¢n o? 18 3 ct, such is

is hid ftr the stringers, it svems lOthal t' eX;ect tlit

at

sore ti

and would certairly rroduce %

stringers w

I

The minmum heel loe

Cfiu118 15,5”0 lbs.

_. __ -- _ A

~v a . f1 Jfla
o churwrw.:wlfl

 

 

OYW

( ' —‘-- ‘ ' ' - L I
r i t
i -1. _ _l
i I?“ 4., _f/ .’ //_ ., ,- ,.- l
:4 , n»;<q«w ~—/,*‘ 5*
I I
stringers ?or mix. conditions.

naximum

be c nsidered

stress in the

would then re L4X30,CCC

vi

“sume one “J el, of

ruck or 12,C¢O lbs.
ocsted directly over

he of the intermediate

 

l'iYIIlfifiLIV?.LIZl? TKT7EFT EJTD I?1_U?T
Then max. rcment equals ?,COC X 9 X 12 eeuels 648,0CO
in lbs.
In desigwirL the str n; r the s sumftion is that all
striwgers will be made alike so maximum carditions of
imgact will govern, in other words, imfsct ?or the end
striniirs.

 

9 rlus 14 ecuils 13'
27: Qfluxlg 37.4%

 

I GGU*1S l les 250 L €7Uw18
lCL “ 530

I equils

0.30 is siec'0ied as a mWXimum

'9

.40
.c

Q

howev»r, therefore,

194,4"0 e“uuls 842,iOO'Rfin!

1,’ I. ' 1 vs ~~ "'\ " " _‘ *\ ‘- -' ‘v' "1“
,‘vr J . i, I
..-lLJL.Ll. K'J-L . .. - »- .LJJ .. . . ., J.
mu"

'fi. ‘—‘ .-, _J——_—.—.,l “—q . ._1

It. of strinier assumed 49#
" " concrete slab is 3.5X.FX150” is 262%

 

Total wt. ier ft. 202#

v. i 9
XiXimom D. L. moment eouils 1/8 wl~ eonels
1/8X302X18X18X12 eouals 147,000#

r- T111 ' ‘-, ‘rv'w'r'n " v- T~rrn-"'r"" ”n smfi or“ "
I‘I J‘kX—LJ'. "T‘A _' ‘ -Ja;-L . . ' .! _ 1"»; I is ' LJJ- '— 1

842,40 I103 147,000 eouils 989,400 inch los.

IVTCRVTDIATE SWDTVC R

A L‘s. .

‘

Sectional jodulus refinirfd eouals 999 400 eousls 61.7

 
 

" " provided " 65.35
Use 12” C. B. C 50 lbs.

OUT 31 “3 Si 31 T" CSIIR

 

Maxitum live moment ylus impact, and dead load
moment for outside stringer wi"l be agproximately one
half of that for an intermediate or 494,700 inch lbs.

5e0tionsl mUQULUb reouirea is 494 700 eouals 30.9

 

6,0.3
" “ provided is 30.69
MAL. tinniiR in 51:11" 014R
rec: “£1 l vars-72, 000

 

”4:0”. _ ________..,_l

 

/6’—'0" .1

.51; 1>

<
m
<

==~355CNx/6£ :: c$333‘#’
AB

1,,
£3, = A5, 000 ~2333’ 2/266 7 7;: /7“/¢:7X. 4,1... J/zea,’

According to rich. State Fighway Dept. specificstions,
Sec. 5.8 under Bridge Design, 60% stould be allowed for

impact at all floor beam and stringer connections so

60¢ of 12,667 eoulls 7,590#. Theretore, hitch angle

s—l

connections must he designed tor 2,667 ylis 7,500
eqles 20,257 lbs. live load.

Deid lowd sfiesr is 5C¥X911us262¥X0 eoUilS 2806#

{‘0

COO nu- 0 ‘1”2 ('1 C?
’ -_ \. ~. 8 1.. tlk.‘ ~~ ', , \ R,- .

Total stewr eonuls L0,£57 llus
Be ring on .361 inches eousls .361X7/8X20,000&s 6,350

assuming 7/8 irch rivets are to be used.

to. of rivets neouired eousls 2? 065 eouwls 3 and or 4
6,?

See llste 1 frr correction details.

as

I‘v1r‘i/NTILJ 11.1 ’-.Cfl F]- {LR B? ‘1'

.11 AJL

 

lresent floor Beam as given by the field exanination
is a 15" I beam 0 42.9# per ft. Trom the Rich State
Highway SieCiL °1C1tiors ,Fig. 12, the single eouivalent
con ce ertr3ted lo d ”or a spin eoudl to two panel lengths

of 18 ft. or a s in of 36 ft. is 20,000 lbs. 3 X 1e

ht

loading, based ugon H-15 103 .din 5. However as this bridge
is to be eXamined to take care of only H-lgf loading,
this concentrated load would be reduced and would eouel
5/6 of 29,000 or 24 ,180 les. axle load according to Hich.
State ri hwev Dept. siecifiCdticns: -----
5.5.1.2 ----- Loddlrg s—so is 8/6, loading H- 2%
is 5/6, Lond3n5 H-lO is 4/6 of lowdin5 F-15, or the loadin5s
09 K-20, U 5 U 2}

L..- L," ’ Ant-

, 1nd H-lO have relative values of

8, 6 5, d 4 resdectively.

 

 

 

 

 

 

 

VLXIVUV IIVH (AD ‘CVTVT IIJI IXEACT
/49a90 / ((1:79 0
¢ 61.0' 61'9”
_. ' ____: ‘ 1
, . 1
—--——-——-— l9~6 7

 

F___/_____00 e 55AM 10/4 .rmGW’

XdXimum moment due to the loading shown:--

 

 

L. L. moment 6.75X12,090# EQUilS 81,600 ft. lbs.
Impact (30%) ,,fol;500 H 24,490 u n
Total 106,050 n n

‘ I T ‘ ‘ f < I. ‘7' ‘ . r ‘ ,nqv-.‘Trr
I 1111; Did“ ltnD Ti_n;£

AgL

 

Concrete slab 18'X.5X15C% eou3ls 13504 ier ft. of F.B.

 

Strin5 QFS 504 XlQ'X6 " 284$ n n n n
19'

Florr Beam 42.9; n n n n

Total Dead Lomds 16773 H n n n

D. L. Kcment is 1/8Xl677X19.5X eouils 79,600ft. lbs.

I"'X1 17‘: 1.311 CR 771.11? "(NEXT
106080 llus 79600 eou1ls 185,680 ft. lbs.

“5'11, LR D" 'M

_4—1. 5“.

 

'k

L-a

Secticnal ulus re 1zired

185 ,680 X 12 eousls 92.8.
(x #4000

 

It is lermissible, socordin5 to the Vich. S‘r11te
Highway Deft's. SgecifiCstiors, in the exam naticn of an
existing structure, to inc e.se the u.usl allowable unit

stress by 50% so 24,080 is used in the above eousticn

7.8 An113rsic of ”’iet3n5 Struotrres. ----- Tor
analysis of oxisti stricter es , the allowable unit
stresses Irevieis] sgeci_ied may be ircrensed by the
followin5 iercent .568: -—---

Fir structural steel ---------------- 50%

7. 8.
7.8.
7.8

FCI‘ CON.creteggoooogooco00.0.000.000.3076
For weed.................no increase...

LQNH:

Fowever, the gresent floor beam apparently has a
sectional modulus of only 58.91 so it is insdeouste, even
when using an 1110;; 'le unit stress of 24000 lbs., and a
new one will have to be 1rovided.

B sed also ugon an allowable unit strgss of 24,0‘C lbs.,

logical

\D
B
m
«.o

a 16" Carn 5ie Bram C 68 lbs. per Pt. 9'

 

secticral

f“
U)
.u

substitute for the {resent "I" be1m. It ht
modulus of 97.08.

This llditienql wt of the new floor beam will in—
crease the bending moment sli5htly, but not enough to

be taken into consideration.

‘V‘Vr («rr‘I r1 I rm 1 \T ‘ fl 1'14 C4 7‘s ‘1) I. Y' r‘\'1~'*‘ rr'vTI' ‘Tfi
I.v..hi UllIk-‘ Lr ;u. tn ..; CL-.- qllkfu)

v-vIVtv ~“r'3 IV w (a? t**"
A 1"» JI lwv' ~'-_VAJ L.L 1 L a7 $ .' 1L.ls

 

Live Load...00000000000000.0000. 24,180 lbs.

Iml‘aC-t 6074......000OOOOOOOOOOOOOOO Jul—’50? "

 

TCtta‘lOOOOOCOOOOOOOOOOOOO0.... 688 "
Dtad LOfldS
Concrete Slab 1350# X 9.75' eouwls 17,150 lbs.

Strine rs 004 x 18 x Z " 2,700 "

 

Flcrr beam 58% X 9.75' " 566 "A_
Total Dead load 16,4l’ "
Total N Ximum Shear - 55,10é "

B-srirg on .375' inches is .375 x 7/8" X 20,000 ecuals
, 6,560 lbs.
Single shear strength of 7/8" rivet is .6 X 10,000 eduzls
a 6,000 lbs.
Double H '2! H H H H 16‘ ’ Off) I!

Bearing controls in the case of connection of the
hltCh'fiflélG t' he floor beam.

See Elite 1 for convection details.

Number 0? rivets required is 55 104 evuuls 9 or 10
6,560

Sirxlo shear c:rtrols 3“ th“ 0098 0? 00"?“Ctihg the

hitch smile t? the truss Ilzte,

V“mb r of rivets reouired ecuwls '5 104 eeuwls 10
6 600
, _

.*d fit .he lower

'5)
" D
a
._J
S
r
fr)
fl
r—v-J
U
,3
4
7.5
u
:3
f“
p—l
.3
'n
H
J
3
A
1')

chord cowuecticrs with t e verticals wed the flcor Beam
end glste. Tue usual allow ble bemrir; stress is $4,000

lbs. but this can he increased 50% accord pg to Sec. 7.9.1

\.

under Bridge Design making an allowable unit stress of

>6,CCO lbs. per sn.-in.

“

Thickness of plate resuired to ccrnect flccr beam

 

to fin Equals ffijlné ecuals .76? in.
2 x 36,000
g 3/8" 11ste msy he usvd to be novrected t0 tke

floor beam 1nd hitch ambles, 3n an aiditiornl 3/8"
plate may be added at the pin correctivv1 to make ededuqte
thickness.

Tumber of rivets renuired to establish reouired

4" X 3/9" x 16,000? eoufils 4
6 C00-g
o ’v'/

 

S~e Elite 1 9cr detiils.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'. . Jm1fl6é'fl M47507“ 05mm:

KC \-

- . .
, A

~g . ’

i _" . '

..
. ‘9 A ..
. I. . a C I
..
U .

 

, Mfr}? Any/e: J»? 71'" 5- '3"
" ' {b/l/IE’Cf/M Fare 65’ "x g” x
. approx. 2" 6 /0/7q

 

   
 

 

 

' I fled/7727 Fla/'9 3/8 163 3r 7 "
Fbof‘fieam /6 ”46. @58 *5

 

 

 

 

 

 

0000.0
0.0000
3‘

A7”

 

 

 

 

 

 

r
d

Egagsagsgagafl ‘
$633313.
WM;

 

 

 

 

 

}

. Ll ‘ _1
U

7,,” 73¢
PL 00R all” CMN£€7ION DETAILS

*1}

 

 

 

 

 

 

I If . " n- v
---.. .- ' ‘. .. . ..
.‘4' . - _ {_z- ‘.

 

 

 

 

UNIT. EST III: ff_...'-.D CITRTQSI" CC? ["1" .-7'-.'*‘I(,.T.’S

 

Stresses due to uni€orm live loading are oomguted
on the b sis of unity panel Iosds ;lscsd in such 3 way
as to obtain maximum str.sses in the di°?€rent members.

The loadin5s wre as follows: -----

Bridge loading — Rt. 9rd to 1; incl.

 

2
U. L0 is lusasaflaf&ee7asa9 enumls 45
:1 IT

5'
r
n

tlLZ eouqls £94/80.2 efiuals 3.67t

 

 

 

 

f: C" t 8. l ‘3; . .J
U233 Loading: Rt. erd to L3 incl.
u. “a LO eouals 35
I1
'\ XX eoudls 36 X 72 - 100.?U3L39duals O
. 1 II
(L0 in L1 UgLE is 235.8/100.8 eouals 2.?4t

Imp 18 153 & 250 A b.54 Lo .L98 A 5.0%
lEZU & SUD uquw¢S 0.465
Z.tObo

 

Loadifig: Rt. 9rd to 1; incl.

Mk ” 28x72 - 121.2U31A esuals O

 

U714 eouxis 1.51t

k.)

 

 

Imp is 17? 8 RFC x 1.51 18 .20? X1 Rl 1s
350 8 555' 0.714

lotal 1.82ét

 

 

 

 

U415 Pouals El x 34.78 equals £;l9t

 

 

 

U51- losdin; Rt. erd to 16 incl.

 

lo eou'ls l&$&7&4&5& Q”UQIS l? is

.\ 11 IT

 

 

 

 

 

] shear
I Upla is 1‘ X 35.78 e"wals l.f€5t
-—rr-

Imgact is (00 9 2V0)l.565 is .3”?
‘ ) Trtal..1.9: t

 

Uc

 

 

 

‘2‘

1} ~——7|
1’ \

¢ -
l
///1
V:77
:4
:1

r\ i
C‘——+—

 

 

 

 

 

 

“L0 I‘IRCt is ( Fl fi L5”)1.C&l 1: .zfié
os~ » r‘fi
(Kl-U J; ‘,V'\/)
”F*\l 1.?Crt
U L Ioaditg Rt. end to L¢ incl.

7 j

 

 

Y SCULlS 27 X 72 & 10?.9U7L8 - 3 X 108

7 efiumls 1&7 e"uals 1.3%

 

 

U819 m1y on ibl' be seeded 1thia h not in at .resent.

tending ?t. erd to Lg 1601,

 

 

’/// Ifi.iCt is ( 45
_ ( 70

Total " 1.042t

 

 

U111 Takes full Ifihel load eruals 1-00t

 

 

~v~ ‘d’ .-' 0 :A ~‘-
Ispsot eeuils 27 8 2o: eoolls .86
" 27.", r‘: 5". ;

total 1.39t

 

U91 Toadlr7° Rt. end to 17 in01.

 

 

2 2
Irv IS :26 X 72 ‘ 1‘08 U- ‘31.;
U312 is 26 X 72 eoue 8 2.180
11 X152 ‘
Imfact is .198 X 2.18 ~ouals .472
Total 2.6120
U317 Loading: Rt. end to 14 incl.

f is 28 x 72 — 126 UQLZ
2.1 I _

 

 

Uq’. l 28 X 2 equals 1.450
v V— I}-.. 3 Ital”)
Irgaot is .208 X 1.45 eouals .722
U414 loadiug: Rt. 0nd to 15 incl.
71' 4 r) - {a (w 9
L&Lé 18 21 X 72 enusls .95 20
Imosct equals .22 X .952 eouals .209

 

"until 1.1610
UrL: loading: 3 . end to 16 incl.

Unis is Shpsr in lsnel 1516 is 10 is 15 is 1.3620

“>3
H
{O

Inject eouals .234 X 1.362 eousls .n

 

H
O
03
m
L.J
0

Total

 

For mlximum stress conditlrns in the encrd members
Of une urldée fiflVULQ U0 1u1ly 1Uaucu. imidou uucu 1UP

u11 uuuru memucrb cflua1s 138 & 200 efluflls 19%
l .I E () 35(5‘1'6

Vcr stresses sew gra;hicil soluticn, Elate 3.

C ‘ [3‘ ‘I’.’ fi‘ "’1 T\ T ITIT. T( {D W 17'” 'vPV H’ \r T‘ .1 ‘-
_-- _ _L. .‘ g .- .

L;.-..-'..J 5'...)

 

Calcul ted <n busis Of'a cg'centrtted load of unity
Ilsced to Lroduce TmIimum strews s.

S;EULSS CLfiLTlfprCIHS:

”In the following 00m1ut3ti0ns, the imfact-is Fig-
ured 00 the “leis that all garels to the 'iiht of the
Lanel ;oint 'h re the load is concentrqted are fully
loaded, ard the irided sgan 1e gth, to be substituted

1 l

in Lee Formula, I enulls L 3 BFC is taven as the dis»
_W‘
1C1: ’5 L)\1(J

run the PighL end u to tt;t ;are1 Ioint where

O

tance L
the load is glined. The imgict 0ceffi0iert “or the
vertical rember U111 is the only eXSertion, in this

else, the imfact be mg taken as 82%.

“1- .G-‘f\v'n'[J 1r‘7' "1'xf‘4
IJ L y l".. 1 ‘45 R. APLD

 

U110 Irad at in 10 eduals 9/11

(‘0

esu is 9 X 72 -

1511; ecu ls .l-Tt

“.2 1:112 ‘3“U“.]S O

Imp. enulls .19 X .735 edu319.1306

Tetal -E745t

 

C017 1.036; at 1/5 , 1.0 9"U.‘:llS 8/1].
TX enuals 8/11 X 72 - 100.8 U213

lenuils .518

Imp efiuels .128 X .518 equlls .1C28

Total .BEOEt

 

LJ ”‘1:

L

3
c“
;_
"J
,2
,1;
(I?
d
\
1 ..
H

.1 ’ J"O
Ix e‘u.1s 7/11 X 72 -121.2 731;
1:31.: e"u L13 .378
Ivy efluals .LCB X .378 e UdlS .0786
1211 .15’Ft
___- _.__._1__----.‘_ -_--.__--1__

 

 

 

U

 

‘3. r' J ’ .,
Féig r" 170 5/11 X 7”.78/"’ envnls .826t
1m: esn 19 .22 X .629 edu 1s .178
_. T twl .7mit
U515 I: i It 16 , lo e“u;1s 5/11 eeugls :Le’r

C535 e“u118 3/1] X 76.78/72 enles .521t

1m; equals .294 X .F-1 enuwls . 22

 

U517

U919

’~

10nd at 17 , 7 elu»1s 4/11 ennuls sheir
C;17 €"H318.4/ll X 36.78/72 equals .418

Imp 80les .SFE X .418 eduils .106

 

:C‘d. ‘.t 118 , 1'11 0711118 8/1.].

" e1u_1s 8/11 X 72 - 126 X 1 8 109.9 U718

:-
‘.‘Klr
.1

 

C7Lg esunls 126 - 52.4 eeuwls 73.6 enuals .671
‘ 100 0 160'0
J.\,.,.J —L\JJ..

In: eeuils .2FE X .671 emu ls .171

Tctql .812t
101d at 19 , 111 6”UJlS 9/11

IV equals 9/11 X 72 - 108 X 1 5 91 U81

'4

U819

 

equils 188 - 58.9 €“U118 49.1 eeua s .510
113 enutls .281 X .fé enuils .1 1

 

T0t%l .F9JE

1--)

“-1
H

 

LLOido‘tt Ll

U111 esusls 1.0C

-r

-Lr; esonls .30

 

Totsl 1.70t

 

 

 

0313 102d st 13 , IO eousls 8/11
TX equals 8/11 X 72 - 108 0:13 eouals 0
£31; eouqls 52.4 eoulls .4850
1C8
In; eousls .108 X .485 €0Uflls .0960
Total .0810
061g load it lé , IO equals 7/11
1' M_ 9 _ 0 ‘
LX ethlS 7/11 X 7N 1&6 Expo
tng eouals 45.8/126 eousls .3640

1m” equals .208 X .364 eduals .07560

 

f‘.
\I

m

1 .42960

\‘1

load at 15 , IO equals 6/11

I equals 6/11 X 72 - 144 0414 equals 0

‘X
U4L4 eouals 39.3/144 e~uals .2730
Imp eousls .22 X .273 eousls .0600
iotel .7330

 

U5L5

10 rousls 5/11 is shear in pan—
el 1515
0515 eousls 5/11 enusls .4650

Load at 1% ,

Imp eouals .224 X .455 eouals .10670
Total .56120

CVCRD T772 RS

 

load at Ll , lo eousls 10/11

1001 eousls 10/11 X 26.91/20 equals 1.220
Imp eoulls .70 X 1.22 eouels .3660

Total 1.5860

 

 

 

 

 

 

 

L0L2 L013 eousls 10/11 X 26.91/20 eousls 1.220

Imp equals .20 X .818 eoulls .366

Total 1.5860
U1U2 load at Lg , LO enusls 9/11

H10 equals 24Cnh - 9/11 X 06

Q
U2h eousls 29.4 equils 1.2260
24
0103 equals 1.226 X 18.43 equals 1.2580
18

Imp eousls .19 X 1.258 eouals .239

Total 1.4970
U2U3 Load at L3, L0 eouals 8/11

M15 eousls 28U3 - 8/11 X 54 eousls O

U203 eousls 8/11 X 54 X 18.43 eousls 1.440

28 __1—8—

Imp equals .198 X 1.44 (quuls .285

Total 1.7250
1213 load at Lg , LO equals 9/11

Mug enuals 241313 - 9/11 x 55 eouals o

1513 equals 9 X 36 eouals 1.225t

11 X 24

Imp equals .19 X 1.225 eouwls .275

Total 1.458t
U3U4 Load at L4' , LO eouals 7/11

M14 eoumls 32 H — 7/11 X 72 eouels O

H eousls 7 X 72 eousls 1.430

11 X 32
U U eousls 1.45 X 18.45 equals 1.4680
3 4 __I8_
Imp eousls .208 X 1.468 equals .306
Total 1.7740

 

800318 0

.278

 

5 , ._.0
1

 

UcU6 eoufils 5 X 108 ecu
a X 22

Imp efiulls .234 X 1.575

Total

T
lrI-e 801 l" 6 Y?
L,

11 X 5
T (M)
imp r3“ 1? .N‘h’ y

d
(+-
is

 

1.0 e ousls 6/11

1.5?0t

"'2
. -7

 

1.867t

IffifCCTICZTT CH (’7 CCIZECICSI.TT:YTT73CRS

TL; CELRD (IhrouChout)

 

 

 

 

/” I
e [‘fv— "’1 2 - 10” Channels 3‘ 1.1.772?
-. "__—:;:—_".“;I .' 1.; -1. .
f . . 1 {late 5/12" x 14"
, 9 ' “W 9 “3
I 411 '21.,- ' Lattice 5/16" x 2"
’7 I ‘L If h §
' I k) u w
: H ' Note: The flela exam-
__ r’:"'1 a ":3 - '
l fftt_xl iration as furnished did not

i give the diétance back to back
of channels but as the larges
chaenels as used in the vertical

members were 7 inches, I assume the b. to b distance to

be 8 inches.

 

 

 

Ah: t“E’-*fi’ Area Ievrr arm‘FTEEn s I ““
Cover l}3§e 4:375__ 5:}563 _§§.58_ ll§.6 _

 

 

 

 

 

9......1 . "8.9:; 0.0 177.9
15.715
250.4

 

 

2: 22.58 eouxls 1.7"
.L2 . L- I. u
Ig—g eouals Ih-h - L82
" 250.4 - 13.315 x:1772
" 211.9

r edu1ls I eoual 21..9 efluwlsdl5.9 ecu 19 3-98"

It may be seen by irsyection that the "r" about
axis V-V is greater than 3.98 because the secticrs are
alone 8" b. to b. so it is unnecessary to solve For that
"r".

VIRT ICAIS

 

Fete: A? in the 0196 of the toy chord, the field

examiniti n did not define tre secticns Very closely but
it s ems logical to ersume that the verticals are box

sections and that ttere must be about 4" c‘eqranae be-

... . A

1

tween by? flin3es of the chanrels.

 

 

 

v .
35 9 3-7" charnels 2 9.8%
INTI IR 9 0n
F—‘j E: 1 rh-h = ~.7;J
- m 7—2
- — I-—/7 Iv-v - I€_ Cf -- Y -- .u-

 

 

 

 

 

 

 

 

 

— v C
:"j "‘ J _-.I__ 7'2 76
’3 r. ' U r 3r n I ’ = '.’ o 1-
:32 4+4.- 8 ”‘3
I w ' "r‘u— FX-
f444342.2' Tv-v = 5.56 =|lc 3.59"
v’ ' 5.76 \
Ung -Uél4 -U5L5 A 2-6" channels C 8.2%
V '7 I!
ll . .
5 A lv-v 18 greater than rh-h as 18
___— _. — _ ___—.— .L.. f',
t I b apparent by 10S3ection so 1t is
1.4:] LT.-.I _L

 

unnecessary to selve for it.

“’.‘..fi
1111.0 - 13le UNIT CLIEEKISI‘IIVIZ SIRISS TEBIE
1113 "r" ILFGTH L llICWABIE AILCW.
ELK ER IN INChJS IN ITCH. 5OL/r 15“oo-501/r & 50%

 

 

 

 

 

 

 

 

 

 

1QU13 3.98 204.0 2560 12,440 18,660
UlUg 3.98 ' 221.2 2780 123220 18,330
E2U21 8.98 ‘ 221.2 2780 12,220 181730
L321. 7.98 221.2 2780 12.220 18 ”"0
_0385 8.98 216.0 2720 123280 18,420
§5U5 2.98 216.0 2720 12,280 1814“0
3213 2.72 288.0 5290 93710 14,565
IEQ1&_ 2.84 204.0 4360 103640 163960
U313. 2.84 204.0 4860 10,640 15,960

 

U5L5 2.54 204.0 4560 103640 153960

 

 

 

IIPSfllt-qnt : l7 ’ r007;

'""%\

or 375 X 18 = €‘>"/':‘C"E

/ ,-' .v‘frv—fiv— ~—v

/'/," l 1' l , I; /
I /
j, 'l ’l/ f ," I" I I I,”
. ~' . , '.' 'I /
. 1 A A A. l J. . l _L“

L
‘
\

\

 

 

 

 

 

o ’ II
fl3u/' ‘.dé
"'<"" " ‘ I — — I?“ 3.
' V '1 - 5
-/"3 " ,4 if.” . Wz
/7JJk2~_ f? / 143

H: "n-'*-fi,v-.-r~-v~-n 7( a .
I -- 1 . ‘
U‘ v.1- .LA.L .lJlj ; \. :1 .

R = 17.22 x 17,500 = 13,100 lbs.

 

2 = 12.32 ;.6,700 = 5,050 lbs. ger 3anel

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

£¢L5 . 15.370; I M ,
A, 43' 7:950 ' vwvw

~ £2 1.17 1- 9.050 42166510;
4.11,“ 9.260 20.0 '5" mm
lg .‘ . 9.930. $.33" ” - ' £52609.
1/. 4L 4.370 ‘ 143315.? I 1/2500
11.4.. 2.305 twig"; ”f. 402295;.
4131... A524” 2.00 ” mogg .7
1/12; 247/ 2.56;" ’ 'I 601350 .
1/. 1.9.37 [5:3 ‘ W .36 750
”511.7 0/"
4/; 1... £305 A._ z 00 .~ 24:65»
”7 L8 0/” ‘ .
z/ z, . +4552. ‘4 z 245 . .. 30.300 2

' -- 27849-0" - ' ......—————-——--~
*1/34: (042‘ MW . ‘. .
1/. L, /. .760 , 4.53 I! 36 750
1/24: . 26 .570 ../4.565 5130819
1/343 _ 2792721 ./5960 ' 7444619
.0444 » [/5‘;"'7) 'I/ n
.1451, we; _ v ' "_I II

 

-.—- “W—

 

 

CCI‘TCLUSILI‘I

I chose this subject for a thesis because it gre-

U)

ented an actual problem in hibbwsy bridge desi n and

because of tee relitiveiy 33111 time wfiich was event

on the hitter of stracturel steel design, esyecislly

J——,.-m ' +1 an, 11 . .1— T -‘|.. - .3,
til-.938, 1.11 vile recall-all, 00.1.1803 VIOI’J‘X. J.t .ilbo LIN,-

.L. - .-, ., .4“ _ 34.. a. 1, . 1,, ‘-.._ _ ._ I ‘. '.'.IJ_ 1
selibed. -3. -._. 1.1013. 0,: ‘_ 031: .111). u; .0: J‘330711J’1O be C 291‘ tic (I 4151...... -.b:?.;.

.1 th T.‘Iic7‘._‘1ga.n State :19‘1’11‘1-23 D(—33n~.rt:::e:f_t '5; 339; c '1 71321;}. O as.
is 1 result of the truss on1lysis, two rrebers

Vere disc vered te be eliittly reek, these nenbers being

1313 end T111. They use not week encugh, however, to be

dwnterous 1nd will grobnbly rot need stren3thening. Ihen

too, the ”actor of safety is treat enouLh, as reiurds

loading, so that ideal conditi ns “er maximum stresses

in the weak members will grobebly never be attained.

As a result 0“ the IfiVQPIngIIOn of the floor beams,
ers as 2811 as their connectitns, I believe
that if the concrete slab roadway is to be jut in glace,
the whole floor system will reed revis7ng. Few stringers,
floor beams, and connecti rs will need to be used, and
I have accordingly designed the same. Their details are
shown on {lite l.

I find that my choice of thesis subject has been
justified. The work his been both interesting and instruct-
ive and I have been benefitted in several ways.

let. I discovered what I believe to be a logical

method fer computing the distribution, due to s cen-

centreted lead, over non-uniform size, unsymmetricelly

s,1ced strinbers.
2nd. I have gained an increase: :enerel dodusintarce
with the Iichigw. State Tighwsy Degurtment's syecificsticns.
3rd. I have learn d the need of orderly tabulitien
of can ututi he and t cir ccmbinstirns.
dth. I hive made use of trdghic‘xl methods of selutio-

for evme 0? the stresses and now know how usepul it can

be.

 

 

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Arnold

 

 

 

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