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ATKINSON " liivcsligation of Thre8-Hin2;e(l Areli Bridge;'''! Civil Engineering 19 6 '^--^^m

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Page 1: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

ATKINSON

" liivcsligation of

Thre8-Hin2;e(l Areli Bridge;'''!

Civil Engineering

19 6 '^--^^m

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Digitized by the Internet Archive

in 2013

#

http://archive.org/details/investigationoftOOatki

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INVKSTKiATIOXOF A

tiiri:e-iii?\(;kd arc h hrii)(;h

1{ V

JKSSK CAMPBELT^ ATKINSON

THESISFOR

]:)EaRKE OF BACHELOR OF SCJKXC^E

IN

CIVIL ENGmEERIAG

COEI^EGE OF ENfilNEERINC;

UNIVERSITY OF ILLIXOIS

i

PRESENTED JUNE 1903

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U N I V E R S I T Y P ILLINOIS

January 10, 1906

This is to certify that the thesis, prepared ohiefly under

the irnnediate supervision of Assistant Professor Ketohun, en-

titled INVESTIGATION OF A THREPI-HIMGED ARCH BRIDGE by JESSE

CAMPBELL ATKINSON is approved by me as fi.3.1filling this part of

the requirements for the Degree of Bachelor of Science in Civil

Enf^ineering.

Head of Department of Civil Engineering

88003

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DEAD LOAD STRESS D/AGRAM.7

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J6

,9"

-7.^ ~7 / <^ X & \^

=z //09./ ^ 76^6.9 = a7.56

J- =^ al :5-x7^^^ ^ </^6.7a ^--973 >c<5'.?7rs)

= 7:^aa.d 7-609.a = a7sa

/t

3.

/'-3£

~ 7-^ A = a.9-^ 6J = '^<9.a.

^^=^ a5s-o9o~ 70 7a - 33. a^'

y^=^ 70^^0 7^ 7^^ =

3e .aa

3a.a.a

^ /7tS

^

Zj^ta^.^-^ ^^y7^ -^t^^t^^ ^^t.^^'-z .^^/^^^^t:/y<c^i^d^.

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i

i

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5/

3

= a a.15'= ajo

i^r^^.^ = ^^<3 r- Za

r^a. 5

:5-6. 6

- ^ iS6,6 = 6 7S6

^ /^OiT-O —SOX ^6. 6 =/3^/a^= /6GSOO 7- 67S6 = a S.O/"

«>z>w'^^^>t3^-^ -= ^ 77:5-00 ^ a.S. <^= 7i5^9<7^'^

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*.^^^c^^c^^-z.^ <i7y2,^.,<L^ .,^^cK>^t,ce>c/<L --^^g^ a^^t>''z^c/,.^ct^e^ct^

— /-.L.= /30 GOO /D./-. = SS^OO

B

a. 5' = a? 6"

6 f- ^,^-9 = 6~0-7

^ a 79.39 i-//. zad.^) ^ ya^5

i^^^^s.s = 7a

~ 9aoo -^axis-o,/^ 6? 7a

= / 3000- '90 X :S-0.7 •^/59'7^'^

^= ^^aoo -i- /5 9'7^ ^..a^^sa^

a A a s^"

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f

i

> s

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J9

^^^C^^ a^-t-t^-^ ,,'i:>^^^.^Ct^ -y^TX^-fi/^ <^^^-<^^>-<Z; .^(2..^'^.^*^Z'^--<1^<::y tr-^^

B

1= c^xS/^.^ = 6dS.^.

7^= /a.^' ^ /s-o"

- ^ /9.d - ^

/J^= 9000 ^ a 6.C ~ 793 6

^ /aaoo ~ 30 ^ a6.6 ^/^era- ///O^O ^ ??36 = /3.?/°

^ = a:5-:TOO i- /:5S7a ^ /- 6^ ^

^^^t^^yt^^^^ . ^^^.o.,..^—

^

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Page 87: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

^^^^^ yOi^^^^C^t^^^Z^^,B1= 6ds,d^ r=^^<sa''

/= // =

(^^c^U^c^ - / 9. 8 7 = a

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i

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t

- / 6 .6

6 .^7

Z3/ 9 S

7^s ^

U ~ Z.Z.=- za^/oo"^ D.L. = asaoo^ \A/. L. s^soo

G Oyj^pOS/Y/ d7/7.

r X <3

L7 X / 6

/'— s&

=. /a-f9 6^ i- = a.5 76.d.

7 = /a.' = soo

/ ^ A ^ soo— 1^.9 = ^o,e

- /07JOO 5^5"^ = 777<7

= /£3 9c^O -f- 7 77<7 = 9.

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/^s "

y^c/c/ ^Oc/g /or c/&7^o//>s ^ 9

^ ^ ^ as ^ ^ /o s-oO(p /n /6s.

7= ^^^^^

<39-9.7'S~ /5S600 X SOO ^

/OK as^oooooo

^^^^^::!^'^--^<:.^"-za>^^^----^..^-'^.'z^cx^'t^f^^z^^^ <3^>>••^'12.'<:-<p^^^>2^<lJI^

/

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Page 93: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

^<3 eoo -r/^^ae = ^. /

^

^

^CU€>^U^ - / 7S 600 -r ^/.<5*3' =^r9e 6

/ o<5 OOP X s __ /ose*^

/oxaepoo^aoo

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i

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JJ/'- 6^

r7 —

7 .

IL

/a. s = t5/. a~

/ ^ 6J

?6^- ^ ^^*^<^0 x 3ey<y^

7o X a&ooo^ 00

Page 96: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

I

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^-5

_ 9^<93/^ A /aao

96

9"

N

r 3 5

L

J' S.io

^^^^^^^^^^^ /yO A = ^3 9l5^ ^

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i

V

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^6

/I

~ -=^^^^/:^/o^ o. l^67oo^ ia/. z.. = t-v^^oo

7- /^./^''^ /'5a e'

- /oooo — -^sk 5o = &e ^o^

/g^ = a.<Pooo-^ 90X30 = /T^oo"^

y^^= aa/^70 ^<36tS<P =a:^.6^'

L

seroo^ / ysoo =

SO. 6/'

ck^^^^^Z'-cf ^'O^d'^Co^-/C-CL^:/^ == SO&/7^~ ^O. = /OOSO^

^= a2La^. ^ ^ <£<9c5*

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Page 101: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

<9 Z.^ -5^'^ -5? \ /s

T

J

To /a/

T a. K 3 X

4 1

J

= <3.S

B/'- 7

7-^ r 3/ 3 ^ a s =37.7

/f—ZOpoo'^- -9^5-^37,7 =SS.o5

^= ^tS-ZGOO^ &303 - :5-5^.5'/'^

^ = / 7&:5-00 -^Z6GO^^ / 7^

yt:?^ctyt:/ .^^-23^^-2?^^= 630300-^ ^^57/^= 9e7-f^

-3" ^

Q Z.S -9^^ ^ ^ z^. a = 7/3, 6

aas. a.y^c^c/ SOc^Q for c/^Z-cy/'/s = 6 7. 7

'

Page 102: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

1

4.

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V // A .saa0300 ^f37 7X /d) ^

/o^ aaooo ooo

= 69a, ^^^^

7t

a. lA/Gjb aa^^/i^ ^^g,q'= a^.r^^"

N

3

= ^53/

B

/ - 7'

Z - 3333 ^ <ax9xaa

/J.^=" ^:^^<a.a

=

7-r-r= 30 9 '^<s^&.6a = 3^:3^'

= aoooa— 9o^ 33:a = /szrs^

393<£30i'<&3a9^ ^6.3 r'''

^ = /^aaoo ^/6773 = e.a^J^

^:3. 70^

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4

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T1

^ As ^ 'I ^ " s "

a/. 76

J

3a ^9/^sE^9^-7-76 —

= soa /^-^ 7/= S9. a.

/OOOO - ^:5-^ 39. a = Sa 3-6"

— aoooo - 9ox3 9.a = /63/a^

y^^ - //9300 -T 76 :37a 7.a.a'

^9. 6^

oc^t^z^^^e^^^^tz^ = -^6 9 3ao~ -^9.6-/=- 99a 3-7

_2"/6

tt

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i

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4?'

/f- /oooo - -^^^3^.9 — 333^^

/^=a.oooo- 90 X

5^

cc^t^c&'O^^a^oU^ ^ ^O06eO7--9^.'^^^ = ^^9a'^

N

^ //6/.^ ^ 99<3 = a/^9

/f= /<700 0- ^<S-^ /?,6 = 9//S

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a \7\/&jb /% aax @ ^a.oi^"^^ <5'f?.^<5*'

-^Z^ ^ 9.7"^ = ss.a

^S7{750^ Sos a = .9a

S ^ ^^^^<!9 ^ 77 ^ y^^-^

/OA aGooo^ooa

^-U^^^^y^T^^ /S<^^ 70 67S= /S^OO^

(6^^A^<.^^a^ — /saoo^/7sr^ = ^^^^

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3^

(^^^^z^^^.^Ot^.^i^^z.^i^^ ^ 7 9^7t57?-r- / 7. 7^9 = 77^aO

^ ^ 70 K a. apoop00

6S?.3-/-7-f^-6

(^2^i^^?-t<^tz,^^t^-^'eyy^l/^iZ^U^^^^^ ^m^a/= 7.3^77i777=7^f77'^

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^.5

/oooo"^

^ - //36^0 ~ /OOOO - //.^6i5'

^ = 37SOO i- a 0000 -

/-^ - 9/:^00~ /0000 - ?,/^47

/ O. 39

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^4

^= /0<3 900 ^ /O OOO = /0,Q9'^

/d <900 r- aoooo -

<^ —/./.= - 90^00^^ o.z.. = -t /^isoo^ uv. ^.^±e.9aoo

7^900 y

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i

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^^^^

rc/J /oc^Q^ cy/^c/ ^&c/c/ /oao/ 3^r&ss aof^//^^.

il ===__=_

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^ = /. ^7s-x 3o^.^.5o =-<:^.^ e^x^ /-^(^ y^o

•VJ

a. ^ /,j7^^3^a^oo ^7o?^a

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Page 121: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

=-- /^/OOO^ i^SOOO:^ soo<^

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so

y^r/: /T ^e^o'/^//?^ on f-^/ns.

ce./?/.

41'

^08000

7S70

606£>o'

606-5-0

3 79SO373:50""

3 73-5 0*

573 iSO"*

6oe-so**

60 6 t5d"

a 73000

7/6" ^76

/? " -^76

'Si"

7 5.3

a /.oa

6.05

S.7

3.6a

^.-57

7 0.3^

i5./

30. 1^

736 SO

/6 5a

/ oao6

/ o / oo"

7 /9ao

^^oo3300*

3 300*

a&oo^7/00*"

7 79ao

3 /so

70d Yo

7ao<^^

7^7

7^oY^/a6y^

3^oY^/aoor/'^

7aoofa

^3Sf^

73 6o/a

7a6</o

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i

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Q'^^<i^^t<z^'A-^^€c^^ 57?<5^0 5.77 = (^7^0"^

5Q>6(i

/.3 X

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Page 127: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

/ 6 as

c^a^ ^ 9ooo ^ S600 - '^^oy^

3V

-flA/eh.P/.

/-f>^

= 6:50 500

Page 128: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

4

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I

i

i

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6^

^ Z-Oiver .. / 6.S3 /jao^y^c/c/ c£0(^o o/uve/^^/ /or c/e'/(7//3 7 65

^

To/a/ ^00 ^

Liv& Lo&c/ A/ox Mo^. =gK ssoaoo x /g =3^_8J_ooo_

Dec/uc/ for ^ - / " m/e^/ /?o/&s —L^-J'

i/rj/'/- = /a.3ooo- /^.5a = Gooo

Ff//C/e^cy=^ 9000 -t~<3oOO =r //^<^o-

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1

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/^ojc. <y>^/> ^/pecy^- = 6 T-fse //as — eooo

A/c^x. o/7C^ shear = ^^/f^""^— ^ 6/^J3 fSee Cooler /i^Jo)

-^^2^ '^^^CcC'^ ^^^5^ ^^t^^l-^^^T^

..-i^ue^^^^^^^^^/^^un^^^^iz^^ --^^ Z^^^e^^^a^L^ /-/= = 93/7

/OOOO - 7^5 X93./7 — ^O/^.

<^// = ^^35 7 = //^^ = a9oa'^

^/4o/ ^// /Ye-^^&rs.

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I

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//o t^cyjh/e ^^?/'/- ^//-ess = /oooo — '^'^^ /^a = 90-5^6^

/£/Y/c/Gr?cy - 6. 6a 6./ — /^^^

A/c/^. /DQ^G/ /o ac/ = a00 000

/^[/ez-Qf^e /oQc/pBr per sfr/rpj&r =^^^^^^ = ^-^^d^

^3i50 ^^^0/0 —7^.^- ^

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Page 137: Investigation of a three-hinged arch bridge · 2015-05-27 · titledinvestigationofathrepi-himgedarchbridgebyjesse CAMPBELLATKINSON is approvedbyme as fi.3.1f illing this part of

6-5

c/ = /^.^- ^^^^ = 6.^' 6 - 6"

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I

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D/l^^/^/\M OF STRJNGER.

si

4-"

~ 9 d • O O O• • # • o

o u O O O O

o • o • o o o

o o o o o o

4« o • o «

a o o

/^// /5 f/oor Bearrps.

C/0/r?joo3/ on of F/oor Se-cr/T^s

,

a Loyver ^ / 6.83

er'

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I

I

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3f/-

6>7

//^/^y<^ ^/^<^^3 ^ / 90J69 - -^0.63 ^ 9 a-? 7

£}ec37</cf /or /o /-/i^^/- /?o/&s ^.7 '5^

_ ;^

^^/Y ^/p&cyr=^ /O^ 367 - 7 = 6 33 7

Z/fre /.oc/c/ ^^oT" s/?ec/r = 9<^7G7

D<^C7C/ = _Z^^^

r^/cy/ - /0^3&r

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