DESIGN OF PLATE GIRDER BRIDGE
Design data: Diameter of pipe, D = Mean dia. Of pipe, Dm = Thickness of pipe, t = Unit weight of water = Unit weight of steel = c#c spacing of cross girder = c#c spacing of main girder = length of main girder = length of s&pport plate1 = length of s&pport plate$ = Thickness of plate of 1 ' $ = length of s&pport plate 3 = Thickness of plate 3 = ( idth of plate 1,$ ' 3 = )ield stress of steel, f* = )o&ng+s Mod&l&s of teel, - =
3 3.016 0.016 1 .!" 3.$" %." $0 0.3 1.61" 0.% 3.$3 0.$ 0.$ $"0 $00000
m m m T#m3 T#m3 m m m m m m m m m 9#mm$ 9#mm$
llowa/le /ending stress stress in comp#tension 0.66 f* = llowa/le shear stress stress 0.% f* = 100 9#mm$ llowa/le /earing stress 0." f* = 1!." 9#mm$ Unit weight of earth = $.$ T#m3
each
16" 9#mm$
DESIGN OF CROSS GIRDER Calculation of loads: Load distriution on cross girder: The cross girders are spaced at e2er* 3.$" m 3.$" m length of pipe, water and plate on /oth sides of cross girder self wt.of cross girder for %."m length is the load for which the cross girder is to /e designed. 4or 3.$" m length, (eight of pipe = 3.! T (eight of water in pipe = $$.5! T (eight of s&pport plates 1 ' $ = $.%1 T (eight of plate 3 = 1.01 T Total weight = 30.$ T This total load is con2erted as &dl on %." m span as cross girder is in/etween two main girder &dl, load#metre = 6.3 T# T#m ss&ming M7 "00 8 !6.5 kg#m as cross girder. girder. (eight of cross girder = 0.0!65 T# T #m Total &dl on cross girder = 6.!1 T# T #m
Co!"utation of #o!ent and S$ear: s the cross girders are connected to main girder /* weld, the s&pports are considered considered as fi:ed s&pports. 6.!1 T#m
%." m
7
Moment at 4i:ed e nd 7 = ;wl$#1$ Moment at 4i:ed end 7 = wl$#1$ Moment d&e to &dl = wl$#! Moment at centre = wl$#$% 4-M 8 7 = 4-M 8 7 = Moment d&e to &dl = Moment at centre =
;11."0 11."0 1.$" "."
Ma:im&m moment = Ma:im&m shear =
Tm Tm Tm Tm Tm
11."0 Tm Tm 1".33 T
11".0 <9 <9m 1"3.3 <9
Co!"utation of Section #odulus: ection mod&l&s , re>&ired = re>&ired =
M # 7ending stress "0000 mm3
"0 cm3
s re>&ired "0 cm3 is lesser than the adopted 1!0!. cm 3, hence re2ise the section as it is economical. Re%ision: ?hoosing from teel hand/ook, section mod&l&s nearing to "0 cm3, we can adopt M7 3"0 8 "$.% elf wt of /eam = 0.0"$% T# T #m Total &dl, w 6.! T#m 6.5 <9#m 6.! T#m 4-M 8 7 = ;11.%% Tm 4-M 8 7 = 11.%% Tm Moment d&e to &dl = 1.16 Tm %." m Moment at centre = ".$ Tm Tm Ma:im&m moment = Ma:im&m shear = re>&ired =
11.%% Tm Tm 1".$" T 653333." mm3
11%.% <9 <9m 1"$." <9 653.33 cm3
s re>&ired 653.33 cm3 is lesser than the adopted "0 cm 3, hence O.<
Pro"eries of t$e IS#B &'( c$osen section: :: = !500 mm3 :: = 136303000 mm% ( t.#m = "$.% kg#m ec.area = Depth D = 4lange, /f = Thick, tf = Thick, tw =
661 3"0 1%0 1%.$ !.1
cm$ mm mm mm mm mm mm mm mm
C$ec) for S$ear: hear force= w@#$ 1".$" T 1"$."3 <9 $ hear stress = A# D.tw "3.!0 9#mm s the calc&lated shear stress "3.!0 9#mm$ is less than 100 9#mm$. ence O.<. C$ec) for Deflection: llowa/le deflection deflection as per B!00 for /eams s per ?la&se 3.13.1.$, Cg.3%, effecti2e length # 3$" = %"00#3$" = 13.!" mm Deflection for fi:ed /eam with &dl = 1#3!% wl%#- ct&al deflection in /eams =
$.66 mm
ince the act&al delection in /eam $.66 mm is less than permissi/le def. 13.!" mm. ence O.<. Therefore we can pro2ide ?ross 7eam of M7 3"0 8 3.$" m ?#? in /etween two Main Eirders.
DESIGN OF *ELDED PLATE GIRDER +#AIN, Calculation of loads: Load distriution on !ain girder: The cross girder weight#metre m<iplied /* %." m width gi2es the point load acting at each point of cross girder on the main girder. This point load will act at all cross /eam e:cepting end cross /eams. elf weight of main girder will act as a &dl thro&gho&t the span of girder. s the main girders are are s&pported on a/&tments, the main /eam is considered considered as a simpl* s&pported /ea C1 C$ C3 C% C" C6 0.$"
3.$"
3.$"
3.$"
3.$" $0.0 m
Coint loads C1 = C Coint loads C$ = C3 = C% = C" = C6
3.$"
3.$"
weight of cross girder &dl = 6.5 <9#m weight of cross girder#m for %."0m = 30".0 <9 T$is load +&('-(. /N, is acting at P01P&1P21P'1P3 P01P&1P21P'1P3 (eight for 3.$"#$ m portion = 1"$."3 <9 (eight for 0.$" m portion, (eight of pipe = 0.30 T (eight of water = 1. T (eight of plates 1 ' $ = 1.$0 T (eight of plate 3 = 0."1 T weight of cross girder = 0.115 T Total = 3.!5 T &dl load = 0.! T# T#m (eight for 0.$" m = 3!.53 T @aods at the ends of cross girder = 151.%6 <9 T$is load +454-23 /N, is a cting at P41P.
151.%6 0.$"
3.$"
30".0
30".0 3.$"
30".0
3.$"
30".0 3.$"
30".0 3.$"
? $0.0 m
F ss&ming the self weight weight of main girder = Total point load, ( = 150!.$6 <9 elf weight of girder = 5".%1 <9 elf weight of girder#m = %. <9#m
(@#%00
4or welded plate girder girder
Ma:im& Ma:im&m m shear shear force force =
G151. G151.%6: %6: $30". $30".0 0 : "#$ "#$ %.!" %.!"H$0 H$0I#$ I#$ 1001.!% <9 Feaction at ' 7 7ending Moment will /e ma:im&m at centre of /eam. Taking moment at centre, Moment 8 ? = F : $0#$ ;151.%6 3.$":3 ; 30".03.$":$ ; 30".0: 3.$" ; %.!" : 10 : " Moment 8 ? = %53!.6 <9m Ma:im&m hear force= Ma:im&m Moment =
1001.!% <9 %53!.6 <9m
Design of *e Plate: ss&ming thickness of we/ we/ plate as $" mm tw = $" mm -cono -conomi mic c dep depth th of we/ we/ pla plate te,, d = 1.1 1.1 : s>.r s>.rtt M M # /endi /ending ng stre stress ss : thi thick ckne ness ss = 1.1 s>.rt s>.rt %53!.6:1000 %53!.6:1000000#16 000#16":$" ":$" d = 1$03.60 1$03.6053 53 mm Therefore depth of plate = 1000 mm Minim&m thickness of plate re>&ired from shear consideration, Taking allowa/le shear stress = 100 9#mm$
3.$"
tw = hear force # shear stress : depth of we/ tw re>&ired from shear = 10.0$ mm ince tw adopted $" mm is greater than 10.0$ mm. O.< 6ence 7e can ado"t 4((( !! 8 0' !! as 7e 7 e "late for "late girdergirder-
Design of Flange Plate: llowa/le /ending stress= stress= 0.66 : $"0= 16" 9#mm$ ppro:imate flange area re>&ired re>&ired = Moment # all./ending stress stress : depth of we/ = $553 $5531. 1.31 31$3 $3 mm$ ss&ming thickness of flange plate plate = "0 mm 7readth of flange plate = rea of flange# thickness of plate = "5!.6 600 mm 4lange o&tstand shall not e:ceed 1$ times the thickness of plate. ct&al o&stand of flange = 600 ; $"#$ $!." mm which is less less than 1$ : "0 = 600 mm. O.< $ 4lange area pro2ided /* the plate = 30000 mm ince flange area pro2ided is greater than flange area re>&ired /* the plate. ence O.<. 600 mm "0 mm thick flange plate compression
$" mm thick we/ plate :
: 1000 mm
mm mm
"0 mm thick flange plate tension
600 mm ?heck for /ending stressB
mm
$G600 "03#1$ 600:"01000#$ "0#$ $I G$"10003#1$I Moment of nertia a/o&t :;: a:is = = 1.!63-010 mm% ct&al /ending stress = 1%". 9#mm $ ince at&al /ending stress is less than the allowa/le /ending stress, hence safe. 6ence 7e can ado"t 3(( !! 8 '( !! as flange "late for "late girdergirder*elded Connection Connection et7een flange and 7e: ori oriJo Jont ntal al shea shearr # mm = A ) # :: :: = 600 K "0 ) = 1000# 1000#$ $ "0#$ "0#$ oriJontal shear # mm = !%6.!1 9#mm (elding is done on /oth sides of the we/ ori oriJo Jont ntal al shea shearr # mm = $ : str streng ength th of of the the wel weld d !%6.!1 $ 0. : siJe of of weld : 1 : 10!
sol2in sol2ing, g, s = !%6.!1 !%6.!1 # $ $ : 0. 0. : 10! weld siJe,s= ".60 mm = 6 mm Cro2ide 6 mm f illet weld. @ength of fillet weld = % : siJe of weld or %0 mm whiche2er is more. = $% or o r %0 mm whiche2er more Therefore pro2ide %0 mm long fillet welds. paci pacing ng of weld eld = str strengt ength h of of wel weld d on on /ot /oth h fac faces es of we/ # hor horiJ iJon onta tall she shear ar#m #mm m pac pacin ing g= $:0. $:0.: :6: 6:%0 %0:1 :10! 0!#! #!%6 %6.! .!1 1 pacing = %$.!" mm sa* %0 mm The clear spacing /etween the fillet weld sho&ld not /e more than 1$ times the thickness of we/ plate for compression and 16 times times the thickness of we/ plate for tension. n an* case, the clear spacing shall ne2er e:ceed $00 mm Ma:im&m Ma:im&m clear clear spacing spacing = 1$:$" = 300 300 mm or $00 $00 mm, whiche whiche2er 2er is less. Cro2ide %0 mm as spacing of fillet weld. weld. T$erefore "ro%ide "ro%ide 3 !! si9e fillet 7eld of 2( !! long at s"acing of 2( !! cc for 7eld connection et7een flange and 7e "lateInter!ediate Stiffener: C$ec) for ;ertical stiffener: s per !00 ; 15!%, ?l. ?l. 6..3.1.a, Cg.!1, (hen the thickness of we/ adopted for the design is less than the thickness of we/ as mentioned in ?l. 6..3.1. a, then then the 2eritical stiffeners stiffeners are to /e pro2ided. tw adopted Ld1 s>.rt T2a cal#!16 1 d1s>.rt f* # 13%% $ d1 # !" 3 4or welded connection, d1 = 1000 mm 2erage shear stress stress = A # dw : tw tw T2a cal. = %0.0 9#mm $ tw from 1 = .6 mm mm tw from $ = 11.6 mm mm tw from 3 = 11.6 mm mm s the thickness adopted for we/ plate plate $" mm is greater than tw from 1,$ '3. ence 2ertical stiffeners are not re>&ired. C$ec) for 6ori9ontal 6ori9ontal stiffener: s per !00 ; 15!%, ?l. ?l. 6..3.1./, Cg.!$, (hen the thickness of we/ adopted for the design is less than the thickness of we/ as mentioned in ?l. 6..3.1./, then the horiJontal horiJontal stiffeners are are to /e pro2ided. tw adopted Ld$ s>.rt f* # 3$00 1 d$#$00 $ 4or welded connection , d$ = "00 : $ = 1000 mm d$ = 1000 mm tw from $ = %.5% mm mm tw from 3 = ".00 mm mm s the thickness adopted for we/ plate plate $" mm is greater than tw from 1'$. ence ence horiJontal stiffeners are not re>&ired. 6ence %ertical and $ori9ontal stiffeners are not re
Bearing Stiffener: 7earing stiffeners are &sed to transfer concentrated laods on the girder and hea2* hea 2* reactions at s&pports to the f&ll depth of the we/. 7earing stiffener at the s&pports are called as end /earing stiffeners. M7 3"0, !.1 mm thick, 100 mm long tw = $" mm $"0
$"0
The /earing stiffeners are designed as col&mns with the length of we/ e>&als $0 times the thickness of we/ from the centre line of /earing stiffener. s the /earing stiffeners stiffeners are pro2ided at the ends and the cross girders are spaced at $"0 mm from the ends of the plate girder, the /earing stiffeners are pro2ided e:actl* at the /ottom of the cross girder, girder, adopting the thickness of cross girder as stiffener thickness. O&stand of stiffener shall ne2er e:ceed 1$ t 1$:!.1 = 5.$ mm and hence 100 mm length on /oth sides of we/ is taken as the /earing length on the stiffener. 7earing area pro2ided = $ : 100 : !.1 $"0 : $" : $ = 1%1$0 mm$ 7ear 7earin ing g area area re> re>&i &ire red d= hea hearr forc force e # 7ea 7eari ring ng str stres ess s = 1001.!% 1001.!% :1000 :1000 # 1!."0 1!."0 $ = "3%3.1% mm ince /earing area pro2ided is more than the /earing area re>&ired. ence O.<. Moment of nertia of plate, :: = $G!.1:1003 #1$ !.1:100 100#$$"#$ $ I :: = 6!1$" mm% radi adi&s of g*rat ration, ion, r = s>. s>.root oot : :: : # rea rea of /ear /eariing ng r= $3.3 $3.3$ $ mm λ = @e # r -ffecti2e length, le = 0. : 1000= 00 mm λ = 30.0$ sa*, 30 4or λ = 30 and f* = $"0 9#mm $, permissi/le stress in a:ial compression from Ta/le Ta/le ".1 of !00 ; 15!%, σ ac = 1%" 9#mm$
σ ac = afe load, C = C = 1%" K 1%1$0 C = $0%%00 9 C= $0% <9 s the safe load $0% <9 on the the /earing area is more than the shear force 1001.!1 <9, hence O.<. Connection Connection et7een Bearing stiffener a nd 7e of "late girder: s for 3"0 mm depth, the cross girder takes care of the /earing , onl* for the remaining depth, the end /earing stiffeners are to /e pro2ided. (eld (eld stre streng ngth th re> re>&i &ire red d = hea hearr forc force e # % : 6"0 6"0 3!". 3!".3$ 3$ 9#mm 9#mm ss&ming 6 mm siJe fillet, fillet, trength of weld = 0. : 6 : 1 : 10! = %"3.6 9#mm s weld strength taken is more than the re>&ired strength strength of weld. ence 6 mm siJe of weld is is O.<.
The length of intermittent weld shall ne2er e:ceed 10 times thickness of /earing plate or $00 mm whiche2er is less. length = 10 : !.1 !1 mm mm or $00 mm ence adopt !0 mm long fillet weld. ?ent enter to cent entre spac spaciing of weld eld = !0 : %"3 %"3.6 .6 # 3!" 3!".3 .3$ $ = 5%.1"06 sa* 50 mm ?#? spacing of weld shall not e:ceed 16 t or 300 mm, whiche2er is less = 16 : !.1= 1$5.6 1$5.6 mm or 300 mm, whiche2 whiche2er er is less. less. ence adopt the weld spacing as 50 mm T$erefore "ro%ide "ro%ide 3 !! si9e fillet 7eld =( !! long at s"acing 5( !! cc for for t$e 7eld connection et7een earing stiffener and 7e-
DESIGN OF AB>T#ENT: AB>T#ENT: T$e Aut!ents are "ro%ided on ot$ sides of Nala to su""ort t$e !ain girders 7$ic$ rest on it for t$e full 7idt$ of "i"e line "ro%ided- T$e lengt$ of t$e aut!ent 7all is 0.-' !0.3 1 2 &
0.3 1.0"
' 6.0" 6.!
%." 0
P
$.
1
1.$"
eel
4
Toe
Design Data: @ength of /&tment = length of portion 1 = Thickness of portion 1 = eight of portion $ = ( idth of portion $ = eight of portion 3 = ( idth of portion 3 = eight of portion % = Thickness of portion % = eight of portion " =
$." %.5" 0." %." 1 0.3 1.0" 1 0.3 6.0"
m m m m m m m m m m
.
0." O
@ength of portion " = $. m Unit weight of earth = $.$ T#m3 Unit weight of concrete = $." T#m3 cti2e earth press&re coefficient, coefficient,
0.33 6.! m
Load Calculation: 1. Total Total weight coming on main girder d&e to pipe weight, water weight and cross girder =
151.%6 : $ 30".0 : " =
$. elf elf weig weight ht of gird girder er for for the the arri2 arri2ed ed dimens dimension ion =
0.6 0.6 : 0.0"0 0.0"0 : $ 1.0 : 0.0$" 0.0$" : $0 : !."0 !."0
3. -nd /earing tiffeners at &pports =
0.1 : 0.00!1 : 0.6"0 : !." : %=
Total load =
150!.$6
0.1
$0%1.!! <9
This $0%$ <9 is shared half e>&all* /* /oth the a/&tments @oad transferred to one a/&tment =
$0%1.!!#$
10$0.5% <9
There are totall* main girders which rests on the /&tment. @oad carried /* one a/&tment # metre length =
10$0.5% : # $."0 = =
$"5.5 <9 # m $60 <9#m
Eart$ Pressure:
6m
1#$ 1#$ :
*eig$t of eart$ on $eel sla: Cortion " weight = 6.% : $.3 : 1 : $.$ =
3".53 T#m 3"5.3 <9#m
4orces and Moments a/o&t /ase of Moment Sl-No-
Descri"tion
1
@oad on the a/&tment
$
cti2e earth press&re
3
elf weight of part 1
Forces +/N, ; $60.00 ; 5$.!1$"
6 ; 165."%6 ;
Le%er ar! +!, 1.6 $.$ $.%"
#o!ent aou #% %16.00 ; $$5.1
%
elf weight of part $
11!."
;
1."
$0.!1$"
"
elf weight of part 3
.!"
;
1.$"
13."!
6
elf weight of part %
."
;
$.1
1"."
(eight of earth on heel of part "
3"5.3
;
3.6
1$53.3
Total
=23-&4
435-''
04.3-'5
C$ec) for Stailit? : 4- O%erturning : O2ert& O2er t&rrning ning mome moment nt a/o& a/o&tt toe, toe, O = Festo estorring ing mome moment nt a/o& a/o&tt toe, toe, O = 4actor of safet* safet* against against o2ert o2ert&rnin &rning g=
3!%. 3!%.31 31 <9mca mca&s &sed ed /* ori oriJonta ontaal al eart earth h pre press ss&r &re e $16 $16.."5 <9m ca& ca&se sed d /* total otal weig eight act acting dow downwar nwards ds Festoring Festoring moment # O2ert&r O2ert&rning ning moment ".66 L $.00 afe
0- Sliding: 4orce ca&sing sliding = 165."" <9m µ( 4orce resisting sliding = (= !%6.31 $"3.!5$$" 4actor of safet* = 1."0 L or = 1."
afe
&- Bearing Pressure: @ocation of res<ant from 0 Ko = M2 ; Mh # A eccentricit* of res<ant, e = eccentricit*, e =
=
$.1$ m 7#$ ; Ko 0.36 m 0.!3 m afe
σ ma: =
A# 7 : 1 16 e#7 = $%".003 $"0 <9#m $. 9o tension, afe.
σ min =
A# 7 : 1 1;6 e#7 = 56.535 <9#m$.
9o tension, afe.
g#m
7
. C 0.$"
151.%6 0.$" F7
<9 133. 133.%" %" <9 <9
toe O +/N!, #6 ; 3!%.306 ;
; ; ; ; &=2-&4
