PPT5-BridgeLoadpdfload and load distribution

load and load distribution

1. CIVE508BridgeEngineering
Loadandloaddistribution

2. Disclaimer:
2
•Manyslidesinthispresentationareadaptedfrom 2007PCABridge
Professors'SeminarbyDr.Cole in MississippiState University.
•All the slides areONLYforeducationalpurposein this class by registered
students.DoNOTcopy, reviseordisseminatepartiallyoraswholefor
any otherpurposeortoanyotherpeoplewhoarenot registeredin this
class. Each student is personally responsiblefor theconsequenceifhe
(she)failsto doso.

3. August
2007
3
Material
properties
Loads
Load
combinations
Philosophy/methodology
LRFD,ASD,LFD, etc.
Models
Available
shapes
"Analysis" "Design"
Structural "Analysis"/ "Design"Overview

4. 4
OBJECTIVE:To assurethe safe andeconomical
designofbridgestructures
LOADS
Theeffectof loads
onthestructure
RESISTANCE
Thestructure'sresistance
tothoseloads

Inorderforthistowork,bothsidesofthestatementmust
refertothesamecondition. Foranyparticularloadeffect,
theresistancemustbetheresistancetothateffect.

5. 5
LIMIT STATES
Alimit stateisaconditionbeyondwhichasystem(oracomponent
ofasystem) ceasestofulfillthefunctionfor whichitwasdesigned.
Thesystemorcomponentisloaded beyond its capability to resist.

6. 6
Types and examplesof commonlimit states
Type: Consequence: Example:
STRENGTH Collapse Exceedcrushingstrengthof concrete
ExceedbreakingstrengthofPSstrands
Buckling ofcompressioncomponent
Fatiguefailureof component
SERVICE Unacceptable
behaviornotinvolving
collapse
Excessivedeflectionatworkingloads
CrackingofPSconcretebeams
Slipof steelboltedconnections
Other"improperbehavior" Excessivefoundationsettlement
Squashingof bearingpads

7. 7
AASHTOLRFDservicelimitstates
AASHTOdesignation Limit state objective Loads
Service I
Limitcompressivestressingirder
and deckto maintainadequate
factor of safetyagainst concrete
crushing
Full value of service
(unfactored ) dead and
liveloadswith55mphwind
Service II
Limit tensile stressin girder to
maintain factor of safety against
steelstructure yielding and slipping
Similar to service I except
for steel
Service III
Limit tensile stressin girder to
maintain factor of safety against
concrete tension cracking
Full service dead load, but
reduced service live load
ServiceIV
Tension inP/S for crack controlw/
10-yr meanoccurrence wind
Full service dead load, but
reduced service live load

8. 8
AASHTOdesignation Limit state objective Loads
Strength I
Provide adequate resistanceto
girder "breaking" failure
Factored live and dead
Loads.w/owind
StrengthII
Provide adequate resistanceto
girder "breaking" failure
Special vehicle
StrengthIII
Provide adequate resistanceto
girder "breaking" failure
W/ wind exceeding 55 mph.
NoLL.
Strength IV Same as above For large-span bridge (high
DL/LL ratio), replace SLS I.
StrengthV Same as above Normal vehicle use with
wind=55mph.

9. AASHTOdesignation Limit state objective Loads
9
Fatigue
Limitstressescaused by repetitive
vehicleliveload
Loads producedby "fatigue
truck"
AASHTOdesignation Limit state objective Loads
ExtremeeventI Earthquake Load combination
Extreme event II Other hazards Load combination

10. 10
"Perhapsthemostdifficultpartofanystructural
designisdeterminingthedesignloads....."
Anonymous
LOADSANDLOADCOMBINATIONS
Regardlessoflimitstate:

11. 11
Regardlessofstructuretype,models areusedtodefinedesignloads:
LOADMODELS
Buildings:ASCE7-MinimumDesignLoadsforBuildingsand
OtherStructures . ASCE7isastandardthatisreferenced
inallmajormaterialperformance specifications(ACI,
AISC,NDS,etc)and buildingcodes(IBC2006,etc.)
Examples:
Deadload
Liveload
Forcesofnature
-volume•density
-loadperunitarea;concentratedloads
-replacewindeffect,seismiceffect, etc.
with"equivalent"staticloads

12. 12
Bridges:AASHTOLRFDBridgeDesignSpecifications.Contains
bothloadmodelsandmaterialperformancecriteria
ThefollowingpageswilllookatAASHTO:
Loadclassifications
Modelsusedtodefineloads
Loadcombinations
Applicationofloadeffectstocomponents
LOAD MODELS ( Continued)

13. 13
AASHTOLRFDLOADDEFINITIONSANDCLASSIFICATIONS
S3.3.2
Permanentloads
DD=downdrag
DC=deadloadofstructuralcomponentsand
non-structuralattachments
DW=deadloadofwearingsurfacesandutilities
EL=accumulatedlocked-inforceeffectsresulting
fromconstructionprocess
EH=horizontalearthpressureload
EV=verticalpressurefrom deadloadonearthfill

14. 14
Transientloads
BR
CE
=
=
vehiclebreakingforce
vehicularcentrifugalforce
CR
CT
CV
EQ
FR
IC
IM
LL
LS
PL
SE
SH
TG
TU
WA
WL
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
creep
vehicularcollisionforce
vesselcollisionforce
earthquake force
friction
iceload
impact
vehicularliveload
liveloadsurcharge
pedestrian liveload
settlement
shrinkage
thermalgradient
uniformtemperature
water load and streampressure
windon liveload
WS =windonstructure

15. 15
Loads normally used for designingprestressedgirder /
slabbridge superstructures:
Permanentloads( "deadloads") :
 DCloads-Componentsandattachmentswhose
weightscanbe computedwithreasonableaccuracy
Girder
Slab,haunch,stay-in-placeforms
Diaphragm
Railings("parapet")/barriers
 DWloads- Componentsandattachments
whoseweightscannot bedeterminedasaccurately
asDCloads
Futurewearingsurface(FWS)
actoncompositesection
Utilitiesandotherfutureloads
act on girder
actsoncompositesection

16. 16
slab
SIPform
haunch
girder
diaphragm
ServiceI, III(elasticanalyses)
Usegirdersectionmoduliito
computestressesingirderdue
totheseloads,plusprestress
StrengthI-DCloads
Useloadfactor=1.25
FWS
railing
ServiceI, III(elasticanalyses)
Usecompositesectionmodulii
tocomputestressesingirder
andslab
StrengthI-DWloads
Useloadfactor=1.50
DC/DWdeadloads

17. 17
Transientloads-AASHTO S3.6.1.2.1
Include:
Vehicularloads("liveloads")
Forcesofnature
Extremeevents(catestrophicloads,suchas
truck-railingcollisions)
Loads normally used for designingprestressedgirder /
slabbridge superstructures( continued ):
TherestofthispresentationwilllookattheAASHTOmodelsusedto
defineandapplyvehicular("live")loads togirdersandslabs,and
truck-railcollisionextremeeventloads.

18. "NOTIONAL"LOADS
18
AASHTOusestheconceptofnotionalloadsto definemodelliveloads:
•Notionalloadsareficticious("model")loadsthathavebeencreatedto
producethesameloadeffects(bendingmoment,shear)asobserved
inrealbridgescausedbyrealtraffic.
•TheAASHTO notionalloadshavebeen calibrated(optimized)basedon
strength. Thus,useoftheseloadsinagirderStrengthI analysisgives
resultsthatmostcloselymatchthosethatwouldproduce strengthfailure
inrealbridgecomponentsusingfactoredrealtraffic loads.
•Thenotionalloadsalsohappentogivegirdercompressivestressesat
serviceloadsthat reasonablymatchthoseproducedbyrealtrafficonreal
bridges. Therefore,thestressesproducedbythenotionalloadsareused
intheServiceI elasticanalysis
•But,thenotionalloadspredictgirdertensilestressesatserviceloadsthat
aregreaterthanthoseproducedbyrealtrafficonrealbridges.Therefore,
thestressesproducedbythenotionalloadsareadjusted(multipliedby
0.80)foruseintheServiceIIIelasticanalysis.

19. 19
DesignTruckLoad
( S3.6.1.2.2)
25 kips25 kips
Design Tandem Load
( S3.6.1.2.3)
4'
DesignLaneLoad
( S3.6.1.2.4)
32kips
8 kips
32kips
14' to 30' 14'
0.64kips/foot
Notional vehicularloads(S3.6.1.2.1)

20. 20
TheDesignTruckandDesignTandem loadsare axleloads:
25kips
25kips
DesignTandem
August
2007
4'
6'
32kips
32kips
8kips
traveldirection
14' -30'
14'
6'
leadingaxle
trailingaxle
DesignTruck

21. 21
Why the variable spacing between centerand trailing axles?
Simply-supportedspans:
Strengthand service limit states:14'spacing(loadscloselygrouped)produces
greatestdesigntruckloadmoment,shearand
deflection(S3.6.1.2.2)
Fatigue limitstate:30'axlespacing (S3.6.1.4.1)
32 328kips
32328 kips
14'14'
30'14'
August
2007

22. 2C
2 ontinuousspans:Example-truck load placement to cause maximum
negativemomentatcentersupportinatwo-span
continuousbridge(Service or Strengthlimitstates)
50'
longspans
32k32k8k 32k32k8k
14' 14' 14' 14'
32k32k8k
shortspans
30'14'
50' 50'

23. 23
Applicationofvehicularliveloads:Serviceand Strengthlimitstates
(S3.6.1.3)
DesignTruckplus DesignLane
OR
DesignTandemplus Design Lane
Usewhichevercausesgreaterloadeffect
32kip32kip8kip 25kip 25kip
0.64k/ft 0.64k/ft
Notethatthedesignlaneloadisnotinterruptedto"providespace"fortheaxleloads

24. 24
Fatigue (S3.6.1.4.1):
Applicationofvehicularliveloads:Fatiguelimit state; Impact
Applyto Fatigue Truck only (donotuselaneload)
32 328kips
30'14'
Impact-"Dynamicimpactallowance"(S3.6.2):
Appliestotruck/tandemloadsonly(doesnotapplytolaneload)
FromAISCTable 3.6.2.1-1:IM
Allcomponents exceptdeckjoints:
Service and Strengthlimit states:33%
Fatigue limit state: 15%
Deckjoints (all limit states): 75%

25. 32328 kips
14'14'
0.64kips/ft
140'
V
LL=liveloadshear
V
Lane
i=1 i=6 i=11
89.4
mirrorimagesym.
79.8
70.2
60.6
51.1
41.5IM•V
Truck=1.33• V
Truck
V
LL=V
Lane+1.33• V
Truck
i=1 i=6 i=11
134.2
116.1
96.9
mirrorimagesym.
82.5
67.2
52.7
i=1 i=6 i=11
44.8
36.3
26.7
21.916.1
mirrorimagesym.
11.2
Simply-supported single-spanbridge:Numerical example (continued )
Similar for Dual Tandem + Lane loads
25

26. Step1:Liveloadmomentdiagramsandenvelopes(continued)
Multi-spanindeterminatebridges
32328 kips
14'14'
0.64kips/ft
L
1 L
2
Loads:
Truckload( similarfortandem load)-trucksononeormorespans
Laneload-loadonall orselectedspansegments
Computeranalysisgenerallyrequired:
RecommendQConBridge*,availableatnocostfromtheWashingtonStateDOT:
www.wsdot.wa.gov/eesc/bridge/software/index.cfm?fuseaction=download&software_id=48
26

27. Multi-span indeterminatebridges -overview(continued )
ApplicationofVehicularLiveLoads:
For negativemomentbetweenpointsof contraflexurecausedbyauniformloadonall
spans,andreactionsatinteriorpiersonly,use:
Case1(S3.6.1.3.1)
•90percentoftheeffectoftwodesigntrucksspacedaminimumof50.0ft.between
theleadaxleofonetruckandtherearaxleoftheothertruck(thedistancebetween
the32-kipaxlesofeachtruckshallbetakenas14.0ft.),
PLUS
•90percentoftheeffectofthedesignlaneload
Case2(notstatedinS3.6.1.3.1):
•100percentofonedesigntruck( varyspacingbetween32-kipaxles),
PLUS
•100percentofthedesignlaneload
Forallothereffects,useonetruckperspanpluslaneload.
27

28. 32328 kips
14'14'
0.64kips/ft
L L
Multi-span indeterminatebridges -overview(continued )
Usethetwo-spancontinuous bridgeshownbelowtoillustratethese requirements:
Fortheuniformly-distributedloadonbothspans:
Pointsofcontraflexure
0.25L 0.25L
Region1
Region2
28

29. Positive live load moment:
1.33• maximummomentproducedbymovingtruckthroughIL-peak( bothdirections)
PLUS
momentcausedbyuniformloadoverfullspanlengthL
29
August
2007
Multi-span indeterminatebridges -overview(continued )
Positivemoment(sameforRegions1and2):
Example: M
x
+
(0xL)
x
L
InfluencelineforM
x
32 k 32 k 8 k
14'14'
8k 32k 32k
14'14'

30. Multi-span indeterminatebridges -overview(continued )
Negativemoment( Region1 ):
Example: M
x
-
( 0x0.75L)
Negativeliveloadmoment:
1.33• maximummomentproducedbymovingtruck(bothdirections)
PLUS
momentcausedbyuniformloadoverfullspanlengthL
x
L
InfluencelineforM
x
32 k 32 k 8 k
14'14'
8k 32k 32k
14'14'
L
30

31. Multi-span indeterminatebridges -overview(continued )
Negativemoment( Region 2 ):
Example: M
L
-
(0.75L<xL)
x=L
InfluencelineforM
x=L
L
32 k 32 k 8 k
14'14'
32 k 32 k 8 k
14'14'
spacing 50'
Negativeliveloadmoment:
1.33• maximummomentproducedbymovingtrucktrain( varyspacing)
90% PLUS
momentcausedbyuniformloadoverfullspanlengthL
Case1
31

32. Multi-span indeterminatebridges -overview(continued )
Negativemoment( Region 2 ):
Example: M
L
-
(0.75L<xL)
x=L
InfluencelineforM
x=L
L
32 k 32k 8 k
14'-30'14'
Negativeliveloadmoment:
1.33• maximummomentproducedby truck( varyaxlespacing)
100% PLUS
momentcausedbyuniformloadoverfullspanlengthL
Note:Theonlytimethatthiscasemaycontrolthenegativesupportmoment
and/ortheinteriorpierreaction isifthetwospans L areveryshort.
32
Case 2

33. 32k 32k 8k
14'14'
0.64k/foot
Vary spacing
from 50' to
140'in ten
steps of 9'
32k 32k 8k
EA B C D
0.25L 0.25L
Negative
moment
inBCD:
90% *
(1.33M
T2
+ M
LANE)
1.33M
T1
+ M
LANE
M
T2=momentcausedby
twodesigntrucks
Multi-span indeterminatebridges:Example
2-spancontinuousbridgespan
33
32k 32k 8k
14'14'
Positive
moment
inABCDE
and
Negative
momentin
ABandDE:
M
T1=momentcausedby
onedesigntruck
140' 140'
QConBridgemomentenvelopeonnextslide

34. Multi-span indeterminatebridges:Example( continued )
FromQConBridge:
34

35. Design Lane Number
Designlanevs.trafficlane
No. of design lanes=w/12.0
W=clearroadwaywidthinft.between
curbs/barriers.
If the actual trafficlanes arelessthan12ft
wide, No. of design lanes=No. of traffic
lanes; width of design lanes =width of traffic
lane

36. Step2-Girdermomentsandshears
36

37. Girder moments and shears
TheDesignTruck (or,alternately,theDesignTandem)andtheDesignLane
loadsare defined to act in a 10-ft-wideDesignLane. They do notaccount for:
•Where thedesignlaneis placedwithintheroadwaywidthofthebridge
•Where thedesignlaneis placedrelativetothegirders
• Thenumber oflanesthatfitwithintheroadwaywidth
ofthebridge
•Theprobabilitythattwoormoreadjacentlaneswillbeloaded
simultaneously
• Theabilityofthebridgedeckto laterallydistribute
theloadinone ormorelane(s)tomorethanone
girder
37

38. Distributinglaneloadstogirdersdependsonseveralthings:
Girder spacing
Girdersclosetogether -
shorterdirectloadpathto girders;
stiffer slabmoregirdersinvolved
Girdersfarapart -
longerloadpathto girders;moreflexible
slab fewergirdersinvolved
38

39. Loadpositionrelativetogirders:
39

40. Slab stiffness-abilityto transferloadstoadjacentgirders
Verystiffslab-loadis
distributedequallyto girders
40
Veryflexibleslab-loadis
carriedbyonlyonegirder
Usual case-loadis distributed
betweengirders,but girders
underloadcarrygreatestshare.

41. deflect+twist
deflect
deflect+twist
Girder flexuralandtorsionalstiffness-functionsofgirder length,momentofinertia(
flexure)and area(torsion):
• Longgirdersaremoreflexiblethanshortgirders, which tends to increaseload
distributionbetweengirders
• Girderswithsmallmomentsofinertiadeflectverticallymorethangirderswith
large momentsofinertia,whichtendstoincreaseloaddistributionbetween
girders
• Girderswithsmallareastwistmorethangirderswithlarge
areas,whichtendsto increaseloaddistributionbetween
girders
41
Example:Singleloadsymmetricallyplacedoverinteriorgirder

42. Numberof adjacentloadedlanes:
TheAASHTOloadingmodelassumesthattherecanbedistributionofvehiclesona
bridge at anygiven time (a"vehicle"is representedby a combinationof a truckor
tandemload,plusalaneload):
•TheDesignVehicleloads(A)arethenominal (reference)loads
•Therecanbeanoccasionalsinglevehicleload( B) greaterthanthe
DesignVehicleloads
•Somevehicleloads(C,D) will belessthantheDesignVehicle loads
A =DesignVehicle load
B
A AA
C
D
C
A
D D
C
42

43. A
C
A
A
D
C
C
Twoadjacent
loads@A
C
D
C
D
A
A
D
D
A
C
D
C
A
A
C
C
C
C
D
D
D
C
C
C
D
C
D
C
Fouradjacent
[email protected]
D
D
D
D
A
C
C
C
D
C
D
D
C
A
A
C
C
C
Threeadjacent
[email protected]
C
D
D
D
A
Singleload
B=1.2A
A
D
A
C
C
D
Multiplepresence factor for adjacent loaded lanes:
43

44. B= 1.20•AA =DesignValue( reference)
C = 0.85•A
44
D = 0.65•A
Multiplepresence factor for adjacent loaded lanes -AASHTOload model:

45. TheAASHTOloadmodelsassumethatthereis thesame probabilitythattherecan be:
•Onevehiclethatis120%heavierthantheDesignVehiclein one lane
•TwoDesignVehiclesin two adjacentlanes
•Threevehiclesthatareeach85%oftheDesignVehicleloadinthreeadjacentlanes
•Fourormorevehiclesthatareeach65% oftheDesignVehicle loadinadjacentlanes
Multiplepresencefactors:
TheAASHTOSpecification(S3.6.1.1.2) usesmultiplepresencefactorstoaccountfor
theprobabilitythatvehiclesofthesefourloadclasseswilloccurinadjacentlanes.
Table3.6.1.1.2-1-MultiplePresenceFactors,m
45
Number of
loaded lanes
Multiple presence
factors, m
1 1.20
2 1.00
3 0.85
3 0.65

46. 14'
14'
GirderMomentsandShearsbytheAASHTO"SimplifiedMethod":
DistributionFactors
Formostprestressedgirder/slabbridges,permits"distribution"ofliveload per
lanemomentsandsheartogirdersthroughtheuseofdistribution factors.
46

47. Laneloadmomentdiagram
Truckloadmomentenvelope
(Dual tandemsimilar )
Totalliveloadmomentfor10'lane
M
LL M
Lane= + ( 1+IM) • M
Truck
Shearsimilar
47
1. Totalliveloadmomentfor10'lane(frompreviousslides)

48. M
LL=M
Lane+ ( 1 + IM ) • M
Truck
"Distribute"
M
L(int)=M
LL• DF
M(int)
M
L(ext)=M
LL• DF
M(ext)
M
L(int)=designlive load
momentfor
interior girders
designlive load
momentfor
exteriorgirder
M
L(ext)=
DF
M(int),DF
M(ext)=
"distributionfactors"
formoment-AASHTO
Tables4.6.2.2.2b-1,
4.6.2.2.2d-1
(DFlabeled"g"inSpec.)
Note:"Distribution"assignsaportionof theliveload
momentM
LLtoindividualgirders (itdoesnotdivide
theliveloadmomentbetweengirders).
2. Usedistributionfactors(DF) obtainliveloadmomentorshearinindividualgirders
Liveloadmomentfor10'lane:
48

49. TheAASHTOSimplifiedMethod( distribution factors ) may be used when:
•Thedeckwidthisconstant
•Thereareatleastfourgirders
•Thegirdersareparallelandhaveapproximatelythesamestiffnesses
•Bridge curvature islimited (see S4.6.1.2)
•The roadwaypart of the overhang,d
de3.0 ft:
49
•Thebridgecross-sectionisoneof thoseshowninTable4.6.2.2.1-1
e

50. Multiplepresencefactorsusedin DistributionFactortables
Thedistributionfactorsincludethefollowingmultiplepresencefactors:
Interiorgirders
m=1.20
m=1.20m=1.00
m=1.00
Exteriorgirders
50

51. Noteson usingDistributionFactorsfromthesetables:
Service andStrengthlimit stateanalyses( moment, shear):
•ComputeDistributionFactorforboth"OneDesignLaneLoaded"and"Two
DesignLanesLoaded"
•UselargerDFtocomputegirdermomentorshear
Fatiguelimit state(momentonly) -singletruck,singlelane,multiplepresencefactor=1
•Obtainlaneliveloadmomentsfortruckonly,rearaxlespacing=30'
•ComputeDistributionFactorfor"OneDesignLaneLoaded"only
•DividecomputedDistributionFactorby1.20toeliminatemultiplepresencefactor
51
Distributionfactortablesapplicabletoprestressed-girder/slabbridges:
Table4.6.2.2.2b-1
Table4.6.2.2.2d-1
Table4.6.2.2.3a-1
Table4.6.2.2.3b-1
MomentsinInteriorBeams
MomentsinExteriorBeams
ShearinInteriorBeams
ShearinExteriorBeams

52. Example:
The "One DesignLaneLoaded"distribution
factorincludesthe1.20multiplepresence
factorshownearlierforasingleloadedlane.
52
Multiplepresencefactorreferencecondition
(multiplepresencefactor=1.0).

53. DF
M(int)(moment,interior girder,twolanes loaded ):
t
s
2
e
g= y
t+ t
h+
t
s
2
c.g.(girder)
y
t
t
s
t
h
L=girderlength,ft
S=center-centergirderspacing,ft
t
s=slabthickness,in
A=girderarea, in
2
I=girdermomentof inertia,in
2
n=modularratio( girderE/ slabE)
e
g =distancebetweencentersof gravityofgirderanddeck,in
K
g=n( I +Ae
g)
2
DF
M(int)= 0.075+

0.1
53
3L12.0Lt
s
Kg
0.2
0.6
S S
9.5






54. Numericalexample: Span:L =140' Girderspacing:S = 8.0'
Slabthickness:t
s=7.5"
Girder:E
g=4,800ksi
Haunchthickness:t
h=1.5"
Slab:E
s
y
t=35.40in.
=4,000ksi
I
g=545,850in
4BT-72girder:A
g=767in
2
Interiorgirder( twoloadedlanes)
t
s
2
e
g= y
t+ t
h+
2
t
s
c.g.(girder)
35.4"
7.5"
1.5"
= 3.75"
= 35.4" + 1.5" + 3.75" =40.65"
n= 1.20
4,800ksi
4,000ksi
E
g
E
s

K
g=n( I +Ae
g)
2
=1.20 (545,850in
4+767in
2( 40.65in)
2)=2,175,910in
4
DF
M(int)=0.075 +
0.1
K
g
3
0.2

0.6
12.0Lt

9.5 L
S S






=0.075+
0.1

54
3
0.6 0.2
8.08.0
12.0140(7.5)
2,175,910

9.5 140 
 



=0.6443

55. DF
M(int)(moment,interiorgirder,onelaneloaded):
DF
M(int)= 0.06 +
0.1

3

g

0.3

0.4
12.0Lt
K

14 L
SS




Numericalexample-continued(seepreviousslide):
n= 1.20
4,800ksi
4,000ksi
E
g
E
s

K
g=n( I +Ae
2)=1.20(545,850in
4+767in
2( 40.65in)
2)=2,175,910in
4
g
DF
M(int)=0.06+
0.1

3
0.4 0.3
8.08.0
12.0140(7.5)
2,175,910

14 140 
 
 


=0.4390
For two loadedlanes(previousslide):
DF
M(int)=0.6443>0.4390
Use
NOTE: Donotapplymulti-presencefactor=1.20(itis includedintheDFexpression)
Numericalexample-conclusion:
55

56. 56

57. DF
M(ext)(moment,exteriorgirder,onelaneloaded):
Leverrule:
P
P
2
P
2
10'lane
6'3' 1'
S+d
e7':
P
2
R
S
d
e
DF
M(ext)= 





RS d
e 1
2SP
S+d
e7':
R
S
d
e
P
DF
M(ext)= 





RS d
e 4
 SP
Assumedhinge
57
P
R
S
P
2
P
2
d
e
1.0'
truckpositionedat
outsideedgeoflane

58. 58
August
2007
Numericalexample: Girderspacing:S=8.0ft d
e=1' -9"=1.75ft
Exteriorgirder,onelaneloaded
S + d
e=8.0ft+1.75ft=9.75ft>7.0 ft
DF
M(ext)=





S d
e 4


S
R
P





8.0 1.754


8.0
=0.7188
R
8.0'
1.75
P
1.0'

59. DF
M(ext)(moment,exteriorgirder,twolanesloaded):
d
e
DF
M(int)= 0.6443
Numericalexample(continuedfrompreviousslides):
1.75
Foroneloadedlane( previousslide):
DF
M(int)=0.71880.6200
Use
DF
M(ext)= 0.77


9.1
1.75
0.6443=0.6200
DF
M(ext)= 0.77

59

9.1
de
DF
M(int)

60. Liveloadmomentfor10'lane:
M
Lane+ ( 1 + IM ) • M
Truck= 4547.2ft-kM
LL=
DF
N(int)=0.6443 ( two loadedlanes )DF
N(ext)= 0.7188( two loadedlanes )
M
L(int)= 0.6443( 4547.2ft-k) = 2930.0ft-k
M
L(ext)= 0.7188( 4547.2ft-k ) = 3268.5ft-k
8.0ft
140ft
Numericalexample( concluded):
60

61. RequirementofLoadandLoad Distribution
Conceptual
Designtruck,tandemandlaneloadfor
differentlimit states;
Procedureofdecidingcriticalliveload
inducedmomentshear(e.g.influence
lines,diagramsandfinallyMLL,QLL)
Multiplepresencefactorandlateral
distribution factors
Examples
Understand2examplesinthisslidesand
canrepeatbyyourself.

62. 62