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Transcript of 40610 - Loads
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Praveen ChompredaMahidol University
First Semester, 2010
Class To ics & Ob ectives
Topics Objectives
Loads on Bridges Students can describe thevarious type of loads on a
Placement of Live Loads for
Maximum Effect
Students can explain the effects
of live load position on theshear and moment within a
bridge girder
tu ents can etermine t emaximum live load effect based
on the desi n code
Distribution of loads withinmulti- irder brid e
Student can determine theportions of dead load and live
load to be assigned to a girder
Class To ics & Ob ectives
Parts of the topics discussed in this class can be found in:
Cha ter 4, es eciall 4.2
Section 5.1-5.4
Section 14.6-14.9
Outline
Loads on Bridges Design Lane
Typical Loads
Dead Load
AASHTO HL93 Loads
Truck
Live Load
Live Load of Vehicle Uniform Load
LL Combinations Pedestrian Load
Dynamic Load Allowance
LL Placement
Influence Line
t er oa s
Fatigue Design Equation
Design Charts
in
Earthquake
Multiple Presence
Distribution to Girders
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Loads on Brid e
DD = downdrag (wind)
BR = breaking force of vehicle=
= ea oa o
structural and
nonstructural components
CR = creep of concrete CT = vehicle collision force (on bridge or at
DW = dead load of wearing
surface
CV = vessel collision force (bridge piers overriver)
=
(horizontal)
EL = secondary forces such as
FR = friction IC = ice
from posttensioning
ES = earth surcharge load
= ynam c oa o ve c es
LL = live load of vehicle (static)
LS = live load surcharge
EV = earth pressure (vertical)
PL = pedestrian load
SE = settlement SH = shrinkage of concrete
TG = load due to temperature differences TU = load due to uniform temperature
= WL = wind on vehicles on bridge WS = wind load on structure
yp ca oa s
Dead Loads: DC/DW
Live Loads of Vehicles: LL
Pedestrian Load: PL
Dynamic (Impact) Loads: IM
Dead Load: DC
Dead load includes the self weight of:
structural components such as girder, slabs, cross beams, etc
nonstructural components such as medians, railings, signs, etc
ut oes not inc u e t e weig t o wearing sur ace asp a t
We can estimate dead load from the materials density
Material Density (kg/m3)
Concrete (Normal Weight.) 2400
Concrete (Lightweight) 1775-1925
Steel 7850
Aluminum Alloy 2800Wood 800-960
Stone Masonr 2725
Dead Load of Wearin Surface: DW
It is the weight of the wearing surface
usua y asp a t an ut t es p pes,
lighting, etc)
large variability of the weight compared
with those of structural components(DC)
Asphalt surface may be thicker than
layer over and over
Density of asphalt paving material
= 2250 kg/m3
Average Thickness of asphalt on bridge
= cm
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Tributar Area for Dead Loads
Dead loads are distributed to girder using Tributary Area method
DC DW
M=wL2/8
=w
DC DW
Section for maximum moment is not the same as the sectionfor maximum shear
For simply-supportedbeams
Maximum M occurs at midspan
Maximum V occurs over the support
As we shall see in the designs of girders, the Critical Section for shear isabout dfrom the support.(where dis the effective depth of section,a roximatel 0.8h
At this point, shear is slightly lower than at the support. If we use shear atthe support for the design of stirrups, we are conservative.
Live Loads of Vehicles: LL
Live Loads of Vehicles: LL
vehicles moving on the bridge
There are several types of
bridge structures depends onmany parameters including:
vehicles
Car
span length
weight of vehicle Van
Buses
ax e oa s oa per w ee
axle configuration
osition of the vehicle on the
Semi-Trailer
Special vehicles
bridge (transverse andlongitudinal)
Military vehicles
num er o ve c es on t e r ge(multiple presence)
girder spacing stiffness of structural members
(slab and girders)
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Live Loads of Vehicles: LL Brid e LL vs. Buildin LL
BRIDGE BUILDING
LL is very heavy (several tons perwheel
LL is not very heavy, typical200-500 k /m2
LL can be series of point loads (wheelloads of trucks) or uniform loads (loads
LL is assumed to be uniformlydistributed within a span
Need to consider the placement withina span to get the maximum effect
Do not generally considerlacement of load within a s an
Loads occur in one direction withinlanes
Loads are transferred in to 2directions
ee to cons er a so t e p acement o
loads in multiple spans (for continuousspan bridges)
Need to consider various
placements of loads for theentire floor
Dynamic effects of live load cannot beignored
Do not typically considerdynamic/impact effect of live
Anal sis Strate for LL Effect in Brid e
Place them Moment/ Shearar ous
LiveLoads
to getmaximumeffects on
Considerdynamic
effects
DistributeLoad to
each irder
from Live Loadto be used in the
span
Design Truck
Design Tandem
Uniform Lane Load
Desi n Lane
Need to know how many lanes there is on the bridge
Design Lane Actual Traffic Lane3.0 m 3.3 m to 4.6 m (3.6 m recommended)
= .
No. of Actual Traffic Lane
Number of Lane must be an inte er 1,2,3, there is no fraction of lane
(no 2.5 lanes, for example)
For roadway width from 6 m to 7.2 m, there should be 2 design lanes, each
equal to of the roadway width
roadway width
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Live Loads of Vehicles: LL
For design purpose, we are interested the kind of vehicle that produce theworst e ect
AASHTO has 3 basic types of LL called the HL-93 loading (stands for
,
Design truck
Design tandem
Uniform loads
1. Desi n Truck
The design truck is called HS-20--
with 20-kips weight on first twoaxles)HS-20
Weights shown on the left arefor each one axle = 2 wheels
= ~ .
Distance between the second andthird axles may be varied topro uce maximum e ect
Need to multiply this load byd namic allowance factor IM
2. Desi n Tandem
Two axle vehicle with 110 kNon eac ax e
Need to multiply this load by110 kNper axle
110 kNper axle
Lead to larger moment than the
HS20 truck for simple-supportbeam with span length less than
13.4 m
Traffic DirectionsLoading
ane
55 kN 55 kN
. m TOPVIEW
1.2 m
3. Uniform Lane Loadin
Uniform load of 9.3 kN/m acting over a tributary width of 3 m. (i.e. the2 .
May be apply continuously or discontinuously over the length of thebridge to produce maximum effect
No dynamic allowance factor (IM) for this load
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Anal sis Strate for LL Effect in Brid e
Place them Moment/ Shearar ous
LiveLoads
to getmaximumeffects on
Considerdynamiceffects
DistributeLoad toeach irder
from Live Loadto be used in the
span
Transverse Placement
ong tu na acement
Live Load Combinations
3 ways to add the design truck, design tandem, and uniform load together
Combination 1: one HS20 truck on top of a uniform lane load per design lane
Combination 2: one Design Tandem on top of a uniform lane load per designlane
Combination 3: (for negative moments at interior supports of continuousbeams) place two HS20 design truck, one on each adjacent span but not less
an m apar measure rom ron ax e o one ruc o e rear ax e oanother truck), with uniform lane load. Use 90% of their effects as the designmoment/ shear
The loads in each case must be positioned such that they producemaximum effects (max M or max V)
e maximum e ect o t ese cases is use or t e esign
Live Load Placement
Need to consider two dimensions
Transversely (for designs of slabs and overhangs)
roadway width
Longitudinally (for design of main girder)
Live Load Placement - Transverse
The design truck or tandem shall be positioned transversely such that thecenter o any w ee oa s not c oser t an:
30 cm from the face of the curb or railing for the design of the deck overhang
min. 2'
Minimum distancefrom curb = 60 cm
Note that if the sidewalk is not separated by a crash-resistant traffic barrier,
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Live Load Placement - Lon itudinal
Need to place the LL along the span such that it produces the maximume ect
For simple supported beam with 1concentrated load, the maximum
Point of Max
Moment
L/2 L/2
However, truck load is a group of concentrated loads. It is not clear whereto place the group of loads to get the maximum moment
REMEMBER: MAXIMUM MOMENT DOES NOT ALWAYS OCCURS
Live Load Placement - Lon itudinal
Methods of finding maximum moment and shear in span
Influence Line (IL) Simple and Continuous spans
Design Equation Simple span only
Design Chart Simple span only
Live Load Placement Influence Line
Influence line is a graphical method for finding the variation of the structura response at a po nt as a concentrate ve oa moves across
the structure
Structural res onse can be su ort reaction, moment, shear, or dis lacement
Live Load Placement Influence Line
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Live Load Placement Influence Line Live Load Placement Influence Line
Live Load Placement Influence Line
Influence line is a powerful visualization tool for the effects of live loadp acements to t e structura response
110 kN 110 kN
For Point Load, theresponse is equal to the
value of point load multiplied-
1.0
0.50.25
0.75
the influence line
IL (RL)
For Uniform Load, the
of the uniform load multipliedby the area under the
n uence ne w t n t euniform load
Live Load Placement Influence Line
1.0
IL (RL)
0.50.25
.
1.00.75
IL (RL)
.0.25
1.0
0.75
IL (RL)
.0.25
1.0
0.50.75
IL (RL)
0.25
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Live Load Placement Influence Line Live Load Placement Influence Line
Mller-Breslau Principle: If a function at a point on a beam, such asreact on, or s ear, or moment, s a owe to act w t out restra nt, t e
deflected shape of the beam, to some scale, represent the influence line of
the function.
Live Load Placement Influence Line Live Load Placement Influence Line
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Live Load Placement Influence Line
Notes
Influence line tells you how to place the LL such that the maximum
moment at a point occurs; i.e. you first pick a point, then you try to
moved around
It does not tell ou where the absolute maximum moment in the s anoccurs, nor its value; i.e. the maximum moment on the point you
picked is not always the absolute maximum moment that can occur in
t e span w ic wi occur at a i erent point an un er a i erentarrangement of loads)
Live Load Placement Influence Line
For series of concentrated load (such as the design truck), the placemento oa or max mum moment, s ear, or react on may not e apparent.
The maximum always occur under one of the concentrated loads but
Two methods
Trial and Errors: Move the series of concentrated loads alon the s anby letting each load on the peak of IL
Use when you have only 2-3 concentrated loads
Can be tedious when you have a lot of concentrated loads
Live Load Placement Influence Line
Train Loading
AREA: American Railroad En ineers Association
Live Load Placement Influence Line
Increase/ Decrease Method
This method determine whether the response (moment, shear, orreaction) increases or decreases as the series of concentrated loads
As the series of loads move into the span, the response increases.
When it starts to decrease, youll know that the last position wasthe one that produce the maximum effect.
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Live Load Placement Influence Line
Increase/ Decrease Method
For shear
Sloping Line Jump
V = Ps(x2-x1) V = P (y2-y1)
For moment
Sloping Line
= -
IL for moment
has no jumps!
Note: not all loads may be in the span at the same time. Loads that havejust moved in or moved out may travel on the slope at a distance less
.
Live Load Placement Influence Line
Example
Live Load Placement Influence Line Live Load Placement Influence Line
For Statically Indeterminate Structures, the Mller-Breslau Principle alsoo s
If a function at a point on a beam, such as reaction, or shear, or moment,
, ,
some scale, represent the influence line of the function
For indeterminate structures, the influence line is not straight lines!
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Live Load Placement Influence Line Live Load Placement - Lon itudinal
Methods of finding maximum moment and shear in span
Influence Line (IL) Simple and Continuous spans
Design Equation Simple span only
Design Chart Simple span only
Live Load Placement Desi n E uation
Another Method: Using Barres Theorem for simplysupported spans
The absolute maximum moment in the span occurs under the load
c oset to t e resu tant orce an p ace in suc a way t at t ecenterline of the span bisects the distance between that load and the
resultant
Resultant 0.73 m
145 kN 145 kN35 kN
L/2 L/2
HS20Point of Max
Moment
Live Load Placement Desi n E uation
Resultant 0.73 m
145 kN 145 kN35 kN
L/2 L/2
HS20
Moment
max
172.181.25 387 kN-mM l
l
max
19.855 66 kN-mM l
l
Mmax occurs at a section under middleaxle located a distance 0.73 m from
Mmax occurs at a section under one ofthe axle located a distance 0.30 m from
midspan midspan
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Live Load Placement Desi n E uationCase Load Configuration Moments (kips-ft) and
shears (kips)
Loading and limitations
(x andl in feet)
Truck loading32 32
xPxV
ll
x
PxxM
4215.4)(
15.4)(A
P = 16 kips
MA
MB
for:
l > 28
x l/3x + 28 l
x 721
A
Bor any x
Truck loading
=32 32
x
ll
xPxV
xll
215.44)(
.
B
= ps
MB
MA
for:
l > 28
x > l/3
14 x l/2
x
x
ll
x
xxM
2
2150)(
C
Tandem loading
is more severe than truck
25 25
llx)(
xlxxM
)(640
loading forl 37 ft
0.64 k/ft
x
x
lxV
264.0)(
2.
D Lane loading
x
Live Load Placement Desi n E uation
If we combine the truck/tandem load with uniform load, we can get theo ow ng equat ons or max mum moment n spans
Live Load Placement - Lon itudinal
Methods of finding maximum moment and shear in span
Influence Line (IL) Simple and Continuous spans
Design Equation Simple span only
Design Chart Simple span only
Live Load Placement Desi n Chart
Bendin Moment in Sim le S anfor AASHTO HL-93 Loadingfor a fully loaded lane
Moment in kips-ft
IM is included
1 ft = 0.3048 m
1 kips = 4.448 kN
1 kips-ft = 1.356 kN-m
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Live Load Placement Desi n Chart
Shear in Sim le S anfor AASHTO HL-93 Loadingfor a fully loaded lane
Shear in kips
IM is included
1 ft = 0.3048 m
1 kips = 4.448 kN
Live Load Placement Desi n Chart
Design chart is meant to be used for preliminary designs.
We assume that maximum moment occurs at midspan this produces.
However, the error is usually small.
Maximum shear occurs at support. However, the chart does not havex = 0 ft. The closest is 1 ft from support.
In general, the bridge girder much higher than 1 ft. Therefore, shear at 1 ft isstill higher than the shear at critical section for shear(at d) so we are still
.
Live Load Placement Desi n Chart
Design Chart for Negative Moment due to Live Load Combination 3at Interior Support of Continuous Beams with Equal Spans
IM is included
Outline
Loads on Bridges Design Lane
Typical Loads
Dead Load
AASHTO HL93 Loads
Truck
Live Load
Live Load of Vehicle
Uniform Load
LL Combinations Pedestrian Load
Dynamic Load Allowance
LL Placement
Influence Line t er oa s
Fatigue Design Equation
Design Charts
in
Earthquake
Multiple Presence
Distribution to Girders
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Pedestrian Live Load: PL
Use when has sidewalk widert an cm
Considered simultaneously with
Pedestrian onl : 3.6 kN/m2
Pedestrian and/or Bicycle: 4.1kN/m2
No IM factor (Neglect dynamiceffect of pedestrians)
Anal sis Strate for LL Effect in Brid e
Place them Moment/ Shearar ous
LiveLoads
to getmaximumeffects on
Considerdynamiceffects
DistributeLoad toeach irder
from Live Loadto be used in the
span
D namicAllowance Factor
(IM)
D namic Load Allowance: IM
Sources of Dynamic Effects
ammering e ect w en w ee s it t e iscontinuities on t e roa sur acesuch as joints, cracks, and potholes
D namic res onse of the brid e due to vibrations induced b traffic
Actual calculation of dynamic effects is very difficult and involves a lot of
unknowns To make life simpler, we account for the dynamic effect of moving vehicles
by multiplying the static effect with a factor
Dynamic Load
Effect due to
Static Load
Effect due to
Dynamic Load
Allowance Factor
D namic Load Allowance: IM
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D namic Load Allowance: IM
Add dynamic effect to the following loads:
Design Truck
Design Tandem
Pedestrian Load
Desi n Lane Load
Table 3.6.2.1-1 (modified)
Component IM
Deck Joint
75%
m t states
All other components above groundFatigue/ Fracture Limit States 15%All Other Limit States 33%
Foundation components below ground 0%
* Reduce the above values by 50% for wood bridges
Anal sis Strate for LL Effect in Brid e
Place them Moment/ Shearar ous
LiveLoads
to getmaximumeffects on
Considerdynamiceffects
DistributeLoad toeach irder
from Live Loadto be used in the
span
u t p e resence o
Distribution Factors
Multi le Presence of LL
Weve considered the effect of load placement in ONE lane
But bridges has more than one lane
Its almost impossible to have maximum load effect on ALL lanes at the same time
The more lanes you have, the lesser chance that all will be loaded to maximum at
Multi le Presence of LL
We take care of this by using
1.0 for two lanes and less for 3 ormore lanesNumber of Multi le
This is already included
(indirectly) into the GDF Tables
Loaded Lane Presence Factor
m need to multiply this again
Use this only when GDF is
1 1.20
2 1.00eterm ne rom ot er ana ys s
(such as from the lever rule,computer model, or FEM)
3 0.85
> .
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Distribution of LL to Girders
A bridge usually have more than one girder so the question arise on howto str ute t e ane oa to t e g r ers
Using AASHTOs table: for typical design, get an approximate
conservative value
No need to consider multiple presence factor
Lane Moment
Girder Moment
Distribution FactorDF
ane ear r er ear
Refined analysis by using finite element method
Need to consider multiple presence factor
AASHTO Girder Distribution Factor
DFs are different for different kinds of superstructure system
DFs are different for interior and exterior beam
roadwa width
Exterior Exterior
Interior
larger one controls) Must make sure that the brid e is within the ran e of a licabilit of the
equation
AASHTO Girder Distribution Factor
Factors affecting the distribution factor includes:
Span Length (L)
Girder Spacing (S)
o u us o e asticity o eam an ec
Moment of inertia and Torsional inertia of the section a c ness ts
Width (b), Depth (d), and Area of beam (A)
L Number of girders (Nb)
DF
For AASHTO method
the type ofsuperstructuresupport eam ec
types)
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DF
Types
DF
Distribution factor for
Beams
DF
Distribution factor for
Beams (continued)
DF
Distribution factor for
Beams
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DF
Distribution factor for
DF
Distribution factor for
GDF
Effects of girderstiffness on thedistribution factor
GDF Finite Element Anal sis
Bridge Model
(a)
(c)
Boundary (Support)Conditions
GDF Fi i El A l i
M d Sh i T i l Gi d
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GDF Finite Element Anal sis
1 21 2
Load distribution in model
Moment and Shear in T ical Girder
At any section, if not using AASHTOs GDF
MLL+IM, Girder = DFM(Mtruck/tadem,LaneIM + Muniform,Lane )m
VLL+IM, Girder = DFV(Vtruck/tadem,LaneIM + Vuniform,Lane )m
At any section, if using AASHTOs GDF MLL+IM, Girder = DFM(Mtruck/tadem,LaneIM + Muniform,Lane )
VLL+IM, Girder = DFV(Vtruck/tadem,LaneIM + Vuniform,Lane )
Placed such thatwe have maximum
LivePlace them Increase the
oa s(Truck,Tandem
to getmaximum
static load byIM to account
Multiplyby DF
from Live Loadto be used in the
and LaneLoads)
effects
effects
es gn o g r ers
Outline
Loads on Bridges Design Lane
Typical Loads
Dead Load
AASHTO HL93 Loads
Truck
Live Load
Live Load of Vehicle
Uniform Load
LL Combinations Pedestrian Load
Dynamic Load Allowance
LL Placement
Influence Line t er oa s
Fatigue Design Equation
Design Charts
in
Earthquake
Multiple Presence
Distribution to Girders
t er oa s
Fatigue
Wind
Earth uake
Vehicle/ Vessel Collision
Fati ue Load F ti L d
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Fati ue Load
Repeated loading/unloading of live loads can cause fatigue inbridge components
Fatigue load depends on two factors
Magnitude of Load Use HS-20 design truck with 9m between 145 kN axles for determination
o max mum e ects o oa
Frequency of Occurrence:
se SL = average a y ruc ra c n a s ng e ane
Fati ue Load
ADT
Average Daily Traffic
(All Vehicles/ 1 Direction)From Surve and extra olate Class of Hwy % of Truck
Table C3.6.1.4.2-1
to future)Max ~ 20,000 vehicles/day
Rural Interstate 0.20
Urban Interstate 0.15
% of Truckin Traffic
Other Rural 0.15
Other Urban 0.10
ADTT
Average Daily Truck Traffic Table 3.6.1.1.2-1
Number of Lanes
Available to Trucks
p(Truck Only/ 1 Direction)
1 1.00
2 0.85
Single Lane (p)
3 or more 0.80SLAverage Daily Truck Traffic
(Truck Only/ 1 Lane)
Wind Load
Horizontal loads For small and low bridges, wind
There are two types of windloads on the structure
oa typ ca y o not contro t e
design
Wind pressure on the
structure itself
river/sea, wind load on the
structure is very important WL = wind on vehicles on
bridge
Need to consider the
aerodynamic effect of the
n pressure on t e
vehicles on the bridge, whichthe load is transferred to the
(turbulence) wind tunnel
tests
bridge superstructure
Wind loads are applied as static
Need to consider the
dynamic effect of flexible
horizontal load ong-span ri ge un er t ewind dynamic analysis
Wind Loads WS WL
WL
WS
(on Superstructure)
WS
(on Substructure)
Wind Load Earth uake Load: E
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Wind Load
acoma arrows ri ge acoma, as ington, A
The bridge collapsed in 1940 shortly after completion under wind speed lowerthan the design wind speed but at a frequency near the natural frequency ofthe bridge
The resonance effect was not considered at the time
Earth uake Load: E
Horizontal load
The magnitude of earthquake is characterized by return period
. .
Small return period (e.g. 50 years) minor earthquake
For large earthquakes (rarely occur), the bridge structure is allowed tosuffer significant structural damage but must not collapse
or sma eart qua es more e y to occur , t e r ge s ou st e nthe elastic range (no structural damage)
Earthquake must be considered for structures in certain zones
Analysis for earthquake forces is taught in Master level courses
Earth uake Load: E
The January 17, 1995 Kobeeart qua e a ts ep center r g t
between the two towers of the
Akashi-Kaik o Brid e
The earthquake has the
magnitude of 7.2 on Richter scale The uncompleted bridge did not
have any structural damages
e or g na p anne engt was
1990 meters for the main span,but the seismic event moved the
towers apart by almost a meter!
Earth uake Load: E
Water Loads: WA Vehicular Collision Force: CT
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Water Loads: WA
Typically considered in the design of substructures (foundation, piers,a utment
Water loads may be categorized into:
Buoyancy (vertical uplifting force)
Loads depend on the shape and size of the substructure
Vehicular Collision Force: CT
Bridge structures are very vulnerable tove c e co s ons
We must consider the force due to
Vehicular Collision Force: CT
Typically considered in the design of substructures (foundation, piers,a utment
The nature of the force is dynamic (impact), but for simplicity, AASHTO
.
Need to consider if the structures t icall ier or abutment are notprotected by either:
Embankment
Crash-resistant barriers 1.37m height located within 3 m
Any barriers of 1.07 m height located more than 3 m
For piers and abutment located within 9 m from edge of roadway or 15 mfrom the centerline of railway track
Assume an equiva ent static orce o acting orizonta y at .m above ground
Vehicular Collision Force: CT
No protection to the bridge
structureBetter protection (still not sufficient)
Vessel Collision: CV Reca
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Vessel Collision: CV
No protection tothe bridge piers
Bridge piers areprotected
Reca
Loads on Bridges Design Lane
Typical Loads
Dead Load
AASHTO HL93 Loads
Truck
Live Load Live Load of Vehicle
Uniform Load
LL Combinations Pedestrian Load
Dynamic Load Allowance
LL Placement
Influence Line t er oa s
Fatigue Design Equation
Design Charts
in
Earthquake
Multiple Presence
Distribution to Girders