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.



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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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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LiveLoads


Considerdynamiceffects

DistributeLoad toeach irder


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


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


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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


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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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.


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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)


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


Train Loading

AREA: American Railroad En ineers Association


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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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

.


Example


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





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


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


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 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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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


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

.


Design Chart for Negative Moment due to Live Load Combination 3at Interior Support of Continuous Beams with Equal Spans

IM is included

Outline


Typical Loads

Dead Load

AASHTO HL93 Loads

Truck

Live Load

Live Load of Vehicle

Uniform Load



LL Placement

Influence Line t er oa s


Design Charts

in

Earthquake

Multiple Presence


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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)



LiveLoads





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


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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



LiveLoads





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


Beams (continued)

DF


Beams

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DF


DF


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


and LaneLoads)

effects

effects

es gn o g r ers

Outline


Typical Loads

Dead Load

AASHTO HL93 Loads

Truck

Live Load

Live Load of Vehicle

Uniform Load



LL Placement



Design Charts

in

Earthquake

Multiple Presence


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


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


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


Typical Loads

Dead Load

AASHTO HL93 Loads

Truck

Live Load Live Load of Vehicle

Uniform Load



LL Placement



Design Charts

in

Earthquake

Multiple Presence


40610 - Loads

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