deck example

8/16/2019 Deck Example

1/100

SIMPLE

BRIDGE

DESICN

USING

PR

ESTRESSED

BEAMS

ON

p

pp


2/100

Simple

Bridge

Design

using

Prestressed

Beams

An introduction to

the

design

of

simply-supported

bridge

decks

using prestressed

concrete

bridge

beams

B

A

NICHOLSON


3/100

11

ISBN

0

95000347 2

X

©

Prestressed Concrete Association

1997

Prestressed Concrete Association

60

Charles Street

Leicester

LE

11

FB

Typeset

by

B. A.

Nicholson.

Design

by

G. Ballantyne.

Printed

by

Uniskill

Ltd.


4/100

CONTENTS

FOREWORD

1

STANDARD

BEAMS 2

1.1

History

2

1.2

Bridge

deck

ypes

4

1.3

Choice

of

section

6

1.4

Standard sections

6

1.5 Practical site

considerations 8

2

BEAM & SLAB DECKDESIGN EXAMPLE

12

3 GRILLAGE MODEL

14

3.1

Introduction 14

3.2

Suitability

of

Grillage Analysis

14

3.3

Grillage

models or

prestressed

beamdecks 16

3.4

Deck idealisation

18

3.5 Section

properties

20

3.6 Edge stiffening

22

3.7 Torsion

24

4

CALCULATIONOFLOADS

26

4.1 Introduction

26

4.2 Definitions

26

4.3

Highway loading

28

4.4 Wind load

32

4.5 Pedestrian liveload

32

4.6

Temperature

effects

32

4.7

Shrinkage

36

5

APPLICATION OF

LOADS

38

5.1 Load

Combinations

38

5.2 Selection

of

Critical LoadCases

38

5.3

Input

to

Grillage Analysis

40

6

PRESTRESSED BEAMDESIGN

44

6.1

General

44

6.2 Design Bending Moments 44

6.3

Serviceability

Limit State

46

6.4 Prestress losses

50

6.5 Ultimate limit

state 56

6.6

Shear

60

6.7

Longitudinal

shear

66

111


5/100

iv

7

FINISHINGS

68

7.1

Introduction

68

7.2

Bearings

68

7.3

Waterproofing

and

surfacing

80

7.4 Joints

82

7.5

Parapets

84

8 SOLID SLAB DECK DESIGN

EXAMPLE 86

8.1

Introduction

86

8.2

Grillage analysis

88

8.3

Design

of ransverse reinforcement 90


6/100


7/100

2 SIMPLE BRIDGE DESIGN

USING PRESTRESSEDBEAMS

STANDARD BEAMS

1.1 HISTORY

The

use

of

precastprestressed

beams in

bridge

decks in the

post

World

War

II

era

owes its success in he main o the

foresight

of he Prestressed Concrete

Development

Group,

which n the 1950's

developed

the firststandard

beamsections

to

beavailable

fromthebeam

manufacturers.

This enabled

factory production

of

he

beams

on

a

large scale, and,

with the dawnof

major

road construction

in

the late 1950'sand its

philosophy

of

grade

separation for

motorways

and trunk

roads,

it

gave bridge engineers scope

to

rationalise

design

procedures usingup-to-date

load distribution theories.

The standard beam sections available

at that time have ofcourse themselves been

developed

and

modified,

and in essence

only

one

really

remains

today

with

any

significant usage.

This

beam,

he inverted

T

beam,

s

used n

bridge

decks in

spans up

to

about 20 metres.

With herapid

development

of

he

UK

motorway

network

n the

1960's,

it

wasclear

that here

was

scope

for

a

standardbeam hatwould enable

larger spans

tobe

achieved.

Consequently,

at

the end of he decade

a

new beam was

introduced

for

spans

from

about

15 to 30metres. This was

designated

the

M

beam,

due o itswidth and ntended

spacing.

These

beams were intended

for

use

in

pseudo-slab bridge

decks with

a

contiguous

concretebottom

flange

using

transverse reinforcement located

hrough

lower

web holes at 600mm centres

along

the beams.

Eventually engineers

realised that he Mbeamcould

be

used more

efficiently

in

beam

and slabdecks

by eliminating

the bottom in-situ concrete and

by

spacing

hebeams

apart

at

up

to

1.5

metre centres. The limitation

on thistype

of

use

proved

to be

the

shear

capacity

of he

beams,

whichhave

a

web thickness of

only

160mm.

Other

beams

developed

around this time were the

U

beam

for

beam and slabdecks

up

to about30 metre

spans,

anda

U

shaped

variation

of he

M

beam

foruse

as

edge

beams

in M

beam

decks.

Eventually,

with the

very popular

M

beam

being

used in

a

manner somewhat different

from its intended

use,

and

bearing

in mind the various

problems

and

limitations his

presented,

a

newbeamwas

developedby

the Prestressed

Concrete Association

in the late 1980's. This was

designated

theY

beam.

The

Y

beam now has three

variants: the

TYbeam,the

Y

beam,and the SY

beam.

Together

these cover all

span ranges up

to

45m. It

is

expected

that

in

due course

inverted T beams and

M

beams

will cease

to

be used

in

favourof he enhanced

properties

of he

Y

beam

anges.


8/100

H

M beam

Inverted T beam

U beam

STANDARD BEAMS 3

TY beam Y

beam SY

beam


9/100

4 SIMPLE BRIDGEDESIGN

USING PRESTRESSED BEAMS

1.2

BRIDGE DECK TYPES

Concrete

bridge

superstructures

using precast

prestressed

concretebeams fall

into

threedistinct

ypes:

slab

decks, pseudo-slab

decks,

andbeam and slabdecks.

Slab Decks

Slab decks can be solid or

voided,

and

provide simplysupported spans

of

up

to

20

metres. Thesedecksusestandard TY or inverted

T

beams

placed

side

by

side. The

space

between them is then filled with in-situ

concrete,

and an overall

covering

of

75mm

completes

the deck.

Continuity

of

hese

decks

canquiteeasilybe

achieved

by

using

einforcement

in

the

in-situ concrete

over the

supports. Suspended

spans using

TYbeams or inverted

T

beamscanbe

lightened

by

introducing

voidformers into the

space

between the beams.

Pseudo-slab

Decks

This

type

of

bridge

structure

is

currently

not

quite

so

popular.

Precast

beams are

incorporated

intoavoidedslab

ype

ofdeck

by

either

adding

an in-situ bottom

flange

and

op flange,

aswith the

original

Mbeam

decks,

or

by using

voidedbeams

e.g.

box

beams).

A voided slab deck is thus created without the inconvenience

of

emporary

works

andsoffit

shutters,

and

provides

a

torsionally

stiffer deck than

ordinary

beam andslab

decks.

Spans

for this

type

of

bridge

deck are

usually

imited

by

the

length

of

precast

beams

that canbe

transported

to

site,

and thereforeare

rarely

more than 30 metres.

BeamandSlab Decks

The mostcommon

type

of

uperstructure

for small

o

medium

spanbridges,

this

ype

ofdeck

comprises

individual

precast

beams

at

discrete centreswith anin-situ concrete

top flange.

M

beams,

TY

beams,

Y

beams,

SY

beams,

and Ubeams can all be used

inthis form

ofconstruction.

Withmost

of

hestandard

range

of

precast

beamsthe in-situ

concrete

top

slab

is

cast

into

permanent

formwork whichislocated nrecesses formed

n he

edges

of he

top

flanges

of he beams.

Typical spans

for this

type

ofdeckare similar

o the

pseudo-

slabdecks

above, being

imited

in the main

bytransportable

beam

components.

Standard

edge

beams are available to

complement

the

Y

beam,

TY

beam,

and

M

beam

anges.

These

provide

avertical visible

face,

and

have he

capacity

to

carry

he

extraloads from

the

parapet

cantilever.


10/100

STANIAiu

BEAMS

5

This solid

slab

deck uses

19

T2

beams.

Service

ducts are included in

the

infihl

concrete

between

he

beams.

This

bridge

deck uses nine

US

beams

at a

spacing

of1

.72m.

Service ducts

run under

the

footpath.

A

carrier drain

runs

through

one

of

he

U

beam

cells.

This

bridgedeck uses

seven Y8

internalbeams

at a

spacing

of

1

.275m,

and

YE8

edge

beams on

each

side.

Service ducts

run under

the

footpath.


11/100

6

SIMPLE

BRIDGE DESIGN USING PRESTRESSED

BEAMS

1.3 CHOICE

OF SECTION

For the

types

of

superstructure indicated above,

the beam

manufacturers provide

standard details

of

he

individual sectionsand their

anges together

with anindication

of

ypical span ranges

for

decks

incorporating

these beams

and

carrying

standard

highway

loads.

Therewill

obviously

besituations

where the choiceofdeck

type

isnot

clearly

indicated

by

the available

span,

and itisalso inevitable

that herewill beareas

of

overlap

where

the choice between

invertedTbeams in a slab

deckor ndividual M or Y beams

n a

beam and slab deck

may

not be

clear cut.

In this

situation

it

may

be

necessary

to

evaluate more than one

solution,

and hestandard sections enable aswift

selection of

the

available ranges

for

comparative design exercises

to

be

undertaken

and cost

comparisons

made.

It is also

possible

within

thestandard

range

of

each beam

ype

to be in a

span

range

that is covered

by

more hanone

specific

beamunit. In thissituation

it

is

usually

cost

effective

o

select the

larger

unit where

there arenorestrictive imitationsonheadroom.

1.4

STANDARD SECTIONS

Design

Although

he various

types

ofstandard

beam

sections are

well

documented

interms

ofdimensions

andstructural

properties,

it is

mportant

to

point

out that these

factory

produced

beams are standard

only

to the extent

that

they

are manufactured

using

standard

shaped

sections. The amount

and

magnitude

of

prestress

applied

to

each

beam is

dependent

on its

individual

situation,

and mustbe

determined

by

the

designer

prior

to

manufacture. The standard sectionsshow

where

prestressing

strands

may

be

located,

but

it isthe

responsibility

of he

designer

todetermine which

of

hese are

to

be

used.

Intheir

literature,

themanufacturers

givesuggestions

for

gooddesign

details. These

should be adhered

to,

as

they

leadto

economy

and

good workmanship.

Manufacture

Precast

prestressed

beams

aremanufactured n

long

lines

of

everal

units

using

straight

strands.

These

are debonded

for

varying

distances

at

the ends

of

each beam

within

the

mould. Thisis

necessary

tomaintain the

stress inthebeam atan

acceptable

level

as the

self-weight bending

moment educes

approaching

the

supports.

Once theconcrete

in

the moulds reaches the minimum

transfer

strength, detensioning

can take

place,

the strands between the beamcan

be

cut,

and the beamsremoved

to

the

storage

area

prior

to

delivery

o site.


12/100

Standard

positions

for

prestressing

strands inaY8 beam.

It is

up

to

the

designer

to

decidewhichof hese strand

positions

o

use.

STANDARD

BEAMS 7

Span

in

metres: 12

14 16 18 20 22

24 26 28 30

32

Beams

at im

centres

Beams

at

2m centres

£

Beam

selection chart for the

Y

beam

range,

takenfrom PCA

literature.

-1-4-

4--I-

-4--I-

4--I-

-4-4-

-4--I-

-I--I-

-I--I-

-4--I-

1300

1200

1100

1000

900

800

+4--I--I-

-4- -4-

4-

260

210

160

-

110

60

0


13/100

S SIMPLE BRIDGE

DESIGNUSING PRESTRESSED BEAMS

1.5 PRACTICAL SITE

CONSIDERATIONS

Handling

Beamsare

usually

manufactured

with

lifting loops,

hus

enabling

on site

lifting

to

be

achieved

witheither

single

or twin cranes

o suit he site

requirements.

However,

TY

beams and

inverted T beams are

usually

lifted

using

a

sling

through

the end web

holes.

Access

to

Site

Itisof

obvious

importance

that there

is

suitable access

to

the

bridges

in order forthe

beams o

be

delivered

and

lifted

off

he trailerby

suitably located cranes.

Of

course,

this also

applies

to

the route to the

construction

site

which

must

allow

the

delivery

lorries

omanoeuvre

their

engthy

loads.

There s

generally

no

problem

in he

transportation

ofbeamsof he

lengths

described

in thisbook.

Camber

Variation in camberof

prestressed

beams

is

nevitablewhenoneconsiders

he olerance

in

prestress

force and

ocation,

togetherwithpossible

variation

in concrete

properties

with

maturity

andclimatic conditions.

It

would

thereforebe

impracticable

o

specify any

limitationon

camber

values, although

a

olerance

oncamber variation between beamshasbeen

adopted.

However,

it

should

been

borne

in mind

by

the

designer

that an

occasional failure

to meet

the

specified

tolerance

on

soffit level variation does

not result n

impossible

constructionconditions.

Thecareful

positioning

of

adjacent

beams

n adeckshould

nearly

always

result n an

evening

outofdifferential camber.

Edge

Details

On

site,

construction

of

parapet

tring

courses

in one

or

more

stages generally

follows

the construction

of

he central deck slab area.

This necessitates the formation

ofa

construction

joint

along

the

edge

beam

prior

to

constructing

thefascia.

Alternatively,

it

is sometimes

possible

to

construct

thefasciaas

a

second

stage casting

in the

manufacturer's

yard, prior

to

delivery

to site

as

analmost

complete

unit. One

advantage

of

this

is

that

the

beam can

be

propped quite easily

at the

works,

thus

enabling

stresses

nthe

precast

beamsection tobeminimised.


14/100

/

STANDARD BEAMS 9

This section

can be

cast on

site

as

a

second

stage

after

the

rest of

the deck,

or

alternatively can

be

cast

onto

the UM beamby

the

manufacturer

so that

the

edge

beam and

parapet

can

be

brought

to

site

as

a

single

unit.

Two

examples

of

edge

details

Second

stage

in-situ

concrete

in-situ

concrete

Cast

by

manufacturer


15/100



Skew

Although

it

is

possible o

manufacture

precast

beams

with skew

ends,

he increase in

cost for each unit and

the

problems

that skew

presents

should be considered

in detail

at the

design

stage.

Firstly,

it

should

be

remembered

thatevena

very

small

change

inskew

angle equires

anew

stop

end for the mould. A

change

from

say

300

to

31° increases the width

by

12mmfor an

M

beam.

To rationalise a

range

of

angles

with a variation

of

10°, say,

would be auseful

andeconomic

possibility

Structural

problems

created

by

skew

in the endsof

precast

beamsrelate

specifically

to

the acute corner,

where the

formation

of

cracks can cause the

corner

of

he flange

to

spall

whenthe beamcambers

during

transfer.

Although

not

structurally significant,

this is

undesirable,

and isbest

prevented by blocking

out the corner to

give

a local

square

end.

An additional

problem

that

presents

itselfwith skew beams is hatof

ocating

ransverse

reinforcement

through

thewebholes. Itisrecommended that thestandard

webholes

permit

reinforcementtobe

placed

forskews

up

to about 35°.

Higher

skewshan this

would

require

special

non-standard

web

holes,

whichwould increase the costof he

beams

significantly,

and

may

evenaffect

the shear

capacity

of hesection. For

high

skew

bridges,

it

is

normallybetter

to

place

thetransverse

deck

reinforcement

at

ight-

angles

o the beams rather han

parallel

to the

abutments.

Transverse Reinforcement

For the transverse

reinforcement

through

the webholes of

precast

beams,

it is

usually

betterto use

anumberof mallerbars rather thana

single large

diameter

bar,

as

lap

lengths

are reduced

and

handling

becomes easier. For some awkward skew situations

it

may

even be sensible

to use untensioned

prestressing

strand threaded

through

the

web

holes

instead of

einforcing bars,

as it ismore flexible.

The

positioning

of ransverse deck

reinforcementwhen

using

solid

edge

beams

may

require

the useof

couplers

atthe

edge

beaminterface.

Temporary Support

Itis

mportant

to ensure

that the beamsarc

supported

so that

they

cannot

topple

over

on site.

Deeper

beams,

particularly

when

beingjacked

to their final level and

during

bearing

installation,

mustbe

assessed to eliminatethis risk.


16/100

STANDARD BEAMS 11

Local

square

end

to M

beam

330

wide

Diaphragm

800 wide

M

beam

bridge

deck

with

45°

skew.

Diagrams

show

endsof

M

beams

embedded

in

a

diaphragm.

tDecks1ab

M

beam

Web

hole at end

ofM

beam,

for

diaphragm

reinforcement

Diaphragm

I

L


17/100

12

SIMPLE BRIDGE

DESIGN USING PRESTRESSED BEAMS

2 BEAM

& SLAB DECK DESIGN

EXAMPLE

Sections 3 to

7

of

his book

consist

of

a

design example

of

a

beam and slab

deck.

This

design

example

shows the

typical sequential

calculations

necessary

for thefull

design

of

a

precast

pretensioned

concreteY beam

in a

simply supported

beam

and

slab

bridge

deck.

The

right

hand

pages

show the numerical

calculations involved ateach

stage,

and the

left hand

pages

contain

explanatory

comments

andfurther information.

The

example bridge

has the

following design requirements:

Span

26.6lm

single

span

Width

7.3m

carriageway, plus

I

.0m

hard

strip

each side

1

.5m

footpath

eachside

Loading

HA

plus

37.5 units HB

Surfacing

100mm

thick

(minimum) plus

20mm

waterproofing

The

following

materials

willbeused:

Precast concrete

=

50N/mm2

fd

=40N/mm2

In-situ concrete

f

=

40N/mm2

Prestressing

strand 15.2

mmdiameter

Dyform

strand

f

=

1820 N/mm2

Area

=

165 mm2

per

strand

The

edge

detailwas chosen

foraesthetic

reasons,

and the outerbeams

placed

as near

tothe

edges

of he

bridge

within his

limit. This ledtothe beam

spacing

of1 275m.

The

span

charts for Y beams

give spans

for beams

at I and 2 metre

spacings.

It is

straightforward

to

interpolate from

this

information

to

make an initial

selection

of

beam

size,

in thiscase Y8.

Clearly

alternatives would have been

possible,

for

example

eleven Y6 beamscould

have been

used,

atabout 1 metre

spacing.

However,

ithas been found hatunless it

is

necessary

to make the deck as shallow as

possible,

it

is

usuallypreferable

to use

fewer but

larger

beams.


18/100

DESIGN

EXAMPLE

13

13350

Overall

llatdstn'p

£rniagew

fw

540 1500 1000

7300

1000 1500 540

1275 1275

Cross

se/

f ridge

decfordes#/,

xgir/e


19/100

14 SIMPLE BRIDGE

DESIGNUSING PRESTRESSED BEAMS

3 GRILLAGE MODEL

3.1 INTRODUCTION

Early

bridge

decks were

analysed

ona

strip

basis. Abnormal

and wheel loads were

crudely

distributed and conservative

designs

resulted.

Experimental

data became

available

todeterminethe ransverse load

carrying

characteristicsofdeckstodetermine

thecorrect

level of ransverse

strength provision

and

todistribute loadmore

ogically

to the

longitudinal

members. For

example,

in the

1950'sMoriceand Little

developed

a Distribution Coefficient

method which was a

simple

hand method based on

experiments

which

allowed

for

the

overall distribution

of

oads

on

a

plate structure

such

as

a

bridge

deck.

It was

satisfactory

for skews

up

to200. This method was one

of everal similar

echniques

extensively

usedin

design

offices

for

approximately

15

years,

until the adventof

omputer techniques

which enabled

larger

andmore

complex

structures

to be

analysed

more

accuratelyusinggrillage,

finite

strip

and

finite element

methods. Of hese threemethods

grillages

offer the widest

range

of tructures

which

can

be

analysed.

Popular opinion suggests they

are also the easiest

to use and

understand.

No

analysis

method

gives

a

rigorous

solution,

and some

degree

oferror must

be

accepted, usually

angingup

to

10%

or

20%

depending

on

complexity.

These

errors

come

fromseveral

sources, including

the idealisation

of he

geometry

andmaterial

properties,

and idealisation of he structural

behaviour.

Grillage analysis

has

found favour as a

bridge engineer'sdesign

tool because it is

perceived

to have

the

following

advantages:

•

Grillage

beams

can be

positioned

to

correspond

with

physical

beams

n

the real

structure,

or

wheremaximum effects are

anticipated.

•

Modern PC versions

have 'user

friendly' input,

often

designed

by

engineers,

and use

pre-

and

post-processors

to

ease

subsequent checking,

searching

and

analysis.

•

Familiarity

of

use in the

design

office

enables

rapid analysis

and

checking,

which isvital ina

competitive

market.

•

Programs

are

relatively cheap,

thus

making analysis

economic.

3.2 SUITABILITY

OF GRILLAGE

ANALYSIS

The

method

can

be

used for

structures with

beamand slabs

decks,

voided slabs or

solid slabs.

Itcan be usedfor

simple

andcontinuous

bridges,

and allow for elastic

supports

andsettlement.

It issuitable for

right,

skew

and curveddecks. This

range

covers hundredsifnot housands

of

bridge

decks

designed

inrecent

times,

and

certainly

covers

all

bridges

with

prestressed

beams.


20/100

GRILLAGE

MODEL 15

NILLAfi

ANAL

418/8

This

km/ge

wi/Ike

aira/ysed

with

a

gill/agea#a/qsiS.

The

an'a/qsiS

wY/be

etformedasitig

he

conipaterprogram

"STAN)

111/181)8

"

from'

T


21/100

16

SIMPLE BRIDGE DESIGN USING PRESTRESSED

BEAMS

3.3 GRILLAGE MODELS FOR PRESTRESSED

BEAM

DECKS

Longitudinal grillagebeams areplaced

on he

line

of

hephysicalbeams,

and

represent

the

composite

action

of

he beam and its

associated section

of slab.

Longitudinal

beams arealso

positioned

along

the

parapet edge

beam. Transverse elements

represent

the

top

slab. Thereare no end

diaphragms

in this

bridge,

but whenthese are

present

they

must also

be

represented

by

appropriate

transverse elements.

This

type

of

grillage

model

is

suitable for beam

and slabdecks

using

M-beamsand

Y-beams.

Because

of

he

usually arge

numberofbeams naT-beam

deck,

it

may

be

preferable

to

model

two or three

beams

by

onegrillage

member. Transverse elements represent

transverse solid

infill

elements.

Because of henon-uniform

shape

of

hese elements

as

they pass

over and

through

he beams their

depth

is

normally

taken to the centre

lineof he ransverse holes. Thewider

spacing

of

model elementsdoes not

materially

affect the transverse element idealisation since the structure acts

as

a

true slab.

However,

care

isneeded

when

evaluating design

moments

shearsand

reactions due

to

thecombination

of

everal

physical

elements into

single

model elements.

U-beam

decks,

although basically

beam and slab

decks,

behave

differently

because

the

transverse stiffness

alternates across the

deck

between stiff

hrough

the

beams

and

flexible between

the

beams.

The

beams

are

positioned

to

try

and

equalise the top

slab

spans

between

and acrossbeams. Onemethod

of

modelling

a

U-beamdeck

is

o

place longitudinal

elements

on

hecentrelineof ach

web. The

longitudinalproperties

for

each

grillage

beam are then

taken as

half

hat of he

composite

box section. As

with the inverted T-beam

decks,

care

is

required

in

evaluating

the

output

since here

are now two

longitudinal

elements

representing

one

physical

beam.

r n

•1

n

•

\U/ \U/

\

p p p p p


22/100

GRILLAGE MODEL

17

oft/re

deck

The

bridge

looks

like

thi;

Their-s/tii

dowHskHdfa'sck7

aNd

tkearetbeevi,

reboM

d,cot/,gog

a,rdso do rot

co#tribite

10te

S

Theci

s-sec1lo,r

oft/re

strgctiiral

elemeirts

oft/rebridge

I

t/reremre'

ri/lage

eams

willbe

/aced

o

ire

ites

oft/re

t/ire

preteirsioired

beams,

airdirom4ra/edge

beams

wi/Ibe

p/aced

a/oirg ireparapetke'ams.

Thustire

grit/age epreseirtatA'r

ft/re

cross-sectloiti

p

Traitsverse memberswillbe

provided

at

1. 9Osr

4rtetva/s

o

epreseirt

ireslab.

Thi

diVides ire

leiigtir

oft/re

deck4rto

14

eqjialsectiirs.

The rodes

of

ire

grit/age

will

geiret-a/ly

beoit

a

grid

of

1900

.

1275,

wir/ciri e//belowa

2,'l

aspect

atio aird

lireref

re

satifactorq.


23/100

18

SIMPLE

BRIDGEDESIGN

USING PRESTRESSED

BEAMS

3.4 DECK IDEALISATION

Grillage analysis

idealises

a

deck into

a

grid

of

interconnected beams. The real

dispersed

effects of

bending,

shearand

torsion

are assumed

o

be

concentrated

in the

nearest

equivalent

grillage

beam.

Variations from

the

true behaviour

arise because

the real slabs

element

equilibrium

requires torques

and wists o be identical

and n

orthogonal

directions,

but

in

grillages

the

joints

can

rotate

differently.

However,

if

a

slab

is

modelled

by

a

sufficiently

fine

grillage

mesh

these anomalies are smoothed

out

tobecome almost

insignificant.

Again,

moments

in

grillage

beams

are

proportional

to

the

beam

curvature

in that

direction.

In real

slabs,

moments

also

depend

on the

orthogonal

direction

curvature,

but

this

error

is

also

sufficiently small

to

be

ignored.

There are

a few

fundamental

requirements

for

competent

grillage

modelling:

•

Place the

grillage

beams coincident

with

the

physical

beams or

ines of

designed

strength.

•

Where

possible, lay

out

the

grillage

o

capture

all

the

load,

and for

ease

of

hape generation

and

section

property

calculations.

•

Transverse elements

should be

spaced

to

try

and reflect

the

aspect

ratio

(length/width)

of he

whole

deck.

•

Skew decks

can

be

analysed

by

orthogonal

or skew

meshes.

If

he

skew

exceeds

20°,

the

model should

be laid out

within 5° of he real

skew.

•

Generally,

transverse members should be

orthogonal

to the

longitudinal

members,

particularly

when

skew exceeds 20°.

•

Bearing

positions

should

be

represented

faithfully,

and

in

skew

bridges

the verticalstiffnessmust

be

modelled with care

as

hey

can have

significant

effect

on

theoretical distribution

of

oad.

Once

the

grillage

model has beenset

up,

it is

recommended

that an initial est load

is

applied

(such

as

auniform

UDL),

to

verify

hat it

is

behaving correctly.

The test

load

case

should

be

checked

against some simple hand calculations (e.g. wL2/8)

o

make

sure

that the results

are reasonable.


24/100

n//aae

mvde/

The

gill/age

wode/is/towit

be/ow

GRILLAGE

MODEL 19

The

(fr-stdkgcast

s/tows he

,ode

rHmbers,

aitdfrtdicates

sti/'orts

a cfrc/e.

The

secoirddhigram

s/tows he

tenrbern#mbethrg.'

15

30

45

60

75

90

105

120

135

150

165

15

50

1

———-

38

1

46i

—

53

—

61

91

106

121

136

68

76-

—

151

t5t

152 164

1 5

———--

16

1

ii

—

18 19

— —

——

——

—

249

262

263

290

156 ISP 158 159

304

130


25/100

20

SIMPLE

BRIDGE DESIGN USING PRESTRESSEDBEAMS

3.5

SECTION

PROPERTIES

Since

he precast

and n-situconcrete

trengths

do not differby

more

than

10N/mm2,

Clause

7.4.1

permits

a modular

ratio

of1.0

to be used.

However

inthe

example

a

more

accurate

valuehas been

calculated

taking

into accountof

he

different concrete

strengths.

The

Y

beams

have

standard notches

50 mm

deep along

he

top

edges.

These allow

formwork

tobe

placed

between

the beams o

support

the deck concrete. In

this

case,

20 mm hick

permanent

formwork

is

used,

sothat he beam

protrudes

30 mm

into the

deck

slab.

The

overall

height

of he section

is

1.590

m.

The

composite

section

properties

are calculated

by

assuming

the

section is

made

up

from the Y8

beam,

a

rectangular

slab

which overlaps

it

by

30mm,andthe small

overlap

area

which must

be subtractedas it hasbeen

counted twice.

The code

permits

stiffnesses

tobe

represented

on

the

gross

concrete

ection

ignoring

the

reinforcement or strand.

This is the

most

straightforward,

since

the

amount of

reinforcement

and

strand

hasnot

yet

been

accurately

determined

at he

analysis stage.

In

some

situations,

such as

continuous

bridges

at

supports,

the

transformed section

may

be

important

and

should

be

used.

Under

transient

applied

forces

the short term

elastic

modulus should

be

used,

and

under

applied deformations

or

long

term

loads

the

long

term

modulus should

be

used.

To save

analysis

time

for

hese

two

situations

a

value

between

long

and

short

may

be

chosen,

ideally

reflecting

the

proportion

of

permanent

to

transient

effects.

Almost

all

analyses

are

executed

on

elastic

models,

even

though

the

code

allows

plastic

methods with

the

approval

of he

bridge authority.

An

elastic

analysis

is

appropriate

for

he

serviceability

limit

state,

which

s

the

most

important

for

the

design

of

he

pretensioned

beams.

The use

of

an

elastic

model

for

he ultimate limit state is

simple

and

conservative. It

is

a lower bound solution

in

which

the

structure

is

in

equilibrium

and

yield

isnot

reached.


26/100

$ectloir

Propemes

&am

lo,,e.'

S

ean,,

prg'erns

rom'

data sheet

74rea

=

0.5847m2

9=0.639

m'

I

=

0,1188s,

Comt'os/te

8/ab

cocretef,

=40

N/nrm'2,

=31

tN/m'nr

&an,

cocretef

=50

N/mwr,

=34

N/m'm't

Mod#/ar atio

=

31/3

4 =0.91

The

actual

area

i

e4jiiredor

a/cu/at/oil

of

he

seiwe,'ht

othetwie Memodularratiowillbe

applied

o theslab.

GRILLAGE

MODEL 21

The

values

forA('y-?

irMi able ca,,

oit/q

be

fl//ed

4r

afterq

has

bee,,ca/cilIated

94/M

=0.737/0.829 =0.889m'

(from'bottomofbean,)

I

=0.2429si

$ectioirmoduilicait

ow

e

calculated'

Thi ast

value

i

asedoi, the

ra

formed

sectiw

properns,

so

willot

ive

the

rue

stresses4 heslab, The

modit'lar

atio iiruistbediVided

ot

of

h/

value

o

ind

the ruesect/onmvduiluis

for

heslabi

Zk

Q,

347

/

.91

=0.381m

(for

actual

stresses

?t

slab)

0220

1.370

Actual

area

ffect,Ve

area

q

A(i-7

I

8/ak

Overlap

'/8

0.280

-0.012

0.585

0.255

-0.011

0.585

1,480

1.385

0.639

0,378

-0.015

0.374

0.0891

-0.0027

0.0366

0.0011

0.0000

0.1188

Totals 0.853m'

0.829sr

O.737m O.2429m'

&ttom

of

eam',

Top

of

ean,,

Top

of

lab,

Zbb =1/9

=0.273

n,3

Z

=

"(1400-7,)

=

0.475

,3

Z

=I/(l.590-9)

=0.347m3


27/100

22 SIMPLE BRIDGE DESIGN USING PRESTRESSED

BEAMS

3.6 EDGE STIFFENING

Most

decks

haveedge

stiffening

for the

parapets.

Manydeck

arrangements cause

the

edge

beam to

be

the most

heavily

loaded.

In

many

instances

these

effects are

complementary,

he

extra stiffness

reducing

stresses from the

extra

oading.

However,

the

combined

stiffliessof he

edge

beamwith he

parapet upstand

may

be

significantly

higher

than the

stiffness

of

the internal

beams,

and

so

may

attract

high

unwanted

loads

into

the

parapet upstand.

Care must be taken in

the

computer

modelling

to

ensure

that the

stiffness

allocated o

the

edge

beamisnot

unrealistically high,

as

this

would

aggravate

the

problem.

To counteract

this

'overloading'

henomenon,

the

following approaches

canbe

taken

when he

apparent

edgebeam nertia

s

significantly

higher han

internal elements:

•

model

the

edge

upstand

as

a

separate

element

(usually

with

less

inertia

than the main

elements).

This reverses

the trend

ofattraction.

•

calculate

the

whole

deck

nertia

including

he

upstands,

and also

excluding

the

upstands.

Then

allocate

half

he

difference

to

each

edge

member.

This is

likely

to be

significantly

less

than the inertia

calculated

for

the

discrete

edge

shape.

•

make he

edge upstand

discontinuous. This

is

becoming

more

popular

as

it also

reduces

thermal and

differential

shrinkage

cracking.

It

does,

however,

require

careful

detailing.

In the

design example,

the

third

method

has

been

adopted.

The

downstand fascia

and

parapet

are cast

after the deck has been

completed,

and are

both

cast in

sections

about

2.5m

long

separated

by

a narrow

gap.

The stiffness of

he

parapet

cantilever

is

included with

the outer

Y

beam.

Edge

longitudinal

elements are included

in the

model

along

he

line

of

he

parapet

support

upstand.

These

elements are

given

very

small

section

properties

so

that

they

do

not

contribute structurally

to the

grillage.

They

are

only

included

to

give

the

grillage

model

a

idy

appearance

the same

size

and

shape

as the

bridge

deck.

They

could be

omittedwithout

affecting

the resultsof

he

analysis.

Ifnominal members are

used

n

this

way,

however,

loads should

notbe

applied

directly

o

these members.


28/100

dge

&am

GRILLAGE MODEL 23

,4n

ir-sltii

coircrete

dowirstan'd

asck

i

eift'ed

ortiri

'ndge.

To

acir/eve

aH

ecoiromia'al

edge

beam

des/gM,

a wo

stage

ct/OH

se'eirce

wi/Ike

ised

1n

tiref tstage,

tire

deci

ast

tj

toiitside

tire

edge

beams.

The

weihtof

he

stage

wo

coirstriict/o.'ri

iq'poned

b'

ire

dec(-

wil-ir

edge

beams

atst

ge

o/,e,

am/a

ri//age

a/ra4fs/

cabecarried

out

accord/irg4'.

Thi

ana/qsi

,

ot

preseilted

ere,

but

ire

secM'npropenies

oft/re

stage

oire

edge

beams obeused4r

tirI

aira4'si

are;

effectiVe

Area

=

O,O2m

9

=O.875m

I

=O.24Om

Iii

tage

two,

tireca,rti/everi

addea

as

well

as

the

dicoirt4uuous

parapet

OH

downstairdfascki.

The

of

ire

cross-sect/oir

i

haded

OH

tire

dkigrarn

asedoir

M'i

cross-sectiw,

the

sectioH

to beused

for

irema4r

gri//ageaira4,s,

caH

becalculatedas

or

ire

,rteriral eam

oir

ire

revious

page,

airclare

as

ollows;

Actual

area =1.044

m2

effectiVe

Area

=

1,003m

7

=l,022m

I

=0.316m4

Parapetedge

member'

Alt/rough

he

gri//age

wi//41cluide

members

ruiir#r4rgalo/ig

the

verq'

edgesof

he ecA

these

are

Hot

struictut'rat

aird

verq

smallva/lieswi//be

iisedfortire

sect4'irpropemes.

slab

members;

These

represeirta

1.900m

sect/oir

of

lab;

I

=mbt/12= 0.911.9000.2203/12

=

0.00153m4

There

is

Ho eNd

dkiphragm,

so theeHdslabmembers

s41rplq

epreseirt

0.950m

of

lab;

I

=

mbd/L2

=

0.91

x

0.950

x

0.

220

12

=0.

00077m4


29/100

24 SIMPLE BRIDGE DESIGN USING PRESTRESSED BEAMS

3.7 TORSION

Torsional

inertia

can

be

difficult

to

calculateprecisely.

A

reasonable estimate can

be

made

by

dividing

the

section

up

into

rectangles.

The torsional inertiaof

he

section is

approximately

given by

the

sum of

he

inertiasof

he

individual

rectangles.

In

beam

and slab

bridges,

the

torsional inertia is

normally

small

compared

to the

bending

inertia,

so

this

approximate

method

ofcalculation is

sufficiently

accurate.

For

rectangular

ections,

C

=

k1b3d

where

b is

the

length

of

he shortside

d is

the

length

of he

long

side

and

k1

is a

factor

depending

on the ratio

d/b

If d/b>

2,

then

k1

can

be

approximated by:

k1

=

1/(1

-0.63

b/d)

This formula should

not

be

used for

elements which

represent

sectionsof

a

wide slab.

In this

case,

the valueused

fork1

must

bereflect

the

whole

slab

action,

and

should

not

be

calculated

for

he individualelements. Slabs wist

in

both longitudinal

and

ransverse

directions,

so

the value

ofC ishalved

for each

direction to

reflect his double

action.

Additionally,

he slab

elements shouldbetransformed

in

accordance with the modular

ratio. The torsional

inertia

of

slab

elements is

thus

given

by:

C

=

'/6mb3d

Torsionless

Design

For

many composite

beams,

as

here,

the

torsional inertia is

an

order of

magnitude

less than the

bending

inertia.

The

analysis

of

uch

bridges

can

be

simplified

by

ignoring

the torsion

constraints.

In

other

words,

torsionless

design

can

be

used.

The

resulting

load

distributionis

less

effective

and his

gives

rise o

slightly

increased

bending

moments.

The

correspondingly

increased

design strength

is considered

adequate

to

carry

the

torques

which

would

be

associated

with

a

full torsion

model.

Torsionless

designs

should

not be used for

significant

skews

or boxbeam

decks which

may

bechosen

for their

high

torsion stiffness

properties

or

where torsional

strength

is

a

significant requirement.

Torsion should

also not

be

ignored

in UM beams and thick

edge

beams such

as YE

beams,

evenif nternal beams are considered orsionless.

Edge

beams can

be

subjected

to considerable torsion

due

to loads from the

parapet

cantilever,

and

cracking

of

these beams couldoccur

if orsion is

ignored

in the

design.


30/100

GRILLAGE

MODEL 25

of

secMi,

bq dea/iiiig

Me

ect

o#i

as

ree

I

-

I127.5x

0.220

2

0.540x

1,080

T

7

0.,50x

0.290

fi$ca/cii/ate

i'rern's

for

e

iidMdia/rectaiig/es;

1. Th,

of

a wider

wo

waq

s/a

80 6

frfb3d/6

=O.91OL203xL2P5/6

=0,0021,?

2

d/b

=

L080/0.34o

=3.18

'1

=(1-0.631'/d)/3

=(1-0.63/3.18)/3

=0.26,

6

=i(1b3d

=0.26P0,34O31,080

=Q,Qjf3j4

3.'

d/b

=

0.P5o/o.29o 2,59

,

=(1-0.63k/d)/3

=

(1-0.63/2.59)/3

=0252

C

='1b5d

=O,252x0.29OO,750

=00046i?

Total

s/o#ali',ern,,

C=00021

0.0113

+

0.0046

=0.018,?

for

costparisoir,

1=0.255,?

The

ken'd4rg

lerthT

i

learlf

ver,'

mwcli

larger

MallMe oii,talbiertki.

To,%#

wi/I

Merefore

be

#regleced


31/100

26 SIMPLE BRIDGE DESIGN


4 CALCULATION

OFLOADS

4.1

INTRODUCTION

The

Departmental

Standard BD 3

7/88,

Loads

for

Highway Bridges,

is

currently

used

to determine

the

loading

on UK

bridges.

BD

37/88

effectively

supersedes

BS

5400

Part2 in he

UK, pending

revisionof

his

Standard,

andit isused

hroughout

this

design example.

The

loads

generally specified

in the

Standard

are

nominal

loads

appropriate

to

a

returnperiod

of

120

years. Design loads

will be obtained

ater

by

multiplying the

nominal

oads

by

load factors

y

given

in the

Standard.

An

additional

factor,

y0,

is

also

introduced

to

obtain

the

design

load effects

(moments,

shears,

etc.)

from the

design

loads. Valuesof

are

given

in

BS

5400Part4

for

concrete

bridges.

4.2 DEFINITIONS

It

is

worthwhile

clarifying

afew

definitions,

as

they may

differ rom

those

used

with

other

structural

design

work:

Dead Load

the

weight

of tructural materials

in the

bridge.

Superimposed

the

weight

ofnon-structural materials

on

the

Dead Load

bridge,

such as road

surfacing, parapets,

etc.

Live

Loads loads

due o

vehicular

and

pedestrian

traffic.

Primary

Live Loads vertical

live

loads

dueto

weight

of

raffic.

Secondary

horizontal loads

due to

change

in

direction

of

Live

Loads traffic

(eg.

centrifugal

forces,

braking,

urching).

Permanent

those

loads considered

to be

acting

at all

times

Loads

(i.e.

DL,

SDL,

and

any

loads

due to

fill).

Transient

all

loads

other

than

permanent

loads

Loads

(i.e.

wind,

temperature,

and live

loads).


32/100

C7ILCUL74TIONOTLOAD

CALCULATIONOF Los

27

Dead

Load

Dead oad

wY/be

car/iedbq

hebeasts

acf-l'tg

%n'e,

with/to

cosipos/te

acz'Ion'.

/f3

&ast

a/oit

e

/irterna/beam'

idge

beam

74ra

=

0.584,m2

(frost

data

s*eet)

Weig'kt

=0,584x24kN/st

=

14.03k/V/st

=

Q584P(f8,)+Q,2c5Q5(s/ab)-

0.

0120(oven'ap)

=0,85325,2

We/g.*t

=0,c5532st224kN/st3

=20.48k/V/st

Area

=0.

5848)

+0.

4592(s/ab+caitt#ever)

=1.044st2

We,kt

=1,044s,224kN/sr5

=25.05

k/V/st

Thi

oad4rg

i

pp/led

o

the

costposie

beast

&

s/ak

strkc$Hre.

Carrkigewa; Aspñaltsiirfach'ig

-f

siip//cltq

assume

stax/st

ist

hi'kness

of

165mst

over

wñole

carnigewai.

ThA

'rc/udesa/b

waitce

for

waterprooflHg rotect/on

boards.

$DL

=0.165st24 /V/st3 =4.0k/V/rn2

=

4.Ok/V/st2

x.

1.275rn =5,1

k/V/st

perbeast

Verge.'

The

wei,t

of

ire

ootpath,

andnon-structural

(d/scontzsruouis)

str4tg

courseand

fasck

wi/I

all

be

taken

as $DL

Total

we,ht

=14.6k/V/st

eack

side

of ridge

8uperh'rposedDeadLoad


33/100

28

SIMPLE BRIDGEDESIGNUSING PRESTRESSED

BEAMS

4.3

HIGHWAYLOADING

Notional lanes

For

the

purposes

of

calculating

the loads to be

applied

to

the

bridge

deck,

the

carriageway

is

split

into

notional

anes.

In this

context,

the

carriageway

is

taken

as

the

distance between

raised

kerbs,

thus

including

the hard

shoulders

(see

Clause

3.2.9.1).

Clause 3.2.9.3 then defines how

the

carriageway

should

be

split

into notional

lanes.

Note that inthis

example

there

are

three

notional

lanes

for

loading

purposes,

even

though

he deck will be

marked

out for

only

two

lanes of

raffic.

HA

Loading

HA

loading

is

a formula

loading representing

normal

traffic

in Great

Britain.

It

comprises

a

uniformly

distributed

load

(UDL)

and

aknife

edge

load

(KEL)

combined,

or

alternatively

a

single

wheel

oad.

For

loaded

lengths

up

to and

including

50

m,

the

UDL

expressed

in kN

per

linear

metreofnotional

laneis

given

by

the

equation:

W

=

336(IIL)°67

where

Listhe

loaded

length

(in

metres)

andW isthe load

per

metreofnotional lane.

The KEL

per

notional

lane

is

always

taken

as

120 kN.

The UDL

and

KEL

are

uniformly

distributed

over the full width

of

he

notional lane

to

which

they

apply.

However,

not all lanes

carry

the

full

HA oadatthe

same

time,

and this isdealt

with

by

means

of

ane

factors.

These

are functions of

he

loaded

length

and the lane

width,

and

are

specified

in

Table 14 of

he

Standard.

The

single

100 kN wheel

load

alternative

to

the UDL

and

KEL

canbe

placed anywhere

on

he

carriageway,

and

occupies

eithera

circular

areaof

340mm

diameterora

square

area

of300mm side.

The

single

wheel oadis

only

significant

in the

local

analysis

of

the

deck

slab,

which

isnot

covered

inthis

design example.


34/100

CALCULATION OF LOADS

29

l-/iahwat

oads

6am'gewa.i

width

=

1,0

(*ardstr')

+

7

3

traffic

aNes)

+1,0

=93m

Three

iot/ona/Iawes

are

rei/red'

Not/offal

aMe

width,

kL

=95

n/S

=5,1 n

/174 load'

Loaded

eirgt/r

=

26.61 m'

/1AUDL

=336(1/L)°6'

=

536(1/26.61)°

k/V/rn

HAAL=120k/V

Wheel oad

=

100

k/V

'si'rgIe oad)

LaMe

factors

kasedoit

L)

3,/&s

Thkle

14.'

a2

=

°157(k

40-L)

+3,

65(L-20))

=

0

013,(3,

1(40-26.61)

+

3.65(26.61-20))

=0,90

&st

aMe

factoi

/3

=

a2

=0.90

$ecoffd

aNe

factoi

/2

=

a2

=090

ThIrd aNe

factoi

133

=

0.60


35/100



HB

Loading

HB

loading represents

abnormal vehicle

loading.

An

example might

bea low load

trailer

carrying

a

power

station transformer,

with tractor

units

at

front

and

rear.

For all

public highway bridges

in GreatBritain theminimum

numberofunits of

ype

HB

loading

that

must

normally

beconsideredis

30,

but this number

may

be

increased

up

to 45 units.

For this

design

example,

the client has

specified

37.5 units

ofHB load.

TheHB vehicleas

defined in the Standard

represents

fouraxleswith fourwheels

per

axle.

One unit

of

oad

represents 10

kNperaxle. Thus he full 45 units

maximum is

equal

to 450 kN

per

axle

or

112.5

kN

per

wheel.

Thedistancebetween he central

woaxles isvariable. For

simply

supported spans,

the smallest

igure

is

obviously

the mostcritical.

As

with the HA wheel load the contactsurface

may

be taken

as circular or

square

with a contact

pressure

of1.1 N/mm2.

Note

thatin this

example

theHBwheel load isless than the

HA

wheel

load. Forslab

design

theHA wheelwill

therefore

be

critical.

Longitudinal

and ransverse

loading

Thisis

only required

for

design

of he

bearings.


36/100

CALCULATION OFLos 31

/15

oad'

Thi

bridge

,

esig',ed

for

37,5 iwits

of/-IS

oad

AyJeload=37,5xl0kN =375k/V

Total/-IS

vehicle

weight

=4

x.375k/V

=

1500k/V

W4'eel

load

=

375

kN/4 =9375

k/V

for

hi

s4ii4siippon'ed

ridge,

theshonest

wheelbasewi/Ike critical

Thus

ditance

bet

wecir

cdiltral

x/es

of

Me 15

vehicle

wi//be

aken'

as

6rn

Jorion'ta/Loads,'

Clause

6,1

0

iVes

the

norn4ra/Ion'gi'tuid4ra//oads.'

HA

/on'gituda/

load

=250k/V

+8

k/V/rn

of/oaded/en'gth

=250kA/+(8k/V/rnx2á.6rn)

=463k/V

Thi

i

pplied

o

on'e n'otion'a/lan'e,

/13

lon'gituidin'a/

load

=25%

of

'orn4ral

/15

wei,ght

=25%

1500k/V

=375k/V

Thii

qp'all.i

ditr,butedbet

ween

the8

wheels

ofapaitof

xles,

butwi/I

Hotbe criticalasiti ess han' the HA

on'gituidin'al

load

Clause

6.11

giVes

the

ornin'altran'sverse oads/

The

n'orn4ral tran'sverse

load

due to

skidd4rg

i

s4tglepo4tt

oad

of300

k/V

acti.Yg

4,

an'q

d,tecti'n

'parallel

o the oad

surface)


37/100

32

SIMPLE BRIDGE

DESIGN


4.4 WIND LOAD

Methods

of

calculating

wind oads are

given

in

Clause 5.3

of

he

Standard.

Combination

2

loading(seepage38)

is

not

significant

n

itseffectona

argeproportion

of

bridges,

such asconcreteslabor

beamand slabstructures 20mor ess

in

span,

1Om

or more in width and

at

normal

heights

above

ground.

Wind

load thereforedoes not

need

to

be calculated

for

most

bridgesdesignedusingprestressed

beams.

4.5 PEDESTRIAN LIVE LOAD

For

oaded

lengths

of

36m and

under,

the

nominal

pedestrian

ive load

is a

uniformly

distributed live load of5.0 kN/m2.

For

superstructures carrying

both

highway

and

pedestrian loading,

a

reduction factor

of0.8

is

applied

to thenominal

pedestrian

live

loading specified

for

footbridges

alone.

Thus,

in

this case

the

pedestrian

ive load

is

4.0 kN/m2.

4.6

TEMPERATURE EFFECTS

Temperature

effects

produce

two

aspects

of

oading,namely

therestraint

tothe overall

bridge

movement due

to the

temperature range,

and the effects of

temperature

differences

(or gradients) through

he

depth

of he

bridge

deck.

Temperature Range

The

temperature range

for

a

particular bridge

is

obtained

by

first

determining

the

maximum andminimum shade air

temperatures

for the location of he

bridge

from

isotherms

plotted

on

maps

of he

UK,

andshown in

Figures

7

and8

in

the Standard.

As these

isotherm

maps

are

derived from

Meteorological

Office

datarelating

to a

return

period

of120

years

(the

bridge

design life),

it

may

be

necessary

to

adjust

the

temperatures

for

a

return

period

of50

years

forcertain

applications

such as

footbridges

and

carriagewayjoints.

Thisis achieved

by

a

straightforward

increaseorreduction in

temperature

as indicated

in

Clause5.4.2of he Standard.

Maximum andminimum

effective

bridge emperatures

are then derived from Tables

10 and 11 in the Standard. Prestressed

beam

bridges

will

always

be

type

4.

The

effective

bridge

temperature

range

is

then used for

designing

the

bearings

and

expansion joints,

or

if

this movement

is

restrained then in

determining

the stress

resultants in the structure.


38/100


33

WZ'td oad

Wi,d

oad

speci%'al/i

calcø/ated

for

t*i

'ridge.

assHnted

Mat

Load

6omk/itat/on

2wi//notbe

critical

footpath

Loads

Nom4ya//,Veoad

for

ootpaths

giVen

it Clause6.5,1,1as

5

('N/m.

h'ice

his

bridge

carr,skikwa.i

oad/itg

as

we//as he

ootpath,

the eduction

factorof

0.8

app/is.

Neduced

nom/iuaload

be

applied

=

0.8

x

5.0

=

4.0

kN/m

Temperature Nange

from

D

37/88,

hgures

7

and

&

Miuimuim

hade ait

eli,t'eratgre

=

18

0

Max/mum

shadealt +3606

from

#uire

9,

bridge

construction

i

ype

4.

from

Tab/es

10and11,

M/iu/'ium

effectiVe bridge emperature

=

11°C

Ma/iuuim

effectiVebridge temperatuire=

+36°C

Temperatureange

=

47°C

Coefficient

of

hermal

e.q.'ansiin

=

12x1

Ct6/°C

Length

between

eansi'nj/iuts

=

27m

(approx)

Nange

of

movement

=

47x

(121O6,)

x

27=0.

0152m

Nange

of

movement

fromcentra/posi'tt'n

=

±76mm


39/100

34

SIMPLE BRIDGE

DESIGN USING PRESTRESSED BEAMS

Temperature

Difference

Positive

temperature

differences

occur

within he

superstructure

when

conditions are

such

that

solar

radiation

and other

effects cause

a

gain

in heat

hrough

the

top

surface

of he

deck.

Conversely,

reverse

temperature

differences

occur

when

conditions are

such hat heatis

lost

from the

top

surfaceof he

bridge

deck as

aresultof

e-radiation

and other

effects.

Temperature gradient

diagrams

for each

of

hese states are

shown

on

Figure

9 in the

Standard.

For

surfacing

of hickness

other

than

100mm

these

can

be

modified

by

reference

to

Appendix

C.

The

coefficient

of

hermal

expansion

for

concrete

and

steel is

takenhere as

I

2x

106.

For

concrete with limestone

aggregates,

a

reduced coefficient

of

hermal

expansion

of

9x10-6

can

be

used.

If he deck

were

fully

restrained

ateach

end,

stresses

proportional

to the

temperature

at each

point

in the

deck would arise.

These

emperatures

and stressesare

shown in

the

top

line

of

diagrams opposite.

The

stress

at the

top

of he

slab,

for

example,

is

calculated as:

Stress

=

E

ci.

T

=

(31,000 N/mm2)

x

(12x106/°C)

x

(13.5°C)

=

5.02 N/mm2

In a

simply

supported

deck

there

is

no

axial

restraint

at the

ends,

and no

moment

restraint.

The

axial

and

moment

components

of

hese stresses will be relieved

by

overall

lengthening

and

hogging

of he deck.

A

self-equilibrating

et

of nternal stresses

will

remain;

they

will exist

without

any

external forces or reactions

on the

deck.

These

nternal stresses

are calculated

by

subtracting

he

axial

and

moment

components

from

the

stresses calculated

for the

fully

restrained

condition.

Stresses

due to

negative temperature

differences

also need to be

calculated. These

are not

presented here,

but

exactly

he

same

procedure

is

followed.

It isworth

noting

that the

serviceability

limit state stresses

determined from these

temperature

difference

diagrams

are

subject

to a load factor

of0.8.


40/100

TestfleratureD/fferen'ce


35

Temeratiire

d/tr/iiz/'M

through

thecross

ect/oH

igiVei,4i iwre

9

ofD

37/88

k,

=0Jim

15.5CC

0,25mfl

Ca/cu/ate

am/force

a#dmoment

omponents

of

hesestresses.

$tress

has

keen

diVideduip

Z#o

fiVe

blocks, 4rd/catedon

dkigram

bove,

jtreaseof

a/cu/at/on.

A

1

1,275x0.15

2

1,275x0J5

3

1,2,75x0,07

4

0.4.zx0.18

5

0.75x0.20

//

74Y

0.626

0214 0154

0651 0.375 0.245

0516 0.086 0,044

0391 0.037 0015

-0.822 0.077 -0.063

Am/force

= =

0787MN

I,,

st'/q

supported

ridge,ne/theraxia/force

ormoment re

4i

act

estra4rea

so

ocked

4t

stresses

are

ca/cui/atedbqsuiktract/ng

these

effects rom'

he

stress

diigram

above.'

Ax/a/re/ease

stress

=

(0.

787

MN)/(0.

829

mi')

=0.95

N/mm

Moment

e/easestress

=

(0.373

M/V&/Z

=

(0.373

MNm)/(0. 475m)

=0.79

N/mm2

at

op'of

eam',

etc.

502

N/mm

PositiVe

teratu1red7ereHce/

Cross

*3

=020m

.5CC

Temperature

Difference

JOiN/mm'

$tresses

41

fui/4i

estrained

deck

=iaT

1,12

1.95

0.96

0.44

0.51

Moment about

centroidal

ax/s

=

=

o.S7SMNm

098N/mm'86N/mm'

095

N/mm'

095

3,18

/mm'

1,02N/mm'

Nestrained

tresses

Moment

from

op

dhtgram

re/ease

re/ease

j37d

144N/m.w'

$eif-

eqii/ibrat4ig

temperature

stresses


41/100

36

SIMPLE

BRIDGE DESIGN USING PRESTRESSED BEAMS

4.7 SHR[NKAGE

When he in-situ

op

iscast on the

precast

beams

some

of

he

shrinkage

of he beams

has

already

occurred. Hence differential

shrinkage

occurs

between he

precast

and

in-situ

concretes,

and his

results

in the

development

of

a

pattern

of nternal stresses.

Clause 7.4.3.4 states

that

he Table

29

shrinkage

values

may

be

adopted.

It

is reasonable

(and usual)

to

assume

thathalf

of

he beam

shrinkage

has

occurred

at the time of

casting

the

top

slab. Hence

the

differential

shrinkage

assumed

in the

calculation is

half

of

he

Table

29

shrinkage

value.

The

effects

of

differential

shrinkage

will

be

reduced

by

creep.

Allowance

ismade

or

this n the

calculations

byusing

a

eduction coefficient,4.

A

value

of

0.43 isnormally

usedforthis

coefficient,

as

given

in

Clause 7.4.3.4.

The

differential

shrinkage

stresses

can be

determined

in

a

similar

manner

to

the

differential

temperature

stresses.

The

restrained stresses are

calculated,

and he

axial

force

and moment

component

are

subtracted

to

give

the

actual internal stresses.


42/100


37

$ñrirkage

DftreHt/a/shr4tk.age

bet

ween

slab

and

dec,('

creates

itterna/stresses.

/tZ

assiimed/a4

the

otal

hithikageoft/re

beam'has

aI(en

p/ace before

thes/ak

i

ast;

Different/al

kr4t.(-age

stra4r,

=

0.5

x.

(-300x106)

=

-150x106

__________________

15ot

I&I

I

Nest

a/nirg

orce

=

£

. x

A

..

=

-15010

'

x

31000

x.

(L2,5

x

0.220)

x

0.43

=

-0,561 MN

(tensi2w)

Nestra/n4rg

stonrent

=

-0.561

x

eccentric/tJ,f

=-0.561X('1,480-

0.889)

=-0,332MNm'

Ca/ri/at/on

of

nternal

stresses

i

i'tri/arto he

calci/ati#r

fortestperatiire

difference.

Nestrai'redstress

=

x. x.

0

=

-2.0

N/m'm

Ax/al

re/ease

=

('0.561M

N,)/1"O.

829nr,)

=

-0.68

N/mnr

Montent elease

=

A4/Z1,

=

-0.332/0.381

=

-0,

5,

N/m'm'

at

op

of

slab,

etc.

Total4,terna/stresses

ares/townon he

ri/tt

and

digram;

-2.0

N/,m -062

N/mi,r -067

I

—

4N15ôN/mm054

N/mm-

-0,66 N/mi

Nestra,'red

Ax/al

Mom'ent

&/f-eii/likrat4rg

stresses

re/ease re/ease

skr4rtage

stresses


43/100

38

SIMPLE

BRIDGE DESIGN USING PRESTRESSED

BEAMS

5

APPLICATIONOF

LOADS

5.1

LOADCOMB1NATIONS

BD 37/88 considers

fivecombinationsof oads. These are

listed in detail

in

Table 1

of he

Standard,

which

also

gives

load factors to be used in each case.

The five

combinations can be summarised

asfollows:

Comb.

1:

Permanent loads

plusprimary

live oads.

(For railway bridges,

secondary

live

load

is

also

ncluded.)

Comb. 2: Wind

load,

plus

loads

in Comb. 1

(but

with some reduced load

factors).

Comb. 3:

Temperature

effects,

againcombined

with

loads from

Combination

1.

Comb. 4:

Secondary

live loads

(each

considered

separately),

in

combination with

permanent

loadsand theassociated

primary

live oad.

Comb. 5:

Bearings

friction,

together

with

permanent

loads.

Load combinations

1

to

3 are the

primary

combinationsto

be

considered

inthe overall

analysis

of he

bridge

deck. In

pretensioned

beam

bridge

decks,

Combination

2

(including

wind

loading)

is

rarely

critical,

and

is

gnored

in the

design example.

This

leavesCombinations 1 and3

to

be

analysed.

For

bridges

in the

UK,

the

requirements

of

BS 5400:Part

4

mustbemodified

according

to

Departmental

StandardBD

24/92,

The

Design

ofConcrete

Highway Bridges

and

Structures,

Use ofBS 5400:Part 4: 1990. Themost

important change

this ntroduces

relates to the Combination

1

loading.

The beams must

comply

with Class 1 SLS

stresslimits foramodified

version ofCombination 1. BS 5400: Part

4

calls

for

a

maximum of25 units

ofHB load for this

condition,

but BD 24/92 reduces the live

loading

to HA alonefor hiscondition.

This

design example

follows the

requirements

ofBD 24/92.

5.2

SELECTIONOF

CRITiCAL LOAD CASES

In this

example,

maximum

midspan

moments will

obviously

be obtained

by

concentrating

the loads as near

to

midspan

as

possible.

This means

putting

the HA

KEL

at

midspan

in

the lanes

to

which

it

applies,

and also

putting

the HB vehicle at

midspan.

Positioning

of heloads to obtain

maximum

bending

momentelsewhere in the

span,

oron skew

bridges,

is

not so

easy.

The

arrangement

of oads which

give

maximum

effects in the various

beams can be found

by

trial and error.

Alternatively,

some

software

packages

will

automatically

analyse

a

multitude

of

different

possibilities

and

report

themaximum effects.

The

temperature

loads in Combination

3

do not cause

any bending

moments

in

the

beams,

andso

will nothave

a

significant

effect

at

ULS.

Only

Combination

1 therefore

needs to be

analysed

at ULS.


44/100

APPL/CA /ON

Of

L

O74D

TO

5N/LM

APPLICATION OF

LOADS

39

Load Cases

Loadcasesmast eselected

forhe'at

the

gri/lageana4sis.

forhe

designof

he

estressed

beams,

onli

he

maxi,wm

moments

(wh'ith

will

occarat

midspan,),

and

he

max/mi/rn

shear

at

theends

of

hebeamsandat are

needed Moments are

reqjiired

othat$L$

and

at

WL'.

On4

WL is

equiredfor

he

shear

ca/calat4ns,

bat

he

cond/tiwWi//a/so be

ana4'sed

to

giVe

mac'wrn

oadson

the

bearings.

&/ow

s

a

sammary

of

he

oadcases

o

be

analqsed

This

has

been

basedon

fiare

13

of

,])

37/88.

Note

that

he

/-/

ye/ride

s

wider han

a

rothna/

ane, When

the

/1

ye/ride

straddles

the

adjicent

ane,

the

K.L

isomitted

from

hat

ane,

and

he ane

factorfor

he 14

IIDL

s

basedonanot/9na/ ane width

of

2.

Sm,

giving

a ane

factor

of

0.

7S9

see

C/aase

6.4.2(b))

HA with

37.5anitsH

Combiratin 1

atL'

nd

11L

Combi'tat,kn3at

HAwith37.5anitsH

Combination1 atãL

ndUL

Combi',at,n

3 at

HA

with37.5an/tsH

to

max/mise

hearand

eactins

in ane

1.'

Combination1

at

$L nd

UL$

HA,

/14

HA,

J3,=O.9,

iL

130.9

iL

/330.6,

iL

HA,

132=0.789

H vehicle

HA,

/3=O.9,

AL

H,

ye/ride

HA,

132=0.789

H4

J3=0.9,

/(.zL

HA

alone'

Combination1 at

and

11L

Combinati'on

3

at

L,neJ

Le2

krne3

f

—

HA,

HA,

I

vehicle

132=0.789

/3=O.9

AL

1

I


45/100

40

SIMPLE BRIDGE

deck example

Documents