13-Bearing

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13
Chapter

Bearing

contents


END BEARING



Plate bearings (Sliding& hinged bearings).



Rocker bearings



Roller bearings



Bearing adopted by Railway Board.



END BEARING

The

bearings

are

provided

at

both

the

ends

of

a

bridge

girder
.

One

end

of

the

bridge

girder

is

fixed

in

position

while,

the

other

end

is

kept

free

for

the

horizontal

movement
.

The

bearings

are

provided

for

the

following

functions
:


1
-

The

bearings

are

provided

to

transmit

the

end

reaction

to

the

abutments

and/

or

piers

and

to

distribute

it

uniformly,

so

that

the

bearing

stress

does

not

exceed

the

allowable

bearing

stress

of

the

material
.


2
-

The

bearings

are

provided

to

allow

the

movement

in

the

longitudinal

direction

(expansion

and

contraction)

due

to

change

in

temperature

and

stresses
.

3
-
The bearings are provided to allow rotation at the ends,
when the bridge girders are loaded and deflections take
place.

For

all

spans

in

excess

of

9

m,

the

provisions

are

made

for

change

in

length

due

to

temperature

and

stress

variation
.

The

provisions

for

expansion

and

contraction

should

be

such

as

to

permit

movement

of

the

free

bearings

to

the

extent

of

10

mm

for

every

10

m

of

length
.

For

spans

greater

than

15
m,

on

rigid

pier

or

abutment,

the

bearings,

which

permit

angular

rotation

at

the

girder

ends,

are

provided,

and

at

one

end,

there

shall

be

a

roller

or

other

effective

type

of

expansion

bearing
.


In

the

design

of

bearings,

provision

shall

be

made

for

the

transmission

of

longitudinal

and

lateral

forces

to

the

bearings

and

the

supporting

structures
.

Provision

shall

be

made

against

any

uplift

to

which

the

bearing

may

be

subjected
.

All

bearings

are

designed

to

permit

inspection

and

maintenance
.



Back


TYPES

END

BEARING

Depending

upon

the

magnitude

of

end

reaction,

and

the

span

of

bridge,

the

different

types

of

bearings

used

for

the

bridges

are

as

follows
:


1
-
Plate

bearings

(Sliding&

hinged

bearings)
.


2
-
Rocker

bearings


3
-
Roller

bearings
.


4
-
Bearing

adopted

by

Railway

Board
.


(Sliding&

Plate bearings
-
1

hinged bearings).


Plate

bearings

are

simplest

type

of

bearings
.

The

plate

bearings

are

used

small

spans

upto

15

m

and

small

end

reaction

of

the

bridge
.

Fig
.

13
-
1

shows

a

plate

bearing
.

The

plate

bearing

consists

of

two

plates
.



BRIDGE GIRDER
bearing plate
Upper sole plate
CIRCULAR HOLE FOR
HINGED BEARING
ELLIPTICAL (SLOTTED) HOLE
FOR EXPANSION BEARING
Fig
13
-
1

A

sole

plate

is

attached

to

the

bridge
.

The

sole

plate

rests

on

bearing
.

The

bearing

plate

is

anchored

to

the

concrete
.

The

two

anchor

bolts

fixed

in

concrete

pass

through

the

bearing

plate

and

the

sole

plate
.

The

size

of

bearing

plate

is

found

by

the

end

reaction

and

the

allowable

bearing

pressure

on

the

concrete
.

The

plates

are

made

rigid

to

distribute

the

end

reaction

as

uniformly

as

possibly

over

the

required

area

of

the

concrete
.


When

the

anchor

bolts

pass

through

the

circular

holes

in

the

sole

plate,

then,

the

plate

bearings

act

as

hinged

bearing
.

One

end

of

the

bridge

girder

is

hinged

or

anchored

to

the

concrete

through

the

hinged

bearings
.


The

hinged

bearings

are

designed

for

the

end

reaction

(vertical

load)

and

the

lateral

forces
.

The

magnitudes

of

end

reactions

used

are

large
.

Therefore,

the

fixed

bearings

designed

for

end

reactions

(vertical

loads)

only

strong

enough

to

take

the

lateral

forces
.

In

order

to

allow

the

longitudinal

movement,

the

slotted

holes

are

provided

in

the

sole

plate
.

In

order

to

reduce

the

friction,

the

surfaces

of

sole

plate

and

bearing

plate

in

contact

are

well

machined

and

smoothly

finished
.

The

sole

plate

can

slide

upon

the

bearing

plate
.

The

plate

bearings

act

as

expansion

bearings

of

sliding

type
.

In

the

expansion

bearing,

the

longitudinal

movement

(expansion

or

contraction)

takes

place

with

change

of

temperature

and

loads


The

longitudinal

force

at

any

free

bearing

shall

be

limited

to

the

dead

load

reaction

at

the

bearings

multiplied

by

the

coefficient

of

friction
.

The

coefficients

of

friction

for

different

surfaces

in

contact

are

given

in

clause

6
.
10

(Egyptian

code

for

loads)
.

The

plate

bearings

have

bearing

two

disadvantages
.

The

edge

of

plate

nearest

to

the

end

of

span

has

a

tendency

to

lift

along

with

the

deflection

of

bridge

girder
.

Therefore,

the

end

reaction

is

not

distributed

uniformly
.

Secondly,

in

order

to

have

longitudinal

movement,

the

sliding

friction

is

to

be

overcome
.

Therefore,

for

the

large

span

bridges,

the

more

efficient

devices

are

necessary
.


The

end

reaction

is

distributed

uniformly

by

providing

a

deep

cast

steel

bed

block

as

shown

in

Fig
.

13
-
2
.


Such

bed

blocks

have

adequate

rigidity
.

The

sole

plate

bearings

are

many

times

made

curved

as

shown

in

Fig
.

13
-
3
.


The

curved

sole

plate

allows

rotation
.

For

large

spans,

the

plate

bearings

are

not

suitable
.

The

hinged

(rocker)

bearings

and

roller

bearings

are

used

in

such

cases
.


The

sliding

bearing

is

the

least

expansive

bearing

for

light

and

intermediate

reactions
.

BRIDGE GIRDER
Fig
13
-
2

Back

BRIDGE GIRDER
ELLIPTICAL (SLOTTED) HOLE
FOR EXPANSION BEARING
CIRCULAR HOLE FOR
HINGED BEARING
Fig
13
-
3

Back

Figure

13
-
4

shows

a

bearing

that

makes

use

of

a

rocker

between

the

bearing

plate

and

the

beam

or

girder
.


Hex . nut and
washer,fixed end
hole fixed end
Slotted hole in rocker ,
exp.end
Performed fabric
pad or grout
Hex . and jam nut
expansion end
Anchore bolts
L
C
brg
Fig

13
-
4

A

similar

detail

in

which

the

anchor

bolts

do

not

pass

through

the

rocker

is

shown

in

Fig
.

10
.
3
.

In

this

case,

the

beam

is

held

in

position

by

means

of

pintles

shaped

like

gear

teeth
.

This

type

of

support

may

be

used

where

resistance

to

uplift

need

not

be

provided
.

For

example,

it

may

be

used

for

inside

beams

of

the

beam

bridge,

with

the

outside

beams

supported

by

bearings

of

the

type

as

shown

in

Fig
.

13
.
5
.


Round hole in rocker,fixed.end
Slotted hole in rocker,exp.end
Exp
Fix
Performed fabric
pad or grout
Driving fit
Pintle detail
L
C
C
L
brg
brg
Fig
13
-
5

Figure

13
-
6
a

shows

an

expansion

bearing

for

larger

bridges
.

Several

variations

are

shown

in

the

view

at

the

right
.

The

sole

plate

may

be

bolted

to

the

girder,

as

at

the

left

of

the

centerline,

or

welded

as

shown

at

the

right
.

Resistance

to

uplift

may

be

provided

by

using

a

hinge

plate,

as

at

the

left
;

if

such

resistance

is

needed,

lateral

movement

is

prevented

by

a

plate

such

as

that

shown

at

right
.

A

corresponding

hinged

end

bearing

is

shown

in

Fig
.

13
-
6
b
.


2 bolts in each side
(b)
(a)
Topered hole
in rocker
PL
2 bolts in each side
Fig
13
-
6

Although

there

is

only

a

line

of

contact

between

an

unloaded

rocker

and

its

bearing

plate,

deformation

under

load

distributes

the

reaction

over

a

finite

area
.

Evidently,

at

a

given

load

this

area

increases

with

increase

in

radius

of

the

rocker,

since

a

rocker

of

infinitely

large

radius

would

have

a

plane

surface

to

begin

with
.

The

allowable

load

must

be

evaluated

in

terms

of

limiting

permanent

deformation
.

Thus

the

yield

point

of

the

material

is

also

a

factor
.

These

bearings

consist

of
:

An

upper

sole

plate
;

in

rolled

steel

riveted

to

the

girder
.

For

hinged

bearing

the

sole

plate

is

provided

with

two

grooves

in

which

two

ribs

in

the

bearing

plate

in

gage

and

thus

the

horizontal

movement

isn’t

available
.




2
R

=

M
2
cm
/
t
4
.
1
I
y
M

=

f


12
t
b

=
I
3
1
1


12
t
b

=
I
2
/
t
2
R

=

f
3
1
1
1



& y = t
1
/
2

t
1



(
3

-

4
)

cm

a
Hinged bearing
Movable bearing
Bearing plate
Upper sole plate
1
b
b
2
b
2
1
b
R/2
t
2
1
t
a
a
rib
rib
R/2

2
-

Abearing

plate

of

cast

steel

(or

cast

iron

for

small

Roadway

Bridges)
.

Fixed

to

masonry

by

ribs
.


The

size

of

the

bearing

plate

is

obtained

from

the

allowable

bearing

pressure

on

masonry

for

granite

&

basalt

or

similar

hard

stones

40

kg/cm
2
.

For

reinforced

with

circular

hoops

70

kg/cm
2
.


R
Bearing plate
B.M.D
2
t
R/2
a
4
a
2
R

=

M

2
cm
/
t
8
.
1
I
y
M

=

f


12
t
b

=
I
3
2
2
2
2
3
2
2
2
get t

steel
Cast

cm
/
t
8
.
1
12
t
b

2
/
t
4
a
2
R
I
y
M

=

f






& y = t
2
/
2

The bearing plates for hinged and
movable bearings are the same size.

The bearing plate shall rest on a
3
mm
sheet of lead and shall provided with
masonry ribs to transmit the
horizontal reaction of the bridge.


ribS
Back

Fig.
13
-
8
shows a typical rocker bearing.

BRIDGE GIRDER
Fig. 13
-
8

2
-
Hinged (Rocker) bearings


The cast steel sole and cast steel bearing block are used in
these types of bearings. A cylindrical pin is inserted in
between the cast steel sole and the cast steel bearing block.
This pin allows rotations at the ends of bridge girder. The
rocker bearing acts as hinged bearing. The end reaction of
a bridge girder is transmitted to the pin

by direct bearing through the sole attached with the girder.
The vertical plates are used to transmit the end reaction.
The number of plates (two or three) depends upon the
magnitude of end reaction. The end reaction is further
transmitted to the cast steel bearing block and then to the
supporting structure.

Two outer vertical plates completely encircle the pin. In
case, the bearing is subjected to an uplift, then, the uplift is
resisted by theses plates. The middle plates provide only
bearing with the cylindrical surface of the pin. The required
bearing area is provided by the product of total thickness of
plates and the diameter of pin. The thicknesses of all the
plates are kept equal. Therefore, the end reaction is
transmitted equally by these plates. The value of bending
moment is found by multiplying force transmitted by outer
plate of the sole to the outer plate of bearing block and
center to center distance between these plates. The size of
base plate is found by the allowable bearing stress in the
concrete and the end reaction.


The

rocker

bearing

are

also

bearings

are

also

subjected

to

lateral

and

longitudinal

forces

in

addition

to

the

end

reaction

(vertical

loads)
.

The

increase

of

end

reaction

due

to

lateral

and

longitudinal

forces

is

also

taken

into

consideration
.

The

lateral

forces

and

the

longitudinal

forces

are

assumed

to

act

at

the

level

of

cylindrical

pin

of

the

rocker

bearing
.

The

base

plate

is

subjected

to

moment

along

both

the

directions
.

The

total

bearing

stress

in

the

concrete

should

not

exceed

the

allowable

bearing

stress
.

The

rocker

bearings

are

designed

for

the

end

reaction

and

then

checked

for

lateral

forces

and

longitudinal

forces
.

Figure

3
.
54

shows

the

rocker

bearing

for

the

hinged

end
.


In

the

rocker

bearing

for

free

end

of

the

bridge

girder

the

underside

of

sole

is

curved,

which

rotates

on

the

horizontal

bearing

plates

and

allows

longitudinal

movement
.

This

acts

as

rocker

type

expansion
.


Back

3
-
Roller bearings.


The

roller

bearings

as

shown

in

Fig
.

13
-
9

are

also

used

for

the

long

span

bridges
.

Fig
.

3
.
55

(A)

shows

a

single

roller

used

in

the

bearing
.




The

rollers

provide

the

rotation

as

well

as

the

longitudinal

movement
.

Fig
.

3
.
55

(B)

shows

number

of

rollers

used

in

the

bearing
.

The

bearings

act

as

roller

type

expansion

bearings
.

The

rollers

are

kept

in

position

by

means

of

dowels,

lugs

or

keys

as

shown

in

Fig
.

3
.
55

(A)
.


The

roller

bearings

for

spans

above

span

35

m

should

preferably

be

protected

from

dirt

by

oil

or

grease

box
.

So

long

as,

the

size

of

rollers

is

small,

the

complete

circular

rollers

are

provided
.

When

the

size

of

rollers

become

large,

then,

the

sides

of

rollers

are

cut

in

order

to

reduce

the

length

of

the

sole,

and

to

make

the

bearings

more

compact
.

These

rollers

with

cut

sides

are

known

as

segmental

rollers
.



BRIDGE GIRDER
SEGMENTAL ROLLER
SEGMENTAL ROLLER
BRIDGE GIRDER
Fig
13
-
9

Back

In

order

to

avoid

overturning

or

displacement

of

these

rollers,

these

are

geared

with

upper

and

lower

plates
.

The

spacing

between

segmental

rollers

and

the

width

of

rollers

may

by

found

as

below
:

It

is

assumed

that

the

rollers

don

not

slip

but

only

roll

during

rolling
.

When,

the

roller

rolls

to

the

maximum

position,

as

shown

in

Fig
.

13
-
10
,


b
d
d+b
d + a
a
B
D/2
D
d
d + a
Fig
13
-
10

then,

the

vertical

axis

of

roller

turns

through

an

angle


,

and

the

center

of

the

roller

travels

through

a

forward

motion,

B
.

Then,

travel
Horizontal
R
roller

segmental

of

Diameter
D
roller

segmental

of

Width
d
D
d
sin



















D
114.6B
sin
D
d
,
Therefore
)
degrees

in
(
D
B
6
.
114
)
radians

in
(
D
B
2
tan
(
3.15
)


(i)


The

distance

between

adjacent

segmental

rollers

a,

(i
.
e
.

the

spacing

between

the

segmental

rollers)

should

be

such

that

the

rollers

do

not

come

in

contact

during

the

forward

motion
.

Then,




(a

+d)

=

(d+b)

sec










(iii)





a

=

b

sec



+

d

(sec


-

1
)






(
3
.
16
)

Where,

b

=

Least

allowable

perpendicular

distance

between

the

faces

of

adjacent,

after

their

revolved

positions
.

The

spacing

between

adjacent

segmental

rollers

a,

is

found,

knowing

b,

d

and


.

The

roller

bearings

are

also

used

to

support

the

cast

steel

sole

with

pin

bearings

as

shown

in

Fig
.

13
-
11
.

In

such

cases

the

roller

also

acts

as

a

hinged

bearing
.

Fig
13
-
11

The

following

points

are

kept

in

mind

while

designing

s

sole

a

pedestal

for

the

roller

bearing
.


1
.


The

sole

transmits

the

end

reaction

to

the

pin
.

The

end

reaction

must

be

distributed

from

the

pin

to

the

various

rollers

uniformly
.


2
.


The

size

and

number

of

rollers

provided

should

be

adequate

to

have

proper

stress

and

free

movement
.


3
.


The

rollers

should

be

so

arranged

that

these

can

be

readily

cleaned

of

accumulated

dirt

and

dust
.


4
-

Segmental rollers (Fig.
13
-
12
) are ordinary used since
they occupy less space than cylindrical rollers.

The rollers may be coupled with the sidebars shown and
the entire nest held in position by tooth guides which
engage slots in the shoe and in the bearing plate. Sidebars
may be omitted if each roller is held by teeth. Lateral
movement is prevented by the tongues shown in the view
at the right.


1
.


Resistance

to

uplift

may

be

provided

by

lugs

that

have

projections

extending

over

the

upper

surface

of

the

base

of

the

shoe

or

by

enlarging

the

base

of

the

shoe

and

providing

slotted

holes

for

the

anchor

bolts
.

The

roller

assembly

may

be

enclosed

with

removable

dust

guards
;

they

are

shown

on

only

two

sides

in

Fig

13
-
12

to

indicate

that

they

are

optional
.

Removable
dust guard
Side bars
Bolt
Cap
Tongue
Pin
The

roller

bearings

consist

of

the

following

parts


1
-
Upper

sole

plate

in

structural

steel

or

cast

steel

or

cast/

steel

riveted

to

the

plate

girder
.


2
-
A

lower

sole

plate

(saddle)

in

cast

steel

with

a

curved

upper

surface

and

a

plain

lower

surface

which

bears

upon

the

rollers
.

Its

dimensions

depend

upon

the

number

of

rollers

their

diameter

and

clearance

left

between

the

rollers
.

It

must

project

on

either

side

to

allow

for

longitudinal

movement

of

the

bridge
.

In

case

of

two

rollers

the

B
.
M
.

at

center

of

plate

=

V

S/

4

In

case

of

three

rollers

or

more

the

saddle

plate

acts

as

a

continuous

beam

of

variable

inertia

by

three

rollers

the

central

one

will

carry

most

of

the

load
.

For

this

reason

it

is

generally

preferred

to

have

the

number

of

rollers

either

(
1
&

2
&

4
&

6
&

8
)
.


R/2
Lower sole plate
Upper sole plate
Lower bearing plate
a
R/2
b
Rollers
1
t



The

rollers

The

size

of

rollers

depends

upon

the

maximum

reaction

on

one

roller

and

the

material

of

construction
.

Formula of Hertz for contact between a plane and cylinder of radius
R and length L is;








r
1
L
V
E
4
3
max





2
E
P
16
9
R





Assuming equal distribution of the reaction V on all
rollers;


L
2
2
EV
8
9
d
L
n
Or
E
nL
V
16
9
R
nL
V
P












For

Cast

Iron
;

E

=

1000

t/

cm
2
,



max

=

5
.
0

t/cm
2

V
32
.
14
d
L
n




For

Rolled

Steel
;

E

=

2100

t/

cm
2
,



max

=

6
.
50

t/cm
2







For

Cast

Steel
;

E

=

2200

t/

cm
2
,



max

=

8
.
50

t/cm
2





For

Forged

Steel
;

E

=

2200

t/

cm
2
,



max

=

9
.
50

t/cm
2










V
8
.
17
d
L
n




L
d
055
.
0
n
V








V
9
.
10
d
L
n




L
d
095
.
0
n
V







V
7
.
8
d
L
n




L
d
117
.
0
n
V



V/2
V/2
The rollers are provided with wider discs to take up the
lateral reaction. The rollers are coupled together by strong
side bars, serving as spacers allowing (
2
-

4
) cm between
every two rollers. The diameter of the rollers shall be not
less than
12
cm and not more than
35
cm.


4
-
The

lower

bearing

plate

It

distributes

the

concentrated

reaction

of

the

rollers

upon

a

wider

bearing

area

of

the

abutment
.

We

generally

assume

uniform

upward

pressure

and

the

plate

acts

as

a

beam

with

over

hanging

ends
.

Back

4
-
Hinged bearings with a
bearing block


It

used

for

longer

spans

and

consist

of

an

upper

sole

plate

riveted

to

the

girder

and

a

bearing

block
.

The

bearing

block

is

made

of

cast

steel

(or

cast

iron

for

small

Roadway

bridges)

with

longitudinal

and

transverse

ribs
.

For

vertical

reaction

only

the

pressure

on

the

abutment
;

b
a
V

=






perm

40
kg/ cm
2

for Basalt and Granite



70
kg/cm
2

for Reinforce Concrete

Including the effect of horizontal reactions in the
longitudinal and transverse directions then:

a
V
t
(0.2-0.3)h
SEC s-s
b
b
t
1
nt
2
H
L
t
(0.15-0.2)h
(0.2-0.3)h
fc
ft
s
t
h
t
s
H
T
6
ab
h
H
6
ba
h
H
b
a
V

=

2
t
T
2
t
L








1.15


perm


The

height

h
t

of

the

hinged

bearing

is

practically

taken

equal

to

that

of

the

opposite

movable

bearing

The

maximum

stressed

section

is

S



S,

it

is

equivalent

to

a

T

section

with

a

web

4

t
1
.

x
u
c
I
y
M

=

f

x
L
t
I
y
M

=

f

4
a
2
V

=

M

and

For

cast

iron

F
t

all

=

400

kg/cm
2





F
c

all

=
1000
kg/cm
2


For

cast

steel


F

all

=

1800

kg/cm
2




Thickness

of

lower

flange

=

(
1
/
3



1
/
5
)

h
t



Total

n

t
1

=

(
1
/
4



1
/
5
)

of

the

total

width

b



Thickness

of

central

web



1
/
6

h
t

The

upper

surface

of

the

bearing

block

must

be

curved

to

a

count

for

end

slop

of

the

girder
.

The

lower

surface

of

the

sole

plate

may

be

either

straight

or

curved
.

The

face

of

the

contact

is

a

line

in

the

unloaded

condition
.

Under

the

load

it

becomes

a

rectangle
.

The

width

which

(b)

increased

with

increase

at

loads
.


Hertz

formula

for

contact

between

two

curved

surfaces
;

v
6 max
t
h /6
b
e
h /6
t
b
1
2
R
R
b = width of area of contact

length

supporting

l
length
unit
per

load
l
V


where
r
/
1
r
/
1
C
C
2
b
2
1
2
1










r
1

& r
2

= radii of upper and lower surfaces






2
2
1
2
2
1
1
1
1
E
4
C
1
E
4
C






where

E

&



=

1
/m

are

the

modulus

of

elasticity

and

Poisson

ratio

of

the

two

materials
.

m

=

3

for

steel

&

m

=

(
2



4
)

for

all

the

materials

Assuming the elliptical pressure distribution over the
narrow strip b


L
b
V
4
L
4
b
V
max
max











For

the

case

E
1

=

E
2

=

E,

and


1

=

2

=


=

1
/
3















2
1
max
r
1
r
1
L
V
E
4
3
For a flat lower surface of sole plate and
1
/r
1

=
0

r
E
L
V
423
.
0
r
L
V
E
4
3
2
max







The allowable pressure

max can be taken much higher
than the working stress;

In compression


max

=
5.0
t/cm
2



Cast Iron


max

=
6.5
t/cm
2




Rolled Steel


max

=
8.5
t/cm
2




Cast Steel


max

=
8.5
t/cm
2




Forged Steel

Forged Steel = Rolled Steel but subjected to temperatures
up to
800


900


1000





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