Transcript Chapter 13

Chapter 13
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 15m, 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.
1-Plate bearings (Sliding&
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
Upper sole plate
bearing 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
CIRCULAR HOLE FOR
HINGED BEARING
Fig 13-3
ELLIPTICAL (SLOTTED) HOLE
FOR EXPANSION BEARING
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
Hex . and jam nut
expansion end
Performed fabric
pad or grout
Anchore bolts
hole fixed end
CL brg
Slotted hole in rocker ,
exp.end
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.
Performed fabric
pad or grout
C
L brg
Slotted hole in rocker,exp.end
Round hole in rocker,fixed.end
Fix
Exp
Driving fit
Pintle detail
Fig 13-5
Figure 13-6a 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. 13-6b.
2 bolts in each side
PL
Topered hole
in rocker
(a)
2 bolts in each side
(b)
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.
R
M = 
2
M y
f=
 1.4 t / cm 2
I
b1t13
I=
12
f=
& y = t 1/ 2
R 2   t1 / 2
b1t13
I=
12
t1  (3 - 4) cm
R/2
R/2
Upper sole plate
t1
Bearing plate
a
rib
b2 b1
Movable bearing
a
rib
b2 b1
Hinged bearing
a
t2
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/cm2. For reinforced with circular hoops 70 kg/cm2.
R
t2
Bearing plate
a
B.M.D
R/2
R a
M= 
2 4
3
M y
b
t
2
f=
 1.8 t / cm
I= 2 2
I
12
R a
 t /2
M y 2 4 2
2
f=


1
.
8
t
/
cm
I
b 2 t 32
12
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.
& y = t 2/ 2
Cast steel
 get t2
ribS
Back
2-Hinged (Rocker) bearings
Fig. 13-8 shows a typical rocker bearing.
BRIDGE GIRDER
Fig. 13-8
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
BRIDGE GIRDER
Fig 13-9
SEGMENTAL ROLLER
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,
d+a
d
d
d+b b
B
D
d+a
D/2
Fig 13-10
a
then, the vertical axis of roller turns through an angle , and
the center of the roller travels through a forward motion, B.
Then,
d
D
d  Width of segmentalroller
sin  
D  Diamet erof segmentalroller
(i)
R  Horizontaltravel
2B
114.6B
tan   
(in radians) 
(in degrees)
D
D
T herefore,
 114.6B
d  D  sin 

 D 

(3.15)
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.
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.
1.
Cap
Bolt
Pin
Removable
dust guard
Side bars
Tongue
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
R/2
Upper sole plate
t1
Lower sole plate
Rollers
Lower bearing plate
b
a
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;
3 E V 1
 max 
 
4  L r
9
E
R
P 2
16

L
Assuming equal distribution of the reaction V on all
rollers;
V
P
nL
9
V E
R

 2
16 nL 
Or
9 EV
nLd   2
8 
For Cast Iron; E = 1000 t/ cm2,
n  L  d  14.32  V
max = 5.0 t/cm2
For Rolled Steel; E = 2100 t/ cm2,
t/cm2
n  L  d  17.8  V
For Cast Steel;
t/cm2
6.50
max
=
8.50
=
9.50
V
 0.095  d  L
n
For Forged Steel; E = 2200 t/ cm2,
t/cm2
n  L  d  8.7  V
=
V
 0.055  d  L
n
E = 2200 t/ cm2,
n  L  d  10.9  V
max
max
V
 0.117  d  L
n
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.
V/2
V/2
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;
V
=
ab
 perm
40 kg/ cm2 for Basalt and Granite
70 kg/cm2 for Reinforce Concrete
Including the effect of horizontal reactions in the
longitudinal and transverse directions then:
HL
V HT
s
ht
t2
b
SEC s-s
(0.15-0.2)ht
(0.2-0.3)h t
s
a
nt1
fc
(0.2-0.3)ht
b
ft
HL  h t HT  h t
V
=


2
ab
ba
ab 2
6
 1.15 perm
6
The height ht 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 t1.
fc =
M  yu
Ix
and
M  yL
ft =
Ix
V a
M= 
2 4
For cast iron Ft all = 400 kg/cm2
Fc all = 1000 kg/cm2
For cast steel F all = 1800 kg/cm2
Thickness of lower flange = (1/3 – 1/5) ht
Total n t1 = (1/4 – 1/5) of the total width b
Thickness of central web  1/6 ht
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;
R1
b
R2
h t /6
h t /6
b
v
e
6 max
b = width of area of contact
 C1  C 2
b2 
 1/ r1  1/ r2
V
where
   load per unit length
l
l  supportinglength
r1 & r2 = radii of upper and lower surfaces




4
C1 
1  12
E1
4
C2 
1   22
E1
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

V  b   m ax   L
4
4V
 m ax 
b  L
For the case E1 = E2 = E, and 1 =2 = = 1/3
3 E V 1 1
 max 
    
4  L  r1 r2 
For a flat lower surface of sole plate and 1/r1 = 0
3 E
V
V E
 max 

 0.423 
4  L  r2
L r
The allowable pressure max can be taken much higher
than the working stress;
In compression
max = 5.0 t/cm2
Cast Iron
max = 6.5 t/cm2
Rolled Steel
max = 8.5 t/cm2
Cast Steel
max = 8.5 t/cm2
Forged Steel
Forged Steel = Rolled Steel but subjected to temperatures
up to 800 – 900 – 1000 C
Back