Chapter 13Chapter 13

Bearing

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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.

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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.

11--Plate bearingsPlate bearings (Sliding& (Sliding& hinged bearings)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.

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.

Fig 13-2

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Fig 13-3

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Figure 13-4 shows a bearing that makes use of a rocker between the bearing plate and the beam or girder.

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.

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.

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

2cm/t4.1I

yM = f

12

tb =I

311

12

tb =I

2/t2R = f

311

1

& y = t1/ 2

t1 (3 - 4) cm

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.

4

a

2

R = M

2cm/t8.1I

yM = f

12

tb =I

322

22

322

2get t steelCast cm/t8.1

12

tb

2/t4

a

2

R

I

yM = f

& y = t2/ 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. Back

Fig. 13-8 shows a typical rocker bearing.

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.

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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.

Fig 13-9

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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,

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,

travelHorizontalR

roller segmental of DiameterD

roller segmental of WidthdD

dsin

D

114.6BsinDd

,Therefore

)degrees in(D

B6.114)radians in(

D

B2tan

(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 = bsec + 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.

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 = VS/ 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).

   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

VE

4

3max

2

EP

16

9R

Assuming equal distribution of the reaction V on all rollers;

2

2

EV

8

9dLn

Or

E

nL

V

16

9R

nL

VP

For Cast Iron; E = 1000 t/ cm2, max = 5.0 t/cm2

V32.14dLn

For Rolled Steel; E = 2100 t/ cm2, max = 6.50

t/cm2

For Cast Steel; E = 2200 t/ cm2, max = 8.50

t/cm2

For Forged Steel; E = 2200 t/ cm2, max = 9.50

t/cm2

V8.17dLn Ld055.0n

V

V9.10dLn Ld095.0n

V

V7.8dLn Ld117.0n

V

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 4-Hinged bearings with a bearing blockbearing 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;

ba

V =

perm 40 kg/ cm2 for Basalt and Granite

70 kg/cm2 for Reinforce ConcreteIncluding the effect of horizontal reactions in the longitudinal and transverse directions then:

6

ab

hH

6

ba

hH

ba

V =

2tT

2tL

1.15 perm

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.

x

uc I

yM = f

x

Lt I

yM = f

4

a

2

V = M

and

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;

b = width of area of contact

length supporting l

lengthunit per loadl

V where

r/1r/1

CC2b

21

21

r1 & r2 = radii of upper and lower surfaces

22

12

21

11

1E

4C

1E

4C

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

Lb

V4

L4

bV

max

max

For the case E1 = E2 = E, and 1 =2 = = 1/3

21max r

1

r

1

L

VE

4

3

For a flat lower surface of sole plate and 1/r1 = 0

r

E

L

V423.0

rL

VE

4

3

2max

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

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