13Chapter

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 bridgegirder. One end of the bridge girder is fixed in positionwhile, the other end is kept free for the horizontalmovement. The bearings are provided for the followingfunctions:

1- The bearings are provided to transmit the endreaction to the abutments and/ or piers and to distribute ituniformly, so that the bearing stress does not exceed theallowable bearing stress of the material.

2- The bearings are provided to allow the movement inthe longitudinal direction (expansion and contraction) dueto 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 forchange in length due to temperature and stress variation.The provisions for expansion and contraction should besuch as to permit movement of the free bearings to theextent of 10 mm for every 10 m of length.

For spans greater than 15m, on rigid pier or abutment, thebearings, which permit angular rotation at the girder ends,are provided, and at one end, there shall be a roller or othereffective type of expansion bearing.

In the design of bearings, provision shall be made for thetransmission of longitudinal and lateral forces to thebearings and the supporting structures. Provision shall bemade against any uplift to which the bearing may besubjected. All bearings are designed to permit inspectionand maintenance.

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TYPES END BEARING

Depending upon the magnitude of end reaction, and thespan of bridge, the different types of bearings used for thebridges are as follows:

1-Plate bearings (Sliding& hinged bearings).

2-Rocker bearings

3-Roller bearings.

4-Bearing adopted by Railway Board.

(Sliding& Plate bearings-1hinged bearings).

Plate bearings are simplest type of bearings.The plate bearings are used small spansupto 15 m and small end reaction of thebridge. Fig. 13-1 shows a plate bearing. Theplate bearing consists of two plates.

BRIDGE GIRDER

bearing plateUpper 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 restson bearing. The bearing plate is anchored to the concrete.The two anchor bolts fixed in concrete pass through thebearing plate and the sole plate. The size of bearing plate isfound by the end reaction and the allowable bearingpressure on the concrete. The plates are made rigid todistribute the end reaction as uniformly as possibly overthe required area of the concrete.

When the anchor bolts pass through the circular holes inthe sole plate, then, the plate bearings act as hingedbearing. One end of the bridge girder is hinged oranchored 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 endreactions used are large. Therefore, the fixed bearingsdesigned for end reactions (vertical loads) only strongenough to take the lateral forces.

In order to allow the longitudinal movement, the slottedholes are provided in the sole plate. In order to reduce thefriction, the surfaces of sole plate and bearing plate incontact are well machined and smoothly finished. The soleplate can slide upon the bearing plate. The plate bearingsact as expansion bearings of sliding type. In the expansionbearing, the longitudinal movement (expansion orcontraction) takes place with change of temperature andloads

The longitudinal force at any free bearing shall be limitedto the dead load reaction at the bearings multiplied by thecoefficient of friction. The coefficients of friction fordifferent surfaces in contact are given in clause 6.10(Egyptian code for loads).

The plate bearings have bearing two disadvantages. Theedge of plate nearest to the end of span has a tendency tolift along with the deflection of bridge girder. Therefore,the end reaction is not distributed uniformly. Secondly, inorder to have longitudinal movement, the sliding frictionis to be overcome. Therefore, for the large span bridges,the more efficient devices are necessary.

The end reaction is distributed uniformly by providing adeep cast steel bed block as shown in Fig. 13-2.

Such bed blocks have adequate rigidity. The sole platebearings are many times made curved as shown in Fig. 13-3.

The curved sole plate allows rotation. For large spans, theplate bearings are not suitable. The hinged (rocker) bearingsand roller bearings are used in such cases.

The sliding bearing is the least expansive bearing for lightand intermediate reactions.

B R I D G E G I R D E R

Fig 13-2

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BRIDGE GIRDER

ELLIPTICAL (SLOTTED) HOLE FOR EXPANSION BEARING

CIRCULAR HOLE FOR HINGED BEARING

Fig 13-3

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

Hex . nut and washer,fixed end

hole fixed endSlotted hole in rocker ,exp.end

Performed fabric pad or grout

Hex . and jam nut expansion end

Anchore boltsLCbrg

Fig 13-4

A similar detail in which the anchor bolts do not passthrough the rocker is shown in Fig. 10.3. In this case, thebeam is held in position by means of pintles shaped likegear teeth. This type of support may be used whereresistance to uplift need not be provided. For example, itmay be used for inside beams of the beam bridge, with theoutside beams supported by bearings of the type as shownin 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

LCCL brgbrg

Fig 13-5

Figure 13-6a shows an expansion bearing for larger bridges.Several variations are shown in the view at the right. Thesole plate may be bolted to the girder, as at the left of thecenterline, or welded as shown at the right. Resistance touplift may be provided by using a hinge plate, as at the left;if such resistance is needed, lateral movement is preventedby a plate such as that shown at right. A correspondinghinged end bearing is shown in Fig. 13-6b.

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 unloadedrocker and its bearing plate, deformation under loaddistributes the reaction over a finite area. Evidently, at agiven load this area increases with increase in radius of therocker, since a rocker of infinitely large radius would have aplane surface to begin with. The allowable load must beevaluated in terms of limiting permanent deformation. Thusthe yield point of the material is also a factor.

These bearings consist of:

An upper sole plate; in rolled steel riveted to the girder. Forhinged bearing the sole plate is provided with two grooves inwhich two ribs in the bearing plate in gage and thus thehorizontal movement isnt available.

2R = M

2cm/t4.1I

yM = f

12tb =I311

12

tb =I

2/t2R = f 311

1

& y = t1/ 2

t1 (3 - 4) cm

aH i n g e d b e a r i n g

M o v a b l e b e a r i n g

B e a r i n g p l a t e

U p p e r s o l e p l a t e

1bb 2

b 2 1b

R / 2

t 21t

a

a

r i b

r i b

R / 2

2- Abearing plate of cast steel (or cast iron for small RoadwayBridges).

Fixed to masonry by ribs.

The size of the bearing plate is obtained from the allowable bearingpressure on masonry for granite & basalt or similar hard stones 40kg/cm2. For reinforced with circular hoops 70 kg/cm2.

R

Bearing plate

B.M.D

2t

R/2

a

4a

2R = M

2cm/t8.1I

yM = f 12

tb =I322

22

322

2get t steelCast cm/t8.1

12tb

2/t4a

2R

IyM = 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.

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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 tolateral and longitudinal forces in addition to the endreaction (vertical loads). The increase of end reaction dueto lateral and longitudinal forces is also taken intoconsideration. The lateral forces and the longitudinal forcesare assumed to act at the level of cylindrical pin of therocker bearing. The base plate is subjected to momentalong both the directions. The total bearing stress in theconcrete should not exceed the allowable bearing stress.

The rocker bearings are designed for the end reaction andthen 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 theunderside of sole is curved, which rotates on the horizontalbearing plates and allows longitudinal movement. This actsas rocker type expansion.

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3-Roller bearings.The roller bearings as shown in Fig. 13-9 are also usedfor the long span bridges. Fig. 3.55 (A) shows a singleroller used in the bearing.

The rollers provide the rotation as well as thelongitudinal movement. Fig. 3.55 (B) shows number ofrollers used in the bearing. The bearings act as roller typeexpansion bearings. The rollers are kept in position bymeans of dowels, lugs or keys as shown in Fig. 3.55 (A).

The roller bearings for spans above span 35 m shouldpreferably be protected from dirt by oil or grease box.

So long as, the size of rollers is small, the completecircular rollers are provided. When the size of rollersbecome large, then, the sides of rollers are cut in order toreduce the length of the sole, and to make the bearingsmore compact. These rollers with cut sides are known assegmental rollers.

B R ID G E G IR D E R

S E G M E N T A L R O L L E R

S E G M E N T A L R O L L E R

B R ID G E G IR D E R

Fig 13-9

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In order to avoid overturning or displacement of theserollers, these are geared with upper and lower plates. Thespacing between segmental rollers and the width of rollersmay by found as below:

It is assumed that the rollers don not slip but only roll duringrolling. When, the roller rolls to the maximum position, asshown in Fig. 13-10,

bd

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 , andthe center of the roller travels through a forward motion, B.

Then,

travelHorizontalRroller segmental of DiameterD

roller segmental of WidthdDdsin

D114.6BsinDd

,Therefore

)degrees in(D

B6.114)radians in(DB2tan

(3.15)

(i)

The distance between adjacent segmental rollers a, (i.e. the spacingbetween the segmental rollers) should be such that the rollers do notcome 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 facesof adjacent, after their revolved positions.

The spacing between adjacent segmental rollers a, is found, knowingb, d and .The roller bearings are also used to support the cast steel sole with pinbearings as shown in Fig. 13-11. In such cases the roller also acts as ahinged bearing.

Fig 13-11

The following points are kept in mind while designing ssole a pedestal for the roller bearing.

1. The sole transmits the end reaction to the pin. Theend reaction must be distributed from the pin to the variousrollers uniformly.

2. The size and number of rollers provided should beadequate to have proper stress and free movement.

3. The rollers should be so arranged that these can bereadily 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 thathave projections extending over the upper surface of thebase of the shoe or by enlarging the base of the shoe andproviding slotted holes for the anchor bolts. The rollerassembly may be enclosed with removable dust guards;they are shown on only two sides in Fig 13-12 to indicatethat they are optional.

Removabledust guard

Side bars

BoltCap

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 curvedupper surface and a plain lower surface which bears upon therollers.

Its dimensions depend upon the number of rollers theirdiameter and clearance left between the rollers. It mustproject on either side to allow for longitudinal movementof the bridge.

In case of two rollers the B.M. at center of plate = VS/ 4In case of three rollers or more the saddle plate acts as acontinuous beam of variable inertia by three rollers thecentral one will carry most of the load. For this reason it isgenerally 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

bRollers

1t

The rollers

The size of rollers depends upon the maximum reaction on oneroller and the material of construction.

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

r1

LVE

43

max

2EP

169R

Assuming equal distribution of the reaction V on all rollers;

L

22

EV89dLn

Or

EnLV

169R

nLVP

For Cast Iron; E = 1000 t/ cm2, max = 5.0 t/cm2V32.14dLn

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

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

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

V8.17dLn Ld055.0nV

V9.10dLn Ld095.0nV

V7.8dLn Ld117.0nV

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 concentratedreaction of the rollers upon awider bearing area of theabutment. We generallyassume uniform upwardpressure and the plate acts asa beam with over hangingends. Back

4-Hinged bearings with a bearing block

It used for longer spans and consist of anupper sole plate riveted to the girder and abearing block.

The bearing block is made of cast steel (orcast iron for small Roadway bridges) withlongitudinal and transverse ribs.

For vertical reaction only the pressure on theabutment;

baV =

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:

aV

t

(0.2-0.3)h

SEC s-sb

bt

1nt

2

HL

t(0.15-0.2)h

(0.2-0.3)h

fc

ft

s t

h ts

HT

6ab

hH

6ba

hHba

V = 2tT

2tL 1.15 perm

The height ht of the hinged bearing is practically takenequal to that of the opposite movable bearing

The maximum stressed section is S S, it is equivalent to aT section with a web 4 t1.

x

uc I

yM = f x

Lt I

yM = f

4a

2V = 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) htTotal n t1 = (1/4 1/5) of the total width b

Thickness of central web 1/6 htThe upper surface of the bearing block must be curved to acount for end slop of the girder. The lower surface of thesole plate may be either straight or curved. The face of thecontact is a line in the unloaded condition. Under the load itbecomes a rectangle. The width which (b) increased withincrease at loads.

Hertz formula for contact between two curved surfaces;

v6 max

t h /6

b

e

h /6t

b1

2R

R

b = width of area of contact

length supporting l

lengthunit per loadlV where

r/1r/1CC2b

21

21

r1 & r2 = radii of upper and lower surfaces

22

12

21

11

1E4C

1E4C

where E & = 1/m are the modulus of elasticity andPoisson 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

LbV4

L4

bV

max

max

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

21max r

1r1

LVE

43

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

rE

LV423.0

rLVE

43

2max

The allowable pressure max can be taken much higher than the working stress;

In compression max = 5.0 t/cm2 Cast Ironmax = 6.5 t/cm2 Rolled Steelmax = 8.5 t/cm2 Cast Steelmax = 8.5 t/cm2 Forged SteelForged Steel = Rolled Steel but subjected to temperatures up to 800 900 1000 C

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