2contents END BEARING Plate bearings (Sliding& hinged bearings). Rocker bearingsRoller bearingsBearing adopted by Railway Board.
3END BEARINGThe 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.
43-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.
5In 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
6TYPES END BEARINGDepending 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 bearings3-Roller bearings.4-Bearing adopted by Railway Board.
71-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 shows a plate bearing. The plate bearing consists of two plates.
9A 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.
10The 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
11The 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.
12The end reaction is distributed uniformly by providing a deep cast steel bed block as shown in FigSuch bed blocks have adequate rigidity. The sole plate bearings are many times made curved as shown in FigThe 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.
15Figure 13-4 shows a bearing that makes use of a rocker between the bearing plate and the beam or girder.Fig 13-4
16A similar detail in which the anchor bolts do not pass through the rocker is shown in Fig 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
18Figure 13-6a shows an expansion bearing for larger bridges 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.
20Although 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.
232- 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.
24& y = t2/ 2The 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
252-Hinged (Rocker) bearings Fig shows a typical rocker bearing.Fig. 13-8
26The 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 pinby 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.
27Two outer vertical plates completely encircle the pin 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.
28The 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.
29In 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
303-Roller bearings.The roller bearings as shown in Fig are also used for the long span bridges. Fig (A) shows a single roller used in the bearing.The rollers provide the rotation as well as the longitudinal movement. Fig (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 (A).The roller bearings for spans above span 35 m should preferably be protected from dirt by oil or grease box.
31So 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.
33In 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 ,Fig 13-10
34then, the vertical axis of roller turns through an angle , and the center of the roller travels through a forward motion, B.Then,(i)(3.15)
35The distance between adjacent segmental rollers a, (i. e 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 In such cases the roller also acts as a hinged bearing.
37The 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.Segmental rollers (Fig ) are ordinary used since they occupy less space than cylindrical rollers.
38The 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 to indicate that they are optional.
39The 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.
40Its 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/ 4In 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).
42Assuming equal distribution of the reaction V on all rollers; The rollersThe 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;Assuming equal distribution of the reaction V on all rollers;
44For Rolled Steel; E = 2100 t/ cm2, max = 6.50 t/cm2 For Cast Steel; E = 2200 t/ cm2, max = 8.50 t/cm2For Forged Steel; E = 2200 t/ cm2, max = 9.50 t/cm2
45The 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 plateIt distributes the concentratedreaction 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
464-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;
47 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:
49 1.15 permThe height ht of the hinged bearing is practically taken equal to that of the opposite movable bearingThe maximum stressed section is S – S, it is equivalent to a T section with a web 4 t1.andFor cast iron Ft all = 400 kg/cm2Fc all = 1000 kg/cm2
50For 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 bThickness of central web 1/6 htThe 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;
52b = width of area of contact r1 & r2 = radii of upper and lower surfaces
53where 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 materialsAssuming the elliptical pressure distribution over the narrow strip bFor the case E1 = E2 = E, and 1 =2 = = 1/3
54For a flat lower surface of sole plate and 1/r1 = 0
55The 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 CBack