Movements of expansion joints depend on the size of the bridge and the arrangement of the bearings. Normally the form of construction depends on the horizontal transla- tion orthogonal to the joint. But it is necessary to consider all translations and rotations to ensure that the displacements will not reach the limits of the joint construction.
To describe the movements of an expansion joint in detail we have to consider three translations and three rotations (fig. 2.3- 1).
52 2 . Expansion Joints
/ /
Fig.2.3-1: Possible movements
These movements result from temperature, displacements due to external loads, and creep and shrinkage in concrete and composite bridges. We may obtain the move- ments (displacements and rotations) from the structural analysis of the system. Move- ments due to loads depend on the location of the loads. The controlling deformations can be determined with influence lines (fig. 2.3-2 and fig. 2.3-3). The influence line of a deflection is the bending line due to a unit load acting in the direction of the con- sidered movement.
1
. -
Fig.2.3-2: Influence line for a translation
I"
Fig.2.3-3: Influence line for a rotation
To obtain the displacement caused by a rotation it is also possible to calculate the rotations; the displacements can be determined from the known rotations.
2.3.1
A change of the environment temperature, creep under normal force and shrinkage lead to a uniform extension or shortening of the bridge (fig. 2.3.1 -1).
The thermal expansion coefficients of steel and concrete have approximately the same value ( a , = 1,0 ... 1,2. / K ). A uniform change of temperature about the cross section causes only a horizontal translation of the joint. This applies to composite bridges, too.
Horizontal translation in the direction of the bridge axis u,
2.3 Calculation of movements of expansion joints 53
Fig.2.3.1 - I : Uniformly extension or shortening
n
Temperature: UXt.” = UT ’ C l i ’ ATi Creep and shrinkage of concrete bridges
i=l
N,, Permanent normal force (compression > 0)
n
Shrinkage: u,,., = -EcbW ’ li E,,, Shrinkage coefficient
i=l
A possible problem is the change of the location of the fixing point or the unknown lo- cation of the fixing point. On arch bridges the superstructure is usually fixed at the crown of the arch. The fixing point is moved by the deformation of the arch due to the asymmetrical load.
Buried expansion joints are often used for short bridges (Chapter 2.4). If the fixing point is situated on longer piers, it acts as a horizontal spring bearing. Due to a movement in the joint a plastic deformation of the asphalt layer occurs and the construction has a certain rigidity. A different rigidity of the expansion joints on the right and left abut- ment and a possible longitudinal deformation can lead to the cracking of the asphalt layer at one abutment. As the rigidity of this joint is higher than the rigidity of the piers the new fixing point is situated near the undamaged expansion joint (fig. 2.3.1-2).
Cracking of the asphalt layer of the buried expansion joint
Fixing point after cracking
I
Fig.2.3.1-2: Change of the fixing point
54 2 . Expansion Joints
In the case of an elastic fixing point there are additional movements at expansion joints due to acceleration and braking forces.
The actual rigidity of piers can differ from the planned rigidity. Moreover, if the bridge is fixed on more than one pier, the position of the fixing point can differ from the planned position.
Creep and shrinkage in composite bridges (acting in the concrete parts of cross- section only) mainly lead to deflections which result in rotations above the y-axis (fig.
2.3.1-4). Creep can be considered using a reduced section area and a reduced moment of inertia, shrinkage by a substitute tensile force Nsh acting on the free shrinking con- crete. N\,, is a compression force acting on the composite cross-section.
-1 -I- - E,,, Shrinkage coefficient
A, Area of concrete
E, Reduced modulus of elasticity of concrete to consider creep Fig.2.3.1-3: Equivalent shrinking force
Fig.2.3.1-4: Deflection under load
Horizontal movements of expansion joints can also be caused by vertical movements of the abutments. They are caused by foundation settlements or by replacement of bearings (fig. 2.3.1-5). Statically indeterminate steel and composite bridges can be prestressed by intentional lifting and/or lowering at the bearings.
yr+ -+
positive definition: cp u x
2.3 Calculation of movements of expansion joints 55
'xd 1
(bn Tn
e _ r C 1
F Y I
~
Fig.2.3.1-5: Displacement of bearings
U X d 1 = 44 ' (e" +e,>
U x d n = $1 ' e, + @" . e ,
If a fixing point is located on a high pier the additional movements due to pier defor- mation must be considered in the structural analysis. The movements can result from acceleration, braking forces, uniform and non-uniform temperature actions.
2.3.2
A horizontal translation in the crosswise direction results if the angle between the joint and the moving direction of the bearing is not 90 O (e. g. in skew bridges). The magnitude of the movement depends on the magnitude of the movement in the direc- tion of the bridge axis and on this angle (fig. 2.3.2-1 and fig. 2.3.2-2).
Horizontal translation in direction of the cross-section u,
u, = sincp. ueff
u y = C 0 S c p ~ U e f f
Fig.2.3.2-1: Skewed bridge
56 2. Expansion Joints
Fig.2.3.2-2: Skewed bearing conditions
2.3.3 Vertical translation u,
Vertical translations u, can be caused by the replacement of bearings (fig. 2.3.3-3) and the geometrical conditions on the abutment (fig. 2.3.3-1 and fig. 2.3.3-2).
u, = u x .tan€)
Fig.2.3.3-1: Sloping bridge with horizontal bearings
Fig.2.3.3-2: Bridge with short cantilever on the abutmen2 h
2.3 Calculation of movements of expansion joints 57
SN+ I /
...
I ...
- 7Hydraulic jack
Fig.2.3.3-3: Vertical displacement of bearings (due to bearing replacement)
2.3.4
In the case of a replacement of one single bearing at one side a rotation cpx occurs (fig.
2.3.4-1). However, it is possible to avoid this movement by uniform lifting over the cross-section.
Rotation around the bridge axis cpx
T r - ...
. . . -
Hydraulic jack Fig.2.3.4-1: Lijting on one side
2.3.5
This deformation is caused by vertical loading and non-uniform temperature. The controlling load positions of the traffic loads can be determined with influence lines.
Rotation around the y-axis cpr
Fig.2.3.5-1: Rotation due to deflections
2.3.6
The deformation cpz is caused by non-uniform temperature action in the horizontal direction, and by wind loads (fig. 2.3.6-1).
Rotation around the z-axis cpz
58 2 . Expansion Joints
. . . . ~ ~ . . . ~ . . . . ' P Z
Fig.2.3.6-I: Non-uniform temperature action