How can I calculate the period of a simple span bridge ?How the period is affected if the Bridge is jointless i.e.there is no joint between the deck slab and the approach slab.
Well, you will find the period of this type of structure much like you would any other system. You start with the basic equation involving the mass and stiffness of the system - the system here is really very basic though.
The system can be treated for simplicity sake as a lumped mass at the center of the bridge. The stiffness of the system will be the typical deflection formulas for simple beams.
If your interested in the transverse, lateral response, then for the case you describe, it will be necessary to use the fixed-fixed case for deflection. The difficulty will be in determining the properties of the bridge cross-section. For slab on girder bridges, the slab will control the properties so an esitmate can be made from there otherwise you'll need to brush up on the parallel-axis theorem and dissmilar properties especially if your dealing with steel and concrete. Anyway, using a unit load (1 kip, or 10 kips or something similar you can find the value of p/delta. The period is easily determined from here.
One word of caution, if your looking for the vertical period of the single span bridge - you will have to look closely at the boundary conditions. Jointless bridges aren't really fixed per se in that direction as the abutment is usually founded on piling. It is the properties of the piling that allow a rotation to take place beneath the abutment beam thereby creating a pin connection. Thus for the vertical case, you need to use the equation for deflection of the pin-pin case.
You mention nothing about the stiffness of the abutments.In your opinion abutment stiffness shall not be included in the calculation of the period of a simple span bridge ?
If you are looking for the first flexural frequency for a simply supported bridge, isolated from the abutment by its bearings:
f1=(PI / (2*(L^2))) * (EI/mass per unit length)^0.5
where E in Pa(N/metre^2)
I in metre^4
mpul in kg/metre
L in metres
f1 in Hz
This formula is found in the Commentary of the Canadian Bridge Code CSA-S6-88
With regards to the effect of a jointless bridge I would not count on the contribution of the approach slab over the life of the bridge as the integrity of the approach slab is a function of the soil beneath.
Yes, there is no account for the abutment stiffness...simply a rule of thumb treatment for determining the fundamental period of the bridge and not higher modes where it is likely that the soil structure interaction will be prominent.
If you'd like to condsider the abutment stiffness then the problem changes to that of a multiple degree of freedom problem that may necessitate a computer solution.
However, the FHWA - Seismic Retrofitting Guidelines for Highway Bridges gives a good example for soil stiffness and pile stiffnesses at abutments. In summary the pile are afforded a stiffness of 40 kips/in/per pile while the abutment is given a value of 200 kips/in/foot of abutment width. Note that while the pile will act at each abutment, the soil stiffness due to passive pressure will only be active for the compression case.