For each degree of freedom, exhibiting the structure, there exists a natural frequency at which the structure vibrates in a particular mode of vibration. So if we are saying that the whole structure has one natural frequency then we are saying that the structure is having only one degree of freedom.
Hi!. If you model your bridge as a SDOF with these properties: mass m and stiffness k.
Then the natural frequency wn in radians per second is: wn=sqrt(k/m) and the cyclic natural frequency fn (in Hz) is calculated with this equation fn=wn /(2*pi).
However, if you model your bridge as a MDOF you will need to calculate the mass and stiffness matrices and obtain the eigenvalue analysis. In this case the square root of the smallest eigenvalue is the natural frequency of the fundamental mode of the structure.
Hi Abhimanyu,
Adding to the point mentioned by Miss Garcia, Bridges are connected by structural member and are either riveted or bolted. So, in either cases the member is completely fixed to each other something like a permanent joint. We can consider bridge as a integrated member only. In my opinion you should have a behavior of SDOF or MDOF but the structure will be integrated.
Hi Abhimanyu,
As you said, a real-world structure has an infinite number of degrees-of-freedom and as a consequence an infinite number of natural frequencies. However, the modal approach allows to reduce the number of DOFs by considering the structural natural modes as the DOFs of the structure.
Then, if you consider only the first mode of the bridge, you will have just the natural frequency related to this mode, i.e. the first fundamental frequency.
Best,
G.
Hello mate,
It is better to model bridge Pier/Abutment as SDOF and compute the time period.
Kindly refer Annex -D for the same of IRC-6-2017.
You are correct. Several modes are there but you can reduce them to three main modes with three natural frequencies when using simplified static equivalent code methods. (This applies to simple short span highway bridges). Why this can be done is because:
1. The mass in bridges (in general) is concentrated at the deck level. And because the deck can be considered as a rigid diaphragm, the whole masses of the bridge can be lumped at the deck (i.e. three translational masses).
2. The bridge has an uncoupled stiffness matrix (i.e. exciting one direction has no response in the other one)
So we will end up with three masses and three stiffness and all are uncoupled so we can consider each one as a single degree of freedom.
If the bridge deck (where most of the mass is, typically) is continuous and relatively wide compared to the span length, then the bridge deck will move as a rigid block. In this case, if we neglect vertical movements, the bridge will have three 'dominant' modes of vibration - 3 'dominant' natural frequencies. These will be two perpendicular translations and a rotation about a vertical axis. As others have mentioned, there are, in reality, as many modes as there are degrees of freedom. But many, many modes can be neglected in typical structures. If, however, the bridge is narrow relative to the span, the situation is different and many more modes will need to be considered to obtain an accurate solution to dynamic loading. In such a case, the deck does not move as a rigid block, but as a horizontal beam spanning between piers/abutments.
- Badges
- Science topic