Calculating Resonant Frequency of a Bridge with Added Support

In summary, when a support is placed one-third of the way along a bridge, the resonant frequency changes due to the altered distribution of harmonics. By taking the length of the original bridge and using the frequency to calculate the wavelength, it can be determined that the new resonant frequency will have a wavelength of 2/3 of the original length. This results in a new resonant frequency, which can be compared to the original frequency.
  • #1
Haftred
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I am having trouble with the following question:

A bridge has a natural frequence of 10 Hz. If a support is placed one-third of the way along the bridge, what is the new resonant frequency?

How should I start this problem?
 
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  • #2
When you place a bridge somewhere between the ends, you alter the way the harmonics are distributed.
 
  • #3
Take "L" to be the length of the original bridge. A wave MUST have a node at the two endpoints where the bridge is fixed so knowing the frequency, you can calculate the wavelength(s) of the resonant frequency in terms of L. If a support is placed at at 1/3 L a resonant frequency must have wave length 2(1/3)L= (2/3)L (2 because there is a node in the middle of a wave length). Calculate the frequency from that (again in terms of L) and compare with the original value.
 

FAQ: Calculating Resonant Frequency of a Bridge with Added Support

What causes waves to damage bridges?

Waves can damage bridges through a process called wave loading, where the force of the water pushing against the bridge can cause structural damage. This is especially common during storms or in areas with high winds.

How do engineers design bridges to withstand wave damage?

Engineers take into account the expected wave conditions in the area when designing bridges. They may use specialized materials or designs, such as sloped surfaces or breakwaters, to minimize the impact of waves on the bridge.

Can bridge foundations be affected by waves?

Yes, waves can affect bridge foundations by eroding the soil around them or causing movement in the foundation. This can lead to structural instability and potential collapse of the bridge.

Are certain types of bridges more susceptible to wave damage?

Yes, the type of bridge can play a role in its susceptibility to wave damage. For example, suspension bridges are more flexible and can better withstand wave loading compared to rigid structures like truss bridges.

How do researchers study the effects of waves on bridges?

Researchers use a combination of field studies and computer simulations to study the effects of waves on bridges. They may also conduct physical experiments in a controlled environment, such as a wave tank, to better understand the behavior of bridges under different wave conditions.

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