Single Degree-of-Freedom Problem

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In summary, the conversation discusses the calculation of the natural frequency and period of a single-bay, single-storey frame with a rigidly jointed beam and columns of negligible mass. The stiffness of the frame is given as EIc=4.5×103 kNm2 and the mass of the beam is 5,000 kg. The resulting values for the natural frequency and period are 4.502 Hz and 0.222 sec, respectively. The conversation also mentions finding the force necessary to deflect the frame 25 mm laterally, but does not provide a solution.
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aminbpy
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1.A 3 m high, 8 m wide single-bay single-storey frame is rigidly jointed with a
beam of mass 5,000 kg and columns of negligible mass and stiffness of EIc =
4.5×103 kNm2. Calculate the natural frequency in lateral vibration and its
period. Find the force required to deflect the frame 25 mm laterally.
Ans: 4.502 Hz; 0.222 sec; 100kn.



ƒ=(1/2π)*(√(k/m)

How can I get the k from given values.
 
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Hope you don't post any more exercises under this same name.
Welcome to PF and please use the template. If you don't understand why, read the guidelines.
 
  • #3
I can imagine a zillion of ways to connect s-b s-f frames with a beam and unknown number of columns. What is it we are talking about ? Were you provided with a drawing of the thing ?
 

FAQ: Single Degree-of-Freedom Problem

1. What is a single degree-of-freedom problem?

A single degree-of-freedom (SDOF) problem is a type of mechanical or structural analysis that involves the analysis of a system with only one independent variable or degree of freedom. This means that the motion or behavior of the system can be completely described by one variable, such as displacement, velocity, or acceleration.

2. What are some examples of single degree-of-freedom problems?

Examples of single degree-of-freedom problems include a simple pendulum, a mass-spring system, a single-mass vibrating system, or a single-story building subjected to earthquake forces. These systems have one degree of freedom because their motion can be described by just one variable, such as the angular displacement of the pendulum or the vertical displacement of the building.

3. How do you solve a single degree-of-freedom problem?

To solve a single degree-of-freedom problem, you first need to determine the equations of motion for the system, which describe the relationship between the input force or displacement and the system's response. These equations can then be solved using mathematical methods such as Newton's laws of motion, energy methods, or differential equations. Finally, the solution can be verified through experimental testing or computer simulations.

4. What are the advantages of using single degree-of-freedom models?

One advantage of using single degree-of-freedom models is that they are relatively simple and easy to understand, making them useful for introductory or conceptual analysis. Additionally, these models can provide insight into the behavior of more complex systems by simplifying them into a single degree of freedom. They can also be used to estimate the response of a system to different types of forces or inputs.

5. What are the limitations of single degree-of-freedom models?

One limitation of single degree-of-freedom models is that they may not accurately represent the behavior of more complex systems with multiple degrees of freedom. This is because they oversimplify the system by reducing it to one independent variable, which may not take into account the interactions and complexities of the real system. As a result, the solutions obtained from these models may not be completely accurate and may require further refinement or analysis.

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