Ⅲ. Verification of Foundation Stiffness Applied to The Design
To explain the error, let's look at the error mentioned in Section 2.2 based on the following simple model.
As shown in the figure above, cantilever columns receiving horizontal force and moment at the end can be separated into columns receiving horizontal force and columns receiving moment, respectively. The horizontal displacement and rotation angle of the end of the column can be found from the mechanical knowledge learned in undergraduate studies.
How did the method mentioned in Section 2.2 apply the basic rigidity of the structure?
The horizontal stiffness was calculated from the displacement by the horizontal force, and the rotational stiffness was calculated from the rotation angle due to the moment.
In other words, rigidity is defined as follows.
However, as previously discussed, horizontal force also causes rotational displacement and moment also causes horizontal displacement.
Since stiffness has not been properly defined, the stiffness can be redefined by reflecting the displacement as follows.
Unlike the previous method, considering additional displacement, is this right?
Let's simply verify it.
As shown in the above results, it can be seen that a load different from the applied load is calculated.
In other words, the method I used when conducting the wind power project was wrong.
Ⅳ. A Study on Stiffness Calculation and Application of Design
In fact, I had never doubted the content. No, I didn't feel the need to doubt it. Then, I got a hint while drinking with an old colleague who accidentally came to ask for advice on studying Professional Engineer exam. The explanation is so boring, so let's go straight to the conclusion.
If the foundation needs to be replaced by a one-point spring, the stiffness matrix should be calculated using the "flexibility matrix".
Let's re-verify the previous example.
In other words, rather than directly obtaining the stiffness matrix and inputting it into the spring, the flexibility matrix should be obtained, and then the spring stiffness should be input by taking the inverse matrix.
The explanation was too long because I tried to explain it more closely to the engineers reading this article.
Then, how can the content be reflected in practice?
In MIDAS and SAP2000, general-purpose structural analysis programs mainly used in Korea, tools that can take this into account have already been installed and provided in the program.
I didn't have to write it, so I just passed it...
Ⅴ. conclusion
Many engineers already know the content of this content and are embarrassed and worried that they might be the only ones who didn't know, but if there are engineers like me who overlooked it and applied it to the design or didn't think about it, I wrote a shameful self-confession to help them a little.
If there is an opportunity, the following article intends to write about the design method in the introduction of Method 1, Method 2, and wind power generator vibration foundations applied to the basic design.
#Foundation stiffness
#Flexibility matrix
#Structural analysis
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A civil structure engineer & architectural structure engineer who loves structures.
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