부정정 구조물의 해석

안녕하세요 오늘은 구조역학 중 부정정 구조물의 해석을 해볼 예정입니다.

일단 기본적으로 알아야 하는 개념은 많은 분들이 안정과 불안정, 정정과 부정정을 잘 못 알고 계신 경우가 종종 있습니다.

안정 : 외력이 작용하는 구조물이 항상 평행을 이루는 상태
불안정 : 외력이 작용하는 구조물이 항상 평행을 이루지 못하는 상태(붕괴)

정정 : 힘의 평행조건식만으로 미지수를 구할 수 있는 상태
부정정 : 힘의 평행조건식만으로 미지수를 구할 수 업는 상태로 부정정이 정정보다 더 위험하다는 절대 아닙니다.

부정정과 정정은 구조물의 안정성과 해석 방법을 구분하는 중요한 개념입니다.

부정정구조물은 힘의 평형조건식만으로는 미지수를 구할 수 없는 상태입니다. 부정정 구조물은 구속조건이 너무 많아서 평형방정식만으로는 해석할 수 없습니다. 이런 경우에는 추가적인 조건식, 즉 변형의 적합조건(Compatibility Condition)을 고려해야 합니다.

부정정구조물의 해석은 구조물의 구속조건과 평형방정식에 의해 미지력을 구하고, 이를 이용해 부재 내부력을 해석합니다. 부정정력수는 부정정 차수로 표현되며, 구조물의 안정성 여유를 나타냅니다.

정정구조물의 해석은 해제조건을 고려한 평형방정식에 의해 미지 반력을 구하고, 이를 이용해 부재 내부력을 해석합니다. 정정구조물은 힘의 평행조건식만으로 미지수를 구할 수 있으므로, 구조물의 구속조건과 평형방정식만으로 해석이 가능합니다.

따라서, 부정정과 정정은 구조물의 안정성과 해석 방법을 구분하는 개념입니다. 부정정구조물은 부정정력이 존재하여 추가적인 조건식이 필요하며, 정정구조물은 힘의 평형조건식만으로 미지수를 구할 수 있습니다. 이를 고려하여 부정정구조물과 정정구조물을 정확하게 분석하고 해석하는 것이 중요합니다.

또한 공기업의 문제 중에선 이러한 부정정 구조물의 특징을 물어보기도 합니다.

부정정 구조물의 특징은 다음과 같습니다.

 

• 정정 구조물에 비해 부재 단면이 작아 재료가 절약된다.
• 처짐이 정정에 비해 감소한다.
• 가늘고 긴 부정정 라멘 또는 아치인 경우는 외관상 우아하고 아릅답다.
• 부정정구조물은 정정구조물에 비해 지점변화, 온도변화, 제작오차, 하중으로 인한 큰 응력발생을 초래한다.
• 부정정구조물은 재료의 성질을 알아야만 정확히 해석이 가능하다.

다음은 부정적 차수 판별 문제입니다.

Hello, today we will discuss the analysis of indeterminate structures in structural mechanics.

 

First of all, it is important to understand the concepts that many people often confuse: stability and instability, determinacy and indeterminacy.

 

Stability: A structure is considered stable when it remains in a state where the applied forces always maintain parallelism. Instability: A structure is considered unstable when the applied forces prevent parallelism, leading to collapse.

Determinate: A structure is determinate when the unknowns can be determined solely by the equilibrium conditions. Indeterminate: A structure is indeterminate when the unknowns cannot be determined by the equilibrium conditions alone.

 

It does not mean that indeterminate structures are more dangerous than determinate structures.

 

In the case of indeterminate structures, the unknown forces cannot be directly determined using the equilibrium equations alone. Indeterminate structures have excessive restraints and require additional conditions to solve the equations. These additional conditions are known as compatibility conditions, which consider the deformations of the structure.

 

The analysis of indeterminate structures involves determining the unknown forces and internal reactions by considering both the equilibrium equations and compatibility conditions. The indeterminacy of a structure is expressed in terms of the degree of indeterminacy, which indicates the level of stability margin based on the structural configuration.

 

On the other hand, the analysis of determinate structures can be performed solely by considering the equilibrium equations. The unknown forces can be determined directly using the equations of equilibrium.

 

Therefore, indeterminate structures require additional considerations beyond equilibrium equations, taking into account compatibility conditions. By understanding the distinction between determinate and indeterminate structures, we can accurately analyze and interpret the behavior of these structural systems.

 

It is worth noting that in public sector exams, questions may also focus on the characteristics of indeterminate structures.

The characteristics of indeterminate structures are as follows:

1. Compared to determinate structures, indeterminate structures require less material due to smaller cross-sectional areas of the members.
2. Deflections are reduced compared to determinate structures.
3. Thin and long indeterminate beams or arches often exhibit elegant and graceful appearances.
4. Indeterminate structures are more sensitive to changes in conditions such as point variations, temperature fluctuations, fabrication errors, and significant stress caused by loading.
5. Accurate analysis of indeterminate structures requires knowledge of material properties.

I hope this explanation clarifies the concepts and characteristics of indeterminate structures.