17.6
응력: 일반 하중 조건
여러 하중이 구조에 동시에 적용되는 실제 조건의 복잡성을 파악하기 위해 xy 평면에 평행하게 정렬된 본체 내의 특정 지점을 통과하는 단면을 시각화할 수 있습니다. 이 단면은 원래 하중, 수직력, 전단력을 포함한 다양한 힘을 받습니다.
단면 평면 내에서 잠재적인 방향성을…
여러 하중을 받는 신체를 생각해 보십시오. xy 평면에 평행한 평면을 사용하여 점을 통해 절개할 때 전단력이 점을 둘러싼 작은 영역에 작용하는 것이 관찰됩니다.
이전에 표시된 하중을 받는 물체의 일부와 수직력이 z축을 따라 작용하는 것을 고려하십시오
전단력은 단면 평면에서 잘 정의된 방향을 갖지 않으므로 x축과 y축에 평행한 두 개의 성분 힘으로 분해됩니다.
그런 다음 각 힘의 크기를 응력 요소를 얻기 위해 면적으로 나눕니다.
응력의 첫 번째 첨자는 응력이 z축에 수직인 표면에 가해진다는 것을 나타냅니다. 전단 응력의 두 번째 첨자는 방향을 식별합니다.
수직 평면의 다른 쪽을 해석하면 동일한 응력 성분이 생성되지만 반대 방향이 됩니다.
yz 및 zx 평면에 평행한 점을 통해 단면을 통과하면 추가 응력 요소를 정의할 수 있습니다.
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Q1: What are stress components and how are they determined at a point in a loaded body?
Stress components are determined by passing a sectional plane through a point in a body and analyzing forces acting on that section. Normal forces and shearing forces are resolved into components parallel to coordinate axes. Each force component is then divided by the area to obtain stress values. This process yields three distinct stress components at any point when sections are passed parallel to different planes.
Q2: What do the subscripts in stress notation indicate?
In stress notation, the first subscript indicates the plane on which the stress acts—specifically, the direction of the surface normal. The second subscript identifies the direction of the stress component itself. For example, τzy indicates shearing stress acting on a surface perpendicular to the z-axis, directed along the y-axis. This notation system clarifies both location and orientation of each stress component.
Q3: How do shearing forces differ from normal forces in stress analysis?
Normal forces act perpendicular to a sectional plane, typically along one axis. Shearing forces, however, lack a single well-defined direction on the sectional plane and must be resolved into two component forces parallel to the coordinate axes. This resolution allows shearing stresses to be calculated by dividing each component by the section area, yielding multiple shearing stress components at a point.
Q4: Why do opposite sides of a sectional plane show stress components in opposite directions?
When analyzing opposite sides of a vertical plane through a point, Newton's third law applies: action and reaction forces are equal and opposite. Therefore, the stress components calculated on one side of the plane are identical in magnitude but opposite in direction on the other side. This symmetry reflects the equilibrium of forces within the body under load.
Q5: How many stress components exist at a point in a three-dimensional loaded body?
At any point in a three-dimensional body, nine stress components exist: three normal stresses (σx, σy, σz) and six shearing stresses (τxy, τyx, τxz, τzx, τyz, τzy). These components are determined by passing sectional planes parallel to the xy, yz, and zx planes through the point. Together, they fully describe the stress state at that location under general loading conditions.
Q6: What do positive and negative signs indicate in stress component values?
The signs of stress components indicate the type of loading: positive values represent tension, where the material is being pulled apart, while negative values represent compression, where the material is being pushed together. This sign convention applies to both normal and shearing stress components, allowing engineers to quickly identify whether a region experiences tensile or compressive loading.
Q7: How does analyzing multiple sectional planes help understand stress under complex loading?
Analyzing sections parallel to different coordinate planes reveals the complete stress state at a point. By examining sections parallel to xy, yz, and zx planes, all nine stress components become defined. This comprehensive approach unravels the complex interplay of forces and stresses under intricate loading conditions, enabling accurate prediction of material behavior and structural failure.