17.6
应力:一般负载条件
为了在现实世界条件中能够掌握多个载荷同时施加到结构上的复杂性，人们可以想象一个与 xy 平面平行，并且与体内特定点平行的截面。 该部分承受各种力，包括原始载荷、法向力和剪切力。
剪切力在截面上具有潜在的方向性，同时被简化为与 x 轴和 y 轴平行延伸的两个分力。 将每个力与面积进行相除，当它的值接近…
考虑一个承受多个载荷的物体。当通过一个与 xy 平面平行的平面穿过某一点进行剖切时，可以观察到剪切力作用于该点周围的一个微小面积上。
考虑一个受到前述载荷作用的物体部分，其中法向力沿 z 轴作用
剪切力在截面上没有明确的方向，因此被分解为平行于 x 轴和 y 轴的两个分力。
然后将每个力的大小除以面积，以获得应力分量。
应力中的第一个下标表示它们作用在垂直于 z 轴的表面上。剪应力中的第二个下标表示其作用方向。
当分析垂直平面的另一侧时，得到的应力分量相同，但方向相反。
通过使截面穿过平行于 yz 和 zx 平面的点，可以定义额外的应力分量。
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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.