Name: stress components on a cube at a point
Uploaded: 2024-03-07T13:22:33.000Z
Duration: 1 min 23 s
Channel: JoVE

다중 하중을 받는 물체의 응력 구성 요소는 점 O를 중심으로 하는 작은 입방체를 고려하여 분석됩니다.
큐브에는 해당 축에 수직인 면에 작용하는 수직 응력 및 전단 응력 요소가 있습니다.
숨겨진 얼굴은 또한 보이는 얼굴의 스트레스와 같고 반대되는 이러한 스트레스를 경험합니다. 따라서 평형이 유지됩니다.
정육면체의 면에 가해지는 응력은 점 O의 응력과 약간 다르지만 정육면체의 한 변 길이가 0으로 줄어들면 이 작은 오차가 사라집니다.
큐브의 자유물체 다이어그램을 고려할 때, 면에 작용하는 수직력과 전단력은 해당 응력 성분에 각 면의 면적을 곱하여 결정됩니다.
그런 다음 평형 방정식을 적용하여 전단 응력 성분 간의 관계를 도출하며, 이는 주어진 점에서 응력 조건을 정의하는 데 6개의 응력 성분만 필요하다는 것을 의미합니다.
또한 전단 응력은 한 평면에서만 발생할 수 없습니다. 따라서 동일한 전단 응력이 수직인 다른 평면에 가해져야 합니다.

스트레스의 구성요소

다양한 하중 조건 하에서의 응력 해석은 복잡하므로 수직 응력과 전단 응력을 포괄적으로 파악해야 합니다. 눈에 보이든 보이지 않든 6개 면 모두에 응력을 받는 점 O의 작은 입방체를 생각해 보세요. 법선 응력 구성요소 σ_x, σ_y, σ_z는 x, y 및 z 축에 수직으로 작용합니다. 전단 응력 성분 τ_xy 및 τ_xz는 이러한 축에 수직인 면에 가해집니다.

흥미롭게도 숨겨진 큐브 면에도 보이는 면의 응력과 동일하고 반대되는 응력이 발생하여 평형이 보장됩니다. 큐브의 측면 길이가 0에 가까워짐에 따라 O의 응력과 큐브 면의 응력 간의 차이는 무시할 수 있게 됩니다.

입방체에 작용하는 힘을 조사하면 전단 응력 구성 요소 간의 중요한 관계를 알 수 있습니다. τ_xy는 τ_yx, τ_yz는 τ_zy, τ_zx는 τ_xz입니다. 이는 9개가 아닌 6개의 응력 구성 요소만이 한 지점의 응력 조건을 정의한다는 것을 나타냅니다.

중요한 것은 전단이 한 평면에서만 발생할 수 없다는 것입니다. 첫 번째 평면에 수직인 다른 평면에는 동일한 전단 응력이 적용되어야 합니다. 마지막으로, 해석된 응력 상황은 고려되는 요소의 방향에 따라 달라질 수 있으며, 이는 다양한 하중 조건에서 응력 해석의 복잡성을 강조합니다.

다중 하중을 받는 물체의 응력 구성 요소는 점 O를 중심으로 하는 작은 입방체를 고려하여 분석됩니다.
큐브는 법선과 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Concept of Stress

스트레스의 개념

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Components of Stress

stress components on a cube at a point

Stress components on a small cube help describe how a body behaves under multiple loading. The cube is centered at point O and has stress acting on all six faces, whether the faces are visible or hidden. Normal stress components σx, σy, and σz act perpendicular to the x, y, and z axes. Shearing stress components also act on the cube faces.

The visible faces carry shear stresses such as τxy and τxz. The hidden faces carry equal and opposite stresses. This balance keeps the cube in equilibrium. As the side length of the cube becomes very small, the difference between the stress at point O and the stress on the cube faces becomes negligible.

Looking at the forces on the cube also shows key links between shear components. The shear stresses satisfy τxy = τyx, τyz = τzy, and τzx = τxz. Because of these relations, only six stress components are needed to define the stress condition at a point, not nine. Shear cannot act in only one plane. An equal shearing stress must also act on a perpendicular plane.

The stress picture can change when the cube is rotated. That means the interpreted stress state depends on the orientation of the element being studied. This makes stress analysis under multiple loading conditions more complex.

Stress Components on a Cube at a Point

normal stress

Normal Stress in Axial Loading

Normal stress acts perpendicular to a material’s cross-sectional area. It appears when a force is applied along the axis of an object, which is called axial loading. Bridge truss members are a practical example of this kind of loading. When a rod carries axial load, internal forces develop across the section. Because these forces act normal to the plane of the section, the stress is called normal stress. Stress here means the average stress over the whole cross-section, not the value at one...

shearing stress

Shear Forces in Bolts and Rivets

Shearing stress is caused by transverse forces acting on an object. These forces create internal forces in the plane where the external forces are applied. The total internal force in that section is called the shear. Average shearing stress is found by dividing the shear by the cross-sectional area. This value is only an average, because shear stress is not spread evenly across the section. It can be zero at the surface and much higher than the average in other areas. Bolts, pins, and rivets...

bearing stress

Bolt-to-Plate Contact Pressure

Bearing stress is the contact pressure between two separate bodies. A common example is a bolt pushed through a plate. The bolt applies a force to the plate, and the plate pushes back with an equal and opposite force. That force is not a single point load. It is made up of many smaller forces spread across the contact surface between the bolt and the plate. Because these microforces are complex, engineers use an average value called bearing stress. Bearing stress is found by dividing the...

applications of stress

Boom and Rod Stress Analysis

Boom and rod stress analysis shows how a pinned support structure carries a load. The boom and the rod are connected by a pin and held in place by brackets and pins. The structure is then separated from its supports so the forces can be studied clearly. A free-body diagram is drawn to identify every force on the boom, the rod, and the load. The reaction forces on both members are found using equilibrium equations. At point P, the reaction causes compression in the boom. At point R, the...

stress on an oblique plane

Axial Load Stress on Inclined Sections

Axial loading creates stress in a material along its central axis. This kind of load can cause compression or elongation, and it produces normal stress. Normal stress acts perpendicular to the material area and can be either tensile or compressive. When the section is not perpendicular to the load, it becomes an oblique plane. On this inclined plane, the stress state includes both normal stress and shearing stress. Shearing stress acts parallel to the area and changes shape without changing...

stress: general loading conditions

Stress Components on a Loaded Body

Stress components on a loaded body can be found by cutting the body through a point with a plane parallel to the xy plane. That section carries the original loads, along with normal forces and shearing forces. The result is a simple way to describe how a structure responds under combined loading. The shearing force in the section can point in different directions within the plane. It is split into two parts that run parallel to the x and y axes. Each part is divided by the area, and as that...

components of stress

Stress components on a small cube help describe how a body behaves under multiple loading. The cube is centered at point O and has stress acting on all six faces, whether the faces are visible or hidden. Normal stress components σx, σy, and σz act perpendicular to the x, y, and z axes. Shearing stress components also act on the cube faces. The visible faces carry shear stresses such as τxy and τxz. The hidden faces carry equal and opposite stresses. This balance keeps the cube in equilibrium.

design consideration

Safety Factors in Structural Design

Safety factors in structural design help engineers choose a material and loading limit that can be used safely. The process begins with a material’s ultimate strength. This value comes from tests that increase force until the material reaches its breaking point or limit. The ultimate load is then divided by the original cross-sectional area to find the ultimate normal stress, or strength. Ultimate shearing stress is another key value used in design. These limits show how much stress a material...

key terms and concepts

Learn how normal and shearing stresses act on a small cube at a point, why only six stress components are needed, and how orientation changes stress analysis.

Stress Components on a Cube at a Point | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Stress Components on a Cube at a Point

Description

Transcript