Name: stress components on a loaded body
Uploaded: 2024-03-07T13:22:33.000Z
Duration: 1 min 15 s
Channel: JoVE

Stellen Sie sich einen Körper vor, der mehreren Belastungen ausgesetzt ist. Beim Präparieren eines Punktes mit einer Ebene, die parallel zur xy-Ebene verläuft, wird beobachtet, dass die Scherkräfte auf einen kleinen Bereich um den Punkt wirken.
Betrachten Sie einen Teil des Körpers, der den zuvor gezeigten Belastungen ausgesetzt ist, wobei die Normalkraft entlang der z-Achse wirkt
Da die Schubkräfte auf einer Schnittebene keine klar definierte Richtung haben, werden sie in zwei Komponentenkräfte aufgelöst, die parallel zur x- und y-Achse verlaufen.
Die Größe jeder Kraft wird dann durch die Fläche dividiert, um die Spannungskomponenten zu erhalten.
Der erste Index in den Spannungen gibt an, dass sie senkrecht zur z-Achse auf die Fläche ausgeübt werden. Der zweite Index in Schubspannungen gibt die Richtung an.
Wenn die andere Seite der vertikalen Ebene analysiert wird, ergibt sich die gleichen Spannungskomponenten, jedoch in entgegengesetzte Richtungen.
Durch das Durchlaufen des Punktes parallel zu den Ebenen yz und zx können zusätzliche Spannungskomponenten definiert werden.

spannung: allgemeine belastungsbedingungen

Stress: General Loading Conditions

Um die Komplexität realer Bedingungen zu erfassen, bei denen mehrere Lasten gleichzeitig auf eine Struktur wirken, kann man sich einen Abschnitt vorstellen, der durch einen bestimmten Punkt innerhalb eines Körpers verläuft und parallel zur xy-Ebene ausgerichtet ist. Dieser Abschnitt ist verschiedenen Kräften ausgesetzt, darunter Originallasten, Normalkräfte und Scherkräfte.

Die Scherkraft, die eine mögliche Richtung innerhalb der Schnittebene besitzt, wird vereinfacht in zwei Komponentenkräfte unterteilt, die parallel zur x- und y-Achse verlaufen. Jede Kraft wird durch die Fläche dividiert, und wenn sie sich Null nähert, werden drei verschiedene Spannungskomponenten (σ_z, τ_zx und τ_zy) definiert. Der Anfangsindex dieser Komponenten bedeutet, dass die Spannungen auf eine Fläche senkrecht zur z-Achse ausgeübt werden, während der zweite Index die Richtung der Komponente angibt.

Die Vorzeichen dieser Spannungskomponenten deuten auf Zug (positiv) oder Druck (negativ) hin. Eine ähnliche Analyse am rechten Körperteil ergibt identische Spannungskomponenten, jedoch in entgegengesetzter Richtung. Zusätzliche Spannungskomponenten können bestimmt werden, indem Schnitte durch den Punkt parallel zur yz- und zx-Ebene durchgeführt werden. Diese Analyse hilft dabei, das komplexe Zusammenspiel von Kräften und Spannungen unter komplizierten Belastungsbedingungen zu entschlüsseln.

Spannung: Allgemeine Belastungsbedingungen

Stellen Sie sich einen Körper vor, der mehreren Belastungen ausgesetzt ist. Beim Präparieren durch einen Punkt mit einer Ebene, die parallel zur xy-Ebene verläuft, wird beobachtet, dass die Scherung ...

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Concept of Stress

Spannungsbegriff

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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 area becomes very small, three stress components are defined: σz, τzx, and τzy.

The first subscript in each symbol shows the surface orientation. It means the stress acts on a surface perpendicular to the z-axis. The second subscript shows the direction of the stress component. The sign of each stress component shows whether the material is in tension, which is positive, or compression, which is negative.

If the body is viewed on the right side of the cut, the same stress components appear in opposite directions. Similar stress components can also be found by making sections parallel to the yz and zx planes. This method helps describe the full set of stresses that can act at a point when several loads act at once.

Stress Components on a Loaded Body

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 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 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.

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 to find stress components on a loaded body using cuts through a point. See normal and shear stresses on xy, yz, and zx planes.

Stress Components on a Loaded Body | 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 Loaded Body

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