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

Si consideri un corpo sottoposto a carichi multipli. Quando viene sezionato attraverso un punto utilizzando un piano parallelo al piano xy, si osserva che le forze di taglio agiscono su una piccola area che circonda il punto.
Si consideri una porzione del corpo sottoposta ai carichi precedentemente indicati, con la forza normale che agisce lungo l'asse z
Le forze di taglio non hanno una direzione ben definita su un piano di sezione, quindi sono risolte in due forze componenti parallele agli assi x e y.
L'entità di ciascuna forza viene quindi divisa per l'area per ottenere le componenti di sollecitazione.
Il primo pedice nelle sollecitazioni indica che vengono esercitate sulla superficie perpendicolare all'asse z. Il secondo pedice nelle sollecitazioni di taglio identifica la direzione.
Quando viene analizzato l'altro lato del piano verticale, produce le stesse componenti di sollecitazione ma in direzioni opposte.
Facendo passare le sezioni attraverso il punto parallelo ai piani yz e zx, è possibile definire ulteriori componenti di sollecitazione.

stress: condizioni generali di carico

Stress: General Loading Conditions

Per cogliere la complessità delle condizioni del mondo reale, in cui più carichi vengono applicati simultaneamente a una struttura, si potrebbe visualizzare una sezione che passa attraverso un punto specifico all'interno di un corpo, allineata parallelamente al piano xy. Questa sezione è soggetta a varie forze, inclusi carichi originali, forze normali e forze di taglio.

La forza di taglio, che possiede una potenziale direzionalità all'interno del piano della sezione, è semplificata in due forze componenti che corrono parallele agli assi x e y. Ciascuna forza viene divisa per l'area e, quando si avvicina allo zero, vengono definite tre distinte componenti di sollecitazione (σ_z, τ_zx e τ_zy). Il pedice iniziale in questi componenti, indica che le sollecitazioni sono esercitate su una superficie perpendicolare all'asse z, mentre il secondo pedice identifica la direzione del componente.

I segni di queste componenti di sforzo, indicano tensione (positiva) o compressione (negativa). Un'analisi simile sulla parte destra del corpo, risulta in componenti di sforzo identici ma in direzioni opposte. Ulteriori componenti di sollecitazione possono essere determinati facendo passare le sezioni attraverso il punto parallelo ai piani yz e zx. Questa analisi aiuta a svelare la complessa interazione di forze e sollecitazioni in condizioni di carico complesse.

Stress: condizioni generali di carico

Si consideri un corpo sottoposto a carichi multipli. Quando viene sezionato attraverso un punto utilizzando un piano parallelo al piano xy, si osserva che il taglio ...

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Mechanical Engineering

Ingegneria Meccanica

Unit 1

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Concept of Stress

Concetto di stress

KEY TERMS AND CONCEPTS

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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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