Name: axial load stress on inclined sections
Uploaded: 2024-03-07T13:22:32.000Z
Duration: 1 min 16 s
Channel: JoVE

Consider a member subjected to axial forces. Introduce a sectional plane inclined to the normal plane, called an oblique plane.
The stresses acting on this oblique plane can be resolved into two components: normal and tangential to the section.
The normal component represents the resultant of normal forces distributed over the section, while the tangential component represents the resultant of shearing forces.
The average normal and shearing stresses can be calculated by dividing the normal and tangential forces by the area of the section.
The normal stress is maximum when the plane of the section is perpendicular to the axis of the member and approaches zero when the sectional plane is parallel to the axis.
The shearing stress is maximum when the sectional plane is inclined at 45 degrees and approaches zero when the sectional plane is parallel or perpendicular to the axis of the member.
Depending on the orientation of the plane, the same load can produce either a normal stress with no shearing stress or both normal and shearing stresses of equal magnitude.

stress on an oblique plane

Stress on an Oblique Plane

Understanding stress on an oblique plane under axial loading is pivotal in material mechanics. This analysis offers insight into a material&#39;s durability and strength, which is crucial for civil engineering and structural design. Axial loading refers to force application along the material&#39;s central axis, causing compression or elongation and leading to normal stress. Normal stress occurs when a force acts perpendicularly to the material&#39;s area, resulting in compressive or tensile stress. When the stress plane isn&#39;t perpendicular to the load, it&#39;s an oblique plane, and the stress state includes both normal and shearing stress. Shearing stress happens when the force acts parallel to the area, deforming the material shape without volume change.
Considering a two-force member subject to axial force P and examining a section at an angle &#952; to the normal plane, the stresses on this oblique plane can be divided into normal (F) and tangential (V) components. Dividing F and V by the section&#39;s area provides the average normal and shearing stresses. The plane&#39;s orientation significantly impacts the material&#39;s stress state. Depending on the plane&#39;s orientation, the same load can induce only normal stress or both normal and shearing stresses of equal magnitude. Such understanding is crucial for designing robust, efficient structures.

Consider a member subjected to axial forces. Introduce a sectional plane inclined to the normal plane, called an oblique plane.
The stresses acting on ...

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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 volume.

A two-force member under an axial force P can be cut by a section at an angle θ to the normal plane. The force on that section can be resolved into a normal component F and a tangential component V. Dividing F and V by the section area gives the average normal stress and average shearing stress.

The orientation of the plane strongly changes the stress on the material. For some angles, the same load produces only normal stress. For other angles, it produces both normal and shearing stress, and these stresses may be equal in magnitude. This idea is important in civil engineering and structural design, where strength and durability matter.

Axial Load Stress on Inclined Sections

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...

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 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 axial loading creates normal and shearing stress on inclined sections, and how plane angle changes the stress state in materials.

Axial Load Stress on Inclined Sections | JoVE K12

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Axial Load Stress on Inclined Sections

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