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

軸方向の力を受けるメンバーを考えてみましょう。法線平面に対して傾斜した断面平面(斜め平面)を導入します。
この斜め面に作用する応力は、断面に接する法線と接する部分の2つの成分に分解できます。
法線成分は断面全体に分布する垂直力の合力を表し、接線成分はせん断力の合力を表します。
平均垂直応力とせん断応力は、垂直力と接線力を断面の面積で割ることによって計算できます。
垂直応力は、断面の平面が部材の軸に垂直なときに最大になり、断面平面が軸に平行なときにゼロに近づきます。
せん断応力は、断面平面が45度傾斜しているときに最大になり、断面平面が部材の軸に平行または垂直なときにゼロに近づきます。
平面の向きに応じて、同じ荷重でせん断応力のない垂直応力が発生するか、同じ大きさの垂直応力とせん断応力の両方が生成されます。

斜平面上の応力

Stress on an Oblique Plane

アキシアル荷重下での斜平面上の応力を理解することは、材料力学において極めて重要です。 この分析により、土木工学や構造設計にとって重要な材料の耐久性と強度についての洞察が得られます。 軸方向荷重とは、材料の中心軸に沿って力を加えることで、圧縮または伸びが生じ、垂直応力が発生することを指します。 法線応力は、力が材料の領域に垂直に作用すると発生し、圧縮応力または引張応力が生じます。 応力面が荷重に対して垂直でない場合、それは斜面となり、応力状態には垂直応力とせん断応力の両方が含まれます。 せん断応力は、力が領域に平行に作用するときに発生し、体積を変化させることなく材料の形状を変形させます。

軸力 P を受ける 2 力の部材を考慮し、法線面に対して角度 θ の断面を調べると、この斜面上の応力は法線 (F) 成分と接線方向 (V) 成分に分割できます。 F と V を断面の面積で割ると、平均垂直応力とせん断応力が求められます。 平面の方向は材料の応力状態に大きく影響します。 平面の向きに応じて、同じ荷重によって垂直応力のみが誘発されることも、同じ大きさの垂直応力とせん断応力の両方が誘発されることもあります。 このような理解は、堅牢で効率的な構造を設計するために不可欠です。

軸方向の力を受けるメンバーを考えてみましょう。法線平面に対して傾斜した断面平面(斜め平面)を導入します。
に作用するストレス...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Concept of Stress

ストレスの概念

KEY TERMS AND CONCEPTS

主要用語と概念

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...

stress on an oblique plane

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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mechanical engineering

Axial Load Stress on Inclined Sections

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