Name: how strain gauges measure deformation
Uploaded: 2024-05-23T12:59:55.000Z
Duration: 1 min 27 s
Channel: JoVE

ひずみは、材料の変形または変位を測定します。垂直ひずみは、荷重が適用される前と後の長さを比較することによって計算されます。
垂直ひずみを測定するためのより正確な方法は、2枚の紙に接着された細いワイヤーで構成される電気ひずみゲージを使用することを含みます。
材料が伸びると、ワイヤの長さが長くなり、ワイヤの直径が小さくなるため、電気抵抗が増加します。この電流の変化を測定することで、正確なひずみが決定されます。
特定のポイントでのひずみ成分は、そのポイントを通る軸全体の垂直ひずみを測定することによって決定できます。軸によって形成される角度の二等分線に沿った3番目の測定により、せん断ひずみが決定されます。
ひずみ測定は、点を通る3本の線に沿って行われ、水平軸とそれぞれの角度を形成します。
対応するひずみ測定値は、法線ひずみ方程式に代入されて、3つのひずみ測定方程式を形成します。
ひずみの測定に使用されるひずみゲージの配置は、ひずみロゼットと呼ばれ、通常は45°または60°の構成です。

ひずみの測定

Measurements of Strain

ひずみは、力を受けた材料の変形を定量化します。通常は垂直ひずみとして測定され、元の長さと比較したときの長さの変化を表します。精度を高めるために電気ひずみゲージが使用されています。これらのデバイスは、材料の表面に接着する裏紙に取り付けられた導電性ワイヤで構成されます。これらのゲージは、機械的変形に応じてワイヤの電気抵抗が変化するピエゾ抵抗効果に基づいて動作します。ひずみゲージは材料が伸びたり圧縮したりすると調整され、受けるひずみに比例してワイヤの抵抗が変化します。

特定の材料点におけるひずみを包括的に理解するには、一定体積での形状変化を説明する垂直ひずみとせん断ひずみを考慮します。この解析には、さまざまな方向に配置された複数のひずみゲージが必要です。ひずみの測定は通常、水平軸に対して定義された角度で設定された線に沿って行われ、これらの読み取り値は全体のひずみ成分を計算するために使用されます。

ひずみゲージロゼットは、複数のゲージを 0°、45°、90°、または 0°、60°、120° などの構成に配置し、多方向のひずみを同時に測定できます。このような配置は、ある時点での詳細なひずみ解析にとって極めて重要であり、構造解析、材料テスト、および部品の検証で広く採用されています。これらの方法論は、エンジニアが材料の挙動を評価し、人工構造物の設計と安全性を強化するために不可欠です。

ひずみは、材料の変形または変位を測定します。垂直ひずみは、荷重が適用される前と後の長さを比較することによって計算されます。
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Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Transformations of Stress and Strain

応力とひずみの変換

KEY TERMS AND CONCEPTS

主要用語および概念

how strain gauges measure deformation

Strain describes how a material deforms when a force is applied. Normal strain compares the change in length with the original length. Engineers use this measure to track stretching or compression in materials.

For higher accuracy, they often use electrical strain gauges. A strain gauge has a conductive wire on a paper backing that sticks to the surface of the material. It works through the piezoresistive effect, which means the wire’s electrical resistance changes when the material is bent, stretched, or compressed.

As the material elongates or shortens, the strain gauge changes with it. That change alters the wire’s resistance in proportion to the strain. To understand strain at one point more fully, engineers also consider normal strain and shearing strain, which describe shape change at constant volume.

This more detailed analysis needs several strain gauges placed at different angles. Strain is often measured along lines set at defined angles to a horizontal axis. The readings are then used to calculate the overall strain components.

A strain gauge rosette makes this process easier by arranging multiple gauges together. Common layouts include 0°, 45°, and 90°, or 0°, 60°, and 120°. These setups allow simultaneous measurements in multiple directions and are widely used in structural analysis, materials testing, and part validation. Engineers use the results to study material behavior and improve the design and safety of engineered structures.

How Strain Gauges Measure Deformation

transformation of plane stress

Plane Stress Changes with Rotation

Plane stress changes with rotation in a material element. The analysis looks at a prismatic element inside a cube under plane stress. As the element turns, the normal stress and shearing stress on its faces change in both size and direction. These changes are described with trigonometric functions of the rotation angle. The forces on the rotated faces are compared with the forces on the original faces that are perpendicular to each principal axis. The equilibrium equations use only the forces...

principal stresses

Stress Circle for Principal and Shear Stress

The stress circle shows how normal stress and shearing stress change with angle on a transformed plane. Its center, C, lies on the vertical axis and represents the average normal stress. The radius shows the amount of stress variation as the plane rotates. Points A and B, where the circle crosses the horizontal axis, mark the maximum and minimum normal stresses. At these points, shearing stress is zero. These points define the principal stress planes, where only normal stress, called principal...

principal stresses: problem solving

Finding Principal Planes and Stress Limits

Principal planes and principal stresses are found by analyzing two planes that meet at right angles under shearing, tensile, and compressive stresses. The goal is to use the given stress values to describe how the material is loaded and to locate the planes where the stress state changes. To find the principal planes, use the formula that relates the plane angle to twice the shearing stress divided by the difference between tensile and compressive stresses. After substituting the known stress...

mohr&#39;s circle for plane stress

Reading Stress Components with Mohr's Circle

Mohr's circle is a graphical way to read the stress state at a point in a material under plane stress. It turns normal stress and shearing stress into a two-dimensional picture. This makes stress transformation easier to analyze. The method uses Cartesian coordinates. The horizontal axis shows normal stress, written as σ, and the vertical axis shows shearing stress, written as τ. Two points, A and B, are plotted from the stresses on the element. Point A is at (σx, -τxy), and point B is at (σx,...

general state of stress

Stress Tensor and Principal Stresses

The stress tensor describes the internal forces inside a material. It is used when a material is under external force or deformation. At a point such as O, the tensor can show the stress components on any plane through that point. A tetrahedral element helps show how these forces act. One face, XYZ, is perpendicular to the line OA. The other faces line up with the coordinate axes, and point O is the origin. The stress on the tetrahedron is split into normal and shear components on each face. <br...

yield criteria for ductile materials under plane stress

yield-criteria-for-ductile-materials-under-plane-stress

Tresca and Von Mises Yield Criteria

Ductile materials can yield when they are loaded beyond a safe stress level. Engineers use yield criteria to check whether structural elements and machine parts can handle the expected load without permanent deformation. The yield point is first found with a tensile test, which measures how the material responds to uniaxial stress. A tensile test is not enough when a part faces biaxial or plane stress conditions. In those cases, more advanced criteria are needed to predict failure. One common...

transformation of plane strain

Plane Strain Under Rotated Axes

Plane strain changes when the coordinate axes are rotated. This matters for long bars and similar elongated structures that are loaded uniformly on their sides. In these members, one dimension is much larger than the others, so deformation is mainly studied in a single plane. At a point such as O, the key strain components lie along the x and y axes. The strain along the z-axis is negligible in plane strain. Together, the x and y strain components describe the deformation state in the xy-plane.

mohr&#39;s circle for plane strain

Principal and Shear Strains on Mohr’s Circle

Mohr’s circle for plane strain shows how normal strain and shear strain change on a graph. The horizontal axis is normal strain, written as ε, and the vertical axis is shear strain, written as γ. It uses two plotted points, X and Y, to represent the strain state. Point X has coordinates (εx, -γXY), and point Y has coordinates (εY, γXY). The center of the circle, O, gives the average normal strain. The radius comes from the relationship between normal strain and shear strain, so the circle...

three-dimensional analysis of strain

Principal Strain Directions in 3D

Three-dimensional strain analysis shows how a material changes shape when it is loaded. It is especially useful for elastic, homogeneous materials. A small cubic element inside the material can expand or contract along principal stress axes. That change turns the cube into a rectangular parallelepiped, which makes the deformation easier to picture. The principal stress axes are orthogonal, or at right angles to each other. Along these directions, the stress does not create shear inside the...

measurements of strain

Strain describes how a material deforms when a force is applied. Normal strain compares the change in length with the original length. Engineers use this measure to track stretching or compression in materials. For higher accuracy, they often use electrical strain gauges. A strain gauge has a conductive wire on a paper backing that sticks to the surface of the material. It works through the piezoresistive effect, which means the wire’s electrical resistance changes when the material is bent,...

key terms and concepts

Learn how strain gauges measure deformation, from normal and shearing strain to rosette layouts used in structural analysis and materials testing.

How Strain Gauges Measure Deformation | JoVE K12

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mechanical engineering

How Strain Gauges Measure Deformation

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