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

변형률은 재료의 변형 또는 변위를 측정합니다. 수직 변형률은 하중이 가해지기 전과 후의 길이를 비교하여 계산됩니다.
수직 변형률을 측정하는 보다 정확한 방법은 두 장의 종이에 얇은 와이어를 접합하여 구성된 전기 변형계를 사용하는 것입니다.
재료가 elongate를 사용하면 와이어의 길이가 증가하고 직경이 감소하여 전기 저항이 증가합니다. 이러한 전류 변화를 측정하면 정확한 스트레인이 결정됩니다.
주어진 점에서의 변형률 성분은 해당 점을 통해 그려진 축에서 수직 변형률을 측정하여 결정할 수 있습니다. 축에 의해 형성된 각도의 이등분선을 따라 세 번째 측정은 전단 변형률을 결정합니다.
변형률 측정은 점을 통해 그려진 세 개의 선을 따라 이루어지며 수평 축과 각각의 각도를 형성합니다.
해당 스트레인 측정은 3개의 스트레인 측정 방정식을 형성하기 위해 일반 스트레인 방정식으로 대체됩니다.
스트레인을 측정하는 데 사용되는 스트레인 게이지의 배열은 일반적으로 45° 또는 60° 구성으로 스트레인 로제트라고 합니다.

변형률 측정

Measurements of Strain

변형률은 힘을 받는 재료의 변형을 정량화하며 일반적으로 정상 변형률로 측정됩니다. 이는 원래 길이와 비교할 때 길이의 변화를 나타냅니다. 정확도 향상을 위해 전기 스트레인 게이지가 사용됩니다. 이러한 장치는 재료 표면에 접착되는 종이 뒷면에 장착된 전도성 와이어로 구성됩니다. 이 게이지는 기계적 변형에 따라 와이어의 전기 저항이 변하는 압저항 효과로 작동합니다. 스트레인 게이지는 재료가 늘어나거나 압축됨에 따라 조정되어 경험하는 스트레인에 비례하여 와이어의 저항을 변경합니다.

특정 재료 지점의 변형률을 포괄적으로 이해하려면 일정한 부피에서 형상 변화를 설명하는 수직 변형률과 전단 변형률에 대해 생각헤 보세요. 이 분석에는 다양한 방향으로 배열된 여러 스트레인 게이지가 필요합니다. 변형률 측정은 일반적으로 수평 축에 대해 정의된 각도로 설정된 선을 따라 수행되며, 이러한 판독값은 전체 변형률 구성 요소를 계산하는 데 사용됩니다.

0°, 45°, 90° 또는 0°, 60°, 120° 등의 구성으로 여러 게이지를 배치하는 스트레인 게이지 로제트를 사용하면 동시 다방향 스트레인 측정이 가능합니다. 이러한 배열은 특정 지점의 상세한 변형 분석에 중추적이며 구조 분석, 재료 테스트 및 부품 검증에 광범위하게 사용됩니다. 이러한 방법론은 엔지니어가 재료 거동을 평가하고 엔지니어링 구조물의 설계 및 안전성을 향상시키는 데 필수적입니다.

변형률은 재료의 변형 또는 변위를 측정합니다. 수직 변형률은 하중이 가해지기 전과 후의 길이를 비교하여 계산됩니다.
더 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Transformations of Stress and Strain

응력과 변형률의 변환

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

How Strain Gauges Measure Deformation

Description

Transcript

Tags