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

La deformazione misura la deformazione o lo spostamento in un materiale. La deformazione normale viene calcolata confrontando le lunghezze prima e dopo l'applicazione di un carico.
Un metodo più accurato per misurare le deformazioni normali prevede l'utilizzo di estensimetri elettrici costituiti da un filo sottile cementato a due pezzi di carta.
Quando il materiale si allunga, la lunghezza del filo aumenta e il suo diametro diminuisce, provocando un aumento della resistenza elettrica. La misurazione di questa variazione di corrente determina una deformazione accurata.
Le componenti di deformazione in un dato punto possono essere determinate misurando la deformazione normale attraverso gli assi disegnati attraverso quel punto. Una terza misurazione lungo la bisettrice dell'angolo formato dagli assi determina la deformazione di taglio.
Le misurazioni della deformazione vengono effettuate lungo tre linee tracciate attraverso un punto, formando i rispettivi angoli con l'asse orizzontale.
Le misurazioni della deformazione corrispondenti vengono sostituite nell'equazione della deformazione normale per formare tre equazioni di misurazione della deformazione.
La disposizione degli estensimetri utilizzata per misurare le deformazioni è chiamata rosetta di deformazione, tipicamente in configurazioni a 45° o 60°.

misurazioni della deformazione

Measurements of Strain

La deformazione quantifica la deformazione di un materiale sotto sforzo, tipicamente misurata come deformazione normale, che rappresenta la variazione di lunghezza rispetto alla lunghezza originale. Per una maggiore precisione vengono utilizzati estensimetri elettrici. Questi dispositivi sono costituiti da un filo conduttivo montato su un supporto di carta che aderisce alla superficie del materiale. Questi misuratori funzionano sull'effetto piezoresistivo, dove la resistenza elettrica del filo cambia in risposta alla deformazione meccanica. L'estensimetro si regola man mano che il materiale si allunga o si comprime, alterando la resistenza del filo proporzionalmente alla deformazione sperimentata.

Per comprendere in modo completo la deformazione in un punto materiale specifico, considerare le deformazioni normali e di taglio, che tengono conto dei cambiamenti di forma a volume costante. Quest’analisi richiede più estensimetri disposti con diversi orientamenti. Le misurazioni della deformazione vengono generalmente condotte lungo linee fissate ad angoli definiti rispetto a un asse orizzontale, con queste letture utilizzate per calcolare i componenti complessivi della deformazione.

Una rosetta estensimetrica, che posiziona diversi estensimetri in configurazioni come 0°, 45° e 90°, o 0°, 60° e 120°, consente misurazioni di deformazione multidirezionali simultanee. Tale disposizione è fondamentale per l'analisi dettagliata delle deformazioni in un determinato momento ed è ampiamente utilizzata nell'analisi strutturale, nei test sui materiali e nella convalida delle parti. Queste metodologie sono fondamentali per gli ingegneri per valutare il comportamento dei materiali, migliorando la progettazione e la sicurezza delle strutture ingegnerizzate.

La deformazione misura la deformazione o lo spostamento in un materiale. La deformazione normale viene calcolata confrontando le lunghezze prima e dopo l'applicazione di un carico.
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Education

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JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Transformations of Stress and Strain

Trasformazioni di tensione e deformazione

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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