Name: shear modulus and angular change
Uploaded: 2024-03-07T13:22:38.000Z
Duration: 1 min 20 s
Channel: JoVE

In a cubic element with a general state of stress, the shearing stresses can deform a cube into an oblique parallelepiped without affecting normal strains. The angular change under shearing stress is the shearing strain.
A cube, when subjected to only shearing stress, morphs into a rhomboid, highlighting the impact of shearing strain.
When the angle between the axes of the cube shrinks, the strain is deemed positive. The shearing stress-strain diagram follows Hooke&#39;s law, where the initial straight line indicates proportionality between shearing stress and strain.
The constant G in Hooke&#39;s law for shearing is termed the shear modulus or modulus of rigidity of the material. It is expressed in the same units as the shearing stress and is less than half but more than one-third of the modulus of elasticity.
For general stress conditions, a generalized Hooke&#39;s law is obtained using the shearing strain relations and Hook&#39;s law.
The constants in these relationships are determined experimentally, which can then be used to predict material deformations from various stress combinations.

schuifspanning

De schuifspanning vertegenwoordigt de hoekverandering van een kubisch element wanneer deze wordt blootgesteld aan schuifspanning. Dit soort spanning kan een kubus in een schuin parallellepipedum veranderen zonder de normale spanningen te beïnvloeden. Het kubieke element ondergaat een aanzienlijke transformatie wanneer het uitsluitend wordt blootgesteld aan schuifspanning. De vorm verandert van een perfecte kubus in een ruitvorm, wat duidelijk het effect van schuifspanning aantoont. De mate van deze rek wordt als positief beschouwd als deze de hoek tussen de assen verkleint.

De relatie tussen schuifspanning en rek kan worden gevisualiseerd via een diagram dat lijkt op een standaard spanning-rekdiagram. De opbrengst en de uiteindelijke sterkte verschillen echter. Dit diagram illustreert de wet van Hooke in actie, waarbij de aanvankelijke rechte lijn een directe evenredigheid aangeeft tussen schuifspanning en rek.

<img alt="Equation 1" src="/files/ftp_upload/15602/15602_Equation_1.svg" style="text-align: center; height: 22px;">
De constante G in de wet van Hooke voor schuifspanning wordt de stijfheidsmodulus of schuifmodulus van het materiaal genoemd. Deze constante wordt uitgedrukt in dezelfde eenheden als schuifspanning. De schuifspanning kan voor een reeks spanningen worden gedefinieerd. Door gebruik te maken van het principe van superpositie kunnen we de algemene vorm van de wet van Hooke afleiden. Deze wet omvat drie constanten. Twee constanten worden experimenteel bepaald, terwijl de derde computationeel wordt verkregen.

<img alt="Equation 2" src="/files/ftp_upload/15602/15602_Equation_2.svg" style="text-align: center; height: 46px;">

Schuifspanning

In a cubic element with a general state of stress, the shearing stresses can deform a cube into an oblique parallelepiped without affecting normal ...

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Mechanical Engineering

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Unit 1

Stress and Strain - Axial Loading

Spanning en vervorming - axiale belasting

KEY TERMS AND CONCEPTS

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Shearing Strain

shear modulus and angular change

Shearing strain is the angular change that happens in a cubic element when it is loaded by shearing stress. Under this stress, the cube can change into an oblique parallelepiped without creating normal strains. If the cube is acted on only by shearing stress, its shape can shift strongly into a rhomboid.

The amount of shearing strain is considered positive when the angle between the axes becomes smaller. This change in angle shows the direct effect of shear on the material. The deformation can be compared with the stress-strain behavior shown on a standard chart, although the yield strength and ultimate strength are different for this case.

The first straight part of the shear stress-strain graph shows Hooke's law in action. In this range, shearing stress and shearing strain are directly proportional. The constant G in this relation is called the modulus of rigidity, or shear modulus, and it has the same units as shearing stress.

Shearing strain can be defined over a range of stresses. Using the principle of superposition, the generalized form of Hooke's law can be derived. This law includes three constants. Two are found by experiment, and the third is calculated from them.

Shear Modulus and Angular Change

normal strain under axial loading

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shearing strain

Shearing strain is the angular change that happens in a cubic element when it is loaded by shearing stress. Under this stress, the cube can change into an oblique parallelepiped without creating normal strains. If the cube is acted on only by shearing stress, its shape can shift strongly into a rhomboid. The amount of shearing strain is considered positive when the angle between the axes becomes smaller. This change in angle shows the direct effect of shear on the material. The deformation can...

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key terms and concepts

Learn how shearing stress changes a cube into a rhomboid, how shear strain is measured, and why the shear modulus G matters in Hooke's law.

Shear Modulus and Angular Change | JoVE K12

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mechanical engineering

Shear Modulus and Angular Change

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