Name: material strain under axial loading
Uploaded: 2024-03-07T13:22:37.000Z
Duration: 1 min 23 s
Channel: JoVE

When a slender bar is subjected to an axial load, the bar material undergoes axial strain, causing it to deform in the axial direction.
Simultaneously, the material also experiences a lateral strain, deforming in directions perpendicular to the axial load.
The material is assumed to be homogeneous and isotropic, making its mechanical properties independent of the position and direction. So, the strain in any transverse direction must have the same value.
Poisson&#39;s ratio is a fundamental constant defined as the negative ratio of the lateral strain and the axial strain induced by the applied load for a given material.
The negative sign used is to obtain a positive value for Poisson&#39;s ratio since axial and lateral strains have opposite signs.
Materials with a high Poisson&#39;s ratio tend to experience greater lateral contraction when subjected to axial loads, while those with a low ratio tend to be less affected.
For instance, rubber has a Poisson&#39;s ratio close to 0.5, which means it experiences nearly as much lateral contraction as axial elongation.

poisson's ratio

Poisson&#39;s ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson&#39;s ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign ensures a positive value for the ratio, as the two strains typically have opposite signs. The value of Poisson&#39;s ratio significantly influences how a material behaves under stress.
Materials with high Poisson&#39;s ratios, such as rubber, which has a Poisson&#39;s ratio near 0.5, contract laterally nearly as much as they elongate axially. Knowing this ratio can predict how much a material will compress in the lateral direction when subjected to an axial load. This information helps design structures to withstand expected stresses and avoid failures. In summary, Poisson&#39;s ratio is a key characteristic of materials essential for predicting their behavior under stress. The anisotropic materials have different Poisson&#39;s ratios in different directions, and cork is known to have a zero Poisson ratio in one direction.

Poisson's Ratio

When a slender bar is subjected to an axial load, the bar material undergoes axial strain, causing it to deform in the axial direction.
Simultaneously, ...

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JoVE Core

Mechanical Engineering

Unit 1

Stress and Strain - Axial Loading

KEY TERMS AND CONCEPTS

material strain under axial loading

Poisson's ratio describes how a material changes shape when it is pulled or compressed along one direction. It links the strain in the direction of the force to the strain that happens sideways. When a slender bar is loaded axially, it stretches along the load and contracts laterally.

Poisson's ratio is defined as the negative ratio of lateral contraction to axial elongation. The negative sign is used because the two strains usually have opposite signs. This keeps the ratio positive and makes it easier to compare materials.

The value of Poisson's ratio affects how a material behaves under stress. Materials with high Poisson's ratios, such as rubber, can contract sideways almost as much as they elongate lengthwise. Rubber has a Poisson's ratio near 0.5.

Knowing this ratio helps predict how much a material will compress in the lateral direction when an axial load is applied. That prediction is useful in design because it helps structures handle expected stresses and avoid failure. Some anisotropic materials have different Poisson's ratios in different directions, and cork is known to have a zero Poisson ratio in one direction.

Material Strain Under Axial Loading

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Stress-Strain Limits in Materials

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Yielding and Strain-Hardening in Metals

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Fatigue Failure in Repeated Loading

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Calculating Rod Stretch from Mixed Loads

Calculating rod stretch from mixed loads starts with breaking the rod into parts. This step is needed when the rod is made of different materials or has changes in cross-section. Each part has its own internal force, cross-sectional area, length, and modulus of elasticity. These values are used to find the deformation of the full rod. For a member with a variable cross-section, the strain is not constant. Instead, it changes with position along the rod. The deformation of a small element is...

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Axial Rod Reactions with Redundant Support

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Thermal Stress in a Composite Rod

A steel-and-brass composite rod can build stress when temperature changes while both ends are restrained. The rod is nonhomogeneous, so its two sections respond differently. To find the compressive load, the problem is treated as statically indeterminate, which means the force cannot be found from equilibrium alone. The analysis begins by disconnecting one support so the rod can expand or contract freely under the temperature change. An unknown force is then applied at the free end. That force...

Poisson's ratio describes how a material changes shape when it is pulled or compressed along one direction. It links the strain in the direction of the force to the strain that happens sideways. When a slender bar is loaded axially, it stretches along the load and contracts laterally. Poisson's ratio is defined as the negative ratio of lateral contraction to axial elongation. The negative sign is used because the two strains usually have opposite signs. This keeps the ratio positive and makes...

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Axial Load Effects on Shear Strain

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saint-venant's principle

Load Effects Away from the Ends

Saint-Venant's principle describes how stress changes in a structural member when a load is applied. It shows that the exact way a load is placed matters most near the point of application. Farther away from that point, the stress pattern becomes much less dependent on how the load was applied. A simple example uses a member with plates on both ends. When the loads are applied at the center of the plates, the plates move toward each other without rotating. The member shortens in length and...

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Stress at Holes and Fillets

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residual stresses

Residual Stresses After Welding and Cooling

Residual stresses are stresses that remain in a structure after the original load or heat source is removed. They often form when different parts of a material undergo uneven plastic deformation, which means permanent shape change. A rod stretched past its yield point is one example. It will not return to its original length, and some stress stays inside even after the load is gone. These stresses can also develop during welding. Heat changes the material during the weld and can cause plastic...

key terms and concepts

Learn how axial loading creates lengthwise strain and sideways contraction, and why Poisson's ratio helps predict material behavior and support design.

Material Strain Under Axial Loading | 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

Material Strain Under Axial Loading

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