Name: finding the plastic neutral axis in bending
Uploaded: 2024-05-23T12:59:43.000Z
Duration: 1 min 21 s
Channel: JoVE

Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below the neutral axis, with stress being -&#963;y above the neutral axis and +&#963;y below the neutral axis.
Here, the neutral axis of the member does not coincide with the centroid of the member.
To locate the neutral axis, consider the resultant of the compressive forces above the neutral axis R1 and the resultant of the tensile forces R2 below the neutral axis.
The compressive and tensile resultant forces form a couple, which is equivalent to the couple applied to the member. This shows that the neutral axis divides the member into cross-sections of equal areas.
The line of action of the resultant compressive and tensile forces passes through the centroids of the two equal areas. 
If the distance between these two centroids is defined as d, then the plastic moment of the member is expressed as half of the product of the area of the cross-section, the magnitude of the stress, and d.

plastic deformations of members with a single plane of symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or experiences severe deformation.
The resultant forces generated by the bending of the member are analyzed to locate the neutral axis. The compressive forces acting above the neutral axis and the tensile forces below it generate resultants with equal magnitude but opposite directions, forming a couple. This configuration indicates that the neutral axis divides the cross-section into two equal areas, each contributing equally to force equilibrium.
The plastic moment of the member Mp, a critical structural parameter, is derived from the relationship between the cross-sectional area, the material's yield stress, and the distance between the centroids of the areas d created by the neutral axis.
<img alt="Plastic moment formula \(M_p = \left(\frac{1}{2} A \sigma_y\right) d\) for structural analysis." src="/files/ftp_upload/15634/15634_Equation_1.svg" style="text-align: center; height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Calculating the plastic moment is essential for predicting the maximum moment the section can handle before significant plastic deformations occur. This consideration is particularly crucial for structural components in dynamically loaded areas, such as seismic zones, emphasizing how material properties and cross-sectional geometry influence a structure's capacity to withstand bending loads.

Plastic Deformations of Members with a Single Plane of Symmetry

Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below ...

plastic-deformations-of-members-with-a-single-plane-of-symmetry

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Bending

KEY TERMS AND CONCEPTS

finding the plastic neutral axis in bending

Plastic bending in a member with one plane of symmetry depends on the plastic neutral axis and the stress pattern across the cross-section. In this state, the stress is uniform above and below the neutral axis. The region above the axis is in compression, so it carries negative stress. The region below the axis is in tension, so it carries positive stress.

The plastic neutral axis does not usually pass through the centroid of the cross-section. This shift can happen when the section is not rectangular or when the member has deformed strongly. To locate the neutral axis, the bending forces are replaced by resultants. The compressive force above the axis and the tensile force below it act with equal size and opposite direction.

These two resultants form a couple, which is a pair of equal and opposite forces that create bending. This balance shows that the plastic neutral axis divides the cross-section into two equal areas. Each half contributes equally to force equilibrium. The plastic moment, written as Mp, depends on the cross-sectional area, the material yield stress, and the distance d between the centroids of the two areas made by the neutral axis.

Finding the plastic moment is important because it shows the largest moment the section can carry before major plastic deformation begins. That makes it useful for predicting how structural members respond to bending loads. It is especially important for parts used in dynamic loading conditions, such as seismic zones, where material properties and cross-sectional shape affect bending capacity.

Finding the Plastic Neutral Axis in Bending

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Plastic bending in a member with one plane of symmetry depends on the plastic neutral axis and the stress pattern across the cross-section. In this state, the stress is uniform above and below the neutral axis. The region above the axis is in compression, so it carries negative stress. The region below the axis is in tension, so it carries positive stress. The plastic neutral axis does not usually pass through the centroid of the cross-section. This shift can happen when the section is not...

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key terms and concepts

Learn how the plastic neutral axis, stress distribution, and plastic moment define bending capacity in a member with one plane of symmetry.

Finding the Plastic Neutral Axis in Bending | JoVE K12

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Finding the Plastic Neutral Axis in Bending

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