Name: stress at holes and notches in bending
Uploaded: 2024-05-23T12:59:43.000Z
Duration: 1 min 13 s
Channel: JoVE

The equation for stress for a member under pure bending having a plane of symmetry and a uniform cross-section assumes that the stress is evenly distributed across the entire cross-sectional area.
However, in real-world applications, the cross-section of a member may vary, or it may have geometric irregularities, such as a flat bar with grooves.
In such cases, the maximum stress is expressed using the stress concentration factor. The stress concentration factor is the ratio of the maximum stress to the nominal stress.
The maximum stress is the highest stress present at the discontinuity, and the nominal stress is the stress calculated using the composite cross-section.
Consider a plate with a U-shaped notch under bending stress. For this scenario, the stress concentration factor increases as the geometry of the notch becomes more pronounced.
For a round bar with a circular hole subjected to pure bending, the stress concentration factor is calculated using the ratio of the diameter of the hole to the diameter of the round bar. &#160;

stress concentrations

The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material&#39;s geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress concentration factor quantifies the increase in stress at points of discontinuity. It is the ratio of the maximum stress at the discontinuity to the nominal stress calculated for the uniform cross-section. This factor is essential in design engineering to ensure that structures can withstand stresses without failing, especially at points where stress is amplified due to geometrical irregularities.
For example, in a plate with a U-shaped notch under bending stress, the stress concentration factor increases with the sharpness of the notch geometry. Similarly, for a round bar with a circular hole subjected to pure bending, the stress concentration factor depends on the ratio of the hole&#39;s diameter to the bar&#39;s diameter. This relationship illustrates that as the diameter of the hole increases relative to the diameter of the bar, the stress concentration factor increases.

Stress Concentrations

The equation for stress for a member under pure bending having a plane of symmetry and a uniform cross-section assumes that the stress is evenly ...

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Mechanical Engineering

Unit 1

Bending

KEY TERMS AND CONCEPTS

stress at holes and notches in bending

Stress at holes and notches in bending shows how a material can carry more load in one small area than in the rest of the cross-section. For a symmetric member under pure bending, the stress is usually treated as evenly spread across the cross-section. That simple assumption works only when the cross-section is uniform and has no irregularities.

When the shape changes, the stress pattern changes too. Notches, holes, and other discontinuities can raise the local stress above the nominal stress for the uniform section. The stress concentration factor describes this increase. It is the ratio of the maximum stress at the discontinuity to the nominal stress calculated for the regular cross-section.

This factor matters in design engineering because parts must resist failure at places where stress is amplified by shape changes. In a plate with a U-shaped notch under bending, the stress concentration factor increases as the notch becomes sharper. In a round bar with a circular hole under pure bending, the factor depends on the ratio of the hole diameter to the bar diameter. As the hole gets larger compared with the bar, the stress concentration factor increases.

Stress at Holes and Notches in Bending

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Pure Bending in Beams and Structures

Pure bending describes how a beam bends under equal and opposite moments. It is a key idea in structural mechanics. Engineers use it to study how prismatic members, such as beams, deform under symmetrical loads without direct forces on the member. In pure bending, the beam experiences bending without axial force or shear force. This makes it possible to predict the stress pattern across the cross-section. The bending stress depends on the bending moment, the moment of inertia of the...

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Neutral Axis and Strain in Bending

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Composite Beam Stress and Neutral Axis

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Stress at holes and notches in bending shows how a material can carry more load in one small area than in the rest of the cross-section. For a symmetric member under pure bending, the stress is usually treated as evenly spread across the cross-section. That simple assumption works only when the cross-section is uniform and has no irregularities. When the shape changes, the stress pattern changes too. Notches, holes, and other discontinuities can raise the local stress above the nominal stress...

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Plastic Bending and the Neutral Axis

Plastic bending changes the shape of a structural member after the bending stress goes beyond the material’s yield strength. Before yielding, the member behaves in a linear elastic way. After yielding, the deformation is permanent. The strain at any point in the member is described in terms of the maximum strain. During elastic bending, the neutral axis, where strain is zero, matches the centroid. Under plastic conditions, that axis shifts away from the centroid. Finding its new position uses...

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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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Bending in elastoplastic members shows how a material responds during loading and unloading. At first, the member behaves elastically, so stress is proportional to strain and follows Hooke's Law. This stage continues until the bending moment becomes large enough to pass the yield strength. Once yield strength is exceeded, plastic deformation begins. Plastic deformation means the material does not fully return to its original shape. It leaves permanent strain and deformation even after the load...

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Eccentric Load Stress in Structural Members

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Unsymmetrical bending happens when a bending moment does not line up with a member’s principal axis. This creates a stress pattern and deflection shape that are more complex than in symmetrical bending. These effects matter when engineers design structures for different loading conditions. In unsymmetrical bending, the neutral axis is the line where stress is zero. It does not always match the geometric axes of the cross-section. Its orientation depends on the relationship between the applied...

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Curved Beam Stress and Neutral Axis

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key terms and concepts

Learn how holes, notches, and other shape changes increase bending stress, and how the stress concentration factor helps engineers predict weak points.

Stress at Holes and Notches in Bending | JoVE K12

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Stress at Holes and Notches in Bending

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