Bending stress and shear stress.

Bending stress is a type of stress that occurs when a material is subjected to a bending moment. It is calculated by dividing the bending moment by the section modulus of the material. Bending stress causes the material to bend or deform.

Shear stress, on the other hand, is a type of stress that occurs when a material is subjected to a force that acts parallel to the surface of the material. It is calculated by dividing the force by the cross-sectional area of the material. Shear stress causes the material to deform or slide along a plane.

Both bending stress and shear stress are important considerations in the design and analysis of structures and mechanical components. They can affect the strength, stability, and performance of a material or structure.

Bending Stress

- Definition:
- Stress induced in a beam or plate when subjected to a bending moment.
- A measure of the internal resistance to deformation caused by bending.
- Formula:
- σ_b = M - y / I
- where:
- σ_b is the bending stress (MPa)
- M is the bending moment (Nm)
- y is the distance from the neutral axis to the point of interest (m)
- I is the area moment of inertia (m^4)
- Variations:
- The bending stress varies linearly from the neutral axis to the extreme fibers.
- The maximum bending stress occurs at the extreme fibers, which are farthest from the neutral axis.

Shear Stress

- Definition:
- Stress caused by the sliding of adjacent layers of material.
- A measure of the resistance to deformation caused by shear forces.
- Formula:
- τ = V - Q / Ib
- where:
- τ is the shear stress (MPa)
- V is the shear force (N)
- Q is the first moment of area (m^3)
- I is the area moment of inertia (m^4)
- b is the width of the cross-section (m)
- Variations:
- The shear stress is distributed unevenly across the cross-section.
- The maximum shear stress generally occurs at the neutral axis.

Key Differences between Bending Stress and Shear Stress

- Source of Stress: Bending stress is caused by bending moments, while shear stress is caused by shear forces.
- Distribution of Stress: Bending stress varies linearly across the cross-section, while shear stress is distributed non-linearly.
- Location of Maximum Stress: Maximum bending stress occurs at the extreme fibers, while maximum shear stress usually occurs at the neutral axis.
- Resistance to Deformation: Bending stress is resisted by the bending stiffness of the material, while shear stress is resisted by its shear modulus.

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