Beam shear refers to the internal shear forces that act on the cross-section of a beam, particularly when the beam is subjected to non-uniform bending. These forces are a result of external loads applied to the beam and are crucial for understanding a beam's behavior and potential failure modes.
Understanding Beam Shear
According to the provided reference on Shear Stress in Beams:
"When a beam is subjected to nonuniform bending, both bending moments, M, and shear forces, V, act on the cross section." This highlights that shear forces (V) are distinct internal forces present alongside bending moments (M) within a beam's cross-section, especially when bending isn't uniform along its length. The reference further notes that "The normal stresses, σx, associated with the bending moments are obtained from the flexure formula," contrasting these normal stresses with the effects of shear forces.
Essentially, beam shear is about the force component that acts parallel to the beam's cross-section, tending to cause one part of the beam to slide relative to an adjacent part. This is different from the bending moment which causes normal (perpendicular) stresses that lead to compression on one side and tension on the other.
Causes of Beam Shear
Beam shear arises primarily from the external loads and reactions applied to the beam. Common scenarios include:
- Concentrated Loads: A single force applied at a point creates significant shear force changes along the beam.
- Distributed Loads: Loads spread over a length of the beam (like the beam's own weight or snow load) contribute to varying shear forces.
- Supports: Reactions at the supports counteract the external loads, introducing shear forces.
Shear Force Diagram
Engineers use shear force diagrams (SFD) to visualize how the shear force (V) varies along the length of a beam.
| Location Along Beam | Shear Force (V) Behavior |
|---|---|
| Between Loads/Supports | Constant or linearly changing |
| At Concentrated Load | Jumps by the magnitude of the load |
| At Support | Jumps by the magnitude of the reaction |
Understanding the shear force diagram is essential for determining the maximum shear force within the beam, which is then used to calculate shear stresses.
Shear Stress vs. Shear Force
It's important not to confuse shear force (V) with shear stress (τ).
- Shear Force (V): The total force acting parallel to the cross-section.
- Shear Stress (τ): The intensity of this shear force distributed over the area of the cross-section (stress = force/area).
While the bending moment causes normal stresses (tension and compression), the shear force causes shear stresses within the material of the beam. These shear stresses are typically zero at the top and bottom surfaces of the beam and maximum at the neutral axis for common cross-sections like rectangles.
Why is Beam Shear Important?
Analyzing beam shear is critical in structural engineering for several reasons:
- Material Failure: Excessive shear stress can cause the beam material to fail in shear, often seen as diagonal cracks in concrete beams.
- Connection Design: Connections between beam segments or between a beam and other structural elements must be designed to handle the shear forces transferred.
- Deflection: While less impactful than bending moment, shear deformation does contribute to the total deflection of a beam.
In summary, beam shear refers to the internal shear forces (V) that develop within a beam's cross-section due to external loads, distinct from the bending moments (M) and associated normal stresses (σx). These forces are a key consideration in the structural analysis and design of beams.
