What is shear force?

Short Answer:

A shear force is the internal force that acts along the cross-section of a beam or structural member when it is subjected to external loads. It tends to cause one part of the beam to slide or shear over the adjacent part.

In simple words, when a beam is loaded, it experiences both bending and shearing actions. The shear force at any section of the beam is equal to the algebraic sum of all vertical forces (loads and reactions) acting either to the left or right of that section. It helps determine how the beam resists the tendency of layers to slide over each other.

Detailed Explanation:

Shear Force

The shear force is an important concept in mechanics of materials and structural engineering. It represents the internal resistance developed within a beam or any structural member when subjected to external transverse loads. When external forces act perpendicular to the length of a beam, they not only cause bending but also try to make one portion of the beam slide relative to another. The force that resists this sliding tendency is called the shear force.

Shear force plays a vital role in determining the strength, safety, and performance of a structure. It helps in the design of beams, girders, and other load-carrying members to ensure they do not fail due to shearing action.

Definition of Shear Force

A shear force at a given section of a beam is defined as:

“The algebraic sum of all vertical forces acting on either side of that section.”

Mathematically, if all the forces acting to the left of a section are considered, the shear force (F) is given by:

The same value will be obtained if forces on the right side are considered, but with an opposite sign.

Shear force is generally expressed in Newtons (N) or kiloNewtons (kN), depending on the magnitude of load.

Cause of Shear Force

When a beam is loaded transversely (that is, the load acts perpendicular to its length), different parts of the beam experience different reactions due to these loads. The external load applied on the beam is resisted internally by both bending moment and shear force.

The shear force acts parallel to the beam’s cross-section and tries to slide one layer of the material over another. For example, if a beam is supported at its ends and loaded at the center, the left portion of the beam tends to move upward, while the right portion tends to move downward. The resistance to this relative movement is the shear force at that section.

Thus, shear force is a direct result of the vertical load distribution on the beam.

Sign Convention for Shear Force

To analyze beams correctly, engineers use a consistent sign convention for shear forces:

  1. Positive Shear Force:
    When the shear force tends to rotate the beam section clockwise on the left-hand side of the section, it is considered positive.
  2. Negative Shear Force:
    When the shear force tends to rotate the beam section anticlockwise on the left-hand side of the section, it is considered negative.

Using this convention helps maintain consistency while drawing shear force diagrams (SFDs) and analyzing beams.

Shear Force in Different Types of Loads

The magnitude and variation of shear force depend on the type of load acting on the beam. The common load cases are described below:

  1. Point Load:
    • When a single concentrated load acts on a beam, the shear force remains constant between two loads and changes suddenly at the point of load application.
    • The change in shear force is equal to the magnitude of the applied load.
  2. Uniformly Distributed Load (UDL):
    • When a load is spread evenly along the beam, the shear force varies linearly.
    • The slope of the shear force diagram equals the intensity of the distributed load.
  3. Uniformly Varying Load (UVL):
    • When load intensity increases or decreases along the beam, the shear force varies parabolically.
    • This occurs in cases like pressure acting on a dam wall or a wind load on a pole.

By knowing the type of loading, the shear force at any point on the beam can be determined accurately.

Shear Force Diagram (SFD)

A Shear Force Diagram (SFD) is a graphical representation that shows how shear force varies along the length of a beam. It helps in visualizing where the shear force is maximum or minimum.

Steps to Draw a Shear Force Diagram:

  1. Calculate reactions at supports using equilibrium equations.
  2. Move section by section along the beam and compute shear force values.
  3. Plot shear force on the vertical axis versus beam length on the horizontal axis.
  4. The diagram will show constant, linear, or curved variations depending on the type of load.

The point where the shear force becomes zero is very important because it usually indicates the location of maximum bending moment in the beam.

Relationship Between Load, Shear Force, and Bending Moment

The relationship between these three quantities helps engineers analyze beams efficiently:

  1. The rate of change of shear force at a point is equal to the intensity of the load at that point:

where w is the load intensity (N/m).

  1. The rate of change of bending moment at a point is equal to the shear force at that point:

These equations show that knowing one of these parameters allows us to find the others by integration or differentiation.

Practical Applications of Shear Force

  1. Design of Beams:
    Engineers use shear force calculations to determine the required beam dimensions and materials.
  2. Safety Analysis:
    Helps ensure beams can safely carry applied loads without shearing failure.
  3. Bridge and Building Construction:
    Used in designing girders, floor beams, and bridge decks to resist vertical loads.
  4. Machine Components:
    Shaft design, riveted joints, and welded connections require shear force analysis to avoid failure.
  5. Civil and Mechanical Design:
    Plays an essential role in load-bearing members of cranes, frames, and towers.

Example

Consider a simply supported beam of span 4 m carrying a point load of 8 kN at its center.

  • Reaction at each support = .
  • Shear force just to the left of the load = +4 kN.
  • Shear force just to the right of the load = -4 kN.
  • The shear force changes sign at the midpoint, indicating the point of maximum bending moment.
Conclusion

A shear force is the internal force developed in a beam or structural member to resist sliding between adjacent layers when external loads act perpendicular to its length. It ensures equilibrium and structural safety by opposing the shearing effect of loads. The analysis of shear forces helps determine how the internal forces are distributed along a beam and identifies critical sections for design. In any structure, understanding shear force is essential to prevent structural failure and ensure long-term durability.