Define shear force diagram (SFD).

Short Answer:

The shear force diagram (SFD) is a graphical representation that shows how the shear force varies along the length of a beam due to external loads and reactions. It helps in visualizing the magnitude and direction of shear force at every point on the beam.

In simple words, an SFD shows where the beam is likely to experience maximum or zero shear, which is essential for safe and economical design. By drawing the shear force diagram, engineers can easily locate the points of maximum shear and identify critical sections of the beam.

Shear Force Diagram (SFD)

Detailed Explanation :

The shear force diagram (SFD) is one of the most important tools in the analysis and design of beams in mechanical and structural engineering. It provides a clear graphical picture of how the shear force changes from one point to another along the beam length when subjected to loads such as point loads, uniformly distributed loads (UDL), or varying loads.

Understanding the shear force distribution helps in determining where the beam might fail or where reinforcements are needed.

Definition of Shear Force Diagram (SFD)

The shear force diagram (SFD) can be defined as:

“A diagram that represents the variation of shear force along the length of a beam under the action of applied loads.”

In other words, it shows how the internal shear force changes from one end of the beam to the other due to different types of external loads acting on it.

Shear force at a section of a beam is the algebraic sum of all vertical forces (including reactions) acting on one side of that section. The shear force may be positive or negative depending on the direction of the forces.

Concept of Shear Force in a Beam

When a beam is loaded transversely, internal forces develop within it to maintain equilibrium. One of these internal forces is the shear force (F), which acts tangentially along the cross-section.

At any given section of the beam, shear force is the force that tends to cause one part of the beam to slide relative to the other part. This force helps resist the applied loads and maintain the beam’s shape.

Mathematically, for a small element of a beam:

where  is the bending moment, and  is the shear force.

Thus, the rate of change of bending moment along the beam equals the shear force at that section.

Purpose of Shear Force Diagram

  1. To know how shear force changes along the length of a beam.
  2. To locate the points where shear force becomes zero — these points often correspond to maximum bending moments.
  3. To identify sections where the shear stress in the beam material will be maximum.
  4. To design the beam cross-section to safely resist these internal forces.

By plotting the SFD, engineers can determine critical sections that may require additional reinforcement or stronger materials.

Procedure to Draw a Shear Force Diagram

To construct a shear force diagram for any beam, the following steps are generally followed:

  1. Calculate Reactions at Supports:
    Use the conditions of static equilibrium ( and ) to find the reactions at supports.
  2. Cut Sections Along the Beam:
    Consider sections along the beam from one end to the other.
  3. Find Shear Force at Each Section:
    For each section, calculate the algebraic sum of vertical forces acting on either the left or right side of the section.
  4. Plot the Values:
    Plot the calculated shear force values on the vertical axis (ordinate) and the corresponding beam positions on the horizontal axis (abscissa).
  5. Join the Points:
    Join the plotted points with straight or curved lines based on the type of load applied:

    • Straight line for point loads.
    • Sloped or curved line for uniformly distributed or varying loads.

Sign Convention for Shear Force

To maintain consistency, the following sign conventions are used while drawing SFDs:

  • Positive Shear Force: When the left portion of the beam tends to move upward relative to the right portion.
  • Negative Shear Force: When the left portion of the beam tends to move downward relative to the right portion.

This convention helps in correctly plotting the SFD on the positive or negative side of the baseline.

Nature of Shear Force Diagram for Different Loads

  1. For Point Load:
    • The shear force changes suddenly (discontinuously) at the point of application of the load.
    • The SFD shows a vertical jump at the point of the load.
  2. For Uniformly Distributed Load (UDL):
    • The shear force varies linearly along the length of the loaded beam portion.
    • The SFD is a straight sloping line.
  3. For Uniformly Varying Load (UVL):
    • The shear force varies parabolically along the loaded length.
    • The SFD becomes a curved line.
  4. For No Load Section:
    • The shear force remains constant.
    • The SFD is a horizontal line in that region.

Key Features of Shear Force Diagram

  • Horizontal Line: Indicates no load between two sections.
  • Inclined Line: Indicates uniformly distributed load.
  • Parabolic Curve: Indicates a varying load.
  • Point of Zero Shear: Represents the section where bending moment is maximum.
  • Sudden Jump: Represents a concentrated (point) load.

Example (Conceptual)

Consider a simply supported beam with a single point load at its center:

  • The reactions at both supports are equal.
  • The shear force is positive and constant from the left support to the midpoint.
  • At the midpoint (where the load acts), the shear force suddenly drops to the same negative value.
  • The shear force remains constant (negative) till the right support.

Thus, the SFD consists of two horizontal lines, one above and one below the axis, with a sudden vertical drop at the center.

Importance of Shear Force Diagram

  1. It helps identify maximum shear force, which is critical for beam design.
  2. It assists in determining bending moment diagrams (BMD) since shear and moment are mathematically related.
  3. It helps ensure that the beam material and shape can safely withstand shear forces.
  4. It provides engineers with a clear visualization of how different loading conditions affect internal shear.
  5. It is used in structural analysis, design of beams, girders, and frames.
Conclusion

In conclusion, the shear force diagram (SFD) is a graphical representation that shows the variation of shear force along the length of a beam. It helps engineers visualize where the maximum and minimum shear forces occur, and these points are essential for safe beam design. The SFD, together with the bending moment diagram (BMD), provides a complete understanding of the internal forces in a beam under various loading conditions. By analyzing the SFD, one can predict and prevent possible shear failures in structural members.