How are bending moment and shear force diagrams drawn?

Short Answer:

Bending moment and shear force diagrams are drawn to show how internal forces vary along the length of a beam when loads are applied. The shear force diagram (SFD) represents the variation of shear force at every point on the beam, while the bending moment diagram (BMD) shows how the bending moment changes along the beam.

To draw these diagrams, we analyze the beam step-by-step from one end to the other, calculate shear forces and bending moments at key points (like supports and load positions), and then plot them. These diagrams help engineers design safe and strong beams by locating maximum forces.

Detailed Explanation:

Bending moment and shear force diagrams

In civil engineering, beams are widely used to support loads in structures. To design these beams properly, we need to understand how internal forces are distributed within them. These internal forces mainly include bending moment and shear force, which arise when external loads act on the beam. To visualize their variation along the length of the beam, engineers use shear force diagrams (SFD) and bending moment diagrams (BMD).

These diagrams are important tools in structural design because they help identify the points where reinforcement is most needed to resist cracking, bending, or shear failure.

How to Draw Shear Force and Bending Moment Diagrams

The process of drawing these diagrams involves a few simple steps:

  1. Identify Support Reactions
  • First, determine the type of beam (simply supported, cantilever, fixed, etc.).
  • Calculate support reactions using equations of static equilibrium:
    • Sum of vertical forces = 0
    • Sum of moments = 0
  1. Divide the Beam into Sections
  • Divide the beam at points where loads are applied or where support exists.
  • These are the points where the internal forces may change.
  1. Calculate Shear Forces
  • Start from the left end of the beam.
  • Move section by section, summing up all vertical forces acting up to that point.
  • When a load is crossed, the value of the shear force changes.
  • Plot the values on a graph:
    • Vertical axis = Shear force
    • Horizontal axis = Length of the beam
  • The resulting graph is the Shear Force Diagram (SFD).

Rules for SFD:

  • A point load causes a sudden jump or drop in the shear force.
  • A uniform load causes a sloped line.
  • No load results in a horizontal line.
  1. Calculate Bending Moments
  • Start again from one end.
  • Use the bending moment formula:
    Moment = Force × Distance from the section.
  • Continue section-wise, adding or subtracting moments caused by loads and reactions.
  • Plot the values:
    • Vertical axis = Bending moment
    • Horizontal axis = Length of the beam
  • The resulting graph is the Bending Moment Diagram (BMD).

Rules for BMD:

  • A point load results in a straight sloped line.
  • A uniform load causes a curved line (parabola).
  • At supports (for simply supported beams), the bending moment is usually zero.
  1. Mark Key Points
  • Clearly indicate maximum shear force and maximum bending moment.
  • Label points of zero shear, as they often correspond to the maximum bending moment.

Importance of These Diagrams

  • These diagrams give a clear picture of how forces act inside the beam.
  • They are used to determine the required size and placement of reinforcement in RCC beams.
  • Help ensure that the design follows safety standards (like IS 456).
  • Allow identification of critical points in the structure, helping prevent failure.
Conclusion:

Shear force and bending moment diagrams are essential tools in structural engineering. They are drawn by first calculating support reactions, then sectioning the beam and finding internal forces at various points. These diagrams show where the internal stresses are highest, guiding engineers in the proper design of beams for strength and safety. They make the hidden forces inside the structure visible and understandable.