How to draw shear force and bending moment diagrams?

Short Answer

To draw Shear Force Diagram (SFD) and Bending Moment Diagram (BMD), first calculate the support reactions of the beam. Then divide the beam into different sections based on applied loads and find shear force and bending moment at each section. These values are then plotted along the beam length.

SFD shows variation of shear force, while BMD shows variation of bending moment along the beam. These diagrams are important in engineering because they help in analyzing beam strength and ensuring safe structural design.

Detailed Explanation:

Beam Analysis Basics

In Strength of Materials, beams are structural elements that carry loads applied perpendicular to their length. When loads are applied, internal forces such as shear force and bending moment are developed inside the beam.

To understand how these internal forces change along the beam, engineers use graphical tools called Shear Force Diagram (SFD) and Bending Moment Diagram (BMD).

These diagrams help in visualizing the internal behavior of beams under different loading conditions such as point load, uniformly distributed load, and varying load.

Steps to Draw SFD and BMD

Step 1: Identify Beam Type and Loads

First, identify the type of beam (simply supported, cantilever, etc.) and all the external loads acting on it.

Loads may include:

  • Point load
  • Uniformly distributed load (UDL)
  • Varying load
  • Applied moments

Understanding load type is important for correct analysis.

Step 2: Calculate Support Reactions

Next, calculate reactions at supports using equilibrium equations:

  • Sum of vertical forces = 0
  • Sum of moments = 0

These reactions are essential for further calculations of shear force and bending moment.

Step 3: Divide Beam into Sections

Divide the beam into different sections based on points where load changes occur. These points are usually:

  • Load application points
  • Support points
  • Points of change in loading

Each section is analyzed separately.

Step 4: Calculate Shear Force

Now calculate shear force at different points along the beam.

Shear force at a section is calculated by taking algebraic sum of all vertical forces acting on one side of the section.

Rules:

  • Positive shear force acts upward on left side
  • Negative shear force acts downward on left side

These values are used to construct the Shear Force Diagram (SFD).

Step 5: Draw Shear Force Diagram (SFD)

Plot the calculated shear force values along the length of the beam.

  • Draw a horizontal reference line representing beam length.
  • Plot shear force values above or below the line.
  • Connect points according to load type.

SFD shows how shear force changes along the beam.

Step 6: Calculate Bending Moment

Next, calculate bending moment at different sections of the beam.

Bending moment is calculated by taking sum of moments of all forces about a point.

Rules:

  • Positive bending moment causes sagging
  • Negative bending moment causes hogging

These values are used for BMD.

Step 7: Draw Bending Moment Diagram (BMD)

Plot bending moment values along the beam length.

  • Draw beam reference line.
  • Mark bending moment values at each section.
  • Connect points smoothly depending on loading.

The highest point in BMD shows maximum bending moment.

Important Rules in Drawing

  • Shear force changes suddenly at point loads.
  • Bending moment is zero at simple supports.
  • Maximum bending moment occurs where shear force is zero.
  • UDL causes linear change in SFD and parabolic shape in BMD.

These rules help in accurate diagram construction.

Importance in Engineering

SFD and BMD are very important in structural and mechanical engineering.

Structural Design

Used to design beams in buildings, bridges, and other structures to ensure safety.

Machine Design

Used in designing shafts, frames, and machine components subjected to loads.

Safety Analysis

Helps in finding maximum stress points to prevent failure.

Material Optimization

Helps in selecting proper size and material for beams and components.

Conclusion

Shear Force and Bending Moment Diagrams are essential tools used to analyze internal forces in beams. The correct method involves calculating support reactions, shear forces, bending moments, and then plotting them. These diagrams are very important for safe and efficient structural and machine design.

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