Lecture on Drawing Shear Force and Moment Diagrams

Introduction

• Objective: Learn how to draw shear force and moment diagrams using two methods: the segment method and the relationship method between shear force and moment diagrams.
• Outline:
  • Segment method: Identifying changes on a beam, cutting the beam, and plotting the shear force and moment for each segment.
  • Relationship method: Using the relationship between shear force diagrams and moment diagrams to plot graphs.
  • Examples provided to illustrate both methods.

Methods of Drawing Diagrams

Segment Method

• Process:
  1. Identify where changes occur on the beam (e.g., force applications).
  2. Cut the beam at those points and calculate shear force and moment.
  3. Plot the values for each segment.
• Example:
  • Calculate reactions at supports.
  • Determine segments based on applied forces and cuts.
  • Write equilibrium equations to solve for shear forces and moments.
  • Use variable x to represent distances for flexible calculation of moments.
  • Key Points:
    • Moments are functions of x.
    • Shear force equations for segments don't require beam length.

Relationship Method

• Understanding Relationships:
  • Positive shear force results in a positive slope of the moment diagram and vice versa.
  • Area under the shear force diagram gives the moment.
  • Derivative of the moment diagram provides shear force.
• Example:
  • Calculate support reactions.
  • Use support reactions and forces to construct the shear force diagram.
  • Calculate areas under the shear force diagram to determine moments.
  • Plot moment diagram using calculated moments and shear force data.

Examples

Example 1: Single Force Application

• Reactions: Solve for reactions at supports (e.g., pin A and roller B).
• Segments:
  • First segment 0 m to 2 m.
  • Second segment 2 m to 6 m.
• Plotting:
  • Shear force: Constant for first segment, changes at force application.
  • Moment diagram: Linear for first segment, calculated via moment equations.

Example 2: Distributed Load

• Reactions: Solve for support reactions using resultant force of the distributed load.
• Segments:
  • First segment: Distributed load from 0 m to 8 m.
  • Second segment: From B to C.
• Diagram Construction:
  • Shear: Equation of equilibrium for shear force, considering distributed load.
  • Moment: Calculate moment using resultant force from distributed load.

Example 3: Complex Load and Moments

• Steps:
  • Determine reactions at supports.
  • Construct shear diagram starting from support reactions and applied forces.
  • Plot moment diagram considering the area under shear force diagram and applied moments.

Example 4: Applied Moments, Forces, and Distributed Loads

• Reactions: Calculate reactions at supports considering distribution load resultant force.
• Segment Analysis:
  • Identify distinct segments based on load applications.
  • Plot shear force and moment diagrams.
  • Notice the effect of distributed loads creating parabolic moment lines.

Conclusion

• Practice is essential for mastering these methods.
• Understanding relationships between shear force and moment diagrams can simplify the process.
• Encourage further sharing of the material for collective learning.