EFFORT TRANCHANT ET MOMENT: Méthode graphique

Introduction

This tutorial will guide you through the graphical method for plotting shear force and bending moment diagrams, essential in the field of materials resistance. Understanding these diagrams is crucial for engineers and architects to analyze structural integrity and ensure safety in construction.

Step 1: Understand the Basics of Shear Force and Bending Moment

Before diving into the graphical method, familiarize yourself with the concepts of shear force and bending moment.

• Shear Force: The force that acts along a section of the beam, causing parts of the structure to slide past each other.
• Bending Moment: The moment that induces bending of the beam due to external loads, causing the beam to bend.

Practical Tip

Use examples of simple beams with known loads to visualize these forces effectively.

Step 2: Identify the Loadings on the Beam

Begin by determining all external loads acting on the beam:

• Point loads
• Distributed loads
• Support reactions

Steps to Identify Loads

1. Diagram the beam and label supports and loads clearly.
2. Calculate the support reactions using equilibrium equations.

Step 3: Draw the Shear Force Diagram

Follow these steps to construct the shear force diagram (SFD):

1. Start at one end of the beam and set the initial shear force to zero.
2. Move along the beam, applying the following rules:
   • For point loads, jump vertically by the magnitude of the load (upward for reactions, downward for loads).
   • For distributed loads, calculate the area under the load curve to find the change in shear force over the length of the load.
3. Connect the points smoothly to form the shear force diagram.

Common Pitfall

Ensure the sign conventions are consistent. A downward force should result in a decrease in shear force.

Step 4: Draw the Bending Moment Diagram

With the shear force diagram completed, proceed to create the bending moment diagram (BMD):

1. Start from one end of the beam where the moment is zero.
2. Use the shear force diagram to calculate the bending moment at various points:
   • The bending moment increases or decreases based on the area under the shear force diagram.
3. Connect the calculated points to form the bending moment diagram.

Practical Advice

Always check that the bending moment at the supports equals zero, as this is a fundamental condition.

Step 5: Analyze the Diagrams

Once both diagrams are complete, analyze them to understand the structural behavior:

• Identify maximum shear forces and bending moments.
• Determine locations of potential failure or critical points in the structure.

Real-World Application

These diagrams are crucial for designing beams in buildings, bridges, and other structures to ensure they can withstand applied loads without failing.

Conclusion

In this tutorial, you learned how to create shear force and bending moment diagrams using the graphical method. By understanding these foundational concepts, you can analyze and design safe and effective structures. As a next step, practice plotting diagrams for various beam configurations and loading conditions to enhance your skills.