4-54 Moment of a Force about specified axis Chap 4 (Hibbeler Statics 14th Edition) Engineers Academy

Introduction

This tutorial guides you through calculating the moment of a force about specified axes, using the A-frame scenario from Hibbeler's Engineering Statics. Understanding moments of forces is essential for analyzing structures and ensuring stability in engineering applications.

Step 1: Understand the Problem Setup

• Identify the Forces: The vertical force F = 80 lb is applied to the A-frame.
• Determine the Points of Interest: Focus on points A and B where the moments will be calculated.
• Visualize the Frame Position: Ensure you have a clear understanding of how the frame is positioned when the force is applied.

Step 2: Calculate the Moment About the Y Axis

• Formula for Moment: The moment about an axis can be calculated using the formula: [ M = F \times d ] where M is the moment, F is the force applied, and d is the perpendicular distance from the axis to the line of action of the force.

• Measure the Distance: Determine the perpendicular distance from the line of action of the force to the y-axis through points A and B.

• Perform the Calculation:

  1. Measure or identify the distance d for both points A and B.
  2. Substitute the values into the moment formula: [ M_y = 80 , \text{lb} \times d ]
  3. Calculate M_y for both points.

Step 3: Calculate the Moment About the X Axis

• Repeat the Moment Calculation: Now calculate the moment about the x-axis using a similar approach.

• Identify the Perpendicular Distance: Measure the distance from the line of action of the force to the x-axis.

• Perform the Calculation:

  1. Use the moment formula: [ M_x = F \times d ]
  2. Substitute the values: [ M_x = 80 , \text{lb} \times d ]
  3. Calculate M_x for the relevant point.

Step 4: Analyze the Results

• Interpret the Moments: Understand the significance of the calculated moments in terms of equilibrium and stability.
• Check for Common Pitfalls: Ensure that distances are measured correctly and that the direction of the moments (clockwise or counterclockwise) is taken into account.

Conclusion

In this tutorial, you learned how to calculate the moment of a force about specified axes using the example of an A-frame being hoisted. Key steps included identifying forces, measuring distances, and applying the moment formula for both the y-axis and x-axis.

For further learning, consider exploring additional chapters in Hibbeler's Engineering Statics to deepen your understanding of force system resultants and equilibrium.