Lecture Notes: Method of Sections for Trusses

Introduction

• Method of Joints vs. Method of Sections
  • Method of Joints: Useful for solving large numbers of truss members.
  • Method of Sections: Efficient for finding forces in a few specific members without solving the entire truss.

Key Concepts

• Equilibrium of Sections:
  • Any segment of a truss in equilibrium means the whole truss is also in equilibrium.
  • Use equilibrium equations or moment equations to solve for unknowns.

Steps to Solve Using Method of Sections

1. Find Reactions at a Support:
   • Determine reactions at one support to simplify calculations.
2. Section the Truss:
   • Cut through the members you want to solve.
   • Treat the cut members as external forces acting on the section.
3. Assume Directions:
   • Assume directions for forces; negative results indicate opposite directions.
4. Use Equilibrium Equations:
   • Apply equations of equilibrium or moment equations to solve for forces.

Important Notes

• Internal vs External Forces:
  • Treat cut members as external forces while solving.
• Compression vs Tension:
  • Force towards a pin: Compression
  • Force leaving a pin: Tension

Example Problems

Problem 1: Solving Members GH, BC, BG

• Objective: Find forces in members GH, BC, BG.
• Steps:
  1. Determine reactions at pin A.
  2. Cut through desired members and forget the opposite side.
  3. Assume forces directions and apply moment equations:
     • Moment about point B to eliminate forces BC, BG.
     • Moment about pin A to solve for force BG.
     • Moment about point H to solve for force GH.
• Conclusion: All forces assumed correctly; GH in compression, BC in tension, BG in tension.

Problem 2: Solving Members BF, BG, AB

• Objective: Find forces in members BF, BG, AB.
• Steps:
  1. Cut truss to isolate top section.
  2. Moment about point B to solve for FG.
  3. Moment about point D to solve for force BG.
  4. Equation for y-axis forces to solve for force AB.
  5. Isolate joint F to identify BF as a zero-force member.
• Conclusion: Efficiently used method of sections with minimal equations.

Problem 3: Solving Members DC, HC, HI

• Objective: Determine forces in members DC, HC, HI.
• Steps:
  1. Calculate reactions at the roller with a moment equation about point A.
  2. Cut through members and assume directions.
  3. Moment about point H to solve for DC.
  4. Equation for y-axis forces to solve for force HI.
  5. Equation for x-axis forces to solve for force HC.
• Conclusion: DC in compression, HI and HC in tension.

Problem 4: Solving Members JI, DE

• Objective: Find forces in members JI and DE.
• Steps:
  1. Determine reaction at roller G with a moment equation about point A.
  2. Cut truss to isolate members.
  3. Moment about pin I to solve for DE.
  4. Moment about point E to solve for JI.
• Conclusion: DE in tension, JI in compression.

Conclusion

• Advantages of the Method:
  • Quickly solves for specific members without extensive calculations.
  • Utilizes simple equilibrium concepts.
• Encouragement to share and review materials to reinforce understanding.