Method of Sections for Solving Trusses

Overview

• Method of Sections: Useful for finding forces in a few members of a truss without solving the entire structure.
• Equilibrium Concept: If the whole truss is in equilibrium, any segment of it is also in equilibrium.
• Application: Use equilibrium equations or moment equations to solve for unknowns.

Steps for Using Method of Sections

1. Identify Members: Determine which members' forces you need to find.
2. Find Reactions: Calculate reactions at one support before cutting the truss.
3. Section the Truss: Cut through the members of interest.
   • Forget one part of the truss (usually the part without reactions).
4. Assume Directions: Assume directions for the cut members (external forces).
   • Negative value indicates the opposite direction of assumption.
5. Solve: Use equilibrium or moment equations to find forces in the cut members.

Analyzing Tension and Compression

• Compression: Force comes toward the pin.
• Tension: Force leaves the pin.

Example Problems

Problem 1: Finding Forces in Members GH, BC, BG

• Reaction at Pin A: Use moment equation about point E.
• Angles Calculation: Use inverse tangent for angles.
• Cut the Truss: Through members GH, BC, BG.
• Moment Equations:
  • About point B to solve for HG.
  • About point A to solve for BG.
  • About point H to solve for remaining member.

Problem 2: Forces in Members BF, BG, AB

• Initial Cut: Forget about the bottom part.
• Moment Equation:
  • About point B to solve for FG.
  • About point D to solve for BG.
• Equilibrium Equations: For member AB using y-axis forces.
• Finding Zero-Force Members: Member BF is zero force due to lack of horizontal forces.

Problem 3: Forces in Members DC, HC, HI

• Calculate Reactions: At the roller, use moment equation about point A.
• Cut the Truss: Through members DC, HC, HI.
• Moment Equations:
  • About point H to solve for DC.
• Equilibrium Equations:
  • For y-axis forces to find HI.
  • For x-axis forces to find HC (note negative value indicates tension).

Problem 4: Forces in Members Ji and De

• Determine Reaction: At roller G, using moment equation about point A.
• Cut Through Members: Ji and De.
• Moment Equations:
  • About pin I to solve for De.
  • About pin E to solve for Ji.

Conclusion

• Efficiency: Method of sections allows solving specific member forces using fewer equations compared to the method of joints.
• Applications: Ideal for engineering problems where specific member forces are needed quickly.

Final Tips

• Share and discuss these methods with peers for better understanding.
• Practice with additional examples to solidify comprehension.