Trusses Overview

Definition and Applications

• Trusses are structural frameworks used in:
  • Bridges
  • Antenna towers
  • Cranes
  • Parts of the International Space Station
• They provide strength efficiently and cost-effectively.

Key Characteristics

• Truss Structure: Rigid structure made of straight members.
• Assumptions for Trusses:
  1. Pinned Connections: Joints can rotate; members can only carry axial loads, not bending moments.
  2. Load Application: Loads are only applied at the joints, not along the members.

Stability and Geometry

• Basic shape of a truss is a triangle (3 members).
  • Triangles are stable under load and do not deform.
• A four-member configuration is unstable (can deform) unless stabilized with diagonal bracing.

Types of Trusses

• Planar Trusses: Members in the same plane, analyzed as 2D structures.
• Common examples: Fink roof truss, Howe truss, Pratt truss, Warren truss.

Methods for Analyzing Trusses

Method of Joints

1. Draw a free body diagram of the truss and determine reaction forces using equilibrium equations.
2. Analyze each joint:
   • Use equilibrium equations to solve for unknown forces.
   • Internal forces:
     • Tension: forces act away from the joint.
     • Compression: forces act towards the joint.
3. Zero Force Members: Members that do not carry any load, often used for stability. Configurations for zero force members:
   • Three members connected, two aligned with no external load.
   • Two members connected not aligned with no external load.

Method of Sections

1. Draw a free body diagram and calculate reaction forces.
2. Make an imaginary cut through members of interest.
3. Use equilibrium equations to solve for internal forces in the cut members.
   • Can analyze specific members without solving the entire truss.

Statically Determinate vs. Statically Indeterminate Trusses

• Statically Determinate: Can determine forces using equilibrium equations.
• Statically Indeterminate: More members than needed, requires different solving methods (e.g., force or displacement methods).

Comparison of Truss Designs

• Howe Truss: Vertical members in tension, diagonal in compression (less cost-effective due to thick long members).
• Pratt Truss: Vertical members in compression, inner diagonal members in tension (more cost-effective).
• Warren Truss: All members the same length, uses fewer members, diagonal members alternate between tension and compression.

Load Variation in Trusses

• As loads move across bridges, some members may alternate between tension and compression.

Space Trusses

• Can be analyzed similarly to planar trusses, but with additional equations (6 equations in total, 3 at each joint).

Conclusion

• Understanding truss structure and analysis is essential in engineering applications.
• Explore various designs and their respective efficiencies for specific uses.