Lecture Notes on Trusses

Summary

Today's lecture covered the fundamental concepts of trusses, their assumptions, types, and methods of analysis. Trusses are crucial components used in various structures like bridges and towers due to their efficiency in using materials and forming strong structures. Key points include the definition of trusses, the assumptions for analysis, the distinction between trusses and frames, popular truss designs, and analytical methods like the Method of Joints and the Method of Sections.

Definition and Basic Assumptions

• Truss Definition: A rigid structure comprised of multiple straight members organized in a specific design.
• Assumptions for Analysis:
  1. Pinned Joints: Assume all joints are pinned allowing rotation but no bending moments.
  2. Load Applications: Loads are only applied at the joints, not along the members.

Characteristics of Trusses

• Members carry only axial loads, either in tension or compression.
• Basic structural shape is a triangle due to its inherent stability and ability to maintain shape under loading.

Truss vs. Frame

• Frames can carry bending moments and have loads applied directly to the members unlike trusses.

Popular Truss Designs

• Includes named designs like the Fink Roof Truss.
• Structures are analyzed as planar trusses in two dimensions, even for some three-dimensional looking structures.

Analytical Methods

Method of Joints

• Uses free body diagrams (FBD) for the whole truss and individual joints.
• Applies equilibrium equations to solve for unknown forces at each joint.
• Each member force discovered is used to understand the force on connected joints.
• Identify zero force members through specific configurations of the truss.

Method of Sections

• Involves cutting through the truss to expose internal forces of interest.
• Uses equilibrium equations to solve forces in specific truss members.
• Effective when interests lie in a few members rather than the entire structure.

Types of Members Based on Forces

• Members are either in tension (trying to elongate) or compression (pushing inward).
• Zero Force Members can occur and often included for stability or unforeseen loads.

Advanced Truss Analysis

• Statically Determinate Trusses: Can be fully analyzed using equilibrium equations alone.
• Statically Indeterminate Trusses: Require additional methods for analysis, like the force method or displacement method due to excess members.

Three-Dimensional Trusses

• Called space trusses.
• Analyzed like planar trusses but use six equilibrium equations.

Practical Application in Design

• Discussion on Howe, Pratt, and Warren trusses which are traditional truss designs used in bridge construction. Differences in member forces (tension/compression) influence material choices and structural integrity.

This lecture provided an in-depth understanding of trusses, ensuring a solid foundation for analyzing and constructing stable and efficient truss structures.