Lecture 27: Structural Analysis ENGI 1313 Mechanics I Lecture 27: Structural Analysis

Chapter 6 Objectives to show how to determine the forces in the members of a truss using the method of joints and the method of sections to analyze the forces acting on the members of frames and machines composed of pin-connected members

Lecture 27 Objective to develop an understanding of truss structures to examine forces in truss elements

What are Trusses? Common Structural Element Framework of bar or strut members connected at nodal points (joints) Stable form is a triangle Build by adding two members (AD & DB) and node (joint) D 3 Bar or strut members (AB, BC, AC) 3 Nodes or joints (A, B, C)

What are Trusses? (cont.) Early Use Greek and Roman architecture used wood trusses Truss Designs Significant number developed and patented over the years

Truss Applications Provide Span Support for Roofing, Flooring or Transportation Bibliotheque Nationale de France http://www.britannica.com

Truss Applications (cont.) Memorial University “The Works”

Truss Applications (cont.) Saynatsalo Town Hall, Finland

Truss Applications (cont.) Pont de Québec

Truss Applications (cont.) Lifting Structures

Truss Node (Joint) Connection Gusset Plate Joint Riveted or bolted connection Considered to act as a pin connection I-35 Mississippi Bridge prior to 2007 Failure

Truss Node (Joint) Connection (cont.) Bolted or Pinned Joint

Planar Truss Deck Load Stringer Beam Truss Joint Reaction Forces Ax FB FC FD Truss Joint Loads Ay Ey

Planar Truss (cont.) Roof Load Purlin Truss Joint Reaction Forces FC FA FD Reaction Forces FE FA Truss Joint Loads Ax Ay Ey

Truss Analysis Assumptions Loads & reactions applied at truss joints

Truss Analysis (cont.) Assumptions Self-weight is generally neglected Typical applied loads >>> bar or strut weight Reaction Forces Truss Joint Loads Self-Weight 0.5WAB 0.5WAB WAB

Truss Analysis (cont.) Assumptions Truss nodes or joints act as smooth pins Bolted or welded connections require force lines of action to be concurrent

Compressive Euler Buckling Truss Analysis (cont.) Two-Force Member Based on assumptions Load effects Tension Elongation Compression Shortening Buckling may occur Compressive Euler Buckling

Truss Analysis (cont.) Equilibrium Equations Statically Determinate What equations are available? Statically Determinate m  # truss members j  # truss joints r  # reaction forces

Unstable Configuration Rigid or Stable Configurations Truss Analysis (cont.) Rigid or Stable Truss Does not collapse under applied load Unstable Configuration Rigid or Stable Configurations

Textbook Problems

Textbook Problems

Textbook Problems

Textbook Problems

Textbook Problems

References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_engmech_1 http://en.wikipedia.org