CIEG 301: Structural Analysis Trusses (Chapter 3)

Overview Commonly constructed from: Wood Iron Steel Trusses are commonly used in: Roof framing Bridges Trusses are structures composed of numerous pin connected members joined together at their end points Trusses are loaded only at their joints Including self weight Truss members are only subjected to the following forces: Tension Compression

Bridge Trusses Gusset plates; floorbeams; lateral bracing

Roof Trusses purlins

Classification Number of unknowns, r r = b + R b = number of bars / members R = number of non-parallel and non-concurrent restraints Number of Equations of Equilibrium 2j j = number of joints Stability and Determinacy: r < 2j  Not stable r = 2j  Stable and Determinant r > 2j  Stable and Indeterminant Degree of indeterminacy = (b + R) -2j

Method of Joints Concept: Each joint of the truss is in equilibrium Determine external forces (reactions) by drawing FBD of entire structure Determine internal forces by drawing FBD of joints Start with joints that have: No more than 2 unknowns At least 1 known force Compression forces “push” Tension forces “pull”

Zero-Force Members P Case 1: Exactly two members sharing a joint with no applied load Case 2: Exactly three members, two of which are colinear, sharing a joint with no applied load F E D A B C EF –FC – BE - BD

Method of Sections Concept: Each section of the truss is in equilibrium Method: Use equations of equilibrium to solve for external reactions if necessary An imaginary line is used to cut the structure into two parts The three equations of equilibrium are applied to each part in order to solve for the internal forces Choose a “cut” that causes no more than three unknowns Sign convention: Draw FBD such that all forces are in tension, i.e., “pulling” on the member, or Determine orientation by inspection Useful when: The forces in only a few members are needed

Examples…