Transcript ADVANCED STEEL DESIGN

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
Roof Trusses
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
 Method:
 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
F
E
D
A
B
C
 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
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…