ENGI 1313 Mechanics I - Memorial University of...
Transcript of ENGI 1313 Mechanics I - Memorial University of...
Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of [email protected]
ENGI 1313 Mechanics I
Lecture 27: Structural Analysis
2 ENGI 1313 Statics I – Lecture 27© 2007 S. Kenny, Ph.D., P.Eng.
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 sectionsto analyze the forces acting on the members of frames and machines composed of pin-connected members
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Lecture 27 Objective
to develop an understanding of truss structuresto examine forces in truss elements
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What are Trusses?
Common Structural Element
Framework of bar or strut members connected at nodal points (joints)Stable form is a triangleBuild 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)
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What are Trusses? (cont.)Early Use
Greek and Roman architecture used wood trusses
Truss Designs Significant number developed and patented over the years
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Truss Applications
Provide Span Support for Roofing, Flooring or Transportation
Bibliotheque Nationale de France http://www.britannica.com
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Truss Applications (cont.)
Memorial University “The Works”
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Truss Applications (cont.)
Saynatsalo Town Hall, Finland
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Truss Applications (cont.)
Pont de Québec
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Truss Applications (cont.)
Lifting Structures
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Truss Node (Joint) Connection
Gusset Plate JointRiveted or bolted connectionConsidered to act as a pin connection
I-35 Mississippi Bridge prior to 2007 Failure
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Truss Node (Joint) Connection (cont.)
Bolted or Pinned Joint
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Planar Truss
Ay
Ax
Ey
FB FC FD
Deck Load
Stringer
Beam
Truss Joint
Reaction Forces
Truss Joint Loads
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Planar Truss (cont.)
Ay
Ax
Ey
Reaction Forces FA
FC
FD
Truss Joint Loads
FA
FE
Roof Load
Purlin
Truss Joint
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Truss Analysis
AssumptionsLoads & reactions applied at truss joints
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Truss Analysis (cont.)
AssumptionsSelf-weight is generally neglected• Typical applied loads >>> bar or strut weight
Reaction ForcesTruss Joint LoadsSelf-Weight
WAB
0.5WAB0.5WAB
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Truss Analysis (cont.)
AssumptionsTruss nodes or joints act as smooth pins• Bolted or welded connections require force lines of
action to be concurrent
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Truss Analysis (cont.)
Two-Force MemberBased on assumptions
Load effectsTension• Elongation
Compression• Shortening• Buckling may occur
CompressiveEuler Buckling
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Truss Analysis (cont.)
Equilibrium EquationsWhat equations are available?
Statically Determinatem ≡ # truss membersj ≡ # truss jointsr ≡ # reaction forces
∑ =→+ 0Fx
∑ =↑+ 0Fy
∑ = 0M
rj2m −=
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Truss Analysis (cont.)
Rigid or Stable TrussDoes not collapse under applied load
Unstable Configuration
Rigid or Stable Configurations
rj2m −≥
( ) 3424 −< ( ) 3425 −= ( ) 3323 −=