Shawn Kenny, Ph.D., P.Eng.Assistant ProfessorFaculty of Engineering and Applied ScienceMemorial University of Newfoundlandspkenny@engr.mun.ca

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 −=

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Textbook Problems

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Textbook Problems

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Textbook Problems

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Textbook Problems

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Textbook Problems

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References

Hibbeler (2007)http://wps.prenhall.com/esm_hibbeler_engmech_1http://en.wikipedia.org