ECIV 320 Structural Analysis I Analysis of Statically Determinate Trusses
Analysis of Determinate Trusses <ul><li>Characteristics </li></ul><ul><li>Slender Members </li></ul><ul><li>Wooden Struts ...
Analysis of Determinate Trusses <ul><li>Characteristics </li></ul><ul><li>Pinned/Bolted Welded Joint Connections </li></ul...
Analysis of Determinate Trusses <ul><li>Loads at Joints </li></ul><ul><li>Members in Tension/Compression </li></ul>
Analysis of Determinate Trusses
Analysis of Determinate Trusses
Analysis of Determinate Trusses
Roof Trusses - Terminology Supports Wood/Steel/RC Columns Masonry Walls Bent: Roof Truss and Supporting Columns
Roof Trusses - Selection Short Spans (<60 ft) Requiring Overhead Clearance
Roof Trusses - Selection Moderate Spans (60-100 ft) May be modified for flat roofs
Roof Trusses - Selection Larger Spans (>100 ft) May have cambered bottom chord
Roof Trusses - Selection Suitable for flat or nearly flat roofs
Roof Trusses - Selection Location of column not an issue Uniform lighting is important
Roof Trusses - Selection Garages and small airplane hangars
Roof Trusses - Selection High rises and long spans Field houses Gymnasiums etc
Bridge Trusses - Terminology
Bridge Trusses - Selection Spans <200ft
Bridge Trusses - Selection Spans <300ft <ul><li>Warren truss with verticals and polygonal upper chord </li></ul><ul><li>Sl...
Bridge Trusses - Selection Longer Spans Subdivided Trusses K-Truss
OK 99 Pond Creek Bridge, Osage County
Warren Truss Bridge
Assumptions for Design <ul><li>Members are joined together by smooth pins </li></ul><ul><ul><li>Center lines of joining me...
Assumptions for Design <ul><li>All loads are applied at joints </li></ul><ul><ul><li>Self weight is neglected IF small com...
Assumptions for Design <ul><li>Axial Force Members </li></ul><ul><ul><li>Tension/Compression </li></ul></ul><ul><ul><li>Co...
Classification of Coplanar Trusses SIMPLE TRUSS - Triangles
Classification of Coplanar Trusses COMPOUND
Classification of Coplanar Trusses
Determinacy No of Bars + No of Reactions = 2(no of Joints) b  +  r  =  2j  -> Determinate
Determinacy
Stability External Stability All reactions parallel or  Concurrent => Unstable
Stability Internal Stability Joints do not exhibit rigid motion Simple truss always stable
Analysis Methods <ul><li>Methods of Joints </li></ul><ul><li>Method of Sections </li></ul>
Method of Joints Truss in Equilibrium => Each Joint in Equilibrium
Procedure <ul><li>Consider one joint at a time – Draw FBD </li></ul><ul><ul><li>Condition: At least one known force; at mo...
Procedure <ul><li>Write equations of equilibrium of node </li></ul><ul><ul><li>Hint: Select x-y CS such that forces on FBD...
Zero-Force Members
Zero-Force Members
Zero-Force Members
Method of Sections Truss in Equilibrium => Each  PART  in Equilibrium
Method of Sections Truss in Equilibrium => Each  PART  in Equilibrium Efficient when forces of only a few members are to b...
Method of Sections - Procedure Free Body Diagram <ul><li>Determine external reactions of entire truss </li></ul><ul><li>De...
Method of Sections – Procedure (cont’d) Free Body Diagram <ul><li>Draw FBD of one part </li></ul><ul><ul><li>Hint: Choose ...
Method of Sections – Procedure (cont’d) Free Body Diagram <ul><li>Establish direction of unknown forces </li></ul><ul><ul>...
Method of Sections – Procedure (cont’d) Equations of Equilibrium Take moments about a point that lies on the intersection ...
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Trusses Analysis Of Statically Determinate

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Trusses Analysis Of Statically Determinate

  1. 1. ECIV 320 Structural Analysis I Analysis of Statically Determinate Trusses
  2. 2. Analysis of Determinate Trusses <ul><li>Characteristics </li></ul><ul><li>Slender Members </li></ul><ul><li>Wooden Struts </li></ul><ul><li>Metal Bars/Angles/Channels </li></ul>
  3. 3. Analysis of Determinate Trusses <ul><li>Characteristics </li></ul><ul><li>Pinned/Bolted Welded Joint Connections </li></ul><ul><li>Gusset Plates </li></ul>
  4. 4. Analysis of Determinate Trusses <ul><li>Loads at Joints </li></ul><ul><li>Members in Tension/Compression </li></ul>
  5. 5. Analysis of Determinate Trusses
  6. 6. Analysis of Determinate Trusses
  7. 7. Analysis of Determinate Trusses
  8. 8. Roof Trusses - Terminology Supports Wood/Steel/RC Columns Masonry Walls Bent: Roof Truss and Supporting Columns
  9. 9. Roof Trusses - Selection Short Spans (<60 ft) Requiring Overhead Clearance
  10. 10. Roof Trusses - Selection Moderate Spans (60-100 ft) May be modified for flat roofs
  11. 11. Roof Trusses - Selection Larger Spans (>100 ft) May have cambered bottom chord
  12. 12. Roof Trusses - Selection Suitable for flat or nearly flat roofs
  13. 13. Roof Trusses - Selection Location of column not an issue Uniform lighting is important
  14. 14. Roof Trusses - Selection Garages and small airplane hangars
  15. 15. Roof Trusses - Selection High rises and long spans Field houses Gymnasiums etc
  16. 16. Bridge Trusses - Terminology
  17. 17. Bridge Trusses - Selection Spans <200ft
  18. 18. Bridge Trusses - Selection Spans <300ft <ul><li>Warren truss with verticals and polygonal upper chord </li></ul><ul><li>Slope of diagonals 45-60 o </li></ul>
  19. 19. Bridge Trusses - Selection Longer Spans Subdivided Trusses K-Truss
  20. 20. OK 99 Pond Creek Bridge, Osage County
  21. 21. Warren Truss Bridge
  22. 22. Assumptions for Design <ul><li>Members are joined together by smooth pins </li></ul><ul><ul><li>Center lines of joining members are concurrent at a point </li></ul></ul><ul><ul><li>In reality some rigidity exists: Secondary stresses </li></ul></ul>
  23. 23. Assumptions for Design <ul><li>All loads are applied at joints </li></ul><ul><ul><li>Self weight is neglected IF small compared to forces </li></ul></ul>
  24. 24. Assumptions for Design <ul><li>Axial Force Members </li></ul><ul><ul><li>Tension/Compression </li></ul></ul><ul><ul><li>Compression Members Usually Thicker </li></ul></ul>Tension Compression
  25. 25. Classification of Coplanar Trusses SIMPLE TRUSS - Triangles
  26. 26. Classification of Coplanar Trusses COMPOUND
  27. 27. Classification of Coplanar Trusses
  28. 28. Determinacy No of Bars + No of Reactions = 2(no of Joints) b + r = 2j -> Determinate
  29. 29. Determinacy
  30. 30. Stability External Stability All reactions parallel or Concurrent => Unstable
  31. 31. Stability Internal Stability Joints do not exhibit rigid motion Simple truss always stable
  32. 32. Analysis Methods <ul><li>Methods of Joints </li></ul><ul><li>Method of Sections </li></ul>
  33. 33. Method of Joints Truss in Equilibrium => Each Joint in Equilibrium
  34. 34. Procedure <ul><li>Consider one joint at a time – Draw FBD </li></ul><ul><ul><li>Condition: At least one known force; at most two unknown forces </li></ul></ul><ul><li>Establish sense of unknown force </li></ul><ul><ul><li>Hint: Assume unknown forces “pulling on pin”; numerical solution (+) tension in member, (-) compression in member </li></ul></ul>
  35. 35. Procedure <ul><li>Write equations of equilibrium of node </li></ul><ul><ul><li>Hint: Select x-y CS such that forces on FBD can be easily resolved into components </li></ul></ul><ul><li>Take advantage of symmetries </li></ul><ul><li>Identify zero force members </li></ul><ul><ul><li>(i) only two members form a joint and no loads or supports on joint </li></ul></ul><ul><ul><li>(ii) three members form a joint; two members colinear => third member zero force </li></ul></ul>
  36. 36. Zero-Force Members
  37. 37. Zero-Force Members
  38. 38. Zero-Force Members
  39. 39. Method of Sections Truss in Equilibrium => Each PART in Equilibrium
  40. 40. Method of Sections Truss in Equilibrium => Each PART in Equilibrium Efficient when forces of only a few members are to be found
  41. 41. Method of Sections - Procedure Free Body Diagram <ul><li>Determine external reactions of entire truss </li></ul><ul><li>Decide how to section truss </li></ul><ul><ul><li>Hint: Three(3) unknown forces at the most </li></ul></ul>
  42. 42. Method of Sections – Procedure (cont’d) Free Body Diagram <ul><li>Draw FBD of one part </li></ul><ul><ul><li>Hint: Choose part with least number of forces </li></ul></ul>
  43. 43. Method of Sections – Procedure (cont’d) Free Body Diagram <ul><li>Establish direction of unknown forces </li></ul><ul><ul><li>Assume all forces cause tension in member Numerical results: (+) tension (-) compression </li></ul></ul><ul><ul><li>Guess Direction </li></ul></ul><ul><ul><li>Numerical results: (+) Guess is correct (-) Force in opposite direction </li></ul></ul>
  44. 44. Method of Sections – Procedure (cont’d) Equations of Equilibrium Take moments about a point that lies on the intersection of the lines of action of two unknown forces

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