Chapter 3-analysis of statically determinate trusses
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The document discusses various types of trusses used in building structures including simple trusses, compound trusses, and complex trusses. It also covers the assumptions made in truss analysis, classifications of trusses based on stability and determinacy, and different methods for analyzing trusses including the method of joints, method of sections, and analyzing zero force members. Several examples are provided to demonstrate how to apply these analysis methods to solve for unknown member forces in various truss configurations.
Chapter 3-analysis of statically determinate trusses
- 3. Trusses Types for Building Structural Analysis IDr. Mohammed Arafa
- 6. ٦ Chapter 2 Dr. Mohammed Arafa
- 8. Truss Bridge
- 13. Assumptions for Design All members are connected at both ends by smooth frictionless pins. All loads are applied at joints (member weight is negligible) Centroids of all joint members coincide at the joint. All members are straight. All load conditions satisfy Hookeís law.
- 14. Classification of coplanar Truss Simple Truss
- 15. Compound Truss
- 16. Stability of Compound Truss
- 17. Complex Truss
- 18. Determinacy For plane truss If b+r = 2j statically determinate If b+r > 2j statically indeterminate Where b = number of bars r = number of external support reaction j = number of joints
- 19. Stability For plane truss If b+r < 2j unstable The truss can be statically determinate or indeterminate (b+r >=2j) but unstable in the following cases: External Stability: truss is externally unstable if all of its reactions are concurrent or parallel
- 20. Internal stability: Internally stable Internally unstable Internally unstable
- 21. Classify each of the truss as stable , unstable, statically determinate or indeterminate. Stable&edeterminatStatically 22)11(22 22 11319 j rb jrb Stable&ateindeterminStatically 18)9(22 19 9415 j rb jrb Structural Analysis IDr. Mohammed Arafa
- 23. STEPS FOR ANALYSIS 1. If the support reactions are not given, draw a FBD of the entire truss and determine all the support reactions using the equations of equilibrium. 2. Draw the free-body diagram of a joint with one or two unknowns. Assume that all unknown member forces act in tension (pulling the pin) unless you can determine by inspection that the forces are compression loads. 3. Apply the scalar equations of equilibrium, FX = 0 and FY = 0, to determine the unknown(s). If the answer is positive, then the assumed direction (tension) is correct, otherwise it is in the opposite direction (compression). 4. Repeat steps 2 and 3 at each joint in succession until all the required forces are determined. The Method of Joints
- 24. The Method of Joints Structural Analysis IDr. Mohammed Arafa
- 25. Example 1 Solve the following truss
- 26. Example 1 Solve the following truss
- 29. Problem Determine the force in each member
- 30. Zero Force Member 1- If a joint has only two non-colinear members and there is no external load or support reaction at that joint, then those two members are zero-force members
- 31. Zero Force Member 2- If three members form a truss joint for which two of the members are collinear and there is no external load or reaction at that joint, then the third non-collinear member is a zero force member.
- 32. Example 2 Find Zero force member of the following truss
- 34. The Method of Section
- 35. 1. Decide how you need to “cut” the truss. This is based on: a) where you need to determine forces, and, b) where the total number of unknowns does not exceed three (in general). 2. Decide which side of the cut truss will be easier to work with (minimize the number of reactions you have to find). 3. If required, determine the necessary support reactions by drawing the FBD of the entire truss and applying the EofE. The Method of Section STEPS FOR ANALYSIS
- 36. 4. Draw the FBD of the selected part of the cut truss. We need to indicate the unknown forces at the cut members. Initially we assume all the members are in tension, as we did when using the method of joints. Upon solving, if the answer is positive, the member is in tension as per our assumption. If the answer is negative, the member must be in compression. (Please note that you can also assume forces to be either tension or compression by inspection as was done in the previous example above.) 5. Apply the equations of equilibrium (EofE) to the selected cut section of the truss to solve for the unknown member forces. Please note that in most cases it is possible to write one equation to solve for one unknown directly.
- 37. Example 2 Solve the CF & GC members in the truss
- 40. Determine the force in members GJ and CO of the roof truss shown. Example 3
- 41. Example 2
- 42. Example 3
- 43. Example 3 Solve the GF & GD members in the truss
- 45. Example 4 Solve the ED & EB members in the truss
- 47. Example 5 Solve the BC & MC members in the K-truss
- 48. T21750)20()15(29000 IbFFM BCBCL TIbFF MBy 12000BJointAt TIbFFF MLMLy 29001200120029000 partcuttingtotalFor the
- 50. Problem 2 Solve All members
- 51. Problem 3 Solve All members
- 52. Problem 4 Solve members CH , CI
- 53. Example 4 Compound Truss Solve the truss
- 54. C46.30)60sin4()2(4)4(50 kNFFM HGHGC
- 55. F & FF & FF & FF & FF JC BJBC IBIJ HJHI AIAB JJoint BJoint IJoint HJoint AJoint
- 56. Example 5 Compound Truss
- 59. Example 5__Compound Truss Solve the truss
- 61. Complex Truss iii xsSS ' Force in members ? 0' x xsSS ECECEC
- 62. 1 1 Complex Trusses + = X x ๐=ECsx+EC´S =x EC´S ECs P A B C DF E r + b = 2j, 3 9 2(6) •Determinate •Stable EC´F P A B C DF E AD= F ADS ECs A B C DF E isx+i´S=iS
- 63. Member AB AC AF FE BE ED FC EC 'iS is ixs iS iii xsSS ' ? 0' x xsSS ECECEC
- 64. Example 5 Complex Truss
- 68. Example 5b
- 71. P b + r < 3j b + r = 3j Statically indeterminate -Check stability • Determinacy and Stability Space Truss Unstable truss b + r > 3j Statically determinate -Check stability
- 72. •x, y, z, Force Components Space Truss 222 zyxl )( l x FFx )( l y FFy )( l z FFz 222 zyx FFFF
- 73. x y z y z x y z x z x y x y z yF zF zF xF xF zF yF short link y x z roller z x y slotted roller constrained in a cylinder y z x ball-and -socket Support Reactions
- 74. Zero Force Member 1- If all but one of the members connected to a joint lie on the same plane, and provided no external load act on the joint, then the member not lying in the plane of the other members must subjected to zero force. Fz = 0 , FD = 0
- 75. Zero Force Member 2- If it has been determined that all but two of several members connected at a joint support zero force, then the two remaining members must also support zero force, provided they don’t lie a long the same line and no external load act on the joint. Fz = 0 , FB = 0 Fy = 0 , FD = 0
- 76. Example 6__Space Truss Structural Analysis IDr. Mohammed Arafa
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