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# 6161103 6.3 zero force members

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### 6161103 6.3 zero force members

1. 1. 6.3 Zero-Force MembersMethod of joints is simplified when themembers which support no loading aredeterminedZero-force members (support no loading )are used to increase the stability of thetruss during constructionand to provide supportif the applied loading ischanged
2. 2. 6.3 Zero-Force Members Consider the truss shown From the FBD of the pin at point A, members AB and AF become zero force members*Note: Consider the FBD of joints F or B, there are five unknowns and the above conclusion would not be reached
3. 3. 6.3 Zero-Force MembersConsider FBD of joint DDC and DE are zero-force membersAs a general rule, if only two membersform a truss joint and no external load orsupport reaction isapplied to the joint, themembers must bezero-force members
4. 4. 6.3 Zero-Force MembersThe load on the truss shown in fig (a)is therefore supported by only fivemembers as shown in fig (d)
5. 5. 6.3 Zero-Force MembersConsider the truss shownFrom the FBD of the pin of the joint D, DAis a zero-force memberFrom the FBD of the pin of the joint C, CAis a zero-force member
6. 6. 6.3 Zero-Force MembersIn general, if three members form a trussjoint for which two of the members arecollinear, the third member is a zero-forcemember provided noexternal force or supportreaction is applied to the jointThe truss shown issuitable forsupporting the load P
7. 7. 6.3 Zero-Force MembersExample 6.4Using the method of joints, determine all thezero-force members of the Fink roof truss.Assume all joints are pin connected.
8. 8. 6.3 Zero-Force MembersSolutionJoint G + ↑ ∑ Fy = 0; FGC = 0GC is a zero-force membermeaning the 5kN load at Cmust be supported by CB, CH, CF and CDJoint D ∑ Fx = 0; FDF = 0
9. 9. 6.3 Zero-Force MembersSolutionJoint F+ ↑ ∑ Fy = 0; FFC cos θ = 0θ ≠ 90o , FFC = 0Joint B∑ Fx = 0;2kN − FBH = 0FBH = 2kN (C )
10. 10. 6.3 Zero-Force MembersSolutionFHC satisfy ∑Fy = 0 and therefore HC is not azero-force member