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### Trusses - engineeing mechanics

• 2. Contents Definition Classification Of Truss Assumption Made In Analysis Methods Of Analysis Zero Force Member
• 3. Definition: “ Trusses are structures consisting of straight slender rods connected only at the their ends” Classification Of Truss : 1) Perfect truss 2) Imperfect or Deficient truss 3) Redundant truss
• 4. 1) Perfect truss : A Truss is said to be a perfect truss if it satisfies the below equation, m = 2j - R or m = 2j - 3 where, m – number of members j – number of joints R – number of reactions. – This type of truss does not collapse under loading. – Examples of perfect trusses are shown in next slide.
• 6. 2) Imperfect or deficient truss : A Truss is said to be a imperfect or deficient truss if it has less member than the required, the equation for imperfect truss is as below m < 2j - R or m < 2j - 3 where, m – number of members j – number of joints R – number of reactions. – This type of truss collapse under loading / they are not stable. – Examples of imperfect or deficient truss is shown in next slide.
• 8. 3) Redundant truss : A Truss is said to be a Redundant truss if it has more member than the required, The equation for Redundant truss is as below m > 2j - R or m > 2j - 3 where, m – number of members j – number of joints R – number of reactions. – This type of truss does not collapse under loading. – Examples of perfect trusses are shown in next slide.
• 10. Assumption Made In Analysis 1. All members have negligible weight. 2. All members have uniform cross section. 3. Members are connected at the joints through pin connections. 4. All the members have only axial force i.e. either tensile or compressive. 5. All the external forces are applied only at the joints.
• 11. Zero Force Member “A zero force member is a member in truss which carries zero force in it and it is provided for the stability purpose.” Rules for identifying the Zero Force member 1. If only two non-collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both members is zero.
• 12. Zero Force Member Rules for identifying the Zero Force member 2. If there are three members at a joint out of which two are collinear and no external force acts / applied on that joint, then the third non collinear member is a zero force member.
• 13. Zero Force Member Rules for identifying the Zero Force member 3. If there are only two members at a joint and the external force is along one of the member, then the other member is a zero force member.
• 14. Methods Of Analysis The analysis of perfect truss is carried out by three different methods: 1. Method of joint 2. Method of section ( Method of moments ) 3. Graphical method – Method of joint is used to find forces in all members of the truss. – Method of Section is used to find forces in selected members of the truss.
• 15. Methods Of Analysis The procedure for method of joint is as follows 1. The support reactions of the truss are first calculated using equations of equilibrium. i.e. H=0, V=0 and M=0 2. Identify Zero force members by inspection. 3. Draw F.B.D of a joint where the maximum unknowns are less than two. 4. Assume unknown forces in members to be tensile i.e. directed away from the point. 5. Use H=0 and V=0 in F.B.D to find the two unknowns. 6. Proceed to the next joint where again maximum unknowns are less than two.
• 16. Methods Of Analysis The procedure for method of section is as follows 1. The support reactions of the truss are first calculated using equations of equilibrium. i.e. H=0, V=0 and M=0 2. Identify Zero force members by inspection. 3. Take an imaginary cutting plane through the truss, dividing it into two parts, such that it passes through members in which forces are to be found. 4. The cutting plane should be taken in such a way that it cuts a maximum of three members in which forces are unknown, preferably. 5. Draw F.B.D of any one part of the truss assuming tensile forces in members cut by the section. 6. Use H=0, V=0 and M=0 to find the three unknowns.
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