ME 201 Engineering Mechanics: Statics Chapter 6 – Part A 6.1 Simple Trusses 6.2 Method of Joints 6.3 Zero Force Members

Simple Truss A structure composed of slender members joined together at their end points “Planar Truss”

Simple Truss To Design members and connections of a truss, necessary to determine forces developed in each member Assumptions: All loadings are applied at the joints Members are joined together by smooth pins Assumptions satisfactory for bolted or welded joints

Simple Truss Each truss member acts as a 2-force member Force directed along axis of member Tension – pull, elongation Compression – push, shorten Several analytical approaches to solving

Method of Joints If truss is in equilibrium, each joint must also be in equilibrium Approach: Sketch Free Body Diagram of Entire Truss Solve for Reactions Sketch Free Body Diagrams of Each Joint 2 unknown limit per FBD ∑ Fx =0 ∑ Fy =0 ∑ Mo =0

Example Problem Given: F = 500 N θ = 45º Find: Force in each member θ

Example Problem Solution 45º 2 m B Ax 500 N Ay Cy θ 2 m B C A F Given: F = 500 N θ = 45º Find: Force in each member Solution: 1-FBD 2-Support Reactions 45º 2 m B 500 N A C

Example Problem Solution 45º 2 m B 500 N A C Given: F = 500 N θ = 45º Find: Force in each member Solution: 1-FBD 2-Support Reactions 3-Joint FBDs Joint A Joint B Joint C 500 N AC AB 500 N BC AB 45º 500 N BC AC 45º

Example Problem Solution BC AB Joint B 45º 500 N AC AB Joint A Given: F = 500 N θ = 45º Find: Force in each member Solution: 1-FBD 2-Support Reactions 3-Joint FBDs B A C 500 T 707 C Results shown in a force diagram

Zero Force Members Zero Force Members support NO loading Used for: Stability Changing Applied Loads

Zero Force Members If only 2 members form a truss joint AND no external load or support reaction is applied to the joint, then the members must be Zero Force Members X X X X

Zero Force Members If 3 members form a truss joint for which 2 members are collinear, the 3rd member is a Zero Force Member, provided no external force or support reaction is applied to the joint. X X