Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_61

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The space truss shown is secured to the fixed supports at , and and is loaded by the force which has equal - and -components but no vertical -component. Show that there is a sufficient number of members to provide internal stability and that their placement is adequate for this purpose. Next determine the forces in members , and . Problem 4/61 (a) Analysis of Truss Stability ● Calculation Process 1. Check Stability Condition: For a space truss to be internally stable, it must satisfy the necessary condition , where is the number of members and is the number of joints. Joints (): There are 6 joints: . Thus, . Members (): Counting the solid lines in the diagram: Base members: (5 members) Vertical/diagonal members from base: (6 members) Top edge member: (1 member) Total . Stability test: . Since , the necessary condition for internal stability is satisfied. 2. Verify Adequate Placement: A truss is stable if it is built of rigid tetrahedral units or if every joint is fixed by three non-coplanar members. Starting from the fixed ground base (): Joint is connected to ground points and . Its stability is ensured by connections to and . Joint is connected to (on ground) and . The vectors of members are not coplanar, so is spatially fixed. A,BE Lxyz CD,BCCE m≥3j−6mj jA,B,C,D,E,Fj=6 m AB,BE,EA,FB,FE FC,FD,BC,BD,AD,CE CD m=5+6+1=12 3j−6=3(6)−6=12m=12 A,B,E FBE CD CE,BF,D CE,CB,CFC Joint is connected to (on ground) and . Similarly, these conne