Ch 3. Forces & Particle Equilibrium Multimedia Engineering Statics Equilibriumand FBD 2-DForces 3-DForces
 Chapter 1. Basics 2. Vectors 3. Forces 4. Moments 5. Rigid Bodies 6. Structures 7. Centroids/Inertia 8. Internal Loads 9. Friction 10. Work & Energy Appendix Basic Math Units Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll

 STATICS - EXAMPLE Example Two Hanging Weights Two boxes are hung from a ceiling and wall as shown in the diagram. Each box is supported by two cables that are interconnected through rings. What is the maximum tension in any rope other than the ropes directly connected to the boxes? Solution In this example, there are two different loads that interact through a system of cables. Since all ropes are connected to at least one ring, it would seem reasonable to focus on the ring objects and make sure they are in static equilibrium. Free-body Diagrams of Ring E Drawing a free-body diagram of ring E, identifies two rope forces, FDE and FEC, that are not known. The direction of the loads are known since the force must act in the direction of the rope. The rope forces can be determined by applying force equilibrium in the x and y directions.      ΣFx = 0      FDE cos30 + FEC cos55 = 0      FDE = 0.6623 FEC      ΣFy = 0      -10 + FDE sin30 + FEC sin 55 = 0      0.6623 FEC (0.5) + FEC (0.8192) = 10 Solving the two equations give, FEC = 8.693 lb FDE = 5.757 lb Free-body Diagrams of Ring C Now that the force in rope EC is know, ring C can be analyzed. Again, drawing a free-body diagram of ring C identifies two unknown forces, FAC and FCB. Applying the equilibrium equations gives,      ΣFx = 0      FCB cos45 - 8.693 cos55 = 0      FCB = 7.051 lb      ΣFy = 0      FAC + 7.051 sin45 - 8 - 8.693 sin 55 = 0      FAC = 10.14 lb Maximum force occurs in rope AC,      Fmax = 10.14 lb

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