Lames theorem

If point A is in equilibrium under the action of three forces, the value of tensions TAB and TAC are respectively - GATE 2025 Design Thinking Approach to Solve the Problem • Empathize: Understand towing constraints and safety requirements. • Define: Resultant force direction and magnitude. • Ideate: Explore rope angles and force combinations. • Prototype: Model force vectors and simulate equilibrium. • Test: Validate with minimum force configuration and real-world feasibility. 2. Shapoorji Pallonji Group is designing the suspension cables for a pedestrian bridge. One cable is inclined at 30° to the horizontal, carrying a load of 100 kN. i) Draw a free body diagram for the cable and load system. (4 Marks) ii) Resolve the load into horizontal and vertical components. (4 Marks) iii) Discuss how this analysis ensures equilibrium of the structure at the connection point. (5 Marks) 3. Tata Projects Ltd. is designing a warehouse roof with multiple beams and cable supports. One joint has three concurrent forces acting at a point. The magnitudes and directions of two forces are known; the third is unknown. (Case-Based Question) i) Draw the free body diagram for the joint. (4 Marks) ii) Use Lami’s Theorem to determine the unknown force. (4 Marks) iii) Check the equilibrium of the particle and resolve all forces into components. (3 Marks) iv) Suggest an alternative force line using principle of transmissibility to optimize structural stability. (3 Marks) Design Thinking Approach to Solve the Problem • Empathize: Understand the physical setup and constraints. • Define: Identify force directions and magnitudes. • Ideate: Explore vector combinations for equilibrium or desired resultant. • Prototype: Simulate force vectors using CAD or MATLAB. • Test: Validate resultant force and angle for r