ES2501: Statics/Unit 16-1: Truss Analysis: the Method of Joints Truss Structure: A structure with slender members pin-connected at their ends, referred as joints, to carry loads at the joints. To be a truss: - Nodal loading only; - All joints pin-connected Hinged support Roller support Real physical Truss Modeling Joint/Node Planar Truss (2D) Statically determinate Truss Truss Truss Space Truss (3D) Statically indeterminate Truss

ES2501: Statics/Unit 16-2: Truss Analysis: the Method of Joints Significance of Assumptions in Truss Analysis: Each member in a truss is a two-force member. Force of the rest of the truss on member AB through a pin at A A A B B Force of the rest of the truss on member AB through a pin at B Two-force member in equilibrium A Two forces must have the same amplitude, opposite direction and along the same line B - Nodal loading only; - No moments at node

ES2501: Statics/Unit 16-3: Truss Analysis: the Method of Joints Sign Convention: In analysis, always starts with the assumed positive direction. Then, a positive result indicates tension and a negative value means compression.

ES2501: Statics/Unit 16-4: Truss Analysis: the Method of Joints Method of Joints (Nodal Analysis): Step 1: Find support reactions; Step 2: Draw a free-body diagram and list equilibrium equations for each joint; Step 3: Select independent equations to solve unknowns. Example 1: Reactions: Free-body diagram of the truss, see the lift figure Take moment about a point with the most unknown forces Equilibrium Equations at Joints: Equilibrium at C: Sign convention “+” --- tension “-” --- compression

ES2501: Statics/Unit 16-5: Truss Analysis: the Method of Joints Example 1: Equilibrium Equations at Joints (con’d): Equilibrium at C: Zero-force member Equilibrium at A: Equilibrium at D: Equilibrium at B: Zero-force member Automatically satisfied

ES2501: Statics/Unit 16-6: Truss Analysis: the Method of Joints Comments: Method of joints uses equilibrium of joints to list necessary equations for unknowns; Method of joints provides complete solution for internal forces for all members Identifying zero-force members in a truss may simplify analysis Sign convention: Use tension as the conventional direction for the internal force of any member “+” --- tension; “-” --- compression Presentation of results: Mark the results on the truss If solving problem manually start with finding the reactions and list equilibrium equations for nodes with least number of unknowns.

ES2501: Statics/Unit 16-7: Truss Analysis: the Method of Joints Comments (con’d): Formulate a set of simultaneous linear equations for a computer solution Re-collection of equilibrium equations For truss For joint C For joint A: For joint E For joint D: For joint B: Select independent 10 equations for 10 unknown: Computer solution Note: there for more than 10 equations but only 10 of them are linearly independent