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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. ES2501: Statics/Unit 16-1: Truss Analysis: the Method of Joints. To be a truss: - Nodal loading only;

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ES2501: Statics/Unit 16-1: Truss Analysis: the Method of Joints

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  1. Truss Structure: A structure with slender members pin-connected at their ends, referred as joints, to carry loads at the joints. ES2501: Statics/Unit 16-1: Truss Analysis: the Method of 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

  2. Significance of Assumptions in Truss Analysis: Each member in a truss is a two-force member. ES2501: Statics/Unit 16-2: Truss Analysis: the Method of Joints 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

  3. 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.

  4. 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. ES2501: Statics/Unit 16-4: Truss Analysis: the Method of Joints 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: “+” --- tension “-” --- compression Sign convention

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

  6. Comments: ES2501: Statics/Unit 16-6: Truss Analysis: the Method of Joints • 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.

  7. Formulate a set of simultaneous linear equations for • a computer solution Comments (con’d): ES2501: Statics/Unit 16-7: Truss Analysis: the Method of Joints Re-collection of equilibrium equations For joint C For truss 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

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