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ME 221 Statics Lecture #15b Sections 6.1 – 6.4

ME 221 Statics Lecture #15b Sections 6.1 – 6.4. Chapter 6: Analysis of Structures. The knowledge of internal forces is a fundamental requirement for true design. The Structural elements are: Trusses Frames Machines. Trusses.

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ME 221 Statics Lecture #15b Sections 6.1 – 6.4

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  1. ME 221 StaticsLecture #15bSections 6.1 – 6.4 Lecture 15

  2. Chapter 6: Analysis of Structures • The knowledge of internal forces is a fundamental requirement for true design • The Structural elements are: • Trusses • Frames • Machines Lecture 15

  3. Trusses Composed of slender straight pieces connected together by frictionless pins where all the loads (no moments) are applied. Each member will act as a two-force member (either in tension or compression). All the forces acting on a truss member are axial. Lecture 15

  4. Frames Are designed to support, prevent or transmit loads (forces, no moments). At least one member is not a two-force member. Machines Are designed to transmit force, motion or energy (forces and moments). Will always have at least one member with multiple forces. Lecture 15

  5. Planar Trusses If the planar truss (2-D) is statically determinant, then the number of joints is related to the number of reactions and internal members by : 2j = m + r j = number of joints m = number of internal members r = number of reactions Lecture 15

  6. PBy PBx B PAY PCy PAx a b PCx Ax C A Ay Cy Analysis of Trusses Using the Method of Joints We need to solve for: (1) - Internal forces FAB, FAC, and FBC (2) - Reactions Ax, Ay and Cy Lecture 15

  7. FAB PAY PAx a FAC Ax A Ay Joint A: FAB cosa + FAC + Ax = -Pax ……………….(1) FAB sina + Ay = -Pay ……………………(2) Lecture 15

  8. At Joint C: FCB PCy b FCA PCx C Cy Lecture 15

  9. PBy PBx B FBA FBC a b At Joint B: Lecture 15

  10. Using Matrix Notation -1 = Using manual calculations Look for joints with 2 unknowns Lecture 15

  11. Example Lecture 15

  12. Example 6 kN A B 3 kN 0.9 m C D E 1.2 m 1.2 m Lecture 15

  13. 6 kN A 4 B 4 5 9 15 3 kN 9 15 5 C 16 16 4 4 E D Lecture 15

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