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ME 221 Statics Lecture #32 Section 6.9. Homework #11. Chapter 6 problems: 2, 3, 6 & 7 – Method of Joints 32, 36, 47 & 53 – Method of Sections 68 & 75 Due Friday, November 21. Quiz #7. Friday, November 21 Analysis of Structures Method of Joints or Method of Sections. P By. P Bx. B.
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ME 221 StaticsLecture #32Section 6.9 Lecture #32
Homework #11 Chapter 6 problems: • 2, 3, 6 & 7 – Method of Joints • 32, 36, 47 & 53 – Method of Sections • 68 & 75 • Due Friday, November 21 Lecture #32
Quiz #7 Friday, November 21 Analysis of Structures Method of Joints or Method of Sections Lecture #32
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 #32
6 kN A 4 B 4 5 9 15 3 kN 9 15 5 C 16 16 4 4 E D Lecture #32
Method of Sectioning 12 kN 12 kN A C E G I B D F H J 4 @ 2.4 m=9.6 m 1.8 m If the question is to find internal forces in selected members of the truss, then one can alternatively use the method of sectioning. Example: Determine the force in members FG and FH Lecture #32
12 kN 12 kN A C E G I FGE 1.8 m FGF FHF B D F H J 12 kN 12 kN A C E G I FEG FFG FEH 1.8 m B D F H J Lecture #32
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 #32
Frames and Machines • Frames and machines have at least one multi-force member • Frames are designed to support loads • Machines are designed to transmit and modify loads • Just like trusses, frames and machines need to be disassembled to determine member forces • Need to draw a FBD for each member Lecture #32
D E C B W A D Cx Cy E Cx FBE Cy W C T T FBE FBE W B A Ax Ax FBE Ay Ay Disassembly Exposes Internal Forces • First, reactions of entire structure • Second, disassemble and solve for internal forces FBE is a two force member Lecture #32
Notes on Previous Problem • Without recognizing BE is a two force member, the problem is not tractable. • MUST draw a FBD for entire structure and each disassembled part • Each FBD may have three unknown forces which are found from SFx = 0; SFy = 0; SMz = 0 Lecture #32
General Procedure • Draw FBD for entire structure and solve for reaction forces SFx = 0; SFy = 0; SMz = 0 • Disassemble into component parts • Recognize two force members • Draw FBD and solve for reaction forces - using SFx = 0 ; SFy = 0 ; SMz = 0 Lecture #32
Frame Example Lecture #32