ME221Lecture #321 ME 221 Statics Lecture #32 Section 6.9

ME221Lecture #322 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

ME221Lecture #323 Quiz #7 Friday, November 21 Analysis of Structures Method of Joints or Method of Sections

ME221Lecture #324 Analysis of Trusses Using the Method of Joints AyAy AxAx P Ax P AY P By P Bx P Cy P Cx CyCy A B C  We need to solve for: (1) - Internal forces F AB, F AC, and F BC (2) - Reactions A x, A y and C y

ME221Lecture #325 6 kN 3 kN E B A C D

ME221Lecture # m 12 kN 12 kN 2.4 m=9.6 m B D F H J A C E G I Method of Sectioning 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

ME221Lecture # m 12 kN 12 kN B D F H J A C E G I F GE F GF F HF 1.8 m 12 kN 12 kN B D F H J A C E G I F EG F FG F EH

ME221Lecture #328 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.

ME221Lecture #329 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

ME221Lecture #3210 Disassembly Exposes Internal Forces First, reactions of entire structure W A B C D E W A B C D E T AxAx AyAy T AxAx AyAy F BE CyCy CxCx W CyCy CxCx Second, disassemble and solve for internal forces F BE is a two force member

ME221Lecture #3211 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  F x = 0;  F y = 0;  M z = 0

ME221Lecture #3212 General Procedure Draw FBD for entire structure and solve for reaction forces  F x = 0;  F y = 0;  M z = 0 Disassemble into component parts –Recognize two force members –Draw FBD and solve for reaction forces - using  F x = 0 ;  F y = 0 ;  M z = 0

ME221Lecture #3213 Frame Example