Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 32:Analysis of Frames and Machines

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 2 Miscellaneous Notes Friday November 9 Lecture Postponed Last Quiz  This week of November 5-9  Method of Joints and Sections for Trusses Remaining Tutorial Sessions  General sessions  Problems will be selected for you to complete  Problem sets will be posted during week of November 11

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 3 Miscellaneous Notes (cont.) Mid-Terms Exams  All exams have not been collected No Record of Mid-Term  Student numbers  Contact me immediately to resolve

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 4 Chapter 32 Objectives to define frames and machines to develop the equations of equilibrium for frames and machines to determine joint forces and support reactions for frames and machines

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 5 Frames and Machines Frames  Stationary  Support loads

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 6 Frames and Machines (cont.) Machines  Moving parts  Transmit or alter effects of loads

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 7 Frames and Machines (cont.) How are Frames and Machines Different from Truss Structures?

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 8 Frames and Machines (cont.) How are Frames and Machines Different from Truss Structures?  Multi-force member(s)

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 9 Analysis of Frames and Machines Key Steps for Analysis 1. Establish coordinate system 2. Draw FBD 3. Identify unknown forces and moments Typically define rectangular components 4. Identify Structural Characteristics Two-force members Connecting members

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 10 Comprehension Quiz Forces common to any two connecting members act with _______ on the other member.  A) equal magnitudes but opposite sense  B) equal magnitudes and the same sense  C) different magnitudes but opposite sense  D) different magnitudes but the same sense Answer: A

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 11 Example When determining the reactions at joints A, B, and C, what is the minimum number of unknowns for solving this problem?  A) 3  B) 4  C) 5  D) 6 Answer: A

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 12 Example (cont.) Any Structural Characteristic to Identify? F AB is a two-force member

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 13 Example (cont.) Use What Equilibrium Equation First?

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 14 Example (cont.) Can the Problem be Solved if the Two-Force Member was not Identified?  Yes  How? Apply Equilibrium Equations to Each Structural Member

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 15 Comprehension Quiz The FBD is shown. If a couple moment was applied at C, does the FBD of member BC at Joint B change?  A) No change  B) Two forces, B X and B Y  C) Two forces and a moment at B  D) One moment at B Answer: A MCMC MCMC

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 16 Comprehension Quiz The FBD is shown. If an additional force is applied to member AB, does the FBD of member BC at Joint B change?  A) No change  B) Two forces, B X and B Y  C) Two forces and a moment at B  D) One moment at B F

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 17 Comprehension Quiz The FBD is shown. If an additional force is applied to member AB, does the FBD of member BC at Joint B change?  A) No change  B) Two forces, B X and B Y  C) Two forces and a moment at B  D) One moment at B Answer: B FF

ENGI 1313 Statics I – Lecture 32© 2007 S. Kenny, Ph.D., P.Eng. 18 References Hibbeler (2007) mech_1