Statics & Dynamics University of Ontario Institute of Technology ENGR 2020

Lecture Outline Introductory details Fundamentals Definitions Solution Style and Technique Vectors

Contact Details Dr. Jean-Claude (John) Stranart (emergency or occasional evening) Subject: UOIT: xxxxx Web site / Web CT fax:

Dr. Jean-Claude (John) Stranart Background Ph.D. University of Toronto M.A.Sc. University of Toronto B.A.Sc. Waterloo Research in mechanics, finite elements, fatigue/fracture, smart structures

Subject Matter/Overview Statics Equilibrium of a Particle Force System Resultants Equilibrium of a Rigid Body Structural Analysis Centre of Gravity/Centroid Friction

Subject Matter/Overview Dynamics Kinematics of a Particle Kinetics of a Particle Force, Acceleration Work, Energy Impulse, Momentum Kinematics of a Rigid Body Kinetics of a Rigid Body Force, Acceleration Work, Energy Impulse, Momentum

Textbook Engineering Mechanics: Statics and Dynamics R.C. Hibbler, 10 th Edition Work book/Study Pack

Lectures 9:10 –11:00 Wednesday & Friday Room UA minute break ~ 10:00 Available for questions after class If something is not clear, bring it up, don’t wait Room change on May 13 (only) –UA 1120 or UA 1140

Tutorial Wednesday 12 – 2 pm Room UA 2120 Is everyone available ? (Midterms)

Office Hours UA 3045 To be determined

Marks/grading Problem Sets (5)25% Project5% –10-15 hours, details to follow Midterm Test 110% –June 1 Midterm Test 220% –July 6 Final Exam40%

Problem Sets Due at the beginning of class on: May 20 June 3 June 17 July 8 July 22 Assigned from Hibbler ~ 20 questions, ONLY 2 marked Est. 6 hours/set

Students What is your background? Why are you taking the course? What do see as the biggest challenges? What is your learning style? What software do you know ? Excel, MatLab, MathCad, Maple

Fundamentals Mechanics Rigid-body mechanics, deformable-body mechanics, fluid mechanics Rigid body mechanics Statics – equilibrium of bodies ie at rest or constant velocity Dynamics Accelerated motion of bodies Include turning, curving,

Fundamentals Basic quantities Length Time Mass Force SI length [m], time [s], mass [kg] force is derived [N = kg m s -2 ] US customary length [ft], time [s], force [lb, lbf] mass is derived [m=W/g, 32.2 lb/ 32.2 ft/s 2 = 1.0 slug]

Fundamentals NameLengthTimeMassForce SImeter [m] second [s] kilogram [kg] newton [N] USfoot [ft] second [s] slugpound [lb, lbf]

Fundamentals Idealisations Particle: has mass but size can be neglected simplifies analysis ie earth w.r.t. its orbit Rigid body Application of load does not change geometry of the body Concentrated force Loading is assumed to act on a point Area over which load is applied is small w.r.t. size of body

Newton’s Three Laws of Motion Basis of rigid body mechanics Assumes non-accelerating frame of reference 1) a particle at rest, or moving in a straight line with constant velocity, will remain in that state provided the particle is not subjected to an unbalanced force

Newton’s Three Laws of Motion 2) a particle subjected to an unbalanced experiences an acceleration that has the same direction as the force and a magnitude that is proportional to the force*

Newton’s Three Laws of Motion 3) for every force acting on a particle, the particle exerts an equal, opposite and colinear reaction

Analysis Procedure Read problem carefully and relate the physical situation to the applicable theory Draw necessary diagrams, tabulate problem data Apply the relevant principles(mathematical expression) Solve the equations Check unit consistency Check significant digits

Analysis Procedure (continued) Evaluate the answer Judgement, common sense Is it reasonable Can the solution be validated by another method?

Solution Style Two aspects to any engineering solution Technical solution that is correct Communication of the solution to others As essential as technical accuracy Solution must be clearly presented and able to be followed

Solution Style Statement of the problem Free body diagram Assumptions, relevant principles Applicable equations Solution Concluding statement Boxed/highlighted

Free Body Diagram Sketch of the particle/body/system isolated from the surrounding system ALL forces which the surroundings exert on the particle/body/system are sketched on the body

Free Body Diagram: Procedure 1)Draw/sketch the particle isolated from its surrounding Include co-ordinate axes 2)Indicate ALL forces that act on the body Active/applied forces – ie loads, weight, magnetic, electrostatic Reactive forces – constraints, supports 3)Known forces are labeled with magnitudes and directions

Free Body Diagram: Procedure 4)Unknown forces represented by letters and arrows (assumed direction) In solution, if ‘negative’ force is obtained, minus sign indicates that the force is in the opposite direction of that originally assumed Examples