Statics & Dynamics University of Ontario Institute of Technology ENGR 2020.

Statics & Dynamics

University of OntarioInstitute of Technology

ENGR 2020

Lecture Outline• Introductory details

• Fundamentals• Definitions• Solution Style and Technique

• Vectors

Contact Details

• Dr. Jean-Claude (John) Stranart• 416-738-4403 (emergency or occasional

evening)• [email protected] [email protected]• Subject: UOIT: xxxxx• Web site / Web CT• fax: 416-978-5741

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, 10th Edition• Work book/Study Pack

Lectures• 9:10 –11:00 Wednesday & Friday• Room UA 1240

• 10 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%• Project 5%

– 10-15 hours, details to follow

• Midterm Test 1 10%– June 1

• Midterm Test 2 20%– July 6

• Final Exam 40%

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/s2 = 1.0

slug]

FundamentalsName Length Time Mass Force

SI meter[m]

second[s]

kilogram[kg]

newton[N]

US foot[ft]

second[s]

slug pound[lb, lbf]

2s

mkg

ft

slb 2

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*

amF

vmdt

dp

dt

dF

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