Engineering Mechanics Introduction PDF

ENGINEERING MECHANICS Engr. Mary Ann Del Mundo Reference: Engineering Mechanics, 2nd edition by Ferdinand L. Singer ATTENDANCE HOUSE RULES A student who has been absent for more than 20 percent of the hours of recitation, lectures, or any other scheduled work in this course...

ENGINEERING MECHANICS Engr. Mary Ann Del Mundo Reference: Engineering Mechanics, 2nd edition by Ferdinand L. Singer ATTENDANCE HOUSE RULES A student who has been absent for more than 20 percent of the hours of recitation, lectures, or any other scheduled work in this course shall be automatically dropped from the class roll and the Registrar shall be advised accordingly. CHEATING IS NOT ALLOWED! Grading System: Syllabus Engineering Mechanics basic concepts Force and Force Systems Analysis of Structures Friction and Frictional Forces Centroids and Centers of Gravity MIDTERM EXAMINATIONS  Kinematics of a Particle Kinematics of a Rigid Body Kinetics of a Particle Work and Energy Impulse and Momentum FINAL EXAMINATION Introduction Engineering mechanics – defined as the science which considers the effects of forces on rigid bodies. Rigid bodies Definite amount of matter the parts of which are fixed in position relative to each other. Body which does not deform under the influence of forces But in real life, there would be some force under which the body start to deform however small. A C B D F E Branches of Engineering Mechanics: Statics – rigid bodies which are and remain at rest Dynamics – motion of rigid bodies caused by the forces acting upon them.  Engineering Mechanics Statics Dynamics Force Systems Applications Kinematics Kinetics * Concurrent * Trusses * Translation * Translation * Parallel * Centroids * Rotation * Rotation * Non-concurrent * Friction * Plane Motion * Plane Motion ACTIVITY Force – defined as that which changes, or tends to change the state of motion of a body. This definition applies to the external effect of a force which will be discussed in Engineering Mechanics. The internal effect of a force is to produce stress and deformation in the body on which the force acts which will be discussed in Strength of Materials. Characteristics of a force: 1. Its magnitude 2. The position of its line of action 3. The direction (or sense) in which the force acts along its line of action Principle of Transmissibility of a force states that the external effect of a force on a body is the same for all points of application along its line of action; i.e., it is independent of the point of application. A force system is any arrangement where two or more forces act on a body or on a group of related bodies. Coplanar forces – when the lines of action of all the forces in a force system lie in one plane. Non-coplanar forces – opposite of coplanar Concurrent Forces – forces whose lines of action pass through a common point Parallel Force Systems – forces whose lines of action are parallel Non-concurrent Force systems – forces whose lines of action neither are parallel nor intersect in a common point. Newton’s Three Fundamental Laws by Isaac Newton First Law: If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion) Second Law: If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force F=mxa Where F = force m = mass a = acceleration Third Law: The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. States that for every action, there is an equal and opposite reaction Free-body diagrams (FBD) – a sketch of an isolated body which shows only the forces acting upon the body The lines are also called as vectors. It represents the direction of quantity and the length of the line representing to some scale the magnitude of the quantity.  AXIOMS OF MECHANICS AXIOM (reference: MERRIAM WEBSTER) 1. a statement accepted as true as the basis for argument or inference 2. an established rule or principle or a self-evident truth Axioms of Mechanics 1. The parallelogram law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces. 2. Two forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action. 3. A set of forces in equilibrium may be added to any system of forces without changing the effect of the original system. 4. Action and reaction forces are equal but oppositely directed.  Axiom 1: The Parallelogram Law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors of these forces. Axiom 2: Two forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action.  AXIOM 3: A set of forces in equilibrium may be added to any system of forces without changing the effect of the original system. BC – Free Vector - one which does not show the point of application of the vector Q – Localized Vector Therefore BC can also be represented as Q Q What are the other free and localized vectors in the diagram?  Figure c: Resultant R – same as in figures a and b Triangle Law: a convenient corollary of the parallelogram law: If two forces are represented by their free vectors placed tip to tail, their resultant vector is the third side of the triangle, the direction of the resultant being from the tail of the first vector to the tip of the last vector. Special case: If the angle between two forces becomes zero of 180o, the forces act along the same line; i.e. the forces are collinear. Dimensional Checks v2 = vo2 + 2as Where: v and vo – ft/sec a - ft/sec2 s - ft ft2/sec2 = ft2/sec2 + ft/sec2 x ft KE = Wv2 2g What is the unit of KE if W – lb v - ft/sec g - ft/sec2 ANS: lb.ft Conversion of Units 1 day = 24 hours 1 hour = 60 minutes Determine the conversion of 3 days into minutes? Ans: 3 days x 24 hrs/day x 60 minutes/hr = 4,320 minutes ASSIGNMENT: Pythagorean Theorem Trigonometric Functions BRING YOUR OWN CALCULATOR. NO CALCULATOR NO SEATWORK/QUIZ