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Fundamental Concepts and Definitions Engineering Mechanics The science which considers the effects of forces on rigid bodies. Statics considers the effects and distribution of forces on rigid bodies which are and remain at rest Dynamics considers the motion of rigid bodies caused by the forces acting upon them Kinematics deals with pure motion of rigid bodies Kinetics relates the motion to applied forces.
Fundamental Concepts and Definitions Basic Quantities Length used to locate the position of a point in space and thereby describe the size of a physical system Time is conceived as a succession of events. Mass is a measure of the quantity of matter that is used to compare the action of one body with that of another. Force a push or pull exerted by one body to another External Force - changes, or tends to change, the state of motion of a body.
Particle has a mass, but a size that can be neglected. Rigid Body can be considered as a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load.
Concentrated Force - represents the effect of a loading which is assumed to act at a point on a body. We can represent a load by a concentrated force, provided the area over which the load is applied is very small compared to the overall size of the body.
First Law Law of Inertia. A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force. Second Law Law of Acceleration. A particle acted upon by an unbalanced force experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force.
Third Law. Law of Action-Reaction. The mutual forces of action and reaction between two particles are equal, opposite, and collinear. Force System any arrangement when two or more forces act on a body or on a group of related bodies.
Coplanar the lines of action of all the forces lie in one plane Concurrent the lines of action pass through a common point Parallel the lines of actions are parallel Non-Concurrent the lines of action are neither parallel nor intersect at a common point.
Fundamental Concepts and Definitions Axioms of Mechanics 1. The Parallelogram Law: The resultant of two forces is the diagonal of the parallelogram formed on the vectors these forces. The forces are in equilibrium only when equal in magnitude, opposite in direction, and collinear in action. 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. Fundamental Concepts and Definitions Scalar and Vector Quantities Scalars quantities which posses magnitude only and can be added arithmetically. Vectors quantities which posses magnitude and direction and can be combined only by geometric vector addition. Multiplication or division of a vector by a scalar will change the magnitude of the vector.
The sense of the vector will change if the scalar is negative. As a special case, if the vectors are collinear, the resultant is formed by an algebraic or scalar addition. Resultant of Concurrent Forces Determine the magnitude and direction of the resultant of the three forces shown.
Determine also the horizontal and vertical component of the resultant. Resultant of Concurrent Forces Determine the magnitude and direction of R if P1 and P2 are lb and lb respectively. P2 lies horizontally while P1 makes with the horizontal.
Resultant of Concurrent Forces A boat moving at 12kph is crossing a river m wide in which a current is flowing at 4 kph. In what direction should the boat head if it is to reach a point on the other side of the river directly opposite its starting point? Moment is the measure of the ability of a force to produce turning or twisting about an axis.
The Principle of Moments Varignons Theorem The moment of a force is equal to the sum of the moments of its components. Determine the resultant moment of the four forces acting on the rod shown below about point O. The force system shown consists of the couple C and four forces.
If the resultant of this system is a lbin. Replace the force and couple moment system acting on the beam in the figure by an equivalent resultant force, and find where its line of action intersects the beam, measured from point O. Equilibrium of a Rigid Body Equilibrium A body is said to be in equilibrium if the resultant of the force system that acts on the body vanishes. Equilibrium means that both the resultant force and the resultant couple are zero. The term free implies that all supports have been remove and replaced by the forces reactions that they exert on the body.
Forces that Act on a Body 1. Reactive Forces Reactions - forces that are exerted on a body by the supports to which it is attached. Applied Forces - forces acting on abody that are not provided by the supports. Equilibrium of a Rigid Body Conditions of Equilibrium 1. Graphical Condition: Under this condition, the forces or vectors are transformed into a force polygon. For equilibrium, the force polygon must close. Directional Condition: If three or more non-parallel forces or vectors are in equilibrium, then they must be concurrent.
For a two-force member, the forces must be equal and opposite. Analytical Condition: If forces or vectors are in equilibrium, then it must satisfy the three static equations:. Three forces 20 N, 30 N, and 40 N are in equilibrium.
Find the largest angle they make with each other. Equilibrium of a Rigid Body A load of lb is hung from the middle of a rope, which is stretch between two rigid walls 30 ft apart. Due to the load, the rope sags 4 ft in the middle. Determine the tension in the rope. Equilibrium of a Rigid Body A simply supported beam is 5m in length. Equilibrium of a Rigid Body The homogeneous kg disk supported by the rope AB rests against a rough vertical wall. Using the given FBD, determine the force in the rope and the reaction at the wall.
A power wrench applies the N m clockwise couple to tighten a bolt at C. Use the given FBD to determine the tensions in the ropes. Equilibrium of a Rigid Body The structure in Fig. Neglecting the weights of the members, determine all forces acting on member BCD.
Analysis of Structures Simple Trusses Truss is a structure composed of slender members joined together at their end joints. Planar Trusses - lie in a single plane and are often used to support roofs and bridges. The weights of the members are negligible. The members are joined together by smooth pins. The applied forces act at the joints. Each member of a truss is a two-force member.
Analysis of Structures Method of Joints When using the method of joints to calculate the forces in the members of a truss, the equilibrium equations are applied to individual joints or pins of the truss.
Analysis of Structures Zero-Force Member member that does not carry a load contributes to the stability of the structure can carry loads in the event that variations are introduced in the normal external loading configuration.
Analysis of Structures Using the method of joints, determine the force in each member of the truss shown in the figure. Indicate whether the members are in tension or compression. One of the supports is usually designed to be equivalent to a roller, in order to permit the elongation and contraction of the truss with temperature changes.
Analyzing the free-body diagram of a part of a truss that contains two or more joints is called the method of sections. Principle: If the truss is in equilibrium then any segment of the truss is also in equilibrium. It permits us to directly determine the force in almost any member instead of proceeding to that member by joint-to-joint analysis.
The cutting plane must not cut more than three members whose internal forces are unknown. Friction Friction force that resists the movement of two contacting surfaces that slide relative to one another. Dry Friction - friction force that exists between two unlubricated solid surfaces. Fluid Friction - acts between moving surfaces that are separated by a layer of uid. The lb block in the figure below is at rest on a rough horizontal plane before the force P is applied.
Determine the magnitude of P that would cause impending sliding to the right. Friction A N block rests in a surface inclined at Determine the horizontal force P required to prevent the block from sliding down.
Angle of friction between the block and the inclined plane is The uniform lb plank in the figure below is resting on friction surfaces at A and B. The coefcients of static friction are shown in the gure. If a lb man starts walking from A toward B, determine the distance x when the plank will start to slide. Substituting and to eqns. Force Systems in Space Assume the three force vectors intersect at a single point. Find the reactions for the equipment shelf shown in the sketch.
The three applied loads act at the center of the volume shown. Supports A and B cannot take reactions in the y direction and support C cannot take a reaction in the x direction. It is a property of the distribution of weight within the body. Center of Mass It is the point through which the resultant inertia force acts on a body.
It is a property of the distribution of mass within the body. Centroid and Center of Gravity Centroid It is the point at which area or volume or line can be concentrated It is the point at which the static moment is zero.
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Marghitu, Wiggins G, phone: , office hours TR: p. Hibbeler, Prentice Hall, Engineering Mechanics, Volume 1 - Statics, by J. Meriam and L. Kraige, John Wiley and Sons,
College Physics — Raymond A. Serway, Chris Vuille — 8th Edition. Introduction to Heat Transfer — Frank P.
Fundamental Concepts and Definitions Engineering Mechanics The science which considers the effects of forces on rigid bodies. Statics considers the effects and distribution of forces on rigid bodies which are and remain at rest Dynamics considers the motion of rigid bodies caused by the forces acting upon them Kinematics deals with pure motion of rigid bodies Kinetics relates the motion to applied forces. Fundamental Concepts and Definitions Basic Quantities Length used to locate the position of a point in space and thereby describe the size of a physical system Time is conceived as a succession of events.
Save extra with 2 Offers. About The Book Mechanics is essentially a deductive science based on a few fundamental principles and has vectorial character. This book has been written with a view to emphasize the vectorial character of mechanics in such a manner so that the material presented may not require any previous knowledge of mathematics beyond elementary calculus. For this reason, products and derivatives of vectors are not used.
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