Rigid bodies

ENGINEERING MECHANICS

science which considers the effects of forces on rigid bodies

RIGID BODY

a solid body in which deformation is zero or negligible.

STATICS

the effects and distribution of forces on rigid bodies which are and remain at rest

DYNAMICS

motion of rigid bodies caused by the forces acting upon them

KINEMATICS

deals with the pure motion

KINETICS

deals with the motion to applied force

FORCE

defined as that which changes or tends to change the state of motion of a body (external: engineering mechanics). To produce stress and deformation in the body on which the force acts (internal: strength of materials)

CHARACTERISTICS OF FORCE

Magnitude 2. Position 3. Direction

PRINCIPLE OF TRANSMISSIBILITY

external effect of a force on a body is the same for all points of application along its action.

UNITS

Commonly used is pound (Ib), kip (1000 lb), and ton (2000 lb). Sometimes, we use metric system force units

FORCE SYSTEM

any arrangement where two or more force act on a body or on a group of related bodies

COPLANAR

when the lines of action of all the forces in a force system lie in one plane

CONCURRENT

lines of action pass through a common point

NON CONCURRENT

lines of action neither are paralle nor intersect in a common point

FREE BODY DIAGRAM

It help the beginner distinguish between action and reaction forces. It is necessary to isolate the body being considered. A sketch of the isolated body which shows only forces acting upon the body

Applied Forces-

forces acting on the free body which are action forces

Reaction Forces-

forces exerted by the free body upon the body

Scalar -

quantities which possess magnitude only and can be added arithmetically

Vectors -

quantities which possess direction as well as magnitude

TRIANGLE LAW

a convenient corollary of the parallegoram law

DIMENSIONAL CHECKS

Equations used in engineering computations must be dimensionally homogeneous - units on each side must be of the same dimensional form.

Significant Figures-

The accuracy of the final result depends upon the least accurate figure used in the computation

RESULIANT

Usually expressed as the effect of a system of forces on a body. The value of this determines to motion of the body.! the resultant is zero, it is in equilibrium (statics), if not, it is not in equilibrium (dynamics).

Component

The effect of the force is to move the body rightward and upward.

Free Body Diagram

A sketch of the isolated body which shows only the forces acting upon the body

Principle of Transmissibility

It states that the external effect of a force on a body is the same for all points of application along its line of action

Vernon's Theoremit

states that the moment of a force is equivalent to the sum of the moments of its components

Engineering Mechanics

The science which considers the effects of forces on rigid bodies.

Kinematicsit

deals with the pure motion of rigid bodies

Kineticsit

relates to the motion to the applied forces

Scalar

Quantities which possess magnitude only

Rigid Body

A definite amount of matter the parts of which are fixed in position relative to each other

Parallelogram Law

The resultant of two forces is the diagonal of the parallelogram formed on the vector

Concurrent

Forces whose lines of action pass through a common point

EQUILIBRIUM

condition where the resultant of force system is zero

FREE BODY DIAGRAM

Isolated view of the body which shows only the external forces exerted on the body

PIN CONNECTED TRUSSES

internal force in a bar is directed along the axis of the bar

PIN CONNECTED FRAMES

members are subjected to bending action

TRUSSES

a structure composed of members fastened together in such a way as to resist change in shape; a rigid structure. To make it rigid,

METHOD OF JOINTS

The assumption that all members of a truss are two-force members carrying axial loads

METHOD OF SECTIONS

in this method, we will cut the truss into two sections by passing a cutting plane through the members whose internal forces we wish to determine

METHOD OF MEMBERS

Three-force member is in general a non-axial member that is not simply in tension or compression. A member of this kind has shear forces perpendicular to the member and subjected to bending loads

FRICTION

The contact resistance exerted by one body upon a second body when the second body moves or tends to move past the first body

CENTER OF GRAVITY

a point from which the weight of a body or system may be considered to act. In uniform gravity it is the same as the center of mass

MOMENT OF INERTIA

Sometimes called as second moment of area

POLAR MOMENT OF INERTIA

Sum of the moments of inertia about any two mutually perpendicular axes

RADIUS OF GYRATION

Usually denoted by k symbol. radial distance to a point which would have a moment of inertia

TRANSLATION

Motion of a rigid body in which a straight line passing through any two