STRUCS mech of solids

Imperfect frame

such frame cannot resist geometrical distortion under the action of loads .

Concurrent forces

the forces which meet at one point

Collinear forces

the forces whose lines of action lie on the same line

Coplanar forces

the forces whose lines of action lie on the same plane

Polar moment of inertia

the moment of inertia about the z - axis

Directional condition

three or more non parallel forces or vectors are in equilibrium , then they must be concurrent

More moment of inertia

translates into lower deflection and lower normal stress .

Varignon's Principle of moments

" If a number of coplanar forces are acting simultaneously on a particle , the algebraic sum of the moments of all the forces about any point is equal to the moment of their resultant force about the same point . "

Parallelogram Law of forces

" If two forces , acting simultaneously on a particle , be represented in magnitude and direction by the two adjacent sides of a parallelogram ; their resultant may be represented in magnitude and direction by the diagonal of the parallelogram , which passes through their point of intersection . "

Effects of forces Rigid bodies

It may change the motion of a body . i.e. if a body is at rest , the force may set it in motion . And if the body is already in motion , the force may accelerate it

Effects of forces Strength of materials

It may give rise to the internal stresses in the body , on which it acts

Newton's first law

It states that everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external agency acting on it .

Newton's third law

It states that for every action there is an equal and opposite reaction

Newton's second law

It states that the rate of change of momentum of a body is directly proportional to the impressed force and it takes place in the direction of the force acting on it .

It is the turning effect produced by a force , on the body , on which it acts .

Moment of a force

" If a force acts at any point on a rigid body , it may also be considered to act at any other point on its line of action , provided this point is rigidly connected with the body . "

Principle of Transmissibility

gravitational acceleration

The vertical component of projectile is under constant ____ ____

equilibrium

Two forces can be in ____ only if they are equal in magnitude opposite in direction and collinear in action

collinear

concurrent forces may or may not be

Friction

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

Kinematics

deals with the bodies in motion , without any reference to the forces which are responsible for the motion .

Kinetics

deals with the bodies in motion due to the application of forces .

Statics

deals with the forces and their effects , while acting upon the bodies at rest .

Dynamics

deals with the forces and their effects , while acting upon the bodies in motion .

Engineering Mechanics

deals with the laws and principles of Mechanics , along with their applications to engineering problems .

Parallel forces

forces are acting in parallel lines

forces or vectors are transformed into a force polygon . For equilibrium , the force polygon must close

forces or vectors are transformed into a force polygon . For equilibrium , the force polygon must close

Concurrent force system

free body in equilibrium

Analytical condition

if forces or vectors are in equilibrium , then it must satisfy the three static equations ; namely : ΣFx ΣFy ΣΜx

Higher moments of inertia

indicate that more force has to be applied in order to cause a rotation

Strength of Materials

is the study of the internal effect of external forces applied to structural member .

Non - Coplanar Force

line of action of all the forces do not lie in one plane

Imperfect frame

m < 2j - 3

Perfect frame

m = 2j - 3

Redundant frame

m > 2j - 3

Perfect frame

made up of members just sufficient to keep it in equilibrium

Concurrent forces

may or may not be collinear

lower moments of inertia

means that only low forces are necessary .

Redundant frame

members in a frame are more than required for a perfect frame

Center of Gravity

of an elementary body where the whole weight of the body is concentrated

Centroid

point at which the total area of a plane figure is assumed to be concentrated .

Parallel - axis theorem

states that the amount of inertia of an area with respect to any axis in the plane of the area is equal to the moment of inertia of the area with respect to a parallel centroidal axis plus the product of the area and the square of the distance between the two axes .

Scalar Quantity

completely defined by its magnitude alone .

Centrifugal force

A force in a circular motion which acts along the radius and is directed away from the center of the circle .

two forces

A given force F can be resolved into ( or replaced by ) ____ ____which together produces the same effects that of force F

Couple

A system of two equal parallel forces acting in opposite directions is said to form a couple

Curvilinear translation

Also called projectile motion where it follows a parabolic trajectory

rectilinear motion

An object is said to be in a ____ ____ when two objects are moving in a straight line and are parallel to each other .

Uniformly Distributed Load

It is a load which is spread on some length of a beam . It is expressed by its intensity ( Newton / meter )

Force

Contains : Magnitude, Direction, Point of application, Line of action

Vector Quantity

completely defined only when its magnitude as well as direction are specified

any action that tends to maintain or alter the motion of a body or to distort it .

Force

tension or compression

Forces can either be

homogeneous

If the body is _____ ( having constant density ) , its center of gravity is equivalent to the centroid .

Method of Joints

In this method , each and every joint is treated as a free body in equilibrium .

Uniformly Varying Load

It has an intensity that varies according to some law along the length of the beam .

Concentrated or Point Load

It is a load applied over a small area .

velocity

The horizontal component of curvilinear translation is at constant _____

Moment of Inertia

The product of force and the square of its moment arm about a reference axis

D'Alembert's Principle

When a body is subjected to an acceleration , there exists a force opposite the direction of motion and equal to the product of mass and acceleration . This force is known as the reverse effective force , REF or inertial force , Ma .

Mass moment of inertia

a quantity that is used in measuring a body's resistance to a change in its rotation direction or the angular momentum .

Friction

a retarding force that always acts opposite to the motion or to the tendency to move .

Frame

a structure made up of several beams that are riveted or welded together

Truss

a structure which is composed completely of axial members that are assumed to be weightless

Mass moment of inertia

also known as rotational inertia

rigid body

an idealization of a body that does not deform or change shape