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