FINALS

also called the
second moment of area, is the
product of area and the square of
its moment arm about a reference

axis.

types of supportss

Numerous methods are available for the determination
of beam deflections. These methods include:

is the moment
of inertia about about the z-axis.

is the distance from an axis of a
body to the point in the body whose moment of inertia is
equal to the moment of inertia of the entire body.

is a characteristic of an object that
describes an imbalance relative to a set of coordinate axes.

Refers to a slender bar that carries
transverse loading; that is, the applied
forces perpendicular to the bar

TYPES OF BEAM

are those
beams in which the reactions of the supports
may be determined by the use of the
equations of static equilibrium. The beams
shown below are examples of statically
determinate beams.

If the number of reactions exerted upon a
beam exceeds the number of equations in
static equilibrium, the beam is said to be
statically indeterminate. In order to solve the
reactions of the beam, the static equations
must be supplemented by equations based
upon the elastic deformations of the beam.

is taken as the
difference between the umber of reactions to the
number of equations in static equilibrium that can
be applied.

Types of Loading

is one whose
unknown external reaction or internal
members can be determined using only the
conditions of equilibrium.

is one whose
unknown forces cannot be determined by the
conditions of static equilibrium alone and will require,
in addition, a consideration of the compatibility
conditions of different parts of the structure for its
complete analysis.

is
measured from the original neutral surface of
the beam to the neutral surface of the deformed
beam.

The change in slope between the tangents drawn to the
elastic curve at any two points A and B is equal to the
product of 1/EI multiplied by the area of the moment
diagram between these two points.

The deviation of any point B relative to the tangent drawn
to the elastic curve at any other point A, in a direction
perpendicular to the original position of the beam, is equal
to the product of 1/EI multiplied by the moment of an area
about B of that part of the moment diagram between
points A and B.

The couple M

force V