Uploaded by Kris Chiu

Deformable Bodies Lecture

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WHAT IS BEAM?
A beam is a structural element that primarily resists loads applied laterally across the beam's axis
(an element designed to carry a load pushing parallel to its axis would be a strut or column). Its
mode of deflection is primarily by bending, as loads produce reaction forces at the beam's support
points and internal bending moments, shear, stresses, strains, and deflections. Beams are
characterized by their manner of support, profile (shape of cross-section), equilibrium conditions,
length, and material. Beams are traditionally descriptions of building or civil engineering structural
elements, where the beams are horizontal and carry vertical loads. However, any structure may
contain beams, such as automobile frames, aircraft components, machine frames, and other
mechanical or structural systems. Any structural element, in any orientation, that primarily resists
loads applied laterally across the element's axis is a beam.
WHAT IS COLUMN?
A column or pillar in architecture and structural engineering is a structural element that transmits,
through compression, the weight of the structure above to other structural elements below. In other
words, a column is a compression member. The term column applies especially to a large round
support (the shaft of the column) with a capital and a base or pedestal,[1] which is made of stone,
or appearing to be so. A small wooden or metal support is typically called a post. Supports with a
rectangular or other non-round section are usually called piers. For the purpose of wind or
earthquake engineering, columns may be designed to resist lateral forces. Other compression
members are often termed "columns" because of the similar stress conditions. Columns are
frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In
architecture, "column" refers to such a structural element that also has certain proportional and
decorative features. A column might also be a decorative element not needed for structural
purposes; many columns are engaged, that is to say form part of a wall. A long sequence of columns
joined by an entablature is known as a colonnade.
WHAT IS TRUSSES?
A truss is an assembly of members such as beams, connected by nodes, that creates a rigid
structure.[1] In engineering, a truss is a structure that "consists of two-force members only, where
the members are organized so that the assemblage as a whole behaves as a single object".[2] A
"two-force member" is a structural component where force is applied to only two points. Although
this rigorous definition allows the members to have any shape connected in any stable
configuration, trusses typically comprise five or more triangular units constructed with straight
members whose ends are connected at joints referred to as nodes. In this typical context, external
forces and reactions to those forces are considered to act only at the nodes and result in forces in
the members that are either tensile or compressive. For straight members, moments (torques) are
explicitly excluded because, and only because, all the joints in a truss are treated as revolutes, as
is necessary for the links to be two-force members. A planar truss is one where all members and
nodes lie within a two-dimensional plane, while a space truss has members and nodes that extend
into three dimensions. The top beams in a truss are called top chords and are typically in
compression, the bottom beams are called bottom chords, and are typically in tension. The interior
beams are called webs, and the areas inside the webs are called panels,[3] or from graphic statics
(see Cremona diagram) polygons.[4]
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