Architectural
Columns
Architecture
In architecture, a
column is that part of a structure whose purpose is to transmit
through compression the weight of the structure. Other compression
members are often termed columns because of the similar stress
conditions. Columns can be either compounded of parts or made as a
single piece. Columns are frequently used to support beams or arches on
which the upper parts of walls or ceilings rest. See Forms in
Architecture.
In the architecture of ancient Egypt as early as 2600 BC the architect
Imhotep made use of stone columns whose surface was carved to reflect
the organic form of bundled reeds; in later Egyptian architecture
faceted cylinders were also common.
The Classical orders
The Roman author Vitruvius, relying on the writings (now lost) of Greek
authors, tells us that the ancient Greeks believed that their Doric
order developed from techniques for building in wood in which the
earlier smoothed tree trunk was replaced by a stone cylinder. This myth
of the transformation of wood into stone still causes controversy today
- did the ancient Greeks invent columns this way for themselves, or did
they imitate the stone construction of neighboring civilization?
The Doric, or Tuscan, order is the oldest and simplest
of the classical orders. It is composed of a vertical cylinder that is
wider at the bottom. It generally has neither a base nor a capital. It
is often referred to as the masculine order because it is represented in
the bottom level of the Colosseum and was therefore considered to be
able to hold more weight.
The Ionic
column is considerably more complex than the Doric. It usually has a base
and the shaft is often fluted (it has grooves carved up its length). On
the top is a capital in the shape of a scroll rolled on both sides.
The Corinthian
order is commonly thought to be named because its legendary origin was in
the Greek city-state of Corinth, however the story of its origin is due
to Callimachus, a Greek bronze worker drawing a design of acanthus
leaves, growing on a small tomb for a new style of capital for the
people of Corinth. In fact, the oldest known Corinthian capital was
found in Bassae, dated at 427 BC. It is sometimes called the feminine
order because it is on the top level of the Colosseum and holding up the
least weight. It is similar to the Ionic order, but rather than a
scroll, the Corinthian capital consists of rows of acanthus leaves. Many
variations have been made on the Corinthian capital. For instance, the
capitals of the Capitol building in Washington, DC is made up partially
of wheat stalks.
The ratio of the length of a column to the least radius of gyration of
its cross section is called the slenderness ratio. This ratio affords a
means of classifying columns. All the following are approximate values
used for convenience. A short steel column is one whose slenderness
ratio does not exceed 50; an intermediate length steel column has a
slenderness ratio ranging from 50 to 200, while long steel columns may
be assumed as one having a slenderness ratio greater than 200. A short
concrete column is one having a ratio of unsupported length to least
dimension of the cross section not greater than 10. If the ratio is
greater than 10 it is a long column. Timber columns may be classed as
short columns if the ratio of the length to least dimension of the cross
section is equal to or less than 10. The dividing line between
intermediate and long timber columns cannot be readily evaluated. One
way of defining the lower limit of long timber columns would be to set
it as the smallest value of the ratio of length to least cross sectional
area that would just exceed a certain constant K of the material. Since
K depends on the modulus of elasticity and the allowable compressive
stress parallel to the grain it can be seen that this arbitrary limit
would vary with the species of the timber. The value of K is given in
most structural handbooks.
If the load on a column is applied through the center of gravity of its
cross section it is called an axial load. A load at any other point in
the cross section is known as an eccentric load. A short column under
the action of an axial load will fail by direct compression but a long
column loaded in the same manner will fail by buckling (bending), the
buckling effect being so large that the effect of the direct load may be
neglected. The intermediate length column will fail by a combination of
direct stress and bending.
In the middle of the 18th century a mathematician named Euler derived a
formula which gives the maximum axial load that a long, slender ideal
column can carry without buckling. An ideal column is one which is
perfectly straight, homogenous, and free from initial stress. The
maximum load, sometimes called the critical load, causes the column to
be in a state of unstable equilibrium, that is, any increase in the
loads or the introduction of the slightest lateral force will cause the
column to fail by buckling. The Euler formula for columns is:
P = (Kπ2EI)/l2
Where
P = maximum
or critical load
E = modulus
of elasticity
I = moment of inertia of cross sectional
area
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l
= unsupported length of column
K = a
constant whose value depends upon the conditions of end support of the
column, For both ends free to turn K = 1; for both ends fixed K = 4; for
one end free to turn and the other end fixed K = 2 approximately, and
for one end fixed and the other end free to move laterally K = 1/4.
Examination of this formula reveals the following interesting facts with
regard to the bearing power of columns. First, that elasticity and not
compressive strength of the materials of the column determines the
critical load. Secondly, the critical load is directly proportional to
the moment of inertia of the cross-section. The strength of a column may
therefore be increased by distributing the material so as to increase
the moment of inertia. This can be done without increasing the weight of
the column by distributing the material as far from the principal axes
of the transverse section as possible consistent with keeping the
material thick enough to prevent local buckling. This bears out the
well-known fact that a tubular section is much superior to a solid
section for column service. Another bit of information that may be
gleaned from this equation is the effect of length upon critical load.
For a given size column, doubling the unsupported length quarters the
allowable load. The restraint offered by the end connections of a column
also affects the critical load. If the connections are perfectly rigid,
the critial load will be four times that for a similar column where
there is no resistance to rotation (hinged at the ends).
Since the moment of inertia of a surface is its area multiplied by the
square of a length called the radius of gyration, the above formula may
be rearranged as follows. Using the Euler formula for hinged ends and
substituting Ar2 for I the following formula results:
P/A = (π2E)/(l/r)2
where P/A is
the allowable unit stress of the column and l/r is the
slenderness ratio.
Since the structural column is generally an intermediate length column and
it is impossible to obtain an ideal column, the Euler formula has little
practical application for ordinary design. Consequently, a number of
empirical column formulae have been developed to agree with test data,
all of which embody the slenderness ratio. For design, appropriate
factors of safety are introduced into these formulae.
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From: Wikipedia, the free encyclopedia.
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