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ARCC 1202 Study Guide - Final Guide: Louvre, Diagrid, Rigid Frame


Department
Architecture Technical
Course Code
ARCC 1202
Professor
Manuel Baez
Study Guide
Final

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Stable / Unstable
History of Structures Exam 4
Stable and unstable equilibrium leading to buckling failure
When a column is pushed sideways in this state where the load is below the
buckling load, the bending will increase but the column will return to its former
position once the horizontal load is removed. The column is in a state of stable
equilibrium. Once the load exceeds the critical load, the state becomes unstable
and excessive lateral deflection (buckling failure) can be expected to occur.
These stable and unstable column states generate interesting
questions: What parameters determine the critical load of
columns? What architectural consequences do these parameters
have? Short and very long columns behave fundamentally
differently, and, therefore, have quite contrasting design
implications.
The Column Capital types
The design of the transition point between column and beam, otherwise known as
the capital, has always been a focal design feature. This basic situation has
historically remained the same regarding the structural direction change from beam
to column, with probable material changes as well.
Exhibition Hall, Monza, Italy (1965), Angelo Mangiarotti, Architect
Prefabricated concrete elements used for columns, beams and the roof deck. The capital is integrated
into the column and is in a hammerhead form; angled tongue-and-groove interlocking joints provide a
rigid connection to the system of beams.

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The Mushroom Column:
The mushroom column is concrete architecture’s unique version to the forming of the capital: the top of
the column dramatically enlarges into a conical shape in order to support a thin slab above for the
smooth load transfer.
Civic Hall, Eslov, Sweden, (1957), Hans Asplund, Architect
Johnson Wax Headquarters, 1939, Frank Lloyd Wright
The authorities doubted the structural capacity of the columns.
Mumbai’s New International Airport, 2014, SOM Architects

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Leonard Euler and the slender column
Leonard Euler (1707 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer.
He mathematically described and predicted how long, thin columns fail in buckling and at what load
they will do so. Euler’s theory is still valid in its original form and it is perhaps the oldest in structural
mechanics that remains in use today.
Stiffness is the crucial aspect of the column that prevents excessive sideways deflection and an
associated buckling failure.
Stiffness can be seen as being influenced by 3 variables in a compressive element:
1. The cross-sectional shape and dimension
2. The elastic properties of the material it is made of
3. The length of the column
The larger the cross-section and the stiffer the material, the more the element is able to resist its
tendency to buckle, and therefore the larger will be the load that it can carry before failure.
Additionally, the greater the length of a compressive element, the less stiff it is (think, for example, of
the behavior of a thin plastic or metal ruler). Therefore, the first two variables are proportional to the
element’s overall stiffness and the third, length, is inversely so.
Large cross-section = Stiff
Narrow cross-section = Stiff
Elastic material = Stiff
Non elastic material = Stiff
Long = Stiff
Short = Stiff
Buckling of columns as a 3D spatial problem
Buckling of columns is also a spatial problem because a column in a
building may buckle in any direction in three-dimensional space. If a
column is unbraced in any direction (meaning that it is free to deflect
sideways over its height), it will probably buckle with respect to one of its
two orthogonal cross-sectional axes.
Columns are usually braced by walls or other building elements in the
direction in which they are least stiff. Columns that are part of external
walls are usually shaped and oriented to have their strongest direction
towards the wind load. These columns are usually braced in their weak
direction by walls parallel to the external wall plane. Additionally, columns
in multi-story buildings are also braced at each floor level by the floor slab.
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