Frames
10/6/07
What is a Frame?
• So far we’ve discussed vertical pieces and horizontal
pieces
• A real building will have both, combined into a Frame
• The horizontal pieces carry the load (the weight) to the
vertical ones, which then transmit it to the ground
• This combination is referred to as post-and-beam
construction if the connections between the beams and
the columns are not rigid (merely pinned)
• Such buildings are classified by the number of horizontal
layers they have: one-level, two-level, three-level and so
on
Bays and Columns
• In a larger structure, such as a warehouse,
it is usually convenient to have internal
supports, and so one often builds in
repeating units called bays
• To ensure that all the columns support the
same load, the columns are not placed on
the perimeter of the building, but instead
offset by half a bay in each direction
Boston City Hall
Boston City Hall
Live Loads and Lateral Stabilization
• In addition to the channeling of dead load,
the building may have to respond to live
loads which cause horizontal motion
• What are the two prime examples of live
loads that cause horizontal motion?
– wind and earthquakes
• The structure must have lateral
stabilization as well
Lateral Stabilization
• Lateral stabilization is based on what
geometric form again?
• Triangles!
– either directly though trusses, or
– indirectly through continuous structures
Rigidly Fixed Connections
• Alternately rigidity can be achieved using
rigid joints that maintain a fixed angle
between two connections
• The simplest way to do this is to rigidly fix
the connections into the ground (vertical
cantilevers!), leading to a classic pole
barn, or more sophisticated structures
Triangles
• Alternately, other points around the frame
can be rigidly connected, to reduce the
overall system to a triangle again
Rigid connections
• Rigid connections of this type act much as
a beam grid, allowing stresses to be
distributed from the beams to their
supporting columns and hence reducing
deflection
• Light frame – timber construction
• How are houses put together?
• Closely spaced columns (also called
studs) take the weight
• Beams take the weight of the upper floors
• Roof support provided by joists (or
preassembled, trussed rafters)
• Plywood covers the studs, helping to
distribute the load and provide shear
resistance, much as a bearing wall does
Industrial Revolution
• The Industrial Revolution not only made
possible new steel structures, it also
changed how wooden structures were
built.
• Metal nails were now cheap and
convenient
• Lumber became available in standard
sizes, such as the 2 x 4 mentioned earlier
in the class
Balloon Frames
• Early light-timber constructions were called
balloon frames
• The studs ran from the ground to the top of the
building
• This simple design was inefficient because
– it required very long studs
– the walls for the upper floors were hard to reach
during construction
– the spaces for the long studs led to accelerating the
spread of flames in a fire
Platform Frames
• The balloon frame has now been replaced
by the platform frame
• Each floor of the structure is constructed
separately
• Floor and walls
• up to another floor and walls
• repeated as necessary
• This makes the system easier to build and
less vulnerable to fire
Light-timber frames
• Light-timber frame buildings are very
versatile and can be built in a wide variety
of shapes
• Examples of older wooden-frame
structures
Horyu-Ji Temple
Scandinavia
Borgund Church
• Similar structures can be built with
masonry, simply by replacing the wooden
studs by brick bearing walls
Faneuil Hall
Faneuil Hall - Interior
Types of Structures
• The textbook covers quite a bit about
smaller wooden structures, to which we
are accustomed
• However it doesn’t go over the
construction of larger, steel-framed
buildings
• To get some insight into those, we’re going
to watch a film on the World Trade Center
on Thusday
Catenary Systems
Funicular Systems
• Funicular systems
– shapes assumed due to applied loads
causing pure tension or compression
• Cables must be under tension
• Catenary cables are weighted more or
less uniformly across their length
• A “pure” catenary is caused by an
unloaded cable
– the shape it assumes under its own weight
Catenary vs. Parabola
• Also applies to a cable weighted evenly
across cable length
• Does NOT apply to a cable where the
weight is the same at each horizontal point
– parabola (x2)
• Fortunately for most cases these shapes
are very similar
• Can approximate the much more
complicated catenary as a simple parabola
Catenary vs. Parabola
Catenary vs. Parabola
2
Parabola: a x
Catenary: a cosh((x-b)/a)
-20
-10
0
10
20
Catenaries vs. Cable-stayed
• Simple cable-stayed structures covered in
Chapter 3
• Although catenaries are more complicated, they
have many similarities to cable-stayed structures
• For example, catenaries usually run between
two main supports, which could be towers
• The amount of horizontal pull felt by each tower
varies with the angle at which the cable attaches
Sag
• A nearly horizontal cable (low sag) will
have a lot of tension, and so a large
horizontal pull
• A nearly vertical cable (deep sag) will have
much less tension, and almost no
horizontal pull
Sag
Sag-to-span Ratio
• Now LOW sag means SHORTER, but greater
force, so a THICKER cable is needed
• DEEP sag means LONGER, but less force, so a
THINNER cable is acceptable
• For a uniformly loaded (parabolic) cable, the
least material requirements occur for a sag-tospan ratio of 1 to 3
• Unfortunately this means too much horizontal
pull on the support towers, and in practice the
ratio is more like 1 to 9
Types of suspension structures
• There are three basic types of funicular
suspension structures
– single curvature
– double cable, and
– double curvature
Single Curvature
Double Cable
• Single curvature and double cable both
curve in just one direction
• The double cable structure adds a second
cable to resist loads that go UP instead of
DOWN
• What could cause such a load?
Double Curvature
• Double curvature are saddle-shaped
• They curve up in one dimension and down
in a perpendicular direction
• This is also designed to fight wind loads
Comparison
Anlan Bridge
•
•
Anlan Bridge in China has existed in some form since the 4th century
Until 1975 it was made of twisted bamboo strands, in eight cable sections,
to cross a 1,000 foot river
Improvements
• Works, but changes shape as the applied load
shifts position
• How can it be made more stable?
– use a stiff bottom plate
– attach to cables
– load is distributed much more uniformly
• The first bridge to use this was the so-called
Chain Bridge in PA
– built in 1801
– spanning about 200 feet
Chain Bridge
Suspension Bridges
• Engineers quickly expanded on this
design, and suspension bridges got longer
and longer
• By the time the iconic Golden Gate Bridge
was built in 1937, the span reached 4200
feet
Components of a Suspension Bridge
Golden Gate Bridge
• Golden Gate Bridge, still among the 10 longest bridges in world
Clifton Suspension Bridge in Bristol, England, designed by Brunel, completed 1864
Buildings
• It is possible to build buildings using this
technique, in addition to bridges
• Minneapolis Federal Reserve Bank and
Dulles Airport Terminal are examples
Minn. Fed. Reserve Bank
Dulles Airport
Double-cable
• Double-cable structures have additional
stabilizing cables beneath the primaries
• This allows the structure to resist uplift
from wind
Denver Airport
Utica Auditorium
Utica Auditorium
Double curvature
• Double curvature are saddle-shaped
– upwards curve carries the weight
– downward fights the wind
• The upward going cables are therefore
called the suspension cables
• The downward curves are the stabilizing
cables
Munich Olympic Stadium
Munich Olympic Stadium
Calgary Saddledome
Calgary Saddledome