Frames
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Transcript of Frames
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
-20 -10 0 10 20
Parabola: a x2
Catenary: a cosh((x-b)/a)
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-to-span 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 CurvatureDouble 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