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