Frames 10607 What is a Frame So far

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 (x 2) • 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

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 4 th 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 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