The Gateway Arch: A Unit Study

The Gateway Arch: A Unit Study
The Gateway Arch: A Unit Study

On June 10, 1967, the Gateway Arch was opened to the public. This structure was the highlight of the Jefferson National Expansion Memorial Park, which had its origins in the 1930s.

The Jefferson National Expansion Memorial Park and the Gateway Arch

The stated purpose of the Jefferson National Expansion Memorial Park was to commemorate the Westward Expansion under Thomas Jefferson. Despite several challenges to the project, including doubts as to whether or not Saint Louis was actually the “gateway to the west,” a final design for the arch was selected. The architect was Eero Saarinen. Though it was decided to build the arch design in 1948, the project took a while to materialize; the ground was broken for the arch a little more than a decade later.

The Construction of the Gateway Arch

When the arch was built, the two halves of the 630 foot tall stainless-steel clad arch were constructed simultaneously with the aid of special cranes that hoisted individual sections, which were then welded in place. These clever cranes actually climbed up the sides of the arch as it went up.

One key concern with the arch was the fact that an error of 1/64 of an inch or more at the foundations would mean that the two halves of the arch would not meet. Happily, this was averted by careful planning, though there were a lot of people (and reporters) who rather anticipated such a failure and waited on site to observe the placement of the last section of the arch.

The remaining of the features of the Jefferson National Expansion Memorial Park were completed by 1976. The park as a whole is a unique tourist attraction, with a highlight being a tram ride that carries visitors up the arch to an observation area at the top of the structure on the inside.

How Arches Work

The arch is a timeless architectural form whose primary function is to span a gap. The arch especially lends itself to stone construction, for arching is basically the only way to span any type of sizable gap with stone.

Arches work in compression, with the forces within the arch pushing down along the curve of the arch to the ground. This is huge with a stone arch, for should the forces no longer be in compression, the stones cannot stay in the arch and the whole structure fails. Yet so effective is the arch in doing its job, that there are many examples of old stone bridges still in use many years after construction, and which use no mortar.

This bridging ability of the arch, however, rests on the correct shape for all the forces to remain in compression.

Arch Shapes

What is the ideal shape of an arch for it to remain completely in compression? As it turns out, the ideal shape of an arch depends on external conditions. However, for a freestanding arch the correct shape is a catenary. A catenary is a shape very similar to a parabola, though it is not perfectly identical.

A catenary is the shape formed by a chain hanging down loosely between two supports. The forces in a hanging chain are in tension, while those in the arch are in compression, therefore identical but inverse. Furthermore, you can pull a chain out and have a flatter arc, though you’ll, of course, have to pull harder on the sides to do so. In the same way, you can flatten an arch out, but you’ll have to resist the increasing tendency of the arch to slide out sideways. This is done by thickening the abutments of the arch. These abutments are solid supports for the arch that are heavy enough to contain and restrain all of the thrust produced by the arch.

The Gateway Arch is a catenary in shape, but that does not tell the whole story. The Gateway Arch is not just any catenary, but is actually what is called a weighted catenary.

A weighted catenary is just like our previous example of a chain hung upside down, but with weights being added to the chain at various points. Obviously, if you hang weights on a chain, the shape of the chain will change from what it was by itself. With this method, you could simulate the ideal shape for an arch of any size or situation, though you might need many weights!

The classic Roman arch is usually unable to stand by itself, unless the arch is quite thick, relatively speaking. The reason large Roman arch bridges stand, then, is due to the weight of the material against the sides (called the “haunches”) of the arch. This weight, caused by the material built up to create a reasonable bridge roadbed, for example, is sufficient to press the stones of the arch firmly together.

In effect, the shape of a Roman arch is wrong for a freestanding arch, but works out extremely well in an arch bridge where that extra weight on the haunches of the arch alters the line of thrust. Inversely, a tall catenary is actually not necessarily an ideal choice for such a structure, though it has been used in building stone arch bridges. This is because the large weight on the haunches of the arch can cause it to buckle if the arch is too thin. 

The shape of the Gateway Arch was determined by “weighting” the shape of its model catenary. Now, obviously, as a freestanding arch, one might question whether a weighted catenary is, from a physics standpoint, the best shape for the Gateway Arch, but yet more factors come into play.

Arch Thickness

Broadly speaking, if an “incorrectly” shaped arch can be made thicker, the forces will remain within the arch. By making the arch thicker, even though more weight is added to the arch, in most cases this still gives the lines of compressive force a greater avenue within the arch to act in. The end result is that the arch is stable, even if the compressive force is not routed precisely dead center throughout the arch.

Another feature of the Gateway Arch is that its thickness gently tapers as it rises. This treatment is occasionally seen even in stone arch bridges, sometimes as a clever method of making the arch thicker where the lines of compressive thrust are not well within the arch. Finally, the Gateway Arch is made of steel, allowing some tension, as steel is strong under tension, unlike other materials.

The Gateway Arch is a classic structure, and its beauty comes from its simple, timeless, and ingenious arch shape.

Suggestions
  • If you have a geography notebook, you can add the Gateway Arch on a Drawing and Writing page.
  • Compare and contrast a catenary with a parabola (you’ll find help in the resources below).
  • Younger students can read Building Big by David Macaulay and provide an oral or written narration.
  • Explore a variety of different shapes.
  • Make a list. Look around you. How many arches do you see?
  • Learn more about Westward Expansion.
  • Build a model of the Gateway Arch.
  • Find and mark the Gateway Arch on a map (see resources below).
  • Trace the Mississippi.
  • Learn more about Lewis and Clark and the opening of the West.
Further Investigation

Frequently Asked Questions
From the National Park Service.

Is the Gateway Arch a Parabola?
Proof at IntMath.com.

Types of Arches
Images and descriptions from HomeStratosphere.com.

Activities

Make a Roman Arch
Activity at National Geographic for younger students.

How to Build the Gateway Arch
Papercraft instructions.

Build with Roman Arches
Worksheet activity for older students.

Parabola Interactive
Play with the parabola to understand the shape.

Roman Arch: Static Physics
Explore arch forces.

Books
Minn of the Mississippi

Minn of the Mississippi by Holling C. Holling
Finally, Minn is a turtle who travels down the entire Mississippi River. Children will enjoy charting Minn’s progress!

Building Big by David Macaulay
Includes a section on bridges. Perfect for learning the basics!

Unit Studies and Lesson Plans

Let’s Build an Arch
Lesson plan at USMint.org.

Bridge Types: Tensile and Compressive Forces
Lesson plan for younger students at TeachEngineering.org.

History and Geometry of Roman Aqueducts
Lesson plan for older students at TeachEngineering.org.

Bridge Basics
70-page download from the National Building Museum.

Notebooking Pages & Printables

Missouri Map
For marking the Gateway Arch.

30 Types of Arch Shapes
Perfect for a notebook!

The Gateway Arch Notebooking Pages
Simple pages for copywork, narrations, or wrapping up!