Arches and beams both need something underneath them while they are being built. Over a deep, fast estuary that something is unaffordable or impossible. The cantilever bridge is the structure that answers the question: what can you build if you are never allowed to put anything in the water?

The answer is to build outward from each pier in both directions at once, keeping the two arms balanced so the pier is never asked to hold an unbalanced load, and then to drop a short suspended span into the gap where the two arms nearly meet. Nothing ever stands on the riverbed. Every stage of construction is a complete, stable structure in its own right.

Underneath the engineering is a piece of mathematics that is easy to miss and is the actual invention. A continuous beam running over three or more supports is statically indeterminate: equilibrium alone does not tell you the reactions, you need the stiffness of the beam as well. Worse, if one pier settles by a few millimetres, the forces everywhere change — and you cannot stop a pier settling.

Heinrich Gerber saw that inserting hinges at the right points makes the whole thing statically determinate again. The reactions then follow from equilibrium alone, they can be computed exactly by hand, and settlement of a pier changes nothing. His Bavarian patent of 1866, Balkenträger mit freiliegenden Stützpunkten, was first built in 1867 over the Regnitz at Bamberg and on the Main at Haßfurt, and the Gerberträger — Gerber beam — went round the world under his name.

The Forth Bridge, opened 4 March 1890, is the form at full scale: main spans of 1,709 feet. Build the demonstration Fowler and Baker used in 1887, then measure why the hinges matter.

Mechanics

Blueprints (36)

The Arm as a Lever

Impact Craters

The Cantilever Bridge

The Suspension Bridge

The Lever Escapement

The Deadbeat Escapement

The Balance Spring

The Anchor Escapement

The Centrifuge

Torque Wrench

Pocket Micrometer

Dial Indicator

Spring Tape Measure

Spirit Level

Micromètre

Addressing Machine

Stapler

Envelope Folding Machine

Rotary Snow Plough

Janney Coupler