Queens’ College Mathematical Bridge

The most recognised bridge on The Backs in Cambridge; The Mathematical Bridge is famed as an example of a perfect bridge – at least in engineering terms.

The poetically recognised ‘Mathematical Bridge’ does not have an official name and is also frequently referred to as either ‘The Wooden Bridge’ or as ‘Queens’ Bridge’.

The bridge’s nom de plume ‘The Mathematical Bridge’ doesn’t even appear in print until at least 1803.*

A version of the bridge has connected one side of Queens’ College to the other since its first construction in 1749.

The red brick building it connects from on one side is the ‘Riverside Building’ and the oldest building (circa 1460) on The Backs in Cambridge. The building contains parts of the President’s Lodge.

The bridge was designed by master carpenter William Etheridge and constructed by local builder, James Essex.

*It’s worth noting that there’s also some confusion regarding which ‘Mathematical Bridge’ is being referenced in 1803 as James Essex built a second bridge in a very similar style between Trinity College and Trinity Hall on the site of the modern day Garrett Hostel Bridge.

The Mathematical Bridge Design

The Mathematical Bridge is a fantastic example of tangent and radial trussing design and it isn’t as complicated as people tend to assume from its name. 

The key thing to notice is that the bridge creates a curve yet is made entirely of straight beams.

In fact, there are only two kinds of load-bearing beams on the bridge. The tangential ones, which are highlighted on the picture below, and the radial beams, which are the ones reaching from the top of the bridge, to the bottom, at regular intervals.

The Mathematical Bridge Design Tangential & Radial Trussing

The original benefit of this design was  that individual timbers could be replaced without dismantling the bridge, or at least in theory.

The clever thing about the bridge is that the forces of tension and compression (which exist on every bridge or arched structure) are basically limited to the two different kinds of beams.

The tangential timbers are almost entirely under compression, while the radial beams being almost entirely under tension, with virtually no ‘bending’ stress.

Or, put another way, in engineering terms the Mathematical Bridge is basically perfect in design.

William Etheridge

William Etheridge came from a long family line of master carpenters and the family was based in nearby Suffolk

William was involved in building the first bridge to cross the Thames at Westminster from 1738-1749. Initially Etheridge worked as the foreman on the project, then took charge of it after the death of its famed designer, James King.

The idea for the design of tangent and radial trussing is a triumph of 18th century engineering and may be attributed directly to James King.

It is James King’s ideas that Etheridge used throughout his bridge-building career.

At the completion of the Westminster Bridge and alongside a greater three-arch project ‘Walton Bridge’ over the Thames in Surrey,  Etheridge was engaged by Queens’ College to design a bridge to cross the Cam.

Queens’ College have a model of the bridge which is believed to be Etheridge’s original design. It shows the single arch crossing with trussing and bolts.

From Queens’ College records we know he was paid a handsome fee of £21.00 for his design.

James Essex, The Younger

Coming with a strong family reputation for build quality, construction work fell naturally to master carpenter James Essex, The Younger.

The Essexes had become well known within the University for the quality of their work.

The Wooden Bridge or Queens’ Bridge is the first recorded build attributed solely to James Essex, The Younger. Needless to say, the building of the bridge enhanced James Essex’ reputation with the University significantly.

So much so, that in 1756 that the younger James Essex was asked to design and build a new building for Queens’ College. If you have ever been on the river you’ll spot the building – named after its designer – The Essex Building.

Metamorphosis of the Mathematical Bridge

The Mathematical Bridge over time has naturally been susceptible to issues caused by the choice of building material – wood. 

Typical problems began to appear caused by constant moisture and consequential decay alongside swelling and shrinkage.
The original oak timber build reached a stage of decay after just 17 years and had to be repaired (1866), before being completely rebuilt in 1905.

The rebuild work was trusted to and completed by another local builder, Mr. William Sindall.

The rebuild kept to the original design switching the wood choice and types of bolt.

The main changes were replacement of the oak timbers with the teak ones which exist today and a change to coach-bolts passing through each joint.

And what of William Sindall’s local building company? It went on to become one of the most respected names in the UK construction industry as part of the ‘Morgan Sindall Group’. Today, it is listed on the London Stock Exchange and employs 6,600 people in the UK (2018).

In fact, the main change to the bridge from the original design is the handrail on the bridge, which was added to facilitate the Queen Mother’s frequent trips to the College.

Mathematical Bridge Copies

A beautiful, strong, sleek bridge with perfect design – let’s copy it! 

WALTON BRIDGE

Etheridge used James King’s system of trussing in his designs for both the bridge at Queens’ and the other project he was working on at Walton in 1748/9.
This larger and impressive triple arch over the Thames at Walton in Surrey was designed once again using the structural trussing design.
Etheridge’s bridge was replaced completely with a new stone structure in 1788 and is now on its 6th variation (with the latest bridge rebuild opening in 2013).

TRINITY HALL & TRINITY BRIDGE

James Essex was such a fan of the design that he replicated the bridge twenty years after building the first bridge (1769) only yards from the original.
The bridge was placed where the modern day Garret Hostel Bridge is sited between Trinity Hall and Trinity College.
However, with no maintenance, by 1812 the bridge had completely decayed. The bridge failed structurally and is documented to have completely fallen on the 2nd July.
Around this time, a generic description for trussing designs of this sort was geometrical construction. This terminology could form a basis for the later evolution of the nom de plume ‘Mathematical Bridge’.

IFFLEY LOCK, THE OTHER PLACE (OXFORD)

Scaled down, the footbridge at Iffley Lock is a simplified copy of Queens’ Bridge.

The bridge at Iffley wasn’t built until 1924 and was designed by Chief Engineer, Griffith John Griffiths (1873-1940).

Griffiths simplified design was also constructed in teak and paid for by the Thames Conservancy.

The joinery at Queens’ has the tangents broken into multiple short lengths with scarf joints: whereas at Iffley each tangent consists of only two lengths of wood bolted together side-by-side at the central arch.

This change means that the Iffley bridge does not satisfy the 18th century design intention that individual timbers could be replaced without dismantling the bridge.

There are other differences at Iffley with its separated radials and cross-beam steel plates support design.

The bridge at Iffley also inspired a copy – duplicated in oak by Winchester College for a footbridge connecting Palmer Field across the water meadows.

The bridge at Winchester was dismantled in 1976 but you can still see where the abutments are today.

The Mathematical Bridge Rumour Mill

As Cambridge’s favourite place to spin a tall tale – the mathematical bridge has formed its own legends.

We have to include this section to debunk common truth-less concoctions that we hear on the river, almost daily!

GENERAL UNTRUTHS

Contrary to what many working on the river would have you believe, neither William Etheridge nor James Essex were students or fellows at Queens’.
Neither Etheridge, nor Essex had ever been to China.

FAILED REASSEMBLY

One of the most repeated untruths on the river, the failed reassembly legend rears its head regularly in the chatter.
We sadly wish to report that no students ever took the original, bolt-less bridge apart, failed to re-assemble it, and therefore constructed it once again with added bolts.
It’s a shame really and this will always be one of our favourite tall tales from the river!
The present 1905 built bridge is held together by coach bolts and nuts whereas the earlier version had iron pins or coach screws at the points. These coach bolts are visible to people passing over the bridge. In the pre-1905 bridge, the fastenings at the joints had not been visible.
One may speculate that perhaps the sight of bolt heads where none had been seen before might have given rise to the myth of the failed re-assembly. This myth has not been found in print earlier than the 20th century.

MATHEMATICALLY NOT NEWTONIAN

There is a further commonly told myth that the bridge was originally designed by Sir Isaac Newton.

This is not true. It’s pretty tricky for even a man as clever as Newton to design and build the Mathematical Bridge at Queens’ a full 22 years after his death.

The Mathematical Bridge Key Facts

  • Connects the banks at Queens’ College
  • The design makes a curved bridge across the river but it’s only built using straight pieces of wood
  • Every load bearing beam is only supporting one type of force – either tension or compression
  • Current bridge was built in 1905 by one of the founders of the Morgan Sindall Group – one of the largest construction companies in the UK
    • The design is a minor triumph of mid-18th century engineering, for which credit goes to James King (d. 1744)
    • It was claimed that, if it were needed to replace a timber in a side truss, then that timber could be removed and replaced without needing to dismantle the entire bridge. This has never been tested in practice

The Mathematical Bridge Further Reading

Queens' Wooden Mathematical Bridge