Skew arch
Encyclopedia
A skew arch is a method of construction that enables an arch bridge
to span an obstacle at some angle other than a right angle
. This results in the faces of the arch not being perpendicular to its abutments and its plan view being a parallelogram
, rather than the rectangle
that is the plan view of a regular, or "square" arch
. In the case of a masonry skew arch the construction requires precise stonecutting
as none of the cuts form right angles but once the principles were fully understood in the early 19th century it became considerably easier and cheaper to build a skew arch of brick
. The problem of building skew arch masonry bridges was addressed by a number of early civil engineer
s and mathematician
s, including William Chapman
(1787), Benjamin Outram
(1798), Peter Nicholson
(1828), George Stephenson
(1830), Edward Sang
(1835), Charles Fox (1836), George W. Buck
(1839) and William Froude
(c. 1844).
Skew bridges are not a recent invention, having been built on exceptional occasions since Roman
times, but they were little understood and rarely used before the advent of the railway.
One notable exception is an aqueduct
, designed by British
engineer Benjamin Outram
, constructed in masonry
and completed in 1798, which still carries the Ashton Canal
at an angle of 45° over Store Street
in Manchester
.
Outram's design is believed to be based on work done on the Kildare Canal in Ireland
in 1787,
in which William Chapman
introduced the segmental oblique arch to the design of Finlay Bridge at Naas
,
employing an arch barrel based on a circular segment
that is smaller than a semicircle
and which was repeated by Thomas Storey
in 1830 in the bridge carrying the Haggerleazes branch of the Stockton and Darlington Railway
over the River Gaunless
near Cockfield, County Durham
with a skew angle of 63° and a skew span of 42 feet (12.8 m), resulting in a clear span of 18 feet (5.5 m) and a rise of 7 feet (2.1 m).
The common method they all used was to clad the timber centring
(also known as falsework
) with planks, known as "laggings", laid parallel with the abutments and carefully planed and levelled to approximate closely the required curve of the intrados of the arch. The positions of the courses in the vicinity of the crown were first marked out at right angles to the faces using long wooden straight-edges, then the remaining courses were marked out in parallel. The masons then laid the stones, cutting them to shape as required.
Contemporary designs by rival engineers were less successful and for a time skew bridges were considered weak in comparison with the regular, or "square" arch bridge and so were avoided if at all possible,
the alternatives being to construct the road or canal with a double bend
, so as to allow it to cross the obstacle at right angles, or to build a regular arch bridge with the extra width or span necessary to clear the obstacle "on the square".
An example of the latter type of construction is Denbigh Hall Bridge, built in 1837 to carry the London and Birmingham Railway
across Watling Street
at an acute angle of only 25°.
Now a Grade II listed structure, the bridge is still in use today, carrying the busy West Coast Main Line
. It was constructed in the form of a long gallery, some 200 feet (61 m) long and 34 feet (10.4 m) wide, consisting of iron girders resting on walls built parallel with the road; the girders, and consequently the faces of the bridge, being perpendicular to the roadway and the railway line being laid out obliquely across the top, the need to build a highly skewed bridge of 80 feet (24.4 m) span was therefore avoided.
The eminent canal engineer James Brindley
never succeeding in working out a solution to the problem of constructing a strong skew arch and as a consequence all his overbridges were built at right angles to the waterway, with double bends in the roadway, where necessary, and to this day many of them cause inconvenience to their users. However, it was the coming of the railway, with its need to cross existing obstacles, such as rivers, roads, canals and other railways, in as straight a line as possible, that rekindled the civil engineer's interest in the skew arch bridge.
The strength of a regular arch (also known as a "square" or "right" arch) comes from the fact that the mass of the structure and its superincumbent load cause lines of force that are carried by the stones into the ground and the abutments without producing any tendency for the stones to slide with respect to one another. This is due to the fact that the courses
of stone are laid parallel to the abutments, which in a regular arch causes them also to lie perpendicular to its faces. For only slightly oblique bridges, where the skew angle is less than approximately 15° it is possible to use the same construction method, laying the stones in courses parallel to the abutments. The result is known as a "false" skew arch and analysis of the forces within it shows that in each corner where the face forms an acute angle with an abutment there are resultant forces that are not perpendicular to the planes of the stone courses whose tendency is to push the stones out of the face, the only resistance to this being provided by friction and the adhesion of the mortar between the stones.
An example of such a false skew arch is the Colorado Street Bridge
in Saint Paul, Minnesota.
Prior to starting work on Store Street Aqueduct, Outram built a number of false skew arches, one of them with a skew angle as great as 19°, as accommodation bridges across the Huddersfield Narrow Canal
. The fact that these inherently weak structures are still standing today is attributed to their light loading.
along the length of its barrel. In an oblique or skew arch the axis of the barrel is deliberately not perpendicular to the faces, the deviation from perpendicularity being known as the skew angle or the "obliquity" of the arch.
For this reason a skew arch needs to be thought of as a three-dimensional object and by considering the direction of the lines of force within the barrel the optimum orientation for the courses of stonework that make the barrel can be decided.
ly, with the masons cutting each voussoir
stone as it was required, and it was not until 1828 that details of the technique were published in a form that was useful to other engineers and stonemasons.
.png)
.jpg)
In his book A Popular and Practical Treatise on Masonry and Stone-cutting (1828), Scottish architect, mathematician, cabinet-maker and engineer Peter Nicholson
first set out in clear and understandable terms a workable method for determining the shape and position of the stones required for the construction of a strong skew arch that enabled them to be prepared in advance of the actual construction process.
Nicholson approached the problem by constructing a development
of the intrados of the arch from the plan and elevation drawings, effectively unrolling and flattening the surface, then drawing the courses perpendicular to the faces, adding the header joints perpendicular to the courses, then finally rolling up the development diagram by projecting
the detail of the intrados back onto the plan and elevation drawings, a technique also used by others who would later offer alternative solutions to the problem. This method resulted in the courses of stone voussoirs making up the barrel of the skew arch following parallel helical
paths between the abutments, giving the view along the barrel an attractive rifled
appearance. Although these courses meet the arch faces at right angles at the crown of the arch, the nearer they are to the springing line the greater their deviation from perpendicularity. Thus Nicholson's method is not the perfect solution, but it is a workable one that has one great advantage over more purist alternatives, namely that since the helical courses run parallel to each other, all the voussoir stones can be cut to the same pattern, the only exceptions being the ring stones, or quoins
, where the barrel meets the faces of the arch, each of which is unique but has an identical copy in the other face.
Nicholson never pretended to have invented the skew arch but in his later work The Guide to Railway Masonry, containing a Complete Treatise on the Oblique Arch (1839), he does claim to have invented the method for producing the templates that enabled the accurate cutting of the voussoir stones used in all skew bridges built between the years 1828 and 1836, citing testimonials from the builders of major works, such as the Croft Viaduct at Croft-on-Tees
near Darlington
. However, by 1836 a young engineer called Charles Fox had improved on Nicholson's helicoidal method and other writers were proposing alternative approaches to the problem.
In performing his calculations Nicholson considered the arch barrel to be made from one ring of stones and of negligible thickness and therefore he developed only the intrados.
The idea was expanded in Charles Fox's 1836 publication On the Construction of Skew Arches, in which he considered the intrados of the barrel and the extrados as separate surfaces mapped onto concentric cylinders by drawing a separate development for each. This approach had two advantages. Firstly, he was able to develop a theoretical third, intermediate surface mid-way between the intrados and the extrados, which allowed him to align the centre of each voussoir, rather than its inner surface, along the desired line, thereby better approximating the ideal placement than Nicholson was able to achieve.
Secondly, it enabled him to develop an arbitrary number of concentric intermediate surfaces so as to plan the courses in multi-ring skew arch barrels, allowing them for the first time to be constructed in brick, and therefore much more economically than was previously possible.
In order to explain how he visualised the courses of voussoirs in a stone skew arch, Fox wrote, "The principle which I have adopted is, to work the stones in the form of a spiral quadrilateral solid, wrapped round a cylinder, or, in plainer language, the principle of a square threaded screw: hence it becomes quite evident, that the transverse sections of all these spiral stones are the same throughout the whole arch. It will be obvious, that the beds of the stones should be worked into true spiral [helicoidal] planes." So, a stone skew arch built to Fox's plan would have its voussoirs cut with a slight twist, in order to follow the shape of a square threaded screw
.
While claiming a superior method, Fox openly acknowledged Nicholson's contribution but in 1837 he felt the need to reply to a published letter written in support of Nicholson by fellow engineer Henry Welch, the County Bridge Surveyor for Northumberland
. Unfortunately the three men became involved in a paper war that, following a number of earlier altercations in which the originality of his writings was questioned, left the 71-year old Nicholson feeling bitter and unappreciated.
The following year Fox, still aged only 28 and employed by Robert Stephenson
as an engineer on the London and Birmingham Railway
, presented his paper encapsulating these principles to the Royal Institution
and from this was born the English or helicoidal method of constructing brick skew arches. Using this method many thousands of skew bridges were built either entirely of brick or of brick with stone quoins by railway companies in the United Kingdom, a substantial number of which survive and are still in use today.
, having also worked on the London and Birmingham Railway under Stephenson before moving to the Manchester and Birmingham Railway
, published a work entitled A Practical and Theoretical Essay on Oblique Bridges in which he also acknowledged Nicholson's contribution but, finding it lacking in detail,
applied his own original trigonometrical
approach and considerable practical experience to the problem.
This book was acknowledged as the definitive work on the subject of the helicoidal skew arch and remained a standard text book for railway engineers until the end of the 19th century.
Buck's trigonometrical approach allowed every dimension of a skew arch to be calculated without recourse to taking measurements from scale drawings and it allowed him to calculate the theoretical minimum angle of obliquity to which a practical semicircular helicoidal skew bridge could be designed and safely built.
The "Buck Limit", as it is known, has a value of 25°40′ or, when quoted in terms of the maximum angle of skew, a value of 64°20′.
Buck paid particular attention to the design of bridges of extreme obliquity, addressing two potential problems he had identified. Firstly, he noted that the acutely angled quoins at the obtuse corners of the plan view were very susceptible to damage during construction, settlement or by accidental blows in subsequent use so he devised a method of chamfer
ing the edge, removing the single acute angle and replacing it with two obtuse angles and, in his own words, "the quantity thus cut off from the acute quoin, is gradually diminished to the opposite or obtuse quoin, where the cutting vanishes; by this contrivance no angle less than a right angle is any where presented on the exterior of the work […] the effect produced is elegant and pleasing to the eye."
Secondly, he recommended that the extrados of the barrel of an arch of great obliquity be formed into rusticated
steps so as to provide a horizontal bed for the spandrel
walls in order to overcome their tendency to slide off the arch barrel.
The bridge carrying the London and Birmingham Railway over the London Road at Boxmoor
in Hertfordshire, adjacent to what is now Hemel Hempstead station
on the West Coast Main Line, is an example of a segmental arch of extreme obliquity that was designed by Buck and incorporates both of these features. Constructed in masonry, with a brick barrel, stone quoins and a 58° angle of skew, it was completed in 1837. Shortly before the railway opened the bridge was the subject of an ink and wash
drawing dated 12 June 1837, one of a series of works by artist John Cooke Bourne
illustrating the construction of the line.
Buck's Essay, containing its criticism of Nicholson's work, was published in July 1839, just a few months before Nicholson's Guide to Railway Masonry, causing the ongoing paper war in The Civil Engineer and Architect's Journal to continue acrimoniously as Nicholson accused Buck of stealing his ideas
and Buck issued a counter-claim.
In 1840, Buck's assistant, the young engineer William Henry Barlow
entered the fray, initially signing himself cryptically W.H.B.,
but eventually declaring publicly his strong support for Buck.
Nicholson, by this time aged 75 and his health failing, had been struggling financially since the bankruptcy of one of his publishers in 1827 and he was in desperate need of the revenue he hoped to receive from sales of his Guide.
While both Fox and Buck had been happy to acknowledge Nicholson's work and had fought a mostly intellectual battle, Barlow's attacks became less gentleman
ly and more personal
causing Nicholson, who later received anonymous public support from the mysterious M.Q.,
considerable distress.
the mathematical purists recommend that helicoidal construction be restricted to segmental arches and not be used in full-centred (semicircular) designs.
Despite this there were many full-centred skew bridges built to the helicoidal pattern and many still stand, Kielder Viaduct
and Neidpath Viaduct being just two examples.
The search for a technically pure orthogonal
method of constructing a skew arch led to the proposal of the logarithmic method by Edward Sang
, a mathematics teacher living in Edinburgh, in his presentation in three parts to the Society for the Encouragement of the Useful Arts between 18 November 1835 and 27 January 1836, during which time he was elected vice-president of the Society, though his work was not published until 1840.
The logarithmic method is based on the principle of laying the voussoirs in "equilibrated"
courses in which they follow lines that run truly perpendicular to the arch faces at all elevations, while the header joints between the stones within each course are truly parallel with the arch face.
While a helix is produced by projecting a straight line onto the surface of a cylinder, Sang's method requires that a series of logarithm
ic curves be projected onto a cylindrical surface, hence its name.
In terms of strength and stability, a skew bridge built to the logarithmic pattern has advantages over one built to the helicoidal pattern, especially so in the case of full-centred designs. However, the courses are not parallel, being thinner towards the most acutely angled quoin (located where the face of the arch makes an obtuse angle with the abutment in the plan view, at S and Q in the development to the left, and at the left hand side of the photograph of the intrados on the right) and thicker towards the most obtusely angled quoin (at O and G in the development and just off the right hand side of the photograph),
requiring specially cut stones, no two of which in a given course being the same, which precludes the use of mass produced bricks. Nevertheless, two courses beginning at opposite ends of the barrel at the same height above the springing line are exactly alike, halving the number of templates required.
In 1838, Alexander James Adie,
son of the famous optical instrument manufacturer of the same name
,
as resident engineer on the Bolton and Preston Railway was the first to put the theory into practice,
building several skew bridges to the logarithmic pattern on that route, including the semi-elliptical Grade II listed
bridge number 74A that carries the line over the Leeds and Liverpool Canal
, which was formerly known as the southern section of the Lancaster Canal
with the intention of connecting it to the northern section, though this was never achieved as the necessary aqueduct over the River Ribble
proved too expensive to build.
He presented a paper on the subject to the Institution of Civil Engineers
the following year and in 1841, academic William Whewell
of Trinity College, Cambridge
published his book The Mechanics of Engineering in which he expounded the virtues of building skew bridges with equilibrated courses, but due to the poor complexity to benefit ratio, there have been few other adopters.
The corne de vache or "cow's horn" method is another way of laying courses such that they meet the face of the arch orthogonally at all elevations.
Unlike the helicoidal and logarithmic methods, in which the intrados of the arch barrel is cylindrical, the corne de vache method results in a warped hyperbolic paraboloid
surface that dips in the middle, rather like a saddle.
Despite being known as the French method of skew arch building, it was actually introduced by English engineer William Froude
whilst working under Isambard Kingdom Brunel
on the Bristol and Exeter Railway
, which opened in 1844.
Although no details of Froude's work in this area survive and despite being better remembered for his work on hydrodynamics, he is known to have built at least two overbridges in red brick with stone quoins using this principle on the line just north of Exeter
, at Cowley Bridge Junction where the A377 Exeter–Barnstaple road crosses at an oblique angle and, about 4 miles (6.4 km) to the northeast, at Rewe
, on the A396, both of which survive and are in daily use.
The brickwork is considerably more complex than in a helicoidal design and, in order to ensure that the courses of bricks meet the faces of the arch at right angles, many had to be cut to produce tapers.
The corne de vache approach tends to result in a structure that is almost as strong as one built to the logarithmic pattern and considerably stronger than one built to the helicoidal pattern but, again, the extra complexity has meant that the method has not seen widespread adoption, especially since the simpler helicoidal structure can be built much stronger if a segmental design is chosen, rather than a full-centred one.
.jpg)
.jpg)
The ribbed skew arch is a form of the false skew arch in which several narrow regular arches or ribs, offset laterally with respect to one another, are used to approximate a true skew arch.
Motivated by the lack of skilled stonemasons in the 18th century United States, the design was first proposed in 1802 for a crossing of the Schuylkill River
in Philadelphia by British-born American architect Benjamin Henry Latrobe
and later championed by French civil engineer A. Boucher.
Because the series of arch ribs are all regular arches this method of construction has the advantage of being less demanding of unskilled artisans but it has received considerable criticism as being weak, susceptible to frost damage, ugly and wasteful of materials.
Although Latrobe's bridge was never built as proposed, his method of construction was later to be used extensively by the Philadelphia and Reading Railroad throughout the Philadelphia area, including an ambitious viaduct designed by Gustavus A. Nicolls with six skewed spans of 70 feet (21.3 m) across the river and six more land-based skew arches, which was built close to the site of Latrobe's proposed bridge and completed in 1856.
Thanks to the reinforcing of the spandrel walls in 1935, the bridge continues to carry rail traffic to this day.
The Midland Railway
in the United Kingdom suffered from no such shortage of skilled workers but as part of its southern extension towards its London
terminus at St Pancras
, it was faced with the need to cross Southdown Road in Harpenden
at an extremely acute angle of approximately 25°,
a figure more acute than the theoretical limit of 25°40′ proposed by Buck, and requiring a bridge with a skew angle of 65°, a situation not unlike that faced by the London and Birmingham railway 30 years earlier at Denbigh Hall. This time the chosen solution was to build Southdown Road bridge
as a ribbed skew arch, which opened for traffic in 1868 and was successfully widened in 1893 when the line was converted to quadruple track.
Despite the aforementioned criticisms of the design, the bridge is still standing and in daily use by express and commuter trains.
A smaller and less extremely skewed example is Hereford Road bridge
in Ledbury
, Herefordshire, which was built in 1881 to carry the Ledbury and Gloucester Railway
at an angle of approximately 45° across the Hereford Road, now a section of the A438.
The railway having closed in 1959,
it is now used as part of a footpath.
Notice that the two bridges in the photographs skew in opposite directions. Southdown Road bridge is said to have a left-hand skew due to the near face being offset to the left of the far face, while Hereford Road bridge has a right-hand skew.
Early skew arch bridges were painstakingly built from masonry blocks, each individually and expensively cut to its own unique shape, with no two edges either parallel or perpendicular.
A fine example of such construction is the famous Rainhill Skew Bridge, which was designed with a skew span of 54 feet (16.5 m), in order to give a clear span across the railway of 30 feet (9.1 m) at a skew angle of 56° by George Stephenson
and built as a full-sized wooden model in an adjacent field before being completed in 1830.
A contemporary skew bridge, built to carry the Haggerleazes branch of the Stockton and Darlington Railway over the River Gaunless in County Durham
proved too difficult for the original contractors, Thomas Worth and John Batie who, after piling the foundations for the abutments and laying the lower courses of masonry, abandoned the work. The contract was re-let to James Wilson of Pontefract
on 28 May 1830 for £420, an increase of £93 over the original tender. As the principles were not completely understood the work continued to prove difficult and its imminent collapse was solemnly predicted right up until the time, a few days before the opening of the branch, the centring was removed and the crown of the arch settled by less than half an inch (13 mm).
_01.jpg)
Arch bridge
An arch bridge is a bridge with abutments at each end shaped as a curved arch. Arch bridges work by transferring the weight of the bridge and its loads partially into a horizontal thrust restrained by the abutments at either side...
to span an obstacle at some angle other than a right angle
Right angle
In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...
. This results in the faces of the arch not being perpendicular to its abutments and its plan view being a parallelogram
Parallelogram
In Euclidean geometry, a parallelogram is a convex quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure...
, rather than the rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...
that is the plan view of a regular, or "square" arch
Arch
An arch is a structure that spans a space and supports a load. Arches appeared as early as the 2nd millennium BC in Mesopotamian brick architecture and their systematic use started with the Ancient Romans who were the first to apply the technique to a wide range of structures.-Technical aspects:The...
. In the case of a masonry skew arch the construction requires precise stonecutting
Stonemasonry
The craft of stonemasonry has existed since the dawn of civilization - creating buildings, structures, and sculpture using stone from the earth. These materials have been used to construct many of the long-lasting, ancient monuments, artifacts, cathedrals, and cities in a wide variety of cultures...
as none of the cuts form right angles but once the principles were fully understood in the early 19th century it became considerably easier and cheaper to build a skew arch of brick
Brick
A brick is a block of ceramic material used in masonry construction, usually laid using various kinds of mortar. It has been regarded as one of the longest lasting and strongest building materials used throughout history.-History:...
. The problem of building skew arch masonry bridges was addressed by a number of early civil engineer
Civil engineer
A civil engineer is a person who practices civil engineering; the application of planning, designing, constructing, maintaining, and operating infrastructures while protecting the public and environmental health, as well as improving existing infrastructures that have been neglected.Originally, a...
s and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s, including William Chapman
William Chapman (engineer)
William Chapman was an English engineer. Born in Whitby, he worked on the construction of the Old and Humber docks in Hull, as well as many drainage and canal projects. He is credited with the invention of the bogie and articulation for rail vehicles.-Personal life:William Chapman was born on 7...
(1787), Benjamin Outram
Benjamin Outram
Benjamin Outram was an English civil engineer, surveyor and industrialist. He was a pioneer in the building of canals and tramways.-Personal life:...
(1798), Peter Nicholson
Peter Nicholson (architect)
Peter Nicholson was a Scottish architect, mathematician and engineer. Largely self-taught, he was apprenticed to a cabinet-maker but soon abandoned his trade in favour of teaching and writing...
(1828), George Stephenson
George Stephenson
George Stephenson was an English civil engineer and mechanical engineer who built the first public railway line in the world to use steam locomotives...
(1830), Edward Sang
Edward Sang
thumb|right|Edward Sang Edward Sang was a Scottish mathematician, best known for having computed largetables of logarithms, with the help of his daughters...
(1835), Charles Fox (1836), George W. Buck
George W. Buck
George Watson Buck was Engineer of the Montgomeryshire Canal in the early 19th Century, and was responsible for the unique lock paddle design....
(1839) and William Froude
William Froude
William Froude was an English engineer, hydrodynamicist and naval architect. He was the first to formulate reliable laws for the resistance that water offers to ships and for predicting their stability....
(c. 1844).
Benjamin Outram and Store Street Aqueduct
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....
times, but they were little understood and rarely used before the advent of the railway.
One notable exception is an aqueduct
Navigable aqueduct
Navigable aqueducts are bridge structures that carry navigable waterway canals over other rivers, valleys, railways or roads. They are primarily distinguished by their size, carrying a larger cross-section of water than most water-supply aqueducts...
, designed by British
British people
The British are citizens of the United Kingdom, of the Isle of Man, any of the Channel Islands, or of any of the British overseas territories, and their descendants...
engineer Benjamin Outram
Benjamin Outram
Benjamin Outram was an English civil engineer, surveyor and industrialist. He was a pioneer in the building of canals and tramways.-Personal life:...
, constructed in masonry
Stonemasonry
The craft of stonemasonry has existed since the dawn of civilization - creating buildings, structures, and sculpture using stone from the earth. These materials have been used to construct many of the long-lasting, ancient monuments, artifacts, cathedrals, and cities in a wide variety of cultures...
and completed in 1798, which still carries the Ashton Canal
Ashton Canal
The Ashton Canal is a canal built in Greater Manchester in North West England.-Route:The Ashton leaves the Rochdale Canal at Ducie St. Junction in central Manchester, and climbs for through 18 locks, passing through Ancoats, Holt Town, Bradford-with-Beswick, Clayton, Openshaw, Droylsden,...
at an angle of 45° over Store Street
Store Street Aqueduct
The Store Street Aqueduct in central Manchester, England was built in 1798 by Benjamin Outram on the Ashton Canal. A Grade II* listed building it is built on a skew of 45 degrees across Store Street, and is believed to be the first major aqueduct of its kind in Great Britain and the oldest still in...
in Manchester
Manchester
Manchester is a city and metropolitan borough in Greater Manchester, England. According to the Office for National Statistics, the 2010 mid-year population estimate for Manchester was 498,800. Manchester lies within one of the UK's largest metropolitan areas, the metropolitan county of Greater...
.
Outram's design is believed to be based on work done on the Kildare Canal in Ireland
Republic of Ireland
Ireland , described as the Republic of Ireland , is a sovereign state in Europe occupying approximately five-sixths of the island of the same name. Its capital is Dublin. Ireland, which had a population of 4.58 million in 2011, is a constitutional republic governed as a parliamentary democracy,...
in 1787,
in which William Chapman
William Chapman (engineer)
William Chapman was an English engineer. Born in Whitby, he worked on the construction of the Old and Humber docks in Hull, as well as many drainage and canal projects. He is credited with the invention of the bogie and articulation for rail vehicles.-Personal life:William Chapman was born on 7...
introduced the segmental oblique arch to the design of Finlay Bridge at Naas
Naas
Naas is the county town of County Kildare in Ireland. With a population of just over twenty thousand, it is also the largest town in the county. Naas is a major commuter suburb, with many people residing there and working in Dublin...
,
employing an arch barrel based on a circular segment
Circular segment
In geometry, a circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center...
that is smaller than a semicircle
Semicircle
In mathematics , a semicircle is a two-dimensional geometric shape that forms half of a circle. Being half of a circle's 360°, the arc of a semicircle always measures 180° or a half turn...
and which was repeated by Thomas Storey
in 1830 in the bridge carrying the Haggerleazes branch of the Stockton and Darlington Railway
Stockton and Darlington Railway
The Stockton and Darlington Railway , which opened in 1825, was the world's first publicly subscribed passenger railway. It was 26 miles long, and was built in north-eastern England between Witton Park and Stockton-on-Tees via Darlington, and connected to several collieries near Shildon...
over the River Gaunless
River Gaunless
The River Gaunless is a river of County Durham in England.Formed just south of the village of Copley, by the confluence of Arn Gill and Hindon Beck , the Gaunless wends its way east, passing the settlements of Butterknowle, Cockfield and Evenwood and through...
near Cockfield, County Durham
Cockfield, County Durham
Cockfield is a village on the edge of Teesdale, County Durham, England. It is situated 8 miles to the south-west of Bishop Auckland, 15 miles north-west of Darlington and 40 miles south-east of Newcastle-upon-Tyne. Remains found on Cockfield Fell suggest there was a settlement in the area during...
with a skew angle of 63° and a skew span of 42 feet (12.8 m), resulting in a clear span of 18 feet (5.5 m) and a rise of 7 feet (2.1 m).
The common method they all used was to clad the timber centring
Centring
Centring , or centering , is the structure upon which the stones of arches or vault are laid during construction. Once the arch is complete, it supports itself, but until the keystone is inserted, it has no strength and needs the centring to keep the voussoirs in their correct relative...
(also known as falsework
Falsework
Falsework consists of temporary structures used in construction to support spanning or arched structures in order to hold the component in place until its construction is sufficiently advanced to support itself...
) with planks, known as "laggings", laid parallel with the abutments and carefully planed and levelled to approximate closely the required curve of the intrados of the arch. The positions of the courses in the vicinity of the crown were first marked out at right angles to the faces using long wooden straight-edges, then the remaining courses were marked out in parallel. The masons then laid the stones, cutting them to shape as required.
Contemporary designs by rival engineers were less successful and for a time skew bridges were considered weak in comparison with the regular, or "square" arch bridge and so were avoided if at all possible,
the alternatives being to construct the road or canal with a double bend
S bridge
An S bridge is a double-curved bridge, shaped roughly like a shallow letter S, used in early 19th century road construction in the United States. They were generally used for crossing small, curving streams with uneven banks. These bridges are found in and around the New Concord, Ohio area.S...
, so as to allow it to cross the obstacle at right angles, or to build a regular arch bridge with the extra width or span necessary to clear the obstacle "on the square".
An example of the latter type of construction is Denbigh Hall Bridge, built in 1837 to carry the London and Birmingham Railway
London and Birmingham Railway
The London and Birmingham Railway was an early railway company in the United Kingdom from 1833 to 1846, when it became part of the London and North Western Railway ....
across Watling Street
Watling Street
Watling Street is the name given to an ancient trackway in England and Wales that was first used by the Britons mainly between the modern cities of Canterbury and St Albans. The Romans later paved the route, part of which is identified on the Antonine Itinerary as Iter III: "Item a Londinio ad...
at an acute angle of only 25°.
Now a Grade II listed structure, the bridge is still in use today, carrying the busy West Coast Main Line
West Coast Main Line
The West Coast Main Line is the busiest mixed-traffic railway route in Britain, being the country's most important rail backbone in terms of population served. Fast, long-distance inter-city passenger services are provided between London, the West Midlands, the North West, North Wales and the...
. It was constructed in the form of a long gallery, some 200 feet (61 m) long and 34 feet (10.4 m) wide, consisting of iron girders resting on walls built parallel with the road; the girders, and consequently the faces of the bridge, being perpendicular to the roadway and the railway line being laid out obliquely across the top, the need to build a highly skewed bridge of 80 feet (24.4 m) span was therefore avoided.
The eminent canal engineer James Brindley
James Brindley
James Brindley was an English engineer. He was born in Tunstead, Derbyshire, and lived much of his life in Leek, Staffordshire, becoming one of the most notable engineers of the 18th century.-Early life:...
never succeeding in working out a solution to the problem of constructing a strong skew arch and as a consequence all his overbridges were built at right angles to the waterway, with double bends in the roadway, where necessary, and to this day many of them cause inconvenience to their users. However, it was the coming of the railway, with its need to cross existing obstacles, such as rivers, roads, canals and other railways, in as straight a line as possible, that rekindled the civil engineer's interest in the skew arch bridge.
The false skew arch
Course (architecture)
A course is a continuous horizontal layer of similarly-sized building material one unit high, usually in a wall. The term is almost always used in conjunction with unit masonry such as brick, cut stone, or concrete masonry units .-Styles:...
of stone are laid parallel to the abutments, which in a regular arch causes them also to lie perpendicular to its faces. For only slightly oblique bridges, where the skew angle is less than approximately 15° it is possible to use the same construction method, laying the stones in courses parallel to the abutments. The result is known as a "false" skew arch and analysis of the forces within it shows that in each corner where the face forms an acute angle with an abutment there are resultant forces that are not perpendicular to the planes of the stone courses whose tendency is to push the stones out of the face, the only resistance to this being provided by friction and the adhesion of the mortar between the stones.
An example of such a false skew arch is the Colorado Street Bridge
Colorado Street Bridge (Saint Paul, Minnesota)
The Colorado Street Bridge also known as Bridge No. L-8803 is a masonry and brick arch bridge in Saint Paul, Minnesota's West Side neighborhood. It is wide and consists of a single oblique span of that was built with the arch courses running parallel to the abutments, leading to a weaker...
in Saint Paul, Minnesota.
Prior to starting work on Store Street Aqueduct, Outram built a number of false skew arches, one of them with a skew angle as great as 19°, as accommodation bridges across the Huddersfield Narrow Canal
Huddersfield Narrow Canal
The Huddersfield Narrow Canal is an inland waterway in northern England. It runs just under from Lock 1E at the rear of the University of Huddersfield campus, near Aspley Basin at Huddersfield to the junction with the Ashton Canal at Whitelands Basin in Ashton-under-Lyne...
. The fact that these inherently weak structures are still standing today is attributed to their light loading.
A more rigorous approach
When considering the balance of forces within a regular arch, in which all courses of masonry that make up the barrel are parallel with its abutments and perpendicular to its faces, it is convenient to consider it as a two-dimensional object by taking a vertical section through the body of the arch and parallel with its faces, thereby ignoring any variation in loadingQuasistatic loading
In solid mechanics, quasistatic loading refers to loading where inertial effects are negligible. In other words time and inertial mass are irrelevant....
along the length of its barrel. In an oblique or skew arch the axis of the barrel is deliberately not perpendicular to the faces, the deviation from perpendicularity being known as the skew angle or the "obliquity" of the arch.
For this reason a skew arch needs to be thought of as a three-dimensional object and by considering the direction of the lines of force within the barrel the optimum orientation for the courses of stonework that make the barrel can be decided.
The helicoidal skew arch
A characteristic of the regular arch is that the courses of stones run parallel to the abutments and perpendicular to the faces. In an oblique arch these two conditions can not both be met because the faces and the abutments are deliberately not perpendicular. Since skew angles greater than about 15° are required for many applications mathematicians and engineers, such as Chapman, abandoned the idea of laying the courses of stones parallel to the abutments and considered the alternative of laying the courses perpendicular to the faces of the arch, and accepting the fact that they would then no longer run parallel to the abutments. Though Outram's Store Street Aqueduct was constructed with this principle in mind it was done so empiricalEmpirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
ly, with the masons cutting each voussoir
Voussoir
A voussoir is a wedge-shaped element, typically a stone, used in building an arch or vault.Although each unit in an arch or vault is a voussoir, two units are of distinct functional importance: the keystone and the springer. The keystone is the center stone or masonry unit at the apex of an arch. A...
stone as it was required, and it was not until 1828 that details of the technique were published in a form that was useful to other engineers and stonemasons.
Peter Nicholson's helicoidal method in stone
Peter Nicholson (architect)
Peter Nicholson was a Scottish architect, mathematician and engineer. Largely self-taught, he was apprenticed to a cabinet-maker but soon abandoned his trade in favour of teaching and writing...
first set out in clear and understandable terms a workable method for determining the shape and position of the stones required for the construction of a strong skew arch that enabled them to be prepared in advance of the actual construction process.
Nicholson approached the problem by constructing a development
Development (differential geometry)
In classical differential geometry, development refers to the simple idea of rolling one smooth surface over another in Euclidean space. For example, the tangent plane to a surface at a point can be rolled around the surface to obtain the tangent-plane at other points.The tangential contact...
of the intrados of the arch from the plan and elevation drawings, effectively unrolling and flattening the surface, then drawing the courses perpendicular to the faces, adding the header joints perpendicular to the courses, then finally rolling up the development diagram by projecting
Projection (mathematics)
Generally speaking, in mathematics, a projection is a mapping of a set which is idempotent, which means that a projection is equal to its composition with itself. A projection may also refer to a mapping which has a left inverse. Bot notions are strongly related, as follows...
the detail of the intrados back onto the plan and elevation drawings, a technique also used by others who would later offer alternative solutions to the problem. This method resulted in the courses of stone voussoirs making up the barrel of the skew arch following parallel helical
Helix
A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...
paths between the abutments, giving the view along the barrel an attractive rifled
Rifling
Rifling is the process of making helical grooves in the barrel of a gun or firearm, which imparts a spin to a projectile around its long axis...
appearance. Although these courses meet the arch faces at right angles at the crown of the arch, the nearer they are to the springing line the greater their deviation from perpendicularity. Thus Nicholson's method is not the perfect solution, but it is a workable one that has one great advantage over more purist alternatives, namely that since the helical courses run parallel to each other, all the voussoir stones can be cut to the same pattern, the only exceptions being the ring stones, or quoins
Quoin (architecture)
Quoins are the cornerstones of brick or stone walls. Quoins may be either structural or decorative. Architects and builders use quoins to give the impression of strength and firmness to the outline of a building...
, where the barrel meets the faces of the arch, each of which is unique but has an identical copy in the other face.
Nicholson never pretended to have invented the skew arch but in his later work The Guide to Railway Masonry, containing a Complete Treatise on the Oblique Arch (1839), he does claim to have invented the method for producing the templates that enabled the accurate cutting of the voussoir stones used in all skew bridges built between the years 1828 and 1836, citing testimonials from the builders of major works, such as the Croft Viaduct at Croft-on-Tees
Croft-on-Tees
Croft-on-Tees is a village and civil parish in the Richmondshire district of North Yorkshire, England. South of Darlington, it stands on the opposite side of the River Tees from Hurworth-on-Tees and is situated on the A167. The bridge over the Tees between Croft and Hurworth marks the boundary...
near Darlington
Darlington
Darlington is a market town in the Borough of Darlington, part of the ceremonial county of County Durham, England. It lies on the small River Skerne, a tributary of the River Tees, not far from the main river. It is the main population centre in the borough, with a population of 97,838 as of 2001...
. However, by 1836 a young engineer called Charles Fox had improved on Nicholson's helicoidal method and other writers were proposing alternative approaches to the problem.
Charles Fox's English method in brick
The idea was expanded in Charles Fox's 1836 publication On the Construction of Skew Arches, in which he considered the intrados of the barrel and the extrados as separate surfaces mapped onto concentric cylinders by drawing a separate development for each. This approach had two advantages. Firstly, he was able to develop a theoretical third, intermediate surface mid-way between the intrados and the extrados, which allowed him to align the centre of each voussoir, rather than its inner surface, along the desired line, thereby better approximating the ideal placement than Nicholson was able to achieve.
Secondly, it enabled him to develop an arbitrary number of concentric intermediate surfaces so as to plan the courses in multi-ring skew arch barrels, allowing them for the first time to be constructed in brick, and therefore much more economically than was previously possible.
In order to explain how he visualised the courses of voussoirs in a stone skew arch, Fox wrote, "The principle which I have adopted is, to work the stones in the form of a spiral quadrilateral solid, wrapped round a cylinder, or, in plainer language, the principle of a square threaded screw: hence it becomes quite evident, that the transverse sections of all these spiral stones are the same throughout the whole arch. It will be obvious, that the beds of the stones should be worked into true spiral [helicoidal] planes." So, a stone skew arch built to Fox's plan would have its voussoirs cut with a slight twist, in order to follow the shape of a square threaded screw
Square thread form
The square thread form is a common thread form for leadscrews. It gets its name from the square cross-section of the thread.-Advantages & disadvantages:...
.
While claiming a superior method, Fox openly acknowledged Nicholson's contribution but in 1837 he felt the need to reply to a published letter written in support of Nicholson by fellow engineer Henry Welch, the County Bridge Surveyor for Northumberland
Northumberland
Northumberland is the northernmost ceremonial county and a unitary district in North East England. For Eurostat purposes Northumberland is a NUTS 3 region and is one of three boroughs or unitary districts that comprise the "Northumberland and Tyne and Wear" NUTS 2 region...
. Unfortunately the three men became involved in a paper war that, following a number of earlier altercations in which the originality of his writings was questioned, left the 71-year old Nicholson feeling bitter and unappreciated.
The following year Fox, still aged only 28 and employed by Robert Stephenson
Robert Stephenson
Robert Stephenson FRS was an English civil engineer. He was the only son of George Stephenson, the famed locomotive builder and railway engineer; many of the achievements popularly credited to his father were actually the joint efforts of father and son.-Early life :He was born on the 16th of...
as an engineer on the London and Birmingham Railway
London and Birmingham Railway
The London and Birmingham Railway was an early railway company in the United Kingdom from 1833 to 1846, when it became part of the London and North Western Railway ....
, presented his paper encapsulating these principles to the Royal Institution
Royal Institution
The Royal Institution of Great Britain is an organization devoted to scientific education and research, based in London.-Overview:...
and from this was born the English or helicoidal method of constructing brick skew arches. Using this method many thousands of skew bridges were built either entirely of brick or of brick with stone quoins by railway companies in the United Kingdom, a substantial number of which survive and are still in use today.
George W. Buck and William H. Barlow
In 1839, George Watson BuckGeorge W. Buck
George Watson Buck was Engineer of the Montgomeryshire Canal in the early 19th Century, and was responsible for the unique lock paddle design....
, having also worked on the London and Birmingham Railway under Stephenson before moving to the Manchester and Birmingham Railway
Manchester and Birmingham Railway
The Manchester and Birmingham Railway was built between Manchester and Crewe and opened in stages from 1840. Between Crewe and Birmingham, trains were worked by the Grand Junction Railway...
, published a work entitled A Practical and Theoretical Essay on Oblique Bridges in which he also acknowledged Nicholson's contribution but, finding it lacking in detail,
applied his own original trigonometrical
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
approach and considerable practical experience to the problem.
This book was acknowledged as the definitive work on the subject of the helicoidal skew arch and remained a standard text book for railway engineers until the end of the 19th century.
Buck's trigonometrical approach allowed every dimension of a skew arch to be calculated without recourse to taking measurements from scale drawings and it allowed him to calculate the theoretical minimum angle of obliquity to which a practical semicircular helicoidal skew bridge could be designed and safely built.
The "Buck Limit", as it is known, has a value of 25°40′ or, when quoted in terms of the maximum angle of skew, a value of 64°20′.
Buck paid particular attention to the design of bridges of extreme obliquity, addressing two potential problems he had identified. Firstly, he noted that the acutely angled quoins at the obtuse corners of the plan view were very susceptible to damage during construction, settlement or by accidental blows in subsequent use so he devised a method of chamfer
Chamfer
A chamfer is a beveled edge connecting two surfaces. If the surfaces are at right angles, the chamfer will typically be symmetrical at 45 degrees. A fillet is the rounding off of an interior corner. A rounding of an exterior corner is called a "round" or a "radius"."Chamfer" is a term commonly...
ing the edge, removing the single acute angle and replacing it with two obtuse angles and, in his own words, "the quantity thus cut off from the acute quoin, is gradually diminished to the opposite or obtuse quoin, where the cutting vanishes; by this contrivance no angle less than a right angle is any where presented on the exterior of the work […] the effect produced is elegant and pleasing to the eye."
Secondly, he recommended that the extrados of the barrel of an arch of great obliquity be formed into rusticated
Rustication (architecture)
thumb|upright|Two different styles of rustication in the [[Palazzo Medici-Riccardi]] in [[Florence]].In classical architecture rustication is an architectural feature that contrasts in texture with the smoothly finished, squared block masonry surfaces called ashlar...
steps so as to provide a horizontal bed for the spandrel
Spandrel
A spandrel, less often spandril or splaundrel, is the space between two arches or between an arch and a rectangular enclosure....
walls in order to overcome their tendency to slide off the arch barrel.
The bridge carrying the London and Birmingham Railway over the London Road at Boxmoor
Boxmoor
Boxmoor, or Boxmoor Village, is a district of Dacorum in Hertfordshire, England. It is now part of Hemel Hempstead. It is a district of mainly nineteenth century housing and meadowland, repeatedly cut through by transport links from London to the The Midlands....
in Hertfordshire, adjacent to what is now Hemel Hempstead station
Hemel Hempstead railway station
Hemel Hempstead railway station is on the West Coast Main Line, on the western edge of the town of Hemel Hempstead, Hertfordshire, England. The station is 39 km north-west of London Euston on the West Coast Main Line...
on the West Coast Main Line, is an example of a segmental arch of extreme obliquity that was designed by Buck and incorporates both of these features. Constructed in masonry, with a brick barrel, stone quoins and a 58° angle of skew, it was completed in 1837. Shortly before the railway opened the bridge was the subject of an ink and wash
Wash (painting)
thumb|Example of a wash drawing by [[R. G. Skerrett]].A wash is a painting technique in which a paint brush that is very wet with solvent and holds a small paint load is applied to a wet or dry support such as paper or primed or raw canvas. The result is a smooth and uniform area that ideally lacks...
drawing dated 12 June 1837, one of a series of works by artist John Cooke Bourne
John Cooke Bourne
John Cooke Bourne was an artist and engraver. He is best known for his lithographs showing the construction of the London and Birmingham Railway and the Great Western Railway. Each set of prints was published as separate books, and became classic representations of the construction of the early...
illustrating the construction of the line.
Buck's Essay, containing its criticism of Nicholson's work, was published in July 1839, just a few months before Nicholson's Guide to Railway Masonry, causing the ongoing paper war in The Civil Engineer and Architect's Journal to continue acrimoniously as Nicholson accused Buck of stealing his ideas
and Buck issued a counter-claim.
In 1840, Buck's assistant, the young engineer William Henry Barlow
William Henry Barlow
On 28 December 1879, the central section of the North British Railway's bridge across the River Tay near Dundee collapsed in the Tay Bridge disaster as an express train crossed it in a heavy storm. All 75 passengers and crew on the train were killed...
entered the fray, initially signing himself cryptically W.H.B.,
but eventually declaring publicly his strong support for Buck.
Nicholson, by this time aged 75 and his health failing, had been struggling financially since the bankruptcy of one of his publishers in 1827 and he was in desperate need of the revenue he hoped to receive from sales of his Guide.
While both Fox and Buck had been happy to acknowledge Nicholson's work and had fought a mostly intellectual battle, Barlow's attacks became less gentleman
Gentleman
The term gentleman , in its original and strict signification, denoted a well-educated man of good family and distinction, analogous to the Latin generosus...
ly and more personal
causing Nicholson, who later received anonymous public support from the mysterious M.Q.,
considerable distress.
Alternatives to the helicoidal method
The helicoidal method of laying down the stone or brick courses championed by Nicholson, Fox and Buck is only an approximation to the ideal. Since the courses are only square to the faces of the arch at the crown and deviate more from perpendicularity the closer they are to the springing line, thereby over-correcting the deficiencies of the false skew arch and weakening the obtuse angle,the mathematical purists recommend that helicoidal construction be restricted to segmental arches and not be used in full-centred (semicircular) designs.
Despite this there were many full-centred skew bridges built to the helicoidal pattern and many still stand, Kielder Viaduct
Kielder Viaduct
Kielder Viaduct consists of seven semi-circular masonry skew arches and was built in 1862 to carry the North British Railway across marshy land, which following flooding to create Kielder Water, became the place where Deadwater Burn joins Bakethin Reservoir...
and Neidpath Viaduct being just two examples.
Edward Sang's logarithmic method
Orthogonality
Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular.-Mathematics:In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle...
method of constructing a skew arch led to the proposal of the logarithmic method by Edward Sang
Edward Sang
thumb|right|Edward Sang Edward Sang was a Scottish mathematician, best known for having computed largetables of logarithms, with the help of his daughters...
, a mathematics teacher living in Edinburgh, in his presentation in three parts to the Society for the Encouragement of the Useful Arts between 18 November 1835 and 27 January 1836, during which time he was elected vice-president of the Society, though his work was not published until 1840.
The logarithmic method is based on the principle of laying the voussoirs in "equilibrated"
courses in which they follow lines that run truly perpendicular to the arch faces at all elevations, while the header joints between the stones within each course are truly parallel with the arch face.
While a helix is produced by projecting a straight line onto the surface of a cylinder, Sang's method requires that a series of logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
ic curves be projected onto a cylindrical surface, hence its name.
In terms of strength and stability, a skew bridge built to the logarithmic pattern has advantages over one built to the helicoidal pattern, especially so in the case of full-centred designs. However, the courses are not parallel, being thinner towards the most acutely angled quoin (located where the face of the arch makes an obtuse angle with the abutment in the plan view, at S and Q in the development to the left, and at the left hand side of the photograph of the intrados on the right) and thicker towards the most obtusely angled quoin (at O and G in the development and just off the right hand side of the photograph),
requiring specially cut stones, no two of which in a given course being the same, which precludes the use of mass produced bricks. Nevertheless, two courses beginning at opposite ends of the barrel at the same height above the springing line are exactly alike, halving the number of templates required.
In 1838, Alexander James Adie,
son of the famous optical instrument manufacturer of the same name
Alexander Adie
Alexander James Adie FRSE was a Scottish maker of medical instruments, optician and meteorologist. He was the inventor of the sympiesometer, patented in 1818....
,
as resident engineer on the Bolton and Preston Railway was the first to put the theory into practice,
building several skew bridges to the logarithmic pattern on that route, including the semi-elliptical Grade II listed
bridge number 74A that carries the line over the Leeds and Liverpool Canal
Leeds and Liverpool Canal
The Leeds and Liverpool Canal is a canal in Northern England, linking the cities of Leeds and Liverpool. Over a distance of , it crosses the Pennines, and includes 91 locks on the main line...
, which was formerly known as the southern section of the Lancaster Canal
Lancaster Canal
The Lancaster Canal is a canal in the north of England, originally planned to run from Westhoughton in Lancashire to Kendal in south Cumbria...
with the intention of connecting it to the northern section, though this was never achieved as the necessary aqueduct over the River Ribble
River Ribble
The River Ribble is a river that runs through North Yorkshire and Lancashire, in northern England. The river's drainage basin also includes parts of Greater Manchester around Wigan.-Geography:...
proved too expensive to build.
He presented a paper on the subject to the Institution of Civil Engineers
Institution of Civil Engineers
Founded on 2 January 1818, the Institution of Civil Engineers is an independent professional association, based in central London, representing civil engineering. Like its early membership, the majority of its current members are British engineers, but it also has members in more than 150...
the following year and in 1841, academic William Whewell
William Whewell
William Whewell was an English polymath, scientist, Anglican priest, philosopher, theologian, and historian of science. He was Master of Trinity College, Cambridge.-Life and career:Whewell was born in Lancaster...
of Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
published his book The Mechanics of Engineering in which he expounded the virtues of building skew bridges with equilibrated courses, but due to the poor complexity to benefit ratio, there have been few other adopters.
The French corne de vache method
Unlike the helicoidal and logarithmic methods, in which the intrados of the arch barrel is cylindrical, the corne de vache method results in a warped hyperbolic paraboloid
Paraboloid
In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point....
surface that dips in the middle, rather like a saddle.
Despite being known as the French method of skew arch building, it was actually introduced by English engineer William Froude
William Froude
William Froude was an English engineer, hydrodynamicist and naval architect. He was the first to formulate reliable laws for the resistance that water offers to ships and for predicting their stability....
whilst working under Isambard Kingdom Brunel
Isambard Kingdom Brunel
Isambard Kingdom Brunel, FRS , was a British civil engineer who built bridges and dockyards including the construction of the first major British railway, the Great Western Railway; a series of steamships, including the first propeller-driven transatlantic steamship; and numerous important bridges...
on the Bristol and Exeter Railway
Bristol and Exeter Railway
The Bristol & Exeter Railway was a railway company formed to connect Bristol and Exeter.The company's head office was situated outside their Bristol station...
, which opened in 1844.
Although no details of Froude's work in this area survive and despite being better remembered for his work on hydrodynamics, he is known to have built at least two overbridges in red brick with stone quoins using this principle on the line just north of Exeter
Exeter
Exeter is a historic city in Devon, England. It lies within the ceremonial county of Devon, of which it is the county town as well as the home of Devon County Council. Currently the administrative area has the status of a non-metropolitan district, and is therefore under the administration of the...
, at Cowley Bridge Junction where the A377 Exeter–Barnstaple road crosses at an oblique angle and, about 4 miles (6.4 km) to the northeast, at Rewe
Rewe
Rewe is a village and civil parish in the county of Devon in England. It lies on the river Culm, north of the city of Exeter and south of the town of Tiverton. Rewe is a linear village, with most of its buildings lying along the A396 road about north of the larger village of Stoke Canon...
, on the A396, both of which survive and are in daily use.
The brickwork is considerably more complex than in a helicoidal design and, in order to ensure that the courses of bricks meet the faces of the arch at right angles, many had to be cut to produce tapers.
The corne de vache approach tends to result in a structure that is almost as strong as one built to the logarithmic pattern and considerably stronger than one built to the helicoidal pattern but, again, the extra complexity has meant that the method has not seen widespread adoption, especially since the simpler helicoidal structure can be built much stronger if a segmental design is chosen, rather than a full-centred one.
The ribbed skew arch
Motivated by the lack of skilled stonemasons in the 18th century United States, the design was first proposed in 1802 for a crossing of the Schuylkill River
Schuylkill River
The Schuylkill River is a river in Pennsylvania. It is a designated Pennsylvania Scenic River.The river is about long. Its watershed of about lies entirely within the state of Pennsylvania. The source of its eastern branch is in the Appalachian Mountains at Tuscarora Springs, near Tamaqua in...
in Philadelphia by British-born American architect Benjamin Henry Latrobe
and later championed by French civil engineer A. Boucher.
Because the series of arch ribs are all regular arches this method of construction has the advantage of being less demanding of unskilled artisans but it has received considerable criticism as being weak, susceptible to frost damage, ugly and wasteful of materials.
Although Latrobe's bridge was never built as proposed, his method of construction was later to be used extensively by the Philadelphia and Reading Railroad throughout the Philadelphia area, including an ambitious viaduct designed by Gustavus A. Nicolls with six skewed spans of 70 feet (21.3 m) across the river and six more land-based skew arches, which was built close to the site of Latrobe's proposed bridge and completed in 1856.
Thanks to the reinforcing of the spandrel walls in 1935, the bridge continues to carry rail traffic to this day.
The Midland Railway
Midland Railway
The Midland Railway was a railway company in the United Kingdom from 1844 to 1922, when it became part of the London, Midland and Scottish Railway....
in the United Kingdom suffered from no such shortage of skilled workers but as part of its southern extension towards its London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
terminus at St Pancras
St Pancras railway station
St Pancras railway station, also known as London St Pancras and since 2007 as St Pancras International, is a central London railway terminus celebrated for its Victorian architecture. The Grade I listed building stands on Euston Road in St Pancras, London Borough of Camden, between the...
, it was faced with the need to cross Southdown Road in Harpenden
Harpenden
Harpenden is a town in Hertfordshire, England.The town's total population is just under 30,000.-Geography and administration:There are two civil parishes: Harpenden and Harpenden Rural....
at an extremely acute angle of approximately 25°,
a figure more acute than the theoretical limit of 25°40′ proposed by Buck, and requiring a bridge with a skew angle of 65°, a situation not unlike that faced by the London and Birmingham railway 30 years earlier at Denbigh Hall. This time the chosen solution was to build Southdown Road bridge
Southdown Road Skew Bridge
Southdown Road Skew Bridge is a ribbed skew arch railway bridge, which carries the Midland Main Line across Southdown Road in Harpenden, Hertfordshire...
as a ribbed skew arch, which opened for traffic in 1868 and was successfully widened in 1893 when the line was converted to quadruple track.
Despite the aforementioned criticisms of the design, the bridge is still standing and in daily use by express and commuter trains.
A smaller and less extremely skewed example is Hereford Road bridge
Hereford Road Skew Bridge
Hereford Road Skew Bridge is a disused railway bridge in Ledbury, Herefordshire. Built in 1881 to carry the Ledbury and Gloucester Railway across the Hereford Road at an angle of approximately 45°, it was built as a ribbed skew arch with stone spandrels and wing walls, and ribs of blue brick.The...
in Ledbury
Ledbury
Ledbury is a town in Herefordshire, England, lying east of Hereford, and south of the Malvern Hills.Today, Ledbury is a thriving market town in rural England. The town has a large number of timber framed buildings, in particular along Church Lane and High Street. One of Ledbury's most outstanding...
, Herefordshire, which was built in 1881 to carry the Ledbury and Gloucester Railway
Ledbury and Gloucester Railway
The Ledbury and Gloucester Railway , was a railway line in Herefordshire and Gloucestershire, England, running between Ledbury and Gloucester. It opened in 1885 and closed in 1964.-History:...
at an angle of approximately 45° across the Hereford Road, now a section of the A438.
The railway having closed in 1959,
it is now used as part of a footpath.
Notice that the two bridges in the photographs skew in opposite directions. Southdown Road bridge is said to have a left-hand skew due to the near face being offset to the left of the far face, while Hereford Road bridge has a right-hand skew.
Construction
A fine example of such construction is the famous Rainhill Skew Bridge, which was designed with a skew span of 54 feet (16.5 m), in order to give a clear span across the railway of 30 feet (9.1 m) at a skew angle of 56° by George Stephenson
George Stephenson
George Stephenson was an English civil engineer and mechanical engineer who built the first public railway line in the world to use steam locomotives...
and built as a full-sized wooden model in an adjacent field before being completed in 1830.
A contemporary skew bridge, built to carry the Haggerleazes branch of the Stockton and Darlington Railway over the River Gaunless in County Durham
County Durham
County Durham is a ceremonial county and unitary district in north east England. The county town is Durham. The largest settlement in the ceremonial county is the town of Darlington...
proved too difficult for the original contractors, Thomas Worth and John Batie who, after piling the foundations for the abutments and laying the lower courses of masonry, abandoned the work. The contract was re-let to James Wilson of Pontefract
Pontefract
Pontefract is an historic market town in West Yorkshire, England. Traditionally in the West Riding, near the A1 , the M62 motorway and Castleford. It is one of the five towns in the metropolitan borough of the City of Wakefield and has a population of 28,250...
on 28 May 1830 for £420, an increase of £93 over the original tender. As the principles were not completely understood the work continued to prove difficult and its imminent collapse was solemnly predicted right up until the time, a few days before the opening of the branch, the centring was removed and the crown of the arch settled by less than half an inch (13 mm).
Examples of skew arch bridges
- Finlay Bridge, Naas, County Kildare by William Chapman (Kildare Canal, 1787).
- Store Street AqueductStore Street AqueductThe Store Street Aqueduct in central Manchester, England was built in 1798 by Benjamin Outram on the Ashton Canal. A Grade II* listed building it is built on a skew of 45 degrees across Store Street, and is believed to be the first major aqueduct of its kind in Great Britain and the oldest still in...
, Manchester by Benjamin Outram (Ashton Canal, 1798). - Rainhill Skew Bridge, Merseyside by George Stephenson (Liverpool and Manchester RailwayLiverpool and Manchester RailwayThe Liverpool and Manchester Railway was the world's first inter-city passenger railway in which all the trains were timetabled and were hauled for most of the distance solely by steam locomotives. The line opened on 15 September 1830 and ran between the cities of Liverpool and Manchester in North...
, 1830), the first skew bridge to carry a road over a railway. - Haggerleazes bridge over the River Gaunless near Cockfield, County Durham, by Thomas Storey (Stockton and Darlington Railway, 1830), the first skew bridge to carry a railway over a river.
- The viaduct between London Bridge and Greenwich stationsLondon Bridge – Greenwich Railway ViaductThe London Bridge – Greenwich Railway Viaduct consists of a series of nineteen brick railway viaducts linked by road bridges between London Bridge railway station and Deptford Creek, which together make a single structure in length. The structure carries the former London and Greenwich Railway...
(London and Greenwich RailwayLondon and Greenwich RailwayThe London and Greenwich Railway was opened in London between 1836 and 1838. It was the first steam railway to have a terminus in the capital, the first of any to be built specifically for passenger service, and the first example of an elevated railway....
, 1834–1836), a long and complex structure, which has subsequently been widened on both its southern (1842) and northern (1850) sides, and also extended westwards to Charing Cross (1864) and northwards to Cannon Street (1866). Helicoidal skew brickwork is visible at several locations where it spans existing roads that cross the line at oblique angles. - Allegheny Portage Railroad BridgeAllegheny Portage RailroadThe Allegheny Portage Railroad was the first railroad constructed through the Allegheny Mountains in central Pennsylvania, United States. It was a series of 10 inclines, approximately long, and operated from 1834 to 1854...
(1834–1854). - Boxmoor Railway Bridge, adjacent to what is now Hemel Hempstead station, Hertfordshire by George W. Buck (London and Birmingham Railway, 1836–1837), a brick arch with stone quoins and a 58° angle of skew built to a very high standard of workmanship by contractors W. and L. Cubitt of London.
- Yalesville UnderpassYalesville UnderpassThe Yalesville Underpass is a 30 degree skew arch bridge carrying the railroad over Route 150 close to its intersection with Route 71 in Wallingford, Connecticut. Built in 1838 for the railroad by William MacKenzie, it is reported to be the first underpass in America...
, Wallingford, Connecticut by William MacKenzie (1838). - Leeds and Liverpool Canal bridge number 74A, near Chorley, Lancashire by Alexander J. Adie (Bolton and Preston Railway, 1838), built to Sang's logarithmic pattern.
- Moulsford Railway BridgeMoulsford Railway BridgeMoulsford Railway Bridge, known locally as "Four Arches" bridge is actually a pair of parallel bridges located a little to the north of Moulsford and South Stoke in Oxfordshire, UK. It carries the Great Western Main Line from Paddington, London to Wales and the West across the River Thames...
, Oxfordshire by Isambard Kingdom Brunel (Great Western RailwayGreat Western RailwayThe Great Western Railway was a British railway company that linked London with the south-west and west of England and most of Wales. It was founded in 1833, received its enabling Act of Parliament in 1835 and ran its first trains in 1838...
, 1838–1839), widened by the building of an adjacent parallel bridge in 1892 to carry a second pair of tracks. - The original West Bridge over the River Avon adjacent to Bath (Spa) station by Isambard Kingdom Brunel (Great Western Railway, 1840), comprising two 80 feet (24.4 m) span skew arches made from laminated timber ribs. It was replaced with the present wrought iron skew lattice girder bridge between 1875 and 1878, using the original abutments and central pier.
- Monkhide Skew Bridge, Monkhide, Herefordshire by Stephen Ballard (Herefordshire and Gloucestershire CanalHerefordshire and Gloucestershire CanalThe Herefordshire and Gloucestershire Canal is a canal in the west of England, which ran from Hereford, the county town of Herefordshire to Gloucester the county town of Gloucestershire, where it linked to the River Severn...
, 1843). - Rewe Skew Bridge, Rewe, Devon by William Froude (Bristol and Exeter Railway, 1844), one of possibly only two examples in Britain of the corne de vache method of brick construction pioneered by Froude, the other being at Cowley Bridge Junction on the same line.
- Rochdale CanalRochdale CanalThe Rochdale Canal is a navigable "broad" canal in northern England, part of the connected system of the canals of Great Britain. The "Rochdale" in its name refers to the town of Rochdale, Greater Manchester, through which the canal passes....
Bridge and Castle Street Bridge, Rusholme, Manchester (Manchester, South Junction and Altrincham RailwayManchester, South Junction and Altrincham RailwayThe Manchester South Junction and Altrincham Railway was a suburban railway which operated a 13.7 km route between Altrincham in Cheshire and London Road Station in Manchester....
, 1849). These are contiguous skew spans, each of six cast iron spandrels, carrying the railway line used by the Manchester to PrestonManchester to Preston LineThe Manchester to Preston Line runs from the city of Manchester to Preston, Lancashire. It is largely used by commuters entering Manchester from surrounding suburbs and cities, but is also one of the main railway lines in the North West and is utilised by intercity services for Scotland and the...
and the Liverpool to ManchesterLiverpool to Manchester LinesThere are two Liverpool to Manchester railway lines between the cities of Liverpool and Manchester in the North West of England. The 'Northern Route' via and to either or follows the route of the original Liverpool and Manchester Railway...
services adjacent to Deansgate stationDeansgate railway stationDeansgate is a railway station in Manchester city centre, England. It is situated approximately west of Manchester Piccadilly in the Castlefield area, at the junction of Deansgate and Whitworth Street West....
. - Yarm Viaduct, Yarm, North Yorkshire by Thomas GraingerThomas GraingerThomas Grainger FRSE was a Scottish civil engineer and surveyor. He was born in Ratho, outside Edinburgh, to Hugh Grainger and Helen Marshall. Educated at Edinburgh University, at sixteen he got a job with John Leslie, a land surveyor.He started his own practice in 1816. In 1825 he formed a...
and John Bourne (Leeds Northern Railway, 1849–51), has two stone skew arches where it spans the river Tees and 41 brick right arches. - Schuylkill River Viaduct, Fairmount Park, Philadelphia by Gustavus A. Nicolls (Philadelphia and Reading Railroad, 1856), a ribbed skew viaduct made of stone.
- Kielder ViaductKielder ViaductKielder Viaduct consists of seven semi-circular masonry skew arches and was built in 1862 to carry the North British Railway across marshy land, which following flooding to create Kielder Water, became the place where Deadwater Burn joins Bakethin Reservoir...
, Kielder, Northumberland by John Furness Tone (North British RailwayNorth British RailwayThe North British Railway was a Scottish railway company that was absorbed into the London and North Eastern Railway at the Grouping in 1923.-History:...
, 1862), a stone skew viaduct constructed in line with Nicholson's instructions. - Puente de los FrancesesPuente de los Franceses (Madrid)The Puente de los Franceses railway viaduct is located in Madrid . Comprising five semi-circular brick skew arches, it was built in the second half of the nineteenth century to carry the railway line from the north across the river Manzanares.- Toponymy :The bridge is named after the nationality...
, Madrid (Compañía de los Caminos de Hierro del Norte de España, 1862), a brick railway viaduct with five full-centred skew arches and stone quoins. - Neidpath Viaduct, Neidpath, Peeblesshire by Robert Murray & George Cunningham (Caledonian RailwayCaledonian RailwayThe Caledonian Railway was a major Scottish railway company. It was formed in the early 19th century and it was absorbed almost a century later into the London, Midland and Scottish Railway, in the 1923 railway grouping, by means of the Railways Act 1921...
, 1864). - Lyne ViaductLyne ViaductLyne Viaduct is a viaduct at Lyne in the Scottish Borders of Scotland. It consists of three stone skew arches and a plate girder approach span over a minor road and was built to carry the Symington to Peebles branch line of the Caledonian Railway over Lyne Water to the west of Peebles...
, Lyne, Peeblesshire (Caledonian Railway, 1864). - Southdown Road Skew BridgeSouthdown Road Skew BridgeSouthdown Road Skew Bridge is a ribbed skew arch railway bridge, which carries the Midland Main Line across Southdown Road in Harpenden, Hertfordshire...
, Harpenden, Hertfordshire by Charles Liddell and William H. Barlow (Midland Railway, 1868), a ribbed skew arch built of brick. - Jackson Street Bridge, Silver Creek, New York (1869).
- Hereford Road Skew BridgeHereford Road Skew BridgeHereford Road Skew Bridge is a disused railway bridge in Ledbury, Herefordshire. Built in 1881 to carry the Ledbury and Gloucester Railway across the Hereford Road at an angle of approximately 45°, it was built as a ribbed skew arch with stone spandrels and wing walls, and ribs of blue brick.The...
, Ledbury, Herefordshire (Ledbury and Gloucester Railway, 1881), a ribbed skew arch made of stone and blue brick. - Seventh Street Improvement ArchesSeventh Street Improvement ArchesThe Seventh Street Improvement Arches are a double-arched masonry highway bridge that formerly spanned the St. Paul and Duluth Railroad tracks in St. Paul, Minnesota. The Seventh Street Improvement Arches are historically significant for its rarity and the technically demanding nature of its...
, Saint Paul, Minnesota by William A. Truesdell (St. Paul and Duluth RailroadSt. Paul and Duluth RailroadThe St. Paul and Duluth Railroad was reorganized from the Lake Superior and Mississippi Railroad in 1877. It was bought by the Northern Pacific in 1900...
, 1883–1884), a pair of helicoidal semicircular masonry arches with a skew angle of 27°. - Colorado Street BridgeColorado Street Bridge (Saint Paul, Minnesota)The Colorado Street Bridge also known as Bridge No. L-8803 is a masonry and brick arch bridge in Saint Paul, Minnesota's West Side neighborhood. It is wide and consists of a single oblique span of that was built with the arch courses running parallel to the abutments, leading to a weaker...
, Saint Paul, Minnesota, by Andreas W. Munster (1888), a false skew arch built with the stone courses parallel to the abutments. - Sickergill Skew Bridge, near Penrith, Cumbria by George Joseph Bell, County Surveyor (a post previously held by Peter Nicholson) and Bridge Master of Cumberland (Raven Beck at Renwick, 1898), a single arch masonry skew bridge that is interesting for having been photographed during construction.
- Stanford ViaductStanford Viaductthumb|rightStanford Viaduct is a railway viaduct in Leicestershire and Nottinghamshire. It is named after the nearby village of Stanford on Soar....
, near Loughborough, Leicestershire (Great Central RailwayGreat Central RailwayThe Great Central Railway was a railway company in England which came into being when the Manchester, Sheffield and Lincolnshire Railway changed its name in 1897 in anticipation of the opening in 1899 of its London Extension . On 1 January 1923, it was grouped into the London and North Eastern...
, 1899), a blue brick structure, the three central arches of which are skewed in order to cross the River Soar. - Bradenham Road Bridge, near High Wycombe, Buckinghamshire (Great Western and Great Central Joint RailwayGreat Western and Great Central Joint RailwayThe Great Western and Great Central Joint Railway was a joint venture supported by the Great Western Railway and Great Central Railway and run by the Great Western and Great Central Joint Committee. The original arrangement was agreed between the two companies in September 1898...
, 1905), a ribbed skew arch built of blue brick, which carries the Chiltern Main LineChiltern Main LineThe Chiltern Main Line is an inter-urban, regional and commuter railway, part of the British railway system. It links London and Birmingham on a 112-mile route via the towns of High Wycombe, Banbury, and Leamington Spa...
over the A4010 road. - Beneath Springfield Road in SwindonSwindonSwindon is a large town within the borough of Swindon and ceremonial county of Wiltshire, in South West England. It is midway between Bristol, west and Reading, east. London is east...
, United Kingdom, the disused Midland and South Western Junction RailwayMidland and South Western Junction RailwayThe Midland and South Western Junction Railway was, until the 1923 Grouping, an independent railway built to form a north-south link between the Midland and London and South Western Railways allowing the Midland and other companies' trains to reach the port of Southampton.-Formation:The M&SWJR...
has a complex bridge consisting of a normal arch and a skew arch butted together; the brick courses in the roof change from normal to helical approximately two-thirds of the way through. This accommodates a road junction above.
External links
- Misoblikva arkaĵo – Esperanto translation of this page
- Brick bridges: Skewed bridges – Southern E-Group's Railway Structures section, Skewed Brick Bridges page
- Skew Arch, Yeovil - Southern E-Group's Railway Structures section, Yeovil Skew Arch page