1 Mr T H Saarinen – ts282@bath.ac.uk

A CRITICAL ANALYSIS OF THOMAS TELFORD’S CRAIGELLACHIE BRIDGE, SCOTLAND

T. H. Saarinen1

1Undergraduate Student, The University of Bath

Abstract: This paper discusses the origins and modifications made to Thomas Telford’s Craigellachie Bridge. Aesthetic analysis and historical context are discussed with respect to the main material, cast iron. Structural analysis is carried out on the overall structure, with recommendations made towards deciding a weight restriction. Future changes have also been suggested in order to prolong the lifespan of this civil engineering landmark.

Keywords: Craigellachie, Thomas Telford, Cast Iron, Arch, Spandrel Lattice.

1 Introduction

Thomas Telford (1757-1834) needs no introduction as an innovator in the field of civil engineering, leaving a vast legacy of roads, bridges, canals and harbours. In 1802, Telford reported that the lack of bridges and the poor condition of the Scottish Highland roads were the greatest weaknesses in the area’s communications, affecting local commerce and inducing emigration of residents [1]. The main purpose of these roads were to provide a transport network between the west coast and the Caledonian Canal, another project of Telford’s. As part of this extensive Highland roads improvement project, Craigellachie Bridge (Fig. 1) was built between 1812-1815, and stands as one of a few remaining cast iron spandrel lattice arch bridges. Spanning 45.7m with a rise of 6.2m, the bridge consists of 4 trussed rib arches of constant 0.9m thickness, with a spandrel lattice consisting of cruciform-shaped struts transferring loading from the deck plates to the arches. The structure is framed by two 15m high masonry abutment towers, complete with arrow slits and castellated battlements. By the 1960s, the bridge was suffering from the effects of 150 years of service particularly from the use of military vehicles during World War II, and was subsequently re-built between 1963-1964. A 14 ton vehicle restriction was placed, and the bridge was by-passed by a reinforced concrete bridge in 1972, currently serving as a pedestrian bridge. In 2007 the bridge was acknowledged as a civil engineering landmark by the ICE and ASCE, as a monument to Thomas Telford’s work. It is a Category A listed structure.

Figure 1: Craigellachie Bridge

2 Aesthetics

The aesthetics of any bridge are complex and subjective, however they may be described by using the principles set out by Fritz Leonhardt’s influential work ‘Bridges’. It should be noted that even if all ten rules are adhered to, a ‘beautful’ bridge may not be created. They do however offer guidance in communicating a bridge’s aesthetic merit. Craigellachie Bridge’s main structural form can clearly be recognised as the sweeping arch spanning the whole width of the River Spey underneath. This arch of constant width and radius is complemented by the slight arch created in the bridge deck, together splaying out towards the abutments revealing the spandrel lattice. The proportions of the members clearly identify the progression of the structural layers; loading is carried from the bridge deck, through the spandrels, into the arch and finally carried into the abutments as thrust. The spandrel lattice helps create order within the structure. The lattice naturally decreases in height from the abutments to the center span, with the spacing appearing justifiable. This size variation is aided with the criss-crossing lattice being connected at their points

Proceedings of Bridge Engineering 2 Conference 2011 April 2011, University of Bath, Bath, UK

of intersection, allowing a smoother line of sight to be followed across the bridge. Viewing the lattice at oblique angles (Fig. 2) may create a complicated geometry due to the overlapping of the lattices, however this has been softened by the use of a light colour, therefore emphasising the outermost layer of spandrels. This colour creates different effects according to the season – in the snowy Scottish winter, the bridge can almost disappear into its surroundings, however autumn the colour emphasises its prominence within its vegetated surroundings.

Figure 2: Oblique view of spandrel lattice

The spandrel members are cruciform-shape in section, a possible refinement to enhance efficiency in strength, allowing slender members to be used. It is interesting however that the mid-height transverse members are circular in section, perhaps to soften the complicated geometry created by the cast iron lattice – however this diversity in section shapes seems almost clumsy, or unnecessary. The deck arch helps reduce the severity of the rise of the main structural arch, creating the illusion the bridge is spanning further than it actually is. The deck depth is perhaps somewhat exaggerated by the beam kerb installed during its 1963 reconstruction. Older portrayals show a much more refined, delicate looking structure, appearing considerably thinner in the middle. The orientation of the abutment face to match the angled lattice proves an elegant design solution, certainly helping the thrust from the structure to be transmitted uniformly. A vertical faced abutment, as seen in later lozenge-lattice arch bridges, would have been an unconvincing visual outcome. The heavy, turreted abutments root the bridge to its surroundings, also helping to frame the bridge along the river. The turrets compliment the bridge’s steep and rocky northern bank, while appearing to grow out of the vegetation. They are not too tall as to obstruct or overcome the arched form of the main bridge structure. However, as the castellated form is somewhat faked or untrue to the time it was built, they may be viewed as crude misrepresentations (Fig. 3). The two main materials, stone and cast iron, create a suiting juxtaposition through the use of texture. The natural ruggedness of the stone abutments

is well contrasted with the smooth, more engineered cast iron. This helps to identify each material’s purpose – the more delicate-looking cast iron spanning the river, transfering loads into the heavy, rooted abutments along the banks.

Figure 3: Turreted abutments

The structure, together with its clearly identifiable long history, helps create vast amounts of character. The use of cast iron helps it both integrate into its immediate environment and reminds one of its industrial beginnings. 3 Cast Iron Cast iron is produced by melting pig iron and other constituents such as scrap iron, and casting the molten mixture into desired shapes. The outcome is a metal with high carbon content (2-5% wt), high concentration of silicon, and a greater concentration of impurities than steel [2]. The high carbon content lowers the overall melting point, allowing for easier casting. It also gives cast iron its high compressive strength, however graphite inclusions induce voids or cracks in the iron matrix, leading to a low tensile strength. Further defects include differential cooling rates due to non-uniform member sizes causing residual stresses. Impurities picked up during casting also vary the overall quality. The behaviour of cast iron is often described as ductile in compression and brittle in tension, causing it to have an undefined yield point in the stress-strain relationship [3]. It has a relatively low resistance to impact due to its brittle nature, meaning that it is likely to fracture under cyclic loading. Any defects in the castings are likely points of weakness under impact loads. Early cast iron was in the form of grey cast iron, with a high carbon equivalent content produced through a low cooling rate, and essentially having no alloying content. Defects such as ‘blowholes’, caused by trapped air against mould faces have a large effect on the overall strength of the member, and were often filled to mask the visible defect. These highlighted defects meant that the quality of cast iron varied even within a single project, and eventually led to the inclusion of the higher factors of safety for cast iron structural design.

4 Cast Iron Bridge Development The use of cast iron as the primary material in bridges lasted for a relatively short period of time, when compared with its descendants such as wrought iron and steel. Prior to to the 18th Century, the production of iron had been restricted by the requirements for large amounts of expensive charcoal. In 1709, Abraham Darby I discovered that coke may be used instead of charcoal, paving the way for large scale cast iron production. However, the use of cast iron as a structural material in Britain did not develop until the later half of that century, with cast iron bridge design first mastered in the Ironbridge (1779) across the River Severn [4]. Early arched cast iron bridges were susceptible to cracking in their rib elements. Notable weak features included rectangular openings in the arch ribs, as well as vertical spandrel members transmitting loads to the arches as point loads. Indeed, confidence in the use of cast iron was at a low due to numerous defects or failures, notably John Rennie’s Boston bridge that required strapping across fractures, soon after its construction in 1801 [5]. One of Telford’s earliest attempts at designing a cast iron bridge culminated in the Buildwas Bridge, a low rise, three rib arch, supplemented by a Schaffenhausen-style arch contribution, influenced by Swiss timber construction principles. Although this last feature was never repeated, other features of the bridge such as bolted-flange connections of the road plates offering lateral stiffness, contributed well to his future designs, such as the Bonar bridge, discussed in the next section. 5 Structural Design The design of Craigellachie Bridge represents a fine use of cast iron in bridge design. First used by Telford in his Bonar bridge (1812), the design represented at its time a viable economic and efficient, portable type of bridge to be used in crossings which were impracticable to achieve by traditional stone designs. The lozenge-lattice arch design showed a great improvement in the use of cast iron, most notably the bridge was designed such that the arch ribs act as the main component transferring thrust into the abutments. The width of the ribs are sufficient in minimising the tension in the arches – a key consideration due to cast

iron’s low tensile strength, and shows a similar practice to that used in the design of masonry arches. Perforation of the arch rib has two key advantages. Firstly, it creates sections with similar sizings to allow equal cooling of the cast iron during production and thus reducing the aforementioned residual stresses. Secondly, perforation reduces the overall usage of cast iron reducing the cost and weight, allowing for its portable nature. This approach of reducing the weight of the members was also followed in the rest of the structure. The lateral grating located on top of the rib arches that provides stability, is perforated in much the same way. The cruciform-section shape of the lattice members also aids in reducing overall weight. Viewing the bridge in elevation (Fig. 4), the spandrel lattice appears light and somewhat unsubstantial. The connection of the straight lattice members allows the spread of loading into the arch more uniformly, showing improvements to the perpendicular or circular spandrel lattice forms seen in other bridges of the time. Lateral stability was provided by cross-bracing members in the spandrel lattice, located about every quarter span along the length of the bridge. Each spandrel member crossing was supported transversely with a solid circular cast iron tube. Further stability was provided in the form of the lateral grating spanning across the top of the arch ribs and through the flange-bolted road plates fixed to the top of the road bearers. The combination of the rib arch, the lateral grating, the lozenge-lattice the roadway bearers into the abutments created a frame-like structure (Fig. 5), allowing temperature effects to be accommodated.

Figure 5: Structural Components [16]

Figure 4: Elevation of the bridge [15]

6 Construction The bridge is located on a local constriction of the River Spey, caused by the underlying geology of the site. The main rock on the site is quartzite [6], which is of extreme hardness, owing to the cliff which rises out of the river and past the bridge on its northern side. The River Spey is a fast flowing river of high energy, prone to flooding even during the summer months. The bridge was therefore built higher than similar bridges by Telford, at a height of 3.7m above mean water level. This provision proved worthy, as the River Spey suffered heavy flooding in 1829, leading to the destruction of many other highland bridges. The casting of the iron work took place in Plas Kynaston iron works in Wales, by William Hazledine who had cast many other cast iron bridge’s of Telford’s. The arch ribs were cast in sections, while the diagonal lattice members were cast according to their location within the spandrel; shorter members towards the crown of the arch were cast in one piece, while longer ones were split up – the crossings were originally made up of two half-length members and one full-length member. The components were transported to site along the Ellesmere Canal and Pontcyssylte Aqueduct, and then by sea to Speymouth where the components were finally brought to site by wagon. The principal method of construction is somewhat unknown. It has been suggested that the bridge was assembled on pre-erected falsework, by in-situ centring [5]. However, site investigations have shown the site to have a deep pool within the river, and due to the hardness of the quartzite rock, may not have formed during the lifespan of the bridge [6]. Therefore other construction techniques suggest a rope or cable was used to tie back arch members, much like modern suspended cantilevered construction. The arch could then have been made rigid once all the members were in place. This would certainly justify the use of such substantial turreted abutments, as their main purpose would have been for this construction process. Alternatively, the cliff face on the northern side could have also been used for such a purpose. A further possibility is the filling in of the deep pool to allow the use of falsework – however this seems somewhat unlikely due to the river’s fast flowing nature and potential difficulties such as settlement causing movement of the centring. 7 Reconstruction After the flooding of 1829, little was written about the bridge until 1902, when the bridge was surveyed for the Road Board of the County of Elgin. The report concluded that the bridge was in good overall condition, except for the deck bearing plates. Repairs were made in the form of transverse spanning I-beams and a concrete filler in-between, to maintain a

similar distribution of weight over the bridge. Major reconstruction occurred between 1963-64, after the Joint Bridge board expressed concern over its condition. The inspection concluded that the arch ribs were still in good condition, however the spandrel lattice was starting to show signs of damage. Half-length diagonal lattice members had become loose, leaving the full-length continuous members to carry loading to the arch. Further, lattice members near the crown of the arch which were inclined close to horizontal, had broken due to the effects of shear and bending. New lattice members were manufactured out of mild steel, however they were put together in a different manner – four half-members were welded to central diamond-shaped piece of steel, forming the ‘X’ shape, as shown in Fig. 6. The external rows of spandrel members were replaced with a section consisting of two 44x12mm flat plates welded to a 100x75x12mm unequal angle section, to replicate the original aesthetic. The two inner rows consist only of the angle sections, to reduce overall cost of fabrication. They are orientated with their flat sides facing each other, such that little original aesthetic has been lost.

The new connection arrangement meant that all of the members would be carrying load, spreading the loading to the arch ribs more uniformly. The members were fixed into the original slots in the arch ribs, with any gaps filled with an epoxy resin. The tops of the struts were tied together with 150x75x10mm angle section members, replacing the original cast iron road bearers. The original deck plates were then bolted to the road bearers. Lateral stiffness was provided in the deck in the form of a reinforced concrete slab, with an average thickness of 282mm, replacing transverse I-Beams installed in 1902. A new kerb and handrail were also fitted, to comply with modern safety standards. Specimen of the original cast iron obtained during reconstruction showed that the quality of cast iron was especially high, with an ultimate tensile strength of 194 N/mm2, around 50% greater than common cast iron, and almost half that of modern structural steel. As mentioned before, the quality of castings within a structure can vary, however it is possible that Telford knew of the potential tensile risk within the structure, therefore specifying a higher quality of iron.

Figure 6: Lattice Joint detail, showing original (left)

and reconstructed (right)

8 Loading The following structural calculations are for the bridge in its reconstructed form, according to BS 5400-2:2006 [7], in conjunction with DMRB Part 3 BD 21/01: The assesment of highway bridges and structures [8]. The loading will be calculated in the form of dead, superimposed and live loading, with relevant partial load factors, !fl, applied depending on the load case. 8.1 Dead and Superimposed Dead Loads The overall dead load of the bridge was estimated as 4.11 MN, assuming the unit weight of cast iron to be 7250 kg/m3, steel as 7850 kg/m3 and reinforced conrete as 2400 kg/m3. This loading is made up of the 4 arch ribs, spandrel lattice, lateral grating, road plates, reinforced concrete slab and the lateral tubes, corresponding to a loading of 16.6 kN/m for one of the middle arch ribs. !fl for dead loading of cast iron bridges is 1.0. Superimposed dead loading was calculated as 2.66 kN/m for the surfacing material, including the !fl of 1.5 for superimposed loads. This was assuming a 50mm layer of tarmac, with a unit weight of 2400 kg/m3. The loading of the handrail and kerb were excluded as calculations are carried out for the middle arch ribs, which do not carry their load. Snow loading was also considered due to the latitude of the bridge, corresponding to a loading of 0.5 kN/m2, or 1.125 kN/m. 8.2 Live Loading Although currently serving as a footbridge, the bridge will be assessed to find the modern vehicular limit that should be imposed on it. This decision was taken as the bridge did take vehicular loading for a long period of time, and even though it has been bypassed by a modern reinforced concrete bridge, it would be interesting to find how the bridge interacts with loading from vehicles. 8.2.1 HA and KEL Loading HA live load is in the form a uniformly distributed load (UDL), calculated from eq (1) below.

W = 336 1L

!"#

$%&

0.67

= 25.95 kN/m (1)

A knife edge load (KEL) of 120 kN can be positioned to cause the most severe impact on the structure. These loadings correspond to a 40 tonne load level – if the structure fails, a suitable load restriction must be applied. HB loading is not covered and would not be suitable for this bridge due to its narrow width, the road’s right-angle turn at the north end of the bridge and the bridge’s historic nature.

8.2.2 Notional Lanes The width between the kerbs installed during the bridge’s reconstruction is estimated as being 3m, giving 1.5 notional lanes, with a main lane of 2.5m width carrying the full HA loading, and the remaining 0.5m carrying a nominal 5 kN/m2. 8.2.3 Pedestrian Loading For loaded lengths in excess of 36m, the pedestrian loading can be calculated as follows:

k = Nominal HA UDL !10L + 270

= 25.95!1045.7+ 270

= 0.82 (2)

UDL = k ! 5.0kN/m2 = 0.82! 5 = 4.11kN/m2

(3)

So for a pedestrian side walk of 0.75m, the loading is therefore 3.08 kN/m.

Figure 7: Transverse Measurements

9 Strength Assessment must be done on a permissible stress basis, with the maximum allowable stresses for cast iron stated in Table (1). The yield strength of the mild steel shall be taken as 230 N/mm2.

Table 1: Permissible Stresses in Cast Iron Stress Permissible Stress (N/mm2)

Compressive 154 Tensile 46 Shear 46

Analysis will take place on the key components of the bridge, namely the 200 year old cast iron arch ribs, the reconstructed mild steel spandrel lattice, the overall roadway and the ability of the whole structure to resist lateral loading and the effects of temperature. 9.1 Arch The arch will be analysed for the worst case loading of HA loading on half of the structure, with the KEL at quarter span. All of the loading is assumed to transfer through to the arch ribs, and the worst case occurs when one middle arch rib is taking all of the HA loading. The arch has been modelled as a two pinned parabolic arch, assuming that only live loading induces bending. The overall stresses can be calculated from the combination of axial forces and bending moments. Analysis will take place in three forms: hand calculations based on theoretical equations, graphical analysis using thrust lines and computational analysis on AutoDesk Robot Structural Analysis.

9.1.1 Theoretical Calculations The loading is as seen in Fig. 8. The maximum moment will occur at quarter span, and can be found through superposition of the UDL and the KEL contributions, as seen in eq. (4). This must be combined with the axial force at that point, found by using eq. (5).

Figure 8: Arch Loading

M =(wLive +wDead +wSuperimposed )L

2

64+ VA ,KELa ! H KELh( )

= 1426.4+159.6 =1586.0kNm

(4)

F =HTotal

cos!= 1428.4cos(13°)

=1466.0kN (5)

The cross-section of smallest area has been chosen to calculate the worst case effects, as seen in Fig. 9. The compressive and tensile stresses are calculated according to eqs. (6) and (7), respectively. These values are discussed in 9.1.4.

Figure 9: Forces on Cross-Section

!C =FCA

= 2251!103

144!113=138.3N/mm2

(6)

!T

FTA

= 1273!103

144!113= 78.2N/mm2

(7)

The loading is carried into the arch via the

spandrel lattice, at a total of 22 evenly spaced locations, deduced using Fig. 4. This therefore means that over a 45.7m span, each point load can be estimated to take a 2.1m stretch of road. Assuming the worst case to occur in conjunction with the KEL, the maximum point load is 217.3kN. The spandrel is connected only at locations in the arch rib where the cast iron is present throughout the cross-section, i.e. they are never above openings in the ribs. The shear stress can therefore be calculated, as seen in eq. (8).

! arch =217.3!103

113! 900= 2.14N/mm2

(8)

9.1.2 Thrust Line Analysis In order to draw the thrust line, the loading was split up into 8 point loads, half of which consisting of live load and dead load, and the other purely with dead loading. Upon calculating the horizontal reaction of the parabolic arch, a trial funicular polygon was drawn, after which the final polygon and line of thrust could be deduced. Fig. 10 shows the final construction. AutoCAD was used for this process for greatest accuracy. The maximum moment has been calculated in eq. (9) using the maximum eccentricity of the thrust line and the horizontal reaction force. The axial force has been calculated in eq. (10).

Figure 10: Thrust Line Analysis

M = He = 2327.5! 0.654 =1522.2kNm (9)

F = Hcos!

= 2327.5cos15°

= 2409.6kN (10)

These correspond to a compressive stress of 153.3 N/mm2 and a tensile stress of 54.6 N/mm2. The shear stress due to the heaviest load is 4.6 N/mm2. It should be noted that although the thrust line deviates from the thickness of the arch, this is a very heavy load case. The construction of a thrust line with the dead loads only show how the thrust line stays within the middle third of the arch width [9], showing the influence of masonry arches in Telford’s intuitive arch shape. 9.1.3 Robot Analysis The arch was set up with the same loading as shown in Fig. 8, yielding a maximum moment of 1302.27 kNm and a total axial force of 1460.0 kN. The compressive stress was therefore calculated as 118.8 N/mm2 and the tensile stress as 59.0 N/mm2.

Figure 11: Bending Moment Diagram from Robot

9.1.4 Comparison of Results The different analysis methods all show that the cast iron fails in tension but is acceptable in both compression and shear. This is an expected result as this is the worst case loading, corresponding to a modern 40 tonne truck, whereas a 14 ton limit was placed on the bridge in 1964. The live load restriction can be calculated using eq. (11), where the worst case tensile stress governs the restriction.

C = Available live load capacityLive load capacity required for HA Loading

= 46N/mm 2

78.2N/mm 2 = 0.588 (11)

Assuming the surface of the road to be in

good condition, and a low HGV traffic flow, BD 21/01 therefore recommends an 18 tonne restriction, with a reduction factor of 0.54 for the live loads. By applying this reduction to the HA and KEL loadings, and carrying out the analysis again in Robot, the maximum compressive stress is 70.6 N/mm2 and the maximum tensile stress is 23.9 N/mm2, both well under the allowable limit. This shows that the arch is capable of taking this loading, however, the rest of the structure may not be able to do so – this must now be assessed. 9.2 Spandrel Lattice 9.2.1 Buckling Depending on the location of axle loads along the bridge, the spandrel lattice behaves in different ways. Loading occurring at the beginning of the bridge is taken by the longer, more vertical spandrel members, causing compression within them axially. Therefore there is a risk of buckling – Fig. 12a shows a loading arrangement for an 18 tonne load limit, causing a wheel load of 90kN. It is assumed that the members are restrained at mid-height by adjoining members, therefore reducing their effective length. The Euler buckling load has been calculated in Eq. (12).

PE = ! 2EILeff2 = ! 2 ! 205!103 !1.89!106

25002

= 611.8kN >> 90kN

(12)

As the spandrel members in the inner rows are angled members, this means that loading will be applied with an eccentricity, causing a combination of bending and axial compression, Fig. 12b. The rough extent of this effect has been calculated by first finding the slenderness ratio in eq. (13), and then using the interaction formula eq. (14), from BS5590-1:2000 [10].

! =Leffrmin

= 250015.9

=157.2 ! pc = 70N/mm2

(13)

FApc

+M x

pbS x+M y

! y Z y

<1.0

90!103

1970! 70+ 0+ 14.3! 90!103

275!103 !16.5!103

= 0.653<1.0

(14)

This calculation assumes the bolt connection to occur such that zero moment is induced in the x-x axis, however gives an indication of the suitability of the member. These calculations are highly dependent on the members being restrained at mid-point – a loose connection would mean a greater risk of buckling. 9.2.2 Bending & Shear Loads concentrated towards centre span create bending in the lattice members, as the load becomes more and more perpendicular to the member. This also increases the shear – the combination of these effects saw the fracture of some of the original cast iron members. As the member’s angle to horizontal decreases closer to midspan, the intensity of the tensile force within the road bearer also increases. The transfer of loading to the arch is therefore less perpendicular, so loads are not transferred as such intense point loads. Fig. 12c shows the loading towards the crown of the arch, and Fig. 12d shows the loading towards the abutments – it is clear to see that loads are transformed more uniformly where spandrel members are inclined more towards the vertical. 9.2.3 Connections with the arch rib The spandrel members are fixed to the original arch rib pockets, in a mortice and tenon joint manner. During the reconstruction these were purposefully made increasingly fixed with the aid of an epoxy resin, so that the transfer of loading is more efficient through the structure – loose connections create redundancy of members. The arrangement of the lattice leads to secondary stresses being induced from the accompanying member in the rib pocket joint, meaning that the overall interaction between the members is complex – which would require a detailed computational analysis to be undertaken.

Figures 12a, b c & d: Lattice Diagrams

9.2.4 Lateral Restraint The lattice is restrained by the 75mm diameter lateral tubing at mid-height, halving the effective length thus reducing the risk of buckling transversely. Interestingly, original designs for Bonar bridge showed restrain longitudinally at mid-height. This would further have reduced the risk of buckling, however was probably omitted due to the complexity created in the connections. 9.3 Roadway 9.3.1 Road Bearers The road bearers have been modelled longitudinally for half of the bridge, by taking their connection with the spandrel lattice as supports, as seen in Fig. 13. The reduced HA has been applied over the whole span and wheel loading has been placed mid-span between a set of supports.

Figure 13: Roadbearer Loading & BMD

! = MyI

= 33.82!106 ! 75

50.5!106= 50.2N/mm2

(15)

If one of the supports is to be removed, thus modelling the redundancy of a spandrel member and hence doubling the span the road bearer has to take, the maximum moment becomes 76.84 kNm, leading to a stress of 114.1 N/mm2. These values are all below the yield stress of steel, however the connections have not been considered. In the original design, these were a weak point as the transfer of loading was not always efficient and the cast iron material was not always sufficient in tension. The details of the current connections are unknown to the author, thus further calculations have not been undertaken. The concrete slab may also offer longitudinal stiffness. 9.3.2 Transverse loading

The roadway consists of the road surface, reinforced concrete slab, the deck plates and the road bearers. The deck plates are mostly original, arranged in pairs along the length of the bridge, bolted together by upturned flanges. The loading has been transformed to correspond to a metre length of bridge, as seen in Fig. 14. It has been assumed that the new reinforced concrete slab takes the transverse loading, due to its relative depth compared with the deck plates and its reinforced nature.

Figure 14: Transverse Loading and BMD

! = MyI

= 41.59!106 !141

1.869!109= 3.13N/mm2

(16)

Any tension would be taken by reinforcement

steel, the nature of which is unknown. As the slab is the key component in resisting transverse loading, it should be thoroughly inspected and tested to deduce an appropriate load restriction. 10 Wind The forces due to wind can be calculated according to Ref. [7], and are especially governed by the bridge’s location within the UK, its exposed area and the topography of the surrounding area. However, the wind calculations in eqs. (17) to (19) only give a rough indication of the effects of wind. Dynamic Pressure:

q = 0.613Vd2 = 0.613! S gVs( )2= 0.613! 1.793! 23.25( )2 =1065.3N/m2

(17)

Nominal Transverse Wind Load:

PT = qA1CDT =1065.3! 54.5!1.1= 63.9kN =1.40kN/m

(18)

Nominal Vertical Wind Load (assuming inclination of 0°):

PV = ±qA3CL = ±1065.3! 205.65! 0.413= ±90.37kN = ±1.98kN/m

(19)

Nominal longitudinal loading has been

disregarded as the bridge has no prominent vertical features, except for the masonry abutments which due to their shape and substantial nature are unlikely to be affected by wind. The vertical loading of 1.98 kN/m has a small effect when acting downwards adding a compressive stress of 2.11 N/mm2 and a tensile stress of 1.46 N/mm2 to the arch. Any uplift is countered by the bridge’s self-weight.

Transverse loading is resisted primarily by the 125x125mm (5x5in) cruciform-section cross-bracing members. Assuming each cross-bracing system to take a quarter-span worth of transverse wind loading and

being inclined at a maximum of 45°, this corresponds to a force of 22.6 kN being transferred into a single member. Due to their large cross-section and low loading in comparison with the spandrel members, it is safe to assume they are sufficient to resist this load. Indeed, the sufficiency of the original bracing was tested at Telford’s Bonar bridge on two occasions [11]; firstly, from a collision with fir-trees consolidated in ice, and the secondly from a collision of a small ship’s masts. The lateral stability proved sufficent enough to destroy the masts, leaving the bridge structure intact. 11 Temperature Effects Temperature effects may be described according to Ref. [7], in two main ways; firstly, overall temperature changes causing thermal expansion of components, and secondly, differences in temperature between the top surface and other levels in the deck. The maximum and minimum air shade temperatures were found to be 36°C and -22°C, respectively. The bridge was erected between August-September 1815 [5], so the outside temperature is assumed to have been 15°C, giving temperature changes of 21°C and -37°C. The effects are shown in Table 2.

Table 2: Temperature change effects

Component (Length)

Thermal coefficient

(/°C)

Strains (µ!)

Extensions (mm)

Arch (47.9m) 10.2x10-6

(Cast iron)

214.2 (max) -377.4 (min)

10.3 (max.) -18.1 (min.)

Spandrel Member (2.5m)

0.54 (max.) -0.95 (min.)

Deck (45.7m)

12x10-6 (Steel)

252 (max) -444 (min)

11.5 (max.) 20.3 (min.)

The nominal compressive stress for the cast iron components are 19.28 N/mm2 in compression and 34.0 N/mm2 in tension. The expansion of the arch increases thrust into the abutments, due to the compressive stress. Combining with the 18 tonne restriction loading, the total compressive stress in the arch becomes 89.9 N/mm2 due to thermal expansion, and the total tensile stress becomes 57.9 N/mm2 due to thermal contraction. Of course, this would only be when combined with the worst case loading outlined, and the full extent of the temperature changes would have to be investigated to place a suitable load restriction. Thermal expansion of the spandrel members would increase the loading into the arch and the deck. Looseness of the arch rib pocket connections may have been to accommodate for this. Thermal contraction however, may have caused the original members to

come loose at mid-height, leading to the redundant members. To calculate the effects of temperature differential through the deck, the bridge has been modelled as a Group 3 construction, meaning a concrete deck on a truss, as seen in Fig. 15.

Figure 15: Temperature Differential

The maximum extra compressive stress in the concrete slab is therefore 2.52 N/mm2 (from a temperature increase of 15°C and assuming it is restrained), and combining with the stress from transverse loading leads to an overall stress of 5.65 N/mm2, well within the compressive strength of most concretes. 12 Natural Frequency Calculation of dynamic effects on bridges are becoming increasingly important in bridge engineering, especially for pedestrian bridges. Vibrations can be quantified by calculating a bridge’s natural frequency, according to eq. (20) from Ref. [12].

F0 =K 2

2!L2EIm

(20)

Where: F0 = Fundamental natural frequency

K = " for simple supports, or 4.730 for built-in supports.

L = Span EI = Flexural stiffness in vertical bending

m = Mass per unit length, not including live loads.

This method has been derived for beam bridges, so the flexural stiffness has been estimated at three key locations so a range of natural frequencies could be found. The end conditions are also ambiguous, so both K values have been used. E has been taken as 90x109 N/m2, L as 45.7m and m as 1725 kg/m.

Table 3: Natural Frequencies

Location I-value (m4)

Simply supported freq. (Hz)

Fixed supports freq. (Hz)

Near abutments 28.683 29.1 65.96 Quarter span 5.08 12.24 27.8

Mid-span 2.798 9.09 20.6

A low natural frequency (<5Hz) leads to vibrations in the structure, which are undesired especially due to cast iron’s brittle nature. A high natural frequency (>75Hz) can cause discomfort for the pedestrian user. The natural frequencies found in Table 3 lie within the desired range, however the arch will inevitably behave in a stiffer manner, due to the compression present. Therefore the natural frequency may be larger than these values, implying the potential for a frequency greater than the 75Hz threshold. Of course, thorough computational modelling would need to take place to quantify the full effect. 13 Future Improvements The reconstruction efforts have prolonged the lifespan of the bridge, showing a great example of restoration without loss of character, however the use of mild steel in the spandrel lattice could be viewed as being insincere from a material point of view. The allowable limit of 14 tons placed in 1964 seems quite arbitrary, but calculations have shown the difficulty in knowing the extent of the axle loads on the spandrel lattice as well as the adequacy of the reinforced concrete slab. The current usage for the bridge does seem most suitable as it will allow the bridge to stay as a monument to the works of Thomas Telford for generations to come. There are a number of improvements that could be made to the bridge, were it to be opened to traffic. Another cast iron bridge based on the Bonar bridge design is the Holt Fleet bridge, built in 1829. It was ingeniously strengthened in 1928 by encasing the lateral grating and arch ribs with a reinforced concrete layer, as well as the reinforcement of the more vertical in each intersecting pair [13], albeit with an arguable loss of character. Current restorations of the deteriorated concrete should allow the bridge to continue serving along a main road link, without a weight restriction. Another option is the use of carbon fibre reinforced plastic (CFRP) - used for its lightweight, high strength, and good resistance to fatigue - as a way of strengthening and stiffening the members [14]. This may potentially allow the current character of the bridge to be maintained, while improving its loading capacity. Any improvements to the bridge to allow modern day traffic are however quite unlikely, due to the modern bridge nearby and the layout of the roads leading up to Craigellachie Bridge. Nevertheless, the mentioned improvement options may be implemented in further prolonging the lifespan of this important civil engineering structure. 14 Acknowledgements The author would like to thank Prof. Roland Paxton of Heriot-Watt University, Edinburgh, for providing insightful extracts from his MSc thesis [9].

15 References [1] Ford, C.R., 2007. Telford’s Highland roads – a new

way of life for Scotland. Proceedings of the Institute of Civil Engineers, Vol. 160, Issue 5, pp 36-42.

[2] Rondal, J. & Rasmussen, K.J.R., 2006. On the

Strength of Cast Iron Columns. Research Report No R289, The University of Sydney.

[3] Bussell, M., 1997. Appraisal of Existing Iron and

Steel Structures. Berkshire: The Steel Construction Institute.

[4] Sutherland, R.J.M, 1997. Structural Iron, 1750-1850.

In: Studies in the History of Civil Engineering, Vol. 9: Ashgate Publishing Ltd.

[5] Paxton, R.A., 2007. Thomas Telford’s cast-iron

bridges. Proceedings of the Institute of Civil Engineers, Vol. 160, Issue 5, pp 12-19.

[6] Lowson, W.W.. The reconstruction of the

Craigellachie Bridge. The Structural Engineer, 1967, 45, No. 1, pp 23-29. Discussion, 1967, No. 8, pp 287-289.

[7] BS5400-2:2006. Steel, concrete and composite

bridge – Part 2: Specification for Loads. BSI. [8] DMRB, Design Manual for roads and bridges. Vol.

3: Highway structures inspection and maintenance. Section 4: Assessment. Part 3: BD 21/01. May 2001.

[9] Paxton, R.A., 1975. The Influence of Thomas Telford

(1757-1834) on the Use of Improved Constructional Materials in Civil Engineering Practice. MSc Thesis, pp 84-100. Heriot-Watt University, Edinburgh.

[10] BS5950-1:2000. Structural use of steelwork in

building – Part 1: Code of practice for design – Rolled and welded sections. BSI.

[11] Smiles, S., 1904. Lives of the Engineers: Metcalfe-

Telford. History of Roads. pp 250. London: John Murray Abemarle Street.

[12] Parke, G. & Hewson, N., ed., 2008. ICE manual of

bridge engineering. 2nd ed. London: Thomas Telford Ltd.

[13] Hammond, B.C., 1934. The strengtheing of a cast-

iron bridge by welded steel bars encased in concrete: the Holt Fleet Bridge, Near Worcester. ICE, No. 162. London.

[14] Moy, S. & Lillistone, D., 2006. Strengthening cast

iron using FRP composites. Proceedings of the Institute of Civil Engineers, Structures & Buildings, Vol. 159, pp 309-318.

[15] Turnbull, G., 1838. Atlas to the Life of Thomas

Telford. Pall Mall: Payne and Foss. Available from: www.canmore.rcahms.gov.uk. [Accessed March 2011].

[16] Anon, c. 1982. RCAHMS, Item DC 10675. Available

from: www.canmore.rcahms.gov.uk. [Accessed March 2011].