Authors: Vikram Pakrashi, Deirdre O’Donnell and Robert Wright (all from the Dynamical Systems and Risk Laboratory) and Denis Kelliher (Research Unit for Structures and Optimisation), Civil and Environmental Engineering, School of Engineering, University College Cork Daly’s Bridge, known locally as the ‘Shaky Bridge’, is an 87m-long pedestrian suspension bridge built in 1926 to provide access over the river Lee, west of Cork City, between Sunday’s Well and the Mardyke. The bridge replaced an old ferry crossing and the design and construction of the bridge was carried out to the specification of Stephen William Farrington, the Cork City engineer (Irish Architectural Archive 2014). [caption id="attachment_19204" align="alignright" width="306"]New Picture Fig 1: Advertisement using the dynamic reputation of the ‘Shaky Bridge’ at a bus-stop in Cork (photo: Brian Clayton)[/caption] The ‘Shaky’ bridge is the only suspension bridge in Cork and only one of four in Ireland (Denenberg, 2007). David Rowell & Co Ltd – a London-based steel company – built the bridge, which opened to the public in 1927. James Daly, a local businessman and butter merchant, partly funded the cost of the project and the bridge is named after him. The bridge is quite lively under pedestrian loading (Horgan, 2013), thus earning its ‘shaky’ title and its place in contemporary popular culture (Figure 1). Daly’s Bridge (Figure 2) consists of two steel lattice towers, one north and one south. Each tower consists of two piers braced together. Saddles mounted on top of the piers carry four cables of high-tension steel – two cables on the upstream side and two on the downstream side. The cables are anchored to the ground with steel sockets (eight sockets in total). The four piers are cast into concrete abutments on the river banks. The walkway is comprised of vertical steel lattice parapets and the timber decking is founded on 16 cross beams, which are supported by 32 hangers that vary in length. These hangers suspend from the main cables connected with a special patent clamp. At the time of carrying out investigation and modelling, it appeared that little to no documentation of this bridge exist in terms of drawings and materials used. Consequently, the modelling of this bridge posed significant challenges. A historical document from David Rowell & Co Ltd, outlining the geometry, construction and the costs of this bridge, was extremely useful in overcoming this challenge. This was in conjunction with a detailed survey of the bridge noting the as-built condition and comparing it to the information gleaned from the historical document. The bridge in Cork seems to be one of many constructed by the same company at different locations. According to local knowledge, some refurbishment work on the walkway of the bridge and the towers were carried out in the 1980s. [caption id="attachment_19206" align="aligncenter" width="448"]New Picture Fig 2: A photograph of Daly’s ‘Shaky Bridge’[/caption]

Inspection and geometric details

The pedestrian bridge is accessed from the south, the Mardyke, via a 43m-long concrete ramp orientated at 90 degrees to the bridge span. The bridge is accessed from the north, Sundays Well, via a level narrow pathway that leads to the northern tower. The main span is 50.96m in length spanning the river Lee and the stay cables are projected back 21.84m and 14.680m on the south and north ends of the structure, respectively. This gives a total structure length of 87.48m. Two pairs of high-tension steel cables form part of the superstructure. Two cables exist upstream (west) and two cables are on the downstream (east) of the bridge, each having a diameter of 38.1mm and a distance of 1810mm between east and west cable pairs. The total true length of each cable is 91.5m. The cables are supported by two towers each of height of 5.75m. Both towers, north and south, consist of two lattice piers each and are braced together at the top. The four piers are cast into abutments with concrete on the banks of the river. The north-tower elevation is 130mm higher than the south-tower elevation. Each pier consists of four corner EA beams and lattice steel girders arrangement joining the corner members. It was observed that the corner EA sections increase in thickness near the base of the tower. The hangers are solid circular steel rods varying in length and suspend from the cables at an average of 1.55m centres. The hangers suspend from a specialised, patent non-slip dished plate clip fixed to the cables (as per David Rowell Document). At the bottom of each hanger, the rod is threaded and fitted through a bored hole near the edge of the cross beams and two nuts are fixed to complete the connection. The 32 hanger dimensions vary non-uniformly from 19mm to 25.5mm in diameter. The 16 cross beams are parallel flanged beam sections with a consistent length of 2060mm. The walkway consists of side parapets, longitudinal diagonal bracing members and timber decking. The parapets are made up of longitudinal top and bottom chords, both T-section beams. The bottom chord is an inverted T-section and is bolted to the cross beams. At each cross beam location, two vertical EA sections join the bottom and top chord T-sections. Lattice steelwork makes up the panels between the vertical EA sections. All panel sections are identical in size, except the most northerly and southerly parapet panels. Additional stay EA beam elements are connected from the edge of each cross beam to the top chord of the parapet. Longitudinal diagonal bracing consists of EA sections connecting east and west bottom parapet chords. The timber deck is founded on longitudinal timber joists, which are founded on the cross beams. The timber decking is independent to the parapet arrangement itself and has a total width of 1450mm. The main geometrical properties of Daly’s suspension bridge are presented in Table 1. Characteristic comparisons between four other suspension footbridges are presented in Table 2. It was observed that Daly’s Bridge lies in the lower quartiles of all the comparisons. The length over the sag ratio is in the lower quartile with respect to the figures shown which illustrates a good depth with respect to the length of the main span. The length over the width factor is in the lower range of the cases shown below illustrating that Daly’s Bridge is a wide bridge in comparison to other bridges. The mass of the deck to the mass of the cables ratio is on the low side of the figures presented which shows a good balance between dead loads weight and cable.
L = 50.96 M Main Span
S = 4.131 M Sag
D = 1.53 M Average Hanger Spacing
H = 4.222 M Tower Heights
2Be = 1.81 M Distance between Main Cables
2Bc = 1.48 M Distance between Longitudinal Beams
2Bd = 1.45 M Deck Width
Md = 157.5406 kg/m Mass of Deck
Mc = 29.2578 kg/m Mass of 4 cables per m
Table 1: Geometric data for Daly's Suspension Bridge
 Structure L/s L/(2be) Md/Mc
Daly's Bridge 12.34 28.15 5.38
Morca 9.96 36.64 22.6
Baraggiolo 15.61 23.21 6.4
Millesimo 16.6 40.38 2.5
Messina 10.79 63.46 0.86
Table 2: Comparison among characteristic features of suspension bridges (adapted from Bruno et al., 2011) The degree of corrosion can be seen to be different in various members. During refurbishment in the 1980s, works included replacement of severely corroded steel members in the towers and parapets and the timber deck was also replaced. The image from the opening of the bridge in 1927 clearly shows a different timber deck from what is currently in place but no other major changes are evident. The parapet members show a high degree of corrosion in some members and a low degree in other members; this is explained by the replacement of some members during the refurbishment. The David Rowell bill issued to the Cork city engineer in 1933 states that four ropes costing £107 for 1 ½ “300’0” and this equate to a 38.1mm diameter rope. The rope measured today at middle span is 38mm. The anchor cables on the north of the bridge are in good condition.

Modelling and checks

[caption id="attachment_19224" align="alignright" width="442"]stay-beams Fig 3: Photograph and model of parapet stay beams[/caption] The bridge was modelled using a commercial Finite Element software package, keeping in mind the best information on geometry, materials and boundary conditions available. As a comparison, Figure 3 presents the photograph and model of the parapet stay beams, while Figure 4 presents the photograph and model of the walkway boundary. Values had to be assumed for the Young’s modulus of steel and for the timber deck in absence of detailed testing. The modulus of elasticity of steel was considered to be in the range on 190-210 GPa for this study, while that value for timber was 11-14 GPa. Figure 5 presents the completed as-built model for the bridge. [caption id="attachment_19226" align="aligncenter" width="712"]walkway-end Fig 4: Photograph and model of walkway end[/caption] The axial force on each of the cables of the model under the self-weight of the bridge was estimated as 37.34kN. A comparable hand calculation of a simplified 2-D model of the structure yielded the value of 41.16kN. Following this check, the bridge was loaded with people at mid-span where the weight of each person was known. Static loading on the as-built model of the bridge (including damaged elements) was plotted against deflections (Figure 6) and this was compared against theoretical predictions from the Finite Element model. The deflections were measured multiple times using the Dumpy Level and a staff for each loading intensity at mid-span. This was possible, since the deflections were significantly large and even distinguishable to the naked eye. [caption id="attachment_19215" align="aligncenter" width="448"]New Picture Fig 5: As-built Finite Element model of Daly’s ‘Shaky’ Bridge[/caption] Figure 6 also depicts the linear fits of predicted load-deflections values and that obtained from field experimentation. Model 5 depicts the Finite Element model most representative of the available data and inspection. There was a good match between the predicted load-displacement behaviour and that obtained from field experiments. Additionally, the linearity of load-displacement relationship of this bridge in apparent from field testing and this justifies the linear elastic Finite Element modelling assumption. [caption id="attachment_19222" align="aligncenter" width="763"]Image 6 Fig 6: Theoretical estimates of load-deflection behaviour of the bridge at mid-span versus experimental studies.[/caption]

Conclusions

The Daly’s ‘Shaky’ bridge in Cork has been a source of some discussion historically and in recent times due to its dynamic nature but a working model of the bridge seems to be absent. In this work, information from historical documents was merged with site inspection of the bridge and an as-built Finite Element model of the bridge was created. A detailed description of the visual inspection of the bridge was created. Computational checks carried out on the bridge indicate a match with simplified hand calculations. Field investigations indicate a match with the as-built Finite Element model for static load-displacement curve at the mid-span. The bridge appears to be within the domain of linear elastic mechanics. The study can be useful for designing and implementing dynamic tests on the bridge. References