I saw this bridge from pretty far away during our boat tour but it immediately caught my interest as it was a perfect little example of a cable stayed, fan-style bridge (stays originate from one point). The Deptford Creek Pedestrian Bridge is even cooler to me after I did some research and realized that it rotates 110 degrees on its main column to open up for boat traffic [1]. I’m interested in analyzing this bridge because it provides an opportunity to thoroughly investigate a cable stayed bridge without making many simplifications.

#### Figure 1: Deptford Creek Pedestrian Bridge from Bank

# Structure Information

The Deptford Creek Pedestrian Bridge was contracted by Raymond Brown Construction Ltd, designed by Flint & Neill, and the engineering firm hired was Eadon Consulting. It was built for a total cost of £5 million and completed in Fall of 2014 with funding provided by a mixture of public and private entities [1]. The surrounding area has been experiencing rapid gentrification and increasing population density over the past few decades as it transitions from wharves and industry to apartments and shops [2]. A walking/biking path called the Thames Path has been added along the Thames on both sides, and before the Deptoford Creek Pedestrian Bridge, walkers had to take a long detour through a non-sightseeing friendly area and cross a road bridge with heavy traffic [1]. In order to solve this problem the area council gave permission for a pedestrian bridge to be built with the goals of: beautifying the area, increasing walk/bike conveniences, and increasing foot traffic to the surrounding shops [1].

# Historical Significance

This bridge is very new (four years old), and thus has little history, and no historical significance to speak of. It is cable stayed, cantilevered and a swing bridge, but does nothing to innovate on any of these models. Deptford Creek is fairly thin (the bridge only spans 165 ft total) and the only major difficulty was the large change in tides that the Thames and its immediate tributaries experience, but this is easily avoided by timing construction periods and even assisted by making concrete foundations easier to pour during low tide. This is an excellent example of a pedestrian cable stayed bridge, but due to its lack of innovation it will most likely not serve as a model for future buildings.

# Cultural Significance

While the bridge has little significance besides assisting in gentrification, the surrounding area and Deptford Creek itself have a long history. Deptford Creek is the tidal portion of Ravensbourne River, and the Deptford Dockyard (a Royal Dockyard) employed many shipbuilders from the 16th to 19th centuries, who made up a large portion of those living in the surrounding area. Sir Francis Drake docked the Golden Hind in Deptford Creek after his circumnavigation of the globe and was knighted onboard in 1580 by Queen Elizabeth I [2]. The Golden Hind was moored in the creek for decades and became a tourist attraction/cultural symbol until it fell apart [2]. In the 19th and 20th centuries there was a large power station and many other industrial buildings along the creek, but in recent years the area has become much more residential with new highrise apartment buildings being built rapidly [2].

When it was proposed and being built, many local citizens were complaining about funding and approvals for apartment buildings that were linked with the proposal. After construction however there have been very few complaints, and generally positive feedback, although some vocal dissidents still argue that the benefits of the bridge were not worth £5 million [1]. The Deptford Creek Pedestrian Bridge is still used today (four years later, not much has changed) as it was initially intended – a pedestrian bridge – that beautifies and shortens the walk along the Thames [1].

# Structural Art

The “Three E’s of Structural Art” are: Efficiency, Economy, and Elegance. When it comes to efficiency, this small span bridge needed to somehow create space for river transit, and swinging was chosen. This reduces the materials needed by a lifting bridge, and the four cable sets use a low amount of materials in the superstructure, which together meant he structure is efficient. The Deptford Creek Pedestrian Bridge is also fairly economic in construction as it cost only £5 million, which although high for a normal pedestrian crossing, is low when also considering the swinging nature of the bridge. The bridge is also quite elegant, with a very simple cable structure, gently tapered deck, and lack of extraneous decoration. The only argument against this bridge being structural art is its small size, but I believe that it fills out the E’s so well that despite this limitation, the Deptford Creek Pedestrian Bridge is structural art.

#### Figure 2: Looking Up at the Mast from atop the Counterbalance

# Structural Analysis

The Deptford Creek Pedestrian Bridge is a cable stayed bridge in the fan style that swings back and forth to open the creek to water traffic. The pivot of the bridge is far to one side which means that the cantilevered deck is much longer and thinner over the river and counterbalanced by a short, thick span on the bank. The deck, mast, and cables are all steel, but the huge column that serves as support and pivot for the swing bridge is mainly concrete (there are mechanical components inside). The structural system is a cable stay bridge and load from the deck is transferred to the cables in tension which compress the deck towards the mast. The cables transfer the vertical portion of their load to the mast which is compressed downwards into the support pivot and foundations. A foundation for the pivot was dug and then concrete was poured in a mini caisson, and the pivot was then cast up around the central motor for swinging the bridge. The deck was prefabricated as one large span and the massive counterweight (120 tonnes) was attached on site when they attached the cables and lowered the bridge by crane. It was not built in sections due to the asymmetry of the cables and the short total span of the bridge.

When analyzing this bridge I was able to find the height of the bridge (50 ft) and the weight of the counterbalance (120 tonnes), but I paced out the bridge length (165 ft), distance between paired main span cables (40 ft), and distance to the four counterbalance cables (15 ft). I used the weight of the counterbalance (264,555.7 lb) along with the height of the mast and the distance to the counterbalance cables to find the total tension in the cables and the lateral compressive forces. First I idealized them to a single cable and then found the angle from horizontal using: tan^-1(50/15) = theta. This gives an angle of 73.3 degrees. Next using the downwards force I found the total tension with the equation: T = 264,554.7/sin(73.3) which gives a total tension of 276,204.3 lb. Then multiplying by cos(73.3) I found the lateral compression of this shorter but thicker section towards the mast to be 79,370.2 lb. For the bridge to be in equilibrium this lateral force would need to be equaled out by the lateral force from the three paired-cable tributary areas on the longer span according to the equation: T1*cos(theta1) + T2*cos(theta2) + T3*cos(theta3) = 79,370.2. The farthest cable from the mast is cable 1, closest is 3.

#### Figure 3: Initial Diagram with Angle and Tension Calculations

First I needed to find all of the angles using inverse tan and the distances from the 50 ft tall mast, which were 40 ft, 80 ft, and 120 ft. This gives angles (from theta1 to theta3) of 22.6 degrees, 32.0 degrees, and 51.3 degrees. Now I needed two more equations in order to get all my tensions (idealizing each paired cable to a single cable) so I looked at the tributary areas of the cables by dividing the span halfway (20 ft) between each cable. This gave (again L1 is farthest from the mast) lengths of: L1 = 45 ft, L2 = 40ft, and L3 = 60 ft. With a constant bridge width and the simplifying assumption of constant deck depth I can assume that this creates proportional masses for each section no matter the density of the steel trusses. Using this proportional relationship to assume downward force in each section, I arrived at the equations of: T3*sin(theta3) = (1.5)*T2*sin(theta2) and T3*sin(theta3) = (1.25)*T1*sin(theta1). When I plugged this into my first equation I got a complex equation that you can check out in my work below because I don’t want to type it out… Ultimately this gives me: T3 = 25,496.7 lb, which I can plug back into my second and third equations I get: T2 = 25,033.3 lb and T1 = 41,423.2 lb. Now that I have all the tensions I wanted to find out just how thick the stays needed to be.

#### Figure 4: Three Angle Calculations and Three Equations for Solving Tensions

To check this I looked at the largest tension per cable, which ends up (logically) being in the four cables on the counterbalance side. I divided the simplified total tension by 4 to get the tension in each cable of 69,051.1 lb, and I had measured the diameter of each cable in my real life visit to be 2in, so that gives a cross sectional area (pi*r^2) of 3.14 in^2. Then I calculated the stress in each cable (stress = F/A) to be 21,979.6 psi, and I checked the tensile yield stress of steel on the internet and got around 50,000, which gives the cables under the strongest load a factor of safety of 2.31.

#### Figure 5: Large Tension 3 equation and Tension Calculations

Next I wanted to check how large the mast would need to be under all the compressive forces (in real life the mast is not a solid structure). To do this I added together all of the tensions multiplied by the sine of their angle. This gave a total downward force of 313,637.5 lb, and I used a compressive yield stress of 250 MPa (36,259.4 psi). Then (with the equation A = F/stress) I found the total solid cross section needed to carry this stress to be 8.65 in^2.

#### Figure 6: Stress Calculations for both Cables and Mast

Design drawings were published in local newspapers when the bridge was proposed in order to show the community what was being planned, and an animation was shown to the community council making the decision.

# Personal Response

I’m personally a big fan (haha get it because it’s a fan style bridge…) of this bridge, I don’t think I’ve walked over a pedestrian swing bridge before, and I really like it’s bare simplicity. You can clearly see the cables taking the weight and that the shorter side is much heavier to balance the span. From far away on the boat I hadn’t been totally sure how the bridge rotated, but after going in person it was clear to see that the end of the main span only just barely rested on the approach and that it could easily spin on it’s massive pivot. I also hadn’t realized that there were four cables on the short approach span, but upon closer inspection they were clearly for dividing up the massive tensile forces needed.

## References

- https://knowyourlondon.wordpress.com/2017/03/31/deptford-creek-pedestrian-swing-bridge/
- https://en.wikipedia.org/wiki/River_Ravensbourne

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