Deptford Creek Pedestrian Bridge

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

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

Cannon Street Railway Bridge

On our bridge tour today, the tour guide pointed out a low slung greenish bridge and began expressing his dislike of its “ugly” appearance. This made me feel like the Cannon Street Railway Bridge deserves some love so I was determined to analyze. The visible brute strength of the thick columns and flat spans caught my attention as it is clearly designed for massive railway loads rather than car or pedestrian passengers like other London bridges.

Figure 1 – Cannon Street Railway Bridge from South Bank

Structure Information

The Cannon Street Railway Bridge was built from 1863-1866 by the South Eastern Railway Company (SERC) and designed by Sir Joh Hawkshaw, a famous English Civil Engineer. The SERC was in control of the rail lines to the London Bridge Station and wanted to expand the lines over the Thames in order to reach the Northern half of London, so they initiated the design for this bridge to the Cannon Street Station [1]. In order to carry a greater capacity of trains, the bridge was widened from 1886-1893 by adding a column on each side for a new total of six (from an original of four) and more decking on top. The bridge was strengthened from 1910-1913 in order to bear heavier trains and strengthened again in 1983 to account for both greater loads and general wear and tear [2].

Historical Significance

The simply supported beam bridge is the oldest and simplest type of bridge, and although the Cannon Street Railway Bridge doesn’t innovate in form it is unique in its massive appearance. With three spans of 45m, numerous thick columns, and 2.6m deep iron girders the bridge clearly looks capable of carrying the 10 rail tracks laid on top of it [2]. It was one of the first rail bridges over the Thames and the only one located in the Eastern part of London and as such a very important connection point in Victorian London as well as today, but it is not a model for modern railway bridges, nor the best example of a period bridge.

Cultural Significance

The bridge remains a very important railway link over the river Thames and helped bring development to the East side of the city when it was built, as this area was mostly still low income housing with little value. As it is almost entirely used for rail traffic and is not a very beautiful bridge it has never become a cultural symbol or tourist attraction. In fact many citizens of London actively criticize its appearance, and our tour guide today related the story of how it was originally going to be named after Queen Victoria, but she disliked its appearance and had them drop that name. In August 1989 two boats collided right next to the bridge in a tragic accident that caused 51 deaths and led to new lifeboat stations at the sides of the bridge [3]. After expansion and two strengthenings over the last 150 years, the bridge is still used today to transport massive amounts of commuters and tourists around London.

Figure 2: Cannon Street Bridge Looking Eastward to Tower Bridge

Structural Art

The three principles of structural art are: Economy, Efficiency, and Elegance. This bridge is most certainly not elegant as Billington would define it. Although the load paths are as simple as possible and clearly visible (bridge girders to columns to ground), the structure could never be seen as “light” or “graceful”. To me the bridge does not fulfill the category of elegance, even though I personally like the stolid appearance and appreciate the unique appearance of the thick repeated columns. When it comes to being efficient, it is difficult to create a beam bridge with massive railway loads that uses a minimum of material when using iron girders and concrete foundations. An arched bridge could have reduced the material usage and added elegance, so I don’t believe that the Cannon Street Railway Bridge fulfills the principle of efficiency either. For economy however, the materials (concrete and iron) were cheap and easily procurable as well as being inexpensive to build with at the time. The wrought iron girders in the bridge deck are all the same size which made production cheaper, these factors together allow the bridge to fulfill the economic principle of structural art. Overall, by hitting only one of the three principles, the Cannon Street Railway Bridge is certainly not structural art, but that doesn’t mean it is not a useful and functional bridge, and I personally like it a great deal.

(The following paragraph written after doing Structural Analysis, skip ahead then come back so it makes sense…)

After calculating just how massive the loads that each beam and column can take, I’ve reconsidered the efficiency of the bridge. This bridge is so redundant and overengineered that I can no longer think of it as efficient. The only possibility is that its so strong to deal with scour, but even that seems unlikely to me. This bridge is definitely NOT structural art!

Structural Analysis

The major construction materials used are iron in the girders (wrought) and the exterior of the columns (cast), and concrete in both the columns and the beam right above lateral beam right above them. There is also masonry and brickwork as the bottom foundation, and construction was began by digging small caissons to the bedrock under the Thames and building these foundations. The original four concrete columns were then poured to about the water level, where the fluted cast iron exteriors were placed and then filled with concrete. Originally the bridge did not have the tapered concrete rings at the top of the columns, these, along with one column on each side (new total of six) were added in later retrofittings. The long wrought iron girders were then transported to the site (most likely by barge) and lifted by crane onto the supports, then riveted together. Finally decking, railings, and rail lines were added to the top to complete the bridge. The bridge has three major spans of 45m and two approaches of 39.6m, the plate girders are 2.6m deep and thick I-beam shaped. The concrete columns, assuming same river depth as at London Bridge, are about 13m tall, and from visual comparisons with the known 2.6m depth of the girders, are around 3m in diameter.

Figure 3: Looking Up at 18 Iron Girders

The Cannon Street Railway Bridge is a simply supported beam bridge without any fancy arches or trusses, all strength and stiffening are directly from the girders in the deck. Load from self weight and live load from trains is transferred directly from the beams into the huge columns. There are no wind airfoils on the side of the bridge, but it has a small cross section, very stiff deck, and extremely strong supports without a long span so wind load has very little effect on overall design or performance. The bridge faces scour from the Thames, but there are no angled diversion bases around the column bases as they are curved and heavy enough to withstand massive lateral forces. This bridge looks so massive that it would take gigantic live loads to cause collapse, but the three possible sources of failure are: tensile yielding in the girders due to bending in the middle of the spans, bearing stress crumbling at the contact point between deck and columns, and buckling in the columns.

To calculate the max bending stress I first found the volume of a single beam over the longest span (45m) assuming a symmetrical cross section with a flange depth of 0.1m, flange width of 0.5m, and web width of 0.2m. The cross sectional area with these measurements is 0.62m^2, and the total volume per central span per beam is 27.9m^3. Using a density of 7.7g/cm^3 for wrought iron from the internet, the weight of a single girder is 214,830 kg and the self load de to weight is 4,774 kg/m. These are very conservative (high) estimates for the weight per beam. Next I used the formula of stress = My/I, where M is max moment, y is max distance to the edge from the centroid, and I is the moment of inertia. Y is 1.3 meters assuming a symmetric girder, and I calculated the moment of inertia to be 0.386m^4. Then to calculate maximum moment, I know that the max bending moment of a simply supported beam with uniform distributed load is w(L^2)/8. I decided that the max bending moment would be the tensile strength of wrought iron which is 160MPa, so I needed to calculate the max train load that the span could support per beam (of which there are 18). So my equation was: 160MPa = (4,774 + T)*(L^2)/8 using superposition where T is the distributed train load on 1 beam. Using this equation the max train load comes out to be almost exactly 183,000 kg/m which is ludicrously high for passenger trains, and shows the deck to be in no danger of collapse due to bending stress.

Figure 4: Distributed Train Load Calculations and Bending Stress Diagram

To calculate bearing stress I found the surface area of the columns, which have a diameter of approximately 4.5m at contact. This gave a bearing area of 15.9m^2, and as there are 18 beams, approximately three of these would be on each column, and I’ve already estimated the weight of a 45m section of beam to be 214,830kg. This means that each column will need to bear the self weight of the deck of 644,490kg along with additional live load from the trains. T find the max live load of the trains before crumbling I used stress = F/A where stress is the compressive strength of concrete which I found online as 25MPa. This gives the equation: 25*10^6 = (644,490 + T)/15.9 where T is now the total train weight on the tributary area (rather than the distributed train load). This gives a final answer of over 395 million Newtons which is PER COLUMN. That’s actually crazy high and basically unachievable for such a small space (the heaviest train ever was three times the necessary force, but over almost 10km) so the bridge is safe from crumbling.

Figure 5: Load Paths all Channel into Columns

Finally to calculate the critical buckling stress of the columns I used the equation: P= (pi^2)*E*I/(L^2). To calculate E (modulus of elasticity) I used the ACI code formula: E = 4700* sqrt(C) where C is the compressive strength of concrete (I used 25MPa just as before) and found E=23500MPa. I calculated the moment of inertia of the column using D=1.5m (ignoring the upper concrete collar) to find I=3.98m^4 and used the length of 13m as stated before. This gives another comically massive final answer of 8793.8 MegaNewtons/m^2 PER COLUMN!!!!!! No train could fit that into the 45m long tributary area, this bridge is crazy overengineered.

Honestly I have no idea how they pitched such a ridiculously strong bridge to the shareholders, I think they just asked for a permit to build any bridge from Parliament and then Hawkshaw went wild. Crazy stuff, maybe my assumptions of size of members was off, but I’m pretty sure they were close….

Personal Response

The first time I saw the Cannon Street Railway Bridge I just walked past it because it looked so lackluster compared to the other bridges (same for London Bridge to be honest). Once we looked at it on the tour I wanted to give it some love because it seemed so neglected, but now that I have analyzed it my opinion has changed. At first I appreciated the bridge because of its strong and thick appearance, but once I realized just how wasteful it is I no longer appreciate it as much. It seems almost sacrilegious (maybe too strong of a word) to make something so bulky and inefficient when there are structural art options available.

 

References

  1. http://www.engineering-timelines.com/scripts/engineeringItem.asp?id=665
  2. https://www.bristol.ac.uk/civilengineering/bridges/Pages/NotableBridges/CannonStreet.html
  3. http://www.bbc.co.uk/news/uk-england-london-28839099

Bankhead Highway Bridge

I saw this dilapidated bridge from Tech Parkway, and walked by later along Northside Drive to get a closer look. Although somewhat nondescript, it caught my attention because I was surprised to see an abandoned structure of its size in the middle of the city. The simplicity and eccentricity of the bridge led me to delve further into its history and decide that it would make for an excellent blog post.

Figure 1 – Bridge Against Atlanta Skyline

Structure Information

The Bankhead Highway Bridge was built in 1912 to carry Bankhead Highway (roughly modern day US 29) over the Norfolk Southern and CSX railroads. It was most likely funded by GDOT and designed by a contractor they hired [1]. At the time of its construction, both the railroad and the highway saw very heavy usage, but eventually highway reroutes caused the bridge to become extraneous. Along with high maintenance costs this led to its abandonment and ultimately the destruction of one of the approach ramps. [2]

Figure 2 – Bridge Location

Historical Significance

This bridge is not at all innovative in either construction or design, but is an excellent example of a trussed steel bridge from the time period. It can be viewed as the typical quick and easy solution for land based spans that needed to carry only the load of cars during the early 1900s [1].

Cultural Significance

During active usage, the bridge provided a major causeway for access to the center of Atlanta which otherwise would have been obstructed by the railway. This railway was not for passengers, but instead long commodity filled trains ran along it. In the early 1900s these lines were an important artery for goods transportation to and from Atlanta [3]. Today the bridge is banned from public access (both vehicle and foot traffic) due to extreme structural integrity problems, and the deck, superstructure, and substructure have all been rated “Imminent Failure” in inspections since 1991 [2]. There is also a missing approach ramp and the bridge terminates abruptly at that side with no guard railing or warnings to keep people from falling. However this does not stop graffiti artists and homeless people from climbing onto it, and these are the only people who currently utilize the structure for anything other than the background of grungy Instagram pics.

Structural Art

The three ideals of Structural Art are efficiency, economy, and elegance, and I would argue that the Bankhead Highway Bridge accomplishes the first two, and closely approaches the third. The steel truss structure itself is composed of smaller trusses, creating a light but very strong superstructure and using a minimum of materials. The trusses support a span made of concrete that rests on reinforced concrete pillars, both span and pillars using a reasonable amount of materials. The bridge is therefore quite efficient, and uses materials that were cheap and commonly produced during the time period. It was also built using fairly quick and easy construction processes, as the land based nature of the span eliminates many of the challenges seen in bridges over bodies of water. Both of these factors lead to the conclusion that the bridge also fills out the economic ideal. When it comes to elegance however the bridge is weakest, and I’m sure Billington would hate it, but I personally appreciate its appearance. The bridge is skewed, meaning that the side trusses are the same length, but displaced a single truss length so that from above the bridge is parallelogram shaped. This is an interesting aspect and drew my eye initially as it can create a subtle optical illusion. I also believe that the truss structure connects solidly with the concrete base and together look simple, but strong. Along with the clearly visible load paths from truss to concrete span to pillars (and laterally through the top truss) I believe that the Bankhead Highway Bridge is Structural Art, although Billington may have disagreed based upon its lack of innovation and heavy looking form.

Figure 3 – View of Bridge from Below Missing Approach Ramp

Structural Analysis

The bridge approaches were simply supported cast in place concrete slabs on concrete pillars, and the truss structure is made of steel and supports the concrete middle span of 99.7 feet. This concrete span is 47.9 feet wide and approximately 2 feet thick and the trusses have a vertical clearance of 13.1 feet [2]. The truss structure is a Warren Truss (equilateral triangles) with added verticals and the trusses themselves are also smaller Warren Trusses but without verticals. The top chords and non vertical horizontal trusses have a hollow rectangular cross section with two sides consisting of trusses and all the other members are just single trussed beams. The trusses are riveted together and it is a through truss, so motor vehicles would pass between the upper and lower chords [1]. The truss is skewed as it crosses the railroad at diagonal angle, and from an elevation view looks like a long parallelogram. The top cord is also trussed in the same manner to provide lateral stability, although due to the small span, stiff base, and minimal footprint from an elevation view, the lateral stiffening is somewhat redundant. There is also a concrete sidewalk cantilevered off both sides of the bridge deck. The building techniques of the time were pretty similar to current bridge building techniques (other than the new automatic bridge building machines), and involved wooden form and scaffolding to pour the concrete and the steel was Bessemer mass produced [1].

As the bridge is not currently in use, the only important load is dead load from the self weight of the concrete span. This load is carried by the truss structure which supports the weight of the large concrete slab through members in both compression and members in tension. The weight is ultimately carried by two thick concrete pillars on either side of the span. In the single remaining approach span, there is no truss structure, so its entirely supported by large columns. Below is a simplified truss structure that represents the sides of the bridge to show in a basic way which members take compressive or tensile forces. The green members are experiencing compressive force and the red members are taking tensile force, while the white member has forces that balance out to zero. When the self weight (simplified in the picture [4]) is applied across the bottom chord,  the max stress in any member is in the outside diagonals and is approximately 0.75x the total force. The total force on the bridge due to the self weight of the concrete using a density of 145 lbs/ft^3 and previously stated measurements is 1,384,932.7 lbs which means that the max force in a member is 1,038,699.5 lbs (the total multiplied by 0.75). The compressive strength of old steel is about 36,000 psi (from an internet database), and the end diagonals on the bridge are the only non-trussed members, I had to assume a cross sectional area of about 50 in^2 from the photos. Using these values and the formula (F/A) the normal compressive stress on the outside diagonals is 27,698.7 lbs/in^2 which is less than the compressive strength of steel but only barely. If any live loads from vehicles were added to the bridge failure would rapidly occur, making it abundantly clear that closing the bridge was the correct choice.

Figure 4 – Simplified Warren Truss with Verticals

Another area of possible failure is in the concrete support columns, which could buckle or crumble from compressive bearing stress as shown in the photo below as green arrows. The four columns each have a symmetrical tributary area of 1/4 of the bridge and so must each support 346,233.2 lbs (total weight/4), and are 20 ft tall (previously stated). The columns are slightly tapered squares, and from pictures I will assume that the area at the top of the beam is 3×3 ft and is about 3.5×3.5 ft at the middle. Using these values (and F/A) the bearing stress on each column is 267.2 lbs/in^2, and the compressive strength of concrete is higher than that by at least a factor of ten, so there is no danger of failure from crumbling at the supports. The critical buckling load would be at the red line halfway down the column in the picture below. Using a modulus of elasticity of 2.9 x 10^6 psi (from internet database) and an estimated moment of inertia of 139,968 in^4 (I=b(h^3)/12 using 3×3 ft approximation) comes out to be 6,9551,102.2 lbs (Pcr = (pi^2)EI/(L^2)), a simply massive number that the bridge would never reach. The Bankhead Highway Bridge therefore is in no danger of failure due to its columns, but instead its trussed superstructure and concrete span.

Figure 5 – Compressive Bearing Stress and Hypothetical Buckling Location

Personal Response

It’s somewhat difficult to see from the pictures, but when I was actually walking around the bridge I was fascinated by the skewed truss. It hadn’t occurred to me that such a design was an option, maybe I had seen some in the past but never really took notice, but it was an exciting departure from the normal truss bridge I’ve always seen. I’ve always had some difficulties with trusses (ever since statics) and it was very interesting to try and trace the load paths in person, and then check my answers through equations during the analysis, and my understanding of the joint and section methods has definitely improved. I would love to go up on the bridge, but it’s kind of hard to get to, probably dangerous, and had some homeless people camped out on it, so I may not actually go for it.

References

  1. http://historicbridges.org/bridges/browser/?bridgebrowser=georgia/bankhead/
  2. https://bridgereports.com/1096608
  3. https://bridgehunter.com/ga/fulton/12151210/
  4. http://ivanmarkov.com/truss-simulator.html