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The Golden Gate Bridge 75th Anniversary

29 May, 2012 (23:32) | Engineering | 1 comment

On 27 May 2012 San Franciscans showed the world just how much the Golden Gate bridge means to them with an amazing fireworks display to celebrate 75 years of service. At the time it was built it was the longest bridge in the world and many said it could not be done. Having visited it and walked over and back (there is no bus stop the other side!), it really is a remarkable structure and location.

Ezra Shaw, Getty Images

Ezra Shaw, Getty Images

To put it in context, when the bridge was designed and built:
  • There were no calculators - as we know them now, "calculators" in the 1930s were office clerks who would spend months solving a single linear system of equations, as is required for an indeterminate structure such as this. This can be accomplished in seconds now even on the cheapest laptop. The command in Matlab is "x = Ab". We have it easy.
  • There were no total stations - setting the bridge out was done with theodolites and good eyesight! Coordinates, angles, and distances were all calculated manually. There were no laser sights or satellites to check the GPS coordinates of the reference points.
  • There was no Microsoft Project - planning and delivery of such a complex project was again carried out manually with (obviously) no help from a computer. Network path analysis was in its infancy, and yet the bridge was built in a nifty 51 months.
  • There was no limit state design or partial factor format codes of practice - instead allowable stress design was used, with far less information available on the material performance under cyclic and dynamic loading than we have today. Aerodynamic forces were not understood nor worried about - the Tacoma Narrows Bridge collapse was a decade later.
  • Finally, and just to get my research in, there was of course no traffic microsimulation assessment of the loading that the traffic would impart to the bridge. This would come nearly 75 years later!
The main span is 1280.2 m. The current longest span is 1991 m (Akashi Kaikyo Bridge, which I also had the pleasure of visiting), which is only 50% longer approximately, and was achieved without any of the above restrictions. In this context, the designers and builders of this bridge, and many others like it at the time, certainly deserve an awe and reverence for their achievements. But surely, don't many other bridges deserve this attention? We trust our lives every day to their builders and the materials, and our economies could not function without them. It is no surprise that "to build bridges" is a very positive metaphor.

Journal paper published – footbridge vibration

16 April, 2012 (20:47) | Engineering, Research | No comments

The paper Enhancement factors for the vertical response of footbridges subjected to stochastic crowd loading has been published in the prestigious Computers & Structures journal. This has an impact factor of 1.719 for 2010. This paper proposes a method of determining statistical enhancement factors to apply to single pedestrian responses to obtain corresponding crowd-induced vibration responses.

The full reference for the paper is: Caprani, C.C., Keogh, J., Archbold, P. and Fanning, P. (2012), ‘Enhancement factors for the vertical response of footbridges subjected to stochastic crowd loading’, Computers & Structures, in press. And it is available from: Abstract The vertical acceleration response of a hypothetical footbridge is predicted for a sample of single pedestrians and a crowd of pedestrians using a probabilistic approach. This approach uses statistical distributions to account for the fact that pedestrian parameters are not identical for all pedestrians. Enhancement factors are proposed for predicting the response due to a crowd based on the predicted accelerations of a single pedestrian. The significant contribution of this work is the generation of response curves identifying enhancement factors for a range of crowd densities and synchronization levels.

Spaghetti Bridge World Record

2 December, 2011 (13:22) | General | 2 comments

The video of spaghetti bridge world record test is below. The bridge weighed 0.982 kg and held 443.58 kg before failing spectacularly. This is an amazing strength-to-weight ratio of almost 452 and beat the previous world record by 92 kg. It was built by two Hungarian students, Aliz Totivan and Norbert Pozsonyi and tested at the 2009 Spaghetti Bridge Championships held at Okanagan College's Kelowna, B.C., Canada. The construction of the bridge is extremely good. Every connection and member is in perfect position, and this means that load paths are equally distributed. As we in DIT have learned from our Spaghetti Bridge tests, it is often the best constructed bridge, and not necessarily the best design that wins.

The importance of units

21 October, 2011 (21:47) | General | No comments

There are some quite serious sites that point out the importance of units in engineering calculations, but a less serious result of an error is the guy who got the wrong slipper! See the news report here.

Nonlinear beam behaviour example

3 October, 2011 (22:19) | General | No comments

This shows the deflection and bending moment history of a propped cantilever loaded with a point load at mid-span. The beam has a plastic moment capacity of 100 kNm and a shape factor of 1.12. A strain hardening modulus of 2% of the modulus of elasticity is used. The model is based on that given in Advanced Analysis and Design of Steel Frames by Li and Li, Wiley 2007.

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