What would the Parthenon look like (if instead of post and beam columns, the supports were arches in the Romanesque styles)?
True, nobody does Allowable Stress anymore. Simple explanation, you compute the maximum stress in the structural steel due to dead load and live load and limit it to some fraction of the steel’s strength. For garden variety steel with a yield stress of 36,000 psi, you’d limit it to 22,000 psi if my memory serves me correctly.
In the 1970s we all went to Load Factor design. The idea is that you know the dead loads more reliably than you know the live loads so you multiply them by different factors. So for that 36,000 psi steel, we would use the entire 36 ksi but multiply the loads by this general expression: 1.3 (DL + 5/3 LL)
Starting in 2010, we’re all using LRFD (Load and Resistance Factor Design). It’s a bit more complicated than can be explained simply.
As far as the rusting steel goes, the Brooklyn Bridge predates the use of steel that was deliberately unpainted (ASTM A588 or Cor-Ten Steel), which was an early 1970s development. That steel would form a patina that protected itself. Trouble is, in certain environments it doesn’t form that patina and rusts readily. Surface rust is no big deal, you can remove it and paint it. It’s when section loss occurs that you have to worry, even then it depends where it is. Middle of the web at midspan, not a big deal. Bottom flange at midspan, could be a big deal.
I read that book and it was fascinating. I’m still amazed that the bridge piling stand on wood! Basically a huge wooden box filled with concrete. It clearly works, but I would have thought that pine wood in the water would be an issue.
British Institution of Structural Engineers, 1976.
This is one of those things that has floated around the Internet for a while and has been mucked about with a bit, Telephone Game style (but the source is right). The exact quote is:
However, if you read on a bit in that article you’ll see Dykes apparently lifted it from somewhere himself, which complicates matters.
I think you might be confused. The caissons were framed from wood, but the wood was removed after the structure was built of poured concrete. The bridge is not standing on wood framed caissons today, which is readily apparent if you’ve ever seen it. Nor is the bridge standing on wooden piling; on the Brooklyn side it sits on bedrock, on the manhattan side it actually is just dug into the riverbottom (originally planned to sit on bedrock, but at over 100ft it was too deep for workers, who had major trouble with the bends at Brooklyn’s 44ft depth)
Wooden pilings that remain totally submerged can last a very long time. I believe that the pilings for the medieval version of London Bridge, have been found, still in place.
The remaining pilings of Old London Bridge aren’t just submerged. They are underground in clay.
I could be wrong (I’m not a civil engineer although I bet it’s a cool job) but it seemed clear to me from the book that caissons were really an upside down box that was sunk and had the mud dug out until it hit bedrock (at least on one side). (I think on the other side, Roebling said we can’t get to bedrock and this is close enough.) It was then filled with concrete and the bridge was buit on the concrete and on the wood.
Could be wrong.
You are confusing box caissons (the modern kind, which are made of concrete themselves and left in place) and open caissons, the wooden sort they used for the Brooklyn Bridge.) The latter were removed after the digging is complete and the concrete poured and set.
The wooden box was there to keep the water out while the men were digging and to allow them to pour the concrete. The wood itself isn’t structural.
Not to kick a dead horse but . . .
Really Not All That Bright So you are saying that there IS NOT wood still in the base of the bridge?
Telemark Are you saying there is wood down there but the breige isn’t on it? I mean if the stone is on top of the wood, how is that not structural?
As noted above, I was convinced that the stone structure of the bridge rested on the wood.
I still have the book, but I’m having trouble finding the exact technical details for the lumber. But I thought the wood was still there and that there were technical reasons for why they would “last forever” in the words of John Roebling. Something about sea worms not being able to reach them, they’d be packed so far down under.
I don’t think there’s actually any common circumstance where elliptical arches are optimal. If an arch needs only to support its own weight, like the St. Louis Arch, then the optimal shape is a catenary (the same shape as a hanging chain). If the arch needs to support weight that’s distributed uniformly horizontally, like a heavy horizontal bridge, then the optimal shape is a parabola. If it needs to support weight that’s proportional to the distance from the arch to the highest point of the arch, like the stone bridges the Romans built, then the optimal shape is a cycloid (the shape traced out by a given point on the rim of a rolling wheel). The parabola is a conic section, but the other two are not, and I don’t think the details of either were known to the Greeks. Nor did the Greeks have sufficient mathematics to prove that those shapes were optimal: That wouldn’t come until the Bernoulli brothers, at least.
You are correct, I was wrong. The wooden top of the caissons still remains in place and it structural with essentially no rot. The bridge towers are built on top of bedrock, concrete where the inside of the caissons used to be, the wooden top of the caissons still in place, and then the stone of the towers.
I too stand corrected.
Yeah, no kidding!
I understand that, but the book did point out several famous bridges made after the Roman period with elliptical arches. As long as the lateral forces can be managed, elliptical are as good as spherical and use considerably less material (or, cover longer spans with less height or fewer pedestals, etc.) But yes, anywhere you might want to use an ellipse, my guess is that either a parabola or catenary would work better, depending on the load distribution.
And I’ll never forget in high school calc where the instructor showed the difference between a suspended parabola (what you get when the load is proportional to dx) and a catenary (what you get when the load is proportional to ds along the chain). I also really enjoyed visiting Barcelona and learning about Gaudi, and seeing the catenary in action and on a grand scale. (Plus his upside-down models.)
I know what cycloids are but didn’t know they were optimal for that kind of span – thanks!
And me.