Ductile And Isotropic

During a short trip to Massachusetts for a project, I took this photo from my seat on the train:

That’s the roof canopy at the Route 128 station¹ outside of Boston. I don’t know why there are so many conduits running the length of the canopy, but the fact that each has its own cut-out in each double-cantilever cross-beam strongly suggests that they are original to the design.² That’s…a lot of holes. Here’s the thing: they don’t really matter.

Steel is, per the title, ductile and isotropic. The ductile part means that it will undergo a significant amount of stretch before it breaks; the isotropic part means its physical properties are the same regardless of which direction force is applied. Those properties matter when we’re looking at the pattern of stresses within a beam. The web of an flanged beam like the one here carries little of the bending moment but almost all of the shear. Cutting holes in the web does not weaken the moment resistance of the beam as long as the shear in the web – which is a necessary part of keeping the bending-induced tension and compression in the flanges in sync – can still get from top to bottom. And because of steel’s material properties and the geometry of the holes³ the shear can still get around, albeit with a little more difficulty. Those holes serve as “stress risers” and, indeed, the shear stress between them is greater than it is in the solid part of the web. If the holes were square, the corners would see particularly high levels of stress, but round holes are easier to make than square ones.

If the beam were made of a non-isotropic, non-ductile material, the holes would be a much bigger problem. Try doing this in a wood beam and you’ve created the dotted line along which the beam will rip.

1. I assumed that station was simply an old suburban station renamed when Route 128 became famous. It tuns out that is oddly wrong. There was a station at that location from 1857 to the 1920s, called the Green Lodge station; the current station was opened in the 1950s specifically as a park-and-ride commuter station. ↩︎
2. You could cut all those holes after the fact, but it’s generally easier to run the conduits around the beams if the beams are existing when the conduit is being installed. ↩︎
3. Leaving enough solid material between the holes, measuring horizontally, was an important detail. ↩︎