The Physics of a Broken Floor Beam

 

    The other day, walking through my friend's house, I took a step that made the floor shake. It was a little offputting, so we took a trip to the basement, where we quickly found a broken floor joist (I just learned that's what they're called) right under where I was standing. Like any good physics 111 student, I immediately thought of how I could write a physics blog about it. I measured the distance between the joists, weighed myself, and estimated some other important values, like a physicist. So here I am, in an attempt to apply what we've learned in class to a probably dangerous broken support beam.

In the first situation, the torque needed to keep me in static equilibrium (not falling through the floor) is evenly distributed between the two joists holding me up. This is good as it means one joist is not bearing an abnormal load. After the beam breaks, one beam is responsible for 3 times the force of the other, which probably isn't good. Luckily, this one break was not enough to send me to the basement without taking the stairs. 

    After figuring out what was happening when I wasn't falling, I wanted to explore what would happen if I did fall through (hypothetically, of course). The first factor I wanted to consider was the torque I would be applying to the lever-arm (floor) if it began to break and rotate about a joist. 

I found that I would be applying 514.5 Nm of torque to the floor, which I can only assume would cause it to break on the other side of the joist as well. At this point, I would be falling into the basement, where I could only try to land on my feet. Assuming I did land on my feet, I assumed it would take me 0.2 seconds to stop by bending my knees. In reality, I probably wouldn't land on my feet but unfortunately, I did not have the opportunity to test this theory. 

If I landed on my feet and braced my fall perfectly, I would endure around 2700 N or 605 lbs of force, which is a lot. In short, one broken beam can probably support one or even two people, but it's still dangerous. It's important to note that immediately after I wrote this physics blog, the beam was replaced. Crisis averted. 

1. www.bigrentz.com/blog/floor-joist