In my concrete design class, we have been calculating the flexural strengths of different shaped reinforced concrete beams. I first learned how to calculate the properties of such beams in strength of materials, CEE 059, last spring. Though I vaguely remembered some of the tricks, the problems we have been doing in class are so much more complicated. First off, the shape of the beam is not necessarily always a perfect rectangle and can be I-shaped or T-shaped, even triangular as my professor joked. Luckily, there is no integration involved in what we have solved so far because we are using a method called equivalent force block. The internal forces on the beam are caused by a bending moment given the self-weight plus any additional loads. It is our job to calculate whether that moment will cause cracking in the concrete or yielding in the steel rebar. The bending forces the top of the beam into compression, which the concrete resists, while the bottom, particularly the steel, is in tension. The problem with finding these forces is that the compression force on the top is distributed unevenly over an unknown area of concrete. So it is pretty much impossible to integrate that distribution over any area other than a perfect rectangle. But by making the distribution into an equivalent uniform distribution, the problem becomes much easier to solve.
Still, this all sounds fairly complicated…and it is. The last class we spent all 75 minutes doing a single problem and our professor filled the board three times over with the drawings, equations, and calculations. I’m a skimpy note taker, only writing down things that are necessary to make studying easier, and have small, compact handwriting but still managed to fill up two whole pages with the work from the problem we did. I was worried about how long it would take to do the homework, which was two of these problems. So after waking up to find classes were cancelled yesterday, I immediately started on the concrete homework. Working side-by-side with my notes I got a feel for the whole process and realized how much simpler it was than I originally thought. I completed the homework in about an hour; here’s one of my solutions (hopefully there’s no mistakes):