# Monthly Mechanics: Prestressed Concrete

This is Part 4 of a series about building materials. Read Part 1, Part 2, and Part 3.

Note: On March 15 a prestressed concrete footbridge under construction at Florida International University collapsed, killing six. An investigation is underway, and I will comment on this tragedy when more information is made public.

If you read Monthly Mechanics regularly (thank you!), you might feel some déjà vu. We already explored reinforced concrete (and a little bit of unreinforced concrete) two months ago in Part 2. But prestressed concrete, while similar in appearance, behaves completely differently.

Recall that plain concrete is strong in compression and weak in tension. Reinforced concrete solves the mismatch by placing steel bars inside the formwork to resist tension once the concrete sets. Prestressed concrete attacks the problem a different way: by trading compressive strength for tensile strength.

How is that possible? Imagine putting a bathroom scale on the floor under a pull-up bar. If you stand on the scale, it reads your weight. (Duh.) Now if you grip the bar, you can take some weight off the scale (by pulling up), or add more weight (by pushing down). Prestressed concrete does the same thing. Instead of your body, prestressed concrete uses steel strands to put the concrete into compression and reset the “zero” point.

Typical prestressed concrete cross-section

To make things even more confusing, there are two types of prestressed concrete: prestressed pre-tensioned, and prestressed post-tensioned. The difference is whether the strands are tensioned when the concrete is wet, or after it dries.

A pre-tensioned beam is cast around a network of parallel strands that have already been pulled tight, like violin strings. After the concrete sets, the strands are cut on the ends. The strands will then try to shorten to their original length, and since now they’re bonded to the concrete they pull the whole beam into compression.

For a post-tensioned beam, the concrete is cast around a series of PVC sleeves, leaving holes that run the length of the beam. Then, the strands are threaded through these holes, attached to the beam ends, and tightened. In this case they pull the concrete beam in from the ends, not its entire length, but the result is the same: the beam is in compression before it ever receives a structure load.

Here’s an example. A concrete beam has length L=10 feet (120 inches) and a structure load of P=500 pounds in the middle. We know that the bending moment in the middle is M=PL/4=15,000 inch-pounds. If the beam is 12 inches square, then the section modulus is S=123/6=288 in3 and there’s a stress of f=M/S=52.08 psi at the top and bottom fiber. Tension occurs at the bottom; compression at the top.

If it’s a reinforced concrete beam, then the steel at the bottom of the beam does all the work in tension. A small portion of the concrete at the top of the beam resists the compression stress.

If it’s a prestressed concrete beam, then the beam starts out with a uniform compression stress of, say, 100 psi. Then the structure load is applied. The total stress is now 100+52.08=152.08 psi at the top fiber, compression, and 100-52.08=47.92 psi at the bottom fiber, also compression. In effect you’ve lost 100 psi of compressive strength but you’ve gained 100 psi of tension strength.

Reinforced concrete beam (top) | Prestressed concrete beam (bottom)

There are high setup costs to manufacture prestressed concrete, but it’s an economical choice for many bridge decks and building floors. Typically the concrete is prefabricated in planks with a rectangular, hollow, or I shape, which makes them easy to work with on site with a crane.

Prestressed concrete bridge beam under construction. (flickr – creative commons)