Driveways, roads, sidewalks, airport runways, piers and jetties for heavy shipping, and buildings area all made of it. Civil engineering students even have competitions where they race canoes made from it. The most widely-used composite structural material in the world is steel-reinforced concrete, and it makes up some part of nearly every piece of infrastructure in the modern world.
But there’s one massive drawback to concrete. Concrete has a tensile strength so low, it’s often totally neglected in design. The traditional means of overcoming this limitation is the incorporation of mild steel rebar to take the tensile loads, while using the concrete to take compressive forces.
But another method reigns supreme for fast fabrication, or where cracks must be tightly controlled.
Prestressed and post-tensioned concrete take another tack: engineers design special steel cables to be pre-stretched during concrete casting, or tightened after casting in special ducts, providing a preload that keeps the concrete under compression under all anticipated design loads.
How does Prestressing Concrete Work?
Concrete is a great bulk material, with relatively good strength under compressive loads, but absolutely terrible strength in tension, to the point that most designers totally ignore any contribution from the tensile strength of concrete.
Concrete. Tension. Bad.
One of the things that really sticks with me from grad school is the memory of our professor in our fourth semester-long concrete design class stopping midway through a very complex lecture on one of her research topics, looking up at all of us, and deadpanning “Concrete. Tension. Bad. If you forget EVERYTHING else I teach you, remember this!”.
The American Concrete Institute provides little guidance for even using the minimal concrete tensile strength that exists, though a well-regarded 1964 study by Winter et. al. provides the following equation for an estimate of one form of tensile strength in concrete:
Running those numbers for a few design concrete compressive strengths gives the following table:
| Compressive Strength, f’c | Splitting Tension, f’.sp |
|---|---|
| 2,500 psi | 300 psi |
| 3,000 psi | 328 psi |
| 3,500 psi | 355 psi |
| 4,000 psi | 379 psi |
| 5,000 psi | 424 psi |
| 6,000 psi | 465 psi |
Obviously, those are some awfully low expected strengths, and once an appropriate safety factor is applied, they don’t leave the designer much to work with.
Ordinary Reinforced Concrete vs Prestressed Concrete
For the last couple of centuries, civil and structural engineers compensated for the terrible tensile strength of concrete by including deformed reinforcement bars, better known as rebar, in the areas of a concrete structural member where they expected tension.
This left the concrete free to crack, which it very much does, but the chunks of concrete between the cracks do serve to transmit the tensile forces to the rebar and tie it together compositely with the compressive region of the concrete section.
When it comes to ordinary reinforced concrete, traditional concrete with rebar, if it’s not cracked, it’s not doing any work.
Eventually, engineers and inventors came up with another workaround. Instead of incorporating tensile reinforcement like ordinary reinforced concrete, prestressed concrete is preloaded so the full section remains in compression under design loads.
This is actually similar to a concrete beam-column design, where the weight of the structure above creates a uniform compressive stress on the column, and the axial stresses from the bending moment are then superimposed on top.
For example, if we have a really simple column with Area A = 100 in² & Section Modulus S.x = 10 in³, and we throw 5,000 lbs of axial load on it, we can calculate the maximum bending moment that would be allowed without imparting any net tensile stresses.
- P/A = 5,000 lbs / 100 in² = 50 psi uniform compression
- That means we can have a maximum of 50 psi of ultimate fiber tension
- 50 psi * 10 in³ = 500 lbs-in of allowable moment
Prestressing works the same way, except in reverse. For a known loading condition, engineers calculate the extreme fiber tensile stresses in the section, then back into what compressive preload is required to maintain compressive stresses over the whole section.
By using draping, engineers can move the location of the applied compressive force up and down in the section, helping them apply those compressive preload stresses exactly where they’re needed to counteract the applied stresses.
Prestressed vs Post-Tensioned Concrete
There are two ways engineers use steel cables to preload compressive stresses into concrete members: prestressing and post-tensioning.
Prestressed concrete is made in a precasting yard, where precasters install the pretensioning cables in the formwork and tension them up prior to pouring the concrete. Once the concrete cures up enough (usually only about a day, as turnover time is profit in the precasting yard so they use heat, steam, and chemical accelerators to speed it up), the cables are cut free, and the section is set aside to finish curing in a storage area of the yard before shipping out to the job site.
On the other hand, post-tensioned concrete is almost always cast in place. The prestressing cables are run through ducting, special sheathing like a garden hose, which allows it to be snaked through the rebar cage and run out the pour stops at the ends fo the formwork.
After the concrete is poured and cured, jacks are used to apply tension to the cables, which are then anchored at the ends to tie them off.
One special application of post-tensioning is large transfer beams, like those used in hotel lobbies, which carry large loads from a column that doesn’t start until the second or third story of the building. As more and more stories of the building are added, these transfer beams often need to be jacked and rejacked to maintain the proper level of prestressing. Just applying it all at the beginning would rip the beam apart without the balancing out from the weight of the structure above.
Where to Look for More
The Precast Concrete Institute (PCI) offers numerous design resources on its website, pci.org, as well as its Precast Design Handbook, the standard referenced in the International Building Code.
I personally had “Design of Prestressed Concrete Structures” by Lin & Burns recommended in my class on prestressed concrete back in grad school, and it served me very well. You can pick up the latest edition on Amazon here.
Don’t forget to swing by PPI2Pass for all your FE, PE, and SE prep needs!