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.

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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.

PrestressedFig1

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.

PrestressedFig2

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.

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

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Monthly Mechanics: Wood

This is Part 3 of a series about building materials. Read Part 1 (Steel) and Part 2 (Reinforced Concrete).

Wood is a convenient material for construction. It literally grows on trees, it’s soft enough to cut quickly with hand tools, and it accepts fasteners easily. That means wood framing has been around a lot longer than steel and concrete – probably as long as humans have built shelters. Wood is still one of the fastest materials to build with, especially with the advent of power tools, and has one of the smallest carbon footprints.

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The convenience of wood construction.

Foresters divide the myriad species of trees into hardwoods (deciduous) and softwoods (coniferous). Hardwoods are denser and best for fine woodworking like cabinetry. It’s softwoods, with their fast growth and straight grain, that are used for high-volume and high-strength applications like framing buildings.

Engineers also care about which wood species is used, but they care even more about the grade. Lumber is either visual graded (i.e. by actual people looking and feeling) or machine graded (i.e. by a mechanical stress test). The straightness of the grain, and the presence of knots (which are really just locations along the original tree trunk where branches grew), has a tremendous effect on the lumber’s structural properties.

If you can find a piece of dimensional lumber made from clear structural redwood, you can enjoy a bending strength of 1750 psi. At the other end of the spectrum is utility-grade eastern hemlock, with a bending strength of 175 psi – an order of magnitude weaker than the redwood. Your typical off-the-shelf dimensional lumber in New England is #2 grade southern pine, with a middle-of-the-road bending strength of 975 psi.

Engineers then adjust these strength values based on the geometry and environment of the structure they’re designing. Things like how big the lumber is, whether it’s braced along its length, whether it’s used on edge or flat, whether it’s repetitive (as in a series of floor joists spaced 16” or 24”), and whether it’s exposed to extreme temperatures or moisture all affect the safe strength to use for design calculations.

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Lumber stamp.

This Old House has a nice explanation here of how to read the stamp on a piece of dimensional lumber. The stamp tells you the species and grade, as well as the moisture content and the mill where it was cut.

For mostly archaic reasons, wood is rarely used for commercial construction in the US, but the tide may be turning. The development of stronger wood products like cross-laminated timbers (CLTs) – layers of lumber bonded together with the grain at right angles, sort of a super-plywood – enables wood construction to go far higher than the four or five stories at which dimensional lumber stick-framing tops out. (CLTs can have a bending strength of 2250 psi or more.) The tallest completed wood building is 18-story Brock Commons in Vancouver, and architects in Tokyo have plans to go as high as 70 stories, a true “plyscraper.”

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Cross-laminated timber fabrication.

In the US, where codes limit wood construction to 85 feet, the tallest wood building is a seven-story office tower in Minneapolis. But with advances in fireproofing, and the strength and stability of the newest wood products, the American Wood Council is lobbying for a change.

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T3 Tower in Minneapolis.

Monthly Mechanics: Reinforced Concrete

This is Part 2 of a series about building materials. Read Part 1 here.

If you measure the #1 building material in the world by weight, steel and concrete are neck and neck. If you measure by volume, concrete wins hands down. The World Steel Association estimates that 1630 million metric tons of steel were produced worldwide in 2016 – a bit over 7000 million cubic feet. Meanwhile, the Royal Society of Chemistry estimates that 2000 million metric tons of concrete are placed each year – over 30,000 million cubic feet.

These are staggering numbers. If you put a year’s worth of concrete all together you could build a solid cube measuring over half a mile on each side. Obviously, concrete has the edge over steel by volume because it’s much less dense. Steel is over 90% iron, and its density is basically the same as pure iron. (Every structural engineer knows this density by heart: it’s 490 pounds per cubic foot.) But concrete is a complicated mixture of different sizes of rocks and sand, Portland cement, water, and various additives, and depending on how it’s mixed a builder can trap a significant amount of air inside or just a little bit. Thus the density of concrete varies.

Rocks might seem heavy, but in fact they don’t get much denser than 150 pounds per cubic foot, so this is the upper limit on the density of concrete. Lightweight mixtures get down to 90 pounds per cubic foot with more entrained air; they’re often specified when concrete doubles as the architectural finish and needs to look sleek. Specialty products, such as autoclaved aerated concrete, are actually so light that they float. But such lightness comes at a big financial cost and reduces the strength as well.

Speaking of strength, concrete as a building material has one serious shortcoming. It works wonderfully in compression, but has almost no capacity at all in tension. That’s why you will never see a concrete chandelier.

Engineers address this shortcoming by putting a little bit of steel inside the concrete. The result is a composite material called reinforced concrete, in which the concrete provides the compressive strength and the steel provides the tensile strength. If the concrete doesn’t need much tensile strength (a slab on grade for example), then a steel mesh or welded wire fabric may be sufficient. In other situations, reinforcing bars (aka rebar) are used. They come in sizes ranging from 3/8 inch diameter to over 1 inch diameter, and they always have bumps on their surface to prevent them from sliding through the hardened concrete.

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Concrete beam cross section analysis. The striped region at the top is the effective concrete area. The dots at the bottom are the steel reinforcing.

In designing a reinforced concrete beam, engineers try to balance tension and compression. Recall that when a beam bends downward, the bottom is in tension and the top is in an equal amount of compression. Reinforcing steel goes in the tension zone. It takes a certain amount of concrete in the compression zone to balance the strength of the steel, and that amount is surprisingly small. (Most reinforced beams are tension controlled, which means the steel fails before the concrete does.) In other words, most of the concrete in a reinforced beam never feels any stress! Its only purpose is to hold the beam together.

UNreinforced concrete structures are rare today, but early builders took advantage of the material’s pure compressive strength to produce spectacular arches and shells. The Pantheon in Rome, finished in the year 128, remains the world’s largest unreinforced concrete dome. In the early 20th century, engineers like Félix Candela and Robert Maillart took unreinforced concrete to its artistic apex; many of their structures still survive.