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.

ConcreteMath

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.

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