Under Pressure: How Concrete Beams React to Being Bent

Let's imagine you have been asked to design a concrete beam for some sections of a building. What do you choose? Pure concrete or reinforced concrete?

The latter, right? But what type of reinforced concrete? Balanced, under reinforced, or over reinforced? 

Here we answer this question and also talk more generally about the history of concrete and its physical properties. For all those "concrete-philes" out there, eat your hearts out!

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How old is concrete?

Before we get into the nitty-gritty of the main topic, let's take a quick look at the interesting history of concrete. 

While you might already be more than familiar with concrete, chances are you may not realize just how old it is. In fact, since it is so ubiquitous today, you probably take this wonder material for granted.

However, this is grossly unfair -- concrete is a very ancient and fascinating material.

Some of the first evidence of concrete-like structures is from around 6500 BC. Evidence exists that early structures like floors, some housing elements, and underground cisterns were built in some regions of Syria and Jordan, and along the Danube. 

The next time a type of concrete appears to have made a widespread appearance was around 3000 BC. Ancient Egyptians commonly used to mix mud with straw to make dried bricks. 

To bind these bricks together, ancient Egyptians would use a combination of gypsum mortar and lime mortars -- including in the pyramids. Mortar of this kind is a type of cement, which is an essential element of concrete.

The Great Pyramids of Giza, for example, used somewhere in the region of half a million tons of this mortar. 

Some studies have found that parts of some pyramids may have been built by using a poured concrete building technique. This method appears to have been used in situ on the pyramids, in place of hauling giant stones. 

One of the most important innovations in early concrete history was the advent of Roman concrete. While the Romans were certainly not the first to invent concrete, they were the first to use it en masse -- as far as we know. By around the 2nd-Century BC, the Romans had, more or less, perfected the technique, using a combination of volcanic ash, lime, and seawater to form the mix. Both the Romans and the Greeks incorporated pozzolanic ash, which prevents cracks from spreading.

This mix was then packed into wooden frames to cure, and once hardened, would stack the concrete blocks like bricks. Roman concrete was so well made, that many Roman concrete structures still stand today, like the dome of the Pantheon. 

After the fall of Rome, concrete would experience something of a hiatus in its development until 1793 when John Smeaton discovered a more sophisticated method of making it. Later, in the 1800s, Joseph Aspdin would go on to invent Portland cement opening the door for our modern use of the concrete.

What is the tensile strength of concrete?

Concrete has been used for many building projects throughout history for one good reason -- it is strong, very strong. Not only that, but it is fairly easy to create and use.

But not all concrete is created equal. Today, the quality of concrete is largely determined by its strength. While the physical properties of concrete will vary slightly depending on its makeup, we do know the characteristics of some common forms of concrete. 

For example, Portland cement (one of the most common forms of concrete) has the following physical properties: 

• Density - ρ : 2240 - 2400 kg/m³ (140 - 150 lb/ft³) 
• Compressive strength : 20 - 40 MPa (3000 - 6000 psi)
• Flexural strength : 3 - 5 MPa (400 - 700 psi)
• Tensile strength - σ : 2 - 5 MPa (300 - 700 psi)

Other forms of concrete, especially those used for structural purposes, will usually be required to have much improved compressive and tensile strengths than that of "vanilla" Portland cement. For example, certain industrial standards, like ACI 318, require concrete to have compressive strengths of 5,000 to 6,000 psi or more.

When we talk about the strength of concrete, it's usually assumed that this refers to its compressive strength -- as detailed above. But, many structural uses of concrete also require it to resist bending, technically called flexure.

This depends on the type of load that the concrete structure in question will be used to resist, be it an entire building or just a single floor of an office. For this reason, different types of concrete are used for different applications in a building.

Depending on its intended use, the concrete in question will need to be assessed for its ability to bend, or not bend (flex), resist tension (stretching), shear (different layers moving in a different direction), and torsion forces (twisting), etc.

With regards to the tensile strength of concrete, testing has revealed that as a general rule, concrete's tensile strength is usually around 10% of its compressive strength (as we see for Portland cement above). 

How much pressure can concrete handle?

The answer to this question depends on what is meant by "pressure". The pressure is generally defined as "the action of a force against some obstacle or opposing force".  

While you may assume this means to press down on something, it can also include bending, flexing, twisting, etc of a concrete structure, depending on its application (e.g. a column, a wall, a floor, etc). Each of these different "pressures" on a piece of concrete will be handled by the concrete in different ways. 

In fact, most concrete formulas will be specifically designed to resist one or another of these forces in different ways, depending on its intended use. If the concrete is to be used for structural columns in a highrise building like a skyscraper, it will need to have very high compressive strength (in excess of 5,000 psi), as well as, high shear and torsion strength. 

If the concrete is for a floor, the compressive force will be less important and it will likely need to have the best tensile and flexure strength available. 

How is concrete strengthened?

Try as you might want to fiddle around with the chemistry of a concrete mix, there comes a point when it needs to have other things added to it. This is where reinforced concrete comes into its own.

Effectively a composite structure, reinforced concrete combines the strengths of concrete and steel to make an even stronger material than either alone. Concrete is very good at resisting compressive forces, but less so for other forces like shear or tension. It is, therefore, generally considered a brittle material. 

Steel, on the other hand, is less able to resist compression but is excellent at resisting shear and tension -- like those imparted by wind, earthquakes, vibrations, etc. This is why steel is often referred to as a ductile material. 

In practice, this means that concrete will resist strain up to a point, but then spectacularly fail. Steel, on the other hand, will first resist, then deform, and finally snap, at much higher levels of strain than concrete. 

By combing the two materials, you create a structure that can resist high amounts of compression, while also being able to stand up to high shear and tensile forces. 

This allows reinforced concrete to be used to create larger spans than would otherwise be safely possible. Reinforced concrete was first created in the 19th-century and revolutionized the construction industry thereafter.

What is the difference between over- and under-reinforced concrete beams?

When it comes to using concrete beams to span a void, the primary force, or load, on the beams is generally downward (thanks to gravity). This will lead to the uppermost part, specifically the constituent fibers of the beam, slumping, leading to compressive forces throughout the upper half of the concrete beam. Conversely, the lowermost half of the beam will undergo tension, or stretching.

There is also a thin area of the beam, exactly in the middle of its cross-section, called the "neutral axis", where fibers experience neither tensile nor compressive forces. 

As we have already seen, resisting compressive force is concrete's bread and butter, but it is less able to resist tensile forces (roughly 10% of its compressive strength). The above scenario is, in effect, something of a potential nightmare. 

So, how can this potential problem be mitigated? If you read the section above, you probably already know the answer -- stick some high-tensile strength steel in the lower part of the beam!

When it comes to adding steel to concrete beams, there are several ways you can do it: 

• Balanced section
• Over reinforced section
• Under reinforced section

Each one has its strengths and weaknesses, as you might imagine. 

Balanced sections, as the name suggests, offers a tradeoff where the top and bottom of the beam reach their maximum strain yields, or limits, at the same time. This is achieved by strategically placing a series of steel rods around the lowermost perimeter (with regards to its cross-section) of the concrete. 

An over-reinforced section, as the name implies, includes more steel than is normally required, to reinforce the concrete beam. The inclusion of more steel at the base of the concrete will result in the "NA" line being closer to the base of the beam than for non-reinforced of balanced sections.

By contrast, under-reinforced section beams have, yes you've guessed it, less high-tensile strength rods than a balanced section. This results in the "NA" of the concrete beam is closer to the top of the concrete beam than either balanced or over reinforced sections.

When put under strain, both balanced and over reinforced sections will result in the uppermost concrete half of the beam failing brittly first. For under reinforced beams, the steel takes the brunt of the strain and will fail long before the concrete.

But isn't that a problem? Actually no. As the steel reaches its strain yield limit it will begin to stretch and bend. 

This will cause the beam to also bend, giving engineers not only a visual indication of an impending disaster but time to do something about it. Balanced and over reinforced sections, on the other hand, will fail in short order before anyone has even the slightest indication there is a problem. 

In either case, the beam will ultimately fail when the concrete is crushed and breaks. 

But, there are other benefits to under reinforced sections too. Over reinforced, and to a point balanced sections, are generally more costly to build when compared to under reinforced sections. 

It is for this reason, that in most circumstances, under-reinforced section concrete beams are generally preferred to either balanced or over-reinforced as they are more economical, and are generally safer. 

So there you go. Next time you find yourself in an argument about which type of concrete beam section to choose, you can now answer with confidence.