# Properties of concrete - modulus of elasticity

## Description

Concrete has relatively high compressive strength, but significantly lower tensile strength. As a result, without compensating, concrete would almost always fail from tensile stresses – even when loaded in compression. The practical implication of this is that concrete elements subjected to tensile stresses must be reinforced with materials that are strong in tension (often steel). The elasticity of concrete is relatively constant at low stress levels but starts decreasing at higher stress levels as matrix cracking develops. Concrete has a very low coefficient of thermal expansion, and as it matures concrete shrinks. All concrete structures will crack to some extent, due to shrinkage and tension. Concrete which is subjected to long-duration forces is prone to creep. The density of concrete varies, but is around 2,400 kilograms per cubic metre (150 lb/cu ft).

Reinforced concrete is the most common form of concrete. The reinforcement is often steel, rebar (mesh, spiral, bars and other forms). Structural fibers of various materials are available. Concrete can also be prestressed (reducing tensile stress) using internal steel cables (tendons), allowing for beams or slabs with a longer span than is practical with reinforced concrete alone. Inspection of existing concrete structures can be non-destructive if carried out with equipment such as a Schmidt hammer, which is sometimes used to estimate relative concrete strengths in the field.

The ultimate strength of concrete is influenced by the water-cementitious ratio (w/cm), the design constituents, and the mixing, placement and curing methods employed. All things being equal, concrete with a lower water-cement (cementitious) ratio makes a stronger concrete than that with a higher ratio. The total quantity of cementitious materials (portland cement, slag cement, pozzolans) can affect strength, water demand, shrinkage, abrasion resistance and density. All concrete will crack independent of whether or not it has sufficient compressive strength. In fact, high Portland cement content mixtures can actually crack more readily due to increased hydration rate. As concrete transforms from its plastic state, hydrating to a solid, the material undergoes shrinkage. Plastic shrinkage cracks can occur soon after placement but if the evaporation rate is high they often can actually occur during finishing operations, for example in hot weather or a breezy day. In very high-strength concrete mixtures (greater than 70 MPa) the crushing strength of the aggregate can be a limiting factor to the ultimate compressive strength. In lean concretes (with a high water-cement ratio) the crushing strength of the aggregates is not so significant. The internal forces in common shapes of structure, such as arches, vaults, columns and walls are predominantly compressive forces, with floors and pavements subjected to tensile forces. Compressive strength is widely used for specification requirement and quality control of concrete. Engineers know their target tensile (flexural) requirements and will express these in terms of compressive strength.

The modulus of elasticity of concrete is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions. The modulus of elasticity of concrete is relatively constant at low stress levels but starts decreasing at higher stress levels as matrix cracking develops. The elastic modulus of the hardened paste may be in the order of 10-30 GPa and aggregates about 45 to 85 GPa. The concrete composite is then in the range of 30 to 50 GPa.

The American Concrete Institute allows the modulus of elasticity to be calculated using the equation shown here.

This equation is completely empirical and is not based on theory. Note that the value of Ec found is in units of psi.

Related formulas## Variables

E_{c} | modulus of elasticity of concrete (psi) (dimensionless) |

w_{c} | weight of concrete (lb/ft^3) (dimensionless) |

f_{c} | compressive strength of concrete at 28 days (psi) (dimensionless) |