Modulus of elasticity of concrete: NBR 6118 formula, table by strength class and NBR 8522-1 test

The modulus of elasticity of concrete measures the stiffness of the material: how much it shortens under a compressive stress. Under ABNT NBR 6118:2023 (the Brazilian standard for the design of concrete structures), for concrete classes C20 to C50, the initial tangent modulus is E_ci = α_E · 5600 · √f_ck, in MPa, and the secant modulus used in design is E_cs = α_i · E_ci. A C30 concrete with granite coarse aggregate has an E_ci of about 31 GPa and an E_cs of about 27 GPa.

For the two most frequently looked-up classes, with granite: C25 has E_ci = 28.0 GPa and E_cs = 24.2 GPa, and C30 has E_ci = 30.7 GPa and E_cs = 26.8 GPa. The 2023 revision of NBR 6118 kept the formulas and coefficients of the 2014 edition. The general concept of the modulus, valid for any material, is covered in the article on the modulus of elasticity (Young's modulus); here the topic is what is specific to concrete. The modulus is measured in a compression test with extensometers mounted on the specimen, and this article follows the order of a lecture: what it is, why there are two moduli, the formulas, the tables, what makes the value vary, the test, worked exercises and the equipment.

What the modulus of elasticity of concrete is

In any material, the modulus of elasticity is the ratio between the applied stress and the strain it produces, E = σ / ε, which is Hooke's law. On the stress-strain curve, it is the slope of the initial portion: the steeper it is, the stiffer the material and the less it shortens under the same load. A concrete beam with a high modulus has a smaller deflection; a column with a high modulus shortens less.

The photo shows a cylindrical concrete specimen between the compression platens, the basic setup of the modulus test under NBR 8522-1 (the Brazilian standard for determining the elastic and deformation moduli of concrete), which adds strain-measuring devices on the specimen itself.

The difference between concrete and steel lies in the shape of the curve. In steel, the initial portion is a straight line up to near yielding. In concrete, the curve starts to bend almost from the beginning. The reason is the structure of the material: concrete is a three-phase composite, made of hardened cement paste, coarse aggregate and the interfacial transition zone between the two. The transition zone is more porous and already contains microcracks before any load is applied, caused by shrinkage and bleeding. Under compression, these microcracks grow, and strain starts to increase faster than stress.

Up to about 30% to 40% of the compressive strength (f_c), the curve is nearly straight and the behavior is practically reversible: when unloaded, the specimen returns to its initial length, which is what characterizes elastic deformation. Above this range, microcracking propagates, the curve bends more and more and part of the deformation becomes permanent. The peak, which is f_c itself, lies near 2 ‰ shortening for ordinary concretes, and NBR 6118 adopts 3.5 ‰ as the ultimate strain for classes C20 to C50.

Since the curve has no perfectly straight portion, "the slope" depends on where it is measured. That is why concrete has more than one modulus, each defined by two points on the curve, and the standard has to state which one is used in each situation.

Eci and Ecs: initial tangent modulus and secant modulus

NBR 6118 and NBR 8522-1 work with two moduli. The initial tangent modulus, E_ci, is the slope of the tangent to the curve at the origin: it represents the stiffness of concrete at low stresses. The secant modulus, E_cs, is the slope of a line joining the origin, or a low-stress point, to a higher-stress point on the curve. Because the curve bends as stress rises, the secant lies below the tangent, and E_cs is always less than or equal to E_ci.

In laboratory practice, the exact tangent at the origin is not measured. NBR 8522-1:2021 obtains E_ci as the slope of the line between two points near the start, 0.5 MPa and 30% of f_c, a line joining two points on the curve called the chord. The exact tangent at the origin cannot be measured accurately, so the standard adopts this chord as E_ci; it falls slightly below the theoretical tangent, and the more linear the concrete, the smaller the gap. The American standard ASTM C469/C469M uses a different chord, up to 40% of the ultimate load. The chart below plots the three lines on the curve of a concrete with f_c = 30 MPa and shows that the higher the second point, the lower the modulus: 31.4 GPa for the tangent, 28.0 GPa for the NBR 8522-1 chord and 27.0 GPa for the secant up to 0.4 f_c.

Modulus of elasticity or modulus of deformation

The title of NBR 8522-1 refers to "moduli of elasticity and of deformation", and the two names have distinct meanings. The modulus of elasticity is E_ci, the initial tangent modulus. The secant modulus of deformation is E_cs, calculated up to a specified stress. In reports and designs, "modulus of deformation" almost always means the secant modulus.

Which modulus to use in reinforced concrete design

NBR 6118 (item 8.2.8) specifies E_cs for elastic design analyses: calculation of internal forces and verification of serviceability limit states, such as deflections. It is taken as a single modulus, in tension and in compression, to evaluate a member or a cross section. E_ci is used in analyses that depend on stiffness under low, sustained stress, such as the global behavior of the structure, creep and prestress losses. Using E_ci instead of E_cs in a deflection calculation underestimates the deformation, because the modulus used is higher than the recommended one.

The same item of the standard completes the elastic description of concrete with two values: Poisson's ratio ν = 0.2 and shear modulus G_c = E_cs / 2.4, valid for compressive stresses below 0.5 f_c and tensile stresses below the tensile strength. Poisson's ratio has its own article.

Formula for the modulus of elasticity of concrete under NBR 6118:2023

NBR 6118 requires E_ci to be obtained from the NBR 8522-1 test at 28 days. When no test is available, which is common at the design stage, the standard allows it to be estimated from the characteristic compressive strength, f_ck, which is the strength with a 95% probability of being exceeded and defines the concrete class (C30 has f_ck = 30 MPa). The estimate uses two expressions, one for each strength group, and two coefficients.

The two expressions for Eci

For group I concretes, C20 to C50, the modulus grows with the square root of the strength:

• C20 to C50: E_ci = α_E · 5600 · √f_ck, with E_ci and f_ck in MPa.
• C55 to C90: E_ci = 21.5 · 10³ · α_E · (f_ck/10 + 1.25)^1/3, also in MPa.

In group II, C55 to C90, the standard replaces the square root with a cube root. In high-strength concrete, the paste is denser and the transition zone is less porous, and the modulus grows more slowly than the strength. Each expression is valid only in its own range: applying the square root to a C70 overestimates the modulus.

The aggregate coefficient, αE

Coarse aggregate takes up most of the volume of concrete and is much stiffer than the paste, so the rock type weighs on the modulus as much as the strength does. The standard accounts for this with the coefficient α_E, which multiplies E_ci:

• Basalt and diabase: α_E = 1.2.
• Granite and gneiss: α_E = 1.0.
• Limestone: α_E = 0.9.
• Sandstone: α_E = 0.7.

Between sandstone and basalt, the modulus of the same C30 varies by 71%. A design calculated with granite and built with sandstone aggregate will have a concrete 30% less stiff than predicted.

The αi coefficient and the secant modulus

The secant modulus is derived from the initial tangent modulus through a coefficient that increases with the class:

• Secant modulus: E_cs = α_i · E_ci.
• Coefficient: α_i = 0.8 + 0.2 · f_ck/80 ≤ 1.0.

For C20, α_i = 0.85; for C50, 0.925; from C80 upward, it reaches 1.0. The coefficient reflects what the previous chart showed: low-strength concretes have a curve that bends early, and the secant falls well below the tangent. High-strength concretes are nearly linear up to close to failure, and the two lines coincide.

The modulus before 28 days

The modulus increases as the cement hydrates, but more slowly than the strength. Between 7 and 28 days, NBR 6118 estimates the modulus at age t from the strength at that age, f_c(t), and the 28-day strength, f_c:

• C20 to C45: E_ci(t) = [f_c(t) / f_c]^0.5 · E_ci.
• C50 to C90: E_ci(t) = [f_c(t) / f_c]^0.3 · E_ci.

This estimate matters, for example, when removing shoring and when prestress is applied before 28 days.

What changed in NBR 6118:2023 and the old rule still in circulation

For the modulus, nothing changed: the 2023 edition kept the expressions and coefficients of 2014. The main change in item 8.2 was the brittleness coefficient η_c, in item 8.2.10.1, applied to concretes above 40 MPa, which does not affect the modulus. What still appears in course notes and websites is the rule from the 2003 and 2007 editions: E_ci = 5600 · √f_ck without α_E and E_cs = 0.85 · E_ci = 4760 · √f_ck. It was withdrawn in 2014. The mix of the two, "E_ci = 0.85 · 5600 · √f_ck", is wrong under any edition.

The table summarizes the current expressions:

Quantity	Expression (NBR 6118:2023)	Validity
Eci, group I	αE · 5600 · √fck (MPa)	C20 to C50
Eci, group II	21.5 · 103 · αE · (fck/10 + 1.25)1/3 (MPa)	C55 to C90
Ecs	αi · Eci	all classes
αi	0.8 + 0.2 · fck/80 ≤ 1.0	all classes
Eci(t)	[fc(t)/fc]0.5 or 0.3 · Eci	7 to 28 days

The expressions apply to normal-weight concrete, with a density of 2,000 to 2,800 kg/m³. Lightweight concrete and ultra-high-performance concrete have their own behavior and methods.

Table of the modulus of elasticity of concrete by class

Table 8.1 of NBR 6118 gives the estimated values of E_ci, E_cs and α_i by class, assuming granite as the coarse aggregate. The values below were calculated with the expressions of item 8.2.8, to one decimal place; the standard rounds to whole GPa (C30: 31 and 27 GPa).

Class	Eci (GPa)	αi	Ecs (GPa)
C20	25.0	0.850	21.3
C25	28.0	0.863	24.2
C30	30.7	0.875	26.8
C35	33.1	0.888	29.4
C40	35.4	0.900	31.9
C45	37.6	0.913	34.3
C50	39.6	0.925	36.6
C60	41.6	0.950	39.5
C70	43.4	0.975	42.4
C80	45.1	1.000	45.1
C90	46.7	1.000	46.7

The chart below shows the same values as bars. Two effects stand out: the gap between E_ci and E_cs narrows with the class until it disappears at C80, and the gain in modulus becomes smaller after the change of formula, in group II. From C30 to C70 the strength rises by 133%, and E_ci by only 42%.

Modulus of elasticity of 25 MPa and 30 MPa concrete

These are the two most frequent questions, and the answer depends on the aggregate. With granite, concrete with f_ck of 25 MPa has E_ci = 5600 × 5 = 28.0 GPa and E_cs = 0.8625 × 28.0 = 24.2 GPa. The 30 MPa concrete has E_ci = 5600 × √30 = 30.7 GPa and E_cs = 0.875 × 30.7 = 26.8 GPa. The next table applies the α_E of each rock type to both classes:

Aggregate (αE)	C25: Eci / Ecs (GPa)	C30: Eci / Ecs (GPa)
Basalt, diabase (1.2)	33.6 / 29.0	36.8 / 32.2
Granite, gneiss (1.0)	28.0 / 24.2	30.7 / 26.8
Limestone (0.9)	25.2 / 21.7	27.6 / 24.2
Sandstone (0.7)	19.6 / 16.9	21.5 / 18.8

C30 in other design codes

Each design code has its own expression, and comparing the same concrete shows the scatter between them. The values below were calculated for f_ck = 30 MPa with reference aggregate. Eurocode 2 and the fib Model Code start from the mean strength, f_cm = f_ck + 8 MPa, which is why they give higher values.

Standard	Expression	C30
NBR 6118:2023 (granite)	Eci = 5600 · √fck	30.7 GPa (Ecs 26.8)
NBR 6118:2007 (withdrawn)	Ecs = 4760 · √fck	26.1 GPa
ACI 318	Ec = 4700 · √f′c	25.7 GPa
Eurocode 2	Ecm = 22 · (fcm/10)0.3 GPa	32.8 GPa
fib Model Code 2010	Eci = 21.5 · 103 · (fcm/10)1/3	33.5 GPa

For comparison with another construction material: reinforcing steel has a modulus of 210 GPa under NBR 6118, 5 to 8 times that of an ordinary concrete. The details are in the article on the modulus of elasticity of steel.

What makes the modulus of concrete vary

The code formulas depend only on f_ck and the rock type, but the actual modulus of a concrete depends on the mix design, the curing and even the way the test specimen is tested. Knowing these factors explains why two concretes of the same strength class can have very different moduli:

• Type and content of coarse aggregate: this is the main factor, and not only because of the rock. In a compilation of results from across Brazil, the concrete density was the variable with the greatest influence on E_ci at 28 days (Leal et al., 2020). More aggregate and less paste give a stiffer concrete.
• Water/cement ratio: more water makes the paste more porous, and pores do not resist compression. A high w/c ratio lowers the modulus, and a low one raises it.
• Age: cement hydration continues after 28 days and densifies the paste; the modulus increases, but more slowly than the strength.
• Curing: insufficient moist curing stops hydration at the surface and leaves the paste more porous and microcracked, with a lower modulus. Controlled temperature and humidity during curing give a more consistent modulus.
• Moisture during the test: a saturated test specimen gives a modulus about 15% higher than a dry one, because the water in the pores helps carry the compressive load.
• Loading rate: very slow loading lets creep act during the test and lowers the modulus; very fast loading overestimates it. That is why NBR 8522-1 sets the loading rate.
• Temperature: at high temperature, as in a fire, microcracking and water loss from the paste reduce the modulus, and the structure deforms more under the same load.
• Quarry: the same "granite" varies from one quarry to another, which the formulas cannot see.

How the modulus of elasticity test of concrete is performed (NBR 8522-1:2021)

The static modulus test follows ABNT NBR 8522-1:2021 (the Brazilian standard for the static modulus of hardened concrete), "Hardened concrete: Determination of the moduli of elasticity and deformation. Part 1: Static moduli in compression". The test specimens are cylinders with a height equal to twice the diameter, usually 100 × 200 mm or 150 × 300 mm, cast and cured according to NBR 5738 (the Brazilian standard for casting and curing concrete specimens). The standard requires at least five specimens of the same concrete: two are broken beforehand, according to NBR 5739 (the Brazilian standard for concrete compression testing), to give the strength f_c that defines the load levels, and three are used for the modulus.

The specimen is centered between the platens of a compression machine or universal testing machine, and the strain is measured by extensometers attached to the concrete itself, on two diametrically opposite gauge lines; the result is the average of the two. The measurement must be taken on the specimen, and not from the machine displacement, because of scale: in the range where the modulus is measured, a 200 mm specimen shortens by less than 0.1 mm, and the crosshead displacement also includes platen seating, the capping and the deformation of the machine itself. Exercise 5 shows the size of the error.

Methods A and B

The standard defines two ways of setting the starting point of the chord. Both use the stress σ_b = 0.3 · f_c as the end point:

• Method A, fixed stress: the starting point is the stress σ_a = 0.5 MPa, and the strain ε_a is read at that stress.
• Method B, fixed strain: the starting point is the strain ε_a = 50 · 10^-6, and the stress σ_a is read at that strain.

Loading and readings, step by step

Loading is applied in cycles at a rate of 0.45 ± 0.15 MPa/s, and each stress level is held for 60 s before the reading. The initial cycles seat the specimen on the platens and stabilize the extensometers. The sequence is:

1. Center the test specimen and attach the extensometers on the two opposite gauge lines.
2. Run the loading and unloading cycles between the initial level (σ_a) and σ_b = 0.3 · f_c, holding each level for 60 s.
3. Read the strains ε_a and ε_b in the last cycle, within the 30 s following each hold.
4. Remove the extensometers and break the specimen to obtain the actual strength f_c,ef.
5. Check the strength: if f_c,ef differs by more than 20% from the f_c used to define σ_b, the result for that specimen is discarded.

Calculation of Eci and Ecs in the test

With stresses in MPa and dimensionless strains, the factor 10^-3 converts the result to GPa:

• Method A: E_ci = (σ_b − 0.5) / (ε_b − ε_a) · 10^-3.
• Method B: E_ci = (σ_b − σ_a) / (ε_b − 50 · 10^-6) · 10^-3.
• Secant modulus of deformation: E_cs = (σ_n − σ_a) / (ε_n − ε_a) · 10^-3, where σ_n is the specified stress.

The stress σ_n for the secant modulus is chosen by whoever specifies the test, usually the structural designer, according to the service stress of interest. The test uses the actual f_c of the broken specimens, not the design f_ck: f_ck appears only in the estimation formulas.

The test according to ASTM C469/C469M

The American standard measures the chord modulus and Poisson's ratio in the same test. The chord runs from the stress corresponding to a strain of 50 · 10^-6 up to 40% of the ultimate load, a slightly higher range than in NBR 8522-1, and the strain is the average of two opposite gauge lines. Because of the higher end point, the ASTM modulus tends to be slightly lower than the E_ci of the Brazilian standard for the same concrete, as the first chart showed.

Static modulus and dynamic modulus

The modulus can also be obtained without loading the specimen to 30% of its ultimate strength, by dynamic methods that measure vibration or wave propagation. ABNT NBR 8522-2:2021 (the Brazilian standard for the dynamic modulus) determines the dynamic modulus of elasticity, E_cd, from the natural vibration frequencies: the specimen receives a light impact, and the resonant frequency gives the modulus. Other references are ASTM C215, by resonant frequency, ASTM E1876, by impulse excitation, and the ultrasonic method of NBR 8802 (the Brazilian standard for ultrasonic pulse velocity).

The two moduli are not the same. In the dynamic method the stress is minimal, the microcracks barely open and the material responds with practically no creep, so E_cd comes out higher: about 20% above the static value in high-strength concretes, 30% in medium-strength concretes and 40% in low-strength concretes. In a study of basalt concretes from the state of Paraná, Brazil, the dynamic modulus was 16% above the static value by impulse excitation and 28% by ultrasound. NBR 8522-1 provides, in Annex B, an empirical correlation, the Popovics model, to estimate E_ci from E_cd and the density. The dynamic method is fast, does not destroy the specimen and is useful for tracking how the modulus develops; the value used in NBR 6118 is the static one, and using the dynamic value without conversion overestimates the stiffness.

Why the modulus matters: estimated or measured

The modulus does not decide whether the structure can carry the load, but it does decide how much it deforms. Deflection of beams and slabs, cracks in masonry supported by them, long-term creep deformation and the global stability of tall buildings all depend on E_cs. A slab with a modulus 15% lower than expected has an immediate deflection 15% larger, and creep amplifies this difference over the years.

The problem is that the code formula is an estimate. Builders and laboratories report that tested values are often below the estimated ones, and some recommend reducing the estimate by 10% to 15% (IBRACON, the Brazilian Concrete Institute, 2023). Published data show the extent of the scatter:

• Borin et al. (2010): in job-site concretes with strength close to 30 MPa, the modulus ranged from 16.5 to 47.7 GPa, with a 20% probability of falling below the estimate of the code then in force.
• Leal et al. (2020): in the compilation of results from across Brazil, the fitted α_E was 1.00 to 1.03 for granite and gneiss, which confirms the code; 1.08 for limestone, above the code's 0.9; and 1.07 to 1.14 for basalt, below 1.2.
• Santos et al. (2017): with 324 specimens of basalt and dolomite from the Triângulo Mineiro region (Minas Gerais, Brazil), the expressions of NBR 6118:2014 and the fib Model Code were the closest to the results.
• North Coast of São Paulo state: a local laboratory reports 30 MPa concretes with gneiss and E_ci as low as 26 GPa, about 17% below the estimate (Sotef, 2025).

The practical conclusion is that of NBR 6118 itself: the modulus should come from the NBR 8522-1 test. In projects where deflection and cracking are critical, the designer specifies the minimum modulus, and the quality control laboratory verifies it with the project's own aggregates.

Worked examples

The six exercises follow the order of the article: estimation by the code, effect of the aggregate, high strength, calculation from the test readings, the error of measuring by the crosshead, and the effect of the modulus on deflection.

Exercise 1: Eci and Ecs of a C30 with granite

Data: f_ck = 30 MPa, granite coarse aggregate, α_E = 1.0.

1. E_ci = 1.0 × 5600 × √30 = 5600 × 5.477 = 30,672 MPa ≈ 30.7 GPa.
2. α_i = 0.8 + 0.2 × 30/80 = 0.875, below 1.0.
3. E_cs = 0.875 × 30,672 = 26,838 MPa ≈ 26.8 GPa.

Exercise 2: the same C30 with basalt, and C25 with granite

With basalt, α_E = 1.2. For C25 with granite, √25 = 5.

1. C30 basalt: E_ci = 1.2 × 30,672 = 36,806 MPa; E_cs = 0.875 × 36,806 = 32,205 MPa, 20% above granite at the same f_ck.
2. C25 granite: E_ci = 5600 × 5 = 28,000 MPa; α_i = 0.8625; E_cs = 24,150 MPa.

Exercise 3: high-strength concrete C70 with granite

C70 belongs to group II, so the cube-root expression applies.

1. E_ci = 21,500 × 1.0 × (70/10 + 1.25)^1/3 = 21,500 × 8.25^1/3 = 21,500 × 2.0206 = 43,443 MPa.
2. α_i = 0.8 + 0.2 × 70/80 = 0.975.
3. E_cs = 0.975 × 43,443 = 42,357 MPa.

With the square root, outside its range, the result would be 5600 × √70 = 46,853 MPa, 8% above the correct value.

Exercise 4: Eci from the test readings (method A)

Teaching data: 100 × 200 mm test specimen; f_c of the specimens broken beforehand = 32.0 MPa; two opposite extensometers with a 100 mm gauge length. Average reading at the 0.5 MPa level: ε_a = 20 · 10^-6. At the σ_b level: ε_b = 325 · 10^-6.

1. Area: A = π × 50² = 7,854 mm².
2. σ_b = 0.30 × 32.0 = 9.6 MPa. Forces at the load levels: 0.5 × 7,854 = 3.93 kN and 9.6 × 7,854 = 75.4 kN.
3. E_ci = (9.6 − 0.5) / (305 · 10^-6) · 10^-3 = 29.8 GPa.
4. Shortening measured over the 100 mm gauge length: 305 · 10^-6 × 100 = 0.0305 mm, or 30.5 µm.

After the readings, the specimen is broken; if f_c,ef falls outside 32.0 ± 20%, the result is discarded.

Exercise 5: the error of measuring by the crosshead

In the same test, the crosshead displacement between the same two forces was 0.122 mm. The concrete, over its 200 mm height, shortened by 305 · 10^-6 × 200 = 0.061 mm; the other 0.061 mm come from platen seating, the capping and the deformation of the machine.

1. Apparent strain: 0.122 / 200 = 610 · 10^-6.
2. Apparent modulus: 9.1 / (610 · 10^-6) · 10^-3 = 14.9 GPa, half the actual value.

The modulus can only be measured with an extensometer on the test specimen, and the same applies to metals in the tensile test.

Exercise 6: effect of the modulus on deflection

Simply supported beam, 5 m span, distributed load of 10 kN/m, 15 × 40 cm cross section, C25 concrete with granite. Moment of inertia of the gross section: I = 0.15 × 0.40³ / 12 = 8.0 · 10^-4 m⁴. Immediate elastic deflection: δ = 5·q·L⁴ / (384·E·I).

1. With E_cs = 24.15 GPa: δ = 5 × 10,000 × 625 / (384 × 24.15 · 10⁹ × 8.0 · 10^-4) = 4.2 mm.
2. With E_ci = 28 GPa, by mistake: δ = 3.6 mm, 14% lower.
3. With basalt (E_cs = 29.0 GPa): 3.5 mm. With sandstone (16.9 GPa): 6.0 mm.

NBR 6118 calculates deflection with the equivalent moment of inertia of the cracked section and adds creep; the exercise isolates only the effect of the modulus. The relationship between stiffness and deflection is also covered in the flexural test.

Common mistakes with the modulus of concrete

The mistakes below appear frequently in design calculations, reports and technical texts, and each has been covered in a section of this article:

• Using E_ci where the code requires E_cs: for deflections and internal forces, this underestimates deformation by 7% to 15% in classes C20 to C50.
• Forgetting α_E: designing with granite and building with sandstone gives a modulus 30% lower.
• Using the superseded rule: E_cs = 0.85 · E_ci, or the mixed form "0.85 · 5600 · √f_ck", has not been valid since 2014.
• Using the wrong formula range: the square root applies up to C50, and the cube root from C55 to C90.
• Using f_ck in the test: σ_b = 0.3 · f_c, with f_c measured on the specimens broken beforehand.
• Measuring strain from the crosshead: the modulus comes out much lower than the actual value.
• Comparing dynamic and static values without conversion: the dynamic modulus is 20% to 40% higher.
• Treating the modulus as a constant: moisture, quarry and procedure change the result, and the variation between laboratories reaches 10% to 15%.

Standards for the modulus of elasticity of concrete

The Brazilian standards cover design (NBR 6118), the static and dynamic tests (NBR 8522-1 and -2) and specimen preparation. The table lists those cited in this article:

Standard	Scope	Edition
ABNT NBR 6118	design of concrete structures (Brazil): Eci, Ecs, αE, αi, table 8.1	2023
ABNT NBR 8522-1	static moduli of elasticity and deformation in compression	2021
ABNT NBR 8522-2	dynamic modulus by natural vibration frequencies	2021
ABNT NBR 5739	compression test of cylindrical specimens	2018
ABNT NBR 5738	casting and curing of test specimens	2015
ABNT NBR 8953	classification of concrete by strength groups (C20 to C90)	not specified
ABNT NBR 8802	ultrasonic pulse velocity	not specified
ASTM C469/C469M	static modulus and Poisson's ratio of concrete in compression	C469/C469M-22
ASTM C215	resonant frequencies of concrete specimens	not specified
ASTM E1876	dynamic modulus by impulse excitation	not specified
ASTM E111	definitions of Young's, tangent and chord modulus	E111-17(2025)e1
ACI 318, Eurocode 2, fib Model Code 2010	design codes with their own modulus expressions	not specified

Two corrections to lists in circulation, including the previous version of this article: NBR 8953 classifies concrete by strength and does not cover ultrasound, which is the subject of NBR 8802; and ISO 6784, cited as the international standard for the static modulus, has been replaced by ISO 1920-10.

Testing machine for the concrete modulus of elasticity test

The ABNT NBR 8522-1 test (the Brazilian standard for the static modulus of elasticity of concrete in compression) requires three things from the equipment: applying compression at a controlled rate and holding the load steps, measuring force with a calibrated load cell, and reading strain with extensometers attached to the test specimen. The machine must also break the specimen at the end of the test: a 100 × 200 mm C30 cylinder fails at about 236 kN, and a 150 × 300 mm cylinder at about 530 kN. The Biopdi M2 universal testing machine line includes floor-standing models of 300 kN, 600 kN and 1,000 kN, load cells rated Class 1 according to ABNT NBR ISO 7500-1:2023 (the Brazilian adoption of ISO 7500-1), and the BioLab software. The panel below shows the machine, the role of each part in the modulus test, and the compression platens.

For 100 × 200 mm specimens up to C25, the recommended model is the 300 kN universal testing machine (MBIOII-300-M2), whose page mentions concrete and NBR 5739:2018 (the Brazilian standard for concrete compression testing); from C30 to C50 on the same specimen, the 600 kN model (MBIOII-600-M2); and for 150 × 300 mm cylinders of high strength classes, the 1,000 kN model (MBIOII-1000-M2). The BioLab software lets you build the test as a script and create custom calculations, such as the chord modulus (σ_b − 0.5) / (ε_b − ε_a). The extensometers suited to concrete specimens and the setup of the NBR 8522-1 routine are defined in the quote. To choose between models, see the universal testing machine guide.