What is the modulus of elasticity E for steel?

The modulus of elasticity (Young's modulus) for structural steel is E = 200,000 MPa (200 GPa) or 29,000 ksi in US customary units. This value is essentially constant across all structural steel grades — A36, A992, S355, S460, G300, and G350 all use E = 200 GPa. Even high-strength steels (A514, S690) have the same E, meaning they have the same stiffness but higher strength.

Does the modulus of elasticity change with temperature?

Yes. E decreases with increasing temperature. At 100 deg C, E retains ~100% of its ambient value. At 400 deg C: ~70% (140 GPa). At 600 deg C: ~31% (62 GPa). At 800 deg C: ~10% (20 GPa). Fire design standards (EN 1993-1-2, AISC Appendix 4) provide temperature-dependent reduction factors kE,ÃÂÃÂ¸ for the elastic modulus as a function of steel temperature.

Is E the same for all directions in steel?

Yes. Rolled structural steel is isotropic at the macroscale — E is the same in all directions (Ex = Ey = Ez = 200 GPa). This is because steel has a polycrystalline BCC/FCC structure with randomly oriented grains after hot rolling. The shear modulus G is related to E by G = E / [2(1+nu)] ÃÂ¢ÃÂÃÂ 200 / [2*1.3] ÃÂ¢ÃÂÃÂ 77 GPa (11,200 ksi) for Poisson's ratio nu = 0.3.

Modulus of Elasticity (E) — Young's Modulus for Steel

The modulus of elasticity (E), also known as Young's modulus, is the measure of a material's stiffness — its resistance to elastic deformation under uniaxial stress. For structural steel, E = 200,000 MPa (200 GPa) or 29,000 ksi in US customary units. This value is essentially constant across virtually all structural steel grades.

Hooke's Law:  ÃÂÃÂ = E * ÃÂÃÂµ
E = ÃÂÃÂ / ÃÂÃÂµ = stress / strain in the linear-elastic region

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Why E is Constant Across Steel Grades

Unlike yield strength (Fy), which varies significantly by grade (36 to 100+ ksi), Young's modulus depends on atomic bonding forces — not on microstructural features like grain size, dislocations, or alloying elements. All carbon and low-alloy steels share the same body-centered cubic (BCC) iron lattice at ambient temperature, resulting in E ÃÂ¢ÃÂÃÂ 200 GPa.

This means:

A36 (Fy = 36 ksi) and A514 (Fy = 100 ksi) have the same stiffness.
A beam made of A36 deflects exactly the same amount as an identical beam of A514 under the same load.
Higher-strength steel does NOT reduce deflection — only a larger I (moment of inertia) does.

Elastic Constants for Structural Steel

Property	Symbol	Value (Metric)	Value (US)
Modulus of elasticity	E	200,000 MPa (200 GPa)	29,000 ksi
Shear modulus	G	77,200 MPa (77 GPa)	11,200 ksi
Poisson's ratio	ÃÂÃÂ½	0.3	0.3
Bulk modulus	K	167,000 MPa	24,200 ksi

The relationship between elastic constants:

G = E / [2 * (1 + ÃÂÃÂ½)]  =  200 / 2.6  ÃÂ¢ÃÂÃÂ  77 GPa
K = E / [3 * (1 - 2ÃÂÃÂ½)] =  200 / 1.2  ÃÂ¢ÃÂÃÂ  167 GPa

Temperature Dependence of E

E decreases with increasing temperature. Fire design standards (EN 1993-1-2, AISC 360 Appendix 4) provide reduction factors:

Temperature (deg C)	kE,ÃÂÃÂ¸ = E(ÃÂÃÂ¸)/E(ambient)	E (GPa)	Notes
20	1.000	200	Ambient
100	1.000	200	No reduction
200	0.900	180	Slight reduction
300	0.800	160
400	0.700	140	Significant softening
500	0.600	120
600	0.310	62	Critical — creep dominates
700	0.130	26	Near total loss of stiffness
800	0.090	18

Design Uses of E

Application	Formula	E Role
Beam deflection	ÃÂÃÂ´ = 5wL^4 / (384EI)	Denominator — stiffer = less deflection
Euler buckling	Pcr = ÃÂÃÂ^2 EI / (KL)^2	Direct proportionality
Column stiffness	EA/L for axial	Direct proportionality
Vibration (natural freq)	f_n = (ÃÂÃÂ/2L^2) * sqrt(EI/m)	Under square root
Frame second-order analysis	Geometric stiffness depends on P, not E	E used in elastic stiffness matrix

Frequently Asked Questions

What is the Young's modulus of structural steel? E = 200 GPa (200,000 MPa) or 29,000 ksi for all common structural steel grades. This value is used uniformly in AISC 360, EN 1993, AS 4100, and CSA S16. Even high-strength quenched-and-tempered steels (A514, S690) use the same E.

Why doesn't higher-strength steel reduce beam deflection? Deflection depends on E and I (moment of inertia): ÃÂÃÂ´ ÃÂ¢ÃÂÃÂ 1/(EI). Since E is the same for all steel grades (~200 GPa), only increasing the section depth or moment of inertia reduces deflection. Using A572 Gr 50 instead of A36 does not change beam stiffness at all — only the strength capacity changes.

What is the shear modulus G for steel? G = 77 GPa (11,200 ksi), calculated from G = E / [2(1+ÃÂÃÂ½)] with E = 200 GPa and ÃÂÃÂ½ = 0.3. The shear modulus governs torsional stiffness (GJ/L) and shear deformation. In most steel beam applications, shear deformation is negligible compared to flexural deformation; however, for short, deep beams (L/d < 10), shear deformation should be checked.

International Code References

AISC 360: E = 29,000 ksi (200,000 MPa), G = 11,200 ksi (77,200 MPa). Commentary Section 3-2.
EN 1993-1-1: E = 210,000 MPa (slightly higher than AISC). Section 3.2.6. EN 1993 uses 210 GPa rather than 200 GPa — a ~5% difference that affects deflection and buckling calculations between US and European practice.
AS 4100: E = 200,000 MPa, G = 80,000 MPa. Section 3.1.4.
CSA S16: E = 200,000 MPa, G = 77,000 MPa. Clause 5.1.

Educational reference only. While E values are standardized, temperature-dependent reductions must follow the governing fire design standard. All structural designs must be independently verified by a licensed Professional Engineer.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.