Does higher-strength steel have a higher modulus of elasticity?

No. All carbon structural steels have the same E = 29,000 ksi (200 GPa) regardless of yield strength. A36 (Fy = 36 ksi), A992 (Fy = 50 ksi), A572 Gr 65 (Fy = 65 ksi), and A514 (Fy = 100 ksi) all have identical stiffness. This means upgrading from A36 to A992 increases strength by 39% but does not reduce deflection. If deflection governs the design (common for floor beams with spans >20 ft), using higher-strength steel provides no benefit. The only way to reduce deflection is to increase the moment of inertia (deeper section) or reduce the span.

How does temperature affect steel's modulus of elasticity?

Steel's modulus of elasticity decreases with increasing temperature. Per AISC 360 Appendix 4 and EN 1993-1-2: at 200 deg C (392 deg F), E reduces to ~90% of ambient; at 400 deg C (752 deg F), ~70%; at 600 deg C (1112 deg F), ~31%; at 800 deg C (1472 deg F), ~9%. This reduction is critical for structural fire engineering — a beam at 600 deg C has only 31% of its ambient stiffness, dramatically increasing deflection even if strength is adequate. Fire protection (spray-applied, intumescent paint) maintains steel temperature below the critical threshold, typically 550 deg C for columns and 620 deg C for beams.

Why does Eurocode use E = 210 GPa while AISC uses 200 GPa?

The difference (210 vs 200 GPa, about 5%) is primarily historical convention, not a material difference. Both values represent the same steel. EN 1993-1-1 adopted E = 210,000 MPa based on European testing tradition, while AISC and AS 4100 use E = 200,000 MPa (29,000 ksi). Canadian CSA S16 uses E = 200,000 MPa. For design purposes, the 5% difference in E propagates to a 5% difference in deflection calculations, which is within typical construction tolerances. For international projects, use the value specified by the governing design code.

Steel Modulus of Elasticity — E Values by Alloy

Q: What is the modulus of elasticity of structural steel?

The modulus of elasticity (Young's modulus) for structural carbon steel is E = 29,000 ksi (200,000 MPa or 200 GPa). This value is constant across all carbon steel grades (A36, A572, A992, A514) because stiffness depends on atomic bonding, not strength. Stainless steel has a slightly lower E = 28,000 ksi (193 GPa). All international structural codes use the same value: AISC 360 specifies E = 29,000 ksi, EN 1993-1-1 uses E = 210,000 MPa (a small 5% difference from 200 GPa due to historical convention), and AS 4100 uses E = 200,000 MPa.

Q: What is the shear modulus of steel?

The shear modulus (modulus of rigidity) for structural steel is G = 11,200 ksi (77,200 MPa or 77 GPa). This relates shear stress to shear strain: tau = G x gamma. G is related to E by G = E / [2(1 + nu)], where nu = 0.30 (Poisson's ratio): G = 29,000 / [2(1+0.30)] = 11,154 ksi (11,200 ksi rounded per AISC). The shear modulus is used in lateral-torsional buckling calculations (the GJ term), torsional stiffness of open sections, and finite element analysis. For stainless steel, G = 10,800 ksi (74,500 MPa).

The modulus of elasticity (Young's modulus, E) is the measure of steel's stiffness. It defines the relationship between stress and strain in the elastic range. For most structural steels, E is approximately 29,000 ksi (200 GPa), but it varies by alloy and temperature.

What Is the Modulus of Elasticity?

Hooke's Law: σ = E × ε

where σ = stress (ksi), E = modulus of elasticity (ksi), ε = strain (dimensionless).

The modulus is the slope of the stress-strain curve in the linear elastic region. A higher E means the steel is stiffer — it deflects less under the same load.

Modulus of Elasticity by Steel Type

Steel Type	E (ksi)	E (GPa)	Notes
Carbon steel (A36, A992, A572)	29,000	200	Standard structural steel
High-strength low-alloy (HSLA)	29,000	200	Same as carbon steel
quenched and tempered (A514)	29,000	200	Strength varies, E stays constant
Stainless steel 304	28,000	193	Slightly lower than carbon
Stainless steel 316	28,000	193	Similar to 304
Stainless steel 410	29,000	200	Martensitic stainless
Tool steel (various)	28,000-30,000	193-207	Varies by grade
Cast steel	28,500	196	Slightly lower than wrought
Steel castings (mild)	29,000	200	Similar to rolled steel
Cold-rolled steel	29,000	200	Cold working does not change E

Key insight: The modulus of elasticity is essentially the same (29,000 ksi) for ALL carbon and low-alloy structural steels, regardless of yield strength. A W14x90 made from A992 (Fy=50 ksi) has the same E as a W14x90 made from A572 Gr 65 (Fy=65 ksi).

Temperature Effects on Modulus

The modulus decreases as temperature increases. This affects deflection calculations for fire-exposed members.

Temperature (°F)	Temperature (°C)	E / E₀ (ratio)	E (ksi)
70	21	1.00	29,000
200	93	0.99	28,700
400	204	0.95	27,550
600	316	0.89	25,810
800	427	0.81	23,490
1000	538	0.71	20,590
1200	649	0.58	16,820
1400	760	0.40	11,600
1600	871	0.22	6,380

E₀ = modulus at room temperature (70°F). Data from AISC Specification Appendix 4 and Eurocode 3.

Related Elastic Constants

Constant	Symbol	Formula	Value (Carbon Steel)
Modulus of elasticity	E	—	29,000 ksi (200 GPa)
Shear modulus	G	E / (2(1+ν))	11,200 ksi (77 GPa)
Poisson's ratio	ν	—	0.30
Bulk modulus	K	E / (3(1-2ν))	24,200 ksi (167 GPa)
Coefficient of thermal expansion	α	—	6.5 × 10⁻⁶ /°F (12 × 10⁻⁶ /°C)

Poisson's Ratio by Steel Type

Steel Type	Poisson's Ratio (ν)
Carbon steel	0.29-0.30
Stainless steel (austenitic)	0.29-0.30
Stainless steel (ferritic)	0.27-0.30
Tool steel	0.28-0.30
Cast iron	0.21-0.26

How E Affects Structural Design

Deflection

Beam deflection is inversely proportional to E:

Δ = 5wL⁴ / (384EI) (simply supported, UDL)

If E decreases (e.g., at elevated temperature), deflection increases proportionally. This is why fire-exposed beams deflect significantly before losing strength.

Buckling

Euler buckling load depends on E:

Pcr = π²EI / (KL)²

Higher E → higher critical buckling load. But since E is the same for all carbon steels, switching from A36 to A992 does NOT change the buckling load (only the yield strength changes).

Vibration

Natural frequency depends on √(E/ρ):

f = (π/2) × √(EI / (ρAL⁴))

Higher E → higher natural frequency → stiffer floor system.

AISC Design Impact

AISC Check	Does E Matter?	Why
Flexural strength (Chapter F)	No	Governed by Fy and section geometry
Shear strength (Chapter G)	No	Governed by Fy
Compression (Chapter E)	Yes	Euler buckling uses E
Deflection (serviceability)	Yes	Deflection ∝ 1/E
Vibration	Yes	Frequency ∝ √E
Fire design	Yes	E drops with temperature

Frequently Asked Questions

What is the modulus of elasticity of structural steel? 29,000 ksi (200 GPa, 29,000,000 psi). This value is the same for all common structural steels: A36, A992, A572, A500, A588.

Does higher strength steel have a higher modulus? No. The modulus is essentially the same (29,000 ksi) for all carbon steels regardless of yield strength. A36 (Fy=36 ksi) and A514 (Fy=100 ksi) have the same E. Strength and stiffness are different properties.

How does temperature affect the modulus of elasticity? E decreases as temperature rises. At 1000°F, E is about 71% of its room-temperature value. At 1200°F, it drops to about 58%. This causes increased deflection and reduced buckling capacity in fire conditions.

What is the difference between modulus of elasticity and yield strength? Modulus of elasticity (E) measures stiffness — resistance to elastic deformation. Yield strength (Fy) measures strength — the stress at which permanent deformation begins. They are independent properties. Steel can be very stiff (high E) and relatively weak (low Fy), or stiff and strong.

Does cold working change the modulus of elasticity? Not significantly. Cold working increases yield strength through strain hardening but does not meaningfully change E. The modulus remains approximately 29,000 ksi for cold-formed steel members.

What is the shear modulus of steel? G = E / (2(1+ν)) = 29,000 / (2 × 1.30) = 11,200 ksi (77 GPa). The shear modulus is used in torsion calculations and shear deformation analysis.

Steel Stress-Strain Curve — Complete stress-strain behavior
Steel Grades — ASTM steel specifications
Deflection Limits — L/240, L/360 criteria
Beam Deflection Calculator — Deflection analysis
Steel Density Table — Density by steel type

Disclaimer

This is a calculation tool, not a substitute for professional engineering certification. All results must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in construction, fabrication, or permit documents. The user is responsible for the accuracy of all inputs and the verification of all outputs.