Modulus of Elasticity — Why Stiffness ≠ Strength
Here’s a fact that surprises many engineers early in their career: 36 ksi yield steel and 36 ksi yield aluminum have the same strength — but the steel is 3× stiffer.
Strength and stiffness are completely independent properties, and confusing them leads to bad designs.
What Is Modulus of Elasticity?
The modulus of elasticity (E), also called Young’s modulus, describes how much a material deforms under load — while still in the elastic (springy) range:
E = σ / ε = stress / strain
It’s the slope of the stress-strain curve in the linear region. A steep slope = stiff material. A shallow slope = flexible material.
The Big Numbers
| Material | E (ksi) | E (GPa) | Notes |
|---|---|---|---|
| Steel (all grades) | 29,000 | 200 | A36, A992, 4140 — all the same E |
| Aluminum (all alloys) | 10,000 | 69 | 6061, 7075 — same E regardless of temper |
| Titanium | 16,500 | 114 | Between steel and aluminum |
| Copper | 17,000 | 117 | |
| Concrete | 3,600 | 25 | Varies with mix (3,000-5,000 psi concrete) |
| Wood (along grain) | 1,200-1,800 | 8-12 | Species dependent |
The Critical Insight
E is a property of the base material, not the alloy or heat treatment.
A36 steel (36 ksi yield) and A992 steel (50 ksi yield) have the exact same E = 29,000 ksi. Heat treating a steel from 36 ksi to 100 ksi yield doesn’t change its stiffness one bit.
Similarly, 6061-T6 aluminum (40 ksi yield) and 7075-T6 aluminum (73 ksi yield) have the same E = 10,000 ksi.
You can’t heat treat your way to more stiffness. You can only get there by changing the base material or adding more material (bigger cross-section).
Why This Matters: The Steel vs. Aluminum Decision
Suppose you’re designing a bracket that must not deflect more than 0.010″ under load. Deflection is proportional to 1/EI. If you switch from steel to aluminum:
- E drops from 29,000 to 10,000 — you lose 2.9× stiffness
- To compensate, you need 2.9× more I (moment of inertia)
- Since I ∝ h³, you need about 1.43× the height (cube root of 2.9)
- But aluminum is 1/3 the density, so the thicker aluminum part might still be lighter
This is the fundamental trade-off in aerospace: aluminum is less stiff per unit volume but stiffer per unit weight (specific stiffness). E/ρ for aluminum ≈ 25.5 vs steel ≈ 25.3 — they’re almost identical on a per-weight basis!
Deflection: Where E Shows Up
The classic beam deflection formula:
δ = PL³ / (48EI) (simply supported, center load)
E and I always appear together as EI — the “flexural rigidity.” This is the number that controls whether your beam, shelf, shaft, or bridge bounces, sags, or holds firm.
Key Takeaways
- E (modulus) = stiffness. Yield/ultimate = strength. They’re independent.
- All steels have E ≈ 29,000 ksi. All aluminums have E ≈ 10,000 ksi. Alloy and heat treatment don’t change E.
- Steel is 3× stiffer than aluminum (per unit area). Per unit weight, they’re nearly identical.
- If your design is deflection-limited, you can only fix it with more material or a stiffer material — not a stronger alloy