Stress-Strain Curve of Concrete – Shape, Key Values and IS 456 Application
The stress-strain curve of concrete tells you everything about how it behaves from the moment a load is applied to the moment it fails. It’s the foundation of limit state design — the method used in IS 456:2000 to design every beam, column, and slab. If you understand this curve, you understand why concrete structures are designed the way they are. This article explains it completely for RTMNU students.
1. Shape of the Stress-Strain Curve
If you plot the compressive stress against the compressive strain for a concrete cylinder as you gradually increase the load to failure, you get a characteristic curve that’s quite different from steel:
- The curve starts with a slightly concave region at very low stresses (micro-crack closure phase)
- Then becomes nearly linear up to about 30–40% of peak stress
- Becomes increasingly non-linear (concave down) as stress approaches peak
- Reaches a peak stress (the maximum compressive strength, f’c)
- Then has a descending branch where the concrete continues to deform even as load decreases (post-peak softening)
- Finally fails (completely loses load-carrying capacity)
This shape — rising to a peak then descending — is completely different from steel, which has a flat yield plateau. It explains why concrete behaves the way it does in real structures.
2. Three Phases of Concrete Behaviour
Phase 1: Nearly Elastic (0 to ~0.4 fck)
At low stress levels (roughly up to 40% of peak strength), the stress-strain relationship is approximately linear. Existing micro-cracks at the ITZ remain closed or propagate very slowly. If the load is removed at this stage, the concrete returns nearly to its original shape — hence “nearly elastic.” This is the range where the modulus of elasticity (Ec) from IS 456 is valid for structural design.
Phase 2: Elasto-Plastic (0.4 fck to fck)
As stress increases beyond 40% of peak, micro-cracks at the ITZ begin to grow and coalesce. The curve becomes non-linear — strain increases faster than stress. By the time peak stress is reached, significant cracking has occurred throughout the specimen. The concrete can no longer return to its original shape upon unloading — plastic (permanent) deformation remains.
Phase 3: Post-Peak Softening
After peak stress, the concrete can still carry load but its capacity decreases with increasing strain. The specimen is physically cracked and fragmenting, but the fragments are held together by aggregate interlock and residual paste bridges. This descending branch is only observable in a stiff testing machine that controls the rate of strain (displacement-controlled test). In a regular force-controlled test, the specimen fails suddenly at peak load.
3. Key Values from the Stress-Strain Curve
| Parameter | Symbol | Value | Significance |
|---|---|---|---|
| Peak (maximum) stress | f’c | 0.85 fck to fck | Actual cylinder strength; IS 456 uses 0.67fck / 0.45fck in design |
| Strain at peak stress | εc | 0.002 | Characteristic strain; concrete reaches max stress at this point |
| Ultimate compressive strain | εcu | 0.0035 | IS 456:2000 maximum usable strain in limit state design |
| Strain at failure (brittle) | εf | 0.003–0.005 | Varies with grade and testing conditions |
| Initial tangent modulus | E0 | ≈ Ec (IS 456) | Slope at origin of stress-strain curve |
The two most important values to memorise: εc = 0.002 (at peak) and εcu = 0.0035 (ultimate, IS 456:2000)
4. IS 456:2000 Design Stress Block
In limit state design (IS 456:2000 Annex G), the actual non-linear stress-strain curve of concrete is replaced by a simplified parabolic-rectangular stress block for the compression zone of beams and columns:
- Parabolic part (0 to εc = 0.002): Stress increases from 0 to 0.45fck (design stress = 0.67fck/γm = 0.67fck/1.5 = 0.447fck ≈ 0.45fck)
- Rectangular part (εc = 0.002 to εcu = 0.0035): Stress remains constant at 0.45fck
The depth of neutral axis, moment of resistance, and all section capacity calculations in IS 456 are based on this simplified stress block. Key results for singly reinforced beam:
- Maximum depth of neutral axis ratio: xu,max/d = 0.479 (Fe415), 0.456 (Fe500), 0.429 (Fe550)
- Total compression force C = 0.36 fck × b × xu
- Lever arm from C to T: C acts at 0.42 xu from compression face
5. Concrete vs Steel — Behaviour Comparison
| Property | Concrete (Compression) | Steel (Tension) |
|---|---|---|
| Initial behaviour | Slightly non-linear from start | Perfectly linear (elastic) |
| Peak/Yield stress | 0.85–1.0 × fck | fy (well-defined yield) |
| Post-yield behaviour | Softening — load decreases | Plastic plateau — large strain at constant stress |
| Failure type | Brittle (sudden, little warning) | Ductile (large deformation before fracture) |
| Ultimate strain | 0.003–0.005 | 0.10–0.25 (very large) |
| Behaviour in tension | Weak — cracks at ~0.0001 strain | Same as compression (symmetric) |
6. Effect of Concrete Grade on Curve Shape
- Higher grade concrete (M40, M50): Steeper initial slope (higher Ec), higher peak stress, but the curve is more brittle — the descending branch is steeper and failure is more sudden. High-strength concrete has less ductility.
- Lower grade concrete (M20, M25): Gentler slope, lower peak stress, but slightly more ductile — the post-peak descending branch is more gradual, giving some warning before total failure.
- This is why high-strength concrete structures need special detailing (confinement reinforcement, spiral columns) to compensate for reduced ductility.
7. Ductility and Why It Matters
Ductility is the ability of a material or structure to undergo large deformations before failure — providing warning and allowing load redistribution. In earthquake-resistant design (IS 13920), ductility is critical:
- Concrete alone is brittle — it fails suddenly with little warning
- When properly reinforced with steel (which is ductile), the composite system — RCC — achieves significant ductility
- Confinement of concrete by closely-spaced stirrups (lateral reinforcement) dramatically increases both strength and ductility of concrete in columns
- The post-peak region of the stress-strain curve is significantly extended by confinement, making the concrete far less brittle
8. Diagram – Stress-Strain Curve Key Characteristics
9. Exam Tips (RTMNU)
- ✅ Two most important values: εc = 0.002 (at peak) and εcu = 0.0035 (ultimate, IS 456) — asked in every exam.
- ✅ Design compressive stress per IS 456 limit state: 0.45fck (= 0.67fck/1.5).
- ✅ Concrete = brittle in compression; Steel = ductile in tension — this difference drives why RCC works so well.
- ✅ Three phases: elastic (0–0.4fck), elasto-plastic (0.4–fck), post-peak softening — describe all three.
- ✅ Higher grade concrete = higher peak but more brittle — important for seismic design discussion.
- ✅ Draw the parabolic-rectangular stress block for IS 456 — frequently asked 5-mark diagram question.
10. Key Takeaways
- Concrete stress-strain curve is non-linear, with three phases: elastic, elasto-plastic, and post-peak softening.
- Peak stress at εc = 0.002; ultimate usable strain per IS 456 = εcu = 0.0035.
- IS 456 uses a simplified parabolic-rectangular stress block: 0.45fck over the compression zone.
- Concrete is brittle; steel is ductile. RCC combines both to create a ductile structural system.
- Higher grade concrete is stronger but more brittle than lower grade concrete.
11. FAQs
Q1. What is the ultimate compressive strain of concrete per IS 456?
IS 456:2000 specifies the maximum usable compressive strain at the extreme fibre as εcu = 0.0035. This is the strain at which the compression zone in a beam or column is assumed to reach its limiting state in limit state design.
Q2. What is the strain at peak compressive stress in concrete?
The characteristic (peak) strain at maximum compressive stress is approximately εc = 0.002. Up to this strain, stress increases (parabolic zone in IS 456 design stress block). Beyond 0.002 up to 0.0035, the rectangular part of the stress block maintains constant stress at 0.45fck.
Q3. Why does the stress-strain curve of concrete have a descending branch?
After peak stress, the concrete specimen has developed extensive cracking throughout. The material is fragmented but the fragments are held in contact by aggregate interlock and residual cement paste bridges. As strain continues to increase, these bridges break down progressively, reducing load-carrying capacity. This gradual breakdown gives the descending branch. It is only visible in displacement-controlled (stiff machine) testing.
Q4. What is the IS 456 parabolic-rectangular stress block?
IS 456:2000 Annex G replaces the actual non-linear stress-strain curve with a simplified design stress block: a parabola from ε = 0 to εc = 0.002 (stress rising from 0 to 0.45fck), followed by a rectangle from εc = 0.002 to εcu = 0.0035 (stress constant at 0.45fck). This simplifies the calculation of compression force and moment of resistance in beam and column design.
Q5. Why does higher-grade concrete have less ductility?
Higher-strength concrete has a denser, more brittle C-S-H gel matrix with fewer micro-cracks available for progressive damage absorption. When the peak load is reached, the failure is more sudden (less gradual) and the post-peak descending branch is steeper. This reduced ductility is why high-strength concrete columns require closely-spaced confining reinforcement (spirals or hoops) to compensate.
🔗 Related: Modulus of Elasticity of Concrete – IS 456 Formula
🔗 Related: Compressive Strength of Concrete – Cube Test
📚 Reference: IS 456:2000 Annex G – Stress-Strain Relationship for Design, BIS