REINFORCED CONCRETE SECTION ANALYSIS

What this calculator checks

The calculator performs the moment-curvature analysis of a reinforced-concrete section and determines its section properties in the uncracked and cracked states, according to EN 1992-1-1. Unlike a check that returns a single number (passes / fails), here you obtain the full behaviour of the section as the moment increases — a curve, not a value.

What the moment-curvature curve tells you

The curve relates the applied moment to the curvature of the section (the rotation per unit length) and passes through three regimes:

1. Uncracked (Stage I) — the tensile concrete still works; the section is stiff, and the stiffness \(EI\) is close to that of the homogenised gross section.
2. Cracking — when the tensile strength \(f_{ct}\) is exceeded, the tensile concrete drops out; the curve changes slope abruptly.
3. Cracked (Stage II) — only the compressed concrete and the reinforcement work; the stiffness falls. Toward the end, yielding of the reinforcement or crushing of the concrete gives the plastic branch, up to the ultimate moment.

The slope of the curve at any point is the bending stiffness \(EI\) of the section in that state — the quantity you need for computing deflections and the distribution of internal forces in statically indeterminate structures.

Why the cracked stiffness matters

A reinforced-concrete beam under service loads works, for the most part, in the cracked state. Using the gross (uncracked) stiffness in a deflection calculation would grossly underestimate the deformations — hence real deflections several times larger than the naive computed ones. The analysis here gives the correct stiffness for each load level.

Input data

• Section geometry and reinforcement layout — the position, number and diameter of bars.
• Materials — the concrete class (with its nonlinear constitutive law), the steel grade.
• Axial force, if present — it shifts the neutral axis and changes the whole curve.
• The range of moment or curvature over which the analysis is traced.

Assumptions and limitations

• Plane sections remain plane (Bernoulli assumption); valid away from discontinuity regions.
• The analysis is of the section, not the member: length effects (tension stiffening between cracks) are treated at member level, in the crack-width check.
• The calculation runs on an external section-analysis engine; the result depends on the constitutive laws chosen for the materials.
• Time-dependent effects (creep, shrinkage) are not treated unless introduced explicitly through the effective modulus.

Related calculations

• Reinforced section — the resistance check (a single \(M_{Rd}\)) of the same section
• Crack-width verification — the cracked-state behaviour at member level
• N·M interaction diagram — the capacity under axial force and moment