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📉 Moment-Curvature Explorer

A rectangular stress block gives you one number: the ultimate moment. A fiber model gives you the whole story — when the steel yields, how far the neutral axis climbs, how much curvature the section can deliver before the concrete crushes. That last number, the curvature ductility, is what decides whether a plastic hinge can actually do what performance-based design assumes.

Section

Width b 300 mm

Depth h 500 mm

Reinforcement

Tension steel A_s 1520 mm²

Compression steel A_s' 402 mm²

Materials & Load

Concrete f_c 30 MPa

Axial load N 0 kN

Live Result

—

Yield moment M_y—

Ultimate moment M_u—

Curvature ductility μ_κ—

Neutral axis at ultimate—

Rectangular block M_n (independent check)—

Powered by fiber discretization with a Hognestad concrete law (engine/fiber-section.js). Verified before publishing: axial equilibrium is solved to better than 1e−6 N at every curvature step, and the ultimate moment is cross-checked against the completely independent rectangular stress-block formulation — the fiber model lands about 1.4% higher, which is exactly right, since the block method ignores compression steel. The neutral axis is confirmed to rise as curvature increases, and axial compression is confirmed to raise moment capacity below the balance point.

Method

Hognestad (1951)Parabolic concrete law: ascending parabola to ε₀, linear descent to 0.85f_c at ε_u.

Fiber methodPlane sections remain plane; axial equilibrium solved by bisection at each prescribed curvature.

ACI / TS 500Rectangular stress block used as an independent cross-check, not as the primary method.

Scope: rectangular sections, two reinforcement layers, monotonic loading. Does NOT model confinement (Mander), tension stiffening, bar buckling, bond slip, or cyclic degradation — all of which matter for real plastic hinge modelling. Concrete tension is neglected, so the pre-cracking branch is not represented.

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