StructFlow

Explainer

How to read a moment–curvature curve: yield, ultimate, and curvature ductility

A moment–curvature curve tells you how much moment a section can resist and how far it can deform before failing. The second matters just as much in seismic design.

1Key points on the curve

A moment–curvature curve usually marks a few key points: the yield point, where the tension steel starts to yield; the peak point, where the moment is greatest; and the ultimate point, where the materials reach their limit and the section loses its load-carrying capacity.

Moment–curvature curves for four concrete models0.000.050.100.150.20050100150200250Curvature φ (1/m)M (tf·m)Unconfined(μφ ≈ 3.25)Mander confined, K = 1.3(μφ ≈ 19.21)HUNG (HPFRCC)(μφ ≈ 12.01)UHPC jacket(μφ ≈ 8.79)
Fig. 1Moment–curvature curves of the same section under four concrete models; dots mark the ultimate points and the values in parentheses are the curvature ductility (computed by the calculation core).

2Curvature ductility

Curvature ductility is the ratio of ultimate curvature to yield curvature. The larger it is, the more the section can keep deforming and absorbing energy after yielding, and the less likely it is to fail suddenly in an earthquake.

3Factors that affect ductility

  • Confinement: the closer the stirrup spacing and the better the confinement, the larger the compressive strain the core concrete can sustain
  • Axial load: the higher the axial load, the deeper the compression zone and, generally, the lower the ductility
  • Materials: high-performance fiber-reinforced concrete and UHPC jackets can markedly increase deformation capacity

4Compare in StructFlow

The moment–curvature tool lets you switch concrete models, adjust axial load and confinement, and pin several curves on one chart, so you can quickly assess the difference in ductility between design or retrofit schemes.

Compare the ductility of your section.

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