Why Verify the Moment–Curvature Curve of a Post-Tensioned Beam?
A verified moment-curvature curve helps the engineer confirm initial and cracked stiffness, neutral-axis movement, PT strand stress development, first yielding, ultimate capacity, and available ductility. Sudden jumps, incorrect stiffness, or unrealistic strand stresses can expose errors in material models, reinforcement locations, strain compatibility, or sectional equilibrium.
What the Tool Calculates
The MATLAB tool performs nonlinear fiber-section analysis of bonded post-tensioned T-beams. It supports multiple conventional reinforcement and PT layers, user-defined concrete behavior, and a nonlinear low-relaxation strand curve. At every curvature step, it solves the axial strain required to satisfy zero axial-force equilibrium.
ΣF = 0 and M = ΣFᵢ(yᵢ - yref)
Ultimate Strength and ACI Phi
The nominal state is identified when the extreme concrete compression strain reaches 0.003. The ACI strength-reduction factor is calculated once from the governing net tensile strain at this state. That single ultimate value is used for the design-strength visualization.
Mᵤ(κ) = φᵤ Mₙ(κ)
Checking Curvature Ductility
PT strand yield can be defined by either a 0.1% or 0.2% offset method. The program finds the first PT layer to reach the selected proof-yield strain and interpolates the corresponding yield curvature. The ultimate curvature is taken at the nominal concrete compression strain.
μκ = κᵤ / κy
Interactive Verification
The engineer can click along either moment-curvature curve to trace curvature, nominal moment, design-strength moment, and neutral-axis depth. The corresponding compression depth c is shaded on the section and changes with the selected curve position. This makes it easier to confirm that neutral-axis movement and the compression-zone development remain physically reasonable.
Conclusion
Moment-curvature analysis is an important verification step, not merely another capacity calculation. A smooth and physically reasonable curve gives greater confidence that the reported strength, strand response, and ductility are consistent with sectional equilibrium and the selected material models.