Abstract

Tendon profile geometry is a structural design variable whose effects on prestressed concrete beams have, until now, been studied separately for shear, ductility, and stiffness response. This paper unifies those threads through a single nonlinear finite element investigation of eight tendon profiles (B0–B7) across two beam depths (300 × 600 mm, L/d = 13.33; and 300 × 900 mm, L/d = 8.48), comprising 16 validation beam models plus an 82-simulation parametric sweep of tendon inclination angle (0–20°). Part A characterizes cracking, yield, and ultimate loads, three-stage stiffness (Ki → Kpc → Ku), ductility index, and deflection serviceability. Ductility is quantified as the peak-displacement-based index μΔ = Δu/Δy; post-peak plateau behavior is additionally quantified through a failure-displacement ductility index (μΔ,f) and an absorbed-energy index (μE), recovered from the full descending load–deflection branch of each model. Key findings: the trapezoidal beveled profile (B6) achieves the highest ductility overall (μΔ = 3.83 in deeper beams, +99.5% over straight); the hybrid parabolic–straight profile (B5) leads ductility in shallow beams (μΔ = 2.16, +14.9%); the five-row distributed trapezoidal profile (B7) achieves the highest post-cracking stiffness in deeper beams (Kpc = 61.93 kN/mm, +7.6%) and highest yield load, but at a ductility cost; and all 16 models satisfy ECP 203-2020 and ACI 318-19 deflection limits at service load. Part B develops and validates a dimensionless shear-inclination efficiency index ηv, calibrated by nonlinear regression on the 82-simulation database: ηv = 1 + 0.14·μps·λps·(d/h)0.6·θ0.9, achieving R2 = 0.93 and RMSE < 5%, with a mean conservative safety margin of 6% across the 16 validation configurations. Sensitivity analysis identifies inclination angle θ as the dominant variable, ahead of depth ratio d/h and distribution index λps. A step-by-step design procedure with a profile-specific compliance table allows ηv to be applied directly to ACI 318-19 or ECP 203-2020 shear predictions: at a sub-minimum stirrup ratio of 0.14%, ηv enables five of eight profiles in shallow beams and three in deeper beams to achieve full code compliance, numerically indicating potential stirrup savings of up to 40%, pending experimental verification and reliability-based calibration before design use. Read together, the two parts show that tendon geometry simultaneously governs shear efficiency, post-cracking stiffness, and ductility—three previously disconnected performance axes—and that the optimal profile choice is depth-dependent and objective-dependent, a distinction current codes do not address. The finite element procedure is validated against six post-tensioned specimens for the global load–deflection response and peak-load agreement (R2 = 0.97 and 0.95, respectively); cracking load, yield point, post-peak plateau behavior, and the shear-governed failure mode of the deeper beams were not independently observed in the same experimental dataset, so the ductility, stiffness-degradation, and shear-governed-failure findings reported here should be read as numerically-derived results requiring further experimental confirmation, distinct from the peak-load response that is directly validated.

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