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Tool · Moment–curvature

Moment–curvature fiber analysis: three concrete models, one chart to compare ductility.

Fiber section analysis that accounts for both cover concrete and confined core concrete, giving the yield, nominal, peak, and ultimate points and the curvature ductility μφ.

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Tool screen

Moment–curvature analysis screen
Fig. 1Moment–curvature curve and material stress–strain relations for a 60 × 60 cm section with fc′ 700 kgf/cm², axial load ratio 0.1, and Mander confinement K = 1.3.

One section, four models

The figure below was computed by the calculation core by applying four concrete models to the same section, showing clearly how confinement and fiber reinforcement affect ultimate curvature and ductility.

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. 2Moment–curvature curves of a 60 × 60 cm section with 10-#10, fc′ 700 kgf/cm², and P = 0.1fc′Ag under four concrete models; dots mark the ultimate points and the values in parentheses are the curvature ductility μφ = φu/φy.

Material models

Core concrete uses the Mander confined concrete model [1, 2]; the HUNG model describes high-performance fiber-reinforced cementitious composites (HPFRCC) [11, 12]; the UHPC jacket model corresponds to research on UHPC jacket retrofit of existing columns [13, 14]. Reinforcement accounts for strain hardening, fracture, and buckling.

References

  1. Mander, J. B., Priestley, M. J. N., & Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of Structural Engineering, 114(8), 1804–1826. doi:10.1061/(ASCE)0733-9445(1988)114:8(1804)
  2. Popovics, S. (1973). A numerical approach to the complete stress-strain curve of concrete. Cement and Concrete Research, 3(5), 583–599. doi:10.1016/0008-8846(73)90096-3
  3. Whitney, C. S. (1937). Design of reinforced concrete members under flexure or combined flexure and direct compression. ACI Journal Proceedings, 33(3), 483–498. doi:10.14359/8429
  4. ACI Committee 318. (2019). Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19). American Concrete Institute. doi:10.14359/51716937
  5. 內政部（Ministry of the Interior, Taiwan）. (2023). 建築物混凝土結構設計規範（Design Specifications for Concrete Structures of Buildings），112 年 8 月 10 日修正發布，113 年 1 月 1 日生效. nlma.gov.tw
  6. 內政部（Ministry of the Interior, Taiwan）. (2023). 建築物基礎構造設計規範（Design Specifications for Foundations of Buildings），112 年 6 月 20 日修正發布，113 年 1 月 1 日生效. nlma.gov.tw
  7. Mononobe, N., & Matsuo, H. (1929). On the determination of earth pressure during earthquakes. Proceedings of the World Engineering Congress, Vol. 9, Tokyo, 177–185.
  8. Sutherland, I. E., & Hodgman, G. W. (1974). Reentrant polygon clipping. Communications of the ACM, 17(1), 32–42. doi:10.1145/360767.360802
  9. National Center for Research on Earthquake Engineering (NCREE). 台灣新型高強度鋼筋混凝土（Taiwan New RC）專區. ncree.niar.org.tw/service/newrc
  10. Chiu, C.-K., Hung, C.-C., Lin, K.-C., Liu, K.-Y., Lee, H.-J., Cheng, M.-Y., et al. (2019). Design Guideline for Building of High-Strength Reinforced Concrete Structures (Draft), NCREE-19-001. National Center for Research on Earthquake Engineering.
  11. Hung, C.-C., & Li, S.-H. (2013). Three-dimensional model for analysis of high performance fiber reinforced cement-based composites. Composites Part B: Engineering, 45(1), 1441–1447. doi:10.1016/j.compositesb.2012.08.004
  12. Hung, C.-C., El-Tawil, S., & Chao, S.-H. (2021). A review of developments and challenges for UHPC in structural engineering: Behavior, analysis, and design. Journal of Structural Engineering, 147(9), 03121001. doi:10.1061/(ASCE)ST.1943-541X.0003073
  13. Shao, Y., Kuo, C.-W., & Hung, C.-C. (2021). Seismic performance of full-scale UHPC-jacket-strengthened RC columns under high axial loads. Engineering Structures, 243, 112657. doi:10.1016/j.engstruct.2021.112657
  14. Hung, C.-C., Kuo, C.-W., & Shao, Y. (2021). Cast-in-place and prefabricated UHPC jackets for retrofitting shear-deficient RC columns with different axial load levels. Journal of Building Engineering, 44, 103305. doi:10.1016/j.jobe.2021.103305
  15. Ou, Y.-C., Alrasyid, H., Haber, Z. B., & Lee, H.-J. (2015). Cyclic behavior of precast high-strength reinforced concrete columns. ACI Structural Journal, 112(6), 839–850. doi:10.14359/51687911
  16. Shen, W.-C., & Hwang, S.-J. (2023). Confinement reinforcement of high-strength reinforced concrete tied columns under high axial load. ACI Structural Journal, 120(3), 145–155. doi:10.14359/51738505

Compare the ductility of retrofit schemes without writing code.

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