Table 5 Existing equations for flexural capacity of beams.

Bare beam

ACI 318 − 19²³

\(\:{M}_{0}={A}_{s}{f}_{y}(d-a/2)\)

ACI 544.1R²⁴

\(\:{M}_{f}={M}_{0}+{\lambda\:}_{f}{V}_{f}{f}_{f}\)

JSCE (2007)¹⁸

\(\:{M}_{0}=0.9{A}_{s}{f}_{y}d\)

fib Model Code 2010²⁵

\(\:{M}_{f}={M}_{0}+{\lambda\:}_{f}{V}_{f}{f}_{f}\left({l}_{f}/{d}_{f}\right)d\)

RILEM TC 162-TDF (2003)²⁶

\(\:{M}_{f}={M}_{0}+{\lambda\:}_{f}{V}_{f}{f}_{f}\left({l}_{f}/{d}_{f}\right)\)

JSCE-SF4 (2002)²⁷

\(\:{M}_{f}={M}_{0}+{\lambda\:}_{f}{V}_{f}{f}_{f}\)

Single-layer CFRP

ACI 440.2R-17²⁹

\(\:{M}_{n}={M}_{0}+{A}_{f}{f}_{fe}(d-{a}_{f}/2)\)

FIB Bulletin 14²⁸

\(\:{M}_{n}={M}_{0}+{A}_{f}{f}_{fe}(d-{a}_{f}/2)\)

Eurocode 2 & TR55

\(\:{M}_{n}={M}_{0}+{A}_{f}{E}_{f}{\epsilon\:}_{f}(d-{a}_{f}/2)\)

JSCE-SF4 (2002)²⁷

\(\:{M}_{n}={M}_{0}+{A}_{f}{f}_{fu}(d-{a}_{f}/2)\)

Multi-layers CFRP

ACI 440.2R-17²⁹

\(\:{M}_{n}={M}_{0}+\sum\:_{i}\left({A}_{f.i}{f}_{fd.i}\left(d-a/2\right)\right)\)

fib Bulletin 14²⁸

\(\:{M}_{n}={M}_{0}+\sum\:_{i}\left({A}_{f.i}{f}_{fd.i}{d}_{i}\right)\)

Post-tensioning

ACI 318 − 19²³

\(\:{M}_{n}={M}_{0}+{M}_{PT}\)

\(\:{M}_{PT}={A}_{p}{f}_{p.\:effective}(d-\frac{{e}_{p}}{2})\)

\(\:{f}_{p.\:effective}=\eta\:{\times\:f}_{pu}\)

\(\:\eta\:=0.60\:for\:60\%\:post-tensioning\)

\(\:\eta\:=0.80\:for\:80\%\:post-tensioning\)