Table 1.

Local buckling design formulas of compression box and I-shape members in current standards and guides.

Design Standard	Considered Geometry	Design Formula 1
Pre-standard for load & resistance factor design (LRFD) of pultruded fibre-reinforced polymer (FRP) structures [177]	Hollow box	$\left(f\right)=\frac{\left(\frac{{\mathsf{\pi }}^2}{6}\right)\left[\sqrt{E_L{E}_T}+v_{LT}{E}_T+2G_{LT}\right]}{{(\frac{b}{t})}^2}$
	I-shape	${(f)}_{flange}=\frac{G_{LT}}{{(\frac{b_f}{2t_f})}^2}$
Prospect for new guidance in the design of FRP [178]	Hollow box	$\left(f\right)=\frac{{\mathsf{\pi }}^2}{b^{2}t}\left[2\sqrt{\left(1+4.139\zeta \right)\left(D_{11}{D}_{22}\right)}+\left(2+0.62{\zeta }^2\right)\left(D_{12}+2D_{66}\right)\right]$ Where: $\zeta ={\left(1+\frac{5}{1-R}\frac{{(D_{22})}_f{b}_w}{{(D_{22})}_w{b}_f}\right)}^{-1}$$,R=\frac{{(f)}_f{}^{ss}{(E_L)}_w}{{(f)}_w{}^{ss}{(E_L)}_f}$
	I-shape	Same as [180]
Structural Design of Polymer Composites EUROCOMP Design Code and Handbook [179]	Orthotropic plate	$\left(f\right)=2{\mathsf{\pi }}^2\frac{\left(\sqrt{D_{11}{D}_{22}}+{\mathrm{H}}_{\mathrm{o}}\right)}{t{b}^2}$ Where: ${\mathrm{H}}_{\mathrm{o}}=0.5\left(v_{LT}{D}_{22}+v_{TL}{D}_{11}\right)+\frac{G_{LT}{t}^3}{6}$
Guide for the Design and Construction of Structures made of FRP Pultruded Elements [180]	I-shape	${(f)}_{flange}=\{\begin{array}{c}\frac{\sqrt{D_{11}{D}_{22}}}{t_f{(\frac{b_f}{2})}^2}\left(K\left[15.1\eta \sqrt{1-\rho }+6\left(1-\rho \right)\left(1-\eta \right)\right]+\frac{7\left(1-K\right)}{\sqrt{1+4.12\zeta }}\right), K\le 1\\ \frac{\sqrt{D_{11}{D}_{22}}}{t_f{(\frac{b_f}{2})}^2}\left[15.1\eta \sqrt{1-\rho }+6\left(1-\rho \right)\left(K-\eta \right)\right], K>1\end{array}$ Where: $\zeta =\frac{D_{22}}{\tilde{k}\frac{b_f}{2}}$$,\rho =\frac{D_{12}}{2D_{66}+D_{12}}$$,\eta =\frac{1}{\sqrt{1+\left(7.22-3.55\rho \right)\zeta }}$$,K=\frac{2D_{66}+D_{12}}{\sqrt{D_{11}+D_{22}}}$

¹$D_{11}$, $D_{22}$, $D_{12}$, and $D_{66}$ are the flexural rigidities of the orthotropic plate. $\tilde{k}$ is the torsional stiffness coefficient. t, b, and h are the section thickness, width, and height, respectively. The subscripts f and w refer to the flange and web, respectively. $E_L$, $E_T$, and $G_{LT}$ are the longitudinal, transverse, and in-plane shear elastic moduli, respectively. $v_{LT}$ and $v_{TL}$ are the in-plane and out-of-plane Poisson’s ratios, respectively. ${(f)}_f{}^{ss}$ and ${(f)}_w{}^{ss}$ are the buckling strengths of the flange and web, respectively, considering simply supported boundary conditions.