This study addresses the unclear mechanisms of shear deformation effects and the contradictory design thresholds in the buckling analysis of pultruded GFRP (glass fiber-reinforced polymer) compression members. By integrating test data from 322 specimens across 17 studies, a large-sample experimental database was established. The Engesser and Haringx shear correction theories were systematically validated, with results indicating that the Engesser model provides the optimal prediction accuracy (R2 = 0.89). Shear deformation can reduce the buckling load by up to 48%. Theoretical derivation revealed the decomposition law of the core parameter: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$P_{{\text{E}}} /\left( {{\text{KGA}}} \right) = \left( {\pi^{2} /K} \right) \cdot \left( {E/G} \right) \cdot \lambda^{ - 2} ,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mtext>E</mtext> </msub> <mo stretchy="false">/</mo> <mfenced close=")" open="("> <mtext>KGA</mtext> </mfenced> <mo>=</mo> <mfenced close=")" open="("> <mrow> <msup> <mi>π</mi> <mn>2</mn> </msup> <mo stretchy="false">/</mo> <mi>K</mi> </mrow> </mfenced> <mo>·</mo> <mfenced close=")" open="("> <mrow> <mi>E</mi> <mo stretchy="false">/</mo> <mi>G</mi> </mrow> </mfenced> <mo>·</mo> <msup> <mi>λ</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> which for the first time clearly identifies the slenderness ratio (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\lambda$</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>) as the dominant geometric factor controlling the shear effect, while the elastic modulus ratio (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$E/G$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mo stretchy="false">/</mo> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation>) is a secondary material factor. Based on this mechanism, a practical design criterion with a threshold of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\lambda =86.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mn>86.6</mn> </mrow> </math></EquationSource> </InlineEquation> is proposed: The Engesser formula must be used for shear correction when <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\lambda \le 86.6,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>≤</mo> <mn>86.6</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> whereas the shear effect becomes negligible (< 5%) when <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\lambda >86.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>></mo> <mn>86.6</mn> </mrow> </math></EquationSource> </InlineEquation>. This threshold is significantly higher than that for steel <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$(\lambda \approx 31.4),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>λ</mi> <mo>≈</mo> <mn>31.4</mn> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> revealing the unique buckling characteristics of GFRP materials due to their anisotropy. The research outcomes provide a theoretical basis and practical tools for the refined design of GFRP compression members.

Shear deformation effects on buckling of pultruded GFRP columns: mechanism and critical threshold

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发表日期：

2026年1月3日

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Hengming Zhang,
Xinyuan Guo,
Rongfeng Lin

摘要

This study addresses the unclear mechanisms of shear deformation effects and the contradictory design thresholds in the buckling analysis of pultruded GFRP (glass fiber-reinforced polymer) compression members. By integrating test data from 322 specimens across 17 studies, a large-sample experimental database was established. The Engesser and Haringx shear correction theories were systematically validated, with results indicating that the Engesser model provides the optimal prediction accuracy (R² = 0.89). Shear deformation can reduce the buckling load by up to 48%. Theoretical derivation revealed the decomposition law of the core parameter: $P_{{\text{E}}} /\left( {{\text{KGA}}} \right) = \left( {\pi^{2} /K} \right) \cdot \left( {E/G} \right) \cdot \lambda^{ - 2} ,$ $P_{E} / (KGA) = (π^{2} / K) \cdot (E / G) \cdot λ^{- 2},$ which for the first time clearly identifies the slenderness ratio ( $\lambda$ $λ$ ) as the dominant geometric factor controlling the shear effect, while the elastic modulus ratio ( $E/G$ $E / G$ ) is a secondary material factor. Based on this mechanism, a practical design criterion with a threshold of $\lambda =86.6$ $λ = 86.6$ is proposed: The Engesser formula must be used for shear correction when $\lambda \le 86.6,$ $λ \leq 86.6,$ whereas the shear effect becomes negligible (< 5%) when $\lambda >86.6$ $λ > 86.6$ . This threshold is significantly higher than that for steel $(\lambda \approx 31.4),$ $(λ \approx 31.4),$ revealing the unique buckling characteristics of GFRP materials due to their anisotropy. The research outcomes provide a theoretical basis and practical tools for the refined design of GFRP compression members.