HYBRID ANALYTICAL APPROACH COMBINING MORRICE AND LITTLE (DESIGN CURVE) WITH FINITE ELEMENT METHODS FOR ORTHOTROPIC BRIDGE DECKS
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Abstract
This study aimed to develop and validate a hybrid analytical framework for the structural analysis of orthotropic steel bridge decks, particularly those with skewed or curved geometries. The primary goal was to improve the accuracy of load distribution and force prediction by integrating the classical Morrice and Little (M-L) design curve method with a finite-element orthotropic-plate model within a MATLAB environment. The study was motivated by the need to reduce the limitations of purely empirical approaches and the computational burden of full-scale 3D finite element (FE) analysis, offering an efficient yet accurate alternative for early and intermediate stages of bridge design.
The methodology involved extracting detailed geometric and material data from a 30 m long, simply supported orthotropic bridge deck modelled in STAADPro v8i, including 3 main girders (W900 × 300 mm), 12 mm thick longitudinal ribs spaced at 300 mm, and 2 m cross-girder spacing. Flexural rigidities (Dx, Dy), torsional constant (α = 0.45), and skew factor (θ = 0.789) were calculated and used in a finite-difference orthotropic plate model (1 m × 1 m mesh with simply supported boundaries). Load effects from a 300 kN HB axle (with a 1.25 impact factor) were applied at mid-span. MATLAB was used to interpolate M-L distribution coefficients, integrate them with global stiffness matrices, and perform moment and deflection analysis. Comparative validation was performed against detailed shell-element results from STAADPro.
Numerical results showed that the hybrid model predicted peak girder bending moments of 5951KNm, closely matching the STAADPro value of 5850KNm, with an error margin of just 1.7%. The mid-span deflection was 19.4 mm, only 2.6% higher than the STAAD result (18.9 mm), and well within the L/500 deflection limit of 60 mm. In contrast, the classical M-L method predicted a more conservative moment of 5380KNm, 8% lower than STAAD. Computational efficiency was significantly improved: MATLAB solved each case in under 0.8 seconds, compared to 45 seconds per case in STAADPro, demonstrating a 50× speed-up. These findings confirmed that the hybrid approach offers a code-compliant, accurate, and computationally efficient solution for the analysis of orthotropic bridge decks, reducing over-design and enabling faster design cycles.
The methodology involved extracting detailed geometric and material data from a 30 m long, simply supported orthotropic bridge deck modelled in STAADPro v8i, including 3 main girders (W900 × 300 mm), 12 mm thick longitudinal ribs spaced at 300 mm, and 2 m cross-girder spacing. Flexural rigidities (Dx, Dy), torsional constant (α = 0.45), and skew factor (θ = 0.789) were calculated and used in a finite-difference orthotropic plate model (1 m × 1 m mesh with simply supported boundaries). Load effects from a 300 kN HB axle (with a 1.25 impact factor) were applied at mid-span. MATLAB was used to interpolate M-L distribution coefficients, integrate them with global stiffness matrices, and perform moment and deflection analysis. Comparative validation was performed against detailed shell-element results from STAADPro.
Numerical results showed that the hybrid model predicted peak girder bending moments of 5951KNm, closely matching the STAADPro value of 5850KNm, with an error margin of just 1.7%. The mid-span deflection was 19.4 mm, only 2.6% higher than the STAAD result (18.9 mm), and well within the L/500 deflection limit of 60 mm. In contrast, the classical M-L method predicted a more conservative moment of 5380KNm, 8% lower than STAAD. Computational efficiency was significantly improved: MATLAB solved each case in under 0.8 seconds, compared to 45 seconds per case in STAADPro, demonstrating a 50× speed-up. These findings confirmed that the hybrid approach offers a code-compliant, accurate, and computationally efficient solution for the analysis of orthotropic bridge decks, reducing over-design and enabling faster design cycles.
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