# On the Use of the Effective Width for Simply Supported Generally Loaded Box-Girders
## 7 Conclusions  
A new method has been proposed for the bending static analysis of simply supported, but generally loaded, rectangular box-girders with undeformable cross-section, undergoing shear-lag. The method is based on (i) expanding the general load in the Fourier series; (ii) finding the effective flange width relevant to each harmonic; (iii) computing, for each harmonic, displacements and stresses by using a beam model with effective geometric characteristics; and (iv) combining the results of all the harmonics. As an alternative to the effects combination, approximate formulae giving ready-for-use expressions for an \"average effective width\" have been derived, based on equivalences at selected points with (i) displacements or (ii) stresses of the more refined model. Results have been compared  
Figure 20: Maximum normal stress (in \(\mathrm{N}/\mathrm{mm}^{2}\)) vs. \(z\): (**a**) DL; (**b**) SL-centered; (**c**) CL-centered. Evaluated with \(b_{en}\) (black continuous line), \(\bar{b}_{e}\) by the normal stresses equivalence (gray line), \(\bar{b}_{e}\) by the displacements equivalence (black dashed line).  
with much more expensive Finite Element analyses to validate the method presented. The following conclusions, relevant to sample loading conditions, have been drawn.  
1. The maximum displacement and stress supplied by the algorithm are in excellent agreement with the FE results, even in the most complex load cases analyzed.
2. The average shear-lag coefficient based on the stress equivalence, gives excellent results in accordance with the literature. Differently from the literature, however, they can be generalized to any load conditions.
3. The displacement-based equivalence generally gives less accurate results. In some circumstances, it describes better the longitudinal trend, while the stress-based equivalence captures the maximum values better.
4. The neglection of the shear deformation of the web, which could be accounted by the Timoshenko beam model, has been proven to not significantly affect the results, as it emerges from the comparison with shear deformable FE.  
In conclusion, based on the excellent agreement of the results with FEM analyses, it is believed that the formulae here derived for the effective width flange of simply supported box girders are reliable and usable. Above all, a methodological and innovative algorithm has been developed, easily implementable for any load distributions of interest to the designer.  
Conceptualization, A.L.; methodology, A.L.; software, F.P.; validation, F.P.; formal analysis, A.L. and F.P.; investigation, F.P.; resources, A.L. and F.P.; data curation, F.P.; writing--original draft preparation, F.P.; writing--review and editing, A.L. and F.P.; visualization, F.P.; supervision, A.L.; project administration, A.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.