Background: Basic helix-loop-helix (bHLH) is a superfamily of transcription factors that is widely found in plants and animals, and is the second largest transcription factor family in eukaryotes after MYB. They have been shown to be important regulatory components in tissue development and many different biological processes. However, no systemic analysis of the bHLH transcription factor family has yet been reported in Sorghum bicolor. Results: We conducted the first genome-wide analysis of the bHLH transcription factor family of Sorghum bicolor and identified 174 SbbHLH genes. Phylogenetic analysis of SbbHLH proteins and 158 Arabidopsis thaliana bHLH proteins was performed to determine their homology. In addition, conserved motifs, gene structure, chromosomal spread, and gene duplication of SbbHLH genes were studied in depth. To further infer the phylogenetic mechanisms in the SbbHLH family, we constructed six comparative syntenic maps of S. bicolor associated with six representative species. Finally, we analyzed the gene-expression response and tissue-development characteristics of 12 typical SbbHLH genes in plants subjected to six different abiotic stresses. Gene expression during flower and fruit development was also examined. Conclusions: This study is of great significance for functional identification and confirmation of the S. bicolor bHLH superfamily and for our understanding of the bHLH superfamily in higher plants.

PurposeThe reinforced concrete open-web sandwich slab is composed of upper rib, lower rib, surface plate and shear key and was applied to long-span structure crossing at 18–30 m. The shear-bearing capacity of shear key, having vital effects on the slab’s bearing capacity, is analysed to present its calculation formula used for the engineering application of the slab.Design/methodology/approachThe shear-bearing capacity of shear key is analysed by the strut-and-tie model and the benchmark model established by the finite element method. Furthermore, the design formula of its shear capacity is given by the parametric analysis of FEM to adjust the result of the strut-and-tie model, using multivariate linear regression analysis of these parameters.FindingsThe calculation result of the benchmark model is compared with those of the strut-and-tie model and the standard formula, which indicates that the result of the strut-and-tie model is closer to that of the benchmark model than that of the standard formula. Moreover, the parametric analysis of the finite element model indicates that the volume–stirrup ratio of the shear key and the compression strength of the concrete have lesser effect on the shear capacity compared with the longitudinal reinforcement ratio and the shear-to-span ratio of the shear key and the relative section height of the rib.Originality/valueThe shear capacity of the shear key is provided in the paper by combining the finite element method and the strut-and-tie model, which is different from the calculation of the shear key in local codes and Chinese code, based on the theory of short corbel and the experiment of member. Furthermore, the formula of the shear capacity could be employed in the design and construction of the RC open-web sandwich slab, mainly used in the public and industrial multi-story building with long span to save the dwindling land resource currently.