Considering the inelasticity properties of eccentric compression columns of reinforced concrete, a uniform equivalent rigidity reduction factor is provided in specifications. As many factors affect the elastoplastic flexural rigidity of reinforced concrete columns and owing to load increase, some concrete tension zones crack, resulting in a lower flexural rigidity of concrete columns, however, the uniform equivalent rigidity coefficient cannot reflect this change rule. To investigate the change rule of flexural rigidity of reinforced concrete columns when considering the deflection second-order effect of compression columns, by testing reinforced concrete eccentric compression columns, a trilinear calculation model is established that can reflect the change rule of elastoplastic flexural rigidity of reinforced concrete columns by analyzing the relationship between bending moment and curvature. Additionally, a formula to calculate the elastoplastic flexural rigidity reduction factor of a reinforced concrete eccentric compression column is obtained via linear regression. This formula can reflect the effects of concrete cracking, axial compression ratio, eccentricity, and reinforcement ratio on the flexural rigidity of concrete columns, as well as predict the flexural rigidity reduction of existing reinforced concrete columns.

It is difficult to determine the effective length coefficient of weakly braced frame columns using the effective length coefficient method. When the stability of braced frame structures is calculated using the effective length coefficient method, it cannot reflect the effect of the brace on the frame, the mutual support of columns on the same floor, and vertical interactions between different floors, which is easy to lead to unreasonable design. In this study, based on a spring-rocking column model, the structural transformation concept was used to transform the second-order problem of determining the critical force of braced frame structures into a first-order problem of calculating the lateral stiffness of the structure. First, the repetitive frame element was used to obtain the lateral stiffness of each floor, and the second-order effect coefficient was used to determine the load stiffness of the floor. Next, the lateral stiffness and load stiffness of each floor was assembled. Finally, the principle in which the load stiffness reduces the lateral stiffness of the structure to zero when the braced frame structure buckles laterally were applied to derive a formula to directly calculate the critical force of the flexural-type brace frame structure. This formula reflects the interactions between the braced structure and the frame, the mutual support of columns on the same floor, and the vertical interactions between different floors. Therefore, it can compensate for the deficiency in which the criterion cannot calculate the critical force of braced frame structures and is suitable for quantitatively analyzing the vertical interactions between different floors of braced frame structures.

Optical remote sensing images acquired in rugged mountains are affected by reflectance distortion caused by both topography and shadows. Most topographic correction (TC) methods normalize sunlit slopes but can become unstable in self shadow and cast shadow, where little or no direct solar radiation reaches the surface. This study builds on the topographic shadow effect correction (TSEC) model and develops TSEC+TC, a partitioned framework for horizontal equivalent normalization. Using a shadow mask extended to penumbra, the framework integrates TSEC for shadowed pixels with conventional TC for sunlit pixels. Both branches target horizontal equivalent reflectance, enabling simultaneous correction of topographic and shadow effects across the scene. We implemented TSEC+TC with path length correction (PLC) and SCS with C (SCSC) models and evaluated it using ten multi-temporal Landsat 8 OLI scenes under different illumination conditions. The results showed that TSEC+TC reduced terrain-related brightness variation and improved land cover classification in the auxiliary comparison relative to uncorrected and TC-only results. For TSEC+SCSC, the R² values between corrected reflectance and cosi were below 0.025 for both Red and SWIR1 bands, and the coefficient of variation of reflectance across aspects was consistently lower than the corresponding values for SE and SCSC, with a maximum of 36.00%. Shadow area analyses indicated that TSEC+TC compensated reflectance distortion in self shadow and cast shadow areas, reduced TC-induced outliers, and better preserved spectral patterns than TC-only correction. Tests using Sentinel-2 MSI and GF-1 WFV imagery provided preliminary evidence of applicability to other sensors. Accounting for the topographic shadow effect improved TC performance in complex mountainous areas.

Based on the activation degree of the frame column stiffness, this paper studies the influence of the axial force area on the critical bearing capacity of the irregular frame and deduce some rules. Based on these rules, this paper corrects the critical bearing capacity of the regular frame and establishes the critical bearing capacity calculation method of the irregular frame. The axial force area ratio method can make up for the current codes can only calculate the critical force of the regular frame, which has great value in engineering application. Compared with the results of ANSYS, the axial force area ratio method has good precision. This method can consider the interaction between columns of the same story and the inter-story interaction.

Concrete beams are often subjected to torsion in the actual project, paste carbon fiber reinforced polymer and wrapped angle is commonly used in the actual project of the two concrete beam reinforcement methods, the use of carbon fiber reinforced polymer and angle for the combination of reinforcement, can be combined with the advantages of the two materials in the improvement of the structural mechanical properties, so that concrete beams can be reinforced to form a combination of superior performance of the structure, the concrete beams subjected to torsion beams for the combination of reinforcement is currently still At present, the combined reinforcement of concrete beams subjected to torsion is rarely involved. In this paper, for the carbon fiber reinforced polymer and angle steel combination of reinforced concrete torsion beams, designed 18 numerical specimens, its torsional stiffness and bearing capacity research, to determine the combination of torsional reinforced concrete beams of the main factors affecting the optimal combination of ratios, and to give the combination of reinforced concrete torsion beams torsional bearing capacity calculation formula. The research results show that the carbon fiber material and the splicing plate can form effective constraints on the concrete torsion beams, and the combined reinforcement method has a significant effect on the torsional load capacity, torsional stiffness and ductility enhancement of the reinforced concrete beams compared with the single reinforcement. The research results can provide technical support for the design and construction of combined reinforcement of concrete torsion columns.

The protection and renewal of traditional residential buildings help to enhance the functionality and adaptability of the buildings, pass on the traditional architectural culture, promote the sustainable development of traditional buildings, and contribute to rural revitalization. This article proposes some practical strategies for the protection and renovation of traditional residential buildings, and elaborates in detail on the long-term development of the reconstruction and renovation of traditional Yi ethnic villages’ residential buildings in Damoyu Village, Kunming City and Dabudong Village, Luoping County. It can provide methodological references for the renovation and reuse of traditional residential buildings.