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This paper aims to obtain a calculation method by hand without iteration.

This paper adopts strains as known quantities to solve the internal forces and deformations of the section, simplifies the deflection curve of the column and obtains nomograms that can calculate the bearing capacity and reinforcement of circular reinforced concrete (RC) columns by hand.

Nomograms include five variables: mechanical reinforcement ratio, relative normal force, dimensionless bending moment, slenderness ratio and ultimate dimensionless curvature. Nomograms corresponding to all classes of concrete have been drawn, and their dimensionless form makes them widely applicable. The calculation results of nomograms are compared and analysed with numerical calculation results, and the difference is within 5%, meeting the engineering requirements.

Calculating the bearing capacity of compression bending components requires considering second-order effects. Therefore, the calculation of the bearing capacity of circular RC columns requires iterative calculation, as it includes dual nonlinearity of material and geometry, and the two are coupled with each other. To calculate the bearing capacity of the section adopting ordinary concrete, it is necessary to solve the transcendental equation iteratively. For high-strength concrete, it can only be solved by numerical integration. A fast calculation method by hand is proposed in this paper.

The purpose of the study is to optimize the blending ratio of Arecanut and cotton fibers to create yarn with the best quality for various applications, particularly home furnishings. The study aims to determine the effect of different blend ratios on the physical and mechanical properties of the yarn.

The study involves blending Arecanut and cotton fibers in various ratios (90:10, 75:25, 50:50, 25:75 and 10:90) at two different yarn counts (10/1 and 5/1). Various physical and mechanical properties of the blended yarn are analyzed, including unevenness, coefficient of mass variation (cvm%), imperfection, hairiness, breaking strength, elongation, tenacity and breaking work.

The research findings suggest that the blend ratio of 10:90 (10% cotton and 90% Arecanut fiber) produced the best results in terms of physical and mechanical properties for both yarn counts. This blend ratio resulted in reduced unevenness, cvm% and imperfection, while also exhibiting good mechanical properties such as breaking strength, elongation, tenacity and breaking work. The blend with a higher concentration of cotton generally showed better properties due to the coarseness of Arecanut fiber. As the goal of the study was to determine the best blend ratio that included the most Arecanut fiber based on its physical and mechanical properties, which is suitable for home furnishing applications, 75:25 Areca cotton blend ratio of yarn count 5/1 proved to be the best.

The study acknowledges that Arecanut fiber must be blended with other commercially used fibers like cotton due to its coarseness. While the study provides insights into optimizing blend ratios for home furnishings and packaging, further research may be needed to make the material suitable for clothing applications.

The research has practical implications for industries interested in utilizing Arecanut and cotton blends for various applications, such as home furnishings and packaging materials. It suggests that specific blend ratios can result in yarn with desirable properties for these purposes.

The study mentions that the increased use of Arecanut fibers can benefit the growers of Arecanut, potentially providing economic opportunities for communities engaged in Arecanut farming.

The research explores the utilization of Arecanut fibers, an underutilized resource, in combination with cotton to create sustainable yarn. It assesses various blend ratios and their impact on yarn properties, contributing to the understanding of eco-friendly textile materials.