網糸の研究-V : 糸の機械的性質に就いて(3)

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In the ?? revious papers, we reported about the relation between εD and εS or P and εS. Applying these relations for strand, we obtained the following formula regarding to the outside diameter of twine, D=D0(1-εD)-2/√3•KD0-1/3E-2/3 (P•sinθ /√3R)2/3where εD: diametral contraction of strand per unit diameter. D0: outside diameter of strand. D: outside diameter of twine. P: tension induced in strand. R: spiral radius of strand axis. θ: inclination of strand axis. K: approaching modulus of strand axis by compression. E: Youngs modulus of fiber. and the following formula regarding to the tension of twine. P=3P•sinθ To calculate above formulas, at first we expressed εs as the function of ε and θ [=tan-1 b (1+ ?? )/2πR0], on the assumption that R=R0=const., and by the methods of previous papers, obtained the approximate values εD and P, where εs and ε are elongations of strand and twine per unit length, b is spiral pitch of strand, and zero sufix shows the each value at no load. Hence, calculating the first formula about diameter with the above εD, P, θ, and R0, weadmitted that the above formula was applied. And also in the case of calculating tension P (the second formula), the values of P and θ are to be calculated using the variable spiral radius R which is induced from the above D and D.
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