第2種曲邊正多角形斷面を持つ中空柱體の捩り應力
1935 年 1935 巻 57 号 p. 83-91
詳細
1935 年 1935 巻 57 号 p. 83-91
For the section of a hollow-cylinder in heading, we can apply the torsion stress function in the following form:-
Ψ=k(1/an-1/γn•cosnθ)-γ2+a2
where n=0 or integer, a=radius of a circle, k_??_0.
The function holds good in the outer region of a circle, and the inner periphery can be obtained by solving the following equation with respect to a parameter γ, .
k(1/an-1/γncos nθ)-γ2+a2=0.
The outer periphery can be determined by taking
Ψ=C2=a2-b2+k(1/an-1/bn)
where b>a.
Then we have the stresses in two directions
Zθ=tG(γ-1/2knγ-1-ncosnθ),
Zγ=tG(1/2knγ-1-nsinnθ).
Between two stresses, it is necessary to consider the value of Zθ on the outer boundary, which becomes maximum at the angles θ=(2s-1)π/n, where s=1, 2, 3……n
