排水管など自重による挫屈について (第1報)

抄録

In this study, the buckling tests of pipe due to its own weight with the diameter 8mm and the length 1, 000-4, 500mm were examined.
As the results of this tests, the following conclusions were obtained.
(1) Empirical formula of deflection curve of the pipe;δ=δ₀(l/l₀)ⁿ (1)
where n=1.17-2.05
(2) Critical length of pipe obtained by using the strain energy of bending ΔUand the total work during the buckling ΔT;l_cr{n(n+1)²/2(2n-1[(n+1)2/2n+1+n-2/n+2-n²+3n/2n+3])}1/3·3EI/q (2)
(3) Relation betweenl_crandl_cr0or the ratio ofl_crandl_cr0l_cr=C·l_cr0={n(n+1)²/2×7.837(2n-1)[(n+1)²/2n+1+n-2/n+2-n²+3n/2n+3]}1/3·l_cr0(3)
For the abovevalue of n=1.17-2.05, the value ofCis less than 1.04, consequeently the above equations about the deflection's curve and the critical length are practically well enough appllcable.
l₀=length of pipe
l=arbitrqry length of pipe
δ₀=deflection of upper end
δ=deflection at the point of length
ΔU=strain energy of bending
ΔT=total work during buckling
l_cr=critical length of pipe
l_cr0=exact solution about critical length of pipe given by Timoshenko
C=coefficient