Roark's Table 35 Formulas for elastic stability of plates and shells
Thin tube with closed ends under uniform external pressure, lateral and longitudinal
8" NOM. (8.625" OD X 0.322" WALL X 7.981" ID) ALUMINUM 6061-T6 EXTRUDED PIPE SCHEDULE 40
radius:
Enter dimensions and properties:
length:
Modulus of elasticity:
Poisson's ratio:
wall thickness:
For the expressions in the case to be valid, the following condition must be true (i.e., condition = 1):
Conditions:
Critical pressure:
The general expression for q' as a function of n (the number of lobes formed by the tube in buckling) is as follows:
To determine q', it is necessary to determine which value of n greater than 2 provides the smallest value of q' for the given t/r.
Find the value of n that corresponds to the smallest computed value of q':
Compute q' using the correct value of n:
Values of experimentally determined critical pressure range 20% above and below the theoretical value given by the expression above.
References:
Ref. 19.
Ref. 20.
Ref. 81.
Ref. 109.
End of Section
Von Mises Formula (Ross; 2nd edition page 101)
Windenburg and Trilling Formula aka David Taylor Model
Windenburg and Trilling Thinness Ratio (Ross; 2nd edition page 105)
Critcal Length for Stiffeners (Southwell 1913)
NASA SP-8007