Two conditions are possible - K ≥ T/4D and K < T/4D. The deflections and moments on the shell at the ring and at midspan between rings are dependent on the relationship between K and T/4D. For a circular tube section, substitution to the above expression gives the following radius of gyration, around any axis:Ĭircle is the shape with minimum radius of gyration, compared to any other section with the same area A.$$ $$ Small radius indicates a more compact cross-section. It describes how far from centroid the area is distributed. The dimensions of radius of gyration are. Where I the moment of inertia of the cross-section around a given axis and A its area. Radius of gyration R_g of a cross-section is given by the formula: Where, D, is the outer diameter and D_i, is the inner one, equal to: D_i=D-2t. Įxpressed in terms of diamters, the plastic modulus of the circular tube, is given by the formula: The last formula reveals that the plastic section modulus of the circular tube, is equivalent to the difference between the respective plastic moduli of two solid circles: the external one, with radius R and the internal one, with radius R_i. The moment of inertia (second moment of area) of a circular hollow section, around any axis passing through its centroid, is given by the following expression: The total circumferences (inner and outer combined) is then found with the formula: Its circumferences, outer and inner, can be found from the respective circumferences of the outer and inner circles of the tubular section. Where D_i=D-2t the inner, hollow area diameter. In terms of tube diameters, the above formula is equivalent to: Where R_i=R-t the inner, hollow area radius. The area A of a circular hollow cross-section, having radius R, and wall thickness t, can be found with the next formula:
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