"Geometrical Properties of Circular Pipe
'<hr /><div style="max-width:150mm"><img style="height:135pt;" alt="circular-pipe.png" class="side" src="https://calcpad.eu/media/mechanics/sections/circular-pipe.png"></div>
'Dimensions
d = ?'%u,'t = ?'%u
d_1 = d - 2*t'%u
'Area
A = π*(d^2 - d_1^2)/4'%u<sup>2</sup>
'Centroid
'<p><i>z</i><sub>c</sub> ='y_c = d/2'%u</p>
'Perimeter
P = π*d'%u
'Second moments of area
'<p><i>I</i><sub>z</sub> ='I_y = π*(d^4 - d_1^4)/64'%u<sup>4</sup></p>
'Polar moment of area
I_x = 2*I_y'%u<sup>4</sup>
'Torsional constant
I_t = π*(d^4 - d_1^4)/32'%u<sup>4</sup>
'Torsional section modulus
W_t = 2*I_t/d'%u<sup>3</sup>
'Radii of gyration
'<p><i>r</i><sub>z</sub> ='r_y = sqrt(I_y/A)'%u</p>
r_x = sqr(I_x/A)'%u1	0.1