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Rg-Calculator for composed solid shapes (SAS)

Shapes can be composed of up to 5 different shapes and/or with different distances from the shape's centroid (center of gravity). Select the geometrical shape, lengths of the axes (a,b,c), or radii (rx,ry,rz) and/or height (h) or torroidal radius (R) in the x-, y- and z-directions. Enter the number (n) of the (equal) sub-shapes and the respective distances (rc) of the sub-shape's centroid to the centroid of the entire shape. The values of the radius of gyration Rg, of the volume (V) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

ellipsoid (rx,ry,rz), hexahedron/tetrahedron/octahedron (rx=ry=rz=a), cylinder (rx,ry,rz=h)
semi-ellipsoid/paraboloid (rx,ry,rz=h), semi-cylinder (rx,ry,rz=h, cut along ry), cone (rx,ry,rz=h)
pyramid (3): (rx=a,a,ry=b,a>b/2,rz=h), prism (3): (rx=a,a,ry=b,rz=h) *(isosceles) triangular base*
pyramid (4): (rx=a,ry=b,rz=h), prism (4): (rx=a,ry=b,rz=h) *rectangular base*
pyramid (5,6): (rx=a,ry=a,rz=h), prism (5,6): (rx=a,ry=a,rz=h) *equilateral base*
pyramid (rhombic): (rx,ry,rz=h), prism (rhombic): (rx,ry,rz=h)
torus o (elliptic): (rx,ry,rz=R), torus # (rectangular): (rx=a/2,ry=b/2,rz=R)
torus (o and #): rx: parallel to the torus plane, ry: parallel to the central torus axis



n: rx (a): ry (b): rz (c/h): rc:
n: rx (a): ry (b): rz (c/h): rc:
n: rx (a): ry (b): rz (c/h): rc:
n: rx (a): ry (b): rz (c/h): rc:
n: rx (a): ry (b): rz (c/h): rc:



Radius of gyration: V: I(0):



Rg-Calculator for composed hollow or plane shapes (SAS)

Shapes can be composed of up to 5 different shapes and/or with different distances from the shape's centroid (center of gravity). Select the geometrical shape, lengths of the axes (a,b,c), or radii (rx,ry,rz) and/or height (h) or torroidal radius (R) in the x-, y- and z-directions. Enter the number (n) of the (equal) sub-shapes and the respective distances (rc) of the sub-shape's centroid to the centroid of the entire shape. The values of the radius of gyration Rg, of the surface area (A) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

ellipsoid (rx=ry,rz), semi-ellipsoid (rx=ry, rz=h)
cylinder (rx=ry,rz=h), semi-cylinder (rx=ry,rz=h), cone (rx=ry,rz=h)
triangle (3): (rx=ry=a,rz=b,a>b/2), rectangle (4): (rx=a,rz=b) *(non)equilateral*
pentagon (5): (rx=a,rz=a), hexagon (6): (rx=a,rz=a) *equilateral*
rhombus: (rx,rz), ellipse: (rx,rz), semi-ellipse (rx,rz, cut along rz)
torus o (elliptic): (rx=ry,rz=R), torus # (rectangular): (rx=ry=a/2=b/2,rz=R)



n: rx (a): rz (b/h): rc:
n: rx (a): rz (b/h): rc:
n: rx (a): rz (b/h): rc:
n: rx (a): rz (b/h): rc:
n: rx (a): rz (b/h): rc:



Radius of gyration: A: I(0):



Rg-Calculator for composed skeletal or wireframe-shapes (SAS)

Shapes can be composed of up to 5 different shapes and/or with different distances from the shape's centroid (center of gravity). Select the geometrical shape, lengths of the line (a), of the polygon (a) or radius (rx) of the (semi)ring. Enter the number (n) of the (equal) sub-shapes and the respective distances (rc) of the sub-shape's centroid to the centroid of the entire shape. The values of the radius of gyration Rg, of the perimeter (L) and of the zero-angle intensity I(0) will be calculated. Units are arbitrary.

line (rx=a), circular ring (rx), semi-circular ring (rx)
triangle (rx=a), square (rx=a), pentagon (rx=a), hexagon (rx=a)
(polygons are equilateral)



n: rx (a): rc:
n: rx (a): rc:
n: rx (a): rc:
n: rx (a): rc:
n: rx (a): rc:



Radius of gyration: L: I(0):



Author: M.Kriechbaum, TU-Graz (2013), e-mail: manfred.kriechbaum@tugraz.at