Calculate the radius of gyration for a bar of rectangular cross section with thickness t and width w for bending in the direction of (a) the thickness, (b) the width, and (c) transverse to a diagonal.

a) R = sqrt (wt³/12wt)

b) R=sqrt (tw³/12wt)

c) R = sqrt (wt³/12xcos45xwt)

Explanation:

Thickness = t

Width = w

Length od diagonal = sqrt (t² + w²)

Area of raectangle = A = tW

Radius of gyration = r = sqrt (I/A)

a)

Moment of inertia in the direction of thickness I = w t³/12

R = sqrt (wt³/12wt)

b)

Moment of inertia in the direction of width I = t w³/12

R=sqrt (tw³/12wt)

c)

Moment of inertia in the direction of diagonal I = (w t³/12) cos 45 = (wt³/12) x 1/sqrt (2)

R = sqrt (wt³/12xcos45xwt)