Question

A strut member used in a roof truss consisting of equal angles of ISA 100 mm x 100mm x 10 mm thick are placed on either sides of 16mm thick gusset plate. The cross sectional area of angle section is 1903 mm${}^2$ and Moment of inertia is
$I_{xx}=I_{yy}=177\times {10}^{4}m{m}^4$
then the minimum radius of gyration is ______.

Answer 1

$I_{xx}=2.I_{CG}$

$I_{yy}=2[I_{CG}+A{X}^2]$

$I_{min}=2I_{xx}$

$r_{min}=\sqrt{\frac{2I_{xx}}{2.A}}=\sqrt{\frac{I_{xx}}{A}}$

$r_{min}=\sqrt{\frac{177\times {10}^4}{1903}}=30.49mm$