Problem 10.66

For a C10 x 20 channels,

A = 5.88 in²

centroidal position = 0.606 in

I_x = 78.9 in⁴

I_y = 2.81 in⁴

Also given are:

E = 29 x 10⁶ psi

L_e = 21 ft

For both channels, the moments of inertia are:

I_x = 2(78.9) = 157.8 in⁴

I_y = 2[2.81 + (5.88)(2.894)²] = 104.11 in⁴,

where the 2.894 = 7/2 - 0.606

The radius of gyration is

Ignoring the lacing bars, the slenderness ratio is

For a yield stress of 36 ksi,

Since the slenderness ratio is smaller than C_c, I use

Thus, .