A built-up beam supporting a condominium balcony is made up of a structural T for the top flange and web and two angles for the bottom flange and web, as shown. The beam is subjected to a bending...

A built-up beam supporting a condominium balcony is made up of a structural T for the top flange and web and two angles for the bottom flange and web, as shown. The beam is subjected to a bending moment M having its vector at an angle θ to the z axis (see figure).

Determine the orientation of the neutral axis and calculate the maximum tensile stress

_t
and maximum compressive stress

_c
in the beam. Assume that
 = 30⁰
and M = 10 kN m.

Use the numerical properties: c₁
= 4.111 mm, c₂
= 4.169 mm, 134 mm, L_s
= 76 mm, A = 4144 mm², I_y
= 3.88
10⁶
mm⁴, and I_z
= 34.18
 10⁶
mm⁴.