Assume the horizontal member can be treated as a beam and assuming the diagonal member may be treated as a rod, what is its axial force as a function of the applied loading $P$ and length parameters $L_i$. Assume that the connection between the beam and the rod may be treated as as socket joint.
Firstly, I have defined the vertical, horizontal and moment reactions at the top and bottom built-in ends as $V_1, H_1, M_1, V_2, H_2,$ and $M_2$ respectively. I have also defined the axial force (assumed tensile) in the diagonal member as $T$.
Vertical equilibrium of the beam:
$P + V_1 - Tsin(\phi) = 0$
Horizontal equilibrium of the beam:
$H_1 - T cos(\phi) = 0$
Moment equilibrium of the beam:
$M_1 + P(L_1 + L_2) - T sin(\phi) L_1 = 0$
Vertical equilibrium of the rod:
$T \sin{\phi} + V_2 = 0$
Horizontal equilibrium of the rod:
$T cos(\phi) + H_2 = 0$
Moment equilibrium of the rod:
$M_2 = 0$
Global vertical equilibrium:
$P + V_1 + V_2 =0$
Global horizontal equilibrium:
$H_1 + H_2 = 0$
When I attempt to solve the simultaneous equation, I get an indeterminate problem and can not solve for the value of $T$.