Forces acting at point $a$ ... $N$ upward, $T_y$ upward, and $T_x$ to the right
Forces acting at point $b$ ... equal reaction forces, $R$ to the left and right
Force acting at point $c$ ... $N$ upward
Force acting at the midpoint of $ab$ ... $W$ downward
Forces acting at the midpoint of $bc$ ... $W$ downward, $T_y$ downward, and $T_x$ to the left.
Geometry ... Vertex angle = $2\alpha \implies$ each base angle = $(90^\circ - \alpha)$. Also, note $\sin(90^\circ-\alpha)=\cos{\alpha}$
$\displaystyle \sum F_y = 0 \implies N = W$
$\displaystyle \sum \tau = 0$ about both rods ...
Torques acting on rod $ab$ about point $b$ yields the equation ...
$W\sin{\alpha} \cdot L + T_x \cos{\alpha} \cdot 2L = N\sin{\alpha} \cdot 2L + T_y \sin{\alpha} \cdot 2L$
Torques acting on rod $bc$ about point $b$ yields the equation ...
$N\sin{\alpha} \cdot 2L = W\sin{\alpha} \cdot L + T_y\sin{\alpha} \cdot L + T_x\cos{\alpha} \cdot L$
Solve the system of torque equations for $T_x$ and $T_y$, then determine $T=\sqrt{T_x^2 + T_y^2}$
thanks.
how do you know the normal reactions at c and a are the same by labeling them both N.?
Also I am not sure why you do not take into account the vertical and horizontal components of the reaction at the hinge for letting forces up=forces down for the whole system?
I understand why you do not take it into account when taking moments through b for the rods as you are taking moments about that point.
symmetry of the rod positions ... what would cause them to differ?
there are no vertical forces acting on the hinge an point b ... the two rods push horizontally on each other at the hinge.Also I am not sure why you do not take into account the vertical and horizontal components of the reaction at the hinge for letting forces up=forces down for the whole system?
ok so the forces at the hinge cancel each other out.
My last question is do you know what the difference between something that is freely hinged and smoothly hinged. I think smoothly means means the x and and y component of the normal reaction cancel out or something?