Equilibrium equations for frame during work external load

Equilibrium equations designation for frame under continuous load q[N/m]. Frame has shape like sign [ which was rotated by π/2 to right side. Frame stands on unmoveble support on the left. Frame stands on moveable support on the right. Considered example is two dimmensional. In example statics equilibrium equations will be written. We will choose coordinate system and assign it to frame. Because lines of forces's vectors acting don't cross in one point, it will be three equations:
• first equilibrium equation for forces or components of forces in X axis direction
• second equilibrium equation for forces or components of forces in Y axis direction
• third equilibrium equation for torques or components of torques to any chosen point