The curved field-frame bar in a cheiroballistra-style ballista is weakest at the curve. Therefore it may be necessary to reinforce the curve separately to prevent the pressure of the spring cord from bending it. This article describes a way to reinforce the curve after forging; it is better if the curve is left thicker in the first place.
The process step by step Edit
Take a piece of round or rectangular steel of sufficient thickness and bend it to roughly the same curvature as the curve in the field-frame bar:
Next cut the bar to correct length and press it against the field-frame bar's curve in a vise:
Weld the piece to the field-frame bar:
Grind the curve to an even surface with an angle grinder and file it smooth. Then heat it in a forge to get rid of the shiny metal surface.