The figure shows a rectangular member OB$,$ made from $0\mathrm{.}5-$cm thick aluminum plate, pinned to the ground at one end and supported by a coil spring at point A$.$ The spring has been measured to deflect $1$ mm with an applied force of $9\mathrm{.}80$ kN$.$ Find the deflection at point B$.$ Use Castigliano$$s method directly without using superposition or indirect geometric extrapolations.

A horizontal beam OB is attached to the vertical support on the left and to the support C suspended the top to point A at the middle through a spring.The width of the beam is $3$ centimeters, and the thickness is $0\mathrm{.}5$ centimeters. Point A is at a distance of $25$ centimeters from point O and $25$ centimeters from point B$.$ A downward force F acts on the horizontal beam at point B$.$

where F$=320$ N

Determine the component of the deflection at B due to the energy in section OA$.($Round the final answer to three decimal places. Include a minus sign if necessary.$)$

The component of the deflection at B is