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A $6$ m long simply-supported beam is prestressed as shown in the figure.

The beam carries a uniformly distributed load of $6$ kN/m over its entire span. If the effective flexural rigidity $EI=2 \times 10^4 \: kNm^2$ and the effective prestressing force is $200$ kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is _____