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The T$-$shaped column as shown is reinforced with $5-28mm$ and $2-25mm$ diameter bar with fy $=415$MPa. $f^{\text{'}}c=27$MPa

a$)$ Determine the location of plastic centroid from the extreme left fiber

b$)$ Determine the factored moment due to the factored load of $1800kN$ applied at $312mm$ from extreme left fiber

c$)$ Determine the factored moment due to the factored load of $1800kN$ applied at $100mm$ from extreme left fiber