A rectangular beam of span $10$ m is $200$ mm wide and $450$ mm deep. The beam is prestressed by a parabolic cable having an eccentricity of $100$ mm below the central axis at mid span and $25$ mm above the centroidal line at support section. The beam carries an UDL of $10k\frac{N}{m},E_c=38k\frac{N}{m}{m}^2$

a$)$ Estimate the short term deflection neglecting the loss of pres'ress.

b$)$ Estimate the long term deflection assuming the loss of prestress as $15\%.$ Assume the creep co efficient as $1\mathrm{.}8.$