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A rectangular concrete beam of cross section $300mm$ by $200mm$ is presstressed by means of $15$ wires of $5mm$ diameter located $65$

$mm$ from bottom of the beam and $3$ wires of $5mm$ diameter located $25mm$ from the top. Assming the presstress in the stess as $840$

MPa.

a$)$ Calculate the stress at extreme fibers at mid$-$span of the section when the beam is supporting its own weight over a span of $6m.$

Weight concrete is $24k\frac{N}{m^3}$

b$)$ Calculate the stress at extreme fibers at mid$-$span if $6k\frac{N}{m}$ liveload is imposed