MEAE $1033/$ SEAA $5313$

$5$

Q$3.$ FIGURE Q$3($a$)$ shows a $7$ m simply supported reinforced concrete beam. The beam carries uniformly distributed load over its entire span which consists of characteristic permanent action $($including selfiveight$)$ of $20\mathrm{.}0k\frac{N}{m}$ and characteristic variable action of $15\mathrm{.}0k\frac{N}{m}.$ The beam cross section with the designed reinforcement is shown in FIGURE Q$3($b$).$ The construction materials used in the design are Grade C$30/37$ concrete and Grade $500$ steel reinforcement. The nominal concrete cover to links is $25$ mm $,$ while the Elastic Modulus of concrete and steel are $26k\frac{N}{m}{m}^2$ and $200k\frac{N}{m}{m}^2,$ respectively.

By referring to Clauses $7\mathrm{.}4$ of MS EN $1992-1-1,$ calculate the long$-$term deflection of the beam at mid span due to the total load given above.

Note: As a guide the calculation of curvature for a crack section can be made using an approximate method and for the first trial, assume that the neutral axis of the beam lies in the web.

$($a$)$ Simnly cinnorted heam

FIGURE Q$3($all units are in mm unless stated othervise$)$