Figure $1\mathrm{.}1$ shows a prismatic beam loaded by a uniformly distributed dead load of $30k\frac{N}{m}.$ The beam is made of material whose Young Modulus of Elasticity is $210$GPa and of cross section shown in Figure $1\mathrm{.}2.$ Use the two figures to answer the following two questions below.

QUESTION $1$

$[60$ Marks$]$

$1\mathrm{.}1$ Determine the shape factor of the beam

$(30$ Marks$)$

$1\mathrm{.}2$ Briefly comment on the significance of the shape factor determined in Q$1\mathrm{.}1(2$ Marks$)$

$1\mathrm{.}3$ Calculate the slope of the beam at B using direct integration method

$(14$ Marks$)$

$1\mathrm{.}4$ Determine the maximum deflection of the beam using direct integration method

$(14$ Marks$)$