SITUATION $5-$ A raliroad tie $($or sleeper$)$ is subjected to two rail loads, each of magnitude $P=130kN,$ acting as shown in the figure. The reaction of the ballast is assumed to be uniformly distributed over the length of the tie, which has cross$-$sectional dimensions $b=300mm$ and $h=250mm.$ Given: $L=1500mm$ and $a=500mm.$ Calculate the following.

$13.$ The magnitude of $q$ in $k\frac{N}{m}.$

A$.52$

C$.158$

B$.68$

D$.104$

$14.$ The maximum bending stress in MPa.

A$.4\mathrm{.}2$

C$.3\mathrm{.}2?$

$$b$.5\mathrm{.}2?$

D$.6\mathrm{.}2$

$15.$ The maximum shearing stress in MPa.

A$.1\mathrm{.}04$

d$.1\mathrm{.}56$

B$.2\mathrm{.}36$

D$.1\mathrm{.}95$