Problem $5\mathrm{.}8-12$

Pts : $16$

A simply supported wood beam of rectangular cross section and span length $1\mathrm{.}2$m carries a concentrated load P at midspan in addition to its own weight $($see figure$).$

a$)$ The cross section has $.$ Calculate the section modulus, $$y

b$)$ The weight density of the wood is $..$ Calculate the weight of the beam, q

c$)$ Calculate the maximum permissible value of the load P if the allowable bending stress, $,$ is $8\mathrm{.}5$ MPa.

d$)$ Calculate the maximum permissible value of the load P if the allowable shear stress, $,$ is $0\mathrm{.}8$ MPa.