For the singly$-$reinforced beam section shown below:

a$.$ Compute the area of steel reinforcement needed for a balance condition. Show

all necessary diagrams used in your calculations: strains, stresses, and forces.

b$.$ Define the range of adequate steel reinforcement ratio: ${}_{\text{m}\text{i}\text{n}}-{}_{\text{m}\text{a}\text{x}}$

Is the amount of reinforcement provided within that range?

Assume $f^{\text{'}}c=5000$ and Grade $60$ steel.

$(20$ points$)$