The bar shown has a uniform cross sectoncel Area and is fixed at both ends. An idealized stress$-$strain relation is also shown. Assume that the relation is ralid in compression as well as in tension.

a$.)$ Determine the value of load $P$ that initiates yielding.

b$.)$ Determine the fully plastic load Pfp

c$.)$ Determine the state of residual stress after load $p_{fp}$ is removed.

a$)P=\frac{\text{G}\text{y}\text{A}\text{L}}{b}$

b$)p_{fp}=2$AGy

c$.)(6a{)}_{\text{r}\text{e}\text{s}}=6y(1-\frac{2b}{L})$ answers the answers to $A,b$ and $C$

$(G_b{)}_{\text{r}\text{e}\text{s}}=O_y(\frac{2a}{L}-1)$

can someone show step by step how these questions were solved?