Assignment #$1($Due: October $2,2024,$ at $5$:$00$pm$)$: The residual stress distribution $($i$.$e$.,$ diagram$)$ of a

rectangular steel plate is shown below. The plate is subjected to a compressive load. Assuming A$572$ steel

$($Grade $50),E=30,000$ksi, and that the member is restrained from

local or global buckling, provide the following:

Before the compressive load is applied, what is the net axial

load on the section? Demonstrate your answer with

calculations.

Draw the stress diagram at $($a$)$ first yield and $($b$)$ second yield

and annotate the stress values at points $1,2,$ and $3.$

Use a computer program to plot the stress$-$strain diagram,

including the effects of residual stress $($assume quadratic

relationship$),$ and indicate the average stress and strain values

at the following points and regions:

a$)$ Proportional limit

b$)$ First yield

c$)$ Second yield

d$)$ Full yield

Submission Instructions: The assignment must be uploaded to Canvas by the stated deadline. Two files

must be uploaded: $(1)$ A PDF file containing the answers to the questions listed above and the rationale,

procedures, and$/$or formulas used to arrive at the answer, and $(2)$ the Excel spreadsheet, Matlab, or Python

file used to develop the plot.