Objective

The objective of this assignment is to design a Wide Flange $($W$)$ beam to support external loading, as illustrated below. To leave a favorable impression on your supervisor, you must perform a comprehensive beam design by selecting the most effective W beam. Additionally, you must write a technical report that thoroughly justifies your selection and demonstrates your analysis techniques.

Design Assumptions

Assume the flange and web shapes with dimensions of as listed in the AISC shapes database version $15\mathrm{.}0($See an excel in project folder on Canvas$).$ Material must be A$36$ Steel $($yielding strength $=36$ksi $).$

Factor of Safety for the structure must be $2\mathrm{.}0$ with respect to yielding in tension or compression and $2\mathrm{.}5$ with respect to yielding in shear.

Assume the material strength in tension equal to its strength in compression.

Approach and Tasks:

Your integrated approach should include the following tasks:

$(1)$ Draw clear and accurate shear and moment diagram of the beam with maximum values labeled and non$-$linear curves identified;

$(2)$ Determine W beam that satisfies both normal stress and shear stress requirement;

$1$

$(3)$ Determine the principal stresses at the web$/$flange junction in the middle of span using Mohr's Circle.

$(4)$ Determine the critical locations on the beam where the shear and moment could possibly combine to exceed the all owable stresses. Discuss your results.