Consider a beam with a square cross section, $2^{\text{'}}$ by $2^{\text{'}},{16}^{\text{'}}$ long. The beam is simply

supported $($i$.$e$.$ pin joints at both ends$).$ This is the same size as the as the column in the

homework $1.$ There is a force of $9600$ lb at the center $($ignore the weight of the beam$).$

a$)(9$ points$)$ What is the moment $4^{\text{'}}$ from the left end of the beam?

b$)(4$ points$)$ What is the moment at the center of the beam?

c$)(9$ points$)$ Using the formula $=-M\frac{y}{\text{I}},$ where, $y$ is distance from the neutral axis, what

is the stress at the bottom of the beam in the center horizontally? At the top? For a beam

with rectangular cross section, the area moment of inertia I measures how a cross$-$section

inhibits stiffness in bending can expressed as $I=b\frac{h^3}{12},$ where $b$ is the base width and

$b$ is the height of the beam, as shown below.

d$)(3$ points$)$ How does this stress compare with the stress in the column? What does this

suggest about the stress caused by bending compared to compression?