$1-$ Calculate the mid$-$span load that induces strain values as shown in the Table below. The

strain gage locations are shown on the next page. All strain gages are parallel to the $hz$ axis

of the beam $($they read ${}_x).$ At some locations, rosette strain gages are used as indicated in

the figure and are labeled as $xxx(0,45,90).$

$2-$ Draw the shear force and bending moment diagrams for the beam under the load calculated

in Item #$1$

$3-$ Using the load in #$1,$ calculate the normal stress in $x$ and $y$ directions and $\{$:${}_y)$ and the

maximum shear stress ${}_{xy}$ at the sensor location assigned to you.

$4-$ Calculate the strain in y directions $({}_y)$ and the shear strain ${}_{xy}$ at the sensor location

assigned to you.

$5-$ Calculate the principal stresses and the angle of principal stresses at the sensor location

assigned to you.

$6-$ Calculate the maximum shear stress and the angle of maximum shear stress at the sensor

location assigned to you.

Assigned load

A simply supported beam with a length of $144in.$ and an effective span $($from support to support$)$

of $138$ in$.$ is loaded at its mid$-$span with a central load. The beam is a standard W$831$ with the

following section and material properties:

Area $=9\mathrm{.}13in.{?}^2$ Depth $=8in.,b_f=8in.,t_w=0\mathrm{.}285in.,t_f=0\mathrm{.}435i$ :

$I_x=110in.{?}^4,I_y=37\mathrm{.}1in.{?}^4,S_x=27\mathrm{.}5in.{?}^3,S_y=9\mathrm{.}27in.{?}^3$

$E=29,000$ksi,$v=0\mathrm{.}3$