A beam having a semi$-$circular open cross$-$section with constant thickness, $t,$ is subject to a horizontal shear force, $V_2.$

a$)$ Find the shear flow distribution, $f,$ as a function of $.$ Sketch the shear flow within the cross$-$section. Use the format shown in the figure on slide $29$ of the chapter $4$ lecture notes.

b$)$ Find the location and magnitude of the maximum shear flow.

c$)$ If the shear flow due to a vertical shear force, $V_3,$ is $f=2cos()\frac{V_3}{R},$ Find the location of the shear center.

Note that $s=R,ds=Rd,$ and $dA=dsdt$