Problem $2$

Consider a $30$ ft $.,$ simply supported W$21$x$44,$ A$992$ steel, with metal deck perpendicular to the axis of the beam

and a uniformly distributed load. Adjacent beams are spaced at $10$ ft $.$ to either side. Assume $3"$ of NW concrete

above the ribs, $f_c^{\text{'}}=4$ksi.

a$)$ Calculate positive flexural design strength, $M_n,$ assuming fully composite, using AISC Table $3-18.$

b$)$ Suppose that one $\frac{3}{4}"$ shear stud is placed in each rib along the length. Calculate the partially composite design

strength, $M_n,$ using Table $3-18$ and $3-20.$ Assume that all studs are in the 'weak' position.

c$)$ Determine $I_{LB}$ for the beam with shear studs as specified in $($b$),$ using Table $3-19.$