Composite beam

Question $4$

The low$-$strength concrete floor slab is integrated with a wide$-$flange steel beam using shear

studs $($not shown$)$ to form the composite beam. If the allowable bending stress for the

concrete is $({}_{\text{c}\text{o}\text{n}\text{c}}{)}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=20$MPa, and the allowable bending stress for steel is $({}_{st}{)}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=165$

MPa $.$ Take $E_{st}=200$GPa,$E_{\text{c}\text{o}\text{n}\text{c}}=25$GPa. Solve the problems below:

$($a$)$ Determine the height of horizontal neutral axis.

$($b$)$ Determine the moments of inertia about horizontal neutral axis.

$($c$)$ Determine the maximum allowable internal moment $M$ that can be applied to the beam.