It is required to do the following task:

The physical model consists of a determinate simply$-$supported steel beam W$24$X$103.$ Assume a modulus of elasticity for the beam equal to $29,000$ksi.

Find the cross$-$sectional area, the moment of inertia with respect to the strong axis, and the section modulus for the W$24$X$103.$

Calculate the reactions forces using the equilibrium equations. Present in a clear format the Free$-$Body Diagram. Present each step in a clear format and by hand calculation. The assigned load for each student are shown in Tablel.

Determine the equations of internal shear and internal bending moment for the beam.

Plot the internal shear force and internal bending moment diagram.

Determine the equations for the deflection and rotation using the differential equation of the elastic curve.

Plot the deflection and rotation as function of $x($using Excel$).$

Calculate the maximum deflection, maximum rotation and the location where they occurred along the beam.

Calculate, for the W$24$X$103,$ the maximum normal stress in tension and compression. Identify the location along the beam where these maximum bending stresses occur.

Calculate, for the W$24$X$103,$ the maximum shear stress. Identify the location along the beam where the maximum shear stress occurs. Since the W$24$X$103$ is a standard section, use the web area to calculate the shear stress

Determine if the cross$-$section profile provided is acceptable by satisfying the following conditions: ${}_{\text{m}\text{a}\text{x}}=1\mathrm{.}5$ inches, ${}_{\text{w}\text{e}\text{l}\text{d}}=50$ksi,${}_{\text{y}\text{i}\text{e}\text{k}\text{l}}=18$ksi and a factor of safety against yielding of $1\mathrm{.}5$ for both cases.

P$1=30$kip ; P$2=5$kip ; P$3=4$kip : w$=0\mathrm{.}4$kip$/$ft