(Solved): The beam shown in Figure 1 has a trapezoidal cross-section as shown, and is subject to a distribut ...

The beam shown in Figure 1 has a trapezoidal cross-section as shown, and is subject to a distributed loading of \( w=4 \mathrm{kN} / \mathrm{m} \). It is known the cross-section has a moment of inertia of \( 50,000 \mathrm{~cm}^{4} \), and the neutral axis is \( \bar{y}=11.9 \mathrm{~cm} \) from the bottom of the trapezoid. Determine: a. Draw the shear and bending moment diagram, with ALL critical information labeled (such as \( \mathrm{V} \) and \( M \) values, and line types). Also make sure to show all steps in detail, such as FBD(s), equations, and/or integral tables depending on the method you use. b. Determine the maximum tensile stress and the maximum compressive stress (separately) in the beam. Where are each of these points located (both along the beam and within the cross section)? Fig \( 1.1 \) A beam with loading Fig \( 1.2 \) The trapezoidal cross section