Problem 7: Figure (a) shows the cross section of a column that uses a structural shape known as W8 x 67 (wide-flange beam, nominally 8 in. deep, weighing 67 Ib/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following cross-sectional properties: A=19.7 in^2, Ix =272 in^4, and ly =88.6 in^4. Figure (b) shows the cross- sectional dimensions for the structural steel section known as C10 x 20 (channel with a nominal depth of 10 in., weighing 20 Ib/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following properties for the cross section: A=5.88 in^2, Ix =78.9 in^4, and ly =2.81 in^4. If a W8 x 67 section is joined to a C10 x 20 section to form a structural member that has the cross section shown in Figure (c), the moment of inertia with respect to the centroidal y-axis of the built-up section is

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