Assume that both figures represent the cross-sections of two different steel beams, each with the same constant laminar density of 60 lb/ft2 : (Place the origin of the xy-coordinate system at the exact center of both figures, and take advantage of the symmetry of both figures, i.e., focus on quadrant I). 1). Verify that the area of both figures is the same. 2). Calculate the polar inertia I0 (stiffness) for the square beam in Figure 1. 3). Calculate the polar inertia I0 (stiffness) for the I-beam in Figure 2. 4). Find the ratio of the stiffness of Figure 2 to that of Figure 1.

LAB 7 (cont'd) Figure 1 Figure 2 11/2 ft 1/4 ft 1 ft 1 ft Assume that both figures represent the cross-sections of two different steel beams, each with the same constant laminar density of 60 Ib/ft": (Place the origin of the xy-coordinate system at the exact center of both figures, and take advantage of the symmetry of both figures, i.e., focus on quadrant D. 1). Verify that the area of both figures is the same Recall, polar inertia of a lamina: 2). Calculate the polar inertia lo (stiffness) for the square beam in Figure 1. 3). Calculate the polar inertia o (stiffness) for the I-beam in Figure 2. . = ] ( x + y) (x,y) dxdy 4). Find the ratio of the stiffness of Figure 2 to that of Figure 1