1 Determine by direct integration the centroid of the area shown. Express your answer in terms of a and b. y=k(x-a)² K Fig. P5.40

22. Moments of inertia The coordinate axes in the figure run through the centroid of a solid wedge parallel to the labeled edges. Find I, Iy, and I, if a = b = 6 and c = 4. Centroid at (0, 0, 0) 3

Problem 3: Locate the centroid x of the area. y = -b-

The horizontal x-axis is drawn through the centroid C of the area shown, and it divides the area into two component areas A1 and A2. Determine the first moment of each component area with respect to the x-axis if a = 0.36 in. and b = 1.08 in.  The first moment of the area above the x-axis is The first moment of the area below the x-axis is

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Using the conjugate beam method

A PFC Channell and a universal beam (UB) Section4 (See Table 1) are welded together to form the composite section as shown in Figure (a). The individual sectional properties are given in Figure (b) and (c) where x, and y, indicate centroidal axes. I. Figure (a) (dimension not to scale) -X- y. Figure (b) UB Section Figure (c) PFC Table 1. Sectional properties UB Section b mm 229 Section mm? 16000 mm 19.6 17.3 mm 11.9 11.2 (10 mm) 986 (x10 mm) 39.3 mm 610UB125 612 610UB113 14500 607 228 875 34.3 13000 610UB101 530UB92.4 602 228 14.8 10.6 761 29.3 4. 11800 533 209 15.6 10.2 554 23.8 530UB82 10500 528 209 13.2 9.6 477 20.1 PFC Channel b mm 100 Channel (x10 mm) 6.48 mm mm 380 mm 17.5 mm 10 (x10 mm) 152 1 380PFC 27.5 7030 300PFC 27.2 5110 300 90 16 72.4 4.04 250PFC 28.6 4520 250 90 15 45.1 3.64

X *16-36. At the instant shown, the shaft and plate rotates with an angular velocity of w = 14 rad/s and angular acceleration of a = 7 rad/s². Determine the velocity and acceleration of point D located on the corner of the plate at this instant. Express the result in Cartesian vector form. X D 0.4 m B Z. 0 0.4 m α 3 A 0.6 m 0.2 m) C 0.3 C-(-0.3 m 0.3 m -y

A/23 The plane figure is symmetrical with respect to the 45° line and has an area of 1600 mm². Its polar mo- ment of inertia about its centroid C is 40(104) mm. Compute (a) the polar radius of gyration about O and (b) the radius of gyration about the x-axis. Ans. (a) ko = 45.3 mm, (b) kxo = 11.18 mm 0 30 mm yo 45° CL 30 mm Problem A/23 X

Determine the centroids and the second moment of the area for the figures shown below abouttheir centroidal axes.