Theory and Problems of Strength of Materials Part 7

Tham khảo tài liệu 'theory and problems of strength of materials part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 176 CENTROIDS. MOMENTS OF INERTIA. PRODUCTS OF INERTIA CHAP. 7 . Determine the moment of inertia of a channel-type section about a horizontal axis through the centroid. Refer to Fig. 7-36. What is the radius of gyration about this same axis Ans. Xí. 231 in4 rX . in . Locate the centroid of the channel-type section shown in Fig. 7-37 and determine the moment of inertia of the cross-sectional area about a horizontal axis through the centroid. Ans. ỹ - mm t. 33 X IO6 mm4 50mm SOmm -J I 2Ữ0 mm -200 mm i H Fig. 7-37 . A plane area has the shape of a parallelogram as shown in Fig. 7-38. The y- and z-axes pass through the centroid of the area. Determine and . Ans. ly bh Iz hb b2 c2 . Determine the product of inertia of a triangle with respect to the X- and y-axes indicated in Fig. 7-39. Arts. b2Ắỉ724 . Determine the product of inertia of the triangle shown in Fig. 7-39 with respect to the axes xe and yG passing through the centroid. Ans. -tfti m. . For the plane area in Fig. 7-40 determine the moments of inertia and product of inertia with respect to the Xc- and waxes passing through the centroid. Also determine the principal second moments of area with respect to the centroid. Ans c 400 X 106 mm4 lff 147 X IO6 mm4 -58 X 10 mm4 C m - 805 X 106 mm4 4 U 142X10 mm4 Fig. 7-40 Chapter 8 Stresses in Beams TYPES OF LOADS ACTING ON BEAMS Either forces or couples that lie in a plane containing the longitudinal axis of the beam may act upon the member. The forces are understood to act perpendicular to the longitudinal axis and the plane containing the forces is assumed to be a plane of symmetry of the beam. EFFECTS OF LOADS The effects of these forces and couples acting on a beam are fl to impart deflections perpendicular to the longitudinal axis of the bar and b to set up both normal and shearing stresses on any cross section of the beam perpendicular to its axis. Beam deflections will be considered in Chaps. 9. 10 and 11. TYPES OF BENDING If .