Strength of Materials

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ...is the intensity of bending stress as calculated from the bending moments for purely transverse loading in Art. 63, and is of the same sign as /" in part of the section and of opposite sign in another part. The stress intensity / will change sign somewhere in the section if the extreme values of /, are of greater magnitude than /," but the stress will not be zero at the centroid of the section as in the case of a beam bent only by transverse forces. The effect of the additional direct stress /o is to change the position of the neutral surface or to remove it entirely. 98. Eccentric Longitudinal Loads.--If the line of action of the direct load on a prismatic bar is parallel to the axis of the bar, and intersects an axis of symmetry of the cross-section at a distance // from the centroid of the section, bending takes place in the plane of the axis of the bar and the line of action of the eccentric load. Thus, Fig. i4r represents the cross-section of a bar, the load P passing through the point C, and O is the centroid of the section. Let A be the area of cross-section, and y, distance OD from the centroid 0 to the extreme edge D in the direction OC, and let I be the moment of inertia of the area of section about the central axis FG perpendicular to OC. Then, .. P in addition to the direct tension or compression. or /," there is a bending moment M = P. h on the section, the intensity of stress at any point distant y from FG being--P = A + A = A +-i (Art. 63) or since I = AJP, where k is the radius of gyration about FG--= A+A?=I(I+/"/) ('+?) W;-being positive for points on the same side of FG as C, and negative on the opposite side. The intensity varies uniformly with the dimension y, as shown in Figs. 141, 142. The...