Tham khảo tài liệu 'theory and problems of strength of materials part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 206 STRESSES IN BEAMS CHAP. 8 Fig. 8-50 From the result of Problem 8-24 for the geometry indicated in Hg. 8-50 we have M Ihyì 2 rvb c - y I i w z For the limiting case when y 0 which is indicated by Fig. 8-49 c of Problem the fully plastic moment of this rectangular beam is bc2avp -Ị-ƠVP Ơ It ts to be noted that the maximum possible elastic moment . when the extreme fibers have just reached the yield point but all interior fibers are in the elastic range of action as indicated by Fig. 8-49 a is bfr _ 6 M 2 Thus for a rectangular cross section the fully plastic moment is 50 percent greater than the maximum possible elastic moment. . Determine the fully plastic moment of a rectangular beam 1 X 2 in in cross section of steel with a yield point of 38 000 lb in2. Compare this with the maximum possible elastic moment that this same section may carry. From of Problem the fully plastic moment is Mr 38 000 38 000 lb in From 2 of that same problem the maximum possible elastic moment is 1 2 2 Mr 38 000 25 400 lb in 6 It is evident that Mp is 50 percent greater than Me. . For a beam of rectangular cross section Fig. 8-51 determine the relation between the bending moment and the radius of curvature when all fibers at a distance y from the neutral axis have reached the yield point of the material. As in Problem we assume that plane sections before loading remain plane and normal to the beam axis after loading. Because of this normal strains of the longitudinal fibers vary linearly as the CHAR 8Ị STRESSES IN BEAMS 207 rt_i Ị T- Vi c Ì Fig. 8-51 distance of the fibers from the neutral axis. Thus if ew denotes the strain of the fibers at a distance y from the neutral axis and er represents the outer fiber strain we have s c yi Consideration of the geometry of an originally rectangular element of length dx along the beam axis as shown in Fig. 8-52 reveals that after bending it assumes the configuration indicated in Fig. 8-52 b . From that sketch .
