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Theory and Problems of Strength of Materials Part 5

Tham khảo tài liệu 'theory and problems of strength of materials part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 116 TORSION CHAP. 5 5.20. A stepped shaft has the appearance shown in Fig. 5-28. The region AB is AI2014-T6 alloy having G - 28 GPa and the region BC is steel having G 84 GPa. The aluminum portion is of solid circular cross section 45 mm in diameter and the steel region is circular of 60-mm outside diameter and 30-mm inside diameter. Determine the peak shearing stress in each material as well as the angle of twist at B where a torsional load of 4ÍXX N m is applied. Ends A and c are rigidly clamped. Fig. 5-2 Fig. 5-29 The free-body diagram of the system is shown in Fig. 5-29. The applied load of 4000 N m as well as the unknown end reactive torques are indicated by the double-headed vectors above. There is only one equation of static equilibrium Tl 7W - 4000 N m 0 Since there are two unknowns TL and Tft. another equation based upon deformations is required. This is set up by realizing that the angular rotation al B is the same if we determine it at the right end of AB or the left end of BC. Using Eq. 5.4 . we thus have 77 1.2 m 7 2.Om 28 X 10 N nr JA 84 X lO N nrVsr The polar moment of inertia in AB is 77 0.045 m 4 Al 0.40 X 10 m and in BC it is At 0.060 m 4- 0.030 m 4 1.19 X lo m4 nius from the above Eq. 7 . we have Tl 0.1877 2 Substituting this relation in Eq. . we find 7i-630Nm and 7 3370N-m CHAP. 5 TORSION 117 The outer fiber shearing stresses in AB are given by _ Tp 630 N m 0.0225 m _ _ . 7 35.2 MPa J 0.40 X 10 m and in BC by _ Tp 3370 N m 0.030 m c Tbc . . Ấ J 5.0 Ml 3 J 1.19xl0 6m4 The angle of twist at B. using parameters of the region AB is 9 - H GJ . . - 0.675 X10 or MB r 28 X 10 N m2 0.40 X 10 m4 5.21. Consider a bar of solid circular cross section subject to torsion. T he material is considered to be elastic-perfectly plastic i.e. the shear stress-strain diagram has the appearance indicated in Fig. 5-30 ơ . Determine the distance from the center at which plastic flow begins in terms of the twisting moment. Also determine the twisting moment for fully .