KAKATIYA INSTITUTE OF TECHNOLOGY & SCIENCE::WA SCIENCE::WARANGAL RANGAL DEPARTMENT OF MECHANICAL ENGINEERING
II/IV B.Tech II – Semester Semester (2013-14) ME 224 MECHANICS OF SOLIDS – II II TUTORIAL SHEET 06 PART – I I 1.
a. Explain the following terms in connection with design of machine members subjected to variable loads: (a) Endurance limit, (b) Size factor, (c) Surface finish factor, and (d ) Notch sensitivity. b. What is meant by endurance strength of a material? How do the size and surface condition of a component and type of load affect such strength? c. Write a note on the influence of various factors of the endurance limit of a ductile material. d. What is meant by `stress concentration'? How do you take it into consideration in case of a component subjected to dynamic loading? e. Illustrate how the stress concentration in a component can be reduced. f. Explain how the factor of safety is determined under steady and varying loading by different methods. g. Write Soderberg's equation and state its application to different type of loadings. h. What information do you obtain from Soderberg diagram? PART – II II 2. Determine the design stress for bolts in a cylinder cover where the load is fluctuating due to gas pressure. The maxim maximum um load on the bolt is 50 kN and the minimum is 30 kN. The load is unpredictable and factor of safety is 3. The surface of the bolt is hot rolled and the surface finish factor is 0.9. During a simple tension test and rotating beam test on ductile materials (40 C 8 steel annealed), the following results were obtained: Diameter of specimen = 12.5 mm; Yield strength = 240 MPa; Ultimate strength = 450 MPa; [Ans. 65.4 MPa] Endurance limit = 180 MPa. 3. Determine the diameter of a tensile member of a circular cross-section. The following data is given: Maximum tensile load = 10 kN; Maximum compressive load = 5 kN; Ultimate tensile strength = 600 MPa; Yield point = 380 MPa; Endurance limit = 290 MPa; Factor of safety = 4; Stress concentration factor = 2.2 [Ans. 24 mm] 4. Determine the size of a piston rod subjected to a total load of having cyclic fluctuations from 15 kN in compression to 25 kN in tension. The endurance limit is 360 MPa and yield strength is 400 MPa. Take impact factor = 1.25, factor of safety = 1.5, surface finish factor = 0.88 and stress concentration factor [Ans. 35.3 mm] = 2.25. 5. A steel connecting rod is subjected to a completely reversed axial load of 160 kN. Suggest the suitable diameter of the rod using a factor of safety 2. The ultimate tensile strength of the material is 1100 MPa, and yield strength 930 MPa. Neglect column action and the effect of stress concentration. [Ans. 30.4 mm] 6. Find the diameter of a shaft made of 37 Mn 2 steel having the ultimate tensile strength as 600 MPa and yield stress as 440 MPa. The shaft is subjected to completely reversed axial load of 200 kN. Neglect stress concentration factor and assume surface finish factor as 0.8. The factor of safety may be taken as [Ans. 51.7 mm] 1.5. 7. Find the diameter of a shaft to transmit twisting moments varying from 800 N-m to 1600 N-m. The ultimate tensile strength for the material is 600 MPa and yield stress is 450 MPa. Assume the stress [Ans. 27.7 mm] concentration factor = 1.2, surface finish factor = 0.8 and size factor = 0.85.
8. A simply supported shaft between bearings carries a steady load of 10 kN at the centre. The length of shaft between bearings is 450 mm. Neglecting the effect of stress concentration, find the minimum diameter of shaft. Given that Endurance limit = 600 MPa; surface finish factor = 0.87; size factor = 0.85; and factor of safety = 1.6. [Ans. 35 mm] 9. Determine the diameter of a circular rod made of ductile material with a fatigue strength (complete stress reversal) σ e = 280 MPa and a tensile yield strength of 350 MPa. The member is subjected to a [Ans. 80 mm] varying axial load from 700 kN to – 300 kN. Assume Kt = 1.8 and F.S. = 2. 10. A cold drawn steel rod of circular cross-section is subjected to a variable bending moment of 565 Nm to 1130 N-m as the axial load varies from 4500 N to 13 500 N. The maximum bending moment occurs at the same instant that the axial load is maximum. Determine the required diameter of the rod for a factor of safety 2. Neglect any stress concentration and column effect. Assume the following values: Ultimate strength = 550 MPa Yield strength = 470 MPa Size factor = 0.85 Surface finish factor = 0.89 Correction factors = 1.0 for bending= 0.7 for axial load The endurance limit in reversed bending may be taken as one-half the ultimate strength. [Ans. 41 mm] 11. A steel cantilever beam, as shown in Fig. 11, is subjected to a transverse load at its end that varies from 45 N up to 135 N down as the axial load varies from 110 N (compression) to 450 N (tension). Determine the required diameter at the change of section for infinite life using a factor of safety of 2. The strength properties are as follows: Ultimate strength = 550 MPa Yield strength = 470 MPa Endurance limit = 275 MPa
Fig. 11 The stress concentration factors for bending and axial loads are 1.44 and 1.63 respectively, at the change of cross-section. Take size factor = 0.85 and surface finish factor = 0.9. [Ans. 12.5 mm] 12. A steel shaft is subjected to completely reversed bending moment of 800 N-m and a cyclic twisting moment of 500 N-m which varies over a range of ± 40%. Determine the diameter of shaft if a reduction factor of 1.2 is applied to the variable component of bending stress and shearing stress. Assume (a) that the maximum bending and shearing stresses are in phase; (b) that the tensile yield point is the limiting stress for steady state component; (c) that the maximum shear strength theory can be applied; and (d ) that the Goodman relation is valid. Take the following material properties: [Ans. Yield strength = 500 MPa; Ultimate strength = 800 MPa; Endurance limit = ± 400 MPa 40 mm] 13. A pulley is keyed to a shaft midway between two anti-friction bearings. The bending moment at the pulley varies from – 170 N-m to 510 N-m and the torsional moment in the shaft varies from 55 N-m to 165 N-m. The frequency of the variation of the loads is the same as the shaft speed. The shaft is made of cold drawn steel having an ultimate strength of 540 MPa and a yield strength of 400 MPa. Determine the required diameter for an indefinite life. The stress concentration factor for the keyway in bending and torsion may be taken as 1.6 and 1.3 respectively. The factor of safety is 1.5. Take size factor = 0.85 and surface finish factor = 0.88. [Ans. 36.5 mm] [Hint. Assume σe = 0.5 σu; τ y = 0.5 σ y; τe = 0.55 σe]
