ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING QUESTION BANK FOR THE MECHANICS OF MATERIALS-I 1. A rod 150 cm long and of diameter 2.0 cm is subjected to an axial pull of 20 kn. If the modulus of elasticity of the material of the rod is 2 x 10 5 N/mm 2 ; determine: a. The stress, b. The strain, and. c. The elongation of the rod. 2. Derive the expression for the normal and tangential stresses on any oblique plane in a bar subjected to tensile loading in the axial direction. 3. Discuss detail about the Elastic Deformation of an Axially Loaded Member. 4. With a neat diagram Discuss detail about the Mohr s Circle. 5. Discuss the type of shear stresses in an I-section and derive expression for the same. 6. Derive the expression for deflection, shear stress and strain energy for close coiled helical spring when it is subjected to axial load W. 7. Find the young's module=us of a brass rod of diameter 25mm and of length 250 mm which is subjected to a tensile load of 50kN when the extension of the rod is equal to 0.3 mm. 8. A tensile test was conducted on a mild steel bar. the following data was obtained from the test: Diameter of the steel = 3cm Gauge length of the bar = 20cm Load at elastic limit = 250kN Extension at a load of 150kN =0.21mm Maximum load = 380kN Total extension = 60mm Diameter of the rod at the failure =2.25cm Determine: (a) The young s modulus, (b) The stress at elastic limit, (c) The percentage elongation, and (d) the percentage decrease in area 9. The unlimited stress for, a hollow steel column which carried an axial load of 1.9 MN is 480 N/mm 2. If the external diameter of the column is 200 mm, diameter the internal diameter. Take the factor of safety as 4. 10. Determine the changes in length, breadth and thickness of a steel bar which is 4 m long, 30mm wide and 20mm Thich is subjected to an animalcule 30kNin the direction of its length=. Take E = 2 x10 2 n/mm 2 and poisons ratio = 0.3
11. Determine the value of young us modulus and poison ratio of a metallic bar of length 30 cm breadth b 4 cm and depth 4 cm when the bar is subjected to an axial compressive load of 400kN. The decrease in length is given as 0.075 cm and increase in breadth is 0.003 cm. 12. A bar of 30 mm diameter is subjected to a pull of 60 kn. The measured extension on gauge length of 200 mm is 0.09 mm and the change in diameter is 0.0039 mm. calculate the Poisson s ratio and the values of the three moduli. 13. A steel bar 300mm long, 50mm wide and n40mm thick is subjected to a pull of 300kN in the direction of its length. Determine the change in volume. Take E= 2 x 10 5. 14. A rectangular bar of cross-sectional area 10000 mm 2 is subjected to an axial load of 20 kn. Determine the normal and shear stresses on a section which is inclined at an angle of 30º with normal cross-section of the bar. 15. The stresses at a point in a bar are 200 N/mm 2 (tensile) and 100 N/mm 2 (compressive). Determine the resultant stress. Also determine the maximum intensity of shear stress in the material at the point. 16. A uniform metal bar has a cross-sectional area of 700 mm2 and a length of 1.5 m. If the stress at the elastic limit is 160 N/mm 2, what will be its proof resilience? Determine also, the maximum value of an applied load, which may be suddenly applied without exceeding the elastic limit. Calculate the value of the gradually applied load which will produce the same extension as that produced by the suddenly applied load above. Take E = 2 x 10 5 N/mm 2. 17. Find the Centre of gravity of the I-section shown in Fig. (a) and (b). 18. Find the centre of gravity of the L-section shown in Fig.
19. A cantilever beam of length 2 m carries the point loads as shown in Fig. 6.15. Draw the shear force and B.M. diagrams for the cantilever beam. 20. The safe stress, for hollow steel column which carries an axial load of 2.1 x 10 3 k is 125 MN/m 2. If the external diameter of the column is 30cm, determine the internal diameter. 21. Find the diameter of a circular bar which is subjected to an axial pull of 160 kn, if maximum allowable shear stress on any section is 65 N/ mm 2. 22. Two wooden pieces 10 cm x 10 cm in cross-section are glued together along line AB as shown in Fig. below. What maximum axial force P can be applied if the allowable shearing stress along AB is 1.2 N/mm 2. 23. At a point in a strained material the principal stresses are 100 N/mm 2 (tensile) and 60 N/mm 2 (compressive). Determine the normal stress, shear stress and resultant stress on plane inclined at 50º to the axis of major principal stress. Also determine the maximum shear stress at the point. 24. Write down relations for maximum shear force and bending moment in case of a cantilever beam subjected to uniformly distributed load running over entire span. 25. Draw the Mohr s Circle of the stress element shown below. Determine the principle stresses and the maximum shear stresses. 26. Given the same stress element (shown below), find the stress components when it is inclined at 30 clockwise. Draw the corresponding stress elements.
27. A cast iron column has internal diameter of 200mm.What should be the minimum external diameter so that it may carry a load of 1.6MN and safe stress is 90N/mm 2. 28. A mild steel rod of 20mm diameter and 300mm long is enclosed centrally inside a hollow copper tube of external diameter 30mm and internal diameter 25mm. The ends of the rod and tube are brazed together and the composite bar is subjected to an axial pull of 50KN. If E for steel and copper are 200GPa and 100GPa respectively. Find the stresses developed in rod and tube. 29. A rod of 3 m long is initially at a temperature of 15 C and it is raised to 90 C. Find the expansion of the rod and if the expansion is prevented, finds the stress in the material. 30. Determine the change in length, breadth and thickness of a steel bar which is 5 m long, 20 mm wide and 15mm thick subjected to an axial pull of 100 KN. In the direction of its length. Take E=200Gpa and Poisson ratio =0.3. 31. Using the analytical method, determine the Centre of gravity of the plane uniform lamina shown in Fig. 32. Draw and describe the graphical method for solving the principal stress problems for various cases. 33. Explain the detailed procedure for drawing the Mohr s circle for the following cases. a) A material subjected to two normal tensile stresses acting perpendicular to each other. b) A material subjected to two normal tensile stresses and a complementary shear stress. 34. What is the use of Mohr s circle? Explain it 35. What types of stresses are caused in a beam subjected to a constant shear forces? 36. Give the angle between the principal planes. 37. What are the planes along which the greatest shear stresses occur? 38. Define strain energy and write its unit. 39. Define the modulus of rigidity and poisson s ratio.
40. What is the strain energy stored when a bar of 6mm diameter 1m length is subjected to an axial load of 4kN, E=200kN/mm 2. 41. Estimate the load carried by a bar if the axial stress 10N/mm 2 and the diameter of bar is 10mm. 42. Explain the effect of change of temperature in a composite bar. 43. Sketch the bending moment diagram of a cantilever beam subjected to UDL over the entire span. 44. In an experiment a bar of 25mm diameter is subjected to a pull of 70kN. The measured extension on gauge length of 200mm is 0.09 mm and the change in diameter is 0.0040mm. Calculate the poisson s ratio and the values of three moduli. 45. The young s modulus and the shear modulus of material are 120GPa and GPa respectively. What is its Bulk modulus? 46. Define point of contra flexure. 47. Define proof resilience and modulus of resilience. 48. What is Thermal Stress? 49. Mention the different types of beams. 50. Define bulk modulus.