PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM - 613 403 - THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310 UNIT - I 1. Define Strength. 2. Define Ductility. 3. Define Brittleness. 4. Define Hardness. 5. Define Weldability. 6. Define Fatigue. 7. Define Creep. 8. Define Cyclic loading. 9. Define Elastic limit. 10. Define Factor of safety and load factor. 11. Define Lateral strain. PART - A 12. Write an expression to find volumetric strain of rectangular bar. 13. Write an expression for the relationship between young s modulus and shear modulus. 14. Write an expression for the relationship between the E,N and K. 15. Name the three elastic constants. 16. What are the conditions to be applied for bars of composite section?. 17. Define Strain energy. 18. Define Proof resilience. 19. Define Modulus of resilience. 20. State Hooke s law.
PART - B 1. a) A cement concrete cube of 150mm size crushes at a load of 337.5KN.Determine the working stress, if factor of safety is 3. b) The rod of hydraulic lift is 1.2m long and 32mm in diameter. It is attached to plunger of 100 mm in diameter under a pressure of 8N/mm 2. If E =2 x 10 5 N/mm 2 find change in length of rod. 2. The following data s were recorded during the tensile test on mild steel specimen. Diameter of specimen= 25mm.Length of the specimen = 30mm, Extension under the load of 15KN is 0.045mm, Load at yield point = 127.65KN, Maximum load = 208.6KN, Neck diameter = 17.75mm, Length of specimen after failure is 375mm. Determine a) Young s modulus b) Yield stress c) Ultimate stress d)% of elongation e) % reduction in area. 3. A steel bar 500mm long, 50mm wide and 12mm thick is subjected to an axial pull of 100Kn. Determine changes in length width, thickness and volume of the bar. Assume E=200 KN/mm 2 and 1/m = 0.3. 4. For given material young s modulus is 1x10 5 N/mm 2 and modulus of rigidity is 0.4 x 10 5 N/mm 2. Find the bulk modulus and the lateral contraction of round bar 50mm diameter and 2.5m long when stretches by 2.5mm. 5. A bar of length 150mm is circular in section and is of uniform diameter of 50mm. It is subjected to an axial pull of 400 KN and the extension in length and contraction in diameter were found to be 0.25mm and 0.02mm respectively. Determine the poisson s ratio and values of elastic constants. 6. A steel bar 2m long, 20 mm wide and 10 mm thick is subjected to an axial pull of 20KN in the direction of its length. Determine the changes in the dimensions and volume. Take E = 2x10 5 N/mm 2,1/m = 0.3. 7. A bar of steel 28mm diameter and 250 mm long is subjected to an axial load of 80 KN. It is found that the diameter has contracted by 0.0042mm. If the modulus of rigidity is 0.8 x 10 5 N/mm 2. Calculate (i) Poisson s ratio (ii) E (iii) K. 8. A steel rod of 30mm diameter is enclosed centrally in a hollow copper tube of external diameter of 50mm and internal diameter of 40mm. The composite bar is then subjected to an axial load of 45KN. If the length of each bar is equal to 150 mm. Determine (i) the stresses in rod and tube; ii) Load carried by each material. Take Es=2 x 10 5 N/mm 2, E c =1 x 10 5 N/mm 2 9. A wagon weighing 40KN is attached to a wire rope and is moving on an inclined plane at a speed of 3.6 km/hr and the wagon is suddenly brought to rest. If the length of the rope is 50 m 50 m at the time of sudden stoppage, calculate the maximum instantaneous stress and elongation produced. Diameter of the rope is 36mm and E=2x 10 5 N/mm 2. 10. A wagon weighing 60Kn is attached to a wire rope. A wagon traveling down a slope at a speed of 4m/sec. If it is suddenly stopped by pulling a rope what is maximum instantaneous stress induce in the rope due to stopping. Assume length of rope is 160mand diameter of rope is 50mm.E=1x 10 5 N/mm 2. Also find tension in rope.
1. Define centroid. UNIT - II PART - A 2. Write down the expression for moment of inertia of a rectangular section about its base. 3. Write down the expression for moment of inertia of a triangular section about its base. 4. Write the formula to determine radius of gyration. 5. Name a few geometrical properties of sections. 6. Define moment of inertia. 7. Define radius of gyration. 8. Define axis of symmetry. 9. State parallel axis theorem. 10. What is the difference between centroid and centre of gravity? 11. Write an expression for moment of inertia of circular section about centroidal axis. 12. State few examples of thin cylinder. 13. What are the three stresses in a thin cylinder when subjected to internal pressure? 14. When is a shell called thin? 15. Name few materials on which thin shells are made of. 16. What are the ways by which a thin cylindrical shell may fail? 17. Define hoop stress. 18. State the formula for finding the change in vol of a spherical shell of dia d, thick t and internal pr p. 19. Write the formula for hoop strain in thin cylinder. 20. What is the relation between volumetric strain and circumferential strain in thin spherical shell. PART - B 1. a). Find the centroid of an inverted T - section with flange 150mm x 20mm and web 100mm x 25mm. b). Find the centroid of unequal angle section 100x 80 x 20mm. 2. Determine the moment of inertia of a hollow rectangular section about x- x and y-y axes. Outer dimension of hollow rectangle being 450 x 300 mm and inner dimensions being 400 x 250 mm calculate also the section modulus and radius of gyration about two axes. 3. A channel section is of size 300 mm x 100mm overall. The bases as well as the flanges of the channel are 10mm thick calculate I xx and I yy.
4. An angle section is of 100mm wide and 120 mm deep overall, both the flanges of the angel are 10mm thick. Determine the position of centre of gravity and also calculate I xx and I yy. 5. A T section is in size 80mm x 130 mm x 10mm with the 80 mm side horizontal. Find the value of moment of inertia about the centroidal horizontal axis. 6. a) A boiler 3m internal diameter is subjected to a steam pressure of 5 bar. Find the hoop and longitudinal stresses, if the thickness of the boiler plate is 14mm. b) A boiler shell is 1.8 m in diameter and 15mm in thickness. The permissible tensile stress in the boiler plate is not to exceed 70N/mm 2. Determine the allowable working pressure of the boiler. 7. A long steel tube of 70mm internal diameter and wall thickness 2.5mm has a closed end and is subjected to an internal pressure of 10MN/m 2. Calculate the value of longitudinal stress and hoop stress set up in the tube. If efficiency of the longitudinal joint is 80% which stress is affected and what is its revised value. 8. Calculate the increase in volume of a boiler shell 3m long and 1.5m diameter, when subjected to an internal pressure of 2 N/mm 2. The thickness is such that the maximum tensile stress is not to exceed 30 N/mm 2. Take E= 2.1 x10 5 N/mm 2 and 1/m = 0.28. Also calculate the change in diameter and length. 9. A cylindrical shell 3m long, 500mm in diameter is made up of 20mm thick plate, if the cylinder is subjected to an internal pressure of 5N/mm 2,find the value of resulting hoop stress, longitudinal stress, change in diameter, change in length and change in volume. Take Poisson s ratio as 0.3 and E = 2x 10 5 N/mm 2. 10. A long steel tube 70mm internal dia and wall thickness 2.5mm, has closed ends and is subjected to an internal pressure of 10N/mm 2. Calculate the magnitude of hoop and longitudinal stress. If the efficiency of the longitudinal joint is 80% state the stress which is affected and what is its revised value.
1. What are types of loads acting on a beam? UNIT - III PART - A 2. What is the difference between udl and uniformly varying load. 3. Define the point of contra flexure. 4. Define shear force. 5. Define Bending moment. 6. Define hogging BM. 7. Define sagging BM. 8. What is a cantilever beam? 9. Write the relationship between load, SF and BM 10. List any four type of beam. 11. What is SFD? 12. What is BMD? 13. Define Slope. 14. Define Deflection. 15. Define Strength of beam. 16. Define Stiffness of beam. 17. Define Flexural rigidity of beam. 18. State relationship between, slope, deflection and radius of curvature. 19. What is radius of curvature? 20. What is meant by beam? PART - B 1.a).A cantilever 5m long carries an udl of 30KN/m over half of its length adjoining the free end. Draw the S.F.D and B.M.D b). A Cantilever of 4m length carries point loads of 40KN, 30KN and 20KN at 2m,3m and 4m respectively, from the fixed end. In addition to them, it carries an udl of 10KN/m over the entire length. Draw SFD and BMD 2.a). A Cantilever of 2m long carries point loads of 20KN at 0.8m from the fixed end and another point load of 5KN at the free end. In addition a udl of 15KN/m is spread over the entire length of the cantilever. Draw SFD and BMD. b). A cantilever 6m long carries concentrate load of 2KN,2KN and 3KN at distances of 2m,4m and 6m respectively from the fixed end. In addition there is a udl of 1.5 KN/m run spread over the entire length of the beam. Draw SFD and BMD.
3.A S.S.B 6m long is carrying a udl of 2 KN/m over a length of 3m from the right end. Draw SFD and BMD. Also find the position and magnitude of maximum B.M 4. A beam 8m long is simply supported at its ends. It carries a udl of 1KN/m over the length of the left half of its span together with concentrated loads of 2KN,3KN,2KN situated at 2m,4m and 6m respectively from the left hand support. Sketch the SFD and BMD. Also find the magnitude and position of maximum BM. 5. A beam is freely supported over a span of 8m. It carries a point load of 3KN at 2m from left hand support and a udl of 2KN/m from the centre upto the right hand support. Draw SFD and BMD. 6. A cantilever 1.8m long and 240mm deep 90mm wide in section carries a concentrated load of 15KN at its free end. Determine the maximum slop and deflection of the beam if E = 2x10 5 N/mm 2 7. A cantilever 2m long carries a point load of 9KN at the free end and udl of 8KN/m over entire length. Find slope and deflection at free end. If E = 200 KN/mm 2 I=25x10 6 mm 4. 8. A cantilever beam AB of 6m long is subjected to a udl of wkn/m over entire span. The depth of the beam is equal to twice the width. Determine the dimensions of the beam so that the maximum deflection dose not exceed 15mm. The maximum bending stress is 100N/mm 2. Take E=2x10 5 N/mm 2. 9. A simply supported beam of span 10m, carries a point load of magnitude 250KN, at the center. If the flexural if rigidity EI of the beam is 1x10 5 KN/m 2.Find the slope of the beam at support section and the defection of beam at midspan section. 10. A beam 3m long simply supported at its end is carrying a point load W at its center. If the slope at the ends of the beam is not to exceed 1 0. Find the deflection at the center of the beam.
1. Define Simple bending (pure bending). 2. Define neutral axis. 3. Define neutral layer. 4. Define section modulus. 5. Define moment of resistance. 6. Define strength of beam. 7. Define stiffness of beam. 8. What is meant by flexural rigidity? 9. Define Radius of curvature. 10. Define centre of curvature. 11. What is flexural strength of beam? UNIT - IV PART - A 12. Write the formula for section modulus for a hollow circular section. 13. Define Force of friction. 14. Define limiting friction. 15. Define Static friction. 16. Define Dynamic friction 17. Define Angle of friction. 18. Define Co-efficient of friction. 19. Define Cone of friction. 20. Indentify the factors on which the static friction depends. PART B 1.a) State the assumption made in the theory of simple bending b). Derive the flexural formula 2.A rectangular beam 300mm deep is simply supported over a span of 4m. What udl/m of the beam may carry, if the bending stress is not to exceed 120N/mm 2. Take I=8x10 6 mm 4. 3. A cantilever beam of span 2m carries a point load of 600N at the free end. If the cross section of the beam is rectangular 100mm wide and 150 mm deep. Find the maximum bending stress induced.
4.A wooden beam of rectangular section 100x200mm is simply supported over a span of 6m. Determine the udl it may carry, if the bending stress is not to exceed 7.5N/mm 2. Estimate the concentrated load it may carry at the center of the beam with the same permissible stress. 5.A rectangular beam 200mm deep and 100mm wide is simply supported over a span of 8m and carries a central point load of 25KN.Determine the maximum stress in the beam. Also, calculate the values of longitudinal fiber stress at a distance of 25mm from the top surface of the beam. 6.A beam of T-section flange 150mm x 50mm web thickness 50mm. overall depth 200mm and 10m long is simply supported a central point load of 10KN. Determine the maximum fiber stresses in the beam. 7.A cast iron water pipe 450mm bore 19mm thick is supported at two points 9m apart. Find the maximum stress in the metal when the pipe is running full. Density of cast iron is 78Kn/m 3 and density of water is 10KN/m 3 8.A cantilever of length 2m carries a udl of 3KN/m over the entire length together with point load of 10KN at the free end. The moment of inertia of the beam section is 260x10 6 mm 4 and its depth is 200mm. Determine the maximum bending stress induced in the beam. 9.A timber joist of 5m span has to carry a load 10KN/m. Find the dimensions of the joist if the maximum permissible stress in limited to10n/mm 2. The depth of the joist has to be twice width. 10.A water main of 1200mm internal diameter and 12mm thick is running full. If the bending stress is not to exceed 56N/mm 2. Find the greatest span on which the pipe may be freely supported. The specific weight of steel and water is 76.8KN/m 3 and 10KN/m 3 respectively.
1. Define pure torsion. 2. Define strength of shaft. 3. Define Torsional rigidity. 4. Define Stiffness of shaft. 5. Define polar modulus. UNIT - V PART - A 6. Write an expression for polar modulus of solid shaft and hollow shaft. 7. Write the torsion equation. 8. Write the relation between strength of hollow shaft and solid shaft. 9. State the reason to use hollow shaft in the place of solid shaft for same power transmission. 10. What is spring? 11. State the applications of laminated spring. 12. Define stiffness of spring. 13. What is meant by bending spring? 14. What is meant by torsion spring? 15. What is meant by compression spring? 16. Sketch a laminated spring. 17. State formula to find the deflection in a spring subjected to an axial load W. 18. What are the types of helical springs? 19. Indentify the different types of stresses, to which a closely coiled helical spring with an axial loading would be applied. 20. State the formula to determine stiffness of spring. PART B 1. a). State the advantages of hollow shaft over solid shaft. b). Compare the solid shaft and hollow shaft. 2.A shaft is to transmit 100KW at 160rpm. The shear stress is not to exceed 65N/mm 2 and the angle of twist in a length of 3.5m is not to exceed one degree. Find a suitable diameter. Take N=8 x 10 4 N/mm 2. 3.A solid shaft 100mm diameter transmit 100KW at 180rpm. Calculate the maximum intensity of shear stress induced and angle of twist in degree in a length 10m. N=0.8 x 10 5 N/mm 2.
4.The external and internal diameter of a hollow shaft are 400mm and 200mm respectively. Find the maximum torque which shaft can transmit if the angle of twist is not to exceed ½ 0 in a length of 10m and shear stress is not to exceed 70N/mm 2. Assume N=80KN/mm 2 5.a). Calculate the power transmitted by a shaft of 100mm diameter running at 250rpm. If the shear stress in the material is not to exceed 75N/mm 2 b). Derive torsion equation 6.a). A closely coiled helical spring is made of steel wire 12mm diameter. The number of coil is 20 and the mean radius of the coil is 75mm. Calculate stiffness of the spring. If N=1.2 x 10 5 N/mm 2 b). A closely coiled helical spring is made of steel wire 10mm diameter has 10 coils of 120mm mean diameter. Calculate the deflection under an axial load of 98N. Modulus of rigidity N=1.2 x 10 5 N/mm 2. 7.Design a closely coiled helical spring of stiffness 20 N/mm deflection. The maximum shear stress in the spring metal is not to exceed 80N/mm 2 under a load of 600N. The diameter of the coil is 10 times the diameter of wire. Modulus of rigidity is 85KN/mm 2. 8.a). Calculate modulus of rigidity of a spring of 10 turns, 65mm mean diameter and wire of 6.5mm diameter. The spring compresses 10mm under a load 70N. b). A closely coiled helical spring has the stiffness of 40N/mm. Determine its number of turns when the diameter of the wire of the spring is 10mm and mean diameter of the coil is 80mm. N=0.8 x 10 5 N/mm 2. 9. a).what are the different types of springs? b).what are the differences between closely coiled helical springs and open coiled helical springs? 10.A closely coiled helical spring is made out of 10mm diameter steel rod. The coil is having 12 complete turns and a mean diameter of 100mm. It carries an axial pull of 250N. Calculate the shear stress induced, deflection under the pull and amount of energy stored in the spring during extension. *******