PES Institute of Technology


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1 PES Institute of Technology Bangalore south campus, Bangalore Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject code : 10ME34 Chapter 1 SIMPLE STRESS AND STRAIN QUESTION BANK 1 List different types of engineering materials. 2 Distinguish between ductile and brittle materials. 3 What do you mean by tensile, compressive and shear forces? Give examples 4 What is stress? What is the difference between shear stress and normal stress? 5 Plot a tensile test diagram for steel. Explain its salient features. 6 The loading on a steel bar of 30mm diameter is as shown in the below figure. Find the elongation of the bar. Take E= 205Gpa. 7 Determine the total compression of a bar made up of three circular crosssections as shown in figure below. The diameter being 10mm, 20mm and 30 mm of the top, middle and the bottom portions respectively. Take E steel =210 Gpa, E brass = 105 Gpa and E copper = 100 Gpa. 8 A 20mm thick and 200mm wide steel plate tapers uniformly to 10mm thickness and 150mm width over a length of 2m. Determine the increase in length when a pull of 18KN is applied. E=200 Gpa.
2 Chapter 2 STRESS IN COMPOSITE SECTION 1 Explain the terms: Stress, strain, shear strain, young s modulus and modulus of rigidity. 2 Define bulk modulus. Deduce the relation E=3K (12v). 3 What is volumetric strain? Show that it is the algebraic sum of three mutually perpendicular strains. 4 Derive a relation between young s modulus, modulus of rigidity and the Poisson s ratio. 5 What do you mean by temperature stresses? Explain. 6 A steel sleeve of 24mm internal diameter and 36mm external diameter encloses an aluminum rod of 22mm diameter. The length of the rod is 0.4mm longer than of the sleeve which is 400mm long as shown in the figure. Determine (i) (ii) (iii) The compressive load up to which only the rod is stressed. The maximum load on the assembly if the permissible stresses in aluminum and steel are 130Mpa and 175Mpa respectively. The deformation of the assembly under maximum load Take Ea = 75Gpa and Es = 205Gpa. 7 A composite bar made up of aluminum and steel is rigidly attached to the end supports at 60 0 C as shown in figure. Find the stresses in the two portions of bar when the temperature of the composite system falls to 20 0 C if (i) the ends do not yield (ii) the ends yield by 0.25mm. Es = 200Gpa; Ea = 70Gpa α steel = 11.7x106 / 0 C; α aluminum = 23.4 x106 / 0 C Crosssectional areas, A s = 250mm 2 ; A a = 375mm 2. 8 A load of 120KN is applied to bar of 20mm diameter. The bar which is 400mm long is elongated by 0.7mm. Determine the modulus of elasticity of the bar material. If the Poisson s ratio is 0.3 find the change in diameter. 9 A steel bar of 10mm diameter is subjected to an axial load of 12KN. If the change in diameter is found to be mm, determine the Poisson s ratio and the modulus of elasticity and the bulk modulus. Take G=78Gpa. 10 An axial load of 56KN is applied to a bar of 36mm diameter and 1m length. The extension of the bar is measured to be 0.265mm whereas the reduction in diameter is 0.003mm. Calculate the Poisson s ratio and the values of the three moduli.
3 Chapter 3 COMPOUND STRESSES 1 Deduce expressions for stresses on an inclined plane in a body subjected to a biaxial stress condition. 2 What do you mean by principal planes and principal stresses? Derive the expression for principal stresses for a body subjected to direct and shear stresses. 3 Show that in a direct stress system, the maximum shear stress in a body is half the magnitude of the applied stress. 4 What is Mohr s stress circle? How is it useful in the solution of stressanalysis problems? 5 A piece of material is subjected to two perpendicular tensile stresses of 300Mpa and 150 Mpa. Determine the normal and shear stress components on a plane the normal of which make an angle of 40 0 with the 300Mpa stress. Also, find the resultant. 6 The stresses on two perpendicular planes through a point are 120Mpa tensile, 80Mpa compression and 60Mpa shear. Determine the normal and shear stress components on a plane at 60 0 to that of the 120Mpa stress and also the resultant and its inclination with the normal components on the plane. 7 Two perpendicular tensile stresses of 300Mpa and 150Mpa act at a point in a material. Draw the Mohr s stress circle and find the normal and shear stress components on a plane the normal of which makes an angle of 40 0 with the 300Mpa stress. Also, find the resultant. 8 The normal stresses at a point in an elastic material are 100Mpa and 60Mpa respectively at right angle to each other with a shearing stress of 50Mpa. Determine the principal stresses and the position of principal planes if (i) both normal stresses are tensile, and (ii) 100Mpa stress is tensile and 60Mpa stress is compressive. Also determine the maximum shear stress and its plane in the two cases. 9 At a certain point in a strained material, direct stresses of 120Mpa tensile and 90Mpa compressive exist on two perpendicular planes. These stresses are also accompanied by a shear stress on the planes. The major principal stress at the point due to these is 150Mpa. Determine the magnitude of the shear stresses on the two planes. Also, find the maximum shear stress at the point. 10 A piece of material is subjected to two perpendicular stresses as follows: (i) Tensile stresses of 100Mpa and 60Mpa (ii) Tensile stress of 100Mpa and compressive stress of 60Mpa (iii) Compressive stress of 100Mpa and tensile stress of 60Mpa (iv) Compressive stresses of 100Mpa and 60Mpa Determine normal and tangential stresses on a plane inclined at 30 0 to the plane of 100Mpa stress. Also find the resultant and its inclination with the normal stress.
4 Chapter 4 STRAIN ENERGY 1 What is strain energy of a material? Derive the expression for the same in different forms. 2 Derive expressions for the strain energy in a threedimensional stress system? 3 Deduce the relation for stress in case of impact and shock loading. 4 A lift is operated by two ropes each 20m long and consisting of 30 wires of 1.5mm diameter. The weight of the cage is 1KN and the rope weighs 3.6N/m length. Determine the maximum load that the lift can carry if it drops through 120mm during operations. E (rope) = 78Gpa and allowable stress = 125Mpa. 5 A weight of 800N falls 30mm on to a collar fixed to a steel bar of 1.2m length. The steel bar is of 24 mm diameter for half of is length and 12 mm for the rest half. Determine the maximum stress and the extension in the bar. Es = 205Gpa. 6 A 100N weight falls by gravity through a vertical distance of 5m when it is suddenly stopped by a collar at the end of vertical rod of 20mm diameter and 10m length. The upper end of the bar is rigidly fixed. Calculate the strain induced in the bar due to impact. E = 200Gpa. THICK AND THIN CYLINDERS 1 What do you mean by pressure vessels or shells? What type of stresses act upon them 2 Distinguish between thin and thick cylinder? 3 What are the assumptions taken in the analysis of thin cylinders? 4 Deduce expressions for the circumferential and longitudinal stresses developed in thin cylinders. 5 Deduce the general equations for circumferential and radial stresses developed in thick cylinders. What are the assumptions made? 6 A mild steel water pipeline of 2m diameter and of 10mm thickness sustains an allowable stress of 140Mpa. Find the maximum pressure in the pipe. What will be the change in the volume of the pipe per meter length under the maximum pressure? E = 200Gpa and υ = A thick hollow cylinder of 200mm internal diameter and 300mm external diameter is subjected to an internal pressure of 50Mpa and external pressure of 25Mpa. Find the maximum shear stress developed in the material at the inner radius. Chapter 5 BENDING MOMENT AND SHEAR FORCE IN BEAMS: 1 What are the main types of supports? Distinguish between any two. 2 How are beams classified? Give brief account. 3 Define the terms shear force and bending moment. Comment on their sign conventions. 4 Derive the relation between bending moment and shear force in a beam. What do you mean by point of inflection or contraflexture? 5 A simply supported beam of 8m span carries point load of 24KN and 40KN at distances of 2m from each end. Draw the shear force and bending moment diagrams. 6 A cantilever of length 6 m carries a point load of 48 KN at its centre. The cantilever is propped rigidly at the free end. Determine the reaction at the rigid prop. 7 A 12 m long beam simply supported at the ends carries a point load of 40KN at 3m
5 from left end and a uniformly distributed load of 10KN/m on the right half of the span. Draw the shear force and bending moment diagrams indicating principal values. 8 A 10m long beam is simply supported at 1m from the left end and 3m from right end. Concentrated loads of 6KN and 8KN act on the beam at the left end and right end respectively. Draw the shear force and bending moment diagrams. 9 Two supports of a simply supported beam are 5m apart. The beam is 8m long with two overhangs of 2m on the left end and 1m on the right end. The beam carries concentrated loads of 40 KN at the left end and 20KN at the right end. In addition, it also carries 40KN load at the mid span and 20KN at 2m from the right end of the beam. Draw shear force and bending moment diagrams for the beam. 10 A 5m long cantilever beam carries a point load of 3 KN at the free end along with three more point loads of 2KN, 2KN and 1KN at 1m, 3m, and 4m respectively from the fixed end. A uniformly distributed load of 2KN/m also acts on the beam starting from 2m and ending at 4m from the fixed end. Draw the shear force and bending moment diagrams. 11 A 5m long overhanging beam of negligible weight has its supports 4m apart, the overhang being on the left end. It carries a uniformly varying load the intensity of which varies linearly from zero at the left end to 60KN/m at the right end. Draw the shear force and bending moment diagrams indicating salient values. 12 A simply supported beam of 8m span carries a uniformly distributed load of 10KN/m over the left half and a counterclockwise couple at 6m from the left end. The reaction at the support is found to be 55KN. Draw the shear force and bending moment diagrams. Chapter 6 BENDING AND SHEAR STRESSES IN BEAMS 1 Prove the relation = = for simple bending. 2 What do you mean by the terms neutral axis and neutral surface? 3 Develop the theory of simple bending clearly stating the assumptions made. 4 A 250mm deep and 150mm wide rectangular beam is subjected to a maximum bending moment of 250KNm. Determine the maximum stress produced in the beam and the radius of curvature for the portion of the beam where bending is maximum 5 A rolled steel joint of Isection has top and bottom flange 150mm x 25mm and web of size 300mm x 12mm. it is used as a simply supported beam over a span of 4m to carry an uniformly distributed load of 80 KN/m over its entire span. Draw bending and shearing stresses across a section at 1/4 th span.
6 Chapter 7 DEFLECTION OF BEAMS 1 Derive the governing differential equation of beams. What are the assumptions made? 2 A cantilever beam of 3 m spa carries a uniformly distributed load of 10KN per meter length over the entire span. Determine the deflection of the free end. E = 200Gpa and I = 80X10 6 mm 4 3 A 6 m long simply supported beam carries a point load W at the midspan. if the slope at the ends of the beam is not to exceed one degree, determine the defection at the load point. 4 Determine the maximum deflection of a simply supported beam of 5 m length and carrying a uniformly varying load from zero at the ends to 8 KN/m at the center. EI = 2 MN.m 2 5 A simply supported beam has a span of 15 m and carries two point loads of 4 KN and 9 KN at 6 m and 10 m respectively from one end. Find the deflection under each load and the maximum deflection. E = 200Gpa and I = 400X10 6 mm 4 6 A simply supported beam is applied a positive bending couple of 8 KN.m at the left end and another positive bending couple of 10 KN.m at the right end. If the beam is 8 m long, find the maximum deflection. EI = 12 MN.m 2. 7 A simply supported beam has a span of 9 m. it carries a load of 72 KN at a distance of 2 m and another 45 KN at a distance of 5 m from the left hand support. Find the deflection and the slope under these loads. 8 A cantilever of length l carries a concentrated load W at the free end. The section of the cantilever is circular of diameter d for half the length from the fixed end and of diameter d/2 for remaining length. Determine the slope and deflection at the mid span and at the free end. Chapter 8 TORSION OF CIRCULAR SHAFTS AND ELASTIC STABILITY OF COLUMNS 1 Deduce the torsion equation stating the assumptions made. 2 Deduce the expressions for maximum stresses in solid and hollow shafts. 3 A 1.5 m long solid aluminum shaft with 60mm diameter is to be replaced by a steel hollow shaft of the same length and same external diameter to transmit the same torque with the same angle of twist over the same length. Determine the diameter of the hollow shaft. Gs = 82Gpa and Ga = 27Gpa. 4 A solid shaft transmits 200KW of power at 80rpm. Determine the diameter of the shaft if the shear stress is not to exceed 75Mpa. If this shaft is replaced by a hollow shaft whose internal diameter is 0.6 of the external diameter while the length, material and the maximum shear stress are the same, find the percentage saving in weight. 5 What is meant by crippling or buckling load? 6 What are the assumptions made in the analysis of struts and columns by Euler s buckling theory? 7 Define slenderness ratio of a column. 8 A 1.5 m long steel bar which is 20 mm x 5 mm in section is compressed longitudinally until it buckles. Applying Euler s formula for pinned ends, determine the maximum central deflection before the steel attains the yield point stress of 320 Mpa. E = 210Gpa.
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