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# Note for Mechanics of Solids - MOS by Shrinivasan K

• Mechanics of Solids - MOS
• Note
• Pondicherry University - PU
• Mechanical Engineering
• B.Tech
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MECHANICS OF SOLIDS (2 MARKS QUESTION BANK) STRESS, STRAIN AND DEFORMATION OF SOLIDS 1.Define tensile stress and tensile strain. The stress induced in a body, when subjected to two equal and opposite pulls,as a result of which there is an increase in length, is known as tensile stress. The ratio of increase in length to the original length is known as tensile strain. 2.Define compressive stress and compressive strain. The stress induced in a body, when subjected to two equal and oppositepushes, as a result of which there is a decrease in length, is known ascompressive stress. The ratio of increase in length to the original length isknown as compressive strain. 3.Define shear stress and shear strain. The stress induced in a body, when subjected to two equal and opposite forces, which are acting tangentially across the resisting section as a result of which the body tends to shear off across the section is known as shear stress and corresponding strain is known as shear strain. 4. Give example for ductile, brittle and malleable materials. a. Ductile materials steel, copper b. Brittle materials wrought iron c. Malleable materials cast iron 5.Define Poisson‘s ratio The ratio of lateral strain to the linear strain is a constant for a given material,whenthe material is stressed within the elastic limit. 6. Write the relationship between modulus of elasticity, modulus of rigidity and Poisson‘s ratio 7.State Hooke‘s law. Hooke‘s law is statedas when a material is loaded within elastic limit, the stress is proportional to the strain produced by stress, or Stress/strain=constant. This constant is termed as modulus of elasticity. 8. Define stress and strain. Stress: The force of resistance per unit area, offered by a body against deformation is known as stress. Strain: The ratio of change in dimension to the original dimension when subjected to an external load is termed as strain and is denoted by e. It has no unit. 9. Define modulus of rigidity. The ratio of shear stress to the corresponding shear strain when the stress is within the elastic limit is known as modulus of rigidity or shear modulus and is denoted by C or G or N. 10. Define modulus of elasticity. The ratio of tensile stress or compressive stress to the corresponding strain is knownas modulus of elasticity or young‘s modulus and is denoted by E. 11. Define Bulk modulus. When a body is subjected to an uniform direct stress in all the three mutually perpendicular directions, the ratio of the direct stress to the correspondingvolumetric strain is found to be a constant is called as the bulk modulus of thematerial and is denoted by K. 12. Define factor of safety It is defined as the of ultimate stress to the working stress or permissible stress.

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13. What is stability? The stability may be defined as an ability of a material to withstand high deformation. 14.Give example for gradually applied load and suddenly applied load. Example for gradually applied load When we lower a body with the help of a crane, the body first touches the platform on which it is to be placed. On further releasing the chain, the platform goes on loading till it is fully loaded by the body. This is the case of gradually applied load. Example for suddenly applied load When we lower a body with the help of a crane, the body is first of all, just above the platform on which it is to be placed. If the chain breaks at once at this momentthe whole load of the body begins to act on the platform. This is the case of suddenly applied load. 15. Distinguish between suddenly applied and impact load. When the load is applied all of a sudden and not step wise is called is suddenly applied load. The load which falls from a height or strike and body with certain momentum is called falling or impact load 16.Define principal planes. The planes on which no tangential or shear stresses are acting are called asprincipalplanes. 17. Define principal stress. The normal stress acting on principal planes is called principal stress. BENDING OF BEAMS TRANSVERSE LOADING ON BEAMS 1. Define beam? BEAM is a structural member which is supported along the length and subjected to external loads acting transversely (i.e) perpendicular to the center line of the beam. 2. What is mean by transverse loading on beam? If a load is acting on the beam which perpendicular to the central line of it then it is called transverse loading. 3. What is Cantilever beam? A beam one end free and the other end is fixed is called cantilever beam. 4. What is simply supported beam? A beam supported or resting free on the support at its both ends. 5. What is mean by overhanging beam? If one or both of the end portions are extended beyond the support then it is called overhanging beam. 6. What is mean by concentrated loads? A load which is acting at a point is called point load. 7. What is uniformly distributed load. If a load which is spread over a beam in such a manner that rate of loading ‘w’ is uniform throughout the length then it is called as UDL. 8. Define point of contra flexure? In which beam it occurs? Point at which BM changes to zero is point of contra flexure. It occurs in overhanging beam. 9. What is mean by positive or sagging BM? BM is said to positive if moment on left side of beam is clockwise or right side of the beam is counter clockwise.

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10. What is mean by negative or hogging BM? BM is said to negative if moment on left side of beam is counterclockwise or right side of the beam is clockwise. 11. Define shear force and bending moment? SF at any cross section is defined as algebraic sum of all the forces acting either side of beam. BM at any cross section is defined as algebraic sum of the moments of all the forces which are placed either side from that point. 12. When will bending moment is maximum? BM will be maximum when shear force change its sign. 13. What is maximum bending moment in a simply supported beam of span ‘L’ subjected to UDL of ‘w’ over entire span? Max BM =wL2/8 14. In a simply supported beam how will you locate point of maximum bending moment? The bending moment is max. When SF is zero. Write SF equation at that pointand equating to zero we can find out the distances ‘x’ from one end .then find maximum bending moment at that point by taking all moment on right or left hand side of beam. 15. What is shear force? The algebraic sum of the vertical forces at any section of the beam to the left or right of the section is called shear force. 16. What is shear force and bending moment diagram? It shows the variation of the shear force and bending moment along the length of the beam. 17. What are the types of beams? 1. Cantilever beam 2. Simply supported beam 3. Fixed beam 4. Continuous beam 5. over hanging beam 18. What are the types of loads? 1. Concentrated load or point load 2. Uniform distributed load 3. Uniform varying load 19. In which point the bending moment is maximum? When the shear force change of sign or the shear force is zero. 20. Write the assumption in the theory of simple bending? 1. The material of the beam is homogeneous and isotropic. 2. The beam material is stressed within the elastic limit and thus obey hooke’slaw. 3. The transverse section which was plane before bending remains plains after bending also. 4. Each layer of the beam is free to expand or contract independently about the layer, above or below. 5. The value of E is the same in both compression and tension 21. Write the theory of simple bending equation? M/ I = F/Y = E/R M - Maximum bending moment I - Moment of inertia F - Maximum stress induced Y - Distance from the neutral axis

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E - Young’s modulus R - Constant 22.Define neutral axis of a cross section The line of intersection of the neutral surface on a cross-section is called the neutral axis of a crosssection. There is no stress at the axis TORSION AND SPRINGS 1. Define Torsion. When a pair of forces of equal magnitude but opposite directions acting on body, it tends to twist the body. It is known as twisting moment or torsion moment or simply as torque. Torque is equal to the product of the force applied and the distance between the point of application of the force and the axis of the shaft. 2. What are the assumptions made in Torsion equation (I) The material of the shaft is uniform throughout. (ii) The twist along the shaft is uniform. (iii) Normal cross sections of the shaft, which were plane and circular before twist, remain plane and circular after twist. (iv) All diameters of the normal cross section which were straight before twist, remain straight with their magnitude unchanged, after twist 3. Define polar modulus Polar modulus is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called torsional section modulus and is denoted by Zp. Or It is the ratio between polar moment of inertia and radius of the shaft. Zp = polar moment of inertia = J Radius R 4. Write the polar modulus for solid shaft and circular shaft. £ = polar moment of inertia = J Radius R J= 𝜋D4 32 5. Why hollow circular shafts are preferred when compared to solid circular shafts? • The torque transmitted by the hollow shaft is greater than the solid shaft. • For same material, length and given torque, the weight of the hollow shaft will be less compared to solid shaft. 6. Write torsional equation T/J=Cᶿ/L=q/R T-Torque J- Polar moment of inertia C-Modulus of rigidity L- Length q- Shear stress R- Radius 7. Write do𝝅wn the expression for power transmitted by a shaft Power P=2 𝜋NT/60 N-speed in rpm
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