CE 6302 Mechanics of Solids 2 marks questions and answers Unit I Stress and Strain Stress and strain at a point 1. A. 2. A.
3. A. 4. A. 5. A. 6. A. 7. A. 8.
Define ‘stress’ The force of resistance offered by a body against the deformation is called the stress. What are the three types of stresses? i. Normal stress – stress – (a) (a) Tensile stress (b) Compressive Compressive stress ii. Tangential stress iii. Bending stress Define Hooke’s law. Stress is proportional to strain within elastic limit. Define ‘elasticity’ of a material. Elasticity is the property by virtue of which a material deformed under the load is enabled to return to its original dimension when the load is removed. Define ‘plasticity’. A material in plastic state is permanently deformed by the application of load, and it has no tendency to recover. Define ‘isotropic’ material. If elastic properties are equal in all directions, it is said to be isotropic material. Define factor of safety. Factor of safety is defined as the t he ratio of ultimate stress to permissible stress. stress. What is the elongation of a uniformly tapering bar of circular cross section with diameter d1 at one end and d 2 at the other end e nd due to constant force P ?
A. The elongation of tapering bar of circular section ,
= 4; where L = length of the bar
and E = Young’s modulus. 9. A round bar of steel tapers uniformly from a diameter of 2.5 cm to 3.5 cm in length of 50 cm. If an axial force of 60000 N is applied at each end, determine the elongation of the bar. Take E=205 kN/mm 2. A. Elongation of the tapering bar of circular section, δ =
4 = 4∗∗∗ = 0.213. ∗∗∗∗
10. A flat steel plate is of trapezoidal form of uniform thickness of 10 mm and tapers uniformly from a width 50 mm to 100 mm in a length of 400 mm. Determine the elongation of the plate under an axial force of 50 kN at each end. Take E=2.05x10 5 N/mm 2.
( (−) ln ∗ ∗4 ln = .∗∗(−)
A. Extension of the tapering bar of rectangular section, δ =
=0.1352 mm.
11. A bar of uniform cross section is suspended from a ceiling. Write the elongation of the bar due to its own self weight.
A. Elongation due to self-weight, δ = or δ = ; where w = self weight, L=Length of the bar, A = Cross sectional area of the bar, E = Young’s modulus and λ = unit weight of the material = 12. Write the elongation of a bar of uniformly tapering section due to self-weight. , where λ is unit weight of the material. A. δ = 13. What is principle of superposition? A. When a structural member is subjected to a number of forces not only at the ends, but also at intermediate points along its length, the resulting strain will be equal to the algebraic sum of the strains caused by individual forces. 14. Define Poisson’s ratio. A. Ratio of lateral strain to linear strain is called Poisson’s ratio. 15. Write the maximum value of Poisson’s ratio. A. 0.5. 16. Define axial rigidity. A. Axial rigidity is defined as ratio of unit stress to unit strain within elastic limit. 17. Define shear modulus A. Ratio of shear stress to shear strain is called shear modulus. 18. Define bulk modulus. A. Ratio of direct stress to volumetric strain is called bulk modulus.
=
19. Write the relationship between Young’s modulus, Bulk modulus and Poisson’s ratio.
A.
= 3 1 ; where E = Young’s modulus, K = bulk modulus and is Poisson’s ratio.
20. Write the relationship between modulus of elasticity, modulus of rigidity and Poisson’s ratio.
A.
= 2 1 ; where E = Young’s modulus, C = modulus of rigidity and is Poisson’s
ratio. 21. Write the relationship between three elastic constants E, C and K, Where E is young’s modulus, C is shear modulus and K is bulk modulus.
+
A. E=
, K and C.
22. Write the relationship between the elastic constants
A.
= − +
5
2
23. If the modulus of elasticity of a material is 2x10 N/mm and m=3, the modulus of rigidity is -------.
A.
= 2 1 C=
= ∗ = 0.75*10 N/mm . + + 5
2
24. If the strains in three mutual perpendicular directions are e x, ey and ez; what is the value of volumetric strain? A. Volumetric strain, ev = ex + ey + ez .
25. What is the value of volumetric strain if the Poisson’s ratio is 0.5.
A. Volumetric strain, ev = ex + ey + ez = 3
1 2 ∗ = 3 {1 2 ∗(0.5)} = 0.
26. A bar of circular section is subjected to normal stress ‘p’, write the expression for volumetric strain.
A. Volumetric strain, ev =
1 2 ∗
27. Define thermal stress. A. When a material undergoes changes in temperature, its length is varied and if the material is free to do so, no stresses are developed. If the material is constrained so that no change in length is permissible, stresses are developed in the material. The stress so developed is known as temperature stress and may be tensile or compressive depending upon the whether the contraction is checked or extension is checked. 28. A bar of steel is held between rigid supports at the ends. When the bar is subjected to an increase in temperature, what is the nature of stress induced in the bar? A. Compressive stress. Reason: whenever temperature is increased bar will try to expand free. But the bar is held between rigid supports. The rigid supports don’t allow the bar to expand. For the equilibrium of the system, the compressive stress is induced in the bar. 29. A compound cylinder consisting of steel core and copper shell (both of same length) are brazed together at the ends. When the temperature is raised, state the nature of stress induced in copper and steel. A. The stress induced in steel is tensile. The stress induced in copper is compressive. 0 30. A rod of 2 m long at 10 C. Find the expansion of the rod when the temperature is raised 0 0 to 80 C, where α=0.000012/ C. A. Expansion due to temperature rise = αtL =0.000012*70*2000 = 1.68 mm. 0
31. A rod is 2 m long at 10 C. If the expansion is prevented, find the stress in the material 0 5 2 0 when the temperature is raised to 80 C. Take E=1*10 N/mm and α=0.000012/ C. A. Temperature stress = αtE = 0.000012*70*1*105 = 84 N/mm2. 32. Define compound bar A. A structural member, composed of two or more elements of different materials rigidly connected together at their ends to form a parallel arrangement and subjected to axial loading is termed as compound bar. 33. Write the equations for a compound bar of two materials rigidly connected and are arranged parallel to each other. A. Equilibrium equation, P1 + P2 = P
Compatibility equation,
=
Thin Cylinders and Shells 1. Distinguish between thin walled cylinder and thick walled cylinder.
≤ ; For thick cylinder ≥ , where t=thickness and d= diameter of cylinder.
A. For a thin cylinder
2. Write the expression for longitudinal stress in a thin cylindrical vessel due to internal pressure ‘p’
, where d= diameter and t= thickness of the cylinder. 4
A. Longitudinal stress, f 0 =
3. Write the expression for hoop stress in a thin cylindrical vessel due to internal pressure ‘p’
A. Hoop stress, f =
4. A seamless pipe of 1.2 m diameter is to carry fluid under a pressure of 1.6 N/mm 2. Taking the permissible stress in the metal as 100 N/mm 2, determine the thickness of the metal required.
A.
≤ , and hence, ≥ .∗ ≥ 9.6 , Hence keep t=10 mm. t≥ ∗
5. Write the expression for the volumetric strain of a thin cylinder by considering internal pressure ‘p’.
A. Volumetric strain, ev=
Strain energy 1. Define strain energy (or) define resilience. A. When a body is stressed within elastic limit the amount of strain energy stored is called ‘resilience’ or ‘strain energy’. 2. Define the term proof resilience. A. When a body is stressed up to elastic limit the maximum amount of strain energy stored is called proof resilience. 3. Define modulus of resilience. A. Proof resilience per unit volume is called modulus of resilience. 4. Write the expression for strain energy stored in an axially loaded bar.
A. Strain energy due to axial force
, where S= axial force in the bar, L = length, A= cross =
section area and E= modulus of elasticity of the bar. 5. What is the maximum stress in the uniform bar when it is suddenly loaded axially? A. Maximum stress due to sudden axial load, f =
, where W = sudden axial load, A = bar cross
sectional area 6. A rod is subjected to a gradually applied load which produces a normal stress of 10 N/mm 2. If the same load is suddenly applied, the normal stress is --------------.
=2 *10 = 20 N/mm . Write the equation for stress induced in a body by the application of load with impact. ℎ Stress due to impact load, f= + √ 2 , where h= load falling height
A. Due to sudden load the stress, f = 7. A.
2
