N = Shear stress / Shear strain

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1 UNIT - I 1. What is meant by factor of safety? [A/M-15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M-15] The capability of a strained body to recover its size and shape after deformation caused especially by compressive stress 3. Define Hooke Law. [N/D-16] It states that when a material is loaded, within its elastic limit, the stress is directly proportional to the strain. Stress α Strain σ α e σ = Ee E = σ /e N/mm 2 where E is young s modulus σ is stress ande is strain 4. Define Poisson s ratio. [N/D- 14, 16] The ratio of lateral strain to the longitudinal strain is a constant for a given material, when the material is stressed within the elastic limit. This ratio is called Poisson s ratio and it is generally denoted by 1/m (or) µ µ = 5. What is meant by Poinsson s ratio? Which material has the higher value of Poisson s ratio? [N/ D- 15 ] When a body is stressed, within its elastic limit, the ratio of lateral strain to the longitudinal strain is constant for a given material, which is known as Poisson s ratio. Poisson ratio (μ or 1/m) = Lateral strain / Longitudinal strain The shear stress is directly proportional to shear strain.

2 N = Shear stress / Shear strain 6. Define Strain Energy. [N/D-15] Whenever a body is strained, some amount of energy is absorbed in thebody. The energy which is absorbed in the body due to straining effect is known as strain energy. 7. Define Modulus of Elasticity. [M/J-14] It is defined as the ratio between the stress to strain is a constant when a material is loaded within an elastic limit. 8. Define Modulus of rigidity. [M/J- 14] It is defined as the ratio between the shear stress to shear strain is a constant when a material is loaded within an elastic limit. 9. Define Bulk Modulus. [N/D-14] It is defined as the ratio between the direct stress to volumetric strain is a constant when a material is loaded within an elastic limit. 10. What are the three types of stresses? [M/J-13] 1. Tensile stress 2. Compressive stress 3. Shear stress 11. Define Lateral Strain and Longitudinal Strain [A/M- 10] When a body is subjected to axial load P, the length of the body is increased. The ratio of axial deformation to the original length of the body is known as longitudinal strain. The strain, at right angle to the direction of the applied load, is called lateral strain. 12. State the relationship between Young s Modulus and Modulus of Rigidity. [M/J -10, 14] E = 2G (1 + 1/m) where E is Young s modulus G is modulus of rigidity and 1/m is Poisson s ratio

3 1. (a) when a square bar of certain material subjected to an axial pull of 160 kn, the measured extension on a gauge length of 200mm is 0.1mm and the decrease in each side of the square bar is 0.005mm. Calculate the modulus of Elasticity, shear modulus and bulk modulus for a material. [A/M-15] [N/D-14]

5 2. (b) A solid cylinder brass bar of 25mm diameter is enclosed in a steel tube of 50mm external diameter and 25mm internal diameter. The bar and the tube are both initially 1.5mm long and are rigidly fastened at both ends. Find the stresses induced in the two materials when the assembly is subjected to an increase in temperature of 50 0 C. Take coefficients of thermal expansion of steel as 12x10-6 / o C and that of brass is 18x10-6 / o C. Modulus of steel as 200 GPa and modulus of elasticity of brass as 100 GPa. [A/M-15], [N/D-14]

8 3. (a) A steel bar 300mm long, 40mm wide and 25mm thick is subjected to a pull of 180kN. Determine the change in volume of the bar. Take E= 2x 10 5 N/mm 2 and l/m= 0.3(16) 13, 16] [N/D-

9 5. 4. (b) An cylindrical shell 1 m diameter and 3 in length is subjected to an internal pressure, of 2 MPa. Calculate the minimum thickness if the stress should not exceed 50 MPa. Find the change in diameter and volume of the shell. Poisson s ratio = 0.3 and E= 200kN/mm 2. (16) [N/D-14,16]

11 6. (a) A composite bar is made with copper flat of size 50mmx 30mm and a steel flat of 50 mm x 40mm of length 500mm each placed one over the other. Find the stress induced in the material, then the composite bar is subjected to an increase in temperature of 90,C. Take coefficients of thermal expansion of steel as 12x10-6 / o C and that of brass is 18x10-6 / o C. Modulus of steel as 200 GPa and modulus of elasticity of brass as 100 GPa. [N/D-15], [A/M-12]

14 7. (b) a thin cylinder sheel, 2m long has 800mm internal diameter and 10mm thickness. If the shell is subjected to an internal pressure of 1.5 MPa, find (i) the hoop and longitudinal stresses developed, (ii) maximum shear stress induced and (iii) the changes in diameter, length and volume. Take modulus of elasticity of the wall material as 205 GPa and Poisson s ratio as 0.3. [N/D-15], [M/J 14]

16 8. A flat steel plate of trapezoidal form of uniform thickness of 20 mm tapers uniformly from a width of 100 mm to 200 mm in a length of 800 mm. If an axial tensile force of 100 kn is applied at each end, Find the elongation of the plate. [N/D-14] 9. A metallic bar 250 mm x 100 mm x 150 mm is loaded as shown in figure. (i) Find the change in volume. Take E= 200 kn/mm 2 and Poisson s ratio = Also find change the should be made in the 4000 kn, in order that there should be no change in the volume of the bar. [M/J-14]

STRESS, STRAIN AND DEFORMATION OF SOLIDS

STRESS, STRAIN AND DEFORMATION OF SOLIDS VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY, MADURAI 625009 DEPARTMENT OF CIVIL ENGINEERING CE8301 STRENGTH OF MATERIALS I -------------------------------------------------------------------------------------------------------------------------------